Friday, April 24, 2020

Understanding Quantum Mechanics #1: It's not about discreteness

This must be one of the most common misunderstandings about quantum mechanics, that quantum mechanics is about making things discrete. But is an understandable misunderstanding because the word “quantum” suggests that quantum mechanics is about small amounts of something. Indeed, if you ask Google for the meaning of quantum, it offers the definition “a discrete quantity of energy proportional in magnitude to the frequency of the radiation it represents.” Problem is that just because energy is proportional to frequency does not mean it is discrete. In fact, in general it is not.



The reason that quantum mechanics has become associated with discretization is entirely historical. The first signs that something was not quite right with the fundamental theories of the 19th century came from atomic spectral lines. Atoms can absorb and emit light only at certain frequencies. If you think that atoms are basically blobs of particles stuck together, which was what people thought at the time, then this makes absolutely no sense.

According to quantum mechanics now, the negatively charged electrons occupy shells around the positively charged nucleus. These shells cannot have any radius, but only certain values of the radius are allowed. Just what shape the shells have and how large they are can be calculated with quantum mechanics. And this explains why atoms can only absorb and emit light of certain frequencies. Because the energy of the light must fit to the energy that moves an electron from one shell to another.

So, yes, the energies of electrons which are bound to atoms are discrete. But the energies of electrons, or of any particle really, are not always discrete, and neither are other measureable quantities. The energy of a photon traveling through empty space, for example, can have any value according to quantum mechanics. The energy is not discrete. Or, if you look at an electron in the conducting band of a metal, it can be at any position. The position is not discrete.

What, then, does it mean to have a quantum theory as opposed to a non-quantum theory? A quantum theory is one in which you have observable quantities that obey Heisenberg’s uncertainty principle. Mathematically, this is not entirely the correct definition. More precisely a quantum theory has operators for observables which do not commute. But for what the physical consequences are concerned, the uncertainty principle is what tells quantum from non-quantum theories. The other important property of quantum theories is that you can have entanglement. We will talk about what this means another time.

For today, the lesson to take away is that quantizing a theory does not mean you make it discrete. This is important also when it comes to the quantization of gravity. Quantizing gravity does not necessarily mean that space and time have to be discrete. Thanks for watching, see you next week.

PS: I did not suddenly lose half my hair; I just messed up my lighting.

153 comments:

  1. The discrete nature of QM often comes with bound states. Scattering states are more continuous. Scattering states in relativistic QM or QFT are easier to manage than bound states. Scattering states do generate particles though, such as the production of mesons, baryons and ultimately generating the Higgs particle. One signature of quantum mechanics is that these gaps in energy δE ≈ E, for E the energy of the system. The scattering of billiard balls on a table for instance is such that if there is any discrete nature it is such that δE/E → 0 This could be compared to digital pool games, where while there is a digital discreteness on some small scale it is such that it approximates what we think of as billiards. The real billiard balls on a table may have some quantization of scattering states, or of states on the “arena” defined by the table. The biggest difference between QM and any discrete, such as digital simulation, system is that δE → ≈ ΔE as a Heisenberg uncertainty spread with ΔEΔt ≥ ħ/2.

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  2. Hello, Typo? - radius twice in 2nd paragraph, 2nd sentence. Energy?
    PS: I love your blog

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    1. Hi Ari,

      Not sure I understand the question. I am referring there to the radius, but the radius can be converted into an energy. The smaller the radius, the larger the energy (referring to the energy necessary to entirely remove the electron).

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    2. This is what is written:
      "These shells cannot have any radius, but only certain values of the radius are allowed. "

      But I think you mean this:
      These shells cannot have any radius - only certain values of the radius are allowed.

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    3. Steven Evans,

      What's the difference? To me it seems to say the same. Sorry for being dumb.

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    4. I wouldn't have pointed it out, except I had to think about it for a sec because the "but" put me off and it seems to be the cause of Ari's confusion.

      In the original sentence there's a second clause (i.e. with a second verb) after the "but", so the "but" sounds like it is with respect to the whole first clause. So one is expecting "only certain values of the radius are allowed" to have a meaning in contrast to "These shells cannot have any radius" because of the "but", but it doesn't.
      e.g. "These shells cannot have radii of completely arbitrary values, but a countably infinite number of values are allowed." is OK because the 2 clauses have contrasting meaning - namely, there are restrictions to the values, but there's still lots of them.

      One could say:
      "These shells cannot have radii of just any values, but only certain values."
      Here there is only a phrase after the "but" and the "only certain values" mirrors "just any values", so "these shells can have" gets carried over from the first clause to the phrase after "but". One cannot write "These shells cannot have radii of any values" without the "just" or equivalent because it's ambiguous - it could mean no values are possible for the radii. Saying that, "just any" is a bit clumsy, so this sentence isn't perfect either.

      Conclusion:
      If one is using a second clause with meaning that supports the meaning of the first clause, one cannot use "but". "-" can be used:
      "These shells cannot have radii of arbitrary values - only certain values are allowed."
      Or, if one wants to use "but", one has to use a phrase after the "but" that mirrors part of the preceding clause:
      "These shells cannot have radii of arbitrary values, but only certain determined values."
      One needs "arbitrary" to avoid the ambiguity of "any", and then one ends up needing to mirror "arbitrary" with something like "determined". So this expression has fewer degrees of freedom, but maybe sounds more polished than bunging in a "-".

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    5. Sabine, I understood what you meant but had to read it twice because it sounds a little odd. I would have written: "These shells cannot have just any radius..."; otherwise the first half of the sentence could be interpreted as the shells not being able to have any radius at all.

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    6. TL;DR
      This avoids the 2 confusions:
      "These shells cannot have radii of arbitrary values, but only certain determined values."

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    7. Ok, thanks. I think I understand what you mean and will keep this in mind.

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    8. Sabine Hossenfelder8:01 AM, April 26, 2020

      But will retain the mistakes in the text;)

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    9. Shells only have sharp radio in the Bohr model. This was a pre-Schrodinger theory that quantized angular momenta of electrons. This gave discrete energy levels, the Rydberg theory, at specific radii. These radii in the full quantum theory are the most probable or most expected value of these radii.

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    10. Sabine Hossenfelder8:01 AM, April 26, 2020

      You are so stubborn sometimes, Dr. H. You were like this with the science doesn't refute religion and the C-12 resonance is anthropic questions. If you are losing the argument, you block. Not that this is an argument.

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    11. As I have said before, the text is a transcript. It's what I have said, and I can't change that, therefore I'll leave the text as it is. Fwiw, I don't think it's actually wrong, it just seems to be easier to misunderstand than I anticipated.

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    12. I don't know what you think I am "blocking". Am I refusing to agree on logically wrong statements that you make. Of course. As to correcting the text, you will find plenty of evidence on this blog that I correct mistakes in the text, so your criticism is refuted by evidence.

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    13. Sabine Hossenfelder2:24 AM, April 27, 2020

      You didn't block here and I see you can't change the text because it's a transcript. My apologies.




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    14. Thanks for the apology, much appreciated.

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  3. If we talk about understanding QM, I think we started on the wrong food when Newton invented what I would now call linear/continuous math. I wonder how his math would have looked like when he discovered the quantum world first before gravity. In the end we got ourselves warped and twisted when using newton's math on the QM-nature. Unfortunately string-theory went a step further and according to me detached itself from nature.

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    1. Marc E,

      Part of Sabine's point is that we use the same math -- what you call "linear/continuous math," i.e., calculus -- in quantum mechanics, and it works.

      Trying to do, say, quantum field theory without calculus would be interesting: you are welcome to try. I wish you luck.

      (Yes, everyone, I have indeed heard of C* algebras, Dirac's matrix ladder approach to solving the simple harmonic oscillator, and all the rest. I still wish anyone luck deriving or calculating Feynman diagrams without calculus!)

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    2. You are drawn into the trap I am trying to explain, so you attach an absolute-truthiness-value to your calculus. Does nature care, or is that that makes QM difficult to understand ? Does it really work ? Why then remains QM so fuzzy ?

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    3. Mathematics took a wrong turn, not when Newton invented calculus, but much later when the notion of a continuum was formalized based on flawed intuitions from classical physics in the 19th century. If mathematics had been formalized based on notions of modern physics, then we would not have introduced a set of real numbers.

      In QFT we are forced to eliminate mathematical artifacts of the flawed system we use, we have to regularize the theory and we can then do computations in the limit that the regularization parameters are removed. This is nature telling us how to correct our mathematical mistakes.

      So, what we need to do to get to a better mathematical basis for calculus, is to always work on a discrete lattice. One can then consider certain continuum limits without invoking a continuum, just like you can compute limits to infinity of functions without having access to infinitely large numbers.

      This then involves a more elaborate limit procedure than we're used to now. It will be similar to how we use the renormalization group in physics. For example, given a lattice model like the Ising model, you can consider the scaling limit of that theory which is a field theory. But we then know that it's a coarse grained version of the original lattice model, rapid fluctuations of the field have already been integrated out in a certain way, which then defines the cut-off of the field theory.

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    4. Marc E wrote to me:
      > You are drawn into the trap I am trying to explain, so you attach an absolute-truthiness-value to your calculus. Does nature care, or is that that makes QM difficult to understand ? Does it really work ? Why then remains QM so fuzzy ?

      You are being silly. Your “trap”?? Oh, c’mon!

      Look: it is perfectly possible to do QM on a finite lattice. You still get all the weirdness – collapse of the wave function, entanglement, and all the rest. Of course, even then, you still need calculus: the wavefunction is a differentiable function satisfying a differential equation in time.

      I.e., calculus.

      “Absolute truthiness”??? What a frivolous person you are.

      Look: quantum mechanics works, better than any scientific theory ever created. And quantum mechanics is based on calculus.

      Is quantum mechanics the final word? I hope not – I am troubled by, in particular, the measurement problem.

      But, there is no sign that the problem is the “absolute truthiness” or lack thereof of calculus. There is every indication that calculus is consistent (yes, I know crackpots claim otherwise: they have no evidence; they are fools). Calculus happens to be a very useful tool in many applications to the physical world.

      You think you of all people can do better without calculus? Don’t just talk about it -- do it!

      Create your wonderful calculus-free version of physics, prove it works, and win your Nobel prize.

      And show me where I can bet a couple million bucks that you will fail. I could use the easy money.

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    5. Count Iblis wrote:
      >So, what we need to do to get to a better mathematical basis for calculus, is to always work on a discrete lattice. One can then consider certain continuum limits without invoking a continuum,

      No.

      Iblis, I have extensive, hands-on experience doing lattice calculations, going back almost exactly thirty-nine years. In grad school, I worked on multi-grid “look-ahead” lattice approximations to the anistropic Heisenberg anti-ferromagnetic chain. In industry, I developed methods to solve the Laplace/Poisson equation on a lattice using multigrid techniques to precondition the conjugate-gradient method. More recently, I have worked on putting fermions on a lattice by geometrically representing the spinors on subdiagonals of the cells. In short, I know a lot about lattice calculations.

      They have their place – basically where we cannot solve the problem using calculus.

      But, they have very severe limitations.

      First, they are simply more complicated than calculus.

      Whether you do the lattice calculation with algebra or numerically, if you do not start out taking the limit and using calculus, then you are left with various numerical artifacts, which are almost always more complicated than a result from calculus. Understanding and controlling these artifacts is a colossal headache.

      More importantly, the real world turns out to be much closer to calculus than to any discrete lattice we can solve numerically. The reason for this is quite simple. If there is any finite, discrete size to space, we have no evidence of it, and, indeed, we know it must be well under a millionth the radius of an atom. But we simply cannot do numerical lattice calculations where our lattice size is many millions of times our lattice spacing (count the number of lattice points in 3-D: it is computationally prohibitive).

      So, even if space did have discrete features at, say, 1.0E-33 cm, that is closer to the “infinitesimal” length implicitly assumed in calculus than to any lattice size we could actually use in practical calculations.

      No, using calculus is the conceptually and practically simpler way to go whenever it is possible. Lattice calculations are only when you cannot, for some reason, use calculus.

      Thant you, Newton and Leibniz!

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    6. PhysicistDave,

      Yes, but my argument is more about the way one sets up calculus rather than whether or not you actually use it. Note that Newton had introduced calculus in a way that was not rigorous according to our modern standards. But when things were made more rigorous by mathematicians later, there was no doubt that the results of the computations would not change, and also that when doing a practical computation, the formalism you would when doing an actual computation would remain the same.

      The price we do pay for having introduced the continuum as a real thing instead of taking continuum limits, is that when the difference really matters like in functional analysis, things become much more complex than what is necessary for physics.

      So, a quantum mechanics student can do quite well using only the math explained in a non-rigorous way his/her quantum mechanics book. The student won't fail an exam on advanced quantum mechanics just because the student does not know how to prove the Hahn-Banach theorem using transfinite induction.

      So, while I agree that calculus is indispensable in physics, this does not prove that there really exists a continuum. There are many different arguments one can make to make in favor of the non*existence of the continuum. Below I pointed to the finite number of states a physical system in a finite volume can have (I forgot to mention the upper limit on the energy, but note that this is going to be enforced by nature due to gravity).

      One can also point to the fact that when doing mathematics whether that's calculus or something else, you can only ever manipulate a finite number of symbols using a finite number of rules. This means that when we claim that some symbol represents some infinitely large object, that this is just an interpretation that's irrelevant. At the end of the day all of mathematics even if that invokes uncountable infinities can be re-interpreted as discrete mathematics.

      A slightly different way to make this point is to consider a thought experiment where we would simulate the entire Earth and people living on it and watch some people invent mathematics and calculus. If we then extract the mathematics the virtual people are doing from that simulation, then since this is something that was cooked up as a result of running the simulation on a finite state machine, it's a result that in principle is 100% part of discrete mathematics.

      There is then no obligation to interpret the symbol R as a set containing an uncountable number of objects for exactly the same reason why if we translate religious people talk about God we should believe that God really exists.

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  4. As always you have made clear as subtilty in the nomenclature of physics that has often led to confusion and misunderstanding,
    An excellent follow up to your discussion of Heisenberg.

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  5. I think Ari has a point, if minor. The quantity that is discrete is the energy. Then, using a classical formula (that's the important point), you can associate a radius to that energy. But that radius has no real physical meaning, it is just the radius of a fictitious classical orbit that would have the same energy. Only as an abuse of language you can say that the radius is discrete. As radius is space, it is really continuous as far as we know.

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    1. This has nothing to do with "classical formula". You solve the Schroedinger equation for the electron orbitals in the potential of the nucleus. They resulting wave-functions are of course not sharply peaked at one radius (ie, they are not delta-functions), but they are not continuously smeared out through space. Instead, they have preferred (max probability) radiuses that are at specific distances to the nucleus. The point is that there is a finite number of solutions to these equations corresponding the oribitals (which I refer to as "shells"). I am talking about radiuses there, not about energies, because otherwise the illustration with radiuses makes little sense.

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    2. Sabine,

      A minor quibble: you wrote:
      >The point is that there is a finite number of solutions to these equations corresponding the oribitals...

      Well, actually, in principle, the principal quantum number can be any positive integer (and of course there are a finite number of angular momentum states for each of these), so there actually are an infinite number of these orbitals. The real point is that they are discrete -- i.e., there is a finite gap in the energy from one principal quantum number to the next.

      To be sure, for all practical purposes, orbitals with really high principal quantum numbers are so loosely bound that they might as well be free. So, there are indeed only a finite number of orbitals that anyone ever worries about.

      All the best,

      Dave

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    3. Dave,

      Sorry, you are right, I didn't mean there is a finite number, I meant they're discrete and countable.

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  6. This essay compelled me to search deeper. I recalled that Poincare had published, in 1911, a paper "On the Theory of Quanta," where he showed of the "necessity and sufficiency" of discreteness. Regards that paper, McCormmach writes "it was not only the hypothesis of quanta that was put to the test, but also its antithesis, the hypothesis of continuity." (Isis,1967, Henri Poincare and the Quantum Theory). R.H. Fowler extended Poincare's paper with "A Simple Extension of Fourier's Integral Theorem and Some Physical Applications, in Particular to the Theory of Quanta " (1921, Proc. Royal Society). R.H. Fowler "fills in the gaps" of Poincare's paper by utilizing Stieltjes' integral. Max Jammer writes: "Poincare conclusively demonstrated that the hypothesis of quanta is the only one which leads to Planck's law of radiation and that the existence of discontinuity in the probability function of the energy distribution is a necessary consequence of any assumed radiation law which leads to a finite total radiation." (page 53, Conceptual Development of Quantum Mechanics). In 1995, Prentis wrote: "Given the significant impact of Poincaré’s memoir on quantum theory and statistical physics, it is surprising that most physicists are not aware of its valuable mathematical and physical ideas." (Poincaré’s Proof of the Quantum Discontinuity of Nature, American Journal of Physics, 63, 339). I do not know if that line from Prentis applies today. Poincare's remarkable 1911 paper is open-access online.

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    1. " "Poincare conclusively demonstrated that the hypothesis of quanta is the only one which leads to Planck's law of radiation "

      Yes, BUT .... that is relativistic quantum field theory while Sabine is explicitly discussing nonrelativistic quantum mechanics. Photons, being massless, are necessarily relativistic.

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  7. When I was coming up many years ago the standard approach, pedagogically speaking, was to present the subject in historical order, i.e. starting with the ultraviolet catastrophe and Maxwell, the photoelectric effect and Einstein, and so on and so on. The current fashion, as I understand it, is _not_ to teach QM this way, starting instead with the wave function, probability, and operator notation (showing how the bra-ket and matrix forms are related, maybe with a bit of history thrown in as an afterthought), etc. Apparently the received wisdom is that the old ordering is more confusing than otherwise, leading to misconceptions of the basics at the very beginning whereas the second does not. Have people who have taught basic QM found this to be true? Or is there yet another ordering they prefer? In the spirit of the original post, of course.

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    1. I've taught QM to chemists for decades. I've tried many approaches.
      Most students never "understand" because they never try. They just think like organic chemists or doctors and memorize.

      I've tried the historical approach, the axiomatic approach using differential equations, and even, on grad students, the matrix approach. All are adequately learned by the best students, not by the average ones (remember, the average chemist is not a math whiz).

      One of the problems, for the better students, is that they ask "why" the Schrodinger equation is as it is. "Why" do we have to stuff the exclusion principle into it. "Why" is the space part a second derivative while the time part is a first derivative. "Why" do we have to stuff spin in as a kludge? "Why" do we need the "wavefunction collapse" kludge? Axioms don't do well.
      Appeal to experiment does not satisfy.


      I and our current department head and his wife (a theoretical quantum person) are the only three people in the whole department who understand this. This even excludes our "molectular electronic structure" theorist!

      The dept head has tried teaching the answer to his best grad students. The answer , of course, it that quantum "mechanics" and the Schrodinger equation is simply wrong. Its not relativistic. One has to start with relativistic field theory and its basis in the Poincare group, and show how one derives the Scchrodinger equation from it (along with, if desired, the Dirac, Klein-Gordon [aka Schrodinger's first try!], and Maxwell equations) either directly or through the Bethe-Salpeter equation. Its trivial to show how the Schrodinger equation comes from either Dirac or Klein-Gordon.

      Sabine will have a fit when I say the following: we also think that we should teach them the mathematics of de Broglie-Bohm, not with the lines as "particle paths" but as lines of probability flux, and how it explains real measurements without breaking unitarity at all!

      But this only works for the very best!
      The rest get even more confused.

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  8. Hi Sabine,

    I thought that historically the first difference between quantum and non-quantum is that light is particles (and later on also particles are wave - the very first unification in my opinion).

    Best,
    J.
    (PS: I also thought the title was impossible :)

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  9. Sabine wrote: "Atoms can absorb and emit light only at certain frequencies."

    Bells, drums, strings have natural frequencies too. And classical physics is just fine for working out the spectra of these objects. Schrödinger's equation is just another classical equation that applies to atoms. Second quantization was invented for a reason! And you don't think of the creation of a photon as a continuous process, do you?

    "quantizing a theory does not mean you make it discrete"

    This dangerously muddies an already murky issue. I'd say that quantization is an ad hoc procedure for guessing a discrete structure from a known continuum limit (e.g. introducing phonons in a lattice). The guesses have been remarkably successful for three of the fundamental forces, but for gravity it is questionable if quantization makes sense at all.

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  10. The number of physically distinct states available for a system in a finite volume is finite. This means that continuous space and time does not lead to a an uncountable number of distinct states like it does in classical mechanics.

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    1. Count Iblis wrote:
      >The number of physically distinct states available for a system in a finite volume is finite.

      But.......

      That is simply false.

      The simplest example of a system in a finite volume is the so-called one-dimensional "particle in a box." It has an infinite number of possible states given by (I neglect the normalization factor):

      ψ(x) = sin(π n x /L)

      where n is any positive integer.

      The End.

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    2. @PhysicistDave: the number of states is infinite only if the box has an infinite depth (in energy), which is of course unphysical. For a finite-depth box, the number of states inside the box is finite. Then you have what atomic and molecular physicists call "the continuum", ie, non localized states that are not trapped inside the box.
      The Real End.

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    3. opamanfred,

      You are making a fool of yourself.

      You wrote:
      >For a finite-depth box, the number of states inside the box is finite. Then you have what atomic and molecular physicists call "the continuum", ie, non localized states that are not trapped inside the box.

      You invoke atomic physics. But, as Sabine and I discussed above, there is an infinite discrete set of states for the atom, all lower in energy than the continuum.

      So, even in that case you are wrong.

      You're faking it.

      Iblis' original claim was that there are only a finite number of states in a finite volume: the only way to rigidly limit yourself to a finite volume is to have impenetrable walls -- i.e., a particle in a box. And then you do have an infinite number of states in a finite volume.

      You relax that initial claim to deal with an atom: still an infinite number of discrete states.

      Bu the way, there is a rigorous mathematical basis that explains your and Iblis' error having to do with the dimensionality of the space of L2 functions (up to sets of measure zero, of course) over a finite domain.

      So, you're zapped no matter which way you turn, oh freddo: whether rigidly confined to a finite volume, or the more physical case of an atom, or rigorous math.

      Perhaps you should remain silent on subjects about which you have no knowledge.

      Y'know, so it will not be quite so obvious that you are faking it.

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    4. What I wrote is true, but you do need to impose an upper limit on the energy content of the closed system, which is entirely reasonable and it's actually going to be enforced by gravity (a black hole will form if you attempt to put too much energy in a finite volume).

      There is no continuum of states if you are very rigorous w.r.t. to the physics. Of course, in practice it can be convenient to pretend that a free particle is not confined to some fine volume. But then you are also free to deal regularize unbounded states by e.g. imposing periodic boundary conditions and then work with a discrete set of states and take the continuum limit at the end of the computations. Such a regularization is always hidden in the math if you don't make things finite, it's in the small print you skip when using a formula on how e.g. the square the Dirac Delta function should be interpreted. You can hide such things, but the reason why the computation has to be done in the way you do it is precisely because the continuum is not really there.

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    5. Count Iblis wrote to me:
      >There is no continuum of states if you are very rigorous w.r.t. to the physics.

      Huh? Who is talking about a "continuum of states"? The states for a particle in a box are discrete, not a continuum, but there is an infinite number of them.

      Iblis also wrote:
      >What I wrote is true, but you do need to impose an upper limit on the energy content of the closed system, which is entirely reasonable and it's actually going to be enforced by gravity (a black hole will form if you attempt to put too much energy in a finite volume).

      Look: you are the one who chose to mention "a system in a finite volume." The only way to get a system in a finite volume is to have impenetrable walls -- i.e., an infinite energy barrier -- or, as you say, periodic boundary conditions. In either case, you do in fact get an infinite number of discrete states. And, we were talking about elementary quantum mechanics, not black holes! You want to use black holes to argue against the "continuum," well, that is a different subject (a subject which no one understands).

      You are simply wrong because you do not know what you are talking about.

      Iblis also wrote:
      > But then you are also free to deal regularize unbounded states by e.g. imposing periodic boundary conditions and then work with a discrete set of states and take the continuum limit at the end of the computations.

      You are hung up on your goofy fear of the "continuum/" You do not need to take the "continuum limit": without taking the continuum limit, you still will get an infinite number of states.

      Iblis also wrote:
      >Such a regularization is always hidden in the math if you don't make things finite, it's in the small print you skip when using a formula on how e.g. the square the Dirac Delta function should be interpreted. You can hide such things, but the reason why the computation has to be done in the way you do it is precisely because the continuum is not really there.

      Seriously, what is wrong with you???

      Why do you keep bringing up your strangely psychotic hostility to "the continuum"?

      Without any kind of "regularization," if you just do a sophomore level analysis of the situation you raised -- i.e., "a system in a finite volume" -- then you get an infinite number of states, whether you use periodic boundary conditions or analyze a particle in a box with impenetrable walls.

      You do not need to "square the Dirac Delta function," you do not need to regularize, you do not need to take any limit -- this is simple sophomore physics.

      I think maybe you are confused in failing to understand that states can be discrete and yet there can still be an infinite number of them? But, that does actually happen when you analyze a particle in a box.

      Look: I have googled earlier comments by you, and it is clear that you have some weird psychological hostility towards "the continuum." Fine: maybe first-year calculus produced some psychological trauma for you and you have never recovered.

      Whatever.

      But you are just mis-reporting the standard results that any competent sophomore physics major can easily calculate: in elementary quantum mechanics, a particle confined to a finite volume does in fact have an infinite number of possible states.

      No regularization, no square of the Dirac delta function, nothing complicated: I spelled out the wave functions explicitly above.

      But you are psychotic about the "continuum" and so keep posting nonsense.

      You have a very serious problem.

      Do you curl into a ball and whimper in the corner whenever anyone utters the words "the continuum"?

      You are one truly bizarre dude!

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    6. You don't need impenetrable walls. If you prepare a particle in some state, then wavefunction of the particle will always have a compact support, due to locality. In a finite time t since you prepared the particle, the particle cannot escape beyond a distance of c t. So, psi(x,t) = 0, for |x| > c t.

      The countable infinite number of states requires that you ignore any upper limits on the energy content of the system. But we know that the physical universe won't allow you to do this.

      And since you've decided to bring in ad hominem arguments, let me bring in hominem reinforcements, a quote from a recent quanta magazine article:

      "Several experts agreed that real numbers don’t seem to be physically real, and that physicists need a new formalism that doesn’t rely on them. Ahmed Almheiri, a theoretical physicist at the Institute for Advanced Study who studies black holes and quantum gravity, said quantum mechanics “precludes the existence of the continuum.” Quantum math bundles energy and other quantities into packets, which are more like whole numbers rather than a continuum. And infinite numbers get truncated inside black holes. “A black hole may seem to have a continuously infinite number of internal states, but [these get] cut off,” he said, due to quantum gravitational effects. “Real numbers can’t exist, because you can’t hide them inside black holes. Otherwise they’d be able to hide an infinite amount of information.”"

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  11. Surely the argument for discreteness rests on the proposition that action is discrete, not energy. As an example, chemical bond energies can be strained to take a continuous range of energies, but their length tends to change according to pλ = h. Here, both sides of the equation refer to action,and h is the quantum of action, from which you can argue for discreteness. It tends to follow also from writing in the form ψ = A.exp(2πiS/h), which, from Euler, makes ψ real and positive at S = nh. (And negative in between at the wave trough).

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    1. I don't understand. If p = h/λ , p and λ can change continuously ! Bound state is another issue

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  12. Ian Miller wrote:
    >As an example, chemical bond energies can be strained to take a continuous range of energies, but their length tends to change according to pλ = h. Here, both sides of the equation refer to action,and h is the quantum of action, from which you can argue for discreteness.

    Hmmm... have you ever actually talked to a chemist about chemical bond length? I think any competent chemist will tell you they are controlled by minima of the energy function, which in turn depends on MO theory, the Exclusion Principle, etc.

    And this stuff about pλ = h? No, I don't think that implies discreteness of chemical bond length! Show us a legit P-Chem book that argues that!

    Ian also wrote:
    > It tends to follow also from writing in the form ψ = A.exp(2πiS/h), which, from Euler, makes ψ real and positive at S = nh.

    Uh, and who cares whether ψ is real or not?? Complex ψ is just fine. I took QM from Dick Feynman (1974-'75) and, unless you know a lot more about QM than Feynman did, I am pretty sure you are just making this stuff up.

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  13. Sabine, can you give me 5 examples of where quantum mechanics is used in industry say examples like 1 making jam and 2 toothpaste and 3 comfy seats in expensive cars ??

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    1. Every transistor, every microchip, every digital camera, laser, electron microscope, and magnetic resonance imaging works only thanks to our understanding of quantum mechanics. If the topic is of interest to you, I recommend Chad Orzel's recent book "Breakfast with Einstein" which I have reviewed here.

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    2. QM is also used a lot in material science/metallurgy today. In addition to developing new materials, it helps us understand things such as "hydrogen cracking" of welds, which plagued the construction of the Liberty Ships in the USA during WWII. Your expensive car was made better by such knowledge.

      Perhaps your point is that humanity got along without it for about 200,000 years? Yes, but we also got along without the wheel for about 190,000 years. How far back in technology would you like to retreat? (Personally I would like to give up the expensive cars in favor of buses and trains albeit with more comfortable seats.)

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  14. Concerning bound systems and the formulation in terms of energy vs radius, it is always, and more technically, angular momentum and changes in angular momentum that is discrete.

    As for "free" particles, ...

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  15. Sabine: “A quantum theory is one in which you have observable quantities that obey Heisenberg’s uncertainty principle.”

    Why this ‘principle’ again? In a previous blog I have explained that this uncertainty is an elementary property of waves. So, we can convert the sentence above into:
    ‘A quantum theory is a theory which treats the wave properties of particles.’ This is more physics than the statement above. And now we can, of course, ask the question: Why does a particle have wave properties? With this question we are back in the development of our physical knowledge. Which I find missing in present physics.

    And I think that we should avoid the notion of ‘principle’.
    Principles have been the building blocks in the system of philosopher Plato. Since Newton we argue with ‘laws’. This was generally taken as a big step forward, also in this blog. So, why go back?

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    1. antooneo,

      Well, and I explained that what you said is wrong. It is still wrong and you will not make it correct by repeating it. Why not try and learn something.

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    2. What is wrong in my description? And where did you explain such? I have carefully read all what you wrote to me in the cases where you did it, and I did not find any objections. So, would you please explain this (again, maybe if I overlooked something ...).

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    3. antooneo,

      Maybe I wrote this in reply to someone else. Sorry in case this was a mixup. The uncertainty principle is a quantum phenomenon. It is not a property of classical waves. If there's no hbar in it, it's not the uncertainty principle. People get confused by the fact that waves obey a property that looks similar to the uncertainty principle, but in this case it's for the position and *wave-number*, not momentum. That's not a quantum phenomenon. That's just a mathematical identity. Also, as I have said elsewhere, the particle-wave debate has long been resolved. It's neither particles nor waves, but wave-functions. There's nothing to debate here.

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    4. Sabine,

      Nothing to debate? I think that we urgently need to debate this matter.

      The particle-wave debate has long been resolved? Where and in which way? - A turning point in history was the Solvay conference in 1927. Here two concepts of particle physics (and so QM) have been discussed. One was the concept of Louis de Broglie (the inventor of particle-wave) which says that a particle is a corpuscle surrounded by a guiding wave. Not very mysterious. And the other was the concept of Werner Heisenberg who refused this concept and presented his model of particle-wave which says that the particle is corpuscle and wave at the same time with the consequence (among others) that this model is inaccessible to imagination. And it needs weird assumptions like the wave collapse and others which are otherwise not needed.

      John Bell has investigated this discussion in his book “Speakable and Unspeakable in Quantum Mechanics”. And he says that he has nowhere found physical arguments against de Broglie’s (easily understandable) model. But Heisenberg’s stronger personality using methods of contemptibility against de Broglie caused the decision. This QM way of Heisenberg was not only refused by Einstein but very strongly by his former friend Erwin Schrödinger. But no chance for them.

      There exist a lot of simple solutions for QM problems (also QG), but no chance to discuss them against main stream. What understanding of science is this? The mentioned (technical) explanation of uncertainty is a good example of it. - The present way of QM has not provided solutions since decades. Why continue this way?

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    5. antooneo,

      If you want to urgently debate something on which there is nothing to debate I suggest you take your debate elsewhere, thank you.

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    6. antooneo,

      What you are talking about is Bohm-de Broglie pilot-wave theory, generally known nowadays as Bohmian mechanics.

      A number of us have talked about this a lot in Sabine's comments: my impression is that most physicists nowadays do know that it is consistent and reproduces the results of QM, at least for the non-relativistic case. (Yes, I know it can be made to work for QFT, but that is less widely known.)

      But part of the problem you are having communicating with people is that, instead of pointing out an alternative, such as Bohmina mechanics, and asking people's opinion, you aggressively tell people that what they know is wrong and that the somewhat unusual approach you like is right.

      They are just going to turn you off, since what they know is not wrong. You are just advocating a different, also not wrong, approach for consideration also.

      If you phrased it that way, people might listen!

      For example, you say:
      >There exist a lot of simple solutions for QM problems (also QG)

      Well... the truth is that maybe Bohmian mechanics provides an approach to QG that could be helpful: I can see how it might help with the famous problem of time, for example (not an original idea with me, of course). It might. But it is nor likely to offer a completely "simple solution"! QG is hard.

      Similarly, when you push neo-Lorentzian mechanics, if you would stop saying Einstein is clearly wrong (a hard point for you to makes since his predictions are identical to the approach you favor!), you could instead make the point that sometimes thinking about how and why an object that is accelerating changes its dimensions from the viewpoint of someone who stays at rest, you might get more attention.

      Harvey Brown in his Physical Relativity: Space-time Structure from a Dynamical Perspective makes much the same point about relativity that I know you are trying to make (and that Bell made in the chapter in his book on relativity). But Brown does not try to say Einstein was wrong, but merely that an approach that sometimes appeals to direct physical laws can illuminate what is happening better than simply appealing to the principle of relativity.

      I keep talking to you because I know that some of your perspective has a point. But you are shooting yourself in the foot by acting as if your alternative perspectives are the only sane perspectives. That is too similar to Steve Evans' view that all religious believers are insane. They're not.

      By the way, Sabine is much more open than most physicists and most professionals in general and, specifically, she knows there are problems in physics.

      If you cannot figure out how to communicate with her, you are not going to get through to anyone.

      Oh, and read Harvey Brown's book if you haven't: I think you will enjoy it and will profit from it if you can emulate his style of discussion.

      All the best,

      Dave

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    7. It all comes down to what people are able to imagine.

      There are people who cannot imagine wave functions and wave function collapse and are not bothered.

      Then there are people who cannot imagine a wave function and thus cannot believe it is a physical or even metaphysical thing.

      Pilot waves are no more imaginable than wave functions.

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    8. Sabine,

      If you find that nothing is to be debated, what is the goal of your physical activity? You are correct that beauty and symmetry are bad criteria for the quality of a theory. But these are minor points. It seems that you taboo the major ones. Many of them are ignored by present main stream. And those are the cause of the great problems.

      Example relativity: Lorentz discussed a thought experiment with Einstein in 1917 showing that Einstein’s arguments against ether have logical conflicts. What Einstein fully admitted. The question is unresolved until now. And further the strong equivalence principle, the fundament of his GRT, is falsified since long time. These are known facts, but nobody cares.

      Example QM: Here we are told that there are specific rules like: E = h * f, constancy of spin, Pauli principle, uncertainty. But, what is the cause for those? We are not allowed to ask this question in Copenhagen QM. Heisenberg’s ban of thinking is still in force.

      What does physics mean? To accept and to believe? Or to look for reasons and causes? – Are you, Sabine, really satisfied by a theory which merely declares rules but explains nothing? Physics means originally something different.

      And btw, the four rules mentioned above can easily, and quantitatively(!), derived from a particle model which follows from the QM approach of de Broglie. You have the other day criticized that reductionism is missing in present physics. Here we can have it but you don’t want it. So, what do you want at the end?

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    9. antooneo wrote to Sabine:
      >If you find that nothing is to be debated, what is the goal of your physical activity?

      antooneo, you treat physics as if it were politics or lawyering: a "debate," as you say.

      Most people who become physicists are smart enough to have become attorneys, but they do not do so because they really do not enjoy "debates."

      Physicists tend to be people who like clean, clear-cut answers, not debates.

      For example, you keep saying things such as:
      >Example relativity: Lorentz discussed a thought experiment with Einstein in 1917 showing that Einstein’s arguments against ether have logical conflicts. What Einstein fully admitted.

      But you never actually show it is true.

      And, quite obviously it is not true. For, as you yourself admit, neo-Lorentzian theory predicts exactly the same observations as Special Relativity.

      But you keep repeating this as some sort of weird "debate" ploy.

      Might work in politics. Might work for a lawyer.

      Not gonna work in physics, my friend. You are wasting your time.

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    10. Greg Feild,

      I think that no physicist has problems to imagine a wave function. The problem with Heisenberg’s approach is that a particle is corpuscle and wave at the same time. This is different from the view of an object, which has only the properties of a wave and of a particle (like a corpuscle which is accompanied and guided by a wave). Heisenberg has explicitly said that someone who has the intention to ‘understand’ physics is working in the wrong field; because the human brain is not able to do this.

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    11. Dave,

      The alternative to debating is annunciation, which has its place in religion. To treat physical questions by annunciation was the use in the dark ages, which are fortunately gone.

      >>> You say: “But you never actually show it is true.”
      (about Einstein’s confession that his position to ether causes logical conflicts)

      Yes, I can show it. There was a letter exchange between Lorentz and Einstein. I can send you a facsimile of these handwritten letters. Which way do you want it?

      Of course the results of Einstein and Lorentz are formally the same. But the method is different. Lorentz assumes an absolute frame which Einstein has always refused. Lorentz and Mach have always argued that rotation (also acceleration) cannot be defined without the existence of an absolute frame. Einstein has conceded this problem but never solved it. And the other point is that the Lorentzian way does not need Einstein’s idea of space-time. Everything can be done by use of Euclidean geometry. This is also the case of general relativity. Neither Minkowski nor Riemann is needed for calculations. Another point is that paradoxes like the Twin Paradox and the Ehrenfest Paradox do not exist as such in the Lorentzian approach. Not to speak about Dark Energy where it is similar.

      To your preceding comment:

      You may be right that it is smarter to present other directions in a smother way. But the problem is to get enough attention so that a true and open discussion is started. The problem with main stream is in relativity (to a certain extend also QM) that the representatives of this direction have based their whole career on the existing convictions. So it is of course a hard step to risk the benefits of what they have achieved. I have earlier mentioned the fate of Louis de Broglie who lost almost everything that he had achieved when he deviated from the direction of Heisenberg.

      So, which way to reach the physical community, which means the decision makers? We have big discrepancies as I have mentioned for relativity. Even worse in QM. The Higgs model for the mass has a conflict of 10^57 with measurement, the concept of vacuum energy of even 10^120. Biggest numbers I have ever heard of. The representatives of QM admit this, but the Nobel Prize was awarded for both. If those strong discrepancies do not cause any openness for solutions, what else can do it?

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    12. antooneo wrote to me:
      >Yes, I can show it. There was a letter exchange between Lorentz and Einstein. I can send you a facsimile of these handwritten letters. Which way do you want it?

      Well, I am sure I will not be able to decipher early twentieth-century German handwriting!

      But, you know, the collected papers of Einstein are available online (in both German and English): if these letters are real, they must be in there. So, tell us the date of the letters (and, if you know, the volume of the Collected Papers) and that should suffice.

      My guess is that Einstein was just being polite to a "grand old man" of the field, or perhaps it was one of those woolly philosophy problems that Einstein got confused about from time to time, but which turned out to be scientifically irrelevant.

      antooneo also wrote:
      >Lorentz and Mach have always argued that rotation (also acceleration) cannot be defined without the existence of an absolute frame. Einstein has conceded this problem but never solved it.

      Well, there is just no problem to solve. In fact, GR has privileged (local) frames: non-rotating, freely falling frames. That is just the way the universe is. I know it bothered Einstein for a while, and some people ignorant of physics even today, but that's the way things are.

      I think some of us have told you multiple times that we just do not care what Einstein thought about anything, except as a matter of historical interest.

      We know a lot more today about relativity than Einstein did.

      Physics is not theology where you constantly must refer to the Church Fathers.

      antooneo also wrote:
      >You may be right that it is smarter to present other directions in a smother way. But the problem is to get enough attention so that a true and open discussion is started.

      Well, you are not going to get that by telling people who know enormously more about physics than you do that they are simply wrong!

      Neo-Lorentzian theory and Bohmina mechanics may be interesting alternative perspectives: I myself think they help illuminate the more conventional approaches, though I doubt either is true. But textbook QM and Einsteinian relativity do give the right answers, as you yourself admit.

      So,if you tell experts in the field that everything they know is wrong, they will just write you off as a kook.

      antooneo also wrote:
      > Another point is that paradoxes like the Twin Paradox and the Ehrenfest Paradox do not exist as such in the Lorentzian approach.

      They do not exist in Einsteinian relativity either. They are apparent "paradoxes" that confuse the neophyte, but they are not really paradoxes.

      The answer lies in the fact that a state of rotation or acceleration is not relative. The (local) existence of acceleration or rotation in GR is absolute.

      I know you do not like that (and, yes, I know it bothered Einstein also) but that is just how GR (and, it seems, nature) works.

      No paradox. Just the real world.

      Dave

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  16. Nice essay!

    Discretization also has the unfortunate side effect of encouraging a particle-first visualization of how light moves through space. Ironically, on this point the old classical model of light as waves that can be spread and diluted without limit works hugely better. Using such waves is the _only_ approach that correctly predicts behaviors such as diffraction and reflection. It is only when the photon arrives that all of this astonishingly dilute energy gets "instantly" collected back into a single atomically tiny location. For the quite doable example of someone on earth using a hydrogen atom to absorb a photon emitted 10 billion years ago (e.g. via an Einstein lens), that works out to a volume reduction of... wait for it: about 3 x 10^109. That's doggone efficient energy collection!

    So this transition from smooth-huge-continuous to small-compact-discrete remains one of the trippiest parts of the quantization issue. It is also exactly the point that Einstein focused on when he started asking questions that annoyed first Bohr, and eventually most of the Copenhagen group (Bohr was low-key, low-pitched, slow-talking, and genuinely amiable... but also absolutely relentless.)

    Einstein simply asked this: If to get the correct final energy distribution in the new quantum theory radiation still must be modeled as going everywhere, and if locality (precious to Einstein!) also applies, why can't multiple people light years apart end up capturing the _same_ photon? How does the rest of the electromagnetic wave get informed, apparently "instantly", that the game is over and the photon has been captured by an atom on some dinky nanoscopic spot in the cosmos called Earth?

    Einstein tended to ask very good, very annoying questions. Alas, I think it's still safe to say even a century later, a deeply satisfying answer on the nature of such distance-independent wave collapses has yet to be devised. We seem to be missing something.

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    1. Terry Bollinger wrote:
      >It is only when the photon arrives that all of this astonishingly dilute energy gets "instantly" collected back into a single atomically tiny location.
      ...
      > How does the rest of the electromagnetic wave get informed, apparently "instantly", that the game is over and the photon has been captured by an atom on some dinky nanoscopic spot in the cosmos called Earth?

      Hey, Terry! Hope you are doing well and surviving the lockdown.

      The issue you raise has bothered me for a very long time: I don't disagree with what you wrote, but I do want to elaborate on it.

      First of all, we should make clear that, as far as anyone knows, there is no mathematical or physical contradiction here, and, in fact, the effect you describe seems really to happen.

      What prevents a paradox is the "no-signalling theorem," based on the zero space-like commutators for the relevant field operators for the electromagnetic field (i.e., photons).

      The problem, of course, is to try to figure out what this means physically.

      For example, it tells you that there must be some limit to how efficiently you can detect one of these "dilute" photons, Otherwise, you could detect, say, every other photon from some distant source, and someone far away, in doing their own detecting, would notice the "missing" photons and so you could send a signal.

      Something like this is already known in classical EM -- you need a really big antenna to catch all the photons! I think it is also connected to the so-called "optical theorem."

      Furthermore, all this illustrates that photons are not merely "particles" somehow guided by a wavefunction; we really are quantizing a field: light really is an electromagnetic field whose energy levels are quantized.

      And yet... you can go to Fock space and then they almost do look like particles.

      I think it is especially interesting to see how this works in the non-textbook interpretations of QM: many-worlds, Bohm-de Broglie, etc.

      Anyway, yeah, I think this is one of those puzzles that ought to cause people to scratch their heads in the same way the two-slit experiment does.

      By the way, do you have a reference to Einstein's being puzzled by this? Does sound like the kind of thing that would really bother him.

      All the best,

      Dave

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    2. Terry Bollinger’s wonderfully descriptive depiction of an electromagnetic wave front moving out from its source to encompass a bubble billions of light years across, only to collapse at a single discrete point in an instant, immediately brought to mind John Cramer’s Transactional Interpretation (TI) of Quantum Mechanics. I believe I first encountered this model in John Gribbin’s “In Search of Schrodinger’s Cat” book, though I wasn’t able to find it on my book shelves. But I did find its sequel, Gribbin’s “Schrodinger’s Kittens and the Search for Reality”, where he also brings it up.

      Here’s an encapsulation of John Cramer’s TI, as best as I can figure from a layman’s perspective: Taking his cue from the Wheeler-Feynman Absorber theory, Cramer recognized that the fully relativized version of Schrodinger’s wave equation described the evolution of a quantum system not only into the future, but into the past as well. The implication was that the Absorber theory, originally applied to light, might be extended to particles as well, since in quantum theory particles are treated as wave packets.

      Schrodinger’s wave equation represents the potential of a quantum system before it collapses into some unspecified future state. The equation is in the form of a complex function containing both real and imaginary parts, and has two sets of solutions. The first solution set is the one utilized by most physicists to calculate quantum processes, and describes the evolution of a quantum system into the future (the retarded wave). The second set of equations, known as the complex conjugate, is a mirror image of the first, and describes the evolution of a quantum system into the past (the advanced wave).

      In TI every quantum event represents a “handshake” across spacetime. An “offer” wave from an excited electron propagates outward in an ever expanding bubble, corresponding to the first Schrodinger wave equation. At some future time the energy of this expanding wavefront is randomly absorbed by a second electron, which then transmits a “confirmation” wave into the past towards the original excited electron, arriving at the exact instant that electron radiated its initial signal. This confirmation wave, which travels into the past, corresponds to the complex conjugate of the first wave equation. Additionally, the original excited electron sends a confirmation wave into the past, while the absorber electron sends an offer wave into the future. These two cancel out, while the primary confirmation wave reinforces the primary offer wave, and the transaction is complete.

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    3. Or ... there are no waves.

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    4. Dave, thank you, my family and I are all well. I hope all is well for you also. Interesting times, these.

      Einstein's phrased his actual question in terms of the two-slit electron experiment, not the worst-case scenario of cosmic photons that I gave. This episode is wonderfully described by Louisa Gilder in The Age of Entanglement, Chapter 13, paragraphs 4-10. Einstein casually introduces as part of his question the need for "instantaneous action-at-a-distance" to prevent multiple copies of the electron from being found. From the description I gather this was the first time the phrase was used in a group setting.

      Gilder takes well-researched descriptions of actual events and treats them as if they were movie scripts, including guidance on the emotional states of the participants. This simple but very human addition makes the simple facts of the events catch fire. When reading the text you can see the group in your mind, hear Einstein speaking, and feel the tension in the room as the group realizes the depth of the difficulty that Einstein has so simply and even humbly dropped on them like a grenade. You feel like you are there.

      In short, it's a marvelous book that I recommend highly for anyone who yearns for some insight into the more personal side of these profoundly personality-driven events that were so critical in the emergence of modern theory. It is also a bit humbling, because it makes you realize that our very humanness can profoundly influence the interpretation and prioritization of equations for which there is universal agreement.

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    5. David, since I'm a fan of the Wheeler-Feynman work you just mentioned, your description of Cramer's Transactional Interpretation is intriguing. I've downloaded his long (40 pages) 1986 paper and have begun going through it. I'll add a further comment after more reading.

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    6. David Schroeder,

      You have accurately summarized John Cramer's "Transactional Interpretation" of quantum mechanics, but I think it is worth explaining why you almost never hear physicists taking his ideas seriously -- i.e., when referring to alternatives to textbook QM, physicists refer to Many-Worlds, Bohm-de Broglie, GRW, but rarely to Cramer.

      The reason is that Cramer's ideas are nonsense, "not even wrong," in Pauli's immortal phrase.

      All that Cramer does is note that if you reverse the time variable t in Schrödinger's equation and then take the complex conjugate, you get back to Schrödinger's equation.

      Indeed.

      But then he uses weird metaphors -- "handshakes" and such -- without ever giving them any physical content.

      Here are the sorts of questions, Cramer ought to answer, but never does coherently, as far as I know:

      Exactly what kind of event actually involves a "handshake" between advanced and retarded wavefunctions? Does it happen at every instant in time for an electron in an atom, for example? Does that mean that at every instant in time the electron really has a definite position, though we cannot know what it is,, due to these "handshakes"? And, therefore, does the electron actually follow out a single path through time that traces through all these positions resulting from the "handshakes"? And then there is the little problem that the wavefunction for an n-particle system exists not in 3-D space but in a 3n dimensional space (Cramer knows this, of course, but just waves it away).

      Occasionally, Cramer tosses off some comment on one or another of these sorts of questions, but never in a way where he actually explains why his comment should be the correct answer. I.e., he is like a bad scifi writer.

      The problem is not simply that Cramer does not answer these questions coherently but that his metaphors are so vague that they do not provide any answer in principle.

      It is telling that one of Cramer's venues for pushing this nonsense has been the Analog scifi magazine!

      By the way, the Wikipedia article on all this is also nonsense: for example, it states:
      >While the ordinary Schrödinger equation does not admit advanced solutions, its relativistic version does, and these advanced solutions are the ones used by TIQM.

      Uh, no. The article is referring to the Klein-Gordon equation, and if you just treat K-G as a relativistic Schrödinger equation, you get well-known contradictions. You actually have to "second-quantize" the K-G equation, and then you get a relativistic Schrödinger equation which does not have the properties the Wikipedia authors claim.

      In fairness to the Wikipedia authors, Cramer may once have said something false like this: he is a very confused guy who just keeps flailing around with various new idiocies trying to defend an idiotic, failed idea.

      An example of this flailing from Wikipedia:
      >In his book, The Quantum Handshake, Cramer has added a hierarchy to the description of pseudo-time to deal with Maudlin's objection...

      A "hierarchy of pseudo-time" -- even worse than some of the crack-pots who comment here. Scifi indeed. And not even good scifi.

      If you look through the references in the Wikipedia article, you will find that, aside from references to Cramer's own work and to references by physicists that have nothing to do with Cramer's work (e.g., to Hugh Everett's many-worlds paper), they mostly seem to refer to philosophers: Berkovitz, Kastner, and Maudlin are all philosophers, for example. (Tim Maudlin, I should make clear, knows that Cramer's stuff is wrong.) Musser has a degree in engineering.

      No doubt Wikipedia does not cite many physicists in the references for the simple reason I have given above: any competent physicist can see that Cramer's ideas are nonsense.

      All the best,

      Dave

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    7. Terry Bollinger,

      Thanks for the reference. I think it is starting to dawn on more and more physicists that QM is even stranger than most of us felt when we were students. Now, why....?

      I know Cramer claims Feynman-Wheeler as an inspiration. Two big differences: first, Feynman-Wheeler basically use Maxwell's equations and actually points out real solutions of those equations. Grant them their combination of advanced and retarded solutions and their absorber assumption... and, well, their theory looks mathematically correct (argument remains, of course).

      Second, whenever someone tries to pin Cramer down on the real details, he keeps gyrating to a new position. Maudlin pushed him into the "hierarchy of pseudo-times" position. Ruth Kastner has tried to save Cramer from himself by pushing the point that a wavefunction for an n-particle system lives in 3n dimensional space, not 3-D space.

      Cramer tries to deal with such matters with rhetorical flourishes as long as he can, and then finally admits the "theory" needs to be changed.

      The real problem is that the "theory" was never there in the first place. Cramer started with this vague intuition that maybe retro-causation (really temporally bi-directional causation) might solve the "spooky action at a distance" problem, an intuition that many of us physicists have had. He added to that, what all physicists know, that time reversal of the Schrödinger equation is connected to complex conjugation.

      But then he just started verbally riffing on those ideas without any real theory. At one time or another, I think he has given answers to the questions I posed above, but he does not derive those answers from a clear theory. He either declaims the answer as it he were the pope of TI or "argues" for them giving a rhetorical presentation like a theologian.

      That behavior is not physics and it does not impress most physicists.

      I';ve been following Cramer and his TI for something like three decades now, and it is not getting better. If anything, what has played out is simply what I rather suspected when I first looked at his stuff some thirty years ago. (I think I first saw it in the analog scifi magazine.)

      It sounds serious until you take it seriously. Then you find out it is more like Scientology (which got its start in the predecessor to analog!) than like science.

      All the best,

      Dave

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    8. PhysicistDave asked: "Does it happen at every instant in time for an electron in an atom, for example?"

      None of the "interpretations" of QM give intelligible answers to this kind of questions. Perhaps it isn't meaningful to ask them. One is presupposing that an electron exists "at every instant in time". "Electrons" do not have definite properties unless they are "measured" -- it might be clearer to say that electrons do not exist most of the time. "Particle" is a classical concept that is foisted on the microworld. What is a continuous world line classically might in fact be a dotted line when looked at on the zeptosecond scale. (Call it zitterbewegung if you like.)

      I found (and still find) the Transaction Interpretation quite attractive. But it falls short as a true interpretation of QM if one thinks of "particles" and "waves" as physically real. The virtue of TI is the shift of focus on events. (Absorption of a photon surely is a discrete event if we can count them.) The "handshake" is a pair of events, and "particle" and "wave" are merely names we attach to special patterns of events (points in spacetime). QFT is a statistical theory of events and the correlations between them.

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    9. Anyone who doubts whether electrons exist should stick their finger in an electrical socket.

      Perhaps this would be considered making a measurement ...

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    10. Physicist Dave,

      Thank you for both of your analyses on Cramer's paper! I will continue reading it today, but my main concern so far is pretty much the same one you noted: Cramer does not seem to start with anything remotely as beautifully quantified as Heaviside's compression of Maxwell's equations. That's a huge hiccup. After a couple of hours I still have no clear idea what Cramer is really proposing. From what you say I never will, because it's not there.

      One of my own warning heuristics for Cramer 1986 is a simple one: If the author can't state clearly in the first couple of paragraphs what the central and quantifiable idea is, beware. You know this excellent principle well, Dave, as you have aptly applied it to my musings multiple times.

      Also, an erratum: I used diameter for the hydrogen atom and radius for the photon radiation sphere, so my calculation was too small by a factor of 2^3=8. Thus instead of 3 billion googols, the correct answer was 24 billion googols... and now if I catch COVID I can die a happy man, since I actually found a situation where I could use the word "googol" (10^100) meaningfully!

      (Some ancient history from late in the last millennium: Yes, "Google" is an unintentional misspelling of "googol".)

      Dave, before I forget: The Cramer handshake terminology reminded me of your observations months ago on how the Radon reconciliation approach to creating a superdeterministic block universe has been applied in the past, which I did not realize when I too suggested it. Can you recommend any good papers (just a title is fine) on applying Radon to block universe reconciliation?

      Cramer's claim of deriving probabilities also reminded me of Zurek's claim in recent years that his version of decoherence predicts quantum statistics. Are you familiar with Zurek's work on that? (This is overkill for this thread, I know. I was just curious, since you seem to know this area well.)

      A final redundant observation: My earlier use of the phrase "superdeterministic block universe" is of course redundant, since observable entanglement has been experimentally proven within the only block universe candidate available to us. Human thoughts and decisions must be part of the block, and thus must be predetermined -- superdetermined -- to correlate properly with all outcomes of all such experiments.

      Delete
    11. Werner wrote to me:
      >None of the "interpretations" of QM give intelligible answers to this kind of questions.

      You're wrong.

      Bohmian mechanics does.

      There are problems with Bohmian mechanics, but this is not one of them.

      Werner also wrote:
      > The "handshake" is a pair of events...

      Unfortunately, there is zero evidence that this "pair" of events ever actually occurs.

      It is John's little fantasy.

      His little elves.

      Delete
    12. PhysicistDave wrote: "Bohmian mechanics does."

      Oh. Conceded. But if Bohmian mechanics is the cure, then I very much prefer to live with the original disease.

      "Unfortunately, there is zero evidence that the "pair" of events ever actually occurs."

      I was thinking of a pair of emission and absorption events. And you probably won't deny that such events actually occur. In the closed-time-path (Schwinger/Keldysh) formalism propagators on the "forward" time branch are accompanied by corresponding ones on the "backward" branch. And probabilities (rather than probability amplitudes) are produced automatically, without the stupid handwaving about "measurement" and wave function collapse. The closed-time-path formalism seamlessly combines unitary evolution with the Born rule.

      Delete
    13. David Schroeder,

      Just to wrap this up before the Backreaction wave moves on, I'm still not quite sure what to make of Cramer's TI. Yes, the retarded-advanced photons absolutely do form a "handshake" transaction in the sense that the two are rather magically locked into each other over space and time. That's apparent just from considering the alternative of how weird things would get if the advanced photon decided to hit some other electron in some other object. A nasty violation of momentum conservation that would be, yes?

      So I don't have any trouble with the handshake idea, as applied to Maxwell photons, though at the same time I would point out that Wheeler-Feynman is only one of many ways to interpret such events. I would for example put out with very high confidence the idea that one could create a computer model in which the entire future concept is replaced for one selected foliation with simple "we don't know yet" states that subsequently collapse under conservation (e.g. of momentum!) into specific states in the future of that one foliation. Undetermined states are a lot blander than atoms a billion years in the future sending photons back, but I've yet to see a single information reason why the situation cannot be modeled that way -- it just requires states that don't look like our usual infinitely-precise particle models. Even more remarkably, as best I can tell such models can also be made relativistically invariant, despite only one frame being "real". That's just virtualization, creating variants of a single underlying reality based on a few additional state bits. It's something computer folks do without even blinking.

      Bottom line: I do like Cramer's focus on those critical handshakes that enforce absolute conservation rules, so it remains an interesting paper. And while I may well just be reading it poorly, every time I've gone over the critical sections I lose track of what's being exchanged in the nominal generalization. Is it still photons? Maybe phonons too? Something else? It needs some clarity, I think.

      BTW, for whatever it's worth I have this same issue of "what is the extension really talking about" for string theory, or more precisely, for the Planck-level superstring extension of the original enormously larger hadron Regge strings. Nowadays the utterly unfettered, non-experimental, concepts-only Planck version of strings is almost always what folks mean by "string theory". I always wonder: What [i]are[/i] those little Plancky strings made out of, anyway?

      For the original and very solidly experiment-based Regge trajectory version of string theory, the string-like excited states showed up in just about every kind of hadron, that is, in anything made out of quarks (2=mesons, 3=baryons). Those strings are very real, consisting of strong force fields. The mystery in that case is not what the strings are made of (the strong force), but why the strong force gets all stringy when it binds together two or three quarks.

      Delete
    14. Werner wrote to me:
      >I was thinking of a pair of emission and absorption events. And you probably won't deny that such events actually occur.

      Sometimes. In an increasingly expanding universe, there will eventually be photons that escape to infinity without ever being absorbed, if I recall correctly,. One of the problems with Feynman-Wheeler theory.

      Werner also wrote:
      > In the closed-time-path (Schwinger/Keldysh) formalism propagators on the "forward" time branch are accompanied by corresponding ones on the "backward" branch.

      Well, I do not think even John Cramer claims any connection to his TI.

      Though if you suggest it to John, he may well try to combine it somehow with his TI in some goofy way.

      Delete
    15. @Terry Bollinger
      I fully agree with you. This old Eintein's objection (1927) to standard QM is also fundamental than the measurement problem. In particular, the dispersed energy should concentrate instantaneously, in violation of limit c which applies to any transport of energy. Any interpretation of QM that does not solve this basic problem is not serious. The dBB theory is not perfect or complete, but it notably solves these two problems.

      Delete
    16. PhysicistDave wrote: "I do not think even John Cramer claims any connection to TI"

      I'm not trying to sell TI. As I said, it falls short of a true interpretation. The closed-time-path formalism (CTP) deals with non-equilibrium processes, which are typical in real detectors. This stuff is quite different from the artificial measuring devices discussed by quantum philosophers. A formalism that integrates unitary evolution and the Born rule should be of interest to anybody thinking about the "measurement problem". Read up on CTP, Dave.

      "In an increasingly expanding universe, there will eventually be photons that escape to infinity without ever being absorbed."

      Isn't it a goofy idea that something expands into the entire universe and collapses to a point in an instant?

      The real problem with quantum theory is its ontology: What is it about? Bohm answers in a backward-minded way, both particles and waves. Copenhagen says neither particles nor waves, but a combination of both. This is avoiding the question. And saying that quantum theory is about "wave functions" is even worse.

      Most physicists think that quantum theory is about photons and electrons (and other "particles", of course. Maxwell and his contemporaries thought that electrodynamics was about the "aether". Do you expect to arrive at a true understanding of quantum theory (in the same sense as we understand electrodynamics today) without a critical re-examination of our basic concepts and their connotations?

      Delete
    17. Terry Bollinger wrote:
      >And while I may well just be reading it poorly, every time I've gone over the critical sections I lose track of what's being exchanged in the nominal generalization. Is it still photons? Maybe phonons too? Something else? It needs some clarity, I think.

      Yeah, the more you try to read Cramer, the more times you see a critical lack of clarity! My English comp teacher taught us that lack of clarity in writing reflects lack of clarity in thought.

      Terry also wrote:
      >BTW, for whatever it's worth I have this same issue of "what is the extension really talking about" for string theory, or more precisely, for the Planck-level superstring extension of the original enormously larger hadron Regge strings.

      Have you heard of duality? I'm afraid the real answer is no one quite knows.

      By the way, you and I had a conflict a while back where you were complaining about renormalization in string theory, which I actually think is OK (though usually badly explained).

      But, in general, the conceptually murky areas of string theory are manifold and, in my opinion, quite serious.

      The string theorists have grabbed a bunch of cute mathematical ideas, tied them together with string and sealing wax, and, as to what it really means... hard to say. It's far from certain that it is all mathematically consistent.

      Classical bosonic strings, by the way, are perfectly well-defined (see Brain Hatfield's book), and this is part of what gives string theory its appeal.

      But as to what all the work in superstring theory in the last fifty years really means, well, hashing that out is a full-employment project for theorists with a philosophical bent for a long time (yeah, it does appeal to me, if only a bit).

      Now, if only we could find some connection to experiment...

      Dave

      Delete
    18. Werner asked me:
      >Isn't it a goofy idea that something expands into the entire universe and collapses to a point in an instant?

      That bothered me for a long time (decades).

      The answer turns out to be fairly simple -- at least if you have access to a whiteboard, which we don't here!

      So, in lieu of a whiteboard, I suggest you google the "Milne universe."

      If that does not produce some diagrams that make it clear, reply here and I will try to explain it.

      Dave

      Delete
    19. Jean-Paul, thanks!

      While I am literally at the opposite end of quantum interpretation in terms of what I think is the most fundamental interpretation (least bits for maximum predictivity) of quantum mechanics [1], I also love how the de Broglie & Bohm (dBB? I like that) interpretation imposes clarity and challenges sloppy thinking. Bell credited dBB style thinking for coming up with his inequality, as it was the only mode of quantum analysis that enabled him to think with sufficient quantifiable specificity to realize that there was something testable in all of that spooky stuff.

      -----

      [1] By “opposite end” I mean this: I am a wave-packet realist. The electron orbital around a proton is the electron, period, just with low spatial resolution — there are not enough bits of spatial locality available locally to keep it from blurring. My wave packets are “dark”, however. By that I mean they are the negative images of the usual “bright” state superposition models. In this more computationally efficient view (fewer states to track), a quantum wave function becomes a literal hole in the bit fabric of reality. Such holes are imbued with meaning and locality by a mix of both universe-spanning and local decoherence superselection rules. Mass, charge, and particle spin are examples of universe-spanning entanglements, while location and momentum are mostly local superselection constraints, e.g. the proton that keeps the electron orbital localized.

      Delete
    20. Dave,

      Thanks for the responses. Incidentally, my comments about “handshakes” of advanced and retarded photons (I can’t help it, I smile every time I type “retarded photons”), that part was straight from Feynman’s own descriptions in one of his popular books, thought I don’t recall which one. He and Wheeler got pretty loopy in all of that, and I think honestly surprised themselves when such weird, photons-from-the-future actually explained electron backreaction (Backreaction! Heh!) with precision and without causality violations. Lovely story, that, and nicely told by Feynman in the highly irreverent style he typically used for his popular audience books, e.g. What Do You Care What Other People Think?”.

      Also, you said:

      “But as to what all the work in superstring theory in the last fifty years really means … if only we could find some connection to experiment …”

      There has been, just this year! And a very solid one statistically. The bottom line: Superstrings are way too big, fat, and chunky to match the exquisite perfection of the Poincaré symmetries, at least in this universe. Poincaré, Lorentz, and Einstein get the score on that one, versus 50 years of cryptic sort-of-math-but-hey-cut-us-some-slack-please efforts to the contrary to force reality to be made out of overly complicated spinning horseshoes. You can get the abstract and PDF by a Google Scholar search on:

      Constraints on Lorentz invariance violation from HAWC

      Delete
    21. PhysicistDave wrote: "I suggest you google the 'Milne universe'"

      This is drifting off topic. I don't expect cosmology to shed much light on the quantum "measurement problem".

      Werner

      Delete
  17. Of course qantum mechanics is about discreteness!
    Google's definition of quantum is indeed no good, you have a point that QM is not about discrete quantums of energy. The correct definition is:
    "A quantum in quantum physics is a discrete amount of some
    physical quantity."
    Example quantums are electrons (discrete quantity is charge) and photons (discrete quantity is field strength).

    ReplyDelete
    Replies
    1. Field is dependent on observer's state of motion. The causal speed limit c is "a discreteness" for all. ;)

      As in every physical theory, also in QM all is in predictions and they are statistical probabilities for observables.

      Delete
    2. Sabine seems to have a rather narrow definition of "discreteness". It is weird to be talking about atoms while denying the concept of "discreteness". Perhaps Sabine envisions a theory of quantum gravity without gravitons?

      Delete
    3. I can see only discrete things in QM with matter structure radii - just as Sabine told.

      The dicreteness with speed c I referred is the discrete direction - all observers agree the direction of linear causal effect of light speeed c action, but at slower speed the direction is dependent on observer's state of motion...

      Delete
    4. Eusa wrote:

      >I can see only discrete things in QM with matter structure radii - just as Sabine told.

      Yes, because as was proven long ago, you understand nothing about quantum mechanics.

      Delete
    5. Dave,

      :) At least I've spent my life studying. But yes - more studying and knowledge less understanding about QM discussions which seem to be full of artefact hype.

      Discrete created when we chose the reference frame - generally there is no disreteness. Emergency is also a way to choose frame.

      Waiting for Sabine's article about entanglement...

      Delete
  18. I miss a statistical point of view in your article, Sabine.

    ReplyDelete
  19. Greg Field - quantization of angular momentum is not fundamental, as it was recognized early that it does not happen in molecules. See Mullikan, R.S. 1932. Phys. Rev. 41: 49-71.

    Physicist Dave: "I don't think that implies discreteness of chemical bond length." Please read what I wrote. Of course the bond length is not discrete - I wrote that the action is. No, I can't find a textbook to support that, especially using MO theory, but, at the risk of self promotion, if we accept VB theory on aromatic compounds as outlined by Herndon in J. Am. Chem Soc. 96 (1974) 7605 - 7614, then I showed that the constancy of pλ permits a very close explanation of the so-called Mills-Nixon effect (see Aust. J. Chem. 50: 795 - 805, 1997) which MO theory can only explain in certain versions - the effect in that theory seems to depend on allocation of constants and disappears in others hands. Now, I admit to being biased, but I like to think that reaching a conclusion based on a principle is better than on the impenetrable allocation of constants.

    Who cares whether Euler's complex number theory is correct? Interesting comment. The point I was trying to make was that it is real at just specific phases (not always real - of course it is mainly complex). However, this is something that occurs sharply once a period hence is not continuous, and since the topic is whether there is anything discrete about quantum mechanics, it seemed relevant. I put it there to offer a point to consider on discreteness.

    As for the reference about "competent chemists", that is a little insulting - at least to the Royal Society of Chemistry, because, according to you, they made an incompetent chemist a Fellow.

    ReplyDelete
    Replies
    1. Ian Miller wrote to me:
      >As for the reference about "competent chemists", that is a little insulting - at least to the Royal Society of Chemistry, because, according to you, they made an incompetent chemist a Fellow.

      Yes, I honestly think they clearly did.

      Nice to know that chemistry is in an even worse state than physics.

      By the way, I myself did some research many years ago on the QM of benzene, and, of course, the wavefunction must be, in some sense, cyclic since benzene is a ring.

      But, you made a general claim about bond lengths -- you did not limit it to bonds in rings -- and your general claim is obvious, total, complete nonsense. Now, if you would like to admit that your claim does not apply to most bond lengths...

      Ian also wrote:
      >Who cares whether Euler's complex number theory is correct?

      "Whether"????? You think this is open to question????

      Boy, of boy, if you think that it is debatable "whether" Euler's identity is true, then the Royal Society of Chemistry really did make a mistake!!!

      Of course, the Royal Society of Astronomy once chose Herb Dingle as Prez, which I suppose is even worse.

      Gotta watch those Royals!

      P.S. Tell me where to find your paper for free on the Web, and I may be able to give you a more detailed critique. Although maybe you would rather I not read it!

      Delete
  20. dtvmcdonald. In support of your statement regarding de Broglie/Bohm, you should see Kocsis, S. and 6 others. 2011. Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer Science 332: 1170 – 1173.

    The observations are stated to fullycomply with Bohm's predictions.

    ReplyDelete
  21. Sabine,
    I contributed a really meaningful comment, and you approve Eusa's completely meaningless response to it...
    Take a position, please.
    @opamanfred: What's your opinion?

    ReplyDelete
    Replies
    1. Franzi,

      If I approve comments, I cannot see whether they are in response to another comment or if so, to which comment. Having said that, I do not feel obliged to have a position on everything anyone puts forward in my comment sections. I would however suggest that if you want to continue a thread that you have already created, you post your comments as replies to the original thread, thanks.

      Delete
  22. "Understanding Quantum Mechanics #1: It's not about discreteness"you say.
    When using the English Language - it is about discreteness in that there are DISCRETE energy levels. You can't have an energy level of just any old size.

    ReplyDelete

  23. As I see it; I do not make claims, but quantum theory has had a development that the equivalence between a classical particle or classical wave with a quantum system is impossible, not even a hybrid. A neophyte like me sees the problem this way: an electron and a positron (two particles) interact and "convert" to gamma radiation; that same radiation later can "become" the same previous particles, the process is so fundamental that there are no intermediate processes (there is nothing discreet there); nothing like it exists in the classical world; well, it can be said that the particles are waves and everything is solved; but the Pauli exclusion principle gives particularity to the electron and the positron; Even classical probabilities are not similar to quantum probabilities, quantum entanglement destroys any equivalence. Without the uncertainty principle, Pauli exclusion, and quantum entanglement (and perhaps the Spin) there is no quantum physics. Sure, I'm speaking generally and "the devil is in the details."

    ReplyDelete
  24. 26-APR-2020

    Hi Dr. Hossenfelder

    Why is Planck's constant really small (say 10^-15 in units eV sec)?
    That number appears to be at the heart of Heisenberg's insight.

    Cheers,
    mj horn
    ps: sorry if you got multiple postings; my browser is way old.

    ReplyDelete
    Replies
    1. mj horn wrote:
      >Why is Planck's constant really small (say 10^-15 in units eV sec)?

      It's not small; in natural units, it is just 1.

      The problem is that you and I and other humans are just really, really big, so that we choose unnatural units that make h-bar seem really small.

      Bu the way, I am not joking here: this really is the general consensus among physicists, to the point that advanced textbooks often use these "natural units," in which h-bar is just equal to 1.

      Delete
  25. Is there a connection between electron "orbits" being discrete and their spatial domain, a finite shell, being compact?

    ReplyDelete
    Replies
    1. The spatial domain is strictly speaking not compact.

      Delete
    2. Sabine,

      Do you mean that the "spatial domain" is not a finite shell? How about the domain of the solid angle? That is compact.

      Delete
  26. Dear dtvmcdonald, dear PhysicistDave, dear Sabine,
    in this order:

    dtvmcdonald
    If I were you, I would start quantum mechanics lectures like this:
    "Hello boys and girls, we have a great mathematical tool here with which we
    can make very precise statements about energy levels and other things. It is very, very useful.
    That is why it is taught. We have no alternative theory. That is why it is taught.
    But we have no good explanation for the mathematical objects.
    It is possible that we did not understand everything at all. "

    In my ears, all explanations of quantum mechanics sound like Claudius Ptolemy
    would say something like, "A planet is an object in the sky that fits my epicyclic theory.
    In a way that's true, but it's useless when someone ask why epicycles exist.

    It is sometimes good to know if you have not understood something.
    And it is even better to know if no one has understood it.


    PhysicistDave
    You said that "we know it must be well under a millionth the radius of an atom"
    The evidence for such small distances is not as good as it is said everywhere.
    I assume you are referring to the scattering experiments in particle accelerators.

    In order to get such statements, one has to use the Fourier transformation.
    However, this already requires infinitely small distances.
    In other words, you have to assume what you want to show.
    That is not correct.


    Sabine:
    In your "superdeterministic" essay you ask for inconsistencies:
    Here it is. In order to get such small distances, you have to assume what you want to show.
    That is not correct.

    Best regards
    Stefan

    ReplyDelete
    Replies
    1. Stefan,

      "In your "superdeterministic" essay you ask for inconsistencies:
      Here it is. In order to get such small distances, you have to assume what you want to show.
      That is not correct."


      First of all what you say is physical nonsense. Fourier transformation is a mathematical tool and also, you can well approximate what happens if you cut of the spectrum. More importantly though what you say is also logical rubbish because a circular argument is not inconsistent.

      Delete
    2. Stefan Freundt,

      There is such a thing as "finite Fourier transforms."

      They are very widely used in actual systems (you probably own such a system!), and they work very, very well.

      You do not need infinitesimal distances for Fourier transforms.

      Delete
  27. Thanks Sabine,

    As a former chemist, the name of QM has always seemed unfortunate, "Wave Mechanics" makes much more sense. If asked, I try to explain QM in terms of waves as in an organ pipe, where waves have to match up to produce a stationary pattern.

    In retrospect, it seems to me that a wave theory was almost inevitable, because it gives us the discrete properties of chemicals. Without such a theory, every atom (and therefore every molecule) would be different, just as every solar system presumably is different in detail.

    ReplyDelete
  28. Physicist Dave: First, as for Euler, I used his relationship, which means I take it to be correct. In response to what I wrote, you wrote: "who cares whether ψ is real or not??" Since I wrote that it was generally complex but due to Euler it did become real occasionally, I assumed you were saying you did not care, hence my "Interesting comment". Just to clarify in case anyone else is puzzled by this, yes, by using the Euler relationship, perforce I believe it. I had hoped that something which changes sharply every half quantum of action might suggest discreteness. I did not anticipate your response.

    You say my claim that action is quantized hence discrete in molecules is nonsense. You know this how? You should explain how you can have an eigenfunction, the phase of which is determined by action, and change the action without changing the number of nodes.

    You asked for an example where action was quantised, so I gave the example of aromatic rings because that is what I thought was the easiest to follow. Since you seem to know so much more about chemistry than me, I assumed you understood VB theory. Sorry for that. I also assumed you would read the Herndon reference before getting so . . . (You use whatever words you feel are appropriate). I got that wrong

    For the benefit of anyone else reading this, the argument goes that in such molecules there are eigenfunctions. An Eignfunction leads to one energy (such a wave can have only one frequency - which, as you may note, has introduced discreteness, the topic of the post) which means a specific velocity (from the kinetic energy, in turn specified from the virial theorem). That means in the VB approach, the electron density in a bond is determined by the weighting given to the canonical structures, and to a first order approximation, which is quite good, all Kekule structures have the same energy. Accordingly, we can assign the relative momentum density to each bond, which gives directly λ in the de Broglie equation.

    The problem for bonds in general is not that that equation does not hold. It is that you cannot assign the momentum, and I assume you know that. Maybe wrongly.

    ReplyDelete
    Replies
    1. Ian Miller,

      I hope I made clear that my objection was to your apparent claim that your idea applied to most molecular bonds. It does not.

      You wrote:
      >The problem for bonds in general is not that that equation does not hold. It is that you cannot assign the momentum, and I assume you know that

      Yes, I do know that, which is why I think it is simply nonsense in that case, which is the predominant case. An equation in which one variable is meaningless is not helpful. Or meaningful.

      Ian also wrote:
      >An Eignfunction leads to one energy (such a wave can have only one frequency - which, as you may note, has introduced discreteness, the topic of the post) which means a specific velocity (from the kinetic energy, in turn specified from the virial theorem). That means in the VB approach, the electron density in a bond is determined by the weighting given to the canonical structures, and to a first order approximation, which is quite good, all Kekule structures have the same energy. Accordingly, we can assign the relative momentum density to each bond, which gives directly λ in the de Broglie equation.

      That seems to me one humongous and illegitimate leap after another. I very much doubt that anything along that line can be made to work even for aromatic structures.

      But, I do agree that the resonance structure for aromatic molecules is very weird, so it is possible I am missing something.

      Part of the reason I am skeptical, of course, is that the simplest MO approach to aromatic molecules is to simply write down the obvious solutions for a particle in a ring: yes, of course, the wavefunction must be periodic, since it is a circle. Pretty obvious. Is anything gained by reinterpreting this as momentum that somehow controls the bond lengths?

      Well, as I said, I did some research on this long ago, and, no, I do not think anything is gained. The MOs must be periodic since they are on a circle. Nothing more.

      Seriously, tell me somewhere on the Web where I can see a copy of your paper for free, and I'll see if I am missing something.

      In any case, it seems we now agree that this does not carry over to molecules without rings, which was my initial point.

      As to Euler, I have noticed that for some strange reason, chemists often seem to give priority to real wavefunctions. For no good reason at all. When you mentioned that the wavefunction became real at certain points, that seemed to me another example -- it does not matter. At all.

      Ian also said:
      >I had hoped that something which changes sharply every half quantum of action might suggest discreteness. I did not anticipate your response.

      Yes, because that does not suggest discreteness!

      In every quantum system, the wavefunction necessarily changes sign if the action changes by π (in natural units of h-bar, of course). This does not suggest discreteness. It is true for discrete and non-discrete systems alike.

      I think we are coming to understand each other. The main issue is whether your observation about aromatic compounds amounts to anything more than the fact that wavefunctions on a circle must be periodic. Hard for me to say unless I can see your paper.

      Dave

      Delete
    2. OK, Ian: I've figured you out.

      From the summary of Ian's book on amazon:
      >t is well-known that the quantal wave function is complex. What is less well-appreciated is, from Euler, that it becomes real at the extremes of crest and trough. This alternative interpretation of quantum mechanics is based on two assumptions: the wave function only imparts physical effects when it is real as opposed to complex...
      ...
      >a simplified procedure for calculating the basic properties of the chemical bond follows and together with the concept that atomic orbitals do not correspond to the excited states of hydrogen, a hitherto unrecognized quantum effect is proposed for the chemical bond. If this is correct, most computational procedures in chemistry are wrongly based.
      ....
      > Finally, and more speculatively [emphasis added -- note it is even more speculative than the earlier nonsense!], it is shown that the binding of deuterium is consistent with the binding being of electromagnetic origin.

      Ooooookay.

      So, the reason I could not make any sense of what Ian has been saying in terms of chemistry is that Ian's "chemistry" has very little to do with the chemistry taught where I went to school -- Caltech and Stanford -- or for that matter at MIT, Harvard, Berkeley, or even the local high school.

      Our pal Ian has his own chemistry, and you can learn about it for a modest price from amazon.

      If for some strange reason you wanted to.

      But, you gotta love that idea that what holds the proton and neutron together in the deuteron is the electromagnetic force.

      You go, Ian!

      Delete
  29. Max Tegmark may write some odd stuff (to some), but if you take what he wrote here seriously, then "discrete? yes or no" shouldn't even be a question.

    "Not only do we lack evidence for the infinite but we don’t need the infinite to do physics. Our best computer simulations, accurately describing everything from the formation of galaxies to tomorrow’s weather to the masses of elementary particles, use only finite computer resources by treating everything as finite. So if we can do without infinity to figure out what happens next, surely nature can, too — in a way that’s more deep and elegant than the hacks we use for our computer simulations. Our challenge as physicists is to discover this elegant way and the infinity-free equations describing it—the true laws of physics."
    — Max Tegmark
    https://www.discovermagazine.com/the-sciences/infinity-is-a-beautiful-concept-and-its-ruining-physics

    ReplyDelete
    Replies
    1. One more reason not to take Max seriously!

      I'd like to see him teach classical physics or electromagnetism, much less QM or GR, without using calculus.

      I do here that once Max was a physicist...

      Delete
    2. "classical physics or electromagnetism, ... QM or GR, without using calculus"

      That has been done via computable analysis, automatic differentiation, differentiable programming, etc. There is still the insertia of our antiquated educational system standing in the way, of course.

      Delete
    3. Philip Thrift wrote to me:
      >[Dave] "classical physics or electromagnetism, ... QM or GR, without using calculus"

      >[Phil] That has been done via computable analysis, automatic differentiation, differentiable programming, etc. There is still the insertia [sic] of our antiquated educational system standing in the way, of course.

      I don't think so, Phil. I think someone has sold you the Brooklyn Bridge.

      Delete
    4. One can (re)present all of physics - everything we know from theory and experiments - using only the Python programming language (other languages may do), referring only to entities constructed in Python (Built-in Types).

      What could be missing (unless there are truly beyond-Turing phenomena that experiments have revealed in physics)?

      Delete
    5. Philip Thrift wrote to me:
      >What could be missing (unless there are truly beyond-Turing phenomena that experiments have revealed in physics)?

      π

      The ratio of the circumference to the diameter of a circle.

      Computing all of the digits of π.

      Never.

      Will.

      Fini..s...h.......

      Seriously, Phil, you are arguing for doing physics without calculus... ever.

      And you offer.... Python?

      Okay, so you are a comedian, but the real Python guys were much funnier.

      Anyone who doubts that Phil is pulling our leg should look up the Wikipedia article on "differentiable programming." Sounds kinda caclulusy, eh?

      It isn't.

      Delete
    6. In any case, what Max Tegmark wrote above is serious ( "to do physic [we] use only finite computer resources"). I have seen nothing yet to refute it.

      Delete
    7. Philip Thrift,

      You are a silly person who is making silly statements.

      You quoted crazy Max as saying:
      >In any case, what Max Tegmark wrote above is serious ( "to do physic [we] use only finite computer resources"). I have seen nothing yet to refute it.

      Obviously, we cannot use "infinite" computer resources!

      But we do not just use "computer resources." We also use mathematical analysis that makes use of the real numbers and calculus -- which involve operations that can only be approximated on computers. And figuring out how to do those approximations typically takes a great deal of effort.

      I have been giving you the benefit of the doubt assuming that you were just making some silly jokes. Apparently, I was too kind.

      You seem to be of that generation that thinks that nothing is real unless you have seen it on a computer.

      You are ignorant and pathetic.

      Delete
    8. One thing I know is, in the end, to follow this teaching of Jesus:

      "Do no cast your pearls [of wisdom] before swine."

      from Wikipedia: A quotation from Matthew 7:6 in Jesus's Sermon on the Mount: "Do not give what is holy to the dogs; nor cast your pearls before swine, lest they trample them under their feet, and turn and tear you in pieces."

      Delete
  30. It appears there are some confusions about what is real in QM. The identification of a wave function, ψ = Re^{iS/ħ} in polar form, is argued to be real for the phase angle S/ħ = 2πn. This is a mathematical idea of what is real. Wave functions are complex valued, and while they have contact on a real number line subspace of the argand plane ℂ this is somewhat separate from saying there is ontology to a wave as a result.

    The action is dependent on energy S = S_E and there may be some spread in energy ΔE so that we have the action S_{E+ΔE}(p, q)

    S_{E+ΔE} = Et + ∫dq√[(2m)(E - U(q)]

    with the integral over a spread in the spatial coordinate q. This integral is effectively ∫pdq contribution to the action from the kinetic energy of a particle. This deviation in the action due to the spread in energy is in the limit ΔE → 0 gives

    lim_{ΔE→0}(S_{E+ΔE} - S_E)/ΔE = ∂S/∂E.

    Now this should be a fascinating equation to anyone who thinks deeply. The value of the right hand side is ∂S/∂E = δt, which is the uncertainty spread in time. If we recall the Hamilton-Jacobi equation -∂_tS = H, this describes a plane of constant action moving in space. What ∂S/∂E = δt tells us is that due to quantum mechanics this plane is spread out some according to time. The condition for classical mechanics is that this spread in time is zero and ∂S/∂E = 0.

    An interesting parallel can be drawn with statistical mechanics and thermodynamics. The correspondence between the Boltzmann factor and the polar wave phase e^{-E/kT} ↔ e^{iS/ħ} implies a Euclidean time τ = iδt = ħ/kT, where the classical condition occurs for τ → 0 and with T → ∞. Similarly, a quantum critical point occurs for T → 0 or τ → ∞. The equation ∂S/∂E = ħ/kT a correspondence between entropy and action, and the reciprocal relationship between the Euclidean time, or the quantum spread in time, and temperature is a form of UV/IR dualism. The high temperature condition, where quantum states are highly perturbed by quantum noise and decoherence, are the classical states. Zurek labels these as einselected states that are stable under quantum decoherence. The IR condition with τ → ∞ or zero temperature is a form of quantum critical point or quantum phase transition. This is a process whereby degrees of freedom of a system or combined or transformed in a way that conserves quantum information. The zero temperature condition is then in a funny way dual to the high temperature condition, such as how the Hagedorn temperature in QCD or string theory is a sort of reciprocal of the transition to a zero temperature condition seen with superconductivity or other Ginsburg-Landau phase transitions.

    Onto the topic of Cramer’s transactional interpretation. I have seen this in a way as a solution to a problem that may not needed to have been solved. The complexification of a wave ψ* gives a Schrödinger equation with time reversed. Then with t → -t we recover the standard wave equation. This was noted by Wigner as how the Schrödinger was time reverse invariant. The Cramer idea is then the time reversed complex waves and the complex waves meet in a way similar to the Feynman-Wheeler advanced and retarded potentials merge. In some sense this is just a way of saying ρ = |ψ⟩⟨ψ|. Then by a certain level of something unknown the density matrix reduces to a trace ρ → Tr(ρ) = sum_ip_i, which is a form of collapse. The transactional interpretation then in effect transforms the unknown physics of wave collapse into another form that is equally unknown. Come to think of it, all quantum interpretations do something similar to this.

    ReplyDelete
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    1. Dr. Crowell as always I find you response to the issues brought forth in Dr. Sabine's presentation fascinating and often showing an understanding of physics far beyond my comprehension. However there is one point brought to my attention by the previous posters mention of Max Tegmark.
      The essential point of his work is that physical reality is in essentially mathematics. Your analysis, for me makes, point that physical reality, as described mathematically, is variously understood but with out definitive basis.
      There are two points which are troubling to me.
      1] The tendency to describe measurements in space while neglecting space as an active participant. The Kazimir effect
      demonstrates that to me.
      2) Although, I have spent many days in my life learning and using mathematics, Mathematics and number remain tools of understanding for the human mind. Number is a relationship
      by the mind. As Dr. Sabine's book points out. it is highly possible for trained minds to create mathematical relationships that fail to reflect physical reality.

      Delete
    2. Lawrence Crowell wrote:
      >Onto the topic of Cramer’s transactional interpretation. I have seen this in a way as a solution to a problem that may not needed to have been solved.
      ...
      >The transactional interpretation then in effect transforms the unknown physics of wave collapse into another form that is equally unknown. Come to think of it, all quantum interpretations do something similar to this.

      Yeah, I basically agree. I hope it is clear that I am not accusing John Cramer of dishonesty. I think he took some interesting intuitions that a lot of us have had, thought that a full theory was just around the corner, and then announced that he had a theory when, in fact, he has never really managed to work it out. Pretty much the same shape the rest of us are in... except we never publicly announced we had a solution! And I think he still honestly thinks he almost has it right, when he really still does not.

      I would say, though, that there is one well-known "interpretation," Bohmian mechanics, at least for non-relativistic QM, that is clear, unequivocal, and well-defined.

      Alas, the way Bohmisn mechanics interfaces with relativity is really freaky, and therefore I, and most physicists, do not believe it is true. But it is a real virtue of Bohmian mechanics that it is clear enough that we can easily spell out why we reject it. Better to be clear and wrong than to be so mushy as to be "not even wrong"!

      On time-energy, there is an obvious sense in which there is most assuredly a time-energy uncertainty principle. When I learned high-energy particle physics, it was just taken as a given that the lifetime of an unstable particle was inversely related to the energy width of the resonance. I was taking QM from Feynman when the ψ/J resonance was discovered in the "November revolution" in 1974. Feynman of course explained that the narrow width meant a surprisingly long lifetime.

      Of course a similar point can be made with more mundane examples such as the intrinsic width of atomic spectral lines.

      There are technical issues here -- "time is not an operator" -- that people still love to debate. But at the level of actual physics, the time-energy uncertainty principle is just true and used all the time.

      All the best,

      Dave

      Delete
    3. @PhysicistDave
      "Alas, the way Bohmisn mechanics interfaces with relativity is really freaky, and therefore I, and most physicists, do not believe it is true"
      Precisely these weakness of Bohmians mechanics is a strengtness if between the experimentally equivalents interpretation of Lorentz transformation, the ugly one - those of Lorentz and Poincaré - is the only one which is logically consistant. But i have no space here to show it. As Sabine write sometimes in his book, coherence must prevail upon beauty.

      Delete
    4. I thought I had responded to this thread. Anyway, I will make this brief.

      @Lockley: Getting spacetime to play an active role with QM is what quantum gravitation is all about. At this time, we really do not have a complete theory on that. With the dynamics of the vacuum state and the Casimir effect, it is the case that in general the vacuum is tied to general relativity. The cosmological constant in Einstein’s field equations is a way of bringing the vacuum into GR. At this time we really have a very incomplete understanding with the quantum description of this.

      @Jean-Paul: It is not so much that Bohm’s QM interpretation, or related by de Broglie and Vigier, are wrong. In a purely nonrelativistic setting, it is alright if one wants to entertain the idea of a particle surfing a pilot wave. In fact, it is an interesting way to consider quantum chaos. The difficulties with it are though considerable, though all quantum interpretations have holes or problems. My advice is not to lean to heavily on any quantum interpretation.

      Delete
  31. Physicist Dave: First, the paper I referred to. I gave a reference. As far as I am aware, that is the only way of getting to it. I should also add that what I have been referring is only minor part of it. That was merely a step to show how to us VB theory to get to a result that MO theory cannot reach, at least in a transparent way.

    You say what I wrote is on humungous leap after another. You are entitled to your opinion, but it is consistent with the general VB approach, and more to the point when applied to every condensed aromatic system for which I could get data, it gave very good agreement with observation. In my opinion the ability to agree with observation has a certain quality to it. Further, you are not following what I am saying when you assert it is wrong. I did not say momentum determines bond length; I stated it was quantized action, which determines the specific phases in the wave function.

    I did not say the wave function was real. What I said was stated alternatively by Lawrence Crowell. As he said, "this is somewhat separate from saying there is ontology to a wave as a result". I agree, but equally it does not say there is not. Ascribing significance to it is a separate premise. My argument is that if you do so ascribe significance it can simplify many procedures and still retain agreement with observation. You argue it makes no difference. That too is a premise, namely that mathematical difference has no physical meaning. At this stage I do not believe we can tell. Asserting it does makes certain calculations a lot simpler, but unless it predicts something different from the alternative, it remains effectively opinion whether it is significant.

    ReplyDelete
    Replies
    1. Ian Miller wrote to me:
      >I did not say the wave function was real. What I said was stated alternatively by Lawrence Crowell. As he said, "this is somewhat separate from saying there is ontology to a wave as a result".

      We're using two different meanings of the word "real." I was using it in the mathematical sense of referring to real numbers vs. complex numbers, not in the ontological sense of real existence vs non-existence.

      As a physicist, I am not of course objecting to your using the wavefunction! I simply think you are making horribly bizarre mathematical errors.

      Take your statement above:
      >As an example, chemical bond energies can be strained to take a continuous range of energies, but their length tends to change according to pλ = h. Here, both sides of the equation refer to action,and h is the quantum of action, from which you can argue for discreteness.

      The equation pλ = h only applies to a state that is a momentum eigenstate, which atomic orbitals and molecular orbitals most assuredly are not. That equation is meaningless when you try to apply it to atomic or molecular orbitals.

      You sort of half-admitted this fact when you said:
      >The problem for bonds in general is not that that equation does not hold. It is that you cannot assign the momentum...

      You are right that you "cannot assign the momentum" for an atomic or molecular orbital. But given that fact, your accompanying statement is nonsense: pλ = h does not hold for orbitals because, as you admit, it is meaningless for orbitals.

      You are spreading pseudo-science because you do not understand very elementary facts about quantum mechanics.

      Ian also wrote:
      > In my opinion the ability to agree with observation has a certain quality to it.

      Yes, a certain pseudo-scientific quality to it.

      Look: massage the numbers enough and you can always find some numerological pattern: indeed, there are mathematical techniques (e.g., Lagrange interpolation) showing that polynomials alone will suffice.

      A similar point holds about your claim "from which you can argue for discreteness." Discreteness of what???

      Gibberish.

      It is not the case that there is somehow one unit of action (is it h or h-bar?) in a molecular bond: that is not how quantum mechanics works at all. If you think it does, you have zero understanding of quantum mechanics.

      What you have said so far, in all honesty, indicates that this is the case. Your statements are weird beyond words.

      Note: I realize you really believe this stuff. But, if so, you somehow failed to learn any quantum mechanics at all.

      You also wrote:
      > First, the paper I referred to. I gave a reference. As far as I am aware, that is the only way of getting to it.

      Well, you are listed on the ResearchGate site as offering to give that paper to people who ask for it. Is that true? I used to have a ResearchGate login: will you send me the paper via ResearchGate if I ask?

      Or is that fake too?

      Delete
  32. Discreteness, Planck constant, QM, John von Neumann, Einstein, Quantum Theory and Mathematical Rigor

    The »QM-idea« of discreteness is strongly related to the Planck constant.
    BUT: The phenomenological meaning of Planck's constant has not really been clarified. The fact is that the indivisibility of Planck's constant has never been justified for over a hundred years to the present day. Max Planck did not justify it because he considered the Planck constant to be an elementary mathematical quantity, the "necessity" of which followed from theory. Einstein did not consider a reason necessary because he believed in Planck's deduction. He shifted the meaning of Planck constant by interpreting the mathematical quantity as a physical quantity.

    [1] Ernst Mach already remarked: "Those who do mathematics can sometimes get the uncomfortable feeling that ones science, even ones pen, surpasses ones in wisdom, an impression that also the great Euler confessed, “could not always be avoided.“ [1]

    Schon Ernst Mach bemerkte: "Wer Mathematik treibt, den kann zuweilen das unbehagliche Gefühl überkommen, als ob seine Wissenschaft, ja sein Schreibstift, ihn selbst an Klugheit überträfe, ein Eindruck, dessen selbst der große Euler nach seinem Geständnisse sich nicht immer erwehren konnte." [1] Vortrag, Sitzung der kaiserlichen Akademie der Wissenschaften zu Wien am 25. Mai 1882

    Hans van Leunen - Eindhoven University of Technology - stated
    „Scholars of the early twentieth century did not recognize that the wavefunction stands for the activity of a type of stochastic process. That process generates a discrete distribution and not a continuous function. Measurements show that this process is a combination of a Poisson process and a binomial process. The binomial process implements the spatial spread of the wavefunction. This knowledge is applied in the Optical Transfer Function (OTF) and in the Detective Quantum Efficiency (DQE) characterization of the imaging quality of image intensifier devices. The process produces a coherent hop landing location swarm. A location density distribution describes that swarm and equals the square of the modulus of the wave function. It acts as a detection probability distributions. This last thing was already known by Hilbert and von Neumann.”

    It could be also helpful to remember what Albert Einstein wrote on quantum mechanics: [2] "The ψ function is to be understood as a description not of a single system but of a system community [Systemgemeinschaft]. Expressed in raw terms: In the statistical interpretation, there is no complete description of the individual system. Cautiously one can say this: The attempt to understand the quantum theoretical description of the individual systems leads to unnatural theoretical interpretations, which immediately become unnecessary if one accepts the view that the description refers to the system as a whole and not to the individual system. The whole approach to avoid 'physical-reality' becomes superfluous. [Albert Einstein's Original-Zitat: „Es wird dann der ganze Eiertanz zur Vermeidung des ‘Physikalisch-Realen’ überflüssig.“] However, there is a simple physiological reason why this obvious interpretation is avoided. If statistical quantum theory does not pretend to describe completely the individual system (and its temporal sequence), then it seems inevitable to look elsewhere for a complete description of the individual system. It would be clear from the start that the elements of such a description within the conceptual scheme of the statistical quantum theory would not be included. With this, one would admit that in principle this scheme can not serve as the basis of theoretical physics.” [2] A. Einstein, »Out of my later years« Phil Lib. New York 1950 page 498

    Further readings: FWIW: One should “deal with” »Quantum Theory and Mathematical Rigor« https://plato.stanford.edu/entries/qt-nvd/ and “try” to understand the mathematical foundation of QM, QFT...

    ReplyDelete
  33. This dichotomy between discrete and continuous is the core mystery in contemporary physics. It borders on magic, even though the formal equations of QM are not in contradiction to physical reality due to the no signaling theorem that Physicist Dave pointed out. I actually had an idea that might resolve this dichotomy, though it’s probably in the realm of crackpottery. In any case, this crackpot idea does possess a mechanism to account for the Cooper-pair mass anomaly first discovered by Tate, et. Al. in 1990. Several hypotheses have been advanced to account for this mass anomaly that link it to Dark Energy, which I mentioned in the comment section of the “Are dark energy and dark matter scientific?” thread. Just maybe, the theories advanced by those physicists could help unlock the discrete/continuous puzzle that nature confronts us with.

    ReplyDelete
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    1. David Schraeder wrote:
      >This dichotomy between discrete and continuous is the core mystery in contemporary physics. It borders on magic, even though the formal equations of QM are not in contradiction to physical reality due to the no signaling theorem that Physicist Dave pointed out. I actually had an idea that might resolve this dichotomy, though it’s probably in the realm of crackpottery.

      Dave, if you are referring to the "no-signalling theorem" as crackpottery, this is just a standard result of quantum field theory accepted by nearly all physicists.

      You wrote:
      >This dichotomy between discrete and continuous is the core mystery in contemporary physics.

      No: this is no mystery at all: this is the one thing in quantum mechanics that is very well understood by all competent physicists and has been since the beginning of QM. It is no more mysterious than the fact that a stretched string or drumhead has a discrete set of resonance frequencies.

      Dave

      Delete
    2. PhysicistDave:

      I’m afraid I worded my comment badly. The “crackpottery” was in reference to my own idea, not the no-signalling theorem. In the double slit experiment where a photon behaves like a (continuous) wave between the source and slits, interfering with itself beyond the slits, and then collapses to a single (discrete) point at the detection screen, where it is absorbed by an individual atom, is the “mystery” I was referring to. The books I’ve read over the years have always cast this as the “central” mystery of QM. For example, on page 65 of Phillip Ball’s “Beyond Weird”, he states, in reference to the double slit experiment, “It is arguably the central experiment in Quantum Mechanics. And no one truly understands it.”

      So it seems to me that the ‘machinery’ behind this process is still beyond the purview of human comprehension. I perfectly see what you are saying with the classical analogy of a vibrating drum. But to me that brings us to the nub of the problem – what exactly is oscillating, or vibrating, in the quantum realm that makes an electron behave like a wave? A wildly speculative answer to this question was the subject of my “crackpot” idea. In respect of the rules I won’t give any details, but I’ve thought of sending the latest iteration of the idea to a professional physicist, like yourself, for evaluation. I’m in the process of rewriting it, so I’ve got some more work to do. I was originally going to contact you on your personal website, so as not to clog up Sabine's blog on peripheral things. But, hopefully, it's OK to mention it at this juncture where wave/particle duality, more or less, is the subject of conversation.

      Delete
  34. "The energy of a photon traveling through empty space, for example, can have any value according to quantum mechanics. The energy is not discrete."
    So let me get this through my thick skull. Heisenberg says that the less we know about time, the more precisely we can know the energy, in theory at least. But this can only be measured practically to a finite level of precision. So doesn't this leave the possibility that the energy could physically take (very finely) discrete values, or rational values, or real values or values in a set of size a large cardinal? And we might never be able to know which. In fact, didn't the post on Planck's length say that time and length measurements (and presumably other observable measurements) become physically meaningless below a certain threshold, which would presumably put a limit on precision of measurements.

    So then is the point that quantizing may not necessarily mean discreteness, but it certainly doesn't mean the kind of whopping great quantum jumps between electron shells inside an atom? It may be a very fine discreteness or it may descend into meaninglessness but we can never measure it in practice to find out?

    ReplyDelete
    Replies
    1. Steven Evans asked:
      >So doesn't this leave the possibility that the energy could physically take (very finely) discrete values, or rational values, or real values or values in a set of size a large cardinal?

      That would violate Special Relativity.

      Normally, when we physicists say "Such and such cannot happen" we mean within currently known laws of physics.

      Steve also asked:
      >So then is the point that quantizing may not necessarily mean discreteness, but it certainly doesn't mean the kind of whopping great quantum jumps between electron shells inside an atom?

      No, you misunderstood Sabine. The discrete energy levels ("quantum jumps") in an atom are real. Sometimes energy levels are discrete, as in an atom, sometimes not. The point is that QM does not invariably require discreteness.

      QM is a theory that predicts lots of different things in lots of different situations. Discreteness is not always a result of QM.

      Dave

      Delete
    2. Dave, thanks for the reply.
      Yes , I thought about it a bit more and understood. The post is simply saying that QM/QFT doesn't require discreteness in general, a confusion many lay people make, and it's the best theory physics has for the small scale.
      I don't immediately see why SR would rule out discrete energies, but as it's off topic maybe that's a conversation for Conversful!

      Delete
  35. Physicist Dave: So you have figured out the bit on deuterium, you declare it nonsense, but you have no idea how it got there. For the benefit of anyone else, a very quick summary: it assumes what I have outlined above. Quantised action, coupled with the wave requirements when applied to hydrogen molecule give the bond distance of H2+ essentially the same as observed, and H2 within 0.8% of observed, solely on electric field coupling. Minor effects get it closer to observed. The energy is calculated to within approximately 1 kJ/mol. Doesn't prove anything, though. Could be an accidental coincidence. (The details of the comment about atomic orbitals that you mention relates to details outlined in Aust. J. Phys. 40 : 329 -346 (1987) where orbital energies are shown to be related to functions of the action and nodal properties. Again, agreement could be accidental, but there are over a hundred accidents.)
    Anyway, back to deuterium. The interesting thing about this wave approach is that through the discrete nature of action (assuming it is) the energy of a state depends only on the geometry and the coupling applied to the antinode (i.e the wavelength). From the reason that electrons pair, and hence a reason for the Exclusion Principle (and Dave, before you get insulting about this, since you know so much about chemistry, propose a version of the Exclusion Principle that permits the SN2 reaction. Mine does, but of course you will say it is ridiculous and you can do better. I await your effort.) then d quarks, if they are separate entities, will have wave functions that should interfere in the same way, if the argument is correct. What I thought was, if I assumed geometric and physical similarity between the atomic and deuterium situation, I would have a geometry, and I could test out by comparing the coupling with that of the strong force, and if they were way off, I was wrong. The problem with that was that to get just over 2 MeV, the coupling was q/εo. Oops! Hence the speculation. Of course I am not asserting that is right, BUT the interesting thing is it automatically makes a prediction of the geometry of deuterium. If it is wrong, so is that reasoning. The model is immediately falsifiable, which is at least a partial standard for models.
    If you want an easier prediction of mine that contradicts what is believed of standard quantum mechanics, the delayed choice quantum eraser result would falsify my approach. Fortunately, there is a variation of the experiment that if I am correct and the waves are always deterministic, should get the opposite result. So Dave, since you are so superior, what is it?

    ReplyDelete
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    1. Ian Miller wrote to me:
      >If you want an easier prediction of mine that contradicts what is believed of standard quantum mechanics, the delayed choice quantum eraser result would falsify my approach.

      No, Ian, I am not interested in your ideas or opinions, for the simple reason that you have proven to be dishonest, extremely dishonest.

      I spent some time and effort trying to figure out what on earth you meant by what seemed to be nonsense, on the assumption that perhaps you were sincere.

      You're not.

      Your earlier posts kept claiming that such and such could be seen to be true on the basis of quantum mechanics.

      So I assumed you actually meant quantum mechanics, the theory worked out by Schrödinger, Heisenberg, Dirac, et al. and taught at most of the world's universities.

      Except none of what you said made any sense: it was all wrong.

      Until I found your book, by accident, on amazon. You were not really trying to use quantum mechanics: you have invented a truly bizarre, new crack-pot theory, let us call it "Ian Mechanics," and you yourself brag in your amazon blurb about the fact that Ian Mechanics gives answers that rather wildly contradict quantum mechanics.

      Ian Mechanics is nonsense mathematically, but, hey, you are entitled to freedom of speech and all that.

      What you are not morally entitled to is deceiving people.

      You could have here simply said upfront that you reject the quantum mechanics worked out by Schrödinger, Heisenberg, Dirac, et al. and that instead you were appealing to a new crack-pot theory, Ian Mechanics, that you yourself had worked out.

      But you didn't.

      You wasted my time and the time of anyone else who tried to make sense of your comments because you did not have the decency to tell us about the little game you were playing.

      You are engaged in a con game, Ian, and I find that contemptible. We only know that you are doing this on purpose because I stumbled on your amazon blurb where you gave away the game.

      I have hated and despised pathological liars and con artists since I was a very young child in grade school six decades ago.

      I see no reason why I should make an exception in your case.

      Delete
  36. PhysicistDave - The ad hominem approach shows something. As an aside I have never hidden that I seek an alternative approach. If you look at Pople's Nobel lecture you will s he set his constants of integration by validating from 250 similar examples. I saw one report that showed that an example of Density Functional Theory had, from memory, about 50 arbitrary constants to assign. The advantage of approaching stationary states from action and waves is you do not need partial differential equations that you cannot solve and taking action as quantised, it must have a precise value. So yes, I have another approach, and I have never tried to conceal it. As far as I know, there is nothing that contradicts quantum physics, and if someone pointed out something that did, or some discrepancy with observation, I would immediately concede. However, Dave's spleen does not qualify as logical falsification.

    You are not interested in anything but further venting so the best I can do now would seem to be to withdraw, and at least save Sabine the trouble of reading this exchange.

    ReplyDelete
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    1. Ian Miller wrote to me:
      > As far as I know, there is nothing that contradicts quantum physics...

      You are being grotesquely, unbelievably dishonest.

      I am not "venting": I am telling the truth about you based on your own book.

      The blurb from your book on amazon has one statement after another that contradicts quantum mechanics. The blurb brags about it.

      There are statements in your blurb that have nothing to do with quantum mechanics such as:
      > the wave function only imparts physical effects when it is real as opposed to complex...

      You even manage to mess up high-school algebra when you claim:
      >What is less well-appreciated is, from Euler, that it becomes real at the extremes of crest and trough.

      Yeah, it certainly is "less well-appreciated" because it is utter and complete nonsense. The wavefucntion in quantum mechanics is only defined up to a constant overall phase: multiply the whole wavefucntion by exp(iφ) for constant real φ, and it counts as the same wavefunction.

      But, then the place where the wavefunction is real will be a different place!

      And, similarly, the idea that we know "from Euler" that the wavefunction "becomes real at the extremes of crest and trough" is utter silliness.

      Take a momentum eigenfucntion, exp(ikx). Where are its peaks and troughs? Why isn't x=π/(2k) giving a value of i, just as much a peak or trough as x=0? And, when you take into account that you can multiply the whole wavefunction by a constant arbitrary phase, it just all becomes pure idiocy.

      And I think you know it, Ian.

      I think you know it is all just a con game.

      Why are you doing this?

      How long did you think you could fool people?

      Is it all just to make a few bucks off the books?

      Delete
  37. 29-APR-2020

    PhysicistDave -

    Oh yeah; the natural units.
    I'm always overlooking that.

    I appreciate the clarification.

    cheers
    mj horn

    ReplyDelete
  38. The ''quantum'' is E=h*f.
    It means:
    Quantum energy has dualistic ability : h-particle, f-wave
    ====

    ReplyDelete
    Replies
    1. This makes zero sense because the equation itself already tells you that if you have one, you also have the other.

      Delete
    2. Correct, ''if you have one (quantum particle), you also have
      the other (waves). For example: if you have ''string particle''
      you have all kinds of waves, depends on string frequancies.
      String theory solved the puzzle of ''wave-particle dualism''
      ===

      Delete
  39. Hi Sabine, et al.

    Thanks for this video. Kind of late to the comments but...
    I had been wondering why they make such a big deal of the "quantum". I just lately came to realize the "quantum of action" is continuously variable because h = momentum * wavelength (actually hit me while reading Ian Millers "The Covalent Bond from Guidance Waves" which does not relate a lot but just the way he stated the equations). This would just mean that any given wavelength of which there are infinite number would have a given momentum proportional to h. It is just inside an atom where the orbitals "force" the electron to absorb/emit a photon of a "specific" wavelength. (am I making any sense?)

    But what really hit me was your diagram (at 1:35) of an atom emitting a photon! The photon is emitted when the electron jumps from a lower orbital (higher energy) to a higher orbit (lower energy)! Was that really intentional? Do all you physicist people just know this and us commoners are kept in the dark? Everywhere else it is shown the opposite which was not making any sense to me. But as in the h proportionality the shorter wavelength has more energy and the longer wavelength (higher orbitals) have lower energy (I think that goes along with the atomic diameter charts I see). I wish it was shown this way more.

    How does that really relate to the energy level diagrams with n1 being 13.6eV and the higher ones shown with lower energy?
    That seems to make sense but why would the Ground State be -13.6eV?
    Because it takes that much energy to remove the electron from the atom (answering my own questions), but why show it that way, just for looks?
    And why do the Schrodinger orbitals have the electron anywhere in there but it releases a photon with a very narrow bandwidth?
    Something is still confusing me about that and I will keep pondering it!
    So many questions, so little time.

    Pete


    ReplyDelete
    Replies
    1. Pete,

      When Ian is in a good mood, he admits that his books have pretty much nothing to do with quantum mechanics as worked out by Schrödinger et al. back in the 1920s and as taught today at most of the world's universities.

      I call his stuff "Ian mechanics," and it is in fact wildly, hilariously wrong.

      If you want to learn something, study palm-reading before you study anything Ian wrote.

      It will prove more useful.

      Delete
    2. Hi PhysicistDave, too bad you do not have anything useful to add to the questions. Ian must rub you guys the wrong way.

      Delete
    3. Peter Becher wrote to me:
      >Hi PhysicistDave, too bad you do not have anything useful to add to the questions. Ian must rub you guys the wrong way.

      Pete, I gave extremely detailed explanations above of what is wrong with our pal Ian.

      Read them.

      How much of my time do you expect me to waste on this jerk??

      Look: if you understood high-school algebra, you should be able to grasp my explanations of why Ian's nonsense is just a con game. If you cannot understand math at that level, go back to high school.

      I do not have infinite time, energy, or patience to deal with guys like you or Ian. I, and some of the other people around here, have spent a great deal of effort to learn advanced math, physics, engineering, etc.

      We are willing to share that with others if the others are polite.

      But if you insist on being an obnoxious ignoramus...well, if your were paying me, I might decide to put up with it.

      Maybe.

      But you're not.

      I replied to you with a friendly warning that Ian is a con artist. I have given details above documenting that fact.

      You do not like that? You are not my problem.

      Delete
    4. Wow PhysicistDave, You are brutal.
      I did not ask anyone to comment on Ian Miller. I just mentioned that I got an incite while reading him. I am just reading various things looking for basic concepts. Seems like QM/QFT/QG could use a little more of that.
      Pete

      Delete
    5. Peter Becher wrote to me:
      > You are brutal.

      Yes, I am most certainly brutal to jerks, liars, and con artists.

      Pete also wrote:
      >I did not ask anyone to comment on Ian Miller.

      You mentioned him in a context that appeared to indicate that you did not know Ian's stuff was utter garbage. I did you the courtesy of enlightening you. You owe me a "thank you."

      Pete also wrote:
      >I am just reading various things looking for basic concepts.

      You will not get it from Ian: he is conning people.

      Pete also wrote:
      >Seems like QM/QFT/QG could use a little more of that.

      We need more liars, frauds, and con artists?

      Delete
    6. Hi PhysicistDave
      Thank you for your opinion of Ian, for what it was worth, 2c.
      You had kept asking for Ian's paper so you could give some feedback on it. I did try to post links to free downloads but Sabine must have not thought it worthy.
      I do think that Ian's chemistry ideas have little to do with QM and he should have named it Bond Wave or something. But I do think that his idea about the wave becoming real will become an insightful idea recognized at some point in the future.
      Pete

      Delete
    7. Peter,

      I do not approve links to websites whose quality management I do not know. You posted links to some preprint server I am unfamiliar with. If you could please stick with journal references. I am sure that Dave will be able to find a pdf should he desire to look at it, thank you.

      Delete
  40. Peter, h IS the quantum of action, and equals 6.626 x 10^-34 J.s. That is constant, and not a "continuously variable". Momentum and wave length are continuously vsriable, but their product is not.

    ReplyDelete
    Replies
    1. That's wrong. Please stop submitting ill-informed comments.

      Delete
    2. Real helpful comment Sabine, ha. Then tell us why it is wrong and what is right! How can it be so wrong if wavelengths are continuous as you say in the video and momentum = h / wavelength?

      Delete
    3. I neither have the time nor the patience to give private lectures to any random dude who comes by my blog with their confusions about quantum mechanics. Sign up for a class. Read a book, or maybe better two. Watch some videos on YouTube and try to actually listen.

      Delete
  41. Hi Sabine
    I cannot imagine why you make such a big deal "That's wrong" about the de Broglie relation and Planck's constant. Seems like a simple answer to set the record strait to your satisfaction. Probably take no longer than your previous answer.
    Pete

    ReplyDelete

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