Have you heard that particle physicists want a larger collider because there is supposedly something funny about the Higgs boson? They call it the “Hierarchy Problem,” that there are 15 orders of magnitude between the Planck mass, which determines the strength of gravity, and the mass of the Higgs boson.
What is problematic about this, you ask? Nothing. Why do particle physicists think it’s problematic? Because they have been told as students it’s problematic. So now they want $20 billion to solve a problem that doesn’t exist.
Let us then look at an actual problem, that is that we don’t know how a measurement happens in quantum mechanics. The discussion of this problem today happens largely among philosophers; physicists pay pretty much no attention to it. Why not, you ask? Because they have been told as students that the problem doesn’t exist.
But there is a light at the end of the tunnel and the light is… you. Yes, you. Because I know that you are just the right person to both understand and solve the measurement problem. So let’s get you started.
Quantum mechanics is today mostly taught in what is known as the Copenhagen Interpretation and it works as follows. Particles are described by a mathematical object called the “wave-function,” usually denoted Ψ (“Psi”). The wave-function is sometimes sharply peaked and looks much like a particle, sometimes it’s spread out and looks more like a wave. Ψ is basically the embodiment of particle-wave duality.
The wave-function moves according to the Schrödinger equation. This equation is compatible with Einstein’s Special Relativity and it can be run both forward and backward in time. If I give you complete information about a system at any one time – ie, if I tell you the “state” of the system – you can use the Schrödinger equation to calculate the state at all earlier and all later times. This makes the Schrödinger equation what we call a “deterministic” equation.
But the Schrödinger equation alone does not predict what we observe. If you use only the Schrödinger equation to calculate what happens when a particle interacts with a detector, you find that the two undergo a process called “decoherence.” Decoherence wipes out quantum-typical behavior, like dead-and-alive cats and such. What you have left then is a probability distribution for a measurement outcome (what is known as a “mixed state”). You have, say, a 50% chance that the particle hits the left side of the screen. And this, importantly, is not a prediction for a collection of particles or repeated measurements. We are talking about one measurement on one particle.
The moment you measure the particle, however, you know with 100% probability what you have got; in our example you now know which side of the screen the particle is. This sudden jump of the probability is often referred to as the “collapse” of the wave-function and the Schrödinger equation does not predict it. The Copenhagen Interpretation, therefore, requires an additional assumption called the “Measurement Postulate.” The Measurement Postulate tells you that the probability of whatever you have measured must be updated to 100%.
Now, the collapse together with the Schrödinger equation describes what we observe. But the detector is of course also made of particles and therefore itself obeys the Schrödinger equation. So if quantum mechanics is fundamental, we should be able to calculate what happens during measurement using the Schrödinger equation alone. We should not need a second postulate.
The measurement problem, then, is that the collapse of the wave-function is incompatible with the Schrödinger equation. It isn’t merely that we do not know how to derive it from the Schrödinger equation, it’s that it actually contradicts the Schrödinger equation. The easiest way to see this is to note that the Schrödinger equation is linear while the measurement process is non-linear. This strongly suggests that the measurement is an effective description of some underlying non-linear process, something we haven’t yet figured out.
There is another problem. As an instantaneous process, wave-function collapse doesn’t fit together with the speed of light limit in Special Relativity. This is the “spooky action” that irked Einstein so much about quantum mechanics.
This incompatibility with Special Relativity, however, has (by assumption) no observable consequences, so you can try and convince yourself it’s philosophically permissible (and good luck with that). But the problem comes back to haunt you when you ask what happens with the mass (and energy) of a particle when its wave-function collapses. You’ll notice then that the instantaneous jump screws up General Relativity. (And for this quantum gravitational effects shouldn’t play a role, so mumbling “string theory” doesn’t help.) This issue is still unobservable in practice, all right, but now it’s observable in principle.
One way to deal with the measurement problem is to argue that the wave-function does not describe a real object, but only encodes knowledge, and that probabilities should not be interpreted as frequencies of occurrence, but instead as statements of our confidence. This is what’s known as a “Psi-epistemic” interpretation of quantum mechanics, as opposed to the “Psi-ontic” ones in which the wave-function is a real thing.
The trouble with Psi-epistemic interpretations is that the moment you refer to something like “knowledge” you have to tell me what you mean by “knowledge”, who or what has this “knowledge,” and how they obtain “knowledge.” Personally, I would also really like to know what this knowledge is supposedly about, but if you insist I’ll keep my mouth shut. Even so, for all we presently know, “knowledge” is not fundamental, but emergent. Referring to knowledge in the postulates of your theory, therefore, is incompatible with reductionism. This means if you like Psi-epistemic interpretations, you will have to tell me just why and when reductionism breaks down or, alternatively, tell me how to derive Psi from a more fundamental law.
None of the existing interpretations and modifications of quantum mechanics really solve the problem, which I can go through in detail some other time. For now let me just say that either way you turn the pieces, they won’t fit together.
So, forget about particle colliders; grab a pen and get started.
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Try this. The quantum formalism developed over many years as a result of our experience of the physics. Just imagine for a moment that it provides a very handy set of equations which summarise this experience in the form of coded information. In this case, 'knowledge' is nothing more than simply 'what we know' about the physics. We know from experience that if we do this, then we get that 50% of the time and we get the other 50% of the time, but we can't tell which of these we'll get next. We encode this experience (or knowledge) as a quantum superposition, and we use the formalism to predict projection probabilities for the two possible outcomes.
ReplyDeleteBecause this is about encoded experience or information, there is no collapse, no spooky action at a distance, and no measurement problem. But, of course, you can't expect this kind of anti-realist interpretation to tell you why nature is set up this way or how any of this actually works. This is very unsatisfying, but there was never any guarantee that we could reduce nature ad infinitum. The philosophers have been warning us for centuries that we are a part of the reality we're studying, and can't expect to discover anything about a reality in the absence of observation or measurement. This doesn't mean 'reality' ceases to exist when we're not looking at it, but it does mean we might have to temper our expectations about what we can know of it.
I don't advocate anti-realism, but I have come to have a very bad feeling about this, especially when the realist alternatives are de Broglie-Bohm (definitely spooky), a conflation with that other great unknown, consciousness, or many worlds ...
She talked about psi-epistemic interpretations!
DeleteI will give a deeper complaint.
If you believe that wavefunctions are about humans' information, then how can you ever assert that a H atom has a certain ground state wavefunction?
This is just the old Bayesian v.s. Frequentist debates to nowhere. The Frequentist cannot explain why they expect a dice they have yet to roll to have 1/6 chance for each side. The Bayesian cannot do much without Frequentists moving fast and breaking things.
Nature seems to hate the intellectually pure.
OK, if you like electronic wavefunctions, consider this. The solutions of the H-atom Schrodinger equation consist of three 2p orbitals, corresponding to magnetic quantum numbers -1, 0, and +1. This is all perfectly fine. But when we come to combine these orbitals to form chemical bonds we prefer to think of these wavefunctions in three spatial dimensions, x, y, and z. No problem. We assign the ml = 0 orbital to the z-direction and form linear combinations of the ml = -1 and +1 orbitals. This gives us a set of 2px, 2py, and 2pz orbitals. This works perfectly well and is a standard procedure in molecular quantum mechanics. Things get even more exciting when we consider more complex molecules. For example, we make sense of the tetrahedral structure of methane using hybrid orbitals formed by taking linear combinations of 2s and 2px, 2py orbitals.
DeleteSo which are the *correct* orbitals?
Jim,
DeleteI totally agree with you that if you see the wavefunction as a complex distribution function there are no measurement problem, no need for an action at distance, no collapse, no many worlds, etc. There is actually no problem at all.
“The philosophers have been warning us for centuries that we are a part of the reality we're studying, and can't expect to discover anything about a reality in the absence of observation or measurement.”
I cannot agree more. The words “observations” and “measurements” are very important here. We want a physical theory which reproduces “measurements”. There is no way (and no need) to know what happens precisely between these measurements.
If you were commenting that as to reply to my comment to yours, I am perfectly fine with the standard quantum practice, that there is no such thing as a preferred basis (i.e. no correct orbitals) for this purpose.
DeleteI am not the one claiming that the wavefunction is real or epistemic! You are the one claiming it is epistemic, and what kind of epistemic is it that you are able to assert that so and so orbitals are px or py?
(But yes, obviously I am more on the realist side. When I am not looking at the Ammonia molecule, it is still there. I likely cannot convince you that it is, though.)
You might be amused that I just ended yet another round of debates with a certified physics professor, who claims that superposing vertically and horizontally polarised light to give 30 degrees linearly polarised light, is not the same thing as your current orbitals business.
I'm not claiming to be an anti-realist. But as a result of all the excellent experiments to test Bell's and Leggett's inequalities (and the realist alternatives this leaves us with), but I have to confess I'm worried about the implications.
DeleteI always find it curious that realists fall back on the counter-argument about the moon being there when nobody's looking. I have no problem with the *assumption* of objective reality, and I have no problem *assuming* entity realism (ammonia molecules). Any scientist would be perfectly comfortable with these philosophical positions. But it doesn't follow that I necessarily have to accept the realism of our *representation* of this reality.
In truth, I have no real idea what the answer is. But I like to keep an open mind (well, except for many worlds …).
Ah, we are thus not in disagreement!
DeleteAFAIK, Bell's inequalities do not imply that a *quantum* local, realist interpretation is ruled out. I admit that I have not learnt of Leggett's inequalities, though.
Actually, it is not so much that we love to "fall back" on the counter argument about the moon. It is that as an enterprise the scientific community needs to be able to win lawsuits like Kitzmiller v. Dover. Giving up realism altogether makes it exceedingly difficult to fight against the Deepak Chopras of the world.
I am also perfectly fine with the fact that our representations will always fall short of reality. In fact, physical modelling is only helpful if we can ignore some useless degrees of freedom.
I am merely trying to understand what quantum theory is actually saying about our universe. It certainly is not claiming that _human ignorance_ is the source of the uncertainty principle.
It is that _Nature Herself does not know beforehand._
Jim, B.F., Isometric: all nice words, but where is the science?
DeleteCan any of you propose an experiment (you know, the bedrock of science) whose results may move this discussion forward? Even an in-principle experiment, one that is - today - impossible to do.
In some ways we might compare the quantum measurement question with the many body problem in classical mechanics. A classical system with 3 or more bodies, usually of course thought of as tiny spheres or points, is not generally integrable. There are some special situations where many body problems are integrable, see Perelman on Lie algebraic methods of integrable systems, and this has a curious analogy with quantum states in over-complete coherent states and condensates, but most many body classical systems have a Lyapunov exponent that puts a finite time limit on how integrable it is in the future given a level of precision in numerics. Quantum measurement questions have some parallel to this, where the detection of a quantum system with a few quantum numbers is made with a large system, that is considered classical in the Bohr approach and though is really a large N quantum system.
ReplyDeleteI have indicated here how this may be a form of self-reference, but I will not belabor that too much as I have written about this hear before. A large N system that detects a small N system in effect is similar to a Turing machine that emulates another. This may lead to problems with a formal incompleteness of quantum mechanics or its postulates. It would then be similar to the problem of N-body dynamics in that there may simply be no mathematical or analytical description of this. It might be that just as Poincare found the problem on the stability of the solar system to be unsolvable the quantum measurement problem might also be unsolvable.
Vaidman and others has looked at problems with coupling a few qubit system to another that does not have a large number of qubits. Recurrence processes are found and this has connections to weak measurements. Still the general problem does appear to be open. So called interpretations all have their limits, and while the Many Worlds Interpretation has become popular in recent decades, I fail to see how it is really preferable to the Bohr Copenhagen Interpretation ---- not that I think it is qualitatively worse. I agree that a ψ-epistemic interpretation, such as Bohr's CI, has a certain problem in that if the wave function is just about knowledge about probable outcomes, this knowledge prior to a measurement points to “something.” Of course we can get into nests of arguments over counter factual definiteness, where if there is none then this prior “something” is null. A dual more “real world” perspective is found with a ψ-ontic interpretations, such as MWI or Bohm, but wave functions are not real valued or in some way Hermitean valued observables. There is I think an uncertainty over ψ-epistemic and ψ-ontic interpretation. This all could be a sort of illusion, for if there are recurrences in weak measurements then what we think of as an absolute collapse may just be an appearance due to our locality and finite duration.
I think it is unlikely we can ever find a dynamical method for determining the outcomes of quantum measurements. This would lead to a confirmation of Bell's inequalities on some level and it would also mean entropy or information bounds on quantum systems is wrong. I think as an interesting problem it would be interesting to tie these two together in some derivation or proof. It would appear that a dynamics that explains quantum measurements would itself violate quantum mechanics.
Quantum mechanics might have lead us into some sort of existential incompleteness as pointed out by some philosophers. We may be at or near the basement of just what it is we can say about existence, and because of this there is a loss of certainty about what we mean by this.
That classical 3-body problem is not generally integrable is nowhere near how catastrophic Bohr style collapse is. The classical system may not be describable by maths for long, but one single solution for all applicable time exists, just that we cannot find it. The qualitative features of the solution as being 3-body, say, is unchanged.
DeleteQuantum superpositions are totally wiped out by collapse. The qualitative type of solution is changed.
And we do not have to provide exact solutions to the measurement problem. It just needs to explain what is happening. Just like in thermodynamics, you can often assume N -> infinity but that they turn into some simple symmetric whole, and use that as your detector states. But no matter what you do here, as long as you stay fully within quantum theory, the results of such a large N computation would give a superposed result. You never get Bohr-style collapse.
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I do not agree with your assertion that Bohr's Copenhagen rules are psi-epistemic. It should be neutral, as the rules does not care if the wavefunction is real or not. It just says that you do so-and-so operations depending upon whether you are measuring or evolving.
The wavefunction is not a physical observable under any interpretation I know of. There is no experiment, even in theory, that you can do, in order to figure out the wavefunction's functional form throughout all space at one single time. Or all time. That it is not Hermitian is not a problem. In fact, you aren't even barking up the correct tree. If you wanted to do something about this, you talk about the associated density operator, which is Hermitian by construction, and even gauge invariant in the basic case.
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I thank you for mentioning the interesting stuff happening about Turing machines and about few qubit systems coupling with others looking like weak measurement.
But I have serious trouble understanding how you would view Copenhagen so favourably. I have extreme reservations about it, such that I think it does serious harm to students' understanding of quantum theory. I think that Copenhagen is disqualified as an interpretation and should only be treated as rules, to stay in textbooks, but be explained by other interpretations.
As for why, well, my very long comment on it is having trouble getting published...
Generally Bohr's CI is considered ψ-epistemic. The wave function does not exist, or is not real in any standard sense. The wave function is just a complex valued functions we employ to predict possible measurement outcomes.
DeleteThe Copenhagen interpretation is not really worse than others. There is the GRW interpretation that says there are spontaneous collapse of wave functions, and for sufficiently large quantum numbers in a system collapse in the entire system happens with some frequency. A measured quantum system can as a whole, system plus apparatus, exhibit a collapse readily. There is some prospect for gravitation playing a role, such as Penrose's hypothesis or the Montevideo interpretation. When compared to the Many Worlds Interpretation, which is ψ-ontological, there is still an open question as to how the observer witnesses one particular outcome and not the others. In either way there is a spontaneous loss of a quantum solution at least as observed by a local measurement.
The CI curiously works in M-theory, where a D-brane is a sort of classical condensate of strings. This means the brane, which is really a classical object, loses all its quantum properties.
I am not a partisan to any quantum interpretation. One may in any discussion of quantum physics employ any of them when it helps with understanding. In general I think there is an ambiguity as to whether the wave function is either ψ-epistemic or ψ-ontic, and quantum waves can manifest either depending upon how an observer or analyst thinks. In general relativity we can think of many fingered time, where how a spatial region is evolved into the future is set by the analyst in a gauge-like fashion. This means there really is no intrinsic universal time. In the same way I don't think quantum waves are intrinsically other ψ-epistemic or ψ-ontic,
Putting Copenhagen aside for a moment, GRW is continually being sent to a corner because experimental evidence of superposed states are only getting bigger and bigger, such that the upper bound of GRW collapse on size is raised and raised. At some point, it would become irrelevant, because if you need a huge size to collapse the wavefunction, then it also has to be less and less relevant for measurements of small quantum systems. We might even already have done enough to rule out GRW style solutions!
DeleteI am not sure if your Many Worlds comment is trying to say that it is not able to answer. The decoherence I understood is fully able to answer that "the observer witnesses one particular outcome and not the others". There is no "spontaneous loss of a quantum solution", but yes, it is a spontaneous loss relative to a local measurement.
As in, the obvious thing to do is to include the human observer with the detector entanglement. Like, we already have
|sys> x |pointer>
so just expand that to
|sys> x |pointer> x |human>
and the unitary evolution would give you
( |u> x |u> x |u> + |d> x |d> x |d> ) / sqrt 2
where every observer sees a self-consistent "collapsed" worldview, even though the universe wavefunction is a superposition. There is simply no need for collapsing in this case. Once you have made your measurement, subsequent experiments proceed from the
|u> x |u> x |u>
for one, and |d> for the other. Each branch's set of observers do not have to care about the existence of the other branch, even though the universe's wavefunction is only going to become horribly complicatedly superposed. As long as there is no longer any chance of interference, the wrong branches might as well stop existing.
Back to Copenhagen, my long comment below has the full treatment, if you would be so kind as to take a look.
DeleteOtherwise, I can summarise the relevant conversation in your case.
Even if you consider the wavefunction as nothing to do with reality, i.e. epistemic, there are serious problems.
It might look like moving the goalposts, but to opponents of Copenhagen, you should be able to understand that calling it epistemic is only going to feel like a massive moving of goalposts in the first place.
Anyway, even if epistemic, one would need to explain how Bell's inequalities are violated. Unless, of course, your solution is the Newtonian "I feign no hypotheses."
Another problem is that, wavefunctions are reset every time you make a measurement. In particular, a postulate is that the result of measurements is such that the original wavefunction is collapsed into the eigen-wavefunction of the measurement's operator.
Prior to this postulate, you could claim that the measurement's operator has a spectrum, has the spectrum's eigen-wavefunctions, where the former has physical existence and the latter is purely epistemic. However, the postulate makes it such that after making a measurement, this "epistemic" wavefunction is now promoted to be the state of the quantum system in question, suitable for the production of predictions.
That is, even if you consider the promoted wavefunction to still be epistemic, that the entire system is still epistemic, sure, you can do that, but how would you explain the mechanism by which all experimental predictions become updated by this epistemic exercise?
Isn't that what it means to explain measurements?
Like, if you feigned no hypothesis earlier, that is still somewhat fine. To not have a hypothesis for this one, is a tad bit too far IMO. As in, if you feign no hypothesis here, you might as well doubt the existence of atoms, because really then no experimental result would be sufficient to convince you from one case to another.
And this is only a part of what problems I have with Copenhagen.
Notice, however, that this kind of measurement problems is quite unique to Copenhagen. As described earlier, decoherence interpretations (other than MW, PW has this too) have smaller measurement problems. They at least explain how a purely unitary evolution into superpositions still manage to produce, at least only an illusion, that each observer sees a self-consistent worldview of collapse into classical results. As such, complaints of the above form do not apply to them. Even the sad case of GRW actually attempted to explain that. Copenhagen simply isn't up to par.
I'm a physics student. I think we can talk of nature's way of solving an equation within imposed bounds, it's longer than "knowledge", but I think something unconscious can solve, but only something conscious can know. Like 1D particle in a well. If the well is big enough, one can ask "how does the particle 'know' that there are bounds to the space in the first place, i.e. it finds itself in a well instead of free space, without first exploring the entire space contained in the well". Or one can say, nature is given a problem and then it solves it instantaneously. I think the collapse problem could be contemplated as such as well.. some type of boundary condition change that forces nature to simultaneously solve a new BC problem, which has a different solution from before because the problem is now completely different.
ReplyDeleteI agree with you (if I understand you correctly) and Victor Quillemin in that photons for example have only the particle reality, but it's equation of motion has wave reality. I think the "duality" thing is misguided and only confuses the matter.
Best,
Chris
Oh Prof Sabine, this is way too short!
ReplyDeleteI would point out that how big measurement is as a problem, is also related to what interpretation you are using.
I DISLIKE Many Worlds. I am ok with Pilot Waves. My own preferred is a time-symmetric transactional (yes, I am a unique unicorn).
But when it comes to Copenhagen, I am not so much hating it as categorically rejecting it as an acceptable attempt at interpretation at all. Yes, historically, Born's probabilistic interpretation is necessarily an interpretation. But any modern quantum interpretation that provide predictions that exactly agree with the Copenhagen prescriptions (by definition) achieve the same results and ADDS an interpretation of why quantum systems do as they do. Copenhagen does not.
As you correctly pointed out, but didn't hammer it home, Copenhagen makes measurements anti-Schroedinger-evolution. It also requires classical measurement equipment and classical measurement results. None of these things exist---we _already_ know that systems visibly large can exhibit quantum superposition, and that as of today, there is no determined upper limit to the size of a system such that quantum superpositions get wiped out. We can literally see the interference effects of the double slit experiment, so why are people not also seeing that it is useless to attempt searching for the size limit such that microscopic laws differ from macroscopic?
Look, it is very prudent in the _search_ for a new theory to make the new theory agree with the old ones. That makes things a lot easier to do, and is also the natural source of classical agreement in Copenhagen. But it is not ok for a deeper theory to be defined in terms of the emergent behaviour it is supposed to produce and explain. Not to mention that all the smart folks dropped the attempts the moment they discovered that multiple different quantum systems can have the same classical limits. But in the interpretation game, we continue to teach as gospel futile stuff.
So, because of the above reasons, I think it is basically criminally negligent to teach Copenhagen as the only interpretation. I do not claim that we can do without the Copenhagen rules, if only simply so that students can connect with the existing literature. But people need to know that interpretations should not be so woeful as to make no sense at all.
1/3
As mentioned earlier, I do not like Many Worlds. But I would concede that decoherence would explain most of the headaches of measurements. At this point, I would like to ask Prof Sabine why she thinks it does not.
DeleteIt is actually rather interesting that the original 1927 Solvay Conference already had the necessary bits of decoherence. It arose from within de Broglie's Pilot Waves. I think it was Pauli who had tried to determine what happens when you try to have one H atom (or QHO) as a photon detector of another system. That is, the original masters already knew the correct method to use quantum systems to figure out the transition amplitudes and all, in the context of Pilot Waves.
Sadly, Pauli then introduced them to another system, where a subtle calculation mistake caused all of them to stop paying attention to Pilot Waves.
The entire 1927 Solvay conference proceedings are now available free online. Search for Quantum at the Crossroads.
Note that the behaviour of decoherence is also apparent in the usual textbook explanation of how you get bubble chamber tracks. The reason why the quantum wavefunction of a decaying particle is spherically symmetric, is not because of a lack of straight particle trajectories. It is because all the various possible directions of straight particle trajectories are superposed into one spherically symmetric mess, and will only be seen as only one particular trajectory upon measurement.
This is the real reason why I think decoherence is at least capable of answering most of the measurement problem questions, even though it leaves us with other headaches. Like, could we be epistemologically consistent if we found ourselves in a branch where the unbiased quantum coin gave 3 million heads in a row?
At least technically, though, there is no necessity that the measured branch of the wavefunction gets full probability. The maths will just work if you continue computation with the original superposed wavefunction, ignoring the wrong branches. If you want probabilities, then just divide the further evolution, by the correct branch's. That gives the same normalisation as the Copenhagen rules.
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It is also because of all these facts that I really think people should literally just stop spending resources into working out spontaneous collapse ideas.
DeleteLike, position measurements collapse wavefunctions to a location. But if you just let free particles propagate, there is no localisation of the momentum (whatever initial momentum distribution is just kept the same) yet there is total delocalisation of the position. If you perform a momentum measurement later, you get a localisation in momentum, but complete delocalisation of position. Two successive momentum measurements give complete agreement on the localisation of the momenta, and complete delocalisation of position. It is only because our detectors themselves are localised that we even have the issue of collapse. That is, if you have spontaneous collapse, how would you even attempt to explain quantum theory's _postulate_ that the two momentum measurements have to be in complete agreement?
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It is very interesting to consider the various variants of Wigner's Friend experiments, but one ought to take heed that quantum particles can measure and collapse other quantum particles, as seen in the bubble chamber tracks. That is, I am not claiming that Consciousness Collapse ideas have been falsified. But at the moment, they are not science. Tying one unknown to a thing that is possibly answerable with the same unknown is a circular argument.
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Before I go into my soapbox, I really would urge that all other interpretations should come together and kill the zombie that is Copenhagen. Otherwise we would never progress. Too many people think that Copenhagen is an unavoidable fact. After the zombie is gone, we can then debate about the leftovers.
Soapbox: I think the reason why quantum stuff are unpredictable, is because the future has some influence, ala Feynman-Wheeler style. Of course, care must be taken to make sure causality is preserved, but otherwise we need to specify the final wavefunction in order to get transition amplitudes because some information about the trajectory in the middle is contained in the future wavefunction bit, propagating backwards in time.
I eagerly await your criticism.
PS: Lost in Math just arrived!
3/3
Bohm QM runs into trouble with relativity. Just do the Bohm polar wave function derivation with the Klein-Gordon equation and you can see the beable or particle moves faster than light. It also is tough to make work with the generation of photons in QED.
DeleteTransactional quantum physics is too much gymnastics to worry about. As I say above interpretations are only as good as they are helpful in communicating something about quantum physics in a way that is understandable in standard language.
Thank you! Now I can tell people the physical motivation why Bohmian mechanics is incompatible with SR.
DeleteTrue, I can agree with the view that interpretations are only as good as they are helpful in communication. But then I would still rule out Copenhagen. I have never found an adherent of Copenhagen who could make any sense of the issues I raise, whereas all the other interpretations, I could see how they attempt to solve, such that the discourse is far more productive.
All interpretations impose auxiliary axioms or physical postulates. The CI says there two distinct worlds, one quantum the other classical. One might object to this sort of dualism, but other interpretations do the same. The GRW interpretation imposes a stochastic rule that wave functions simply spontaneously collapse, which leads to a dualism between the deterministic wave dynamics of QM and this stochastic rule. However, we know from a measurement perspective QM has stochastic properties, even if the formalism of QM is deterministic. With CI the collapse occurs because a quantum system is absorbed into a classical system and so it can not have quantum superpositions. GRW is similar in that a classical system composed of a lot of quantum systems has lots of collapse in many moles of matter during any interval of time. So any quantum system that couples into that is subject to this spontaneous behavior.
DeleteMore ψ-ontic interpretations such as MWI have a global wave function, but local observers are spontaneously carried along with one state or path in a decoherence set of states. There really is not much more explanation for why that appearance is so. Bohmian QM has its issues as well, for with measurements the quantum potential has to be nonlocally “reset,” and Bohmian analysts often use standard QM to do this! There are also the issues with relativity and the inability to really do particle physics or QED.
So with interpretations it is all a minefield, where you can step on any particular mine. None of these has a solution to the measurement problem. If we ever did come up with a formalism that told us how an outcome occurs, say one of the diagonal probabilities in the decohered density matrix, this would imply some sort of information process that would uphold on this “substratum” the Bell inequalities. In other words it would contradict QM itself.
What would it be like to exist in a universe where there are no special "observers" and no "collapse", only the Schrödinger equation?
ReplyDeleteYes, I've been watching Sean Carroll videos, and I've seen various comments from Bee about MWI. I would find it of great value, however, to see Bee tackle the question above, which is about that which we can observe.
Don't mind me. I am also interested in the same.
DeleteCharlie (and B.F.): But how is this science?
DeleteCan you outline an experiment (or several, of different kinds), even if it's in-principle only, whose results would help move this discussion forward?
If you can't, why do you think you're doing science?
QM is just a statistical description of classical electrodynamics, hence the measurement problem is an artifact of not realizing this. Try repeating Boltzmann's derivation of thermodynamics from classical mechanics, you'll run into the self-force problem. So instead, you can derive from the basic tenets of classical electrodynamics, viz., Maxwell's equations plus local energy-momentum conservation, equations for the ensemble quantities and - lo and behold - those are satisfied by QM currents (charge and energy-momentum currents).
ReplyDeleteThere is also a lesson here pertaining to your previous post about super-determinism. Classical electrodynamics, being a relativistic theory, begs for its ensembles to be defined in terms of 4D spacetime `structures' (world-lines etc.). That those can be mapped to initial velocity-position pairs (or to initial position - final position pairs if you ask a `retrocausalist') is a misfortunate accident. Luckily, the self-force problem excludes applying this map in the case of classical electrodynamics, thereby revealing the prosaic nature of QM.
Yehonatan Knoll,
DeleteDo you think it is possible to test your theory, ECD (extended charge dynamics) using computer simulations? SED (stochastic electrodynamics) is trying to simulate the hydrogen atom (with not very good results, but there is still hope). Do you think ECD would do better? What about a simulation of a double slit experiment?
Thanks!
Andrei,
DeleteECD is a detailed ontological theory - it describes the individual spacetime structures I mentioned above. Your expectation to derive from the ECD equations a statistical description of ensembles of ECD solutions, is unrealistic in this case. This reflex of yours, I believe, comes from statistical mechanics and SED, but note that in both cases one doesn't derive statistical descriptions solely from the corresponding ontological theories. In the case of stat-mech you add the ergodicity POSTULATE; In SED - a very specific distribution of phases and amplitudes (BTW, SED is incompatible with the basic tenets of electrodynamics hence this entire program is ill founded). The extended nature of ECD particles apparently necessitates an infinity of such additional POSTULATES. I circumvent this brute force construction by writing equations for the ensemble quantities and showing that QM currents satisfy them. I could have gone a step further, POSTULATING simplicity criteria such that QM becomes the simplest (perhaps unique) solution, but why bother - what justification does the ergodicity POSTULATE have other than its success in reproducing thermodynamics? QM, then, is a complementary (statistical) fundamental theory, on equal footings with ECD.
Nonetheless, ECD is far from being experimentally sterile.
Yehonatan Knoll,
DeleteCan you be more specific about the "basic tenets of electrodynamics" SED is contradicting? From what I could understand they only add to classical EM the assumption of the zero-point field (ZPF) which in their case is not produced only from charges (there is a free-field component). They claim that such an assumption is consistent with Maxwell's theory.
In regards to computer simulations I was thinking about fully simulating a system (the motion of each particle and the magnitude of e-m fields at each location) without any statistical assumptions. So, you can start with a "universe" of, say 10 or 100 particles (I don't know what are the computational limitations for that) and try to see what happens. It might be the case that the results you get approach QM's predictions so you could provide strong evidence for the theory. A two-slit experiment, even in a simplified version would require, probably too many particles to simulate, but a hydrogen atom should be doable. I understand that besides the system under consideration (the hydrogen atom in this case) you also need to provide an environment (other charges in the universe that provide for your ZPF) but you could add one particle at a time to the simulation and observe if the increased number of particles improve the results.
Andrei,
DeleteSED is based on Dirac's alleged solution to the classical self-force problem, which violates energy-momentum conservation (see towards the end of appendix D in https://arxiv.org/pdf/0902.4606.pdf).
As for simulations - surely there are infinitely many 100-particle solutions so, to derive QM from them, you would need to define some measure on that abstract space and convince the community that all worlds but a set of measure zero adhere to QM statistics and that your measure is somehow "natural" (I can't see the source of your optimism...) And then what? Write a paper? (my greatest problem with quantum foundations is that they are aiming soooo low). I regard ECD's compatibility proof with QM a sanity check only, moving on to explore its radical implications to seemingly unrelated fields.
Some physicists have a problem with the wave function because they imagine some kind of physical object. Then, they have all kinds of troubles to give a meaning to this "object".
ReplyDeleteIt is not even an observable. Hermitian operators acting on a Hilbert space express observables.
A normal distribution of velocities in a gas poses no conceptual problem. Nobody thinks that this distribution is a physical object. Why the wave function and measurement does poses multiple problems?
It is just a probability distribution and the "epistemic" view is basically a fancy word for the Copenhagen interpretation.
The classical Maxwell-Boltzmann gas velocities distribution is compatible with a mechanistic view of tiny little billiard balls with well-defined positions and momenta at all times. The need for a distribution is merely that humans are ignorant. This is not the case with quantum.
DeleteOne great shock out of quantum physics is that classical _logic_ and hence classical _probability_ theory is not the one used by Nature. We had to invent quantum logic and quantum probability theory, and the mathematicians are quite happy playing with new toys.
The moment you attempt to portray that the quantum measurement problem is merely failing to see classical probability facts, you are missing the point.
B.F.
DeleteYour position seems to be (please correct me if I’m wrong): "the world is classical but non-local". Your ingredients must be classical mechanics with superluminal interactions or hidden variables. If you want to "restore" a classical world and a classical field such as the Bohmian pilot wave you have to measure the value of ψ(x,y,z,t) at some spacetime point and build some kind of potentiometer.
My position is: "the world is quantum-mechanical and local" because nature respects locality, Lorentz invariance and is quantum mechanical. In this case, the wave function is best interpreted as a complex distribution function and the “collapse” as an update of the experimenter’s knowledge. There are no need of more elementary steps, underlying phenomena(s) or classical fields.
Following this point of view, the Copenhagen interpretation is therefore the most appropriate interpretation (QBism is a mostly a modern rephrasing of Copenhagen. It’s ok). In this view there are no “measurement problem”, no “hidden variables”, no “superluminal interactions”, …
Arguing about this is a good and formative exercise but without new unknown phenomena nothing more is needed in QM. We had better build new colliders than thinking about these “problems”.
The opposite is true.
DeleteThe Bohmian view is that the world is quantum, local and realist. It does have an unobservable non-local pilot wave, but the reality itself is the driven particle, and that is local. There is nothing classical about Bohmian pilot waves---it even literally derives a quantum potential and force.
Measurement problem is a feature of Copenhagen. It is rather incredible that you deny this fact.
I'd put it like this: how do we get from the 'possible' to the 'actual'? F
ReplyDeletePlease don't shut up and calculate. Please talk. Please question. I don't want to be a blind man in the world of colors.
ReplyDeleteHuman knowledge works this way: there is experience, and experience is stored as knowledge in the memory. And thought is the response of memory. That is, registering or recording, and then storing in memory. If we say that the wave function encodes knowledge, then that knowledge is limited. Knowledge is always limited. This means that the wave function embodies memory, is talking about memory. This presupposes recording. How can it encode knowledge if it cannot record in the first place? So, if I may ask in all my humbleness, is recording going on at the quantum level?
"If we say that the wave function encodes knowledge, then that knowledge is limited."
DeleteWhat do you mean by "knowledge" here? What does it mean for "knowledge" to be "limited"? How is that "knowledge" encoded in the wavefunction?
What did you mean when you said "that the wave function embodies memory"?
We typically use wavefunctions to predict the future, not query the past. It is not like looking up a history textbook.
You cannot predict the future if you dont see a pattern. A pattern as the past modified in the present becomes the future. This is the movement of time. Now, you are saying in the wavefunction is all the knowledge (all the paths) of where the particle will land up. Is that what you mean?
Delete"The moment you measure the particle, however, you know with 100% probability what you have got; in our example you now know which side of the screen the particle is. This sudden jump of the probability is often referred to as the “collapse” of the wave-function and the Schrödinger equation does not predict it." And if it has knowledge why does it not predict the collapse or that single possibility that is chosen among all the possibilities held as knowledge?
"This is the movement of time."
DeleteThis statement does not seem to hold information.
"Now, you are saying in the wavefunction is all the knowledge (all the paths) of where the particle will land up. Is that what you mean? "
Not even sure what you are trying to mean with it.
"And if it has knowledge why does it not predict the collapse or that single possibility that is chosen among all the possibilities held as knowledge? "
The quote you gave, right before this statement, tells you that the wavefunction does not deal with the collapse. It does not predict it, it does not know it has to happen, the collapse is a postulate that arbitrarily modifies the wavefunction from outside.
Then, what could you even mean by "knowledge" in "that single possibility that is chosen among all the possibilities held as knowledge?"
What do you mean by knowledge?
Delete"One way to deal with the measurement problem is to argue that the wave-function does not describe a real object, but only encodes knowledge, and that probabilities should not be interpreted as frequencies of occurrence, but instead as statements of our confidence."
What is the import of this statement?
How has the word "knowledge" been used in this statement?
What are your observations on knowledge in the context of the wave function?
Neither me nor Prof Sabine subscribe to the epistemic view. She is, rightly, asking what anybody taking that view is meaning by knowledge. I simply join her.
DeleteYou are the one claiming that
"Human knowledge works this way: there is experience, and experience is stored as knowledge in the memory. And thought is the response of memory. That is, registering or recording, and then storing in memory."
You need to explain how that even makes sense.
Pencil grabbed. Paper grabbed. Five minutes later, paper stabbed violently and repeatedly with pencil. Killed them both.
ReplyDeleteYou're being inconsistent.
ReplyDeleteThe measurement problem is not "science", according to the definition of "science" that you use to argue against the multiverse and string theory.
I quote you: Scientists say that something exists if it is useful to describe observations.
We know exactly what quantum mechanics predicts. And despite the fact that the usual treatment of quantum mechanical measurement is horrendously clunky, it seems to me very unlikely that any "solution" to the measurement problem will give different predictions than standard quantum mechanics. I would say that's less likely than the next generation accelerator discovering a new and unexpected particle (although maybe not less likely than experimental confirmation of string theory).
So why are you encouraging people to investigate the "measurement problem" and are discouraging people from thinking about the multiverse and string theory? (Or do you think solving the "measurement problem" will actually give a theory with different predictions? Why?) I admit I can see one possible argument—there are currently many more people working on string theory than on the measurement problem, and to have the best chance of making progress, we need to distribute resources evenly. But it still seems inconsistent to me.
Peter,
Delete"do you think solving the "measurement problem" will actually give a theory with different predictions? Why?"
It will not give different predictions from quantum mechanics, it will give more predictions. Why? Because solving the measurement problem requires a more fundamental theory from which quantum mechanics derives.
"why are you encouraging people to investigate the "measurement problem" and are discouraging people from thinking about the multiverse and string theory?"
I explained in my blogpost that the measurement problem is a consistency problem. It requires a solution. It's the type of problem that has historically led to breakthroughs. I have explained this here.
I do not "discourage people" from thinking about the multiverse. I merely point out that talking about the existence of entities that are by assumption non-observable is not science.
I do not know what your comment about string theory refers to.
Do you mean that you hope that when you measure a diagonally polarized photon, you will be able to make a more definite prediction of whether it will be vertically or horizontally polarized, rather than a 50% probability of each? Doesn't Bell's Theorem say this is impossible without violations of Einstein's special theory of relativity?
DeletePeter,
Delete"Do you mean that you hope that when you measure a diagonally polarized photon, you will be able to make a more definite prediction of whether it will be vertically or horizontally polarized, rather than a 50% probability of each? Doesn't Bell's Theorem say this is impossible without violations of Einstein's special theory of relativity?"
That's exactly what I am saying, yes. As to Bell's theorem, no theorem is better than its assumptions.
I actually think the right solution to the "measurement problem" is not to find a new theory underlying quantum mechanics that we can intuitively understand; it's to find a way to train our intuitions so that we can think about quantum mechanics without hurting our brains.
DeleteBut the usual treatment of quantum mechanical measurement à la Copenhagen interpretation doesn't accomplish either one.
As I explained in my blogpost, it's not just a matter of training intuitions, it's a real inconsistency. If you think quantum mechanics is a fundamental theory, you should be able to derive the measurement process since an apparatus is an emergent object. If you want to get rid of reductionism, you have to explain when and where and how that's supposed to happen.
Delete“Do you mean that you hope that when you measure a diagonally polarized photon, you will be able to make a more definite prediction of whether it will be vertically or horizontally polarized, rather than a 50% probability of each? “
DeletePeter Shor,
Put it another way, a photon that passed through a vertical polarizer has 0.5 probability of passing thru a diagonal polarizer. This is not the place for my theory but I hope I would be allowed to say this. My realistic theory explains why the probability is 0.5. The full explanation requires my entire research papers. I revised the mathematical foundations of QM. I call it “Quantum Algebra.”
From Quantum Algebra, I derived the equation that yields the 0.5 probability of passing thru a diagonal polarizer. It is a simple equation that uses discrete probability. It also explains why P = 0 for a horizontal polarizer and why if you put a diagonal polarizer in between the vertical and horizontal polarizers, the probability becomes non-zero. Can QM textbooks explain that?
Sabine is right. The essence of measurement problem is that QM cannot explain the existence of definite observation results. The framework is built on top of the basic fact that all measurement results are definite, and yet it cannot explain this. This is a glaring insufficiency for a purportedly universal physical theory.
DeleteSabine,
Delete" If you think quantum mechanics is a fundamental theory, you should be able to derive the measurement process since an apparatus is an emergent object. "
But it would be possible to do that without making any new quantitative predictions. So your hope to get testable theories from this line of research is only that, a hope.
Andrew,
DeleteIt's more than a hope, I think it's actually possible to derive. Alas, I haven't done that and neither has anyone else, because pretty much no one is thinking about it. I hope this will change in the soon future.
Sabine,
Delete"It's more than a hope, I think it's actually possible to derive."
So you're thinking specifically about superdeterminism?
But even a "successful" theory of superdeterminism might permit predictions only in principle, not in practice.
It is possible to derive what? The measurement process from current fundamental QM? I thought the whole thrust of your blog was that this is not possible and thus a real inconsistency.
DeleteIf you wish to derive the measurement process from QM... something *else* must be introduced, yes? And that *else* is hoped to make additional predictions on-top-of current QM, right?
So, when you say above it is 'actually possible to derive' what are you referring to?
I agree with Andrew Dabrowski. I think we should be able to explain the measurement process and decoherence better than our current theories do (and that doing this is clearly worthwhile), but I believe there is only a tiny chance of ever being able to predict the results of measurements any better than standard quantum theory does.
DeleteWhich is why I accused Sabine of being inconsistent. Finding a better explanation of the measurement process is not "science" according to her definition of science.
Possible to derive that any solution to the problem leads to quantitative new predictions that are measurable at least in principle (whether they are measurable in practice remains to be seen). I was responding to the above question from Andrew.
DeletePeter,
DeleteI have no idea what you think my definition of "science" is. I do not think I have ever put forward one. I have merely pointed out some instances in which scientists work on things that are clearly not science because these topics are equivalent to religion. I hope you notice the difference. Pointing out that the emperor is naked isn't the same as spelling out a dress code for emperors, if you excuse the somewhat crude analogy.
Also, as I have said repeatedly, this isn't just about "finding a better explanation" it is about removing an actual inconsistency.
Sabine,
DeleteIf we change Peter's "according to her definition of science" to "according to her criteria for science" then I think his point stands.
How can we solve the measurement problem?. In my understanding:
ReplyDelete- Not by using the "measurement postulate".
- We just need to use dynamical models. Instead of the typical wave-packet reduction, we can use the dynamical model of an apparatus coupled with environment that interacts with our quantum system.
- The use of these models imply that we need to rethink concepts like: the wave-function collapse or unitary system evolution. Both opposing concepts created the measurement problem; but there are no sharp collapses in quantum systems; instead, there are gradual interactions with environment that leave these quantum systems without their superposition property.
- Despite unitary evolution of an isolated system is indeed possible, in the real world: systems tend to get coupled with environment. In fact, manufacturers of quantum computers spend a lot of money in keeping their Qbits within their superposition property (is the record now 40 min.?); but finally all Qbits lose this property. The most natural way to lose it is with thermal noise. I was thinking also that a different way for losing superposition of any quantum system could be electromagnetic noise or even also gravitational noise (e.g., near supermassive black holes or near less and less massive bodies down to certain limit).
- I had the chance to comment this last issue in person to Mr. 't Hooft. He told me that during all his work, he never related gravitational noise with quantum collapse (in general terms, he was not very happy with most of the above, specially on how we could add noise into a unitaryly evolving quantum system).
- Recall that all the above is just a speculation supported by some mathematical models; there are many other speculations allowed.
The prototype of decoherence is already used by the pioneers during the 1927 Solvay conference.
DeleteThe Schroedinger evolution of a quantum system with its environment, if the environment is also considered as a huge quantum system (as opposed to the master equation style evolution that is not necessarily unitary), ends up with a superposition of "collapsed" states. Really, what happens is that the quantum system and its environment becomes entangled such that the results of the experiment are also written onto the environment, and the superposed-but-incompatible branches stop interacting with each other. But they are still superposed.
Thermal effects are considered too. Some people claim that thermal noise is a good way to store the entropy changes this brings about, but I have trouble seeing how the unitary transform, which is necessarily entropy-preserving, could do that.
And the incompatibility of "spooky action at a distance" with Special Relativity isn't "by assumption" (a phrase that seems to me to imply that it might not be correct). In fact, it's a theorem that you can prove starting with the standard formulation of quantum mechanics.
ReplyDeleteIt's by assumption because in Copenhagen you are not supposed to ask what "really" happens.
DeleteRather than starting your investigation of the measurement problem from the standard Copenhagen interpretation of quantum mechanics, it seems to me that you should first learn some quantum information theory and proceed from there. Then you will know what things are assumptions (and so might turn out to be false), and what things are theorems.
DeleteI think I stated that wrong. It's a theorem that "spooky action at a distance" has no observable consequences.
DeleteI have stated explicitly in my blogpost that I am talking about the Copenhagen interpretation. I know the no-signalling theorem, not sure what makes you think I don't, but thanks anyway.
DeleteSabine,
ReplyDelete"You’ll notice then that the instantaneous jump screws up General Relativity."
For us nonphysicists, could you elaborate in this? How exactly does GR get screwed up?
General Relativity is a local theory. In particular, it has a local conservation law for all types of energy. It's incompatible with energies jumping around discontinuously.
DeleteSabine,
Delete"[GR is] incompatible with energies jumping around discontinuously."
Again it's not obvious to a nonphysicist why this is a problem: the energies don't jump around, rather one superposition is chosen over the others.
Try to figure out where the energy is before and after measurement.
DeleteSabine wrote:
Delete"General Relativity is a local theory."
Electro-Magnetism (EM) is also a local theory. When the electron's wave function collapses, electric charges "jump around". Yet EM is consistent with QM, because EM itself is quantized.
This is exactly why we are certain that GR also has to be quantized. Otherwise it would lead to contradictions.
That's one of the reasons, yes. But just saying it's quantized doesn't explain what's happening during measurement, that being my point. Of course QED doesn't explain that either.
DeleteSabine,
Delete"Try to figure out where the energy is before and after measurement."
In superposition k it's in location k. After measurement only one superposition remains. What am I missing?
That's non-local and not compatible with GR. You cannot use it as a source. Two sides of the equation would not be identical. It's not working.
DeleteSabine,
Delete"That's non-local and not compatible with GR."
But it is local in each superposition.
I imagine I'm pretty exasperating, maybe someone could just refer me to a good treatment of this issue for nonphysicists.
Andrew Dabrowski,
DeleteMaybe this book here by George Musser helps.
[1] I was taught that Schrödinger equation is not compatible with Einstein's Special Relativity
ReplyDelete[2] I believe that it cannot run both forward and backward in time as Schrödinger equation 'describes' the kind and diffusion of the wave packet which is the time inreversible process - one needs at least Klein — Gordon equation (originally invented by Schrödinger) But Dirac equation is the right choice
[3] conceptually Schrödinger equation is a double approximation compared to Dirac equation, as besides [1] and [2] it is also spinless
[4] the existence of spin (spin charge, more exactly 1/2-spin) as ‘quantum counterpart of classical electric charge is in my opinion the only essence of quantum mechanics
[5] any physical and / or philosophical speculations on measurement based on Schrödinger equation are almost worthless
[6] with ‘quantum metric -- non-linear solution of Dirac equation -- one can sacrifice 'unitarity of wave function' and win its continuos decoherence due to topology of particle world-lines
SG,
Delete[1] This is a semantic problem (which we actually discussed on this blog before). You are thinking of the Schroedinger equation with a particular Hamiltonian, that being the non-relativistic one, which is incompatible with SR. I am thinking of the Schroedinger equation as having a non-specified Hamiltionian and a suitable choice (think Dirac) is very well compatible with SR. In any case, I hope we agree that there's no conflict between QM and Lorentz-invariance.
[2] Look, it's a linear differential equation that's trivially solvable if you have the operator. Of course you can run it forwards and backwards as you wish. Whether these solutions actually make physical sense is a different question entirely.
[3,4] And how is that relevant for anything?
[5] See [1]
[6] Awesome.
First, the Schrodinger equation is itself not compatible with special relativity. It cannot describe massless particles like photons. Specifically it cannot describe emission and absorption of real photons. One treats them in plain QM as CLASSICAL fields, and fudges spontaneous emission by ad-hoc addition of Fock states with and without the photon. But this is not a serious problem with this discussion, because there are plenty of cases, like the two-slit experiment, or Stern-Gerlach with the magnet treated as a classical field (which is OK in plain QM).
ReplyDeleteThat assumed, its actually trivial. One assumes ... correctly and exactly ... unitary evolution of system + "apparatus". One ... that is, a human ... or a sentient computer ... "observes" only after the fact, perhaps, if a computer, only picoseconds, a long time actually.
The "measured" part of the wavefunction ... a particle's momentum or position ... does actually collapse, smoothly, as it interacts with the measurement apparatus. However, other aspects of the particle's wavefunction (the parts tied to the measurement by non-commutating variables) expand. These are tied to other degrees of freedom of the apparatus, and expand hierarchically to macroscopic proportions. The process in the classical world is called "amplification" but the devices used are of course quantum.
That's all there is to it in plain QM.
The argument starts when one tries to explain this in relativistic field theory (even real photons). This IS very tricky. One has to worry about "infrared" divergences (solved) and "ultraviolet" ones (unsolved ... this the THE question, of course, that string theory and LQG worry about). Getting these right with a naive treatment of Fock states and perturbation theory is tricky.
And yes, we actually DO teach this to our students, at least the best ones.
I don't know if it's helpful here to try to clear up some confusion, but here goes...
ReplyDeleteThe standard quantum formalism taught to undergraduate students typically doesn't include von Neumann's 'Process 2' (the collapse postulate). The standard formalism (state vectors in Hilbert space) is completely silent on the question of interpretation. The formalism does not = the Copenhagen interpretation. If you prefer an axiomatic approach to the formalism then you could argue that this is influenced by Bohr/Heisenberg/Born et al: there is usually a completeness axiom, something about Hermitian operators and expectation values, the Born Rule (quantum probability), and the unitary time-dependent Schrodinger equation. None of this tells you how you should interpret the wavefunction.
Although the Copenhagen interpretation is anti-realist, it relies very heavily on an arbitrary distinction between quantum and classical worlds, or what John Bell used to call the 'shifty split'. THERE ARE OTHER ANTI-REALIST INTERPRETATIONS WHICH DO NOT ASSUME SUCH A SPLIT. Among them I'd include Carlo Rovelli's relational interpretation, information-theoretic interpretations, consistent (or decoherent) histories, and QBism. So, rejecting realist interpretations does NOT necessarily mean agreeing with Copenhagen.
The anti-realist interpretations are passive. You can call them 'shut up and calculate' interpretations if this makes you feel better. They basically tell us that there's 'nothing to see here', they do not help in any way to transcend the current formalism and offer no promise of eventually discovering deeper structures.
For this reason, many physicists prefer to interpret the wavefunction realistically. This brings with it a whole world of pain, because if we now have to consider the wavefunction as representative of the real physical state of a quantum system, we have to figure out what we do about superpositions and we have no choice but to invoke a collapse postulate. Peter - I do not think this is at all unscientific. Assuming a realistic, statistical (local) hidden variable interpretation led to Bell's inequality and eventually to Leggett's inequality and some really exquisite experiments designed to test these. This is surely science.
But the fact that local and crypto non-local theories are effectively ruled out by experiment leaves us in a bit of a bind, with a choice between what I think of as unpalatable evils - non-local (and spooky) de Broglie-Bohm, spontaneous collapse, consciousness, and many worlds. Take your pick.
YES HELPFUL THANK YOU!!
DeleteIt is obvious that holding on to a realist view is painful. I am in literal mental pain every day as I do hold such a view.
But I am not even sure how to live with epistemic view. If you would indulge me, I would like to know, for example, how "human's best informational understanding" could make a prediction that violates Bell's inequalities and yet be unquestioned.
As in, if there is no reality beneath the equations, what would it mean that we can prepare a system to provide results like that?
Actually, I suspect that I am not really needing to hold tight to realism. Instead, I just want some mechanism to explain the results as predicted by quantum theory, without some of the bizarre notions. I am even willing to give up locality and strict causality.
Have you watched the Veritasium video about de Broglie-Bohm as silicone oil drops? Here:
https://www.youtube.com/watch?v=WIyTZDHuarQ
As in, I used to not like pilot waves, but seeing with my own eyes how a simple system like that could reproduce quantum theory with a realist model, made me like it now. Of course, it is a shame that it still has problems with SR (but I don't know why---people just assert that they don't fit together, without stating why or even citing some source).
"...unpalatable evils - non-local (and spooky) de Broglie-Bohm..."
DeleteWhat you seem to be suggesting is that the physical reality must be either local or non-local. Indeed, that either/or approach seems to unnecessarily hobble any discussion of QM interpretations.
It seems perfectly reasonable however, on the basis of our observations, to think that physical reality can contain both local and non-local aspects in exactly the same way it can contain both positive and negative electric charges. This in turn suggests that the interplay of local and non-local phenomena are essential to the dynamics of the cosmos. Reductio ad <2 = reductio ad absurdum.
I'm certainly not looking to hobble any discussion of QM interpretations (actually I have a new book out next year which examines a selection of anti-realist and realist interpretations).
DeleteWhat I am suggesting is that whether there is a 'measurement problem' or 'spooky action at a distance' or 'non-local causation' really depends on your own philosophical preferences or prejudices, and I think it's helpful to acknowledge this.
I accept that many scientists (I suspect Sabine included) don't like this because science is supposed to be 'better' than philosophy, and should be able somehow to tease out the 'right' answer in ways that no amount of philosophizing could ever achieve.
But, at risk of repetition, science is about the tension between theoretical ideas and concepts and empirical facts. The quantum formalism is a magnificent triumph of science, but the formalism (and its empirical foundations) are completely silent on the question of how its theoretical concepts should be interpreted. And as soon as you start to speculate about these, you're engaging in philosophy.
This is not to say that such speculative metaphysics is pointless. You might come up with some new ideas which suggest some new experiments, which is exactly what David Bohm and John Bell did. But these experiments have been done, and the formalism remains inscrutable. The problem now is that if you still prefer a realist interpretation, you're obliged to turn to de Broglie-Bohm or many worlds, which look pretty much untestable, and it is here that the metaphysics starts to overwhelm. Yes, arguably spontaneous collapse (GRW) or Diosi-Penrose mechanisms are testable, and - if it happens - the MAQRO mission is designed to do just this (see maqro-mission.org). But I have a bad feeling that I know how these experiments will turn out.
The bottom line is that I think we might have to start to come to terms with the possibility that the anti-realists might be right, or at least take an interest in what they have to say.
bud rap,
DeleteYour comment about the suggestion of reality being only either local or non-local is not true.
Or rather, the reason why we have to do as we now do, is because experiments have upheld Bell's conclusion. This means that a classical, realist, local view of our universe is not possible.
However, even in QFT, we proved that signalling is local.
So, there are a few things you can do. You could give up locality, or you could choose something else. If you give up classicality, for example, you get de Broglie-Bohm. This is closest to what you are thinking about, because there is one local reality, but the pilot wave is non-local, so it is a mix of two exactly as you wanted.
Not even sure what you wished to illustrate with your "both positive and negative electric charges"
Jim,
Delete"if you still prefer a realist interpretation, you're obliged to turn to de Broglie-Bohm or many worlds"
I was very much enjoying your entire comment, but when it came to this part, I was suddenly overwhelmed with a need to ask you what you meant by "realist" there. Are you only applying the term to wavefunctions, or to quantum theory, or to the universe?
I mean, none of us here are claiming that the universe is a mental construct, Deepak Chopra style anti-realism, right?
As in, if I search inside myself deeply, I think I am totally ok with "wavefunctions are computational gimmicks". I am also ok with spooky action at a distance, though the no-signalling theorem is necessary---we still want, and have, causality (you meant correlation above). But then there is still a measurement problem in terms of the non-local correlation.
That is, yes, you can shift the problems around so that it doesn't appear in each bit. But you cannot magically will the problem to go away. Science has to be comprehensive---it does not have to have answers right away, but it needs to have at least one fully self-consistent way to answer questions.
"But I have a bad feeling that I know how these experiments will turn out."
Come, let us shed tears together.
"The bottom line is that I think we might have to start to come to terms with the possibility that the anti-realists might be right, or at least take an interest in what they have to say. "
Errm, given that no quantum textbook in existence fails to cover Copenhagen, I am going to have to point out that the opposite to your statement is the one that needs to happen.
Jim,
Delete...science is supposed to be 'better' than philosophy, and should be able somehow to tease out the 'right' answer in ways that no amount of philosophizing could ever achieve.
Let's get this straight, with regard to understanding the nature of physical reality, science has made enormous strides over a few centuries, whereas philosophy has no such comparable track record. Scientific knowledge can be used to launch rockets to the moon and beyond. The only thing philosophy has ever launched is an argument. In the physical realm to which it applies, science is demonstrably better than philosophy.
...science is about the tension between theoretical ideas and concepts and empirical facts.
To the extent this captures the current state of theoretical physics, as a discipline primarily concerned with the study of mathematical models, it is a fairly accurate description. Unstated, however, is that in the current reality, theoretical physics weights theoretical models more heavily than it does empirical evidence.
Your description, therefore, does not constitute an adequate definition of science but merely illuminates the extent to which modern science has become estranged from the empirical approach that is definitional to science, as in:
Science is the open-ended investigation into the nature of physical reality employing the complimentary probes of empiricism and logic.
The term, logic, should be considered broadly inclusive of both mathematics and philosophy. Framed in this way it should be clear why attempts to philosophize or mathematicize a way around scientific questions wind up in dead-ends like QM.
Sure QM "works", as did Ptolemaic cosmology, but it goes nowhere. A century on and QM has no meaningful physical interpretation except for, potentially, Bohmian mechanics and that is widely disfavored in the theoretical community for what seems to be mostly mathematical, philosophical, or aesthetic reasons.
It also seems unreasonable to lump Bohmian mechanics in the same "untestable" category as many worlds. MWI is nothing but a metaphysical conjecture. In as much as BM suggests a chaotic energy substrate as the source of the pilot wave effect, this has the potential, at least, to be an observable phenomenon.
The bottom line for me, anti-realism is inherently anti-science. Post-empirical science is an oxymoron.
OK, so you're (potentially) a Bohmian, and happy to declare that any anti-realist interpretation must be anti-scientific. Good for you.
DeleteIn my new book (out next year) I do indeed explain that anti-realist 'nothing to see here' interpretations are passive, whereas realist interpretations (MWI excepted) are active, in that they provide motivation for new experimental tests. I also say that when it comes to pushing the empirical boundaries of QM, it goes against the grain of human nature not to try. For me, de Broglie-Bohm requires the swallowing of too much metaphysics - 'spooky' non-local causation due to the quantum potential, 'empty waves', and so on. Bohmians claim to have fixed its compatibility with special relativity and, without knowing the details, I'm prepared to take what they say at face value. I'd defend anyone with a plausible and hopefully decisive experimental test of Bohmian mechanics, but I'll be honest - I'm not very optimistic.
All I'm advocating is that we try to keep an open mind. Anti-realism AT THE LEVEL OF REPRESENTATION is not anti-scientific - how can it be? What I find dismaying is how those who for whatever reasons have become wedded to a particular interpretation appear to want to shout down all who disagree or take issue. It reminds me of another specifically human behaviour ...
B.F.
DeleteMy new book feature four realist propositions:
#1 The moon is there when nobody looks at it or thinks about it (reality is objective)
#2 If you can spray them then they are real ('invisible' entities such as electrons are objectively real)
#3 The base concepts (i.e. the wavefunction in QM) represent the real properties of real physical things
#4 Scientific theories provide insight and understanding, allowing us to *do* some things that we might not otherwise have considered or thought possible
Like most (if not all) scientists, I'm happy to accept #1 and #2. But I argue that QM challenges #3, and that adopting an anti-realist *representation* doesn't necessarily mean rejecting #1 and #2. The real difference between anti-realism and realism at the level of #3 is that the former are rather passive, the latter much more active in the sense of motivating new experimental searches. Anti-realist interpretations don't encourage us to *do* anything differently, as suggested by #4.
To repeat, many student textbooks present the standard quantum formalism and might even mention 'Copenhagen' without acknowledging the historical nuances, or even that there's actually no such thing - the 'Copenhagen interpretation' is a catch-all for a whole bunch of different arguments made by different theorists down the years. However, it is fair to say that Bohr argued for complementarity and a distinction between quantum and classical worlds that was never properly demarcated. Von Neumann confused matters considerably with his theory of measurement, which dispensed with an arbitrary distinction, applied the quantum formalism to classical objects and so necessitated the introduction of his projection postulate, aka the collapse of the wavefunction.
In the spirit of open-mindedness, I think it's helpful to acknowledge that there are other anti-realist approaches that don't fall foul of 'Copenhagenism'.
The moon is a crystal ball to us, but have we ever asked how the moon looks like to a fly. What is it that makes a fly-moon a fly-moon and a human-moon and human-moon?
Deletebud rap,
DeleteI am very much on your side, that I dislike MWI, I like Bohmian, I hate anti-realism, and applaud your parallel between QM and Ptolemaic cosmology.
But I am quite persuaded by Prof Sean Carroll's view that MWI is the most QM of QM. There is nothing else than Schroedinger, and there is no need to add the particle of Bohmian pilot waves. There is no need to add any other ingredient. As such, we should treat it as the most basic QM interpretation. As in, that should be the thing to compare to, not Copenhagen.
Also, seeing as Ptolemaic cosmology is the stamp-collecting before Newtonian mechanics could be born, trying to portray it as anti-science is a bit too much.
BM is obviously also not testable, in that the pilot wave and the particle are postulated to be untestable.
Otherwise, again, I am on your side, and I hate string theory too...
Sabine, you're not using a general enough version of the Schrodinger Equation.
ReplyDeletehttps://latex.codecogs.com/gif.latex?\langle&space;\psi_k^{final}&space;|&space;\delta_k&space;S_k&space;|&space;\psi_k^{init}&space;\rangle&space;=&space;-&space;i&space;\hbar_k&space;\delta_k&space;\langle&space;\psi_k^{final}&space;|&space;\psi_k^{init}&space;\rangle
The above equation generalizes Schwinger's Quantum Action principle so that each particle has its own Action and Wave-function (and, potentially, its own hbar). Each particle, thus, has its own Lagrangian and Hamiltonian as well (and we end up with an expanded set of allowed dynamics).
This gives us the following generalization of the Schrodinger Equation to a family of PDEs instead of a single PDE so that now, each particle has its own wavefuncion: https://latex.codecogs.com/gif.latex?i&space;\hbar_k&space;\frac{d}{dt}&space;|&space;\psi_k&space;\rangle&space;=&space;\hat{H_k}&space;|&space;\psi_k&space;\rangle
Now that we have a generalization of the Schrodinger Eq where each particle has its own wavefunction (instead of the system), we can interpret the wavefunction of each particle as part of the particle's guidance system and, with a tiny bit more, we can solve for stochastic trajectories.
Sabine,
ReplyDeleteMaybe I missed this, but I can't see how anyone could claim that the "Psi-epistemic" interpretation of QM to be true in light of quantum behavior, e.g. the double slit experiment. There are two different, physically distinguishable, distributions of electrons on the screen if we measure which slit it went through or not. Measuring which slit it goes through collapses the wave function so that there is no interference from the wave function going through the other slit. So in this case, a collapsed wave function cannot represent only an update to the observer's knowledge since a change in his knowledge cannot give a physically different electron impact distribution.
I hope that's clear.
Alex
"General Relativity is a local theory."
ReplyDeleteYes it is, and therefore it is illogical to apply GR to the imagined "totality" of the cosmos. The cosmos is a non-local phenomenon - by observation.
I'm puzzled how we can keep quantum systems from decohering even for a short amount of time. Aren't there forces acting on it that we can't block, such as the force of gravity not just from Earth but from all objects in the universe? And the quantum system such as a quantum computer has other forces acting on it that balance the force of gravity from the planet.
ReplyDeleteWhy do these forces, however small, not cause the quantum system to decohere? After all, they are interacting with the thermal environment.
Why doesn't gravity from a distant planet acting on a quantum system cause it to decohere? The forces of the system on the distant planet are so small that Heisenberg's uncertainty principle prevents you from measuring the state of our system by looking at the distant planet.
DeleteWhen it comes to quantum theory, forces are the wrong way to look at things (unless your are Bohm).
DeleteAnd at such tiny scales, the gravitational interaction is too small to matter.
Not to mention that the atoms, say, and the equipment they are in, are both bathed in the gravitation. Which means that effectively they cannot see each other as affected _differently._
This is a bit like the falling elevator. You cannot tell if the elevator is accelerating or is under gravity. The quantum system is equally incapable of telling.
There are, though, people who wish to use gravitation to collapse wavefunctions. Penrose, for example. It is not much successful, but still, people do try.
Peter Shor,
DeleteIt's good that you mentioned the reason why the gravity does not induce "collapse" for microscopic systems (Heisenberg's uncertainty principle). You may see that such an argument cannot be made for hypothetical macroscopic superpositions (such as dead/live cats or human observers). In such a situation you can measure the state of the system by looking not necessarily at a planet but at any object around you. This implies that thought experiments like "Schrodinger's cat" or "Wigner friend" can never be realized, even in principle, making them useless for understanding QM.
Andrei: I don't see any such thing.
DeleteWhy should gravity induce collapse if you fasten all the observing equipment tightly to the box containing Schroedinger's cat, put the cat in an inner box which is inertially decoupled from the outer box, and locate the experiment in perfect vacuum a long, long, long way from any other gravitating bodies?
Peter Shor,
DeleteThe gravitational field has infinite range, it does not matter how far you place the box from other objects. Let's say that I place a grain of sand in orbit around this box at whatever distance you find convenient. I then measure its orbit and deduce from it the mass distribution inside the box (in the same way the interior of a planet is investigated by space probes by accurately monitoring their orbits). No matter how many boxes you use, if there is a cat moving inside, a change of mass distribution will take place and this will influence the orbit of the sand grain.
Dr. Hossenfelder:
ReplyDeleteIf we remove the presumption that Consciousness is anything special (ie it is a product of brain operation with no new physics), then wavefunction collapse (if it is real) due to "observation" is just one instance of it being environmentally triggered.
Meaning even though Schrödinger's equation works perfectly, there is some constraint it is missing. You previously mentioned gravity and mass, perhaps there is a limit to how much superposition mass can have, based on the superposition of multiple gravitational fields; e.g. there may be limits to the distance between superpositions of a single mass, limits not currently accounted for in Schrödinger's equation.
In general, statistical progressions or distributions typically do have environmental limits not represented in the equations. For example if I fit a Normal Distribution to the heights of human first graders, it extends infinitely in both directions; but no matter how perfect the fit, there are obviously environmental factors unaccounted for. We won't find any first graders under 150 mm tall, or any over four meters tall. I don't know what the limits are, but I know those are outside them.
So it seems possible the measurement problem is tied to the quantum gravity problem, but, under the assumption consciousness is nothing special, the measurement problem might be easier to explore experimentally, and that might put constraints on any quantum gravity theories.
This post is too long, too full of hidden angst. Just point people to Einstein's brilliant exposition in the original EPR (Einstein-Podolsky-Rosen) paper. No one has ever gone beyond Einstein's transcendant clarity there. They only think they have.
ReplyDeletepsi is a tool for computing probabilities in configuration space. Relativistic quantum field theory adds much more than philosophical discussions, but leaves open the big question: why a probabilistic theory?
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteIf you have a question, I recommend you ask it rather than leaving stupid comments. Also, please read the above comments because I don't like repeating myself, thanks.
Delete"The wave-function moves according to the Schrödinger equation. This equation is compatible with Einstein’s Special Relativity and it can be run both forward and backward in time. If I give you complete information about a system at any one time – ie, if I tell you the “state” of the system – you can use the Schrödinger equation to calculate the state at all earlier and all later times. This makes the Schrödinger equation what we call a “deterministic” equation." This is the part that interested me. Imagine the progression: wave function evolving in time, decoherence, measurement. How much of this process is really time reversible? Can we "begin" with the measurement and play the movie backward from that point through all prior states?
ReplyDeleteAs I said, as long as you only use the Schroedinger equation, it's reversible. The measurement process isn't reversible, but that's not the major problem with it.
DeleteMy opinion is that since all the 'interpretations' of quantum mechanics that we have so far are *very* contrived, we haven't understood something fundamental.
ReplyDeleteSabine, I wonder if this article glosses over too many assumptions in the basic premises to be helpful.
ReplyDeleteStart with: "Particles are described by a mathematical object called the “wave-function,” usually denoted Ψ (“Psi”)."
This statement contains an assumption that in my mind, I think of as "the cult of the incident particle' i.e. The presumption that what the Schrodinger equation represents, is the incident particle.
Surely it is better to step back and say something like. The Schrodinger equation provides a basic description of patterns that arise when sets of particles (and fields) are closely interacting. The Schrodinger equation has limitations, it does not provide a good description of multi-particle systems and does not include important relativistic effects that predict particle spin and matter-antimatter as discovered by Paul Dirac when applying special relativity to quantum mechanics.
To me, the same presumption, that what we are seeing or measuring in using QM to predict what we might see, is is quite literally the same as making the assumption that the wave equation is the same thing as a [articular particle, and that the outcome of some interaction records some 'property of the particle wave-function' records a property of a particle in the same way a classical measurement does, when in fact it is not clear that the wave function for a system/interaction is one and the same thing as a description of individual particle.
Perhaps it is better to say that the Schrodinger equation does provide us a tool to describe the structure of the patterns of dynamic interactions, and that we can often use it to estimate where we can find a particle. (and so on)
To me, the measurement and collapse 'problems' look to involve ad-hoc moves necessary to construct a position wherein Schrodinger's work needed to be seen as a vindication Bohr's earlier ideas.
If one takes on the difficulties that arise as a consequence as if they are 'the problems', one is unwittingly adopting Bohr's assumptions as fact.
There is nothing in the Schrodinger equation that says that the results it gives for say, a Hydrogen atom, can be taken to mean that it is a description of one electron. You could just as well take it to be describing the proton in the atom, or the way that the pattern of interactions produced by 'transient' virtual photons moderate the fields between two particles to produce a stable modes.
Your first point is really just not being nice. Yes, her language is phrased in QM, but it is obvious from the context that the difficulties do not go away if you use QED to try and properly handle multiple particles and their creation/annihilation. The "Schroedinger evolution" and the measurement problem persists against Copenhagen no matter how much deeper you dig.
DeleteAs for the later parts, yes, it is true that difficulties arise as a consequence of trying to shoehorn modern QT into Bohr's conception. However, even if you take that the wavefunction is pure theoretical fiction, or the equivalent in QED, you still have to grapple with "What does it mean for us to live in a universe where Bell's inequalities are exceeded?" This particular variant of the problem is devoid of ontological baggage, referencing only verified experimental facts.
Finally, until you have evidence otherwise, it is quite necessary to associate the electron wavefunction with the electron. The theory requires it, if only to correspond with experiments. As in, you need a way to connect all the tinkering with the experimental knobs to the theory's operators, and it makes no sense for you to have the theory's operators be about combing the hair on the cosmic teapot. Instead, it is about "We did this to the electron, so apply this operator, following the theory's prescription, to the wavefunction"
Of course, we might be combing the cosmic teapot. That is fine. We'll change our minds the moment you give us good evidence that this is what we are doing.
Sabine, given the problems with decoherence, etc, is there a good reason for rejecting Einstein's interpretation of ψ.ψ*, i.e. prior to measurement you don't know; after it you do? Everyone asserts there is a superposition prior to measurement, but they cannot possibly know because how can you, until you observe? Even with something like the rotating polariser experiment, you cannot know the photons did not have a determined polarization at creation, and if you follow through by using the Malus law, you still get the observed results.
ReplyDeleteDecoherence isn't the problem. I don't know what makes you think so.
DeleteComplete layperson here. Wondering if this has anything to do with an article that intrigued me, saying “measurement” could be equated to progressively greater levels of entanglement causing decoherence. This seems to me to make wave function collapse/discontinuity a natural process rather than something spooky.
ReplyDeleteNo, decoherence does not solve the measurement problem. As I wrote, you still need to update your probability to 100%. Decoherence cannot do that for you. It's not just that we don't know how it works, we know it cannot work.
DeleteProf Sabine,
DeleteWhy is it necessary to update the probability to 100%?
Consider us making measurement X and then Y, yielding x1 and x2, y. Isn't / sufficient to get the correct probabilities?
As in, probabilities in QT could well be just "This measurement result's probability RELATIVE to that initial branch"
(Obviously, the scheme is easier to implement in density operators.)
If you think that the wave-function describes reality, you need to update it because that's what we observe. If you think it does not, please read my comments about Psi-epistemic approaches.
DeleteProf Sabine,
DeleteWithin my above comment I did explain how we could work with _wavefunctions in agreement with observation_ and not need to update the full wavefunction. To ease the conversation I fuller flesh it out below.
Yes, I think the wavefunction describes reality.
I am specifically asking you why it is necessary for updating in order to agree with "that's what we observe".
The scheme I am proposing is this:
Assuming that the initial, pre-measurement, state is
|X,Y>
= n1 ( c1a |x1,a> + c1b |x1,b> )
+ n2 ( c2a |x2,b> + c2b |x2,b> )
When we measure X, we get
x1 with prob n1^2 and
x2 with prob n2^2
When we next measure Y
*the branch that measured x1 gets
a with prob (n1 c1a)^2 / n1^2 = c1a^2
b with prob (n1 c1b)^2 / n1^2 = c1b^2
*the branch that measured x2 gets
a with prob (n2 c2a)^2 / n2^2 = c2a^2
b with prob (n2 c2b)^2 / n2^2 = c2b^2
You can see for yourself that it is trivial within this scheme that the relative probabilities are exactly the same as Copenhagen predictions.
What is definition? The root meaning of that word is "to set the bounds to". What is a program? It is a pattern of functioning, that translates everything according to the pattern. What is that defines? It is a program that defines, sets the bounds to, according to the program or the pattern. The program is the frame of reference according to which things are interpreted. The fly is a biological program, right, just as the human is a biological program, right. So, there is the fly-program and the human-program, and there is a thing, which according to humans is rotten. The same thing smells attractive to the fly-program but offensive to the human-program. The thing is "really" offensive to the human beings, and the same thing is "really" attractive to flies. That is a fact, a reality. Now, my question is how can the same thing present two different realities: attraction and offensiveness? Therefore, is the thing really attractive or offensive? Where is the attraction or offence? Is the attraction or offence in "the thing" or in "the program"? Please answer this question.
ReplyDeleteIf the root meaning of the word is what you say it is, have you ever considered that the etymology of the word is no longer relevant to the actual meaning of the word today? I love etymology, but this can sometimes happen.
DeleteWhat does it mean to assert that "program" defines? Pushing problems back often does not succeed in anything other than creating more problems.
You don't have to go so far to make one reality consisting of attraction and offensiveness. Stalkers exist in our world. There is no theoretical troubles with one reality having those parts.
Now I see that you dont see. But why dont you see? Your programming, your conditioning, which is the observer, interferes with observation, and you miss the catch. Psychologically, the observer is prejudice or bias.
DeleteYour prejudice, you bias stalks you like your shadow.
DeleteLet me be nice to the impressionable young minds that are reading.
DeleteGokul's last two comments ended the conversation, because such moralistic proclamations are do not contain logical arguments to persuade a different view.
No scientist should be using these kinds of peer pressure tactics. If they have a point to say, they will give a logical argument, and you can either be persuaded by the correctness of the argument, or point out where the mistake is, or discover that the premises are different and see if it makes sense to agree to disagree, or that one side's premise is wrong.
The more fundamental theory than Copenhagen interpretation and wave-function is the theory of probability in math. A thought experiment: There’s a coin in one of my closed hands. You don’t know where it is. Using the theory of probability, you assign P = 0.5 that it is in my right or left hand. I know it is in my left hand. So to me, the probabilities are left P = 1 and right P = 0
ReplyDeleteWhen I open my hands and you see the coin in my left hand, your probability turns from P = 0.5 to left P = 1. Imagine the coin is a subatomic particle. This is the measurement problem or “collapse of the wave-function.” In probability theory, it is simply your transition from uncertainty to certainty. This is consistent with the Psi-epistemic interpretation but inconsistent with Psi-ontic.
Now imagine the coin emits radio waves. Before I open my hands, you can detect the radio waves and infer that the waves near my left hand are stronger than near my right hand. Using this information, you adjust the probabilities to left P > 0.5 and right P < 0.5
The radio waves are real. You can pass the waves through two holes and produce an interference pattern. And they are also a measure of probability. The stronger the waves, the higher the probability. This sounds like Born’s probability waves. It’s not a wave-particle but literally wave and particle. This sounds like De Broglie-Bohm’s pilot wave theory.
I’m not saying this is correct. I’m saying physicists should think out of the box. The Copenhagen interpretation is not gospel truth. We don’t discover theories, we invent them.
One reason why quantum theory is so shocking, is that it showed that classical logic, and hence classical probability theory, is not the one used by our universe. The resulting quantum probability theory is quite fun and, on hindsight, better corroborates reality.
DeleteYou should learn a lot more about physics before trying to tell physicists to think out of the box, when in fact your suggestion is the first few things tried.
There is no General Rule that says the correct theory must be nonsensical and inconsistent. Theories are invented to explain observations. Different theories or interpretations could explain the same set of observations. If quantum theory is nonsensical and inconsistent, it's quite possible theorists just don't know what they're talking about. But they always blame nature for it.
DeleteYou should unlearn what you learned in school. Start by formulating a realistic theory that violates Bell's inequality (as I did). Bell himself said, what Bell's theorem has proved is our lack of imagination.
The opposite is true.
DeleteThere is a general rule that forbids theories to be inconsistent. We literally do not even consider attempts that are shown to be inconsistent. We kill theories, like Phlogiston, when we discover that they are inconsistent.
Quantum theory is perfectly logical and consistent. It is also correct, at least for now. The standard interpretation of quantum theory is woeful, and we are complaining about that.
Maybe you should learn about what is known, before attacking strawmen.
We can stand on the same side attacking Copenhagen. But your criticisms of quantum theory puts you in the anti-science camp. I highly doubt you should feel comfortable there.
An instant wave function collapse and a real (Psi-ontic) wave function would be a contradiction of special relativity. This not a problem of quantum mechanics, it is a problem of the interpretation.
ReplyDeleteThe many-world interpretation solves all these contradictions. There is no wave function collapse, everything is deterministic and there is no measurement problem.
The many worlds interpretation replaces the measurement postulate by postulate about what constitutes a detector. This doesn't solve any problem, it merely renames it. If you do not understand what I say, please write down a definition for "detector" in many worlds.
DeleteProf Sabine,
DeleteI was of the impression that any environment, be it even as simple as one QHO that is just contrived nicely to act as a detector (i.e. don't pick one incapable of absorbing the photon coming out), is sufficient?
As such, it is typically not written anywhere except the basic detector bits of the Cartesian product wavefunction.
Would be very happy if you can link me something if I am wrong.
What is the main objection to the stochastic interpretation of QM, other than non-locality?
DeleteIn case you mean that pretty much any environment causes decoherence, that's right. But mostly we talk about detectors because we care about what we get when we measure something.
DeleteNo, that's not what I meant, apologies. I was simply wondering why stochastic electrodynamics isn't more popular as an interpretation of QED, because the vacuum seems to make for a nice pilot wave.
DeleteSabine,
ReplyDeleteTo avoid the wave collapse: Aside from the generalized Schrodinger Eq and Schwinger's Quantum Action that I gave above (which gives each particle its own wavefunction), you also need to slightly reinterpret Schwinger's Quantum Action Principle by allowing that the states are complex, not just real. This lets you define phase-space wavefunctions (which is impossible in real phase-space, but possible in complex phase-space), which you can propagate forward with the Feyman Path Integral over phase space. Once you have the phase-space wavefunctions, we can go another step and construct stochastic dynamics consistent with the wavefunction via the Differential Monte Carlo Markov Chain with
Prob(dx, dp | x, p, t, dt) proportional-to Prob(x + dx, p + dp | t + dt), which is calculated from psi(x,p;t) as |psi(x+dx, p+dp; t+dt)|^2
Since we in phase-space instead of either position or momentum space, measurements now update the wavefunction in a manner consistent with the above trajectories and without wavefunction collapse.
In short:
DeletePick up your pencil and start thinking about complex wave functions, differential monte carlo markov chains, and systems of PDEs instead of just 1 PDE.
Unless... that is... you're not determined.
DeleteIndividual quantum measurement outcome numbers can’t be predicted by the Schrödinger equation, but the number outcomes from ordinary measurements can be predicted by the equations of physics.
ReplyDeleteShouldn’t we first ask why the numbers change at all? Presumably, the equations of physics merely represent relationships between variables. Presumably, the equations of physics do not represent engines which produce number change in the variables, and then process this number change.
So, maybe the scope of the problem is: 1) why do any numbers ever change; and 2) what do numbers represent anyway?
Hi Lorraine,
DeleteI think that you have things about right in general, though let me propose something about “numbers” as well. I don’t consider them to “exist out there”, but rather only as a product of a conscious mind that happens to think them. We naturalists believe that only causal dynamics “exist out there”, and numbers ain’t that! So 1) numbers will only change when a given conscious entity perceives such a change, though in the real world there will simply be causal dynamics — no numbers and thus there can be no change in what doesn’t even exist. And 2) numbers represent quantities perceived by the conscious entity.
Some day we should have a community of professionals which is able to straighten this sort of thing out. Thus platonists like Max Tegmark should find themselves outside the main scientific community, and I think to its betterment.
Philosopher Eric,
DeleteI agree that numbers as such don’t exist “out there”. But they surely represent something definite that exists “out there” that our minds have picked up via making a measurement. Maybe numbers represent another level of relationship, on top of the law of nature relationships, which also represent something definite that exists “out there”: i.e. the world is literally built out of them.
Anyway, both the quantum measurement case and the ordinary measurement case are about similar things (numbers) that have moved to a new value. The equations of physics take one type of number change for granted, but physics is puzzled by the other type of number change. But surely, both types of number change are linked.
How about this Lorraine. Does “seven-ness” exist any more absolutely than “Lorraine-ness”? I for one don’t think so. I consider all of our terms to exist as mere epistemic constructs. And even “causality” should be such a construct. It could even be that instead “God plays dice”. If I believed that then it would be effective to call me a “supernaturalist”, or yet another human construct.
DeleteQuantum strangeness either exists because our models do not effectively represent what’s going on, or rather because causality itself fails. Thus a person can either be a modest naturalist like Einstein, or an arrogant supernaturalist like his critics.
Philosopher Eric,
DeleteThat’s making a big assumption to assume that such things as “sevenness” or “Lorraineness” exist.
With the qualification that “seven” merely represents something that exists, “seven” doesn’t have an independent existence: it applies to a variable which in turn represents e.g. relative mass or relative position, or even number of sheep in a paddock. On the other hand I, Lorraine, do (temporarily in the scheme of things) have an independent existence. The words “the sixth great species extinction” and “climate change” are not “mere epistemic constructs”: they are deliberately constructed symbolic representations which we use to communicate information about the world, including our inner world.
With the qualification that words and sentences are deliberately constructed symbolic representations that we (we, who really exist) use to communicate information about the world, we are trying to clarify any structure that might underlie “quantum strangeness” and “causality”.
Lorraine and Eric are close to what I have been talking. The observer defines the reality, the number or whatever you want to call it. Superposition is a fuzzy reality, not well defined, the moment you introduce an observer by way of a detector, the observer "refines" the definition or the superposition, the fuzziness disappears and the wave function collapses. Now what constitutes the observer? What is the observer? The observer is a program, a hardware program. And it is this hardware program or rather the influence of this hardware program that refines the fuzzy definition or the superposition into a better definition or a single possibility and the wave function collapses.
DeleteThe act of measurement is the influence of the observer or the hardware program. There is measurement when the program runs.
DeleteWell said Lorraine. Personally I’m a great fan of Rene Descartes. “I” am the only element of Reality that I can ever know exists with perfect certainty. All else may effectively be termed “belief”. If you exist then you could say the same about yourself, not that you could ever “prove” to me that you or anything else exist. So that’s all I meant by “mere epistemic constructs”. To me “seven” and “Lorraine” seem like useful terms given my beliefs, though it’s all just epistemology. Some refer to this position as “radical skepticism”. To me it’s simply being appropriately modest.
DeleteWanting to understand the measurement, the best way is to study its idealization: Stern-Gerlach experiment.
ReplyDeleteWe experimentally know that in strong magnetic field particles with spin prefer parallel or anti-parallel alignment.
It can be understood from energy perspective: magnetic dipoles precess in magnetic field until parallel or anti-parallel.
So starting with a random spin direction, in strong magnetic field it has tendency to release abundant energy (as EM radiation) - leading to parallel or anti-parallel alignement.
There is no magic in measurement - just deexcitation to a lowest energy state, non-unique in this case.
Being instant (against e.g. SR) is just one of idealizations of quantum formalism - experiment is slowly reaching this time resolution, for example already showing for photoemission that it is not in fact instant, but take e.g. 20 attoseconds: https://science.sciencemag.org/content/328/5986/1658
What you say here does not explain how a superposition turns into only one result. It misses the entire point of the discussion.
DeleteStern-Gerlach has also analogue of superposition, e.g. performing second one rotated 90 degrees, we can see intermediate beam as 1/2-1/2 superposition.
DeleteThe problem is being able to obtain probabilities e.g. violating Bell inequalities, due to squares of Born rules, like in Malus law.
To understand this possibility, we need to accept time/CPT symmetry of our physics (e.g. Lagrangian mechanics): replacing time-asymmetric "local realism" with time-symmetric one: like e.g. Feynman's path ensembles.
Considering the simplest: uniform path ensemble ( https://en.wikipedia.org/wiki/Maximal_Entropy_Random_Walk ), we also get the squares (one psi from past, second from future like in two state vector formalism) and can violate Bell-like inequalities.
I am myself preferring time-symmetric transactional interpretation as you are describing.
DeleteBut you have not made sense of the complaint I raised. By your original comment, why would a 1/2-1/2 superposition give up half the time, down half the time, as opposed to smear into both all the time? Or any other possibility.
Until you do that, you have missed the entire point of the discussion.
Hey... Schrödinger equation is not compatible with Special Relativity
ReplyDeleteRead comments above, I have already explained this twice.
DeletePeter Shor's solution (1:47 PM, August 13, 2019):
ReplyDelete"to find a way to train our intuitions so that we can think about quantum mechanics without hurting our brains"
I think this is probably right.
"quantum theory is the science of preparing systems in one state and detecting them in another state; everything that happens in between is philosophy"
- https://ndpr.nd.edu/news/philosophy-of-physics-quantum-theory/
I suppose if some day some sort of little gremlins were discovered that made up the quantum substrate, then there would be science.
Philip,
DeleteAs I have explained, this is throwing out reductionism.
Philip,
DeleteI agree with Sabine here. The "shut up and calculate" approach is entirely unsatisfactory for many reasons. For one thing, it gives up any hope of intuition.
Perhaps some downward (and backward) causation is what is needed.
DeleteYou say it's throwing out reductionism but I don't see how it is. It's just interpreting in a particular way certain facts about / consequences of the theory which reductionism has brought us to so far. Knowledge is referred to in a psi-epistemic "QM is QPT plus mechanics" interp. simply because it's a probabilistic theory and, unlike a classical theory, probability can't be 'in principle'-exorcised from it. As a fan of [super]determinism you may find that unsatisfactory but calling it an abandonment of reductionism seems like something Maudlin would say.
DeletePaul,
DeleteI already explained why that is. What is it that you do not understand about my explanation? For all we presently know "knowledge" isn't fundamental but emergent. There is no definition of "knowledge" in terms of quarks and gluons etc. If you want to make "knowledge" primary you are saying it cannot be derived, which is a break with reductionism. You now have to tell me where and why reductionism stops working and how that is compatible with our observations.
Neo-Copenhagenists simply refuse to even acknowledge the problem, but that doesn't make it go away.
I don't understand why you say it's a break with reductionism. Presumably, we're talking about theory reductionism here. So QM is a theory and it's the result of reductionism taken as far as we've been able to take it so far. Its psi-epistemic interpretation is a break with "representationalism" rather than reductionism.
DeleteNeo-Copenhagenists just don't have the metaphysical distaste for non-representational theories that others seem to have. To them - us - "the essence of QM is that it forces us to take an intrinsically probabilistic view of the world", as Tom Banks put it.
As for my intuition, the only "gremlins" I have ever had in mind are those in path integrals.
Delete"The ultimate vision of those who take path integral quantum theory as fundamental to all of physics is a path integral formulation of quantum gravity and quantum cosmology."
Path Integrals and Reality
Adrian Kent
- https://arxiv.org/pdf/1305.6565.pdf
Sabine,
DeleteI think we could use a psi-epistemic approach without contradicting reductionism. We can define "knowledge" as those physical parameters that are measured, or can in principle be measured in a certain experiment. For example, in a two-slit experiment placing detectors at the slits will result in a which-path measurement result. This is a fundamental property of the system (position of an electron relative to the slitted barrier) that is in principle describable in terms of electrons and quarks. We may also say that the measurement result represents "our knowledge" about the system but, if you want, you may avoid using such a formulation.
In the theory of stochastic electrodynamics the electron does take a well-defined path during a two-slit experiment even when an interference pattern is produced. But we cannot measure that path because placing detectors at the slits will change the pattern because of e-m interactions. So, the wave-function will reflect this inability to perform a which-path measurement. By analogy with classical statistical mechanics we can say that the probabilistic description offered to us by the wave-function reflects our lack of knowledge about the true state of the system. But, just like in the case of classical statistical mechanics we do not need to conclude that we have to deny reductionism.
"Knowledge" is the observer. The observer interprets, describes or defines according to his or its knowledge.
DeleteThis looks like an interesting place to have discussions about this. If you get into the specifics of quantum field theory (operators on Fock spaces, the need for renormalization / regularization etc.), you can see it's JUST a model. It's like saying the sun is a sphere. Sure, it's sort of a sphere but there's much more to it than that when you zoom in. "Particles" correspond to normal modes in some kind of structure. If it's spin 1, you can have how many of these waves on top of each other as you wish. If it's 1/2 spin, you either have that mode or you don't.
ReplyDeleteWhy don't physicists say: "we just don't know?"
Physicists are very happy, and often say, that we don't know.
DeleteBut often it is the case that we do know something, and hence cannot truthfully say we don't know.
Your disembodied multiple comments make no sense.
You are zooming into only layers of abstractions (or complications).
DeleteObservation.
ReplyDelete"I" am the only being I can have confidence has observed events. I am only aware of the observations of others because I have observed accounts of their observations.
Observation feels definite. Maybe that is because consciousness only exists as multidimensional slices through a greater hyperdimensional space, which can no more be experienced in its entirety than our eyes can see all wavelengths of the EM spectrum.
Yep, many-worlds. This hypothesis can ultimately be tested when my consciousness persists beyond the falsifiable limit of chance we apply to particle collider observations.
See you in 2091.
Rather than consiousness we can use the word observer.
DeleteHow can the Schrödinger equation tell us the “state” of the system (“determinism”) AND not predict any outcome even theoretically? And how is “determinism” reconciled with the incompatibility between “the measurement problem” and the Schrödinger equation?
ReplyDelete“No. The wave function does not describe a state of the particle [system]. It describes our knowledge of what the result of a measurement would be if we were to carry out a measurement.”
The state of a system under quantum theory does not include all possible classical information. It includes all possible quantum information, which is a little less.
DeleteWe can predict from Schroedinger's equation that a system that started out in an energy eigenstate will always, exactly, stay in the same energy eigenstate. The probability is 1, is perfect. So, your first question is already a mistake.
The experimental tests of Bell's theorem mean that it is not human ignorance. It is that Nature Herself does not know in advance.
I read all the posts and replies carefully, and I learnt a lot. Thank you.
ReplyDeleteThe observer defines reality. In the absence of an observer there is only the thing; the thing takes on a meaning only when we introduce the observer; different observers give different meanings to the same thing. Each meaning is a reality. Then what is reality? The meaning an observer gives to a thing by his or its own virtue. What is actuality? The thing, I am putting it very simply. It is "a" thing separate from other things as long as there is an observer. Remove the observer and there are no separate things, it is just "one" thing. We said in the beginning of this post that the observer defines reality. To put it shortly, the observer "defines". Then Sirs! In the absence of the observer, if there is "one" thing, isn't that thing "undefined". Because there is no observer who defines, right. The undefined is the actuality.
So let us start with "the undefined". Let us introduce the most simple observer. This observer will abstract a reality, a definition out of the undefined. The moment the observer abstracts, the actuality is broken or fragmented. The definition as opposed to the rest of the undefined. We now complicate the "most" simple observer i.e., make it more complex and turn it into a simple observer. The "definition" improves. If you go on complicating the observer, the abstraction becomes more and more well defined; the definition becomes increasingly well defined. Ultimately, we land up with the human observer who is the most complicated or complex observer. Then the definition of the abstraction, or simply the definition is the most well defined. Let us say this is the ultimate reality or the best reality so far.
Now, working backwards: we undo the complication layer by layer. Then the definition begins to decrease....and once I have undone the least complicated observer i.e., removed the observer altogether there is "the undefined". Rather than say reductionism breaks down, we can say when we completely undo the observer there is "the undefined".
The observer is a quantum system. So none of what you said there is going to work.
DeleteSuperposition is the least possible definition; thereafter it is only the undefined. The detector is the observer that abstracts a definition out of the superposition and collapses the wave function.
ReplyDeleteHi Sabine,
ReplyDeleteI think your article here is the simplest/clearest explanation of the "measurement problem" that I've ever seen. Thank you for that.
Now, I've for a long time thought that Carlo Rovelli's Relational QM has a lot of merit, but if I understand your blog post here correctly, I think you would take issue with: https://arxiv.org/abs/quant-ph/9609002
Rovelli argues that the measurement problem is not a real problem, because it pre-supposes that observer independent physical states are real. The main assumption that leads to the measurement problem according to Rovelli is:
"the notion of true, universal, observer-independent description of the state of the world. If the notion of observer-independent description of the world is unphysical, a complete description of the world is exhausted by the relevant information that systems have about each other. Namely, there is neither an absolute state of the system, nor absolute properties that the system has at a certain time. Physics is fully relational, not just as far as the notions of rest and motion are considered, but with respect to all physical quantities." ^ Rovelli
I guess this falls into your criticism of psi-epistemic interpretations.
Yes, it does. I wrote about Rovelli's relational approach here.
DeleteProf Hossenfelder I read your write up on Carlo Rovelli's Relational QM, and it looks like I have not been talking nonsense in your blog.
DeleteSabine Hossenfelder is right regarding the Copenhagen interpretation. I was a witness of a discussion involving Heisenberg and von Weizsaecker at the Max Planck Institute in Goettingen regarding the meaning of the Copenhagen interpretation. While von Weizsaecker was a strong defender of the Copenhagen Interpretation, Heisenberg had a different take, contained in his book Physics and Philosophy: His opinion was that unless the experiments force us, we are unlikely to give up the simple calculation scheme of quantum mechanics. Besides Einstein the most famous dissidents were Schroedinger and Feynman. It was stated that because of his prestige by his Bohr model done in his youth, Bohr brainwashed a whole generation of physicists with his "Copenhagen Interpretation".A clue to the mystery of quantum mechanics is contained at the end of Einstein's 1916 paper on gravitational waves, where he remarks that atoms should emit gravitational waves, even at a very small rate, whereby matter would become unstable.In a paper I had published in Z. Naturforsch. 71(2016), 53-57, I got a clue for a possible solution by Schroedinger's famous "Zitterbewegung" papers in the Berl Ber.1930-1931. Schroedinger wanted to understand the Dirac equation, and what he found was that a Dirac particle oscillated rapidly,which according to the work by Hoenl, Papapetrou and Bopp,can be understood that a Dirac particle is composed of a mass pole with a superimposed mass dipole, as a pole dipole particle. But because the computed positive and negative masses making up the dipole were very large and = 3.31x10^11 GeV, their oscillation must lead to the Watt-Less emission of short wavelength gravitational waves, as Einstein had anticipated, and as I had shown could explain the quantum potential in Madelung's transformation of the Schroedinger equation.
ReplyDeleteI have recently discovered a particularly simple explanation for Zitterbewegung under the assumptions that: 1) Electrons are classical objects with a finite size, on the order of their Compton's wavelength (no contradiction with experiment....) and 2) The Dirac wave-function encodes the properties of an ENSEMBLE of electronic solutions (different electrons or a single one at different epochs, as in the H atom). It can then easily be shown that the Dirac equation consistently describes the wave-function only when the latter is localized on scales much larger than the (Compton-) size of an electron. And indeed, Zitterbewegung `comes to life' only when this condition is violated, meaning that it is an artifact of misusing Dirac's equation.
DeletearXiv:1804.00509 [quant-ph]
Sabine, I saw a quote by Einstein in a video online (I'm trying to find it again so I can reference it, but you know how that goes). It is not that quantum mechanics is 'incomplete'. But that quantum mechanics is a 'limiting case' of another, deeper theory. That seems right-on to me. We have the measurement problem. We have the totally unclear relationship(s) between the quantum state and an ontological state. We have only very contrived 'interpretations' of qm. We calculate by series expansions that are known not to converge (WTF?).
ReplyDeleteIt seems clear that we haven't understood something fundamental. Do you agree?
Are there any experiments, even in-principle experiments, which could help resolve the quantum measurement problem? I may have missed it, but the blogpost is devoid of any mention of anything like this.
ReplyDeleteIf so, what are they, and how might they help with resolution?
If not, how - in key aspects - does this problem differ from wondering how many angels can dance on the head of a pin?
Yes, there are. Basically, if you reduce noise sufficiently much you should see correlations in measurement outcomes that, according to quantum mechanics, should not exist. This requires to minituarize the experiment as much as possible, keep it cool, and repeat measurements as quickly as possible. Unfortunately, no one wants to do such an experiment. They prefer to do the same Bell-type tests over and over again.
DeleteThanks Sabine.
DeleteThose requirements seem somewhat similar to some efforts to create an NISQ (Noisy Intermediate-Scale Quantum) computer. Perhaps someone will be motivated to borrow some of those technologies to perform the sort of experiment you describe.
JeanTate,
DeleteYes, that's a very good point. I have actually thought about this. However, the problem is that no existing approach to quantum computing relies on repeated measurements under near identical setting. Instead, it's basically all about not measuring the system (until the calculation is done).
Even though I loathe special relativity and love instantaneous mathematical interaction without a cosmic speed limit, I still need to be non-believing in the popular interpretation of the Bell tests and that it supposedly violates locality and proves entanglement at great distances.
ReplyDeleteThe reason is simple. In a Bell test of two entangled particles having opposite spin: Two parallell detectors will give 100% opposite spin reading, which means that the spin is 100% correlated in one dimension. Two perpendicular detectors will give 50% opposite spin reading, meaning that the spin is 0% correlated in two perpendicular dimensions. Now the big fans of "spooky action" entanglement love the result of two detectors having a 45 degree angle between the detectors, because this gives an opposite spin 85% of the time, meaning that there is a 70% correlation between these two "half way" dimensions. According to normal linear summation of probabilities there should have been a 50% correlation at 45 degree angle, and not a 70% correlation, which in turn creates an impression of violated locality through Bell's inequality. But this is a strange way of interpreting this QM phenomena. When we modulate between two dimensions in a circle, we do not have a linearly changing property, but a sinusoidal changing property. The cosine of 45 degrees is not 0.5 (50%) but 0.7 (70%), meaning that these two detectors have 70% correlated properties in one dimension, which gives 85% opposite spin. That is simple mathematics which in turn opposes the assumption of broken locality.
For some reason QM communities from ancient times believe that the 45 degrees between detectors should give only a 50% correlation of spin properties, but simple mathematics indicate that a 45 degree angle in a circle represents 70% correlation of value in one dimension. The fact that we can send polarized light into a perpendicular configuration by using several intermediate polarization filters would rather be a strong argument for locality and not against. After all, by strictly local interaction we can assume the polarized light having changed properties after passing each filter.
Entanglement might be an illusion. So where is this hidden information about the states of entangled particles? Angular momentum is a quality that can be carried by a moving constituent of energy without representing the directional momentum of the particle. Angular momentum changes between two perpendicular dimensions as a sinusoidal modulation.
Love your articles, Sabine
Many people still consider "incompleteness" as something very weird and rare, in many cases as a result of a language trickery or self reference; but "how common is incompleteness and unprovability?"
ReplyDeleteIn Peano Arithmetic and similar systems independent/irreducible/unprovable statements are pervasive, they are "corare" in a topological sense. They are as pervasive as irrational numbers are in the set of Real numbers.
As Chaitin said: “What is the meaning of Godel for daily work in
mathematics?. . . How common is incompleteness and unprovability? Is
it a very bizarre pathological case, or is it pervasive and quite common?
Because if it is, perhaps we should be doing mathematics quite differently.” These results show that unprovability is a common phenomenon.
(https://www.cs.auckland.ac.nz/~cristian/crispapers/independ_exception.pdf)
In view of these results from Information Complexity Theory it seems that the standard approach used by theoretical physicists of assuming that a few fundamental principles are enough(complete) to fully describe Reality is a wishful and narrow approach: the presence of irreducible/strong emergent properties should be expected, Reductionism is intrinsically limited.
The obsession to "reduce" everything to "basic principles" ignores the potential presence of irreducible/strong emergent properties leading to unnecessary obfuscation and dead-ends.
These results in formal Mathematics also reinforce the scientific method: Nothing can replace the constant observation and testing of Reality since its irreducible properties can't be predicted; serendipity discoveries always will be waiting for people not blinded by dogmatism and orthodoxy.
I should know better than to try this, but hey, I'll do it. My impression is that the "detector" in many worlds is anything that produces some definite value in any evolving wave function, anywhere. And every time this happens, there is a branch into yet another of the many worlds. Let us say in other words that any interaction that creates some definite state in any system, (neutron star, chemical process, gas cloud, whatever) is equivalent to an experimenter in his/her laboratory making a measurement. Another way to fame this would be in terms of intersecting world lines, events in the GR sense. I've been looking at new work on De Broglie's ideas and David Bohm's. Some correspondence there to many worlds, with the interesting idea that these other worlds are populated by "sterile" wave functions-- universes with no content. There is even some suggestion in some of this work that the presence of these divergent universes could be detected. This is what I got out of reading a long wikipedia article on the subject of pilot wave theories. They seem to be getting respectable in some quarters, and some have extended the ideas to be compatible with Special Relativity. I've ordered some texts and books on the subject. May they serve me well...
ReplyDeleteThere is a similar issue with classical electrodynamics. The field theory alone is useless. You need to add to it the Lorentz dynamics (energy-momentum in the field). Since the machinery for this doesn't strictly work with the idea of energy-momentum as it lives in classical mechanics, an inconsistency sets up and demands a resolution. That resolution has in fact never been provided. The situation is improved in QED but not resolved. (Most obvious symptom - infinite energy density around a point charge.)
ReplyDeleteAll these things were once the subject of intense discussion. Most of it came to an abrupt halt in the "shut up and calculate" era.
-drl
Philosophically, the undefined is "it". "It" is indescribable, because the moment you describe "it", "it" is no longer "it", "it" is "you". This is because "you" are a "program". So, "the observer is the observed" J Krishnamurti
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteI was just wondering after all that talk about definition, reality, actuality whether gravity is emergent, I dont know, I am just wondering aloud.
ReplyDeleteThe interlocking and beautiful harmony of the symbols you all manipulate convince your amazingly capable minds that the scene they portray is one in tune with reality.
ReplyDeleteMy simple little mind looks on in stunned horror, and with some admiration of your abilities, while all of you play this clever game comprising puzzles lacking any hope of resolution.
In the words of one of the finest minds among us, a most eminent manipulator of symbols, you are all truly 'Lost in Math'.
Sadly, seduced by the beauty Sabine so accurately exposes as leading you astray, you press on with your futile argument.
Even those aware of the cage in which they dwell seem completely unable to engineer their escape.
Such sharp minds – honed to a fine edge – then wasted on dissecting phantoms.
Philosophy means love for wisdom or love for learning. To know that you dont know, and to know that the known can prevent further knowing is the beginning of learning. If you did not know that you did not know will you make an attempt to know? What is the known? "The observer". "The whole movement of life is learning". Is evolution possible without learning. "The observer" obstructs observation, interferes with observation. Observation does not guarantee discovery but there can be no discovery without observation. Here, we are all learning.
DeleteI more or less agree with your conclusion, Agnosco Ignis, but for a different reason.
DeleteWith one or two exceptions (OK, maybe three), none of the >150 comments to this blogpost discuss experiments, as in experiments whose results might help resolve the measurement problem.
I find this very puzzling.
Surely the very first thing a scientist would do (after clearly defining the problem) is try to think how the problem could be resolved, even if only in principle, by experiment.
The wavefunction squared is a probability function, modelling what we know about a system. If you do a measurement you obtain information about the system and you have to update the function. That's no different than for a classical system. Take for instance the Monthy Hall problem. Once you are told that a goat is behind a certain door your initial probability function collapses to a new one. So why then does nobody have a problem with the "collapse of the goat probability function" in this case?
ReplyDeleteMarkusM,
DeleteI totally agree with you. It is a wonder to me why some people have problems with QM. It seems to me that they are trying to inject some classical mechanics in the game.
They end up with bizarre "superluminal actions", "hidden variables", “non-local things” or other unnecessary, superfluous, ugly and potentially wrong stuff.
MarkusM,
DeleteCan you please describe what do you thing happens in an EPR experiment without any reference to hidden variables? What is your local explanation of the observed results?
Whenever I see an opportunity to bring in the "observer" or the "observer effect" I go ahead and do it; whether it be philosophy, psychology or Quantum Mechanics. Please dont misunderstand me.
ReplyDeleteSabine,
ReplyDeleteI take it that you are arguing that QM needs extension to remove the measurement contradictions and to take into account a physical theory associated with Measurement.
My question is where you think that this "extension" might arise from. As you will know, Penrose has an extension directly related to Gravitation (still to be tested). Do you see Gravitation (you remark on the contradiction with GR) as the source of this extension?
Other possibilities might be:
(1) Information style extensions of QM;
and/or
(2) Reformulations of the QM Mathematics, adding new axioms;
and/or
(3) New physics.
The problem exists. Particle physicists have a severe and problematic issue. It's called HIGGS (which stands for Highly Insane Great Gullibility Stress).
ReplyDeleteSabine,
ReplyDeleteLast comment from me. The original Aspect experiments involved the creation of circularly polarised photons which, through conservation of angular momentum, were entangled in opposite left-circular and right-circular states. But they measured the correlation between the photons' linear polarization states, rotating one polarizer with respect to the other.
Of course this is no problem as far as the formalism is concerned. We change the basis using the different projection amplitudes for left-vertical, left-horizontal, right-vertical, right-horizontal and vice versa. What we get is a superposition of entangled linearly polarized photons.
Where do the projection amplitudes come from and what do they represent? You might want to argue that real photons in real circularly polarized states are somehow also intrinsically linearly polarized, but it's difficult to do this without invoking some kind of local hidden variable or variables, which were actually ruled out by the Aspect experiments, and all others since.
Alternatively, the projection amplitudes simply summarise what we know about the behaviour of photons from long experience with Malus' law, and fiddling about with circularly polarized light and some quarter wave-plates.
You can still bring that back to a 'measurement problem' if you want to, but my question isn't actually about measurement per se. What do you think we're doing when we change the basis of the wavefunction?
The singlet state of two spins |ψ⟩=|↑⟩|↓⟩−|↓⟩|↑⟩/√2 is first prepared and then evolves from the time and place where photons were in contact (locality).
DeleteWhen measuring, we get +1/2 or -1/2 whatever the choice of the projection axis is.
The anti-correlation is conserved and was there since the beginning.
There is no measurement problem.
isometric,
DeleteThe state is not a local object, its evolution does not take place in space-time.
Your explanation is not local.
If we assume superdeterminism i.e. distance parity or whatever, we can limit the problem to a local one as opposite phases of state to measure - it's purely entanglement phenomenom. If particles bounce in two steps; between matter and antimatter i.e. there is no solid argument to consider which is which (matter or antimatter), only the spacetime continuum consisting the measuring device itself can define relations...
ReplyDeleteAbout Higgs strangeness: why exactly (10 + 10)² / 3 times proton mass?
Prejudice, bias, ideology, dogma, religion and scientific orthodoxy are all software observers; whereas, the detector in QM, the fly and the human in biology are all hardware observers.
ReplyDeleteSabine,
ReplyDeletethank you for your well understandable explanations to QM, the Schrödinger equation and the breakdown of it and the string theory.
Now I understand even better why I do not like the break down of the wave function and the string theory. But do you know why Schrödinger is incorrect? The wave length of a particle deduced from its momentum is incorrect (follows from an incorrect understanding of SR). Easily visible: Assume an electron in motion which has a momentum and - according to de Broglie - a wave length which can cause an interference pattern at a double slit. Now assume an observer who moves with the electron. In the frame of this observer the momentum is =0 and so the wavelength is infinite. And so there cannot be an interference pattern. But in reality there is of course one.
Why does no one notice this?
In the rest frame the wave-length isn't infinite, it is given by the (inverse of the) mass.
DeleteLet us start with a superposition of 100% fuzziness of definition; then, let us introduce a detector of 100% observer influence. What will happen to the fuzziness of superposition? The Wave function collapses. That is the detector refines the fuzzy definition by 100%. And let us say the fuzziness becomes 0%.
ReplyDeleteLet us reduce the observer influence of the detector to 75%, this refines the fuzziness by 75% and the fuzziness drops to 25%.
Let us now reduce the observer influence to 50%, this refines the fuzziness by 50%. That is the superposition is 50% defined and 50% fuzzy.
What happens when we reduce the observer influence to 0%, the superposition is untouched by the observer, untouched by measurement and the interference pattern returns.
This comment has been removed by the author.
ReplyDelete