Tuesday, May 14, 2019

Quantum Mechanics is wrong. There, I’ve said it.

[Image: needpix.com]

So, you have developed a new theory of quantum mechanics. That is, erm, nice. No, please don’t show it to me. I’m almost certainly too stupid to understand it. You see, I have only a PhD in physics. All that math has certainly screwed up my neural wiring. Yes, I am sorry. But I have a message for you from the depth of abstract math: We know that quantum mechanics is wrong.

Seriously, it’s wrong. It’s as wrong as Newtonian gravity is wrong, as hydrodynamics is wrong, and as spherical cows are wrong. Quantum mechanics is an approximation. It works well in some cases. It does not work well in other cases.

You see, in quantum mechanics we give quantum properties to particles. But we know that, strictly speaking, the interactions between these particles must also have quantum properties. If we give these interactions quantum properties, we call that “second quantization.” It is not used in quantum mechanics. Second quantization results in a larger mathematical framework called “quantum field theory”. The Standard Model of particle physics is a quantum field theory. Sometimes we use the word “quantum theory” to refer to both, quantum mechanics and quantum field theory together.

Moving from quantum mechanics to quantum field theory is more than just a change of name. Quantum field theories inherit many properties from quantum mechanics: Entanglement, uncertainty, the measurement postulate. But they bring new insights – and also new difficulties.

The best known insight brought by quantum field theory is that particles can be created and destroyed, and that each particle has an anti-particle (though some particles are their own anti-particles). Another remarkable consequence of quantum field theory is that the strength of interactions between particles depends on the energy by which one probes the interaction. The strong nuclear force, it turns out, becomes weaker at high energies, an odd behavior that is known as “asymptotic freedom.”

The probably best known difficulty of quantum field theories is that many calculations result in infinity. Infinity, however, is not a very useful prediction. Such results therefore have to be dealt with by a procedure called “renormalization,” whose purpose is to suitably subtract infinity from infinity to get a finite remainder. No, there is nothing wrong with that. It works just fine, thank you.

Quantum field theories lead to other complications. For example, we know how to calculate what happens if two electrons bump into each other and create a bunch of new particles. This is called a “scattering event”. But we don’t know how to calculate what happens if three quarks stick together and form a proton. Well, we do know how to put such calculations on super-computers in an approximation called “lattice QCD”. But really we don’t have good mathematical tools to handle the case. At least not yet.

But let us come back to quantum mechanics. You can use this theory to make predictions for any experiment where the creation and destruction of particles does not play a role. This is the case for all your typical quantum optics experiments, Bell-type tests, quantum cryptography, quantum computing, and so on. It is not merely a matter of doing experiments at low energy, but it also depends on how sensitive you are to the corrections coming from quantum field theory.

So, yes, quantum mechanics is technically wrong. It’s only an approximation to the more complete framework of quantum field theory. But as the statistician George Box summed it up “All models are wrong, but some are useful.” And whatever your misgivings are about quantum mechanics, there is no denying that it is useful. 


  1. Small quibble - you can't really say hydrodynamics is wrong, any more than you can say 'gravity is wrong' (as opposed to 'Newtonian gravity is wrong). You might say, for example, Navier-Stokes is wrong, or an approximation, but hydrodynamics is an area of application, not a theory.

    1. I am referring to hydrodynamics as in the hydrodynamic limit. Besides that, if I write Navier-Stokes, the result is just that no one understands what I say, as you certainly know full well. Aren't you the guy who complained that I refused to explain Special Relativity with lasers and rocket ships?

  2. Aw come on. Quantum Field theory is quantum mechanics. Hydrodynamics is classical mechanics.

    1. CIP,

      As you almost certainly know full well, that's not how we use the word, neither in teaching nor in practice, and it's also not how it's become common use in science writing. Whenever someone speaks of the "foundations of quantum mechanics", they speak about quantum mechanics the way I explained it above, as with a Hamiltonian rather than a Hamiltonian density and a potential rather than an interaction. (Or the respective density in the path integral.)

    2. But one thing that's true is that even 'regular' QM can be expressed in path integral formalism; it's not that outlandish to think that tools that deal with some of its peculiarities (basically everything involving complex amplitudes and interference of competing paths, which is sort of the bread and butter of "quantumness") may in theory be transported then to a quantum field theory framework. With a further layer of complexity, of course, but when has QFT ever been simple anyway?

  3. Slightly off topic, I guess, but question came reading the first lines of this post. Let's say I think I have a brilliant theory that unifies Quantum Mechanics and Generalized Relativity, explains Dark Matter, etc etc. (Don't worry, I don't have any, really!).

    Which would be the magic words you would need to hear before even considering the idea to read the first page of it?


    1. I'd have stopped reading right at "Generalized Relativity".

    2. Bear with me, english is not my first language, I was translating from italian. Let's say General Relativity...

    3. Andrea,

      It is actually a very good question! Currently a claim of any new theory like that would be on par with "I proved that P != NP". That is to say, an out of the blue discovery/proof is very very unlikely, too unlikely to be taken seriously. The best one can hope for would be an incremental advance. It took 25 years to construct Quantum Mechanics from the initial inklings of quantization. QFT took a few more decades to fully flesh out. Relativity only took half as long, thanks to Einstein. The efforts to fit the two into the same framework have been going on ever since, with the best and very motivated minds out there, with very limited success. Anything new would have to open up an entirely new way of thinking about what we already know, explain long-standing puzzles almost as a byproduct, and make new exciting predictions. You can look into the existing credible, yet so far unsuccessful attempts: String theory, Loop Quantum Gravity, even Entropic Gravity.

    4. I generally do not read unsolicited theory proposals sent to me. It's entirely pointless to send them to me. Do not do it. There is no turn of phrase that will change anything about it. The moment you send me your theory you have already disqualified. Because I cannot think of any reason an actual researcher would do that. A real researcher would send their breakthrough insights straight to Ed Witten.

    5. Ed will thank you for that, not!

    6. "Which would be the magic words you would need to hear before even considering the idea to read the first page of it?"

      Maybe "accepted for publication in <insert name of prestigious journal here>"?

    7. Ok, for sure my question was naive, but it wasn't meant to be offensive to all the real scientist doing real research and publishing on peer reviewed journals.

  4. It seems a better framework could be made by "formulating quantum mechanics entirely as a theory of quantal histories, without ever needing to call on state-vectors, measurements, or external agents as fundamental notions."
    -- Rafael Sorkin

  5. "Usefulness" is a good thing. I am not a physicist but I think about such things as well as I can in my simplistic model making world. I find there are ideas which to me seem patently insane and yet are very useful in thinking about problems that interest me. Sometimes the usefulness that emerges out of the crazy ideas that practical thinking eschews is what moves us forward.

  6. Good thanks. But existence of anti-particles is not an "insight" by QFT. Relativistic QM learns that.

    1. One might not be led to QFT, but still accepts/understands anti-particles (by RQM). The point is the emergence of anti-particles is actually at 1st quantization level (although relativistic).

      After all the post was good. Thanks again

  7. So, for someone who learned QM in college but never got to relativistic QM and QFT, can you recommend any self-study materials for these topics?

    1. Kevin,

      Your best choice, I think, would be Anthony Zee's "QFT in a nutshell" and Mandl & Shaw's, which is just called QFT. Bjorken & Drell's "Relativistic Quantum Fields" I have found also really useful to make the step from quantum mechanics to quantum fields, but the book is really out of date and more of historical interest at this point.

    2. … a (0+1)-dimensional quantum field theory is just quantum mechanics as A. Zee sums it up.
      It is an excellent book and contrary to other he starts with the path integral and then connects to second quantization.

  8. Does the problem of how our perceived ordinary "classical" reality emerges from QFT always reduce to how QM reduces to classical reality; or does QFT pose additional conceptual challenges? E.g., does QFT throw some wrinkles into the measurement problem that are not there in QM?

    1. Arun,

      That is a most excellent question. It is one of my frustrations that people who work on the foundations of quantum mechanics never seem to be talking about quantum field theory, even though we know that the full story must be told with QFT. One of the obvious additional challenges that comes with QFT is Lorentz-invariance, which doesn't go together well with collapse models. Roughly speaking I'd say that QFT is more of a challenge for actual modifications, whereas it doesn't do much to interpretations, which remain basically unaffected (for all I know).

    2. Sabine,

      Since you said “… people who work on the foundations of quantum mechanics never seem to be talking about quantum field theory” I remember a comment to you, Tim and Carl , see here (**):
      … how to incorporate QFT (e.g. Lamb shift, Casimir effect) into BM is not yet decided whether it still is deterministic or indeterministic as Roderich Tumulka did, where particle creation in Fock space is a random, a Markov process. QFT is important, because e.g. the electrostatic 1/r, which in non-relativistic BM is just given, is an emergent property (one photon exchange) from QFT.

  9. ""..is that particles can be created and destroyed, ...""

    I always thought that particles are created in matter/antimatter pairs and vanish soon after,
    can one create particles that persist?
    (So that total number of this particles in
    universe is higher afterwards?)

    1. Georg,

      ? Of course you can create particles that persist. Particle number is not a conserved quantity. Every proton-proton collision at the LHC creates a large number of particles from the energy of the collision. What you cannot do is create particles from vacuum. (At least not if space-time is flat. You can if it is curved or expanding, eg near a black hole or in the early universe.)

  10. So quantum field theory is not yet wrong, but quantum mechanics is wrong?

    1. If you understand that "wrong" here means merely it is an approximation that you cannot always use, yes.

  11. “All models are wrong, but some are useful.” And whatever your misgivings are about quantum mechanics, there is no denying that it is useful.

    Sure all models are wrong, especially in the trivial sense that all models are, of necessity, conceptual simplifications of the thing being modeled. But some models are more wrong than others and a more wrong model can be more useful than a less wrong model (cf. Ptolemaic vs Copernican cosmology).

    If you only distinguish between models on the basis of "usefulness" you can easily dismiss a model with potentially more explanatory power than a more "useful" model with little or no explanatory power.

    The ultimate goal of science is to understand the nature of physical reality, isn't it? Surely, the provision of useful calculational tools, for engineering or other purposes, isn't the primary purpose of science, or is it, in your view?

    It seems to me, that this second, transactional view of science cannot be considered the fundamental purpose of science without essentially relegating scientific understanding to an afterthought. The results then look like this:

    ...a procedure called “renormalization,” whose purpose is to suitably subtract infinity from infinity to get a finite remainder. No, there is nothing wrong with that. It works just fine, thank you.

    There is nothing wrong with that if all you want to do is get the right calculational result. However, accepting that approach obscures the failure of QFT to even produce a correct calculation without an ad hoc intervention. That failure means that the QFT model is, itself, a failure, except in a very limited transactional sense.

    QFT has no scientific explanatory power because it is constructed on a metaphysical framework (it's all just fields) that does not correspond to physical reality. QFT does not further scientific understanding any more than the big bang model does. Both models are scientifically inert because neither one resolves to a qualitative model that bears any resemblance to physical reality.

    You can thank mathematicism for this mess. As long as mathematical models carry more weight, and are more closely studied, than empirical reality, the "crisis in physics" will continue.

    1. As far as We can observe, Science is more a Complex Primates Social Endeavor, not an Ontological Entity with A Subjective Phenomenology called Understanding ...

      Ok, If You want to Point Out for an Ultimate Goal for Science ... Then, That goal is To build "Perfectible Models" about Specific Objects of Study linked to Objective Observables ...

      Therefore, Apes can understand those Scientific Models but If They believe that Their Understanding belongs to Science, Obviously, They don't Understand what is Science.

    2. There is, of course, a relativity of wrong (something any diatribe like this would do well to acknowledge), but Ptolemaic cosmology was NOT more useful than Copernican. It only seemed to be to the people using it. But it was all a delusion.

  12. Then again ... . What if quantum mechanics is the ultimate theory of physics? This does not necessarily mean QFT or strings or anything other than plain vanilla QM. Maybe spacetime is just a sort of veiled form of QM.

    We have this little issue of not being able to define reality in QM. Whether QM is ψ-epistemic or ψ-ontic is a choice made by the analyst or observer. This is in some ways reflects some measure of the indefinability of existence, which some of the existentialists, thinking of Dostoevsky, alluded to. Seeking out quantum interpretations is a sort of role play of Fyodor's underground man. This might reflect the ultimate end.

    We might just have the ultimate understanding of things in our hands, maybe in that QM text such as Cohen & Tannoudji.

    1. It is Cohen-Tannoudji - one guy - it was my first encounter with QM.
      And reading Dostoevsky when I was a teenager set me into my first existential crisis ;-)

    2. A little brain glitch on my part with Cohen-Tannoudji. I write below more on this issue.

  13. Is Verlinde's modified gravity a QFT? How about loop quantum gravity?

  14. Utter nonsense. Quantum mechanics is a complete framework of mechanics in and of itself. It is not an approximation to the more complete framework of quantum field theory (in a similar sense of Newtonian gravity being an approximation to Einsteinian gravity). Quantum field theory is simply quantum mechanics applied to each of the infinite degrees of freedom of a field. (That is, the quantum mechanical observable for the field and the first derivative of the Lagrangian w.r.t. the field does not commute at *each* point in spacetime. This generates the quantum mechanics for each point.) Contrary to how it is sometimes introduced, quantum mechanics is not merely a theory of single particles that breaks down with relativity and particle creation and annihilation, that is then saved by quantum field theory. Quantum mechanics is a theory of mechanics that exactly describes an individual degree of freedom, or equivalently, a theory of information that exactly describes the dynamics of a qubit. It does that with no room for correction. It turns out that the real world is best described by this theory of information acting on each degree of freedom in a field.

    1. Where do you think the "V" in the Hamiltonian comes from?

    2. "Quantum field theory is simply quantum mechanics applied to each of the infinite degrees of freedom of a field." Exactly, and therefore quantum field theory IS quantum mechanics. An infinite number of degrees of freedom is of course just an idealisation to the real world and therefore the infinities you get at the end of the day are just artifacts that you want to get rid of to make sense of the results.

    3. What "V"? A physical description of what you're referring to will help me understand you. Thanks.

    4. The potential, Souvik. There is no potential in QFT, there are only interaction terms.

    5. Since Sabine recommended A. Zee: the electrostatic 1/r is an emergent property (one photon exchange) from QFT.
      And to bring this into the context of GR, the old gravitational potential 1/r appears, because in the trajectory of the classical test particle on the static spacetime the time component in the metric dominates the space component.
      For the electrostatic potential 1/r to appear from QED also the two particles have to be static.
      But contrary to GR now in QED the space component of the photon propagator dominates the time component - way off mass shell, having no energy but only momentum.
      This is a blunt violation of the relativistic energy-momentum relation, but the QM exchange particle only exists in the unitary evolution of QM.

    6. What do you think any interaction term in a field theory, or even a mass term really is? Deep down it is a potential. This becomes clear if you discretize the field into a lattice and think again about the mechanics of a single node in relation to the field Lagrangian you're writing. The mass term is quadratic in the field strength for a point in spacetime and quite literally a potential energy for the field taking a non-zero value. Heck, it looks like the potential energy of a spring with spring constant k = mass "m". The dispersion relation in such a medium yields waves with mass "m". A Yukawa interaction term is also a potential energy from the point of view of either of the two fields involved, for a given node in the lattice. I haven't mentioned quantum field theory yet, because the above is true for field theories in general. To get a quantum field theory, we simply promote the field strength (and its canonical conjugate) to an observable and apply quantum mechanics *as exact truth*. Quantum mechanics sees the spring-like potentials for mass and potentials that couple multiple fields, nods wisely, and evolves each degree of freedom exactly as QM should. And this gives us quantum field theory.

      At no point is QM corrected or treated as an approximate theory to something else. We build QFT out of QM, and that's quite a different thing. We do not build general relativity out of Newtonian gravity. I suppose QM is not a theory of what we thought it was, of elementary particles and objects in spacetime. It is the exact mechanics of a single degree of freedom, or qubits of information. We've seen this in physics before, string theory was supposed to model strong interactions and nearly died doing that.

    7. Souvik,

      The potential comes from the interaction terms, not the other way round, though this is of course to some extent semantics. Look, think of the treatment of the hydrogen atom in quantum mechanics. It has a potential, but no exchange particles. It's an approximation. You can't derive QED from it. QED will give corrections to this treatment. To get QED, you need additional assumptions, notably gauge symmetry.

    8. The potential in the treatment of a hydrogen atom is classical. That makes *the potential an approximation*, but not quantum mechanics! The 1/r potential emerges from a deeper theory, but given a 1/r potential, quantum mechanics is an exact theory of the evolution of ONE DEGREE OF FREEDOM. I'm sorry, this is not semantics. This does not mean QM is an approximation to QED. d|psi>/dt = iH|psi> is always *exactly* true where |psi> is the state of 1 degree of freedom. How H is constructed, classically, quasi-classically, relativistically, non-relativistically, is none of QM's business -- if you give it something realistic, it will give you a realistic state evolution. I just showed you how all interaction terms and mass terms are potential terms in the QM Hamiltonian when you deconstruct a quantum field theory and stare at 1 field degree of freedom. QFT (and even string theory) is built out of QM like a Swiss watch is built out of lots of tiny gears. I'm sorry, but your critique of QM is based on a misunderstanding of what it is a theory of and how it relates to QFTs.

      Local U(1) gauge symmetry in the QFT of a charged field generates QED in the gauge field. What does this mean for the QM happening at each degree of freedom? It means the measuring apparatus, i.e. the gauge, is allowed to vary in how the field strength \phi is measured from point to point. QM hums away at each point, and gives us a wave equation for the gauge field itself, i.e. light. At no point is QM compromised!

      To turn the tables, a strong case can be made that QFT is compromised as a complete theory because freedom in the gauge field show up as Fadeev-Popov ghosts. That means there's redundancy in the theoretical structure of QFT, though it can be managed for experimental predictions.

      There actually are a few good reasons to doubt the completeness of quantum mechanics, 't Hooft and Smolin have been bringing it to the forefront recently. I came upon your blog post through Don Lincoln sharing it on Facebook. I was expecting a real critique of QM. Instead I find a graduate-school level misunderstanding of what both QM and QFTs are. This is not even wrong. :(

    9. Souvik,

      What you want to call quantum mechanics is simply not what is taught today as quantum mechanics. If you want, you can of course keep your vocabulary. I have no problem with that. I have zero interest to discuss the definition of words Souvik-style.

    10. Souvik,

      With respect to your “d|psi>/dt = iH|psi> is always *exactly* true …” you might want to consider what is more “*exactly* true”: a Hamiltonian H, the time component of a four-vector and a time variable t, which both are different in different reference frames OR a Lorentz invariant Lagrangian in QFT.
      And with respect to gauge and redundancy I recommend reading “Why Gauge?”.

    11. Are you sure what you're thinking of as quantum mechanics is not just quantum chemistry? You wouldn't call classical mechanics a study of the simple pendulum, would you? Classical mechanics is a framework of kinematics and dynamics, expressed in Newtonian, Hamiltonian or Lagrangian form, that is broader than its use case for analyzing a pendulum. Similarly, quantum mechanics is a framework for mechanics, where conjugate variables of motion are promoted to operators on a Hilbert space and state vectors in the space correspond to a system's physical state. You may have been introduced to quantum mechanics through studying a particular system like the hydrogen atom, and seem to have conflated that with the core framework of quantum mechanics itself. The core framework, I can assure you, is taught as quantum mechanics at upper-undergraduate and graduate level courses.

    12. Souvik,

      I've been taught an axiomatic approach to quantum mechanics, so the answer to your question is "no." Look, I am using the word "quantum mechanics" to mean "that what is the content of almost all textbooks on quantum mechanics". And also what popular science articles on quantum mechanics are about. As I said, I have no interest in debating what you think people should mean when they say quantum mechanics, that's entirely besides the point.

    13. Textbooks on quantum mechanics beyond high school, i.e. at an undergraduate level introduces the theoretical formalism early on, like Sakurai motivates it through Stern Gerlach and EPR experiments. Quantum mechanics applied to the hydrogen atom or quantum chemistry in general is merely the opening gambit for some pedagogical paths to the subject. In that case, quantum mechanics of 1 d.o.f. is not the right model for the system, we need quantum mechanics applied to a field to get progressively better results. So I think the article is misleading for the public. Especially when there's a lot of excitement about quantum computing in the air.

      @ Reimond. Thanks for the nice paper by Rovelli! He's right, gauge fields show us that all fundamental physical quantities are relative. Gauge theories are a very important insight, I agree. But when you introduce gauges in a quantum field theory and try to minimize Feynman's path integral for the field (which you alluded to, and yeah, that's my favorite way of thinking about QFT), you end up double-counting field states. It is an annoyance we learn to deal with in graduate school by introducing extraneous fields that don't make physical sense, and this makes many people feel we're bandaging a theory that could've been "tighter". There was a time in the history of QFT when only the elite could work on it because we were stuck in the Hamiltonian picture, and one had to time order events. Then Feynman came along and gave us the Lagrangian picture, and everything became easy enough for graduate students to pick up without dedicating 20 years to washing sushi rice (something Julian Schwinger actually complained about!). So I wonder if someone will show us a radically different way to picture QFT that will do away with FP-ghosts one day. :D

    14. Souvik,

      Rovelli talks about the “… relational structure of physical quantities.”
      Your “… minimize Feynman's path integral …” does not make much sense. You either mean you vary the Lagrangian to get the equations of motion or you might mean the classical limit ℏ→0 again giving you the classical equations of motion. E.g. varying the Dirac Lagrangian gives you the Dirac eq. It describes an electron and its antiparticle, but both are on-mass shell and you still are not able to calculate effects where virtual, i.e. off mass shell particles are needed like in Lamb shift or in the anomalous magnetic moment.
      For this you need QFT/QED. QM alone does not give you virtual, i.e. off mass shell particles.

      Another bit weird sentence was “quantum mechanics is a framework for mechanics …”. Did you ever wonder why the evolution in quantum theory (QT) is unitary/linear and thus allows superposition, while systems in classical mechanics are usually non-linear? This unitarity in QT is crucial to get the correct probabilities and energy levels. We still have to figure out how our “classical” world emerges from QT and why we do not see fat Schrödinger’s cats. My bet is that the measurement problem is the pivotal element.
      But “Decoherence can't solve the measurement problem…” as Sabine said e.g. here - thus, we have to think a bit more precise.

  15. Good insight. Quantum theory is just an approximative even a statistical approach.

    Maybe it could be worth the trouble try considering particles as classical objects (observables) and including quantum phenomena with conserved states and entanglement only in the concept of spacetime. Maybe we would have to define the interactions being the spacetime structure, so why not?

  16. You're in good company when you say, "Quantum Mechanics is wrong." along side of Lee Smolin and Roger Penrose. :-)

  17. Hi Sabine,
    I trust your day is going well.
    Tantalizing intro, and nice 'wrap-up' to your post.
    You had me scared for a moment.
    (I thought you might have come up with something truly disturbing, lol)
    The statement' All models are
    Wrong' is a generality and, as such, lacks precision.
    It might be better said that
    'Most theoretical predictive
    models,inherently, have
    a rather high probability
    of inaccuracy'.
    (or of being 'wrong')
    And personally,(professionally)
    - It is only of minimal interest
    to me to hear that someone
    has found something 'useful'
    in a trash heap somewhere.
    (- and I hear it all the time)

    (for you,a play on words
    and numbers)
    -Love Your Work

  18. I seem to have hit a nerve by mentioning the complex version of Euler-Lagrange theory. For that, I am very sorry.

    Though you've misunderstood since the complex Euler-Lagrange theory can be formulated for Field Theory as well.

    I only messaged you, btw, because of your past interest in super determinism. Sorry for trying to strike up a conversation.

  19. Sabine,
    It’s great to hear your assertion that quantum mechanics is “useful” rather than “true”. Though that merely puts the field in line with the rest of science, I haven’t gotten the sense that modern physicists have quite understood this. Claims of fundamental randomness and voids in causality come across as ontological and thus arrogant, not epistemic and thus responsible. Surely it’s merely “useful” for us to consider wave function collapse to be random — in the end it may or may not be.

    I suppose it was Einstein who goaded physicists into using ontological rather than epistemic terms through his famous “God doesn’t play dice” assertion. Perhaps He does and perhaps He doesn’t. But to the extent that He does, nothing exists to discover. This is to say that reality must then function “magically”.

  20. Souvik makes a decent appeal for QM as a final theory. A quantum state as isomorphic to quantum information. The invariance or conservation of quantum information, a quantum variant on conservation of phase space volume in classical mechanics, means if this is some sort of approximation then quantum information may not be conserved. The Runge-Lense vector in Newtonian mechanics is an invariant, but with relativity it is not. The precession of the periapsis of orbits is a case of this. If quantum mechanics is an approximation then Tr(ρ) may not be constant and observables that are constants of motion determined by [ρ, O] = 0 are no longer conserved. Quantum mechanics is then maybe the ultimate enforcer of conservations laws as a symmetry "protector." Quantum mechanics has the geometry of the Fubini-Study metric, which does in many ways fill a role of that sort.

    QFT is the extension of QM with there being restrictions on commutation of observables off the light cone and with operators that can describe the infinite number of oscillators as each point in spacetime. This is where as I see it approximations occur. The Wightman condition for zero commutator of observables, which is a curious restriction on quantum nonlocality, works if the fields can be extended globally in spacetime. This is not in general the case with curved spacetime. In addition the Bekenstein bound on black holes and its extension to the Bousso bound means quantum gravitation is not workable in general Hilbert spaces with infinite dimension. Black hole entropy S = kA/4ℓ_p^2 and similar extensions to cosmology means that even if there are an infinite number of quantum states no local observer can access that many. So QFT may have problems with that as well.

    Smolin has come out with a book touting the incompleteness of QM and as I understand is appealing to the Bohm interpretation of QM. While I think Bohm QM has some limited utility, when I see people appealing to that as an argument for the incompleteness of QM I tend to suspect they have fallen off the horse.

    1. A Though Experiment:

      Imagine that -suddenly - all mankind lost their Eyes ...

      After some Centuries ... How would They Think about concepts as "Space" and/or "Space-Time"??

      How would be Their Maths ???

    2. QFT, in the Stanford Encyclopedia of Philosophy, sounds like the doctrine of a secret or religious society:

      "In contrast to many other physical theories there is no canonical definition of what QFT is. Instead one can formulate a number of totally different explications, all of which have their merits and limits. One reason for this diversity is the fact that QFT has grown successively in a very complex way. Another reason is that the interpretation of QFT is particularly obscure, so that even the spectrum of options is not clear."
      Meinard Kuhlmann
      - https://plato.stanford.edu/entries/quantum-field-theory/

    3. Blind people are able to construct spatial relationships between objects by echolocation. Their hearing adapts to become very sensitive so they can in effect "see" things that are close to them through hearing. Blind tap their canes not to just see what is ahead of their feet, but to also send sonar clicks they in effect see with.

      As for QFT, it is an adaptation of QM so that quantum calculations can be done for relativistic particles in spacetime. It is a bit of an open ended gemish. There were those into axiomatic quantum field theory, mostly at French universities, and it is not really clear that any definitive came out of that.

    4. For calculations, I might look at Relativistic Path Integral Monte Carlo. Something like that, as it something I might understand. :)

      Path Integral Monte Carlo method for relativistic quantum systems

      "Relativistic generalization of Path Integral Monte Carlo method has been proposed and some possible applications have been discussed."

    5. Quantum Monte Carlo is one approach to relativistic QM problems. This constructs a lattice with gauge potentials along the edgelinks. These can be computed according to differences between adjoint group actions at the vertices. These group actions g = e^{iθ}, with θ = ∫A·dx construct the pure gauge potentials δg = iδθg = iAA·δxg and in the language of differential forms iA = g^{-1}dg. Now one evaluates Wilson loops around the two dimensional plaquette ∮A = ∯dA = ∯F. The 2-form F has the gauge field tensor for the electric and magnetic, or Yang-Mills analogues for QCD. This field is evaluated on the surface of the plaquette.

      The Monte Carlo routine assigns the group actions in a random manner, or better put pseudo-random, with a random number generator. You then let the algorithm run. There are various ways to do this. The spacetime with a 4-dimensional lattice T^4 or S^4 can be Euclideanized and the dynamics approaches some equilibrium. One can also work with a three dimensional lattice and time evolve it, so as the number of iterations increases or equivalently with time the dynamics approaches an egodic state. This has the advantage of using less storage space, but it requires some tricky digital filtering. If you do numerical quantum mechanics you find that without some filtering the code can diverge as small errors exponentially increase.

      Back in the late 80s as a green horn student I wrote a lattice gauge program. In fact I wrote several, one employing the Euclideanized approach, another the time evolved 3-d lattice and a Regge calculus for the Kasner spacetime with gauge potential on the Regge lattice. Those who have gone further than I ever did now work with supercomputers that evaluate QCD gauge theory with the addition of quarks as fermion fields on the edgelinks. The scaling properties of these lattices, where if one decimates the lattice to perform more IR physics gives an approximate theory of the anti-screening properties of QCD. This has lead to some numerical estimates of the proton mass and how QCD confinement gives known baryon masses. This has proven to be pretty successful.

      The difficulty of course is that in doing this you are running a model without a direct analytical understanding. This is a numerical approximation to problems related to the mass-gap. QCD is horribly difficult to obtain bound state solutions. As a rule scattering states are easier to compute than bound states. Lattice QCD has some problems in that the IR divergence of QCD is avoided with the lattice scale, the more lattice voxels or plaquettes then the lattice size grows and the IR physics → 0. It is a sort of renormalization cut-off. Lattice gauge theory gives some practical answers, but we are still left with the deep question over the nature of Yang-Mills mass-gap.

    6. Lawrence,

      in d=1+1, large N expansion, sigma model, dimensional transmutation generates a mass by trading a dimensionless coupling for a dimensional mass scale, the UV cut-off. See David Tong eq. (4.28) or A. Zee here.
      If you think that in d=3+1 for the Yang-Mills mass gap problem a specific, fine-tuned, not natural, cut-off orders above the Planck mass would help drop me an email. But it comes with a prize (no, not that prize ;-) – this cut-off exists only if spacetime cannot be in superposition i.e. gravity is not quantized. But spacetime will be discretized, very smoothly via this cut-off.
      (Btw a non-perturbative effect because e^{-1/x²} cannot be Taylor-expanded around zero).

  21. "What you cannot do is create particles from vacuum."

    In my amateur opinion, surely that is what could be done. The higgs is one field in the vacuum and that should be usable to make other particles from.

    "creates a large number of particles from the energy of the collision."

    IMO the energy is essential but not sufficient to make particles. Any solution which annihilates/creates particles from pure energy using annihilation and creation operators can be expected to have trouble with infinities as infinities are the flip side (=1 divided by 0) of creating stuff from nothing. (Assuming energy is insubstantial.)

    Early chemistry suffered, I believe in the phlogiston period, from not coping with stuff taken from gases in interactions. Now we may be suffering from not coping with stuff taken from the vacuum. If every stuff is conserved [including vacuum fields] rather than being created/destroyed that could lessen the risk of having infinities?

  22. Sabine -
    Quoting the opening of your third paragraph above
    "... the interactions between these particles must also have quantum properties. If we give these interactions quantum properties, we call that “second quantization.”

    What is perhaps the most fundamental property of interactions is that which governs amplitude and phase of energy/information transmission. If we give these interactions quantum properties, it seems to me that first and foremost is impedance quantization for all forces and potentials, not just scale invariant quantum Hall impedance of vector Lorentz force.

  23. Nice article. I am more concern with the usefulness of the models. I dwell in the classical world doing atom-scale simulations, and I have started to venture into QM in search of insights and new discovery leads. So far I have only reached a complexity wall. From my limited perspective of a new comer, it seems like QM debates just circle around semantics, and thought models that are hard to test. It is not clear if people who agree are referring to different ideas, and those who disagree to the same, because of the subtle lingo and its multiple interpretations. In the classical world I live, I have a saying: if you know it then you code it, or if you code it, it is proof you know a concept is right. How do the experts know their theoretical work works? How do we know there is another Einstein who actually gets it and no one listens to? and, if the model is not useful and testable, what is the point and how do we know it is right? I am just wondering what my child-like innocent thoughts provoke, before I start understanding QM in more depth and I am molded to the established frameworks. Critiques welcome.

  24. How can you believe in quantum mechanics if you are saying it is wrong? Is it not an easy way out to say that all models are wrong? And how can you say that QFT based on QM is less wrong than QM?

  25. I particularly liked that quote from George Box. Also I think this article is another reason to argue that General Relativity should be redone using axioms and fundamental assumptions that I see as already being implicit in Special Relativity.

    1. It is not too difficult to develop General Relativity using axioms and fundamental assumptions. What's hard is combining it with quantum mechanics.

  26. So if I had an idea about how to resolve the Frauchiger-Renner paradox by considering the minds of the experimenters as a kind of fermion, and the information exchange between them as exchange of gauge bosons of a hitherto unrecognized gauge field that is related to the measure of the observer in some way I need help in figuring out, Ed Witten is the guy I should try to talk to? Because I think this might sort out the whole thing quite nicely, and since I am not a physicist, I don't know who to ask to tell if I am right.

    1. Definitely. Go ask Witten. He'll be super excited.

    2. Sabine said, Definitely. Go ask Witten. He'll be super excited. ROFL

    3. Thank you, Sabine, for taking the time to answer me. I'm sure we would disagree on a lot of things, but I believe that's because the *things* are in disagreement. I think I can provide some insight into the recent disagreements about measuring the age of the universe in different ways as well. I just can't do anything with that insight by myself, and I don't have the resources (time and attention) to write a paper on it, because I could easily be completely wrong. I want to interact with somebody, preferably in real time via video call or in person, who I trust understands my ideas and can tell me what is wrong with them, if anything. Louis' response got me to write some of my ideas down that's too big for the comments here. I started out with a response to Louis and ended up with something I think I might be able to take to Ed Witten at some point. Thanks. Louis.

    4. blackswan,

      Sabine and Louis are trying to tell you diplomatically that physicists will not take you seriously unless and until you go to the trouble to learn a great deal of physics.

      Same thing in medicine, civil engineering, and most other fields.

      Sorry, but that is reality.


      (usually "PhysicistDave," but am having trouble with Google)

  27. Sabine,

    Let me refer to your misgivings about lattice QCD when you say “But really we don’t have good mathematical tools to handle the case”. What you wrote in Nautilus “… quantization procedure for Yang-Mills theories is a logical nightmare” I absolutely agree with, when done in the perturbative way. Spin-statistics connection violating ghost fields (Faddeev-Popov) are not nice, even if they are not real physical particles.
    But the way lattice gauge theory does it I find very satisfactory. Keeping the entity tr F,,F’’ with ,,’’=μν intact as well as the gauge symmetry, only violating Lorentz symmetry a bit by putting it on a grid. In the continuum limit, i.e. lattice spacing a → 0 binding energy can be calculated via expectation value of the Wilson loop (1). And as you wrote “… Nothing wrong with that for a pragmatist like me …”. Yes, absolutely it works and says that only 9% of the mass of a proton comes from its quarks.
    Interesting is that both in lattice QCD and Ising model probabilities are important to sample the configuration space. Probabilities are the hallmark of thermodynamics and QM measurements (2).
    I guess nature tells us again, that there is a deeper connection between temperature and time or as A. Zee says ”Some physicists, myself included, feel that there may be something profound here that we have not quite understood.”

    (1) The sampling is performed with a Monte Carlo method. This is analog to the sampling of the partition function of an Ising model with the Boltzmann factor to determine e.g. the critical exponents at the critical temperature via renormalization group or just heat capacity or magnetization at any temperature.
    (2) boldfaced, since QM alone says nothing when probabilities are realized. As you say in your book "They just calculate probabilities but never discuss how the probabilities turn into measurement outcomes."

  28. Sabine,
    Your article is a good read, though it leaves me uncertain as to what is solid in physics. Here you describe the limited accuracy and utility of QM and QFT while in your May 2nd article on free will you remind us that:

    “Physics deals with the most fundamental laws of nature, those from which everything else derives. These laws are, to our best current knowledge, differential equations. Given those equations and the configuration of a system at one particular time, you can calculate what happens at all other times.”

    What body of physical law do you refer to here?

    1. Don,

      Both QFT and QM are "solid". I am afraid I do not understand the comment. What I am saying is that QM is an approximation and in that sense the wrong theory to use for some situations.

      The most fundamental laws that I am referring to there are, as I say, differential equations. We currently get those from QFT and General Relativity. Please keep in mind that while QFT and GR might one day turn out to be approximations, this does not mean they are no longer valid.

    2. Hi Sabine,

      So are you saying that all the precise, numerical results that come from predictions in quantum mechanics (like the Lamb shift) are not enough to make QM a completely accurate theory? Thank you for finally acknowledging that accurate measurements of predictions proposed by a theory does not make it a complete theory...it is really refreshing to hear that. I see QM as a mathematical framework, not a physical theory (oh oh, I guess I just outed myself as a Bohmian or other non-Copenhagenist type!). We know there are many mathematical approaches within classical physics (Lagrangian, path integrals, energy methods) that lead to the sane answer for a problem. I appreciate what you have echoed from Feynman ("nobody understands QM") and Dirac that we really could use a better version of QM that is closer to the physical reality (assuming you fall into this camp, which I recognize a lot do not). I know we have many experiments showing "no hidden variables", but that approach assumes a better theory requires new variables, which it may not. Ok, I apologize for my pro-Bohmian rant, I really do appreciate the honest discussion of this subject!

    3. mh,

      Unfortunately, you seem to have misunderstood my blogpost. The Lamb shift is not a prediction of QM, it's a prediction of QFT. I am saying we know that QM is "wrong" in the sense that it is only an approximation.

    4. Thanks for the explanation,I got the gist of QM not being useful for applications were particles get destroyed or created (vacuum modeling issues) and the Lamb shift is related to vacuum interactions so it"s covered by QFT. I had just used it as an example of how a mathematical model can be very accurate numerically without providing a viable physical explanation. I agree that QM is an approximate model that is still useful. Thank you for pointing this out, I have never heard this in my undergrad or graduate classes ( Quantum optics).

    5. mh, could you provide one or more examples of theories which provide "a viable physical explanation"?

  29. Interesting topic.

    In contrast to early imprecise versions of quantum theory, QFT obtains precision by first assuming infinitesimal points as givens, even though it is fully recognized experimentally that such points cannot exist in the real universe. This abstract use of "not real" precision levels, ones that at best exist only at enormous energy levels, must then be factored out by clever, well-designed calculation methods, including renormalization, to produce a final result that is experimentally meaningful and precise.

    Not to be an alarmist, but when this kind of overly-precise-data-structure situation arises in computer science, the resulting models and algorithms are inevitably grotesquely inefficient due to the phenomenal levels of over-calculation followed by backtracking that they precipitate. After all, if you try to navigate from LA to San Diego by insisting on first representing every square centimeter of turf in between, your result will be precise, but your trip may prove a bit slow.

    The potential for better navigation methods is particularly true if almost a century ago some smart folks realized that those square centimeters don't really even exist in causal history unless you make it a point of peering closely at every one of them. Quantum uncertainty is not a hazard when it comes to calculating reality, it's a gift. It says that says that things get uncertain because some details simply do not exist below a certain energy level. That is, a pragmatic, non-malicious form of quantum uncertainty pops up unavoidably if your reality is simply energy- and bit-limited.

    This is as opposed to reality being composed of an almost-infinite suites of almost-infinite-energy Planck-scale reality fluctuations that magically manage to exactly cancel each other out before, say, collapsing the universe into a singularity. The Planck approach is a lot more fun, though.

    Hmm. So... aside from calculation models, I wonder if the actual quantum physics might also avoid grotesque levels of backtracking by taking a gentler top-down approaches that accepts and leverages quantum uncertainty as the inevitable result of getting a bit too close to the metal, so to speak?

    The alternative is a universe that is inherently anti-Occam's razor when it comes to efficiency. Bleh. Really?

    (Anti-Occam's = Macco's Balloon: Blow up a simple idea until it becomes a ginormous jiggling juggernaut of scope, concepts, complexity, and equations. I'm not one to point fingers, so I'm sure string theory is an exception to Macco's Balloon... :)

  30. Suppose, someone does find some good way to resolve all the known riddles of quantum mechanics (such as the measurement problem) using some new approach which is even backed by sound enough a maths (like differential equations, dynamical theory, and computational simulations based on them). Suppose you get convinced that such an approach should work.

    Even then, such a development should still be regarded as representing not a true expansion in knowledge, but merely as a minor gimmick added to an already huge grab-bag of tricks---one which has its own unresolved problems anyway.

    Further, for the same reason, the originator of such an approach is not to be treated with the same first-class respect as accorded to, say, a Maxwell or a Feynman. Especially by those (physicists and mathematicians) who do know QFT. Instead, the entire question of evaluation of his thesis should be dismissed with the suggestion that he be asked to further study also the QFT, and also solve all its riddles too, before any of his output may be taken up for any further serious consideration.

    Do I catch the drift right?



    1. Hello Ajit,
      I’d like to give your question a try (which should in no way hinder Dr. Hossenfelder from correcting each of us if she likes). If someone today were to figure some things out regarding QM in a way that’s experimentally verified, they’d actually be revered as strongly as any physicist might be. No worries there!

      To me the theme of this post gets to something that many physicists seem not to sufficiently grasp. It’s that science is provisional, or our best estimate. It concerns phenomena rather than noumena. Nearly all scientists seem to grasp this, and even physicists generally seem to grasp this — that is except in the case of quantum mechanics. Here they tend to make ontological claims about “fundamental randomness”. Back in school I remember hearing the oxymoron of “natural uncertainty” (or literally “causal magic”, not that they grasped what they were saying). I was offend by this from day one. Apparently only Einstein had my back, and continues to be belittled for his interpretation of QM.

      In truth however his position was ontological as well, and thus he went beyond science just as surely as the other side continues to. This is to say into “metaphysics” rather than just “physics”. The saving grace for Einstein and I (and you I think given the posts I’ve read at your site) is that our metaphysics puts us in the full naturalist camp, while their metaphysics renders them only quasi-naturalists.



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