Nature Physics on quantum foundations

[ohwilleke]

Quantum theory is NOT weird but the most comprehensive theory about Nature we have today.

Not really a fair criticism.

The fact that a theory is comprehensive and accurate description of Nature doesn't preclude it from being weird.

"Weird" is a word generally used in reference to "common sense" and a typical person's intuition about how the world works. Weird is a close synonym of "counterintuitive."

Every shred of physical intuition gained from daily life, some of it hard wired into our brains, is based on a classical worldview that works for Newtonian mechanics and Maxwell's equations, but fails miserably in the domain of quantum theory in half a dozen or so distinct respects. Yet many people aren't even seriously exposed to quantum theory for the first time until they are college students with STEM majors (assuming that they ever go to college and that they ever major in STEM).

Calling quantum theory "unnatural" would indeed have been inappropriate, but "weird" is right on target.

 

[Morbert]

"It is easy to dismiss research into the foundations of quantum mechanics as irrelevant to physicists in other areas. Adopting this attitude misses opportunities to appreciate the richness of quantum mechanics."
I'm ok with foundations work being irrelevant to most physicists. My interest in foundations wasn't because I thought foundations work could invigorate other research projects. Almost the opposite: I became interested in foundations in the hope that it could better articulate how physicists and chemists already understand quantum mechanics.

When QM is introduced axiomatically in undergrad, it's usually in terms of some procedure of unitary evolution + measurement + state reduction. But huge areas of physics and chemistry make use of QM without this procedural approach, and alternative interpretations can better overlap with these areas. (E.g. I find consistent histories interesting because it nicely complements the way many of us already think about electron transport calculations in transistors)

 

[gentzen]

We are probably talking past each other.

That is quite possible. My reaction to your "intended interpretation" was dominated by your reference to GRW (paired with my limited knowledge of why such objective collapse theories differ from standard QM):

My preference is a blend of the statistical and transactional interpretations, and ... GRW. At least the original GRW is (to my mind) rather ad hoc, but I like the idea that only events are real. A short coordinated "wiggling" of electrons in a detector, for example, constitutes what we could call the measurement of the polarization of a photon.

GRW is known to allow both a "flash ontology" (or "flashes ontology") and a "mass density ontology". (I guess that some objective collapse theories are commited to a "mass density ontology", i.e. theories like the Diósi–Penrose model.) So I guessed that your "events" would be similar to the "flashes" for GRW.

Why should vagueness be an important ingredient? ... Does randomness constitute enough "vagueness"?

The "flashes" for GRW have infinitely accurate spacetime coordinates. For GRW, even their randomness seems to be not enough to get rid of that excess accuracy again. But for Bohmian mechanics, the randomness is sufficient, so an unconditionally true answer to that question seems impossible.

The trouble with excess accuracy is that the information content of a system with a finite energy in a finite spacetime region should better not be infinite. It is convenient to work with real numbers for mathematical models, but their infinite accuracy forces you to have some mechanism (like "vagueness") to avoid that their infinite accuracy has experimentally observable consequences.

For me, QED is a fundamentally statistical theory. ... I don't want to create a new theory. I think QED is perfect, and I only aim to see it more clearly as a theory of a special kind of point process in spacetime

I guess that the mechanism for QFT to get rid of the excess accuracy (related to "point process in spacetime") is renormalization. You find "points of view" like the following in modern QTF1 lecture notes:

Many points of view; one is that it is our own fault: QFT is somewhat idealised; it assumes infinitely extended fields (IR) with infinite spatial resolution (UV); there is no wonder that the theory produces infinities. Still, it is better to stick to idealised assumptions and live with infinities than use some enormous discrete systems (actual solid state systems).

There is also a physics reason why these infinities can be absorbed somehow: Our observable everyday physics should neither depend on how large the universe actually is (IR) nor on how smooth or coarse-grained space is (UV).

 

[Fra]

Every shred of physical intuition gained from daily life, some of it hard wired into our brains, is based on a classical worldview that works for Newtonian mechanics and Maxwell's equations

Hmmm... I don't think it's how my brain is wired. My brain, and I think yours, makes use of inferences, abduction, lossy retention and actions influenced by subjective expectations that has been tuned by evolution, even though we may not think of it. These things are IMO in excellent harmony with quantun weirdness if you only embrace the inside observer view So I see good reasons why we WILL ultimately see how natural QM is, and we will look back and wonder how Newtons mechanics ever made sense

/Fredrik

 

[WernerQH]

The trouble with excess accuracy is that the information content of a system with a finite energy in a finite spacetime region should better not be infinite. It is convenient to work with real numbers for mathematical models, but their infinite accuracy forces you to have some mechanism (like "vagueness") to avoid that their infinite accuracy has experimentally observable consequences.

I don't subscribe to the view that information is physical. It belongs to our theories and models. And we can safely ignore excess digits.

I guess that the mechanism for QFT to get rid of the excess accuracy (related to "point process in spacetime") is renormalization.

Yes, it is useful (no, necessary!) to ignore the scales that are not relevant. We couldn't do physics otherwise.

You find "points of view" like the following in modern QTF1 lecture notes:

Thank you. Your posts always contain interesting pointers.

 

[A. Neumaier]

The events that I have in mind are interactions of electrons and photons, for example.

How do you turn this into an unambiguous definition of what events are? Without that, your talk is fuzzy words only...

manifolds glued together - I'm lacking the proper mathematical term

The term is ''double cover of standard spacetime''

 

[Peter Morgan]

Having looked through the above posts, in which the measurement problem and "collapse" appear repeatedly, as so often, I commend to people here the mathematics in my recent paper in JPhysA 2022, "The collapse of a quantum state as a joint probability construction", https://arxiv.org/abs/2101.10931 (the DOI for the published version may be found there, but there's very little difference), as a way to rethink the measurement problem.
I'll leave the paper mostly to tell its own story, though I emphasize it is very far from complete, but I'll mention here that it constructs in Section 4 what I call a "super-Heisenberg picture" that we can think of as empirically equivalent to the Heisenberg, interaction, and Schrödinger pictures (but not as unitarily equivalent because it absorbs unitary evolution and non-unitary "collapse" into a unitary evolution of the measurement operators so that the quantum state is completely static).

 

[OscarCP]

Not to discuss the foundations of QM, but just to recommend to anyone who might not know, but perhaps may be interested, to have a look at a Website called "World Science Festival" that I have recently discovered.
It has a large collection of lecture-long (one hour and a quarter, or longer) videos of lectures, interviews and panel discussions on topics in the main sciences, and tons of them on physics, cosmology, astrophysics and geophysics.
To give you an idea, in two occasions in the last two weeks I "attended" for free a lecture by Stanford's Leo Susskind on the Higgs boson, with a remarkable preliminary introduction to quantum fields, and another with a panel discussion on whether quantum physics is complete, incomplete or what? that included Utretcht University's Nobel laureate Gerard T'Hooft, who made some very interesting and a few also surprising remarks about "or what?"
The lectures, interviews and panel discussion explanations are usually conducted in a style that makes them accessible to the educated and interested layman, are mostly at the undergraduate intro level, but particularly in the discussions and interviews -- always conducted by a very knowledgeable host -- "bleeding edge" ideas tend to pop up along with the more basic stuff. And always with the personal views on the subject at hand of some top physicists.
For someone that did not know about this: in my opinion, worth giving it a try.

 

[Fra]

I don't subscribe to the view that information is physical. It belongs to our theories and models. And we can safely ignore excess digits.

My problem with this take on the "problem" described by gentzen is that

1) it is ambigous in what way you choose to ignore it, analogous to changing the order of limits at will. This is ad hoc procedure we all know from physics. By my point here is still not from the stringent math side, you also loose the conceptual and inferential clarify when doing this. We loose the ability to reason rationality because the input is a soup already, so it can be nothing but soup coming out.

2) I think it also inflates "theory space", if you have ignored these things for a long time (which we have done) then at some point in evolution you have completely lost track of what is happning, and you can no longer tell which complexions of theory space that have physical significance, and what is mathematical extrapolations. I think this makes improving the theory in a rational way harder. This has always disturbed me, and I think we could do a little bit better. We have some actual fine tuning to do, but it's tricky enough without trying to fine tune ghosts.

/Fredrik

 

[Morbert]

How do you turn this into an unambiguous definition of what events are? Without that, your talk is fuzzy words only...

I don't know if this serves @WernerQH 's purposes, but Froehlich gives a useful notion of events in QM, motivated by event algebras in probability theory:

https://arxiv.org/abs/1905.06603

 

[A. Neumaier]

I don't know if this serves @WernerQH 's purposes, but Froehlich gives a useful notion of events in QM, motivated by event algebras in probability theory:

View attachment 314130

https://arxiv.org/abs/1905.06603

Useful? Giving the name 'event' to some construct doesn't make it an event in any realistic sense.

What does it mean for such an event to happen, i.e., to be real? is there a trajectory of real events? Or are there events happening at the same time in different places? etc.

 

[ohwilleke]

Hmmm... I don't think it's how my brain is wired. My brain, and I think yours, makes use of inferences, abduction, lossy retention and actions influenced by subjective expectations that has been tuned by evolution, even though we may not think of it. These things are IMO in excellent harmony with quantun weirdness if you only embrace the inside observer view So I see good reasons why we WILL ultimately see how natural QM is, and we will look back and wonder how Newtons mechanics ever made sense

/Fredrik

You can't viscerally experience phenomena associated with quantum but not classical physics without scientific instrumentation. The scales are beyond those are senses are designed to experience. Our brains use Newtonian type assumptions as we walk, run, jump, fall, and view the world around us with our own eyes.

QM can be taught better to make it seem somewhat less weird, and can be more familiar, but Newtonian mechanics will always make sense because it is descriptive of almost everything we experience personally and perfectly adequate for the lion's share of practical application. (If there is snark in this answer, I apologize for missing it, it is hard to read tone in writing sometimes.)

 

[Morbert]

Useful? Giving the name 'event' to some construct doesn't make it an event in any realistic sense.

What does it mean for such an event to happen, i.e., to be real? is there a trajectory of real events? Or are there events happening at the same time in different places? etc.

According to Froehlich, if $\{\pi_\xi,\xi\in\chi\}$ is a potential event, then the event $\xi$ that actually occurs is the event that selects the state of the system after the occurrence (see equation 9 in the paper). It's useful insofar as he uses it to reformulate quantum dynamics as a stochastic branching process, where measurements are no longer fundamental. (Measurements according to Froehlich are special events that generate a large amount of entropy)

 

[Fra]

but Newtonian mechanics will always make sense because it is descriptive of almost everything we experience personally and perfectly adequate for the lion's share of practical application.

What I had in mind was far more intuitive to us humans than falling objects or ballthrowing.

I was thinking of human-human interactions and the laws of social interactions. Try to describe that in the Newtonian paradigm.

/Fredrik

 

[A. Neumaier]

According to Froehlich, if $\{\pi_\xi,\xi\in\chi\}$ is a potential event, then the event $\xi$ that actually occurs is the event that selects the state of the system after the occurrence (see equation 9 in the paper). It's useful insofar as he uses it to reformulate quantum dynamics as a stochastic branching process, where measurements are no longer fundamental. (Measurements according to Froehlich are special events that generate a large amount of entropy)

So the state of the system is something objective that changes if and only if an event happens? Thus the Schrödinger equation does not govern the change of states? What then?

 

[Fra]

You can't viscerally experience phenomena associated with quantum but not classical physics without scientific instrumentation.

You mean the detectors with irreversible pointers that we conceptually keep on the external/classical side of the cut? Those are the idealisation yes. But isn't the imperfectness in that ideal the problem? Where is the "classical side" in a quantized gravitational system? At the future infinity?

/Fredrik

 

[Morbert]

So the state of the system is something objective that changes if and only if an event happens? Thus the Schrödinger equation does not govern the change of states? What then?

The time evolution of the state would indeed not be governed by the Schroedinger equation, and would be objective and fundamentally stochastic. This stochastic process is accounted for with a filtration and a state space that Froehlich calls "the non-commutative spectrum" of the system.

Although the wavefunction is considered objective, what are considered real are the events. I'm not very familiar with GRW but I believe it also considers events to be what are real, and so the ETH approach presented by Froehlich might rigorise GRW.

 

[WernerQH]

I don't know if this serves @WernerQH 's purposes, but Froehlich gives a useful notion of events in QM, motivated by event algebras in probability theory:

https://arxiv.org/abs/1905.06603

Thank you for the reference. I've seen Fröhlich's paper before, and I sympathize with his philosophy, but my notion of event is much more primitive: a point in space-time where a field excitation is created or destroyed. For me the creation of a photon is a real physical event, but it does not happen in an instant. It is a composite event. In a medium with a refractive close to 1, the emissivity (${\rm W~m^{-2}~Hz^{-1}~sr^{-1}}$) can be written as $$
\epsilon = { \mu_0 \omega^2 \over 8 \pi^2 c} \sum_{\mu\nu} {\bf e}_\mu^* {\bf e}_\nu
\int_{-\infty}^{\infty} dt \int d^3x\ e^{-i(kx - \omega t)} \langle j_\nu(0,0) j_\mu(x,t) \rangle
$$ suggesting that an emission event actually comprises four primitive (strictly localized) events ($\Psi,\Psi^\dagger,\Psi,\Psi^\dagger$). Between the times (events) $j(0)$ and $j(t)$ the "state" of the system, whether the photon has been created or not, is in limbo. Evolution is not strictly Markovian. It takes a short, but non-zero time until a fact ("photon has been emitted") is established. And experiments are always reported post factum. :-)

The time evolution of the state would indeed not be governed by the Schroedinger equation, and would be objective and fundamentally stochastic.

Absolutely. Continuous and deterministic evolution according to Schrödinger's equation does not square with the graininess and randomness that we experience in the real world. I agree with Fröhlich that it is an intellectual scandal that it still seems necessary to graft extra "measurement" processes on the evolution of the real world.

 

[A. Neumaier]

The time evolution of the state would indeed not be governed by the Schroedinger equation, and would be objective and fundamentally stochastic. This stochastic process is accounted for with a filtration and a state space that Froehlich calls "the non-commutative spectrum" of the system.

Although the wavefunction is considered objective, what are considered real are the events. I'm not very familiar with GRW but I believe it also considers events to be what are real, and so the ETH approach presented by Froehlich might rigorise GRW.

What is the difference between real and objective? How can something nonreal be objective, and how can something nonobjective be real?

 

[Fra]

Froehlich gives a useful notion of events in QM, motivated by event algebras in probability theory:

View attachment 314130

https://arxiv.org/abs/1905.06603

This caught some of my attention, i will try to read it later. Thanks for the link! Part of what caught my attention is a claim that its not a pure interpretation but should yield different predictions and some other things such as stochastic evolution, it sounds like having similarities to my preferred views. But i need to read it all to make sure I don't jump into conclusions... will report back... it will take some time due to some traveling where reading is tricky.

/Fredrik

 

[Morbert]

What is the difference between real and objective? How can something nonreal be objective, and how can something nonobjective be real?

Maybe there is ultimately no distinction, in the sense that an objective quantum state is a representation of some objective character about the system. The distinction I had in mind was nomological vs material (something could be objective but not material), similar to the distinction Goldstein et al make here:

"We propose that the wave function belongs to an altogether different category of existence than that of substantive physical entities, and that its existence is nomological rather than material. We propose, in other words, that the wave function is a component of physical law rather than of the reality described by the law"

 

[Demystifier]

How can something nonreal be objective

In this context I think a good example is Lagrangian in classical mechanics. It is objective in the sense that it does not depend on the observer, but nonreal in the sense that it is only a mathematical tool to compute properties of real physical classical objects such as particles.

 

[A. Neumaier]

In this context I think a good example is Lagrangian in classical mechanics. It is objective in the sense that it does not depend on the observer, but nonreal in the sense that it is only a mathematical tool to compute properties of real physical classical objects such as particles.

The Lagrangian depends on the observer, as anyone is free to add a total derivative without changing the dynamics. Thus it is like coordinates.

 

[Demystifier]

The Lagrangian depends on the observer, as anyone is free to add a total derivative without changing the dynamics. Thus it is like coordinates.

That's not what "dependence on observer" in physics means. Even dependence on coordinates, in general, does not imply dependence on observer. For example, if something is not invariant under the transformation from Cartesian to spherical coordinates, it has nothing to do with dependence on observer. The dependence on observer refers to transformations that can be interpreted as physical changes of the observer, for example a spatial translation (corresponding to an observer translated in space), a rotation (corresponding to a rotated observer), or a boost (corresponding to an observer moving with a velocity). You can translate, rotate or boost the observer, but you cannot add a total derivative to the observer.

 

[A. Neumaier]

The dependence on observer refers to transformations that can be interpreted as physical changes of the observer, for example a spatial translation (corresponding to an observer translated in space), a rotation (corresponding to a rotated observer), or a boost (corresponding to an observer moving with a velocity). You can translate, rotate or boost the observer, but you cannot add a total derivative to the observer.

Well, much more depends on observers! Different observers do not even get identical measurement results (unless the observers are idealizied).

 

[Demystifier]

Well, much more depends on observers! Different observers do not even get identical measurement results (unless the observers are idealizied).

Since we don't know on which specific property of the observer it depends, we usually interpret it as statistical measurement errors.

 

[Fra]

Since we don't know on which specific property of the observer it depends,

This area you mention is what to me is one of thw open question in an intrinsic theory of measurement. Ie to generalize quantum process tomography, constrained to using only information ar hans to an inside observer. If one elaboratea this, the observer choice will influence much more than just spacetime transformations, as the observers internal structure at depth will influence what ia optimally inferred (via the generalization of "process tomography" but this process ia not understood yet.)

/Fredrik

 

[Fra]

I read the Frölich paper and I fail to connect to this thinking or choice of analysis in any significant sense. Perhaps I missed something but I see some some vauge exceptions...

"We must therefore clarify what should be added to the formalism of QM in order to capture its fundamentally probabilistic nature and to arrive at a mathematical structure that enables one to describe physical phenom-
ena (“events”) in isolated open systems S, without a need to appeal to the intervention of “observers” with “free will” – as is done in the conventional “Copenhagen Interpretation of QM”

Indeed one could ask what the freedom to choose detector settings in bell type of gedanken experiments, translates to, when imagine describing the WHOLE system must evolve unitarily? ie. when we try to include and "agent" in the system, but described from the perspective of another agent, what does the "freedom to choose measurement" correspond to? I share the idea that this is indeed a kind of random process. Ie. the agents making measurements must be a kind of spontaneous and random stoastich process. In my personal views, I see the agent as doing a random walk (or basically throwing dice). So the "free will" is allowed from the perspective of the external agent, but from the agent itself I think it's just doing a random walk. If we label the freedom to make a random step as free will, then it does not take anything else. But of course the random walk could be "guided", but the agents subjective bias. So from the external agent, it doesn't not necessarily appear random as randomness would be subjective. Randomness just means inability to predict, which may be due to limited information processing capacity, not too dissimilar to pseudorandom generators.

"(H;U) do not tell us anything interesting about the physics of S, beyond spectral properties of the operators U(t; t0)"

If I interpret what they want to say, they say the Hamiltonian does not say anything about the "internal structure" of S, and thus the "physics of the internal interactions". I symphatize with this, as the hamiltonian is inferred "as a whole" from the outside, which is why for complex systems it lacks insight of the origin, and often bings us into a fine tuning situation. But I do no not see how the EHT view solves anything as i see it. I would prefer to phrase this subquesion so that, if S containts of "interacting observers", then to understand the physics of S (and how it's parts are put together) we need to understand the physics of interacting observers on part with any interacting and to construct larges systems from parts, from allowing the parts to "communicate" and see how the Hamiltoninan of such a system emerges from it's parts. This would give us the insight of the physics of S, AND the overally hamiltonian of the composite S; as seen from an external perspective. But this to me, requires a new theory, and I do not how their EHT stance helps out in that quest?

The beef with how unitary evolution of the whole system, may not be consistent with the stepwise evolution with internal measurements, where one assumes that that the classical results obey the bell-type correlations does not seem like a problem to me as the latter sitation is injecting information that does not exist in the original state, so there is not reason why the two expectations should be the same, as I don't consider the latter case an isolate system, so there is no paradox. That the "expectations" on a isolated system, is violated when the assumption of isolation is broken, is not a conceptual problem.

/Fredrik

 

[gentzen]

Indeed one could ask what the freedom to choose detector settings in bell type of gedanken experiments, translates to, when imagine describing the WHOLE system must evolve unitarily? ie. when we try to include and "agent" in the system, but described from the perspective of another agent, what does the "freedom to choose measurement" correspond to? I share the idea that this is indeed a kind of random process. Ie. the agents making measurements must be a kind of spontaneous and random stoastich process.

I don't like the use of the word "spontaneous" in this context. In a FAPP sense, we do have "freedom to choose measurement" in modern Bell experiments, but not in a "spontaneously random" way. We use our freedom beforehand to decide on a protocol from where to take the randomness. But it is never an instantaneous randomness, but always processes where some uncertainty in time is present regarding the moment when the decision got determined.

So from the external agent, it doesn't not necessarily appear random as randomness would be subjective. Randomness just means inability to predict, which may be due to limited information processing capacity, not too dissimilar to pseudorandom generators.

I fear saying "randomness is subjective" without also being willing to take and defend some form of Bayesian interpretation is too lazy. It is simply not the same as saying that "randomness hardly ever absolute".

 

[gentzen]

The Lagrangian depends on the observer, as anyone is free to add a total derivative without changing the dynamics. Thus it is like coordinates.

Well, then take the quotient structure given by the equivalence relation that the difference is a total derivative.

OK, I know that taking the quotient is easier said than done. Sometimes it miraculously just works, like for identical particles in Bohmian mechanics. Othertimes it doesn't "really" work properly, like for spacetime foliations in Bohmian mechanics. And you can never be sure whether other people really agree that taking some quotient is the right thing to do, or even "necessary" in the first place. Especially in cases where the quotient seems to make trouble like for spacetime foliations, the number of people willing to bite the bullet and claim that there should be one objective preferred foliation (instead of trying to fix the quotient) quickly grows.

But I find it a bit unfair to attack only the Bohmians in this respect. I think the problem already occurs in mathematics itself for the topological quotient space. Sometimes it is a "patchwork construction", for example when arbitrarily gluing different spaces together, or gluing borders of a single space together to get a completely different space. And sometimes it is a "natural construction", like when taking the quotient by a discrete subgroup which operates continuously on the space.