A Implications of quantum foundations on interpretations of relativity

[Demystifier]

I don't understand this.

See the second paragraph in #3.

 

[A. Neumaier]

For me the fact that space-time has the structure of Minkowski space is not an interpretation but a consequence.

But this alleged fact is already false in general relativity...

 

[Demystifier]

But this alleged fact is already false in general relativity...

He said consequence of special relativity.

 

[Elias1960]

Summary: If the Bell theorem is interpreted as nonlocality of nature, then what does it tell us about the meaning of Einstein theory of relativity?
According to ether theories, there are absolute space and absolute time, but under certain approximations some physical phenomena obey effective laws of motion that look as if absolute space and time did not exist. The original Lorentz version of ether theory was ruled out by the Michelson-Morley experiment, but some more sophisticated versions of ether theory are still alive.

Sorry, but what is known as the Lorentz ether is simply equivalent to SR (and therefore an interpretation of SR) and therefore not ruled out by the Michelson-Morley experiment. And which versions you think about?

4. Spacetime+foliation interpretation. This interpretation posits that in addition to spacetime, there is some timelike vector field nμ(x)nμ(x) that defines a preferred foliation of spacetime, such that nμ(x)nμ(x) is orthogonal to the spacelike hypersurfaces of the foliation. This preferred foliation defines a preferred notion of simultaneity.

The Lorentz ether is here only a particular case, where the foliation is defined by a preferred inertial frame.

What different interpretations of QM can tell us about those interpretations of relativity? Which interpretations of relativity seem natural from the perspective of which interpretations of QM?

There is a quite simple general answer: All realistic as well as all causal interpretations require a preferred foliation. Here, "realistic" means that the EPR criterion of reality holds, and "causal" means a notion of causality which includes Reichenbach's common cause principle. This follows from variants of Bell's theorem, which use, beyond Einstein causality, only EPR realism resp. Reichenbach's common cause principle.

 

[martinbn]

The past, presence and future exist on an equal footing.

How is that specific to relativity? It seems like a general philosophical position. In fact it seems very non-relativistic in spirit. What is present in relativity? A choice of simultaneity convention? Which one?

 

[Elias1960]

What about block universe? Is that a consequence or an interpretation?

An interpretation. In interpretations with a preferred frame, that preferred frame also defines the presence objectively, and the relativity of simultaneity is reduced to an impossibility to identify the preferred frame by local observations.

How is that specific to relativity? It seems like a general philosophical position. In fact it seems very non-relativistic in spirit. What is present in relativity? A choice of simultaneity convention? Which one?

A philosophical position that assumes a block universe exists too, it is named fatalism. In fatalism, the future is predefined, thus, already existing in the same way as the present. In what I would simply name common sense, the future, as well as the past, have a different status, only what is present exists.

This difference is an objective one, a property of the world, not of observations of the world. Once the preferred frame cannot be identified by observation, it cannot be a choice by an observer. The observer can only guess which is the correct preferred frame (and the CMBR frame gives a quite plausible guess).

The preferred frame interpretations are, indeed, very non-relativistic in spirit. Relativistic symmetry holds only for some observable effects, it is not a fundamental symmetry, and in particular not a symmetry of space and time. This is what makes them much better compatible with similarly non-relativistic interpretations of quantum theory.

A class of interpretations of QT which depends on a preferred frame for extensions into the relativistic domain can be easily identified: If we look at the Schrödinger equation in the configuration space, it gives a continuity equation for the density $\rho(q)$:
$$\partial_t \rho(q,t) + \partial_i ( \rho(q,t)v^i(q,t)) = 0. $$

All one needs is to give the corresponding $\rho(q,t)v^i(q,t)$ a physical interpretation, as a probability flow.

 

[Michael Price]

What about block universe? Is that a consequence or an interpretation?

A consequence. The block universe has always seemed, to me, a consequence of pre-Minkowski classical physics, which describes time as a fourth dimension. Nothing in SR (or GR) changes this.

I don't get your point 4, though. There is no preferred foliation for time after Einstein and Minkowski, and no preferred foliation problem, just as there is no preferred basis problem in quantum mechanics.

 

[Michael Price]

How is that specific to relativity? It seems like a general philosophical position. In fact it seems very non-relativistic in spirit. What is present in relativity? A choice of simultaneity convention? Which one?

Just as there is no preferred position, so there is no preferred time. Seems entirely relativistic to me.

 

[vanhees71]

Bell is also famous for the discovery of anomalies in relativistic quantum field theories (particularly the $\mathrm{U}(1)_{\text{A}}$ anomaly, known as the Adler-Bell-Jackiw anomaly).

 

[vanhees71]

I don't think that it makes much of a difference whether you use photons or massive particles to check Bell's local deterministic HV result against QT results. Entanglement is a very universal phenomenon, for which it doesn't make a lot of a difference in which concrete way you realize it. That there are so many Bell tests using photons is simply, because it's technically easier to prepare entangled states with photon Fock states and keep them unperturbed by interactions with "the environment".

Concerning the other questions, it's clear that one must be careful how to think about photons. First of all you cannot divide photons. Of course you can have a process like parametric down conversion were a laser photon interacting with a BBO crystal splits into an entangled photon pair but that's not the split of the original photon but you get two photons with about half the frequency and corresponding wave numbers (fulfilling the phase-matching condition for the wanted preparation of a biphotonic Bell state).

Photons have no wave functions since they do not have a position observable. A photon is by definition a single-quantum Fock state of the electromagnetic field. A true photon state must also be normalizable, i.e., it has a finite width in energy and momentum.

What happens with a photon in an experiment depends of course on its setup. E.g., if you want to make a polarization measurement you can just use a polarization filter and a photodetector behind it. The (ideal(ized)) polarization filter either absorbs the photon or let's it through, with probabilities depending on the polarization state of the incoming photon and the direction of the polarization filter, given by Born's rule. The photons coming through have the corresponding linear polarization determined by the orientation of the polarization filter. The (idealized) polarization filter is in this case described by a corresponding projection operator, which you can interpret in a FAPP sense as a "collapse". I'd simply call it filtering ;-).

Another possibility is to use a (idealized non-absorbing) birefringent crystal. Then the photon is deflected in different directions with probabilities again given by the incoming photon state and the orientation of the crystal, preparing states which are a superposition of the two possible outcomes leading to an entanglement between the polarization and the momentum of the photon. Here the birefringent crystal can be formally described by a unitary operator. Here I think most collapse proponents would not call this a collapse, because what's prepared is a superposition and which polarization state and momentum an individual photon has taken when going through the crystal must be subsequently measured with photodetectors placed at positions to measure the momentum of the photon, and the collapse proponents then call this a collapse, though of course you don't have a photon left, because it's simply absorbed by the photodetector.

 

[Buzz Bloom]

the past, the presence and the future exist on an equal footing.

I would much appeciate your explaining the quote above in some detail. It seems to be quite ambiguous regarding the role of an observer.

 

[Demystifier]

I would much appeciate your explaining the quote above in some detail. It seems to be quite ambiguous regarding the role of an observer.

Why do you think so?

 

[PeterDonis]

Bell's "theoroms" only applies to particles with spin

No, Bell's theorem says nothing about spin. The particular example Bell used to show that QM's predictions violate Bell's theorem used the spin of a spin-1/2 particle, but that does not mean the proof of the theorem itself involves spin. It doesn't. It is much more general than that.

his theorems and his derived inequalities do not capture all of classical physics

They do in the only way that matters for the theorem: every classical theory of physics satisfies the premises of the theorem.

and collapse to "theories" when applied to classical theories that reject the integrity of the photon

First, I have no idea what you mean by "collapse to theories" here. Bell's theorem is not a theory of physics. It is a mathematical theorem that puts a limitation on the predictions of any theory of physics that satisfies its premises.

Second, of course there is no such thing as a "photon" in classical physics. That has nothing whatever to do with what Bell's theorem says about the possible predictions of any classical physics theory.

95 % of experiments do not use Bell inequalities

If you mean they don't use the particular form of the inequalities that Bell put in his paper, yes, this is true. Other forms of the inequalities turn out to be easier to compare with experimental data. But all such inequalities are still derived from the general form of Bell's theorem.

One interpretation of these results is that the the integrity of the photon should be questioned.

Another interpretation is that photon detectors in those earlier experiments were not accurate enough to give a meaningful test of whether the relevant inequalities were violated or not. As detectors become more accurate, the experiments give better tests, and those tests are making it clearer and clearer that the predictions of QM are valid and that the relevant inequalities are violated.

(Note, btw, that the objections to the term "photon" in the Lamb paper you reference, while they are worth considering--@vanhees71, for example, has expressed similar concerns in this thread as well as many other threads here on PF--have nothing to do with Bell inequality tests. Bell inequality tests are about observables, such as clicks in photodetectors; you don't have to adopt a "photon" interpretation of the underlying theory in order to evaluate those observables and how their measured values in experiments compare to Bell-type inequalities.)

 

[Buzz Bloom]

Demystifier said:the past, the presence and the future exist on an equal footing.

It seems to be quite ambiguous regarding the role of an observer.

Why do you think so?

When I try to guess what you mean, I come up with the following.

Since the past is fixed, all events are facts. No conceptually possible alternative facts exist as a part of the past. I am guessing tha you mean that for the future to be on an equal footing there can be no alternative possibilities actually occurring in the future. That is, the events of future are completely deterministic.

The ambiguity which confuses me is that I also think you do not mean this because of the randomness of QM influencing alternative possibilities becoming the measurements of the future. For example, assuming the multi-world interpretation, when a measurement is made the observer exists in only one of two (or more) possible future worlds depending on the actual value of the measurement observed.

I can offer some other examples of the ambiguity if you think that would be helpful to your understanding of my confusion regarding what you intend.

Regards,
Buzz

 

[PeterDonis]

assuming the multi-world interpretation

This is not a good choice for your argument since the MWI is deterministic; there is no randomness at all in the MWI.

 

[Demystifier]

Since the past is fixed, all events are facts.

The point is that future events are also fixed facts, according to the block-universe interpretation. And it doesn't require determinism, probabilistic laws are also compatible with that. In the lack of determinism, we cannot compute the future events from the present ones. But it doesn't change the fact that the future event will be what it will be. If in the future a random event A will happen, then it is a fact that A will happen. It will happen randomly, but if it will happen, then it will happen. I don't know if it makes sense to you, but that's the idea of block-universe interpretation. It's up to you to decide whether you like this interpretation or not.

 

[vanhees71]

(Note, btw, that the objections to the term "photon" in the Lamb paper you reference, while they are worth considering--@vanhees71, for example, has expressed similar concerns in this thread as well as many other threads here on PF--have nothing to do with Bell inequality tests. Bell inequality tests are about observables, such as clicks in photodetectors; you don't have to adopt a "photon" interpretation of the underlying theory in order to evaluate those observables and how their measured values in experiments compare to Bell-type inequalities.)

To clarify my point of view: I don't object against the use of photons. I only object against the bad habit to sell it in terms of "old quantum theory", i.e., Einstein's flawed point of view that photons can be qualitatively understood as if they were massless point-like particles. Einstein himself was very critical against his own "heuristic viewpoint", and as we know today, he was right in being sceptical against this mishmash of quantum and classical ideas.

A photon is a well-defined concept within modern relativistic local quantum field theory. It's part of the Standard model of elementary particle physics and as such has withstood many attempts to disprove it (to the dismay of many HEP physicists who look for "physics beyond the standard model", because it seems pretty clear that it's incomplete; at least it's likely that there are more particles, explaining the nature "dark matter", and some additional mechanism of CP violation to explain our very existence).

Also almost all tree-level results of QED (like the photoeffect, Compton scattering) are identical with the semiclassical approximation (electrons/charged particles quantized; em. field classical). The most simple effect that really needs the quantization of the em. field is spontaneous emission (discovered by Einstein in 1917 when rederiving Planck's black-body radiation law from the kinetic-theory viewpoint).

To give historical justice one should mention that already Jordan in the famous "Dreimännerarbeit" quantized the electromagnetic field within the scheme of "matrix quantum mechanics". At this very early time, however, most physicists disregarded the need for quantizing the em. field, mostly due to the fact that you come very far with the semiclassical theory. Usually today one quotes Dirac as the discoverer of field quantization and spontaneous emission, but he was somewhat later.

 

[vanhees71]

So what? We all agree that classical Maxwell electrodynamics works fine as an approximation. The 95% of experiments are those within the domain where that approximation works. The other 5% are not. And if we're talking about quantum foundations, as we are in this thread, approximations are irrelevant. Your theory needs to explain all the experimental results, not just 95% of them.

Indeed, and particularly everything related to entanglement and the violation of Bell's inequalities and all that cannot be explained by the semiclassical theory (charges quantized, em. field classical). Other examples is the HOM experiment and quantum beats. For a very good and pedagogical discussion, see

J. Garrison and R. Chiao, Quantum optics, Oxford University
Press, New York (2008),
https://doi.org/10.1093/acprof:oso/9780198508861.001.0001

 

[fresh_42]

I had to delete some posts. Please remain focused on provable facts rather than opinions.

Also please refresh your browser. You are answering to posts which aren't visible anymore!

 

[Buzz Bloom]

This is not a good choice for your argument since the MWI is deterministic; there is no randomness at all in the MWI.

Hi Peter:

I was not trying to make any argument. I am trying to describe my confusion regarding the post in which @Demystifier said "the past, the presence and the future exist on an equal footing." I just searched the entire thread, and I can not find the post in which Demystifier said this. The quote seems to have vanished, perhaps due to some recent editing.

I am now also confused by what you posted: "there is no randomness at all in the MWI." I may have misunderstood what I read in Wikipedia.

https://en.wikipedia.org/wiki/Many-worlds_interpretation​

The many-worlds interpretation (MWI) is an interpretation of quantum mechanics that asserts that the universal wavefunction is objectively real, and that there is no wavefunction collapse.[2] This implies that all possible outcomes of quantum measurements are physically realized in some "world" or universe.​

I interpret this to mean that an observer in one of the many worlds who makes a measurement (which has several or many possible values) will become a corresponding multiple of himself, each in a different world corresponding to a particular value being the result of the measurement. Therefore, each observer in one of the post-measurement produced worlds will be in a randomely chosen world of the many possibilities. If this is incorrect, would you please explain the correction.

Regards,
Buzz

 

[PeterDonis]

I am now also confused by what you posted: "there is no randomness at all in the MWI." I may have misunderstood what I read in Wikipedia.

You should not be trying to understand QM in general, let alone the MWI, by reading Wikipedia.

We have had previous threads on this aspect of the MWI, and I'm pretty sure you were involved in at least one of them, though it might have been a while ago. If you want to rehash the issue again, it should be moved to a different thread.

 

[Buzz Bloom]

We have had previous threads on this aspect of the MWI, and I'm pretty sure you were involved in at least one of them, though it might have been a while ago. If you want to rehash the issue again, it should be moved to a different thread.

Hi Peter:

At my advanced years I do forget things. I do not remember participating in a previous discussion of MWI.

What I would like to understand is whether or not I have misunderstood the Wikipedia text I quoted. If you think I should start a discussion of this topic in a new thread, I will do that. I also would like to understand the implication regarding randomness in my understanding it you find my understanding of the Wikipedia MWI article to be correct.

Regards,
Buzz

 

[PeterDonis]

What I would like to understand is whether or not I have misunderstood the Wikipedia text I quoted. If you think I should start a discussion of this topic in a new thread, I will do that.

Yes, please do. It would be too far off topic in this one.

Also, your question should not be whether you have misunderstood the Wikipedia text; Wikipedia is not a good source for actually learning the physics. You really need to look at a QM textbook or paper that talks about the MWI.

 

[mitochan]

Hello. If I remember well Louis de Broglie wrote on his book about experiment of a particle in a box. Say we divide the box half and half and bring them to Tokyo and Paris . We will find a particle in Tokyo half or Paris half when opened. In this situation the particle, as source of spacetime curvature, change geometry in Tokyo or in Paris but it is not decided before opening. Can this be a case mentioning relation between quantum entanglement and GR ?

 

[PeterDonis]

Can this be a case of relation between quantum entanglement and GR ?

No, because GR is not a quantum theory; there is no way in GR to represent a superposition of two different spacetime geometries, which is what the QM side of your thought experiment would require. We would need a quantum theory of gravity to model such an experiment.

(Note that a single particle's effect on the spacetime geometry would be many, many orders of magnitude too small to measure, now or for the foreseeable future; but it is possible to construct thought experiments where some kind of quantum uncertainty could lead to a superposition of possible positions for an object whose effect on spacetime geometry is measurable.)

 

[mitochan]

Thanks. I observe a difficulty in the experiment by myself. Procedure of carrying half boxes would cause measurement of their inertia and collapse the wavefunction before their arrival.

 

[Demystifier]

the post in which @Demystifier said "the past, the presence and the future exist on an equal footing." I just searched the entire thread, and I can not find the post in which Demystifier said this. The quote seems to have vanished, perhaps due to some recent editing.

It's in the first post, item 2.

 

[vanhees71]

vanhees71 said:

What was Bell's opinion of QM"?

Barry

I'm not so sure about this. For me the great merit of Bell's idea is that he brought a pretty unsharp philosophical question about "reality" and the also pretty enigmatic ideas proposed in the (in)famous EPR paper (which Einstein himself didn't like too much) to a clear scientific empirically decidable question, namely whether with a local deterministic hidden-variable theory, starting from a clear mathematical definition of the statististical meaning of such a theory, all statistical predictions of quantum theory can be reproduced. The important point is that he could derive his famous inequality concerning measurements on ensembles, which holds within this class of local deterministic hidden-variable theories but are violated by the predictions of QT. In this way he found theoretically a general scheme, which allows it to decide whether or not a local hidden variable theory can always be constructed leading to the same statistical predictions as QT. I'm not sure, whether Bell expected QT to hold or the local determinstic hidde-variable theories.

At this time it was very difficult to realize such experiments, but there were experimentalists at the time who took up the challenge. The first being successful was Alan Aspect who prepared entangled photon pairs with a atomic cascade using a laser. That was a breakthrough in the preparation of entangled photon states, and he could successfully demonstrate the violation of the Bell inequality for a certain set of measurements on the polarization states of polarization-entangled photons and thus show that, within the uncertainty of the experiment, QT correctly predicts the correlations between the photon polarizations contradicting the predictions of any local deterministic hidden-variable theory:

https://en.wikipedia.org/wiki/Aspect's_experiment

Today the quantum opticians have much more efficient sources for entangled photons making use of non-linear optics possible with strong lasers: There you can produce entangled photon pairs in many kinds of entangled states at high rates, and the corresponding quantum-optics experiments became very accurate, confirming the violation of Bell's inequalities at very high confidence levels. Also many even more exciting experiments could be done, including "quantum eraser experiments, using postselection schemes a la Scully et al" (e.g., Kim et al), "quantum teleportation", "entanglement swapping" (e.g., Zeilinger et al).

Today this field of "quantum informatics" enters a phase, where you can use it for practical purposes, with applications like quantum cryptography and also quantum computing.

 

[Buzz Bloom]

It's in the first post, item 2.

Hi @Demystifier:

Thank you very much for for your response. From time to time my memory plays tricks on me. What I remember is that the item I quoted from was about MWI. I have no understanding at all of the "Spacetime interpretation".

Regards,
Buzz

 

[Fra]

Hello. If I remember well Louis de Broglie wrote on his book about experiment of a particle in a box. Say we divide the box half and half and bring them to Tokyo and Paris . We will find a particle in Tokyo half or Paris half when opened. In this situation the particle, as source of spacetime curvature, change geometry in Tokyo or in Paris but it is not decided before opening. Can this be a case mentioning relation between quantum entanglement and GR ?

Maybe you have something like this in mind?
"GR=QM? Well why not? Some of us already accept ER=EPR [1], so why not follow it toits logical conclusion?"
-- Susskind, https://arxiv.org/pdf/1708.03040.pdf

In a more speculative setting, I think there are very interesting possible "interpretations" of spacetime as well as the observer equivalence constraints, that are suggestive toward particular research directions for QG and unification.

In my preferred interpretation, one can not understand the constraints of neither SR nor GR, without also considering how spacetime emerges among interacting "observers". I am closest to an operational interpretation that was mentioned in the first post. The only problem of Einsteins derivation from the two postulates of (observer equivalence) and (invariant upper bound on speed) is that the postulates implicitly containts assumptions about spacetime. My "interpretation" would be to relax postulate one, and replace ti with observer democracy rather than equivalence. In this case the constraints becomes emergent, along with spacetime and matter. There are also many indications that upper bound on speeds follow naturally in information geometric constructions; so the second postulates is likely not needed either. I admit that in my own work I should probably work better to maintain a list of references, which is my I refrain from getting too deep. But these suggesttions have arised in several published places but different authors as well as from my own considerations. A random googling finds for example this, givign you a hint of the general idea, I didnt analyse that paper to depth, but it gets you in the ballpark...

Stochastic Time Evolution, Information Geometry, and the Cram ́er-Rao Boun
" As a consequence of the Cram ́er-Rao bound, we findthat the rate of change of the average of any observable is bounded from above by its variance times thetemporal Fisher information. As a consequence of this bound, we obtain a speed limit on the evolution of stochastic observables: Changing the average of an observable requires a minimum amount of time givenby the change in the average squared, divided by the fluctuations of the observable times thethermodynamic cost of the transformation.
"
- - https://arxiv.org/abs/1810.06832

If you consider a true _intrinsically_ construcible measure of evolution to an agent, then a kind fo stochastic evolution (or probabilistic evolution) seems the only thing at hand.

/Fredrik