# Questions on QFT & QM

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## Summary:

I've heard that QFT is the unification of SR and QM but much of the stuff I have read in lay literature seems to suggest certain conflicts that [should] theoretically remain. I'm hoping to resolve my confusion.

## Main Question or Discussion Point

It was recommended that I start separate threads, as I have quite a number of questions on QM & QFT. I'm including all the relevant information/quotes in this thread just for the sake of reference, but there are fewer questions. It might seem like an excessive amount of information but it's all relevant to the questions I have - as the questions arise out of the info. The questions are posted spearately and clearly at the end, if anyone gets fed up with reading through the post.

To give my background:
I am approaching this from a lay backgroud, so that is the source of my information - which I know is not necessarily ideal. I've kind of reached a point where I need help to parse some of the information that I have been reading and to get a clearer understanding.

My main area of interest is the nature of time and this has naturally brought me into contact with Relativity and Quantum Theory, so my questions tend to be focused more in that context.

Locality in Quantum Theory

I was always under the impression that QT was fundamentally non-local. But the more I read about QFT the more it seems as though non-locality isn't an issue. But this seems to conflict with statements like this:
Problem of localization in a quantum field theory. Schroedinger’s equation evolves wave-functions in a non-local way, so there seems to be a problem with superluminal propagation.
Perimeter Institute Roundtable

This seems to imply that there is a "problem of localisation" in QFT because Schroedinger’s equation evolves wave-functions in a non-local way. They seem to be saying that there is some issue with superluminal propagation. This would appear to be a conflict with the local realism of Relativity.

I have, however, read that QFT is provably local and that there is no issue of superluminal propagation with regard to signaling and hence no issue with regard to causality - and so there is no such conflict with Relativity.

I take some context from what Lee Smolin says in Time Reborn p.142
despite the successes of quantum field theory, many physicists, beginning with Einstein, have wanted to go beyond it to a deeper theory that gives a complete description of each individual experiment--which, as we have seen, no quantum theory does. Their searches have consistently found an irreconcilable conflict between quantum physics and special relativity.

As long as we’re just checking the predictions of quantum mechanics at the level of statistics, we don’t have to ask how the correlations were actually established. It is only when we seek to describe how information is transmitted within each entangled pair that we need a notion of instantaneous communication. It’s only when we seek to go beyond the statistical predictions of quantum theory to a hidden-variables theory that we come into conflict with the relativity of simultaneity.
This makes it sound like there is actually a conflict but if we don't probe too far [or if we are unable to], then it isn't a problem. I'm reminded of a quote from Wolfgang Rindlers Relativity: Special, General, and Cosmological where he's talking about length contraction: "We cannot and need not know the details of all this, but we know a priori that there must be a detailed mechanical explanation".

Smolin goes on to say
To describe how the correlations are established, a hidden-variables theory must embrace one observer’s definition of simultaneity. This means, in turn, that there is a preferred notion of rest. And that, in turn, implies that motion is absolute. Motion is absolutely meaningful, because you can talk absolutely about who is moving with respect to that one observer--call him Aristotle. Aristotle is at rest. Anything he sees as moving is really moving.
End of story.

In other words, Einstein was wrong. Newton was wrong. Galileo was wrong. There is no relativity of motion.

This is our choice. Either quantum mechanics is the final theory and there is no penetrating its statistical veil to reach a deeper level of description, or Aristotle was right and there is a preferred version of motion and rest.
Smolin appears to be saying that the choice is between QM being the final theory or a hidden variables theory (which would necessitate a preferred reference frame and therefore absolute motion/simultaneity).

He goes on to say
This means giving up the relativity of simultaneity and embracing its opposite: that there is a preferred global notion of time. Remarkably, this does not require overthrowing relativity theory; it turns out that a reformulation of it is enough. The heart of the resolution is a new and deeper way of understanding general relativity theory which reveals a new conception of real time.
He seems to be suggesting that both choices above - QM as a final theory or a hidden variables theory - lead to the abandoning of relativity of simultaneity.

This would seem to imply that the non-locality and/or absolute time of QM [as a final theory] conflicts with relativity, or that the requirement, in a hidden variables theory, for a preferred reference frame conflicts with relativity.

Time in Quantum Mechanics

The idea that Quantum Mechanics employs an absolute notion of time is one I had started to take for granted, because I had encountered it so often.
In quantum mechanics, time is universal and absolute; its steady ticks dictate the evolving entanglements between particles. But in general relativity (Albert Einstein’s theory of gravity), time is relative and dynamical
Quanta Magazine article (source of citation in wikipedia: the Problem of Time)

In quantum mechanics the situation is rather similar. There is a t in the quantum state and the Schroedinger equation, but it is time as measured by an external clock, which is not part of the system being modeled
A Possible Solution For The Problem Of Time In Quantum Cosmology. (Kaufmann & Smolin).

Quantum mechanics has one thing, time, which is absolute. But general relativity tells us that space and time are both dynamical so there is a big contradiction there. So the question is, can quantum gravity be formulated in a context where quantum mechanics still has absolute time? Or does time have to give. The answer, yes or no, is interesting. If the answer is no, then perhaps some experiment can probe whether or not time is absolute?
Perimeter Institute Roundtable

But, again, QFT would seem to contradict this because it employs the notion of time used in SR which is relative and dynamical, and incorporates the relativity of simultaneity as opposed to absolute time.

QFT and Quantum Gravity

I know the search for a theory of Quantum Gravity is ongoing and not without its issues. One such issue is that of "the Problem of Time". The above quote from the Perimeter Roundtable, with regard to QM having "time which is absolute", is made in the context of QG is often how the problem of time is expressed.

There are other problems referenced in lay literature, such as:
After working with the Standard Model for several decades, we are now simultaneously more confident that it’s correct within the limited domain in which it has been tested and less confident of its extendability outside that domain.
Lee Smolin Time Reborn

Relativity gives nonsensical answers when you try to scale it down to quantum size, eventually descending to infinite values in its description of gravity. Likewise, quantum mechanics runs into serious trouble when you blow it up to cosmic dimensions. Quantum fields carry a certain amount of energy, even in seemingly empty space, and the amount of energy gets bigger as the fields get bigger. According to Einstein, energy and mass are equivalent (that’s the message of E=mc2), so piling up energy is exactly like piling up mass. Go big enough, and the amount of energy in the quantum fields becomes so great that it creates a black hole that causes the universe to fold in on itself. Oops.
Relativity versus quantum mechanics: the battle for the universe (Guardian website)

Put this in the context of this quote from João Magueijo Faster than the Speed of Light (p.250)
The root of all the evil was clearly special relativity. All these paradoxes resulted from well-known effects such as length contraction, time dilation, or E=mc2, all basic predictions of special relativity. And all denied the possibility of establishing a well-defined border, common to all observers, capable of containing new quantum gravitational effects. Quantum gravity seemed to lack a dam—its effects wanted to spill out all over the place; and the underlying reason was none other than special relativity.
And this:
it is meaningless to try to unify QFT so heavily suffering of infinities with GR. We also highlight difficulties of the QFT-treatment of entanglement.
Andrei Khrennikov (2016) The Present Situation in Quantum Theory and its Merging with General Relativity

Questions
• Has QFT completely superceded Quantum Mechanics or is there a domain where QM applies but QFT doesn't and vice versa - not necessariy only with regard to Quantum Gravity?
• Is the "problem of superluminal propagation" referred to in the Perimeter Roundtable quote above an issue in any way, in the way that Smolin suggests (i.e. going beyond "the statistica"), or is it competely resolved?
• Is there any issue whatsoever with regard to the conceptualisation of "time" between QM and GR; does QM have "time which is absolute" while GR has relative time; is the relativity of simultaneity indispensible in QFT or future theories of Quantum Gravity.

I have more, related questions and even these ones could be expanded, but I will see where these ones go.

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DarMM
Gold Member
QFT is considered more fundamental, but QM is often used where QFT would be intractable.

QFT in its standard formalism doesn't have superluminal propagation. One hidden variable mechanism for entagled correlations involves superluminal propagation.

QFT doesn't have absolute time as it is formulated on Minkowski space.

QFT is considered more fundamental, but QM is often used where QFT would be intractable.

QFT in its standard formalism doesn't have superluminal propagation. One hidden variable mechanism for entagled correlations involves superluminal propagation.

QFT doesn't have absolute time as it is formulated on Minkowski space.
Thanks DarMM. I was aware of these points re: QFT already. My connfusion arises based on the information posted in the OP. The quote from the perimeter roundable talks about the "problem of localisation in a quantum field theory" and the "problem of superluminal propagation". Lee Smolin in Time Reborn appears to suggest that that "something must be going on in each individual experiment" and so, if we seek to go beyond the statitstical predictions of QM/QFT - to a hidden variables theory - then the issue of locality arises in such a way as to conflict with relativity i.e. non-locality/superluminal propagation.

The Perimeter Roundtable also states that QM has "time which is absolute", which again would conflict with the notion of time in relativity.

Taken with Smolin's statements, it would seem to imply - indeed Smolin does imply - that the resolution would appear to necessitate the jettisoning of relativity of simultaneity.

The Khrennikov quote above - "it is meaningless to try to unify QFT so heavily suffering of infinities with GR. We also highlight difficulties of the QFT-treatment of entanglement." - along with the quote from Magueijo suggest issues with QFT (and SR) with regard to Quantum Gravity.

Does Minkowski spacetime necessitate the relativity of simultaneity, or is that an interpretation of it?

DarMM
Gold Member
Only one of the mechanisms for entanglement involves superluminal propagation. So if you do seek to go beyond the statistical predictions (and not everybody thinks you can) there isn't necessarily cause to give up locality.

QFT doesn't have absolute time, non-relativistic QM does but that's not a surprise since it is non-relativistic.

Your other questions are going into issues more suited for another thread. One seems to be about renormalization, e.g infinities in QFT.

vanhees71
Gold Member
QFT is considered more fundamental, but QM is often used where QFT would be intractable.

QFT in its standard formalism doesn't have superluminal propagation. One hidden variable mechanism for entagled correlations involves superluminal propagation.

QFT doesn't have absolute time as it is formulated on Minkowski space.
QFT is the (up to now) only successful formulation of relativistic quantum theory. Non-relativistic QM is an approximation, which works very well in its realm of applicability.

QFT is local in the sense of microcausality, and that indeed by construction rules out any superluminal signal propagation as it must be given the causality structure of special-relativistic spacetime.

There are long-range correlations, in the literature often somwhat sloppily called "non-local". This has nothing to do with faster-than-light propagation of causal signals nor is it contradicting anything in standard relativistic QFT. These long-range correlations are also well-established nowadays by experiment. There are zillions of successful Bell tests with all kinds of real-world systems in the lab. Photons are just particularly simple to handle precisely today (with the advent of the laser and parametric down conversion to produce "high-luminusity" sources for entangled photon pairs).

In relativity there is no absolute time whatsoever and that's why there's no absolute time formulated on Minkowski space. To the contrary Minkowski space is the precise mathematical description of special-relativistic spacetime.

Hint to the OP: Confusion arises from reading confusing books/papers. First understand no-nonsense textbooks on relativistic QFT. To really understand it, I recommend to aim at understanding

Weinberg, Quantum Theory of Fields, vol 1, Cambridge University Press

and (complementary to Weinberg)

Duncan, The conceptual Framework of Quantum Field Theory, Oxford University Press

These are rather advanced treatments though. For an introduction, more suited for a first study, my favorite is

M. D. Schwartz, Quantum Field Theory and the Standard Model, Cambridge University Press

Only one of the mechanisms for entanglement involves superluminal propagation. So if you do seek to go beyond the statistical predictions (and not everybody thinks you can) there isn't necessarily cause to give up locality.
Apologies, this is an example of where my limited understanding comes into play. What do you mean by "one of the mechanisms"? Are there different interpretations of QFT, one of which involves superluminal propagation?

QFT doesn't have absolute time, non-relativistic QM does but that's not a surprise since it is non-relativistic.
I get that QFT doesn't have absolute time, I guess I'm just confused as to why the preimeter roundtable, as well other sources, raise it as an issue with regard to the unification of QM with GR ina theory of Quantum Gravity. If QFT doesn't have absolute time, then it shouldn't be an issue.

Your other questions are going into issues more suited for another thread. One seems to be about renormalization, e.g infinities in QFT.
I'm just referencing the issue of infinites to try and give a more complete picture of the "model" I have in my mind. It would seem that Magueijo places the "blame" on SR for those issues, and Smolin seems to suggest that whether one takes QM to be a "final" theory or one seeks to go beyond it to a hidden variables theory, both avenues lead the giving up of relativity of simultaneity.

DarMM
Gold Member
Apologies, this is an example of where my limited understanding comes into play. What do you mean by "one of the mechanisms"? Are there different interpretations of QFT, one of which involves superluminal propagation?
If you want to have a non-statistical account of entanglement one of the possible ways of explaining it is by positing a superluminal connection between particles. "Interpretation" can be a loose term in Quantum Theory as some of the interpretations are actually different theories.

I get that QFT doesn't have absolute time, I guess I'm just confused as to why the preimeter roundtable, as well other sources, raise it as an issue with regard to the unification of QM with GR ina theory of Quantum Gravity. If QFT doesn't have absolute time, then it shouldn't be an issue
It's discussing a particular issue regarding Quantum Gravity which would be beyond this thread. There is an apparent problem with using the Schrodinger equation in dealing with gravity for reasons related to how it treats time. This can be seen as more due to quantum theories requiring a background, not so much the issue of absolute time in the sense of Newtonian vs Relaitivistic mechanics.

However QFT doesn't use absolute time.

I'm just referencing the issue of infinites to try and give a more complete picture of the "model" I have in my mind
What I'm saying is how exactly those issues with infinities relate to Relativity or whether they really are issues is really another topic.

whether one takes QM to be a "final" theory or one seeks to go beyond it to a hidden variables theory, both avenues lead the giving up of relativity of simultaneity
The simple fact is neither do. Giving up Relativity of Simultaneity is just one option in the latter hidden variable case.

QFT is the (up to now) only successful formulation of relativistic quantum theory. Non-relativistic QM is an approximation, which works very well in its realm of applicability.
Am I right in saying that QFT forms the basis for the Standard Model?

Is the the realm of applicability of QM a subset of QFT; as in, does QFT apply everywhere QM applies?

QFT is local in the sense of microcausality, and that indeed by construction rules out any superluminal signal propagation as it must be given the causality structure of special-relativistic spacetime.

There are long-range correlations, in the literature often somwhat sloppily called "non-local". This has nothing to do with faster-than-light propagation of causal signals nor is it contradicting anything in standard relativistic QFT. These long-range correlations are also well-established nowadays by experiment. There are zillions of successful Bell tests with all kinds of real-world systems in the lab. Photons are just particularly simple to handle precisely today (with the advent of the laser and parametric down conversion to produce "high-luminusity" sources for entangled photon pairs).
I've come across literature stating the above about QFT being local. I'm most likely be wide of the mark on this one, but was the implication of the EPR paper to suggest that QM must be an incomplete theory because its non-locality contradicted the locality of SR, and its restriction on superluminal transmission of information of. Did the EPR paper try to demonstrate that there must be hidden variables, with the violation of Bell's inequality demonstrating that any hidden variables theory must be non-local?

Is the issue of superluminal propagation negated by the fact that no signal is transmitted superluminally and therefore loca causality is not violated?

In relativity there is no absolute time whatsoever and that's why there's no absolute time formulated on Minkowski space. To the contrary Minkowski space is the precise mathematical description of special-relativistic spacetime.
Thanks vanhees. I'm more familiar with relativity than I am with QM, so I have an understanding of that. Does Minkowski space absolutely necessitate relativity of simultaneity? I know it is the mathematical description o SR spacetime, but I read that
Poincaré anticipated the seminal work of Herman Minkowski on the four-dimensional formulation of special relativity.
Pablo Acuña L. On the Empirical Equivalence between Special Relativity and Lorentz’s Ether Theory.

Poincaré derived the mathematics of Minkowski starting from a foundation that included absolute time. I know he was working on an ether theory, but its suggeted in the same paper that the ether can be removed because it plays no role in predictions. But, would this suggest that the absolute reference frame could also be removed to leave the mathematics Minkowski without relativity of simultaneity?

Hint to the OP: Confusion arises from reading confusing books/papers. First understand no-nonsense textbooks on relativistic QFT. To really understand it, I recommend to aim at understanding

Weinberg, Quantum Theory of Fields, vol 1, Cambridge University Press

and (complementary to Weinberg)

Duncan, The conceptual Framework of Quantum Field Theory, Oxford University Press

These are rather advanced treatments though. For an introduction, more suited for a first study, my favorite is

M. D. Schwartz, Quantum Field Theory and the Standard Model, Cambridge University Press
Thanks for the suggestions, I'm always on the lookout for decent references. I sometimes struggle with formal textbooks, if they are too technical - although I have been getting better at just continuing through them.

vanhees71
Gold Member
As I said, non-relativistic QM is an approximation of relativistic QFT in the same sense as classical Newtonian mechanics is an approximation of classical relativistic mechanics.

I think the math of the Minkowski space is nearly unavoidable when dealing with special relativity, and Poincare as one of the best mathematicians of his time had to see this imediately. The math of the Lorentz transformation is also not such a big deal. It has been discovered, though not in the final most general form, by Woldemar Voigt already 1898 or so, when checking the transformations that leave the wave equation invariant.

Of course, it was difficult for him as for even the physicists at this time to give up absolute space and absolute time in the Newtonian sense. Interestingly, usually the most brillant mathematicians when working in physics get the physics wrong (Weyl and "gauge theory", von Neumann and the physical meaning of quantum mechanics are the most (in)famous examples).

If you want to have a non-statistical account of entanglement one of the possible ways of explaining it is by positing a superluminal connection between particles. "Interpretation" can be a loose term in Quantum Theory as some of the interpretations are actually different theories.
If you seek to have a non-statistical account, is the only other option a hidden variables theory?

Would that be where one might get into theoretical interpretations of the "wave function", and what it represents? I'm not looking to get into it here, just wondering if that's where that conversation would lead.

I'm just thinking this in the context of Smolin's statement that "something must be going on in each individual experiment" as a reason for going beyind the statistical.

It's discussing a particular issue regarding Quantum Gravity which would be beyond this thread. There is an apparent problem with using the Schrodinger equation in dealing with gravity for reasons related to how it treats time. This can be seen as more due to quantum theories requiring a background, not so much the issue of absolute time in the sense of Newtonian vs Relaitivistic mechanics.

However QFT doesn't use absolute time.
At the risk of sounding like a parrot of Lee Smolin, he and Kauffmann outline that issue in A Possible Solution For The Problem Of Time In Quantum Cosmology.
In classical mechanics one begins with a space of configurations C of a system S. Usually the system S is assumed to be a subsystem of the universe. In this case there is a clock outside the system, which is carried by some inertial observer.
...
In quantum mechanics the situation is rather similar. There is a t in the quantum state and the Schroedinger equation, but it is time as measured by an external clock, which is not part of the system being modeled.
I guess this is where the idea that QM has "time which is absolute" comes out of.

I've [attempted to] read The Problem of Time: Quantum Mechanics versus General Relativity by Dr.Edward Anderson in which he outlines that issue of background dependence [of QM] vs. indepedence [of GR] and the attempts to resolve it. Unforunately, I don't have the level of math required to fully appreciate it, but he writes very lucidly in the non-mathematical parts to explain the implications. I must go back to it again and see if I can take more from it.

What I'm saying is how exactly those issues with infinities relate to Relativity or whether they really are issues is really another topic.
I getcha.

The simple fact is neither do. Giving up Relativity of Simultaneity is just one option in the latter hidden variable case.
Is QFT incompatible with a hidden variable theory then? I'm just wondering how giving up RoS is an option of QFT includes RoS.

With regard to the quote from Kaufffmann and Smolin above, that the 't' in the Schrödinger equation "is time as measured by an external clock", how is that reconciled with the relativity of simultaneity?

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As I said, non-relativistic QM is an approximation of relativistic QFT in the same sense as classical Newtonian mechanics is an approximation of classical relativistic mechanics.
Thanks, I've come across that idea alright. Just lookinng to be absolutely clear in my own mind: QFT applies everywhere that QM applies, but QM might be used for convenience sake?

I think the math of the Minkowski space is nearly unavoidable when dealing with special relativity, and Poincare as one of the best mathematicians of his time had to see this imediately. The math of the Lorentz transformation is also not such a big deal. It has been discovered, though not in the final most general form, by Woldemar Voigt already 1898 or so, when checking the transformations that leave the wave equation invariant.
From the information I've come across, the mathematics of Minkowski definitely seem to be unavoidable when deaing with SR. I'm more wondering if relativity of simultaneity is unavoidable when dealing with the mathematics of Minkowski.

Would Poincaré's derivation from absolute foundations suggest that RoS isn't a logical necessity of Minkowski mathematics, but an intepretational one?

Apologies, I don't mean to repost stuff from a previous post, but I'm just wondering if I am in the right ball park with the following, or am I way wide of the mark?
I've come across literature stating the above about QFT being local. I'm most likely be wide of the mark on this one, but was the implication of the EPR paper to suggest that QM must be an incomplete theory because its non-locality contradicted the locality of SR, and its restriction on superluminal transmission of information of. Did the EPR paper try to demonstrate that there must be hidden variables, with the violation of Bell's inequality demonstrating that any hidden variables theory must be non-local?

Is the issue of superluminal propagation negated by the fact that no signal is transmitted superluminally and therefore loca causality is not violated?

PeterDonis
Mentor
Notice the title: the problem of time in quantum cosmology. Quantum cosmology is not the same as QFT. Quantum cosmology involves quantum gravity, and we don't have a good theory of quantum gravity. Smolin is one of the people working on trying to find one. So papers like this one are not good ones to try to learn the basics of QM or QFT from; his presentation of them leaves out a lot because he is focused on the particular issue he is working on and is assuming a lot of advanced background knowledge in his readers.

I guess this is where the idea that QM has "time which is absolute" comes out of.
He skips completely over QFT here, which is surprising to me, but is a good illustration of what I just said above: he's not trying to teach you the basics of anything, he's expounding a particular speculative solution to a particular problem he's working on, that requires a lot of advanced background knowledge to follow.

I'm more wondering if relativity of simultaneity is unavoidable when dealing with the mathematics of Minkowski.
It is, it's built in the structure of relativity.

DarMM
Gold Member
If you seek to have a non-statistical account, is the only other option a hidden variables theory?
No there is the option of interpreting the formalism as is in a non-statistical manner, e.g. Many Worlds and the Thermal Interpretation.

Would that be where one might get into theoretical interpretations of the "wave function", and what it represents?
Yes basically.

Is QFT incompatible with a hidden variable theory then? I'm just wondering how giving up RoS is an option of QFT includes RoS.
Nobody has built a hidden variable theory consistent with QFT yet to my knowledge. The hope is that one can.

With regard to the quote from Kaufffmann and Smolin above, that the 't' in the Schrödinger equation "is time as measured by an external clock", how is that reconciled with the relativity of simultaneity?
You can transform between the $t$ parameters of different frames.

Notice the title: the problem of time in quantum cosmology. Quantum cosmology is not the same as QFT. Quantum cosmology involves quantum gravity, and we don't have a good theory of quantum gravity. Smolin is one of the people working on trying to find one. So papers like this one are not good ones to try to learn the basics of QM or QFT from; his presentation of them leaves out a lot because he is focused on the particular issue he is working on and is assuming a lot of advanced background knowledge in his readers.
I understand that there are issues with Quantum Gravity (QG) and that it is still a "work in progress", but there are still statements made that have implications for things like QM and QFT.

The point referenced from that article was with respect to the conceptualisation of time in Quantum Mechanics, specifically the 't' in the Schrödinger equation. He likens it to time in classical mechanics with a clock outside the system. This is a fairly common statement with regard to QM.

I understand that QFT is not based on absolute time, but my confusion arises from statements like the above - where the above is representative of an oft repeated tome.

Is Smolin incorrect in his statement about the 't' in the Schrödinger equation being given by a clock outside the system and being akin to time in classical mechanics. Taken in the context of the statement from the Perimeter roundtable [as per the point below].

He skips completely over QFT here, which is surprising to me, but is a good illustration of what I just said above: he's not trying to teach you the basics of anything, he's expounding a particular speculative solution to a particular problem he's working on, that requires a lot of advanced background knowledge to follow.
The statement that QM has "time which is absolute" isn't from Smolin, it's from the perimeter roundtable discussion. And, while it is in the context of QG, it would appear to be pertinent to QM and QFT. I understand that the basics are not being taught here but the statement that QM has "time which is absolute" is pretty categoric. It's difficult to see how such a statement can be taken to mean "time is relative and dynamical" particularly when, in the same point, it is juxtaposed with the statement "But in general relativity (Albert Einstein’s theory of gravity), time is relative and dynamical".

The purposee off the statement is to demonstrate an issue between the conceptualisations of time in both theories.

As I said, the confusion arises because you would wonder why such an issue is raised - in any capacity - if QFT completely resolves it.

This is where the statements from Magueijo, Khrennikov, and the guardian article - about the generalising of QFT to a theory of QG - provide context. Together with Smolin's statement about time in the Schrödinger equation.

Why would the point about absoute time in QM be raised in the context of QG, if QFT isn't based on absolute time?

It is, it's built in the structure of relativity.
Is it built into the structure of the mathematics of Minkowski though? I'm asking based on Poincaré's derivation of the mathematics from a foundation of absolute time.

No there is the option of interpreting the formalism as is in a non-statistical manner, e.g. Many Worlds and the Thermal Interpretation.
Ah, I see. I was wondering where the MWI came in. This is probably splitting hairs, but, is the MWI just a particular interpretation of the statistical theory?

Nobody has built a hidden variable theory consistent with QFT yet to my knowledge. The hope is that one can.
Would the requirement of a preferred reference frame for a hidden variable theory preclude the possibility of that?

You can transform between the $t$ parameters of different frames.
ah, I haven't come across this before. thanks. I don't fully understand it though, apologies. Would you be able to elaborate on it a bit?

DarMM
Gold Member
Ah, I see. I was wondering where the MWI came in. This is probably splitting hairs, but, is the MWI just a particular interpretation of the statistical theory?
Yes. Roughly in the Copenhagen Interpretation a term saying "There is a 40% chance of seeing spin up" is read in MWI as "In 40% of the worlds the spin is measured as up"

Would the requirement of a preferred reference frame for a hidden variable theory preclude the possibility of that?
Not necessarily. It just has to give QFT effectively, i.e. replicate its predictions in the regimes we have observed. However it will be quite a task to do so.

ah, I haven't come across this before. thanks. I don't fully understand it though, apologies. Would you be able to elaborate on it a bit?
It's just transformations between frames as in Special Relativity. Lorentz transformations.

PeterDonis
Mentor
Is Smolin incorrect in his statement about the 't' in the Schrödinger equation being given by a clock outside the system and being akin to time in classical mechanics.
No. But the Schrodinger Equation is non-relativistic QM. I was surprised that Smolin didn't mention QFT at all.

the statement that QM has "time which is absolute" is pretty categoric
Yes, but it only refers to non-relativistic QM. We know that because Smolin specifically talks about the Schrodinger Equation, which is not an equation of QFT.

Why would the point about absoute time in QM be raised in the context of QG, if QFT isn't based on absolute time?
I don't know. But, as I said, Smolin is not writing for you. He's not writing a pedagogical paper. He's describing a very advanced speculation in a very advanced topic, and he's assuming a lot of advanced background knowledge in his readers. So his paper is not a good one to be reading if you don't have that advanced background knowledge; it will cause you more confusion than it resolves.

In any case, QFT isn't based on absolute time, because relativity isn't. That's just a fact. Smolin simply left that out. As I said, I don't know why; you'd have to ask Smolin. But you cannot argue that, since Smolin didn't explicitly talk about QFT, QFT must be the same as non-relativistic QM. That's simply not a valid argument. And I highlighted the fact that Smolin is writing for an advanced audience, not for you, to highlight the fact that you cannot draw conclusions from what he doesn't say. You need to learn the basics from basic sources, like introductory textbooks; you should not expect to be able to infer them from what is left out of advanced papers.

PeterDonis
Mentor
Poincaré's derivation of the mathematics from a foundation of absolute time.
Please give a reference. I'm not aware of any such derivation.

Is it built into the structure of the mathematics of Minkowski though?
Since it's built in relativity, it's also built in any mathematical formulation of it.

I'm asking based on Poincaré's derivation of the mathematics from a foundation of absolute time.
I don't understand what you mean and why is there any "absolute time" involved in the discussion of relativity.

DarMM
Gold Member
No. But the Schrodinger Equation is non-relativistic QM. I was surprised that Smolin didn't mention QFT at all
This doesn't negate your points, but QFT has the Schrodinger equation as well. One rarely deals with it though.

DarMM
Gold Member
The statement that QM has "time which is absolute" isn't from Smolin, it's from the perimeter roundtable discussion. And, while it is in the context of QG, it would appear to be pertinent to QM and QFT
Smolin's discussion is basically about background independence in Quantum Gravity and a hidden variable theory of sorts. As @PeterDonis has said trying to learn about QM and QFT from such advanced subjects is not a good idea. Inferring things as "pertinent" is not valid as he is discussing a subject way beyond what you are talking about.

PeterDonis
Mentor
DarMM
Gold Member
For the wave-functionals.

$$i\frac{\partial}{\partial t}\Psi\left[\phi,t\right) = \hat{H}\left(\hat{\phi},\hat{\pi}\right)\Psi\left[\phi,t\right)\\ \phi \in \mathcal{S}^{'}\left(\mathbb{R}^{d-1}\right)$$

With $\mathcal{S}^{'}\left(\mathbb{R}^{d-1}\right)$ the space of tempered distributions on a spacelike hypersurface. In general it can require more renormalizations than the Heisenberg picture.

EDIT: This is for a single scalar field only

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