# Questions on QFT & QM

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PeterDonis
Mentor
For the wave-functionals
for a single scalar field only
Ah, ok. In other words, with a particular choice of inertial frame and for only one particular kind of field.

DarMM
Gold Member
Ah, ok. In other words, with a particular choice of inertial frame and for only one particular kind of field.
My example only uses one field for brevity, but it can be formulated for arbitrary field theories. Even Yang-Mills.

It's in a specific frame, as such inducing a foliation of the spacetime. Though of course still Lorentz invariant.

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"
Ah yes, that makes sense. I was familiar with MWI just not that detail.

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.
I see. Thanks.

It's just transformations between frames as in Special Relativity. Lorentz transformations.
I was thinking that, I just can't parse the link. I'll try to walk it through.

The 't' in the Schrödinger equation is provided by a clock outside the system. This is, I believe, what generally leads to the idea that QM employs an absolute notion of time - as per the various quotes above. How does transforming between the 't' parameter of different reference frames change this? Or rather, how is it to be interpreted?[/quote]

No. But the Schrodinger Equation is non-relativistic QM. I was surprised that Smolin didn't mention QFT at all.

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.
Apologies, I've come across the idea of NRQM before but don't fully understand why the likes of Smolin and the others I quoed would talk NRQM when QFT supercedes it. Is there any domain where NRQM applies that QFT doesn't? If QM is completely subsumed by QFT why would there be any reason, whatsoever to raise such an issue?

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.
Not all the quotes are from Smolin. There are some from his book Time Reborn which is written for a lay audience, but there are some from João Magueijo from his book Faster than the Speed of Light , and there are some from the perimeter roundtable.

The statement from the perimeter roundtable is the most explicit it say that QM has "time which is absolute" and it juxtaposes this with the time of GR which is "relative and dynamical". The clear intention is to highlight the contradictory nature of the two. Granted, this is in the context of QG, which presupposed some background knowledge, but I struggle to see how any amount of background knowledge could change the thrust of the point, given that it is so explicit and given the pursposeful juxtapositioning.

Also, it's confusing as to why these scientists would even consider raising such an issue if QFT completely negated it.

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DarMM
Gold Member
The 't' in the Schrödinger equation is provided by a clock outside the system. This is, I believe, what generally leads to the idea that QM employs an absolute notion of time - as per the various quotes above. How does transforming between the 't' parameter of different reference frames change this? Or rather, how is it to be interpreted?
If the $t$ in the Schrodinger equation can be transformed into the $t$ in a different coordinate system with a different notion of simultaneity then time isn't absolute in the Newtonian sense.

Please give a reference. I'm not aware of any such derivation.
Poincaré anticipated the seminal work of Herman Minkowski on the four-dimensional formulation of special relativity. However, unlike relativity in four-dimensional space-time, in the ether theory these properties represent mere mathematical niceties that do not have a physical meaning.
Pablo Acuña L. On the Empirical Equivalence between Special Relativity and Lorentz’s Ether Theory.

his achievements in this area were largely mathematical: formulating the notion of the Lorentz group andfinding its invariants, formulating the notion of a four-vector andfinding quantities that transform like four-vectors, interpreting the Lorentz transformations as rotations in four-dimensional space. These are results that follow from the mathematical structure of the equations, not from any physical understanding of their significance; they paved the way for the powerful mathematical formalism developed by later workers in the field, but did not provide the essential physical insight that provides the formalism with its application.

And PhysicsForums own policy on LET and Block Universe suggests the predictive equivalence between the two interpretations.

Since it's built in relativity, it's also built in any mathematical formulation of it.

I don't understand what you mean and why is there any "absolute time" involved in the discussion of relativity.
Does it form part of the minimal interpretation of the mathematics, or is it part of the Einsteinian interpretation.

As I mentioned in this post Poincaré [appears to have] derived the mathematics of Minkowski spacetime from a foundation of absolute time, which is why I would question the idea that relativity of simultaneity is baked into the mathemaical formalism.

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.
I appreciate that but not all the quotes are from Smolin and some of them are taken from literature aimed at the lay audience. The quotes taken from the perimeter roundtable are perhaps not meant for a lay audience and may presuppose a level of background knowledge, but the statement about "time which is absolute" is so explicit and it's juxtaposition with the "relative and dynamical" time of GR so intentional that I struggle to see how any level of background knowledge could alter the meaning.

Even if it is made in the context of QG, the question would remain as to why it is raised as an issue at all.

As I mentioned in this post Poincaré [appears to have] derived the mathematics of Minkowski spacetime from a foundation of absolute time
And I see no justification of such claims in what you've quoted. Mathematics of Minkowski spacetime is internally inconsistent with the notion of absolute time, period.

and some of them are taken from literature aimed at the lay audience
Which, per PF rules, is not a suitable source for a discussion. The main issue is not absolute time, because there is none in QFT, it's the 'background dependence' of the theory.

If the $t$ in the Schrodinger equation can be transformed into the $t$ in a different coordinate system with a different notion of simultaneity then time isn't absolute in the Newtonian sense.
I'll try to clarify my own misunderstanding.

How I'm interpreting it is that you have the quantum system under consideration, with time 't' being provided by a clock outside the system. You're saying this can be transformed into the 't' of another frame.

I'm imagining a system of two relatively moving observers where the time is given by a clock outside the system i.e. common time for both observers and this 't' can be transformed to the 't' of another frame.

DarMM
Gold Member
The quotes taken from the perimeter roundtable are perhaps not meant for a lay audience and may presuppose a level of background knowledge, but the statement about "time which is absolute" is so explicit and it's juxtaposition with the "relative and dynamical" time of GR so intentional that I struggle to see how any level of background knowledge could alter the meaning
And yet you have read it wrong. As @weirdoguy has said they are discussing background dependence, not time being absolute in the Newtonian sense. The contrast is between the background dependence of QM and the background independence (i.e. dynamic background) of GR.

Again it's not about absolute time in the Newtonian sense.

DarMM
Gold Member
I'm imagining a system of two relatively moving observers where the time is given by a clock outside the system i.e. common time for both observers and this 't' can be transformed to the 't' of another frame.
Yes and can be done so in a way that is Lorentz invariant.

And I see no justification of such claims in what you've quoted. Mathematics of Minkowski spacetime is internally inconsistent with the notion of absolute time, period.
I'm basing it on Poincaré's derivation of the mathematics. Did he not derive the mathematics of Minkowski independently of him? That is why I ask if they are "baked" into the mathematics.

Which, per PF rules, is not a suitable source for a discussion. The main issue is not absolute time, because there is none in QFT, it's the 'background dependence' of the theory.
apologies, we can limit it to the statement from the perimeter roundtable

And yet you have read it wrong. As @weirdoguy has said they are discussing background dependence, not time being absolute in the Newtonian sense. The contrast is between the background dependence of QM and the background independence (i.e. dynamic background) of GR.

Again it's not about absolute time in the Newtonian sense.
ah, OK. I've read a bit about the background dependence vs independence problem. I'll go back and have a look at that. Thanks

Did he not derive the mathematics of Minkowski independently of him? That is why I ask if they are "baked" into the mathematics.
Apparently he did, but if he only focused on mathematics he could not base it on the notion of absolute time since time is not a mathematical concept. It sais in your quote that he 'formulated the notion of Lorentz group' and the thing is that the mathematical structure of Lorentz group is inconsistent with absolute time. Actually the structure of Lorentz group leavs barely no room for different physical interpretations.

vanhees71
Gold Member
Apologies, I've come across the idea of NRQM before but don't fully understand why the likes of Smolin and the others I quoed would talk NRQM when QFT supercedes it.
I fail completely to understand why Smolin talks at all...

Apparently he did, but if he only focused on mathematics he could not base it on the notion of absolute time since time is not a mathematical concept. It sais in your quote that he 'formulated the notion of Lorentz group' and the thing is that the mathematical structure of Lorentz group is inconsistent with absolute time. Actually the structure of Lorentz group leavs barely no room for different physical interpretations.
I see. Would it be compatible with timelessness?

If time is not a mathematical concept, would that not mean that relativity of simultaneity is not "baked" into the mathematics of Minkowski?

Yes and can be done so in a way that is Lorentz invariant.
Why isn't that at odds with relativity? I thought that there is a time 't' or each particle in relativity, such that if you were to have a clock outside the system, then that would be a separate reference frame

I fail completely to understand why Smolin talks at all...

DarMM
Gold Member
Why isn't that at odds with relativity? I thought that there is a time 't' or each particle in relativity, such that if you were to have a clock outside the system, then that would be a separate reference frame
Lorentz transforming between different $t$ coordinates is directly a part of Relativity, I can't see how it would contradict it. You're free to use any reference frame to anaylse the situation and able to transform among them. That's all in accord with relativity. I don't see the contradiction.

Lorentz transforming between different $t$ coordinates is directly a part of Relativity, I can't see how it would contradict it. You're free to use any reference frame to anaylse the situation and able to transform among them. That's all in accord with relativity. I don't see the contradiction.
I don't see one myself, it's just that I don't have a clear idea of it.

I'm not sure if the following makes sense, but I'm imagining a system of lets say two particles. How I'm understanding it is that QM uses a common time for both particles, while relativity would have relative, dynamical time for each particle.

EDIT: or maybe it's more a case of there is a common time for the experimenter in the lab and the reatively moving particle? As I say, I'm not entirely clear on it myself

DarMM
Gold Member
It's just as it is in Relativity the various systems can be analysed in any other frame. $t$ is just the time of the frame in which one performs the analysis.

Do you know the mathematics of Relativity.

It's just as it is in Relativity the various systems can be analysed in any other frame. $t$ is just the time of the frame in which one performs the analysis.

Do you know the mathematics of Relativity.
Unfortunately not. I wish I knew in high school what I know now. I would have made different choices.

Am I wide of the mark when I think that QM can have a common time for a system of relatively moving particles, while relativity would have relative time for each particle?