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Lynch101

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__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:

https://www.perimeterinstitute.ca/research/conferences/convergence/roundtable-discussion-questions/what-are-lessons-quantumProblem 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.

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 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

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).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.

He goes on to say

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 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.

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.

__Questions__- Does Schroedinger’s equation evolve wave-functions in a non-local way?
- If so does this imply a problem with superluminal propagation?
- Is the idea of non-locality gone from QM with local QFT replacing it?
- How does QFT resolve these issues of simultaneity and non-locality?
- Is non-relativistic QM finished and replaced by QFT or are there areas where ordinary QM applies that QFT doesn't?
- Are there other areas, besides particle physics, where QFT applies but QM doesn't?
- Can QFT be formulated without relativity of simultaneity?

__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.

Quanta Magazine article (source of citation in wikipedia: the Problem of Time)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

A Possible Solution For The Problem Of Time In Quantum Cosmology. (Kaufmann & Smolin).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

https://www.perimeterinstitute.ca/research/conferences/convergence/roundtable-discussion-questions/what-are-lessons-quantumQuantum 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?

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.

__Questions__- Is the Perimeter Roundtable quote correct, does QM have "time which is absolute"?
- If QM has "time which is absolute", how does QFT resolve this?

__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.

There are other problems referenced in lay literature, such as:

[/quote]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.[/quote]

Lee Smolin

*Time Reborn*

Relativity versus quantum mechanics: the battle for the universe (Guardian website)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.

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.

__Questions__- In the Smolin quote about the Standard Model above, do the limitations apply to QFT also?
- Are there approaches to QG that seek to unify QFT? Do String Theory, LCQ, and MWI attempt to do this?
- Are there resolutions to the issues that Magueijo mentions above?

__Wave Function Collapse Thought Experiment__I may have this all wrong, but I will outline my question and hopefully someone can point out where I've gone astray.

The standard thought experiment with Alice and Bob each being sent one of a pair of entangled particles. I think I've seen it formulated before whereby [in a given referecence frame], Alice and Bob measure the particles simultaneously. Then, in relatively moving reference frames the order of them measuring the particles changes depending on the motion of the frame (as a result of relativity of simultaneity).

From my understanding, the wave function for each of them collapses the instant it is measured by one of them, but because they cannot communicate/signal each other faster than the speed of light, there is no violation of causality. Am I even in the right ball park with this?

__Questions__What about in the case where only one of them makes a measurement? Let's say Bob just doesn't bother to measure his particle. Does the wave function for his particle still collapse? If so, and in accordance with the relativity of simultaneity, will there be a reference frame in which the wave function of Bob's particle spontaneously collapses and causes the collapse of Alice's particle? Is the wave function in QM completely non-physical?

Again, am I even in the right city with this one (not to mention the right ball park)?