# A QFT and Entanglement

1. Nov 8, 2018

### Nusc

Why is it that nonrelativistic quantum theory (NRQT) does not have PCT, whereas QFT does? How would you characterize the collapse of the wave function in terms of PCT? What is its PCT transform?

How does QFT address EPR?

Many physicists universally accept the Copenhagen interpretation and move on as with renormalization.

Those who were discontent with renormalization, acknowledge it, and those like Dirac and Feynman made attempts to tackle the issue. Dirac disregard the notion of the point charge and attribute structure to the electron in handling radiation reaction. He was not successful but made some interesting remarks; he tried to resurrect the notion of the aether arguing how it was not incompatible with relativity when one considers quantum indeterminancy, the other involved monopoles and emphasized the use of strings.

2. Nov 9, 2018

### Demystifier

PCT theorem refers to a property of the Lagrangian or Hamiltonian of the system. The collapse, on the other hand, is not governed by the Lagrangian or Hamiltonian. Hence PCT theorem is not relevant for the collapse.

More generally, collapse and EPR are just two aspects of the measurement problem in quantum theory. The core of this problem does not depend much on the Lagrangian or Hamiltonian of the system. Hence, as far as the measurement problem is concerned, it is not so much important whether one works with NRQM or RQFT, the problem is essentially the same.

3. Nov 9, 2018

### vanhees71

I'd say it's even simpler. While P and T (space reflection and time reversal) are transformations (for many aspects of the world even symmetry transformations) which can be formulated in both special relativity and Newtonian physics and thus in both relativistic and non-relativistic QT. However C (charge conjugation) cannot be even defined in non-relativistic physics, because there's no way to define what an anti-particle is, while this is a necessary concept for any relativistic local and microcausal QFT, including the corresponding symmetry for all physics except if the weak interaction is involved. BTW, it is now independently measured that the weak interaction violates all the discrete symmetries built with C, P, and T, i.e., C, P, T themselves and also CP. What it doesn't violate, however, is the combined "grand reflection" CPT, and that's in some sense good news since any relativistic local and microcausal QFT, the fundament of the entire Standard Model of elementary particle physics, necessarily implies symmetry ander the "grand reflection", CPT.

There's no need to bring EPR up here at all. Of course, relativistic QFT has no problem with EPR, because it describes on the one hand the observed strong correlations described by entanglement without violating relativistic causality, and it does this by construction, fulfilling the socalled Linked Cluster Principle. This clearly shows that entanglement doesn't imply any "spooky action at a distance". It's only the nonsensical idea of collapse introduced by some early Copenhagen physicists. AFAIK Bohr himself never insisted on the collapse; in this sense he was a wise guy. Of course, Einstein was on the right track in criticizing this Copenhagen flavor of QT vehemently, although the EPR paper is infamous in the sense as Einstein himself rightfully didn't like it, because he had a much better understanding of the putative problem and tension between locality, causality and non-classical long-range correlations described by entanglement. The problem for Einstein was not so much this tension but the long-ranged correlations themselves, but that he correctly described as the "inseparability" of long-distant parts of quantum systems which can be independently observed (like two entangled photons can be registered in principle light years away and still have the strong correlations in entangled properties, usually their polarization state in the usual Bell experiments with polarization-entangled photons from downconversion sources).

4. Nov 9, 2018

### Nusc

Thanks for your input!

Do you have the reference article for this?

Also can you respond to this thread?
https://www.physicsforums.com/threads/what-is-mass.959594/#post-6085102
Thanks again!

5. Nov 10, 2018

### vanhees71

6. Nov 11, 2018

### stevendaryl

Staff Emeritus
I would say that the word "clearly" is not appropriate here, since it's possible to come to the opposite conclusion.

7. Nov 11, 2018

### DarMM

It describes that they exist, certainly, but not how they come about (i.e. what's causing the strong correlations) that's the contentious part.

8. Nov 11, 2018

### stevendaryl

Staff Emeritus
Right. Whether it's QFT or nonrelativistic quantum mechanics, the theory has two parts:
1. Probability amplitudes are computed using unitary evolution.
2. Upon a measurement, measurement results occur nondeterministically with probabilities given by the Born rule (the square of an appropriate amplitude)
The issue about nonlocality is about #2, not #1. So pointing out that QFT fulfills the Linked Cluster Principle is irrelevant. (Well, it's relevant to proving that part #1 satisfies locality, but it's not relevant to part #2).

9. Nov 14, 2018

### vanhees71

Sure, with philosophical rather than physical arguments ;-)) SCNR.

10. Nov 14, 2018

### vanhees71

But as for any state the cause of entanglement is the preparation procedure to bring the system into this state, e.g., for polarization entanglement of photon pairs you can use parametric down conversion at an appropriate BBO.

Another very simple way to prepare a highly entangled state between a proton and an electron is to put them in a box together and wait unti hydrogen atoms have formed ;-))).

11. Nov 14, 2018

### vanhees71

2. is just defining the physical meaning of the formalism. There's nothing nonlocal going on. As any part of the theory its justification is simply that it works with real-world experiments/observations all the time!

Of course, this minimal interpretation leaves many philosophers unsatisfied since they want for some reason more from the natural sciences than these are supposed to deliver.

12. Nov 14, 2018

### DarMM

Firstly can't you have entanglement between systems that have never been in physical contact due to vacuum entanglement, it's not always our preparations that do it possibly? I might be wrong on this.

Secondly, although the preparation might be a cause, it's not a decorrelating explanation, a sub condition of Reichenbach's principle. See: https://arxiv.org/abs/1402.0351
Hence the preparation is necessary, but does not fully account for the correlation.

Many people don't find this satisfying, but I don't think they're all philosophers, many physicists think the same.

I mean what you are saying is equivalent to "put water in the ground and the plant grows, anything further is philosophy". A perfectly consistent position and a valid one for QM (where AntiRealist interpretations have strong arguments in their favour). However I don't think the equivalent of "I see, but how exactly does the plant grow?" is silly nonsense that only a philosopher would worry about.

13. Nov 14, 2018

### DrChinese

Entanglement swapping is such an example. In fact, the entangled particles need not have ever co-existed.

14. Nov 14, 2018

### kurt101

But with entanglement swapping there is still a mutual friend particle that each of the particles that never met each other had to physically interact with in order for the entanglement swapping to occur. So even though there is no direct physical contact, there is indirect physical contact (i.e. physical contact through the mutual friend or chain of friends). At least that is my understanding of it, please correct me if I am wrong!

15. Nov 15, 2018

### stevendaryl

Staff Emeritus
I don't think so. If you produce one pair of entangled particles, $A$ and $B$, and another pair, $C$ and $D$, then a measurement involving $B$ and $C$ can force $A$ and $D$ to become entangled (I think). In terms of "mutual friends", $B$ and $C$ never met until after $A$ and $D$ were far away.

16. Nov 15, 2018

### DarMM

.........and I thought QM was odd before. I think my head just short-circuited!

17. Nov 15, 2018

### Hendrik Boom

Wouldn't the person doing both measurements then be the particle connecting both systems?

18. Nov 15, 2018

### stevendaryl

Staff Emeritus
Let's make up a cast of characters: Alice, Bob, Charlie, Daniel, Eric.

1. Charlie creates a pair of particles and sends one to Alice and the other to Eric.
2. Daniel creates a pair of particles and sends one to Bob and the other to Eric.
3. Eric performs a measurement on the pair of particles he received.
4. Afterwards, Alice's particle and Bob's particle are entangled.
Alice and Bob have no mutual friends. Alice has only interacted with Charlie. Bob has only interacted with Daniel. Eric has never interacted with either Alice or Bob. There is an interaction chain connecting Alice to Bob, but it goes both forward and backward in time: Bob backward to Daniel, forward to Eric, backward to Charlie, forward to Alice. So Eric is sort of the mutual friend connecting Alice and Bob, but he's not in their past---they never met Eric or received anything from him.

19. Nov 15, 2018

### Mentz114

Fascinating. I think that Eric has to perform something that leads to 'unitary collapse' - like total interference or state recombination. If Eric uses an interference device then we have to pick those cases where no photon emerges. This is based on my recollection of the 2016 experiment* in Delft where two diamond nitrogen vacancies are entangled by swapping with emited photons.

*arXiv:1508.05949v1

20. Nov 15, 2018

### DrChinese

That's correct. The "meeting" of B & C can occur at any time, either before or after measurement of entangled A & D.

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