Is non-linear quantum mechanics (even) plausible?

In summary: The original claim was not made in the paper, and it is not possible to have a non-linear quantum mechanics in the classical regime. In summary, the claim that "There is good reason (theoretically) to believe that linearity fails at high enough energies" is not supported by the paper and is not possible in the classical regime.
  • #1
Derek P
297
43
The question is prompted by a claim raised in another thread that "There is good reason (theoretically) to believe that linearity fails at high enough energies."

I've put this with an A prefix because it is going to be about some damned difficult maths, I know. But please try to avoid the actual maths and just explain the physical principles involved - if you can. I always had the impression that the physical picture - which is counter-intuitive enough with linear QM - becomes impossible if there is any non-linearity at all.
 
Physics news on Phys.org
  • #2
Derek P said:
The question is prompted by a claim raised in another thread that "There is good reason (theoretically) to believe that linearity fails at high enough energies."

I have given the paper a quick read and I don't see where it is either making or supporting such a claim. Hopefully @Mentz114 can weigh in and clarify where in the paper the claim is made, or what in the paper supports it.
 
  • Like
Likes Derek P
  • #3
Years ago, Steven Weinberg was a proponent of non-linear generalizations of quantum mechanics (I attended two talks that he gave on this), but then flaws were pointed out. From the the first edition of his graduate-level book "Lectures on Quantum Mechanics"

"Page 340 Any attempt to generalize quantum mechanics by allowing small nonlinearities in the evolution of state vectors risks the introduction of instantaneous communication between separated observes.3

3 N. Gisin Helv. Phys. Acta 62 363 (1989); J. Polchinski, Phys. Rev. Lett. 66 397 (1991)."
 
  • Like
Likes Derek P and Mentz114
  • #4
Derek P said:
The question is prompted by a claim raised in another thread that "There is good reason (theoretically) to believe that linearity fails at high enough energies."

I've put this with an A prefix because it is going to be about some damned difficult maths, I know. But please try to avoid the actual maths and just explain the physical principles involved - if you can. I always had the impression that the physical picture - which is counter-intuitive enough with linear QM - becomes impossible if there is any non-linearity at all.

PeterDonis said:
I have given the paper a quick read and I don't see where it is either making or supporting such a claim. Hopefully @Mentz114 can weigh in and clarify where in the paper the claim is made, or what in the paper supports it.
I think what struck me is that the classical wave function is non-linear, so in the classical 'regime' superposition is not possible. At no point is anyone suggesting that QM can or should be non-linear.

My use of the phrase 'at high enough energies' should be taken to mean 'in the classical regime'.:wink:

The title of this thread is is inapposite given that neither I nor the authors of the paper claim it is possible.

[to my biographer - this is my 5000th post]
 
Last edited:
  • #5
George Jones said:
Years ago, Steven Weinberg was a proponent of non-linear generalizations of quantum mechanics (I attended two talks that he gave on this), but then flaws were pointed out. From the the first edition of his graduate-level book "Lectures on Quantum Mechanics"

"Page 340 Any attempt to generalize quantum mechanics by allowing small nonlinearities in the evolution of state vectors risks the introduction of instantaneous communication between separated observes.3

3 N. Gisin Helv. Phys. Acta 62 363 (1989); J. Polchinski, Phys. Rev. Lett. 66 397 (1991)."
That is interesting because it is non-linear processes that create entangled pairs ...

[Moderator's note: one sentence deleted.]
 
Last edited by a moderator:
  • #6
Mentz114 said:
That is interesting because it is non-linear processes that create entangled pairs

A measurement is non-linear time evolution in FAPP quantum mechanics, but entanglement can be produced by unitary, linear time-evolution effected by interaction Hamiltonians.
 
  • Like
Likes Derek P and Mentz114
  • #7
Mentz114 said:
My use of the phrase 'at high enough energies' should be taken to mean 'in the classical regime'.

In which case there is nothing to discuss with regard to "non-linear quantum mechanics", so this thread can be closed.
 
  • Like
Likes Derek P

1. Is non-linear quantum mechanics a valid theory?

There is ongoing debate among scientists about the validity of non-linear quantum mechanics. Some argue that it goes against the fundamental principles of quantum mechanics, while others argue that it is a plausible extension of the theory. Further research and experimentation is needed to determine its validity.

2. How does non-linear quantum mechanics differ from traditional quantum mechanics?

Non-linear quantum mechanics proposes that the equations governing quantum systems are not linear, meaning that the effects of the system are not proportional to the cause. This differs from traditional quantum mechanics, which is based on linear equations.

3. What evidence supports the plausibility of non-linear quantum mechanics?

Some experimental results, such as the double-slit experiment, have been interpreted as evidence for non-linear quantum mechanics. However, these interpretations are still being debated and more evidence is needed to fully support the theory.

4. How does non-linear quantum mechanics relate to other theories, such as string theory?

Non-linear quantum mechanics is a separate theory from string theory, which is a proposed theory of quantum gravity. However, some scientists have explored the potential connections between the two theories and how they could be combined.

5. What are the potential implications of non-linear quantum mechanics?

If non-linear quantum mechanics is proven to be a valid theory, it could have significant implications for our understanding of the quantum world and potentially lead to new technologies and applications. However, more research is needed to fully understand the potential implications of this theory.

Similar threads

Replies
19
Views
1K
Replies
3
Views
590
  • Quantum Physics
Replies
7
Views
986
Replies
21
Views
935
Replies
36
Views
3K
Replies
30
Views
2K
  • Quantum Physics
Replies
7
Views
965
  • Quantum Interpretations and Foundations
11
Replies
370
Views
9K
  • Quantum Physics
2
Replies
65
Views
7K
Back
Top