Is non-linear quantum mechanics (even) plausible?

[Derek P]

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]

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.

 

[George Jones]

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.<sup>3

3</sup> N. Gisin Helv. Phys. Acta 62 363 (1989); J. Polchinski, Phys. Rev. Lett. 66 397 (1991)."

 

[Mentz114]

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.

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'.

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]

 

[Mentz114]

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.<sup>3

3</sup> 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.]

 

[George Jones]

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.

 

[PeterDonis]

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.