In my paper "Nonlinearity of quantum mechanics and the solution of the problem of wave function collapse". Communications in Theoretical Physics. 2015. V.64, No. 1, 47-53. I argue that quantum mechanics is nonlinear.
Any scattering of particles (for example, obtained in a Large Hadron Collider) is a nonlinear process.
Article Nonlinearity of Quantum Mechanics and Solution of the Proble...
I think that this nonlinearity can help to find solution of measurement problem in quantum mechanics
I have yet to read your paper, but I think non-linearity is just one way of explaining the measurement problem.
From the very beginning it's taught that QM is linear. Since it concerns states and their behaviours, QM is formulated in a vector space (Hilbert Space), but so far I haven't come across any kind of non-linear vector space. Is it just our construction? Or is it inherent in the theory of vector spaces?
I think (and this is purely my thinking from what I have learnt...so might be wrong!) is that QM cannot be non-linear. Yes, there might be a phenomena or two which might exhibit non-linearity, but claiming QM itself is non-linear is a bold step (Hats off to you for that!!). Heck, it might mean everything I have learnt so far is wrong!!
Now all the above is just my viewpoint and would like to emphasize again that I have not read your paper. No one said QM has to be linear, it might be possible for it to be non linear, all I am saying that this might be big...really big if true!!! Hats off man for the same!!!
There is proof that QM should be linear if one has speed of light as information barrier. It is connected with the no-copy theorem. I used to read the paper but have forgotten who is it from. Look in google on no-copy theorem. It is connected with the notion to make multiple replicas of an entangled electron and in a way overcome sl limit. Linearity of QM prevents this. How you address this issue?
Look at this also:
http://homepage.univie.ac.at/Markus.Aspelmeyer/lecture/PLA_263_263_Jordan.
I would be glad to here what you think about this.
As far as I understand Weinberg constructed nonlinear generalization of quantum mechaqnics. Of course it is possible but such models were not supported by experiments. My idea is that quantum mechanics is nonlinear without additional terms.
Hilbert space is a vector space. I never heard about non-linear vectors. And how is it exactly an approximation? I think it's inherent.
This is approximation because linear operations themselves are approximations.
http://www.fisicafundamental.net/relicario/doc/dieks.
Do you mean something different by nonlinearity? Because Disks proves that:
"The linear character of the quantum mechanical evolution laws turns out to be an essential element in preventing such causal anomalies from occurring."
I mean that superposition principle is an approximation. In many cases such an approximation is valid, but in general it is not valid because particle movement is described by the system of equations. These equations in general are nonlinear and Schredinger equation is only approximation.
Read this answers:
http://physics.stackexchange.com/questions/73605/why-does-nonlinearity-in-quantum-mechanics-lead-to-superluminal-signaling
In my opinion they prove that any no linearity (even the slightest) leads to superluminality. Look especially the second answer.
Do you agree with it?
As far as I understand Aaronson proposed some changes in quantum mechanics. But I think that quantum mechanics is nonlinear without changes.
What about superluminality - I think that this process is not forbidden. For example, phase of the wave function can change with arbitrary speed.
I am not sure about this. But if this is so I don't see contradiction in nonlinearity.
Here you can see why:
^ Sommerfeld, Arnold (1907). "An Objection Against the Theory of Relativity and its Removal". Physikalische Zeitschrift 8 (23): 841–842.
In fact I have an idea about instant communication from 2007 with two entangled electrons without use of the FTL-preventing classical channel from Bennett 's protocol. Though I am pretty unaware in it, in the sense that maybe I omit something which prevents its protocol from happening. I am sure it can not pass in any Journal too.
By the way I think that quantum computation can change with taking into account nonlinear processes of creation and annihilation of particles. Measurement of the state is an important part of quanrum computer, but in my paper it was shown that measurement apparatus can be quantum (not classical). That is we need quantum-field computing!
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