Comments on: Quantum mechanics and the square root of Brownian motion

By: A first paper on square root of a Brownian motion and quantum mechanics gets published! « The Gauge Connection

Tue, 20 Nov 2012 10:35:06 +0000

[...] of posts on the link between the square root of a stochastic process and quantum mechanics (see here, here, here, here, here), that I proved to exist both theoretically and experimentally, I am [...]

By: mfrasca

mfrasca — Sat, 10 Nov 2012 13:24:05 +0000

Hi Ohad,

Thank you for your interest about my work. In this case or pdf are the same thing but here happens to be complex and the interpretation should be somewhat changed.

Marco

By: Ohad Asor

Ohad Asor — Sat, 10 Nov 2012 12:45:08 +0000

one thing I didn’t figure out yet:
in (8), the Kolmogorov (btw, how did you choose bwd/fwd?) is about the pdf. but you mention psi there. so, is that psi the wave function or its norm squared?

By: Ohad Asor

Ohad Asor — Sat, 10 Nov 2012 12:27:31 +0000

Hi,
Big fan of this work. No words to tell how much.
Would love to cooperate in research with you.

By: Johnson noise and its square root « The Gauge Connection

Johnson noise and its square root « The Gauge Connection — Fri, 23 Mar 2012 09:57:37 +0000

[...] my recent work on stochastic processes and quantum mechanics (see here and here), after I showed its existence with numerical computation (see here), this time I moved [...]

By: Quantum mechanics and stochastic processes: Revised paper posted « The Gauge Connection

Tue, 31 Jan 2012 11:05:00 +0000

[...] paper on arXiv (see here). The idea has been described here. A full account of this story is given here. The interesting aspect from a physical standpoint is the space that is fluctuating both for a [...]

By: Carl Brannen

Carl Brannen — Tue, 31 Jan 2012 02:57:52 +0000

The presence of the square root suggests that pure density matrices are a better description of pure states than state vectors, and of course mixed density matrices can represent states that state vectors alone cannot.

I think that the primary utility of state vectors and spinors is that their mathematics is linear. That is, they’re advantageous for our representation of reality rather than (necessarily) being what most naturally represents reality. So I see them as a mathematical tool; the fundamental physics is in density matrix form. (Or propagators.)

One way of seeing that QM is inherently nonlinear is to note that tripling a wave function doesn’t create a model of a quantum state in any way different from the original one. This is in distinction to a truly linear theory like classical E&M where tripling the charges, currents, voltages, etc., creates a new state that represents a different physical state than the original.

By: mfrasca

mfrasca — Fri, 27 Jan 2012 11:18:11 +0000

Dear Giulio,

Thank you a lot for your interest on my work. Please, note that there is a problem in the definition of the stochastic integral as it is given there. Sums like do not appear to converge for $0<\alpha<1$ and so the integral in the Riemann sense does not exist. So, I am in need for a proper definition of this integral to make all the argument consistent. I am open to whatever good proposal.

About the form of the Schroedinger equation you are right, there a term proportional to multiplied by the derivative of the wave function. This should be corrected using a potential that can remove it. It is interesting to note that, in 3 dimension, I would expect a gauge coupled equation to come out.

Regards,

Marco

By: Giulio Vandin

Giulio Vandin — Fri, 27 Jan 2012 10:58:35 +0000

I have a question on the equation (10), which you call the “Schroedinger equation” for a free particle. But doesn’t the term proportional to the first spatial derivative of psi affect its temporal evolution? This way it looks like some kind of damped oscillator with complex damping constant: with a straightforward calculation you get solutions which indeed oscillate like the plain-wave solutions of the free particle equation, but for great times the solutions tend to the trivial zero solution. Did I interpretate in a wrong way? I’m very interested in understanding this article, because I was thinking about it on my own, and with your permission I would like to talk about it during a seminar within a course of Statistical Physics of Complex Systems I’m attending.

By: Carl Brannen

Carl Brannen — Fri, 27 Jan 2012 00:07:00 +0000

I also had a question answered at math stack exchange, one having to do with the bases of a finite Hilbert space: http://math.stackexchange.com/questions/28413 . The paper associated with it is now under review at Jour. Math. Phys.