SciRate Comments

Comment on 0808.2474 by jt

Paper Id: 0808.2474
Paper Title: Making Almost Commuting Matrices Commute
Authors: M. B. Hastings

jt said: A very impressive proof of a long-standing open problem.

Comment on 0807.2936 by alex.marina

Paper Id: 0807.2936
Paper Title: The dipole-quadrupole theory of surface-enhanced Raman scattering
Authors: A. M. Polubotko

alex.marina said: It is a review of mainly specific topic. I tried to cite only valuable papers, which are not mistakble. Those, presented ideas only and not confirmed by serious arguments are omitted.

Comment on 0708.2515 by QuantumMoxie

Paper Id: 0708.2515
Paper Title: Verschraenkung versus Stosszahlansatz: Disappearance of the Thermodynamic Arrow in a High-Correlation Environment
Authors: M. Hossein Partovi

QuantumMoxie said: I only just discovered this paper while working on some research. I think the results it presents are immensely profound, particularly from a foundational standpoint, but also from a practical standpoint. Pretty impressive stuff, in my opinion.

Comment on 0808.1260 by pak

Paper Id: 0808.1260
Paper Title: From Inference to Physics
Authors: Ariel Caticha

pak said: QUOTE: "From the point of view of entropic dynamics the problem is not to explain the arrow of time, but rather to explain the reversibility of the laws of physics."

Much better than that barely intelligible Categories paper a few days ago!

Comment on 0807.4935 by pak

Paper Id: 0807.4935
Paper Title: Quantum Communication With Zero-Capacity Channels
Authors: Graeme Smith, Jon Yard

pak said: So how does this work then? Is the information carried by entanglement between the two (individually) zero-capacity channels?

Comment on 0807.3841 by QuantumMoxie

Paper Id: 0807.3841
Paper Title: Evasion of uncertainty relations with very small probability
Authors: Kazuo Fujikawa, Koichiro Umetsu

QuantumMoxie said: They missed a key point since they never discussed the operator-based uncertainty relations (i.e. the ones Schrödinger derived) which are a purely classical statement about the behavior of operators. It would seem to have relevance for what they are attempting to do.

Comment on 0807.4935 by QuantumMoxie

Paper Id: 0807.4935
Paper Title: Quantum Communication With Zero-Capacity Channels
Authors: Graeme Smith, Jon Yard

QuantumMoxie said: I love papers like this.

Comment on 0807.4935 by patrick

Paper Id: 0807.4935
Paper Title: Quantum Communication With Zero-Capacity Channels
Authors: Graeme Smith, Jon Yard

patrick said: A delightfully simple observation that shakes quantum Shannon theory to its foundations! Great paper.

Comment on 0807.3369 by Benni

Paper Id: 0807.3369
Paper Title: A new look at Bell's inequalities and Nelson's theorem
Authors: Benjamin Schulz

Benni said: I have now updated my paper. It now contains an explanation of this object of a conditional probability with respect to a sigma algebra, which Nelson introduced here.

I made a similar explanation as is given by Faris in

"Probability in quantum mechanics," appendix to David Wick, The Infamous Boundary: Seven Decades of Controversy in Quantum Physics , Birkhauser, Boston, 1995.

It is somewhat simple, since it uses coin tossing experiments to define the notations. Maybe such things can be understood by mathematicians, too....

If someone thinks that this is not rigorous enough, or even have some suggestions to write it in a better way, I would be too pleased.

But thank you for your comments quantumcurious.

Comment on 0807.3369 by Benni

Paper Id: 0807.3369
Paper Title: A new look at Bell's inequalities and Nelson's theorem
Authors: Benjamin Schulz

Benni said: Dear Quantumcourious, thank you for your corrections of P(X_t \in A')=P(Y_t\in A')

But to your point:

But the set {\cup \omega: \omega \in \bar \mathcal F} would be just be \Omega, again strange.

It would be \Omega. In fact, trivial!
But exactly this is ment in section 2. Why do you not allow me to make trivial examples? Is there anything against trivial statements?

And well, in fact: A \cap \bar \mathcal F = A is ment in the introduction. This is trivial too. In fact.

The third sigma algebra F_x is introduced later in section 4. Then, it is certainly not trivial anymore.But since we deal only with rather trivial probability spaces, where the possible events are only {up} and {down}, I do not think of anything which would prevent equations 33 and 34 to be correct or made the statements at the end of section 4 impossible.

Unfortunately, I have, at my hands, only the references cited by Nelson. His most rigorous threatmenton this is a conference paper cited in my article:

Field theory and the future of stochastic mechanics, pp. 438–469 in Stochastic Processes
in Classical and Quantum Systems (Proceedings, Ascona, Switzerland, 1985), ed. by S.
Albeverio, G. Casati, and D. Merlini, Lecture Notes in Physics 262, Springer-Verlag, Berlin,
1986. [See correction in 45.]

and the contribution of Faris cited in the paper. You might read them yourself. Unfortunately, they are somewhat "short" and do not explain things in full, since they were intended for professional mathematicians.

If you contact me per e-mail, I can send you copies. I would be glad to get more rigour in my paper.

The proof, where you seem to make your arguments against it (the proof in section 4), is from W. Faris in an Appendix of a book. Faris was a student of Nelson and is now Professor at Arizona.
http://math.arizona.edu/~faris/publications.html

"Probability in quantum mechanics," appendix to David Wick, The Infamous Boundary: Seven Decades of Controversy in Quantum Physics , Birkhauser, Boston, 1995.

You can see his proof partly at google books:
http://books.google.de/books?id=FxypunelyRwC&dq=d+wick+infamous+boundary&pg=PP1&ots=AfXTACaBfH&sig=m4OQjZCOLMMuXFmIPBskB8oY2w8&hl=de&sa=X&oi=book_result&resnum=1&ct=result#PPA216,M1

(unfortunately, the page, where the conditional probability with respect to a sigma algebra is defined, cannot be seen through google books. But Faris refers to Nelsons proof and it seems to be the same definition which Nelson had in mind,

I can see no error in both works.

You are probably a mathematician. I'm only a physicist. Of course, I have heard the usual lectures in stochastic processes, but well, If you would help me to get more riguour in this, I would appreciate it.

By the way, thank you for your comments