Dear Rajiv,
It is indeed a great pleasure to hear from you!! :-) My apologies for this delay in replying, and thanks so much for carefully going through my essay. I had browsed through your interesting essay when it appeared, and I will read it again next week.
>I see impressive arguments at places, but wanted to know if you have clarity in your mind as to what those mathematical arguments in fact map to in reality? That is, do you have physical insights for every step in the argument?
At the level of the underlying non-commutative special relativity, it is difficult for me to form a visual picture. But I think physical insight is there: our conceptions are being prejudiced by thinking of quantum mechanics on an ordinary space-time background. We have trouble understanding what the wave function represents. But the wave function makes a lot of sense on a non-commutative background.
>From 'stochastic element responsible for randomness', can one infer that CSL is an indeterministic model If so, then can one identify the source of stochastic behavior even if one cannot have a definitive formulation for the process?
CSL is a phenomenological model which assumes a stochastic process to exist, without specifying where that process is coming from. It might come from gravity, or from Trace Dynamics (statistical fluctuations about equilibrium) - we have ideas, but we do not know for sure.
> One thing I liked most is that in CSL the space-time emerges from collapse. But, I could not figure out how the collapse would choose the values for (t,x,y,z), I mean when to appear and where to appear. I am sure, you do not depend on probability field, do you? You have also given a fundamental constant rc=10^-5 cm; so there is a sense of relative distance and location within the span of emerged universe. Moreover, after the collapse if there is a measure of space and time, then why is it called 'illusion'?
When to appear and where to appear: it is random indeed. By illusion I meant that if you examine microscopically you realise there is no such thing as space ad time.
>The collapse rate seems to be about a few times in the whole life time of the universe. "Between every two collapses, the wave function follows the usual Schrodinger evolution." So after a collapse, how does it regain its global configuration quality to be able to collapse again causing relocalization, or does it remain confined to the space? And why does a collection of N nucleons, or let me suppose M atoms function like unified object to acquire the amplification factor of N.lambda. Then can one consider some arbitrary distribution of N neucleon, not necessarily bound?
The collapse rate is of the order of the age of the universe for a nucleon. It increases linearly with mass [the rate] becoming very very rapid for macroscopic objects. After a collapse, a particle does not remain confined - it expands again, because of ordinary Schrodinger evolution. So it is a repetitive cycle of collapses and expansions. But for a macroscopic object collapses happen so very rapidly that it appears confined at one place.
Amplification: Consider two particles A and B, with A in a superposition of two position states A_1 and A_2, and B in a superposition of two position states B_1 and B_2. If they are bound, then their states are entangled:
(A_1 B_1 A_2 B_2)
If they are not bound, they are in a product state: (A_1 A_2) * (B_1 B_2)
If they are bound, the collapse of EITHER A or B causes the state of both to collapse: say to A_1 B_1.
So any one of them collapsing causes both to collapse. Hence the amplification.
But if they are not bound, collapse of one does not cause the other to collapse: say if A collapses, the state goes to A_1 * (B_1 B_2). B is unaffected..no amplification.
My best wishes to you in this contest,
TP
