Hi TP,

Nice to see that you are an established veteran at FQXi. You are a member, and have received acclaim and prizes at previous essay competitions. I am new to this forum.

I read your current essay twice, once just when it was posted, and then read again yesterday. You have turned out to be quite a story teller, writing has become very persuasive. Congrats on both counts!

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?

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?

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'?

Since I do not understand the nitty gritties of CSL, and the math or physical insights, I would have many questions. But even if you answered, I may not understand. 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?

In a lighter vein, so far the observations (experiments) shaped the path of conceptual and theoretical development. But then theoreticians are going to have the last laugh by producing theories in plenty such that each conforms to all observations yet widely different in their projection of reality. Daunting it is to think that the underlying mathematics is potent enough to support them all.

Rajiv

    Dear Tejinder,

    I enjoyed your essay in which you focus on the emergence of space-time and quantum mechanics form a supposed underlying theory (trace dynamics). Myself, I discuss emergence on a different scale (goal-oriented macroscopic dynamics from underlying microscopic dynamics, no matter whether the latter is deterministic or stochastic, classical or quantum). But back to your interesting essay. You write: "A serious limitation of the CSL model is that it is non-relativistic, and dedicated efforts to make a relativistic version face serious difficulties." You may be interested in the work of Roderich Tumulka, who introduced a relativistic version of GRW:

    R. Tumulka A Relativistic Version of the Ghirardi-Rimini-Weber Model J. Statist. Phys. 125 (2006) 821-840, arXiv:quant-ph/0406094.

    R. Tumulka Collapse and Relativity p. 340-352 in A. Bassi, D. Duerr, T. Weber and N. Zanghi (eds), Quantum Mechanics: Are there Quantum Jumps? and On the Present Status of Quantum Mechanics, AIP Conference Proceedings 844, American Institute of Physics (2006), arXiv:quant-ph/0602208.

    Cheers, Stefan

      5 days later

      Dear Alan,

      Greetings. It is good to meet you again here. Thank you for your comments and for reading my essay. And my apologies for this delay in replying to your comment.

      I remember your viewpoint from our discussion during an earlier contest. I will read your essay before the rating deadline end of next week.

      My best regards,

      Tejinder

      Dear Tejinder Singh,

      Thank you for an excellently written and self-consistent essay focusing, at time quite rigorously, on the nuances of quantum theory to look for how goals originate in the classical regime. In fact, I paused to contemplate where you say "Classical mechanics is a limiting case of quantum mechanics. Yet, in order to arrive at the canonical quantum theory, one must first know the classical theory." I agree that from our historial vantage point, replete with the chauvinisms of science that we have acquired over time, this is how "canonical quantum theory" has evolved. A perspective we may have to shed in order to make meaningful progress in this regard.

      You essay has given me a lot to think about and I wanted to let you know I have in the meantime rated it too.

      Regards,

      Robert

        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

        Dear Stefan,

        Greetings. Thanks so much for reading my essay. I look forward to reading yours.

        Thanks also for telling me about Tumulka's work, which actually I am acquainted with. We discuss it briefly in our review article arXiv:1204.4325 (Section II). It is promising undoubtedly; I think the challenge is to include interactions.

        My best wishes,

        Tejinder

        Dear Robert,

        Thank you so much for reading and appreciating my essay. That is very kind of you.

        Let us hope that there will be an experimental breakthrough in the next few years, which can tell us decisively about the validity of the CSL model.

        My best regards,

        Tejinder

        Thanks TP,

        I understood a few things more about CSL. In my mind, it was always clear how time could emerge, of course from a different consideration, but not how space could emerge. In fact, often I thought of space being the only reality and everything else emerges from it. Anyway, my essay does not deal with any of such things, I only worried about the information aspect. See, I could follow yours, but I am not sure if you could follow mine with as much comfort ! May be you are a better story teller.

        Amplification is understood now, but then, does it mean that all nucleons in a macroscopic body could be considered as forming a single entangled state? The answer you already gave as yes.

        Rajiv

        Dear Tejinder,

        This is a remarkable Essay, despite a bit speculative. I particularly appreciated your observations on the limitations of quantum theory. It was an intellectual pleasure for me reading your Essay, thus, I decided to give you the highest score.

        By the way, today I have read also your GRF Essay in arXiv. It is another intriguing work. Maybe I will attempt to apply your new length scale for quantum gravity in my future works on my Bohr-like black hole model. Congratulations and good luck in both of the Contests. I hope you will have a chance to read our Essay on gravitational waves.

        Cheers, Ch.

        http://fqxi.org/community/forum/topic/2862

          Dear Prof T. P. Singh

          A short glimpse and I have a feeling I'm reading a breakthrough. I will have to go on details of the space in which TD resides.

          I have difficulty understanding one thing. I don't have any knowledge of Gauge Theory so forgive my ignorance.

          How do we form another L^2 Hilbert Space using 2 Hilbert Spaces each of two different N-particle systems? The trace operator you use hints at the quaternions, if I understood it correctly.

            Dear Ch.,

            Thank you so much for your kind remarks and good wishes, and also for seeing my GRF essay. I will be honoured if you consider this new length scale in your work. i am talking to some colleagues about looking for possible experimental tests of this new length.

            Best wishes,

            Tejinder

            Dear Dr. Malik,

            Thank you so much for your kind appreciation.

            If I have understood you correctly, can we not form the new Hilbert space simply as a direct product of the states of the two different systems?

            There possibly is a connection with quaternions, but I am not sure of this. You may want to see Stephen Adler's historical account of his discovery of TD, which was preceded by his work on Quaternionic quantum mechanics, on which he has a book.

            My best wishes,

            Tejinder

            Dear Tejinder,

            I enjoyed very much your essay, in which you discuss CSL and its emergence from TD, the proposal of suppression of quantum superposition at large scales by nonlinearity, and the relation with goals. I agree that superposition has to be suppressed somehow at higher levels, since the classical level doesn't seem to suffer from it (section |7> of my essay). In fact I have a proposal of several experiments that I hope will find some sort of superselection which I hope to suppress superposition in Searching for microscopic classical cats (although in a way compatible with both linear and a possible nonlinear formulation of QM). Best luck in the contest!

            Best regards,

            Cristi Stoica

            The Tablet of the Metalaw

              Tejinder,

              I hope to hear from you over on mine before we imminently have to do our final scoring. I identify some very important new physics that you're well qualified to falsify.

              You know the problem; "Standard quantum theory has no answers. Do these unanswered questions call for new physics?" Not t really entirely 'new' either.

              Very best

              Peter

                Dear Tejinder,

                very interesting essay with provocative thesis (quantum theory as emergent theory) But I like it very much (also along the line of my thinking).

                Therefore you got a high mark from my side.

                Maybe you are also interested to read my essay? This time not bout exotic smoothness and the fractal spacetime.

                All the best

                Torsten

                  Dear Cristi,

                  Greetings, and many thanks for your kind comments.

                  Thanks also for pointing to your essay, which actually I had already read (and rated) and enjoyed reading, though I did not leave a comment :-)

                  Best,

                  Tejinder

                  Dear Peter,

                  Greetings. I had already read your essay with pleasure, and rated it too. Though I have not left any comment.

                  And I agree! QM needs something done to it! :-)

                  My best wishes to you for success in this contest,

                  Tejinder

                  Dear Torsten,

                  Many thanks for your kind remarks on my essay.

                  Best,

                  Tejinder