Dear Jochen,

Thank you for your time to read the essay.聽 I very much appreciate your comments.聽 They were very resourceful.

Firstly your take on General Relativity (GR) with respect to Einstein聽and Hilbert's aim is beautifully captured.聽 Second your elaboration on the modelling aspect involving probabilities is very well said!聽 I wish I had articulated it that way in the essay!聽

On a point on GR, I feel that for a conceptual undestanding the light cone as the fundamental structure is the best method.聽 This is mathematically well captured by the null tetrad formulation.聽 However its spin coefficient equations are mathematically "ugly."聽 Hence I feel even with GR, beauty is only skin deep when one puts understanding as the priority.聽

I have downloaded all your links and I greatly appreciate your time to mention those.聽 I will also read your essay (along with some others) during the weekend.聽

I am very interested to know more about your ideas on how the goal of finding a comprehensible foundation聽of quantum聽physics took you to topics regarding incompleteness.聽 I am looking forward to reading your essay.

Cheers,

Del

Dear Sherman,

Thank you for your comment.

I agree with you that a new era is dawning in particular in regards to the extraordinary growth of quantum information science:聽Its novel technologies best articulate the shocking narratives of quantum physics, and the design of those technologies give a much needed resurgence to focusing on the foundational questions.

Cheers,

Del

I have a comment and a question. The Born rule is tacked onto quantum mechanics and accepted without question. I have often wondered how well it has been tested experimentally. Would we know if there were departures from the Born rule at very high energies (say, cosmic rays), for example?

My question refers to your statement: 'Far more profound are atypical time intervals. These are ones that exhibit Lorentz violations as they cannot be compressed. They do occur but very rarely.' Can you apply your analysis to the famous ambiguity in defining tunnelling time?

    Dear Professor Davies,

    I greatly appreciate your time and your comments with questions.聽 To answer accordingly:

    Born rule: I do not know whether the Born rule has been tested at this extreme energy environment.聽 However, another curious place would be in the technological development of quantum computers聽(QC).聽 It would be nice if turns out that the ever increasing entangled set of qubits in a QC ends up fundamentally聽deviating from the Born rule (ultimately the final stages of the quantum algorithm is a measurement).聽聽Certainly in this environment, there will be more聽people interested with "skin in the game" given the various QC applications (finance, security, etc).聽聽

    Tunnelling time:聽 Your suggestion is brilliant!!! That would be a very interesting analysis.聽 In fact it may be the exact right place to start looking at how to progress this and develop this into a toy model with some predictive power.聽 I wish I had thought of that!聽 I will spend some time reading the literature in this area and think about this.

    Cheers,

    Del

    Dear Del,

    I have wished that all the essays concentrated on the problems that you have addressed about QM. Namely, superposition and Born's rule , because these are really the sticking point.

    My system, while not entirely clear, however it point to that the probability density is in fact the density of energy contained in the particle, because as I calculate the associated "lines" and interpret them as energy they very much agree with the standard results of QM and QFT. Moreover also gravity appears and EPR is automatic since the system is inherently nonlocal. All from a system which is so simple and I discovered it by chance and was not after "mathematical beauty".

    while I use probability in my programs but that is only for convenience. The system is similar to geometric probability as in line-line and line-circle picking where the results are obtained by probability but it is not the only way.

    We seem to disagree on time, however maybe as the theory becomes more mature a different perspective might be in order. Thank you.

    Reality is a simple mathematical structure literally, hence computable

      a month later

      Hi Del Rajan, I read your essay with great interest. Compression is very interesting as a fundamental concept. I did not understand if the atypical time and the typical time consider them fundamental or emerging. : "time is intrinsic to chance" I hope for your clarifications

      Best wishes for your wise

      Hi sorry if I repeat my comment but I noticed errors in my English therefore I tried to write better I read your essay. I found your essay really interesting. Very interesting that the compression of information is taken as a fundamental concept. I have not been able to understand, however, how you consider the atypical and typical time intervals: are they fundamental or emerging? The atypical time interval I think I understand that it is rare and fundamental?Your sentence: "This alludes to the notion that time itself is intrinsically random"Therefore, if randomness is fundamental, time should also be fundamental?

      I hope for your clarifications. Thank you in advance and best wishes for your essay!

        9 days later

        Dear Marco,

        Sorry about the delayed response.聽 The essay contest closed over a month ago hence I did not check the comments.

        Thank you for your time to read the essay.

        The essay includes a technical endnotes' section which explains how I arrive at the notion of typical/atypical time intervals.聽 However this is merely a heuristic argument which I emphasized is underdeveloped: I assume that the 'time compression' has the聽same mathematical backbone as classical compression (quantum compression as articulated in Schumacher's pioneering quantum coding paper also builds largely on the mathematical backbone of classical compression).聽 Analogous to typical and atypical sequences/states, one can then look at typical and atypical time intervals.聽 In the endnotes, this is also extended to the spatial case with some comments made on the Lorentz transformations.

        Cheers,

        Del