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Del Rajan

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

Dear Adel,

Thank you for your time to read the essay and your comments.

Yes I agree with you that the sticking point is the Born rule.聽

Thank you for sharing your essay and I will have a look.聽聽

Cheers,

Del

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 Jochen,

I truly enjoyed reading your essay with its very original path backed by rigorous arguments.

I found it beautiful that you related the undecidability of those values to Bell's results.聽 聽 And that ultimately there there may be deep relationship between mathematical undecidability and physical unknowability聽 Falls out elegantly if one takes the "reconstructing" program.聽聽

I also saw that you highlighted the existence of a joint probability distribution regarding the CHSH inequalities.聽 This statement also reminds me of the crucial conditions behind the entropic Bell inequalities.聽聽I would be very curious to know how you will advance your program.聽 In particular whether this will have implications to nonlocalities across time (Leggett-Garg inequality and its entropic versions).聽聽

Thank you for the wonderful essay and I wish you the best for the contest.聽 I have give you a well deserved top vote!

Cheers,

Del聽

Dear Flavio,

What a wonderful essay!聽 It took me on a very insightful journey and I have given it a top vote!聽聽

I enjoyed the historical background, the articulation of the principle of infinite precision, and relating this to ideas on Kolmogorov complexity, information theory and measurement.聽 Your central thesis along with bringing these various topics together was very聽crafted.聽 I very much enjoyed your "surgical" approach to breaking topics and finding their underlying essence.

Good luck for the contest!聽

聽

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

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 Michael,

Thank you for your kind comment and your time to read the essay.

Your idea on observers is interesting.聽 I find that the standard definition of an observer in quantum theory is not well-defined. Whether the brain will play a part in a future theory is unknown.聽 Of interest to you may be the work of Penrose &聽Hameroff where they investigate whether quantum superpositions could exist in microtubules.聽

More pragmatically there has been research on how quantum聽computing can improve artificial intelligence.聽 There is a paper called "Quantum Machine Learning" by Lloyd et al that covers this area well.

Thank you for pointing me towards your essay.

Cheers,

Del

Dear Lockie,

Thank you for taking your time to read my essay.聽 I appreciate your kind comments.

Yes in my essay, the typical and atypical time intervals are purely predicted on the notion that compression is perhaps the appropriate mathematical technique for fundamental physics.聽

Thank you for pointing out your ideas on the intersection of time and typicality. I look forward to reading your essay.聽 (The link above did not work but I have found your essay on聽https://fqxi.org/community/forum/topic/3397)

Cheers,

Del聽

Dear Tejinder,

Thank you for your most kind comments and your time to read the essay.聽 To elaborate on some of the points you mentioned:

Collapse models:聽 I have a basic undertanding聽of GRW collapse models as well as the one proposed by Penrose.聽 For me, the measurement problem is not so fundamental; it is only fundamental if one assumes quantum information (i.e. the quantum state) has a direct physical manifestation.聽 Whether it does or not is hotly debated and in the essay I do provide a reference to Leifer's review paper on this topic.聽 For me, the more fundamental question is what do the amplitudes themselves physically represent?

Trace Dynamics:聽 I must admit that I am unfamiliar with this theory but it sounds very interesting and novel.聽 Hence I look forward to reading your essay.聽 Thank you for pointing that out.

Cheers,

Del

Dear Hippolyte,

Thank you for taking the time to read my essay.聽 I appreciate your kind comments and critical feedback.聽 To elaborate on some of your points:

1. Indefinite causal structures: The theory put forth with the process operator and its extension聽to graphs via quantum causal models is of great interest to me.聽 Besides the quantum switch concepts, I feel quantum causal models may provide a basis for novel information-theoretic applications (especially in distributed algorithms).聽 More fundamentally, the notion of unordered time which I briefly mention in the essay can be related to some formal concepts in their theory, and I do provide a reference to the recent Bell's theorem for temporal order.

2. Copenagen interpretation:聽 As mentioned in the essay, there is no consensus on what the intepretation聽states (there are various versions) but that the overarching theme is that a description beyond quantum theory is not needed.聽 I mention 'shut up and calculate' as a refined version of the latter theme given it has the commonality of ignoring a desire for a deeper description.聽 I also provide a reference to聽David Kaiser's article on the historical inception of the 'shut up and calculate' mindset.聽聽

I will be most interested to read your essay and the idea that time may emerge from self-referential structures.聽 Thank you for that and I will have a read.

Cheers,

Del

Dear聽Rafael,

Thank you for your time to read the essay.聽 I appreciate the kind feedback.

Yes I am very interested in the connection.聽 What I imagine would be interesting (in relation to spacetime) would be looking at the concept of compression in relativistic quantum information (RQI).聽 Whether an RQI version of Schumacher's coding theorem would give a novel insight into spacetime.聽

I will most certainly be interested to read your essay and its utilization of compression.聽 聽聽

Cheers,

Del

Dear Edwin Eugene Klingman,

Thank you for your time and for your kind feedback.

In regards to your comments regarding non-locality and aspects on quantum information, a further interesting point would be the PBR theorem.聽 It is profound in that it looks at the reality of quantum information, or alternatively introduces a non-locality far more stranger than Bell non-locality.

Thank you for pointing me towards your essay.聽 I will read it and good luck for the contest.

Cheers,

Del

Dear Flavio,

Thank you for your time to read the essay and your most kind comments.

It is quite interesting that the technological aims of the 20th century provided a basis for 'shut up and calculate' whereas聽in this century the technological development associated to quantum information makes it difficult for this attitude to be unchallenged.

I am very interested to read your work on integrating the Komogorov聽complexity with physics.聽 It certainly sounds like an innovative path and an exciting聽exploration.聽 聽

I will most certainly read your essay and good luck with the contest.

Cheers,

Del聽

Dear Vladimir,

Thank you for your message.聽 To elaborate on the points you mentioned:

Modern derivations of incompleteness are found in algorithmic information theory (AIT).聽 Central in these derivation is compression.

Furthermore both classical and quantum information聽theory state compression as the fundamental result through their coding theorems. Information theories seem to be about compression, not information.

If we assert that the Universe is made of information, then an educated guess is that compression is to be found in its deeper laws.聽聽

Perhaps the advancements on incompleteness (namely AIT) provides a better scaffold for fundamental physics than harnessing the frontiers of geometry/topology.

I will read your essay. Thank you again for your time and your most kind comments.

Cheers,

Del

Thank you for your message and your thoughts. I will have a look.

Cheers,

Del

Essay Abstract

G枚del's undecidability results showed the incompleteness of formal axiomatic systems.聽 A more concrete demonstration of incompleteness is predicated on Turing's work on uncomputability.聽聽Perhaps the most illuminating reason for incompleteness can be seen through algorithmic information theory where Chaitin used incompressibility.聽 Rather remarkably, incompressibilty聽highlights that incompleteness can be treated to be pervasive phenomenon throughout pure mathematics.聽 Using this work, Chaitin has pointed out that compression can be generalized to a universal concept.聽 In align with this, we argue to embrace compression as a primary method in physics akin to the geometrization of physics in the 20th century.聽 To warrant such a direction, we examine聽how compression already聽exists聽at a foundational level in current information theories associated to physical systems (both classical and quantum).聽 We proceed to argue that applying the concept of compression to the structure of spacetime provides us with a novel path forward in fundamental physics, which includes addressing the conceptual problems in quantum physics where "God plays dice."聽 We provide speculative聽mathematical ideas for how such a spacetime-information theory could be developed.聽 This alludes to the notion that time itself is intrinsically random.

Author Bio

Del Rajan is a quantum information scientist at the Victoria University of Wellington in New Zealand.

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