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What Is “Fundamental”
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How can mindless mathematical laws give rise to aims and intention?
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Trick or Truth: The Mysterious Connection Between Physics and Mathematics
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How Should Humanity Steer the Future?
January 9, 2014 - August 31, 2014
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It From Bit or Bit From It
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Which of Our Basic Physical Assumptions Are Wrong?
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Is Reality Digital or Analog?
November 2010 - February 2011
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What's Ultimately Possible in Physics?
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Del Rajan: on 7/11/20 at 10:48am UTC, wrote Dear Marco, Sorry about the delayed response.  The essay contest closed...

MARCO BORRELLI: on 7/2/20 at 3:57am UTC, wrote Hi sorry if I repeat my comment but I noticed errors in my English...

MARCO BORRELLI: on 7/1/20 at 19:18pm UTC, wrote Hi Del Rajan, I read your essay with great interest. Compression is very...

Del Rajan: on 5/19/20 at 11:16am UTC, wrote Dear Adel, Thank you for your time to read the essay and your comments. ...

adel sadeq: on 5/19/20 at 0:17am UTC, wrote BTW, my system seem to agree with this interpretation, but not exactly in...

adel sadeq: on 5/19/20 at 0:02am UTC, wrote Dear Del, I have wished that all the essays concentrated on...

Del Rajan: on 5/18/20 at 9:01am UTC, wrote Dear Professor Davies, I greatly appreciate your time and your comments...

Paul Davies: on 5/17/20 at 23:07pm UTC, wrote I have a comment and a question. The Born rule is tacked onto quantum...


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FQXi FORUM
September 19, 2021

CATEGORY: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) [back]
TOPIC: Does God play dice with time itself? by Del Rajan [refresh]
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Author Del Rajan wrote on Apr. 24, 2020 @ 14:26 GMT
Essay Abstract

Gödel's undecidability results showed the incompleteness of formal axiomatic systems.  A more concrete demonstration of incompleteness is predicated on Turing's work on uncomputability.  Perhaps the most illuminating reason for incompleteness can be seen through algorithmic information theory where Chaitin used incompressibility.  Rather remarkably, incompressibilty highlights that incompleteness can be treated to be pervasive phenomenon throughout pure mathematics.  Using this work, Chaitin has pointed out that compression can be generalized to a universal concept.  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.  To warrant such a direction, we examine how compression already exists at a foundational level in current information theories associated to physical systems (both classical and quantum).  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."  We provide speculative mathematical ideas for how such a spacetime-information theory could be developed.  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.

Download Essay PDF File

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Satyavarapu Naga Parameswara Gupta wrote on Apr. 28, 2020 @ 08:48 GMT
Respected Professor Del Rajan,

Your well understood and well studied words...... Theoretical problem: What do the complex amplitudes represent?..........

That is a real question. Can we avoid fully those complex numbers? as the results will be complex and can not be physically placed.

Hope you will have a look at my essay " A properly deciding, Computing and Predicting new theory’s Philosophy" ---- which described Dynamic Universe Model ; where complex numbers are avoided and got many nice results, and many predictions came true....

Best regards

=snp

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Author Del Rajan replied on Apr. 28, 2020 @ 11:37 GMT
Thank you for your message and your thoughts. I will have a look.

Cheers,

Del

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Vladimir Rogozhin wrote on May. 9, 2020 @ 16:53 GMT
Dear Del,

I read with great interest your essay with deep ideas and conclusions aimed at overcoming the crisis of understanding in the philosophical basis of fundamental science. First of all, I want to note these thoughts, which, in my opinion, are important for finding a way to understand the structure of the Universe, the nature of the phenomenon of information:

“Crudely stated, progress was measured in every parameter except understanding. It is our view that an understanding of quantum physics is necessary for genuine progress. ”

“Mathematically modeling the physical world without deep understanding can be compared to machine translation without comprehension. Only with the addition of understanding in our physics can we regard ourselves as an advancing intelligent species. ”

"...we want to harness compression as a primary mathematical technique for the aim to make deeper discoveries of the physical world."

"Our view to resolve the confusion is remove the focus on information in information theories. Rather it is compression in these theories that is fundamental, and whose character we imagine will be found in the deeper laws of the Universe."

I believe that in order to overcome the crisis of understanding in the basis of fundamental science, it is important to remember the philosophical covenant of Paul Florensky:. “We repeat: worldunderstanding is spaceunderstanding.” My high score. I wish you success!

I invite you to see my ideas .

With kind regards,

Vladimir

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Author Del Rajan replied on May. 10, 2020 @ 11:03 GMT
Dear Vladimir,

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

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

Furthermore both classical and quantum information 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.  

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

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Flavio Del Santo wrote on May. 10, 2020 @ 11:51 GMT
Dear Del (if I may),

thanks for a grat essay, well-argued and full of inspiring ideas. I liked your didactical crystal clear introduction to quantum theory and information theory. I appreciate very much your motivation for "understanding" as opposed to the notorious "shut up and calculate" (I have myself written several works about this, also from the historical point of view). Also, your genius idea is to abond the widespread "conventionalism" (as Popper colled it) of "wonder at the austerely

beautiful simplicity of the world as revealed in the laws of physics" as a research program, and substitute it by randomness. If you will have time to read my essay, you will see that my research program with Nicolas Gisin make use exactly of Kolmogorov complexity to find fundamental limits in physics and propose suitable alternatives. I will be most interesed in your feedback.

Meanwhile, I give your essay a top rating, being among the best I read this year.

All good wishes and good luck with the contest!

Flavio

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Author Del Rajan replied on May. 11, 2020 @ 04:33 GMT
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 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 complexity with physics.  It certainly sounds like an innovative path and an exciting exploration.   

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

Cheers,

Del 

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Edwin Eugene Klingman wrote on May. 10, 2020 @ 19:35 GMT
Dear Del Rajan ,

A truly excellent and enjoyable essay!

You make so many wonderful observations, connecting lack of physical evidence to support various views and inability to derive the Born Rule, lack of evidence to support the assumption that non-locality is false, and finally, “nobody knows what quantum information is.” that I must restrain myself from expounding on each of these. Instead I will focus on what seems to be your main hypothesis, that, at a deep level the Universe is random. Several current essays relate to,this assumption.

First, John Bell stated

No one can understand this [deBroglie] theory until he is willing to think of psi as a real objective field rather than just a ‘probability amplitude’.

If one assumes, as I do, that this physical field is self-interactive, then it is essentially non-linear. Bill McHarris’s essay points out that:

the behavior of simple but non-linear classical dynamical systems...can be startlingly similar to quantum mechanical systems in multitudinous ways.

This implies an essentially non-algorithmic system, and Schultz’s essay claims that the limitations on knowability [the ‘no-go’ theorems] do not apply to non-algorithmic patterns.

Your compression ideas are fascinating, and require some digesting. In the mean time I invite you to read my current essay, Deciding on the nature of time and space, and welcome your comments.

Best regards,

Edwin Eugene Klingman

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Author Del Rajan replied on May. 11, 2020 @ 04:40 GMT
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.  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.  I will read it and good luck for the contest.

Cheers,

Del

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Rafael Alves Batista wrote on May. 10, 2020 @ 23:35 GMT
Dear Del,

Great essay. One of the most interesting ones for sure.

I find it interesting how you made the connection between compression and the structure of spacetime itself. In my essay (https://fqxi.org/community/forum/topic/3523) I use similar notions of compression in a slightly different way, combined with finitist notions. You might be interested in taking a look at it.

All the best,

Rafael

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Author Del Rajan replied on May. 11, 2020 @ 04:49 GMT
Dear Rafael,

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

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

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

Cheers,

Del

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Anonymous wrote on May. 11, 2020 @ 16:35 GMT
Dear Del,

Congratulations for your interesting and very well written essay.

I completely relate with your argument that an esthetic principle, as the one of Dirac's, is not enough. And your ''principle of mathematical randomness'', i.e. taking randomness as fundamental, seems (to me) to be one of the best tracks to move forward. I also enjoyed your proposition to focus on compression rather than information, and your proposal on typical and atypical time is really interesting. Working on quantum causality on quantum indefinite causal orders, I would have liked to have an analysis of these compared to your ideas.

"The emergence of time in this intrinsic random manner suggests that God not only plays dice but plays dice all the time and with time itself." My essay aims at arguing for the fact that quantum "paradoxes" might emerge from self-referential issues (i.e. God does play dice, and this fundamental randomness in quantum theory as a source which might be analog to the undecidable propositions in mathematical logic). As an epilogue, I propose a (not very developped) intuition that time itself might emerge from self-referential structures. If you have the time to read it, I would be very interested to have your feedbacks on it.

All the best,

Hippolyte

PS : Correct me if I am wrong, but it seems to me that you identify the Copenhagen interpretation with "shut up and calculate". However, there are rather Copenhagen interpretationS (nuances between Bohr, Heisenberg, Pauli... views) and they do not defend the "shut up and calculate" view, but rather refined forms of realisms, that could be said to be carefully based on structures and relations (cf. the section "The Heirs of Copenhagen" in my essay).

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Hippolyte Dourdent replied on May. 11, 2020 @ 19:03 GMT
I forgot to log in, sorry for this !

Best,

Hippolyte Dourdent

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Author Del Rajan replied on May. 12, 2020 @ 03:54 GMT
Dear Hippolyte,

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

1. Indefinite causal structures: The theory put forth with the process operator and its extension to graphs via quantum causal models is of great interest to me.  Besides the quantum switch concepts, I feel quantum causal models may provide a basis for novel information-theoretic applications (especially in distributed algorithms).  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:  As mentioned in the essay, there is no consensus on what the intepretation states (there are various versions) but that the overarching theme is that a description beyond quantum theory is not needed.  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.  I also provide a reference to David Kaiser's article on the historical inception of the 'shut up and calculate' mindset.  

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

Cheers,

Del

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Anonymous wrote on May. 11, 2020 @ 17:06 GMT
Dear Dr. Rajan,

Your essay is beautifully written and a pleasure to read. You ask all the good questions about quantum mechanics - whether randomness is fundamental, the origin of the Born probability rule, the possibility of there being randomness in time, and the deep foundational issues that plague quantum gravity research.

I wanted to mention here that there has been much progress on these questions, in a manner which moved away from `shut up and calculate'. It started with the Ghirardi-Weber-Rimini-Pearle theory of spontaneous localisation in 1986. They provided a falsifiable and dynamical explanation of the quantum measurement problem, and of the absence of macroscopic superpositions. The theory is currently being tested in a few labs in Europe.

Subsequently, Stephen Adler sought to derive quantum theory from a deeper underlying formalism - his theory of trace dynamics. The deeper theory is a deterministic matrix dynamics from where quantum theory, Born rule, randomness, and spontaneous localisation are emergent phenomena.

Recently, I have shown how to include gravity in Adler's framework, using the mathematics of non-commutative geometry. This has lead to the new theory of Spontaneous Quantum Gravity, where indeed God plays dice with time, but only in an emergent sense. Underlying quantum indeterminism is determinism at the Planck scale.

I discuss these developments in my essay in this contest: The pollen and the electron. Since many of the deep questions you raise are addessed and answered in my work, I hope you will find it interesting.

My best wishes to you in this contest,

Tejinder.

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Member Tejinder Pal Singh wrote on May. 11, 2020 @ 17:08 GMT
My apologies. The anonymous in the previous post is me...I forgot to log in. Sorry!

Tejinder

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Author Del Rajan replied on May. 12, 2020 @ 04:04 GMT
Dear Tejinder,

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

Collapse models:  I have a basic undertanding of GRW collapse models as well as the one proposed by Penrose.  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.  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.  For me, the more fundamental question is what do the amplitudes themselves physically represent?

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

Cheers,

Del

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Lachlan Cresswell wrote on May. 13, 2020 @ 13:24 GMT
Dear Del,

A most interesting, dense and deep essay which I enjoyed reading.

I was particularly interested in your conclusion re typical and atypical time intervals. In my theory of time (not covered in my essay) I also have typical intervals (relates to relative time, and flow rate of time) and atypical intervals (relates to expansion of aether, cosmological time - thus working at boyh the smallest and largest scales.

In my essay I discuss the 3 Un's as they have affected me, and I cover another aspect of time from a new point of view - philosophical presentism.

Good luck with the ratings - you deserve high scores!

Regards

lockie Cresswell

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Author Del Rajan replied on May. 14, 2020 @ 05:18 GMT
Dear Lockie,

Thank you for taking your time to read my essay.  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. 

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

Cheers,

Del 


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Michael muteru wrote on May. 13, 2020 @ 19:26 GMT
Hi Rajan. very important points you raise there on quantum spookiness in a very simple and elegant manner. very well done, you certainly earn my votes.Forgive me, but to be sincere this year's contest raised within me Questions which to date make me more than just suspicious about us as Quantum observers.When quantum event occurs in nature,Do quantum effects of an opposite Nature happen in our brains to counter observation ridding us access to Reality ?maybe you may please see my take on Anthropic bias here -https://fqxi.org/community/forum/topic/3525.all the best to you thanks.

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Author Del Rajan replied on May. 14, 2020 @ 05:27 GMT
Dear Michael,

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

Your idea on observers is interesting.  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.  Of interest to you may be the work of Penrose & Hameroff where they investigate whether quantum superpositions could exist in microtubules. 

More pragmatically there has been research on how quantum computing can improve artificial intelligence.  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

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Jochen Szangolies wrote on May. 14, 2020 @ 18:09 GMT
Dear Del,

this was a very exciting essay for me to read---thank you for submitting it to this contest! You provide a highly original perspective, and argue it well. I like the starting point: Einstein and Hilbert, each poised in there respective quest for certainty, set up to be foiled by incompleteness and quantum unpredictability. It's perhaps no accident their names are, together,...

view entire post


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Author Del Rajan replied on May. 15, 2020 @ 11:21 GMT
Dear Jochen,

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

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

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

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

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

Cheers,

Del

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sherman loran jenkins wrote on May. 14, 2020 @ 19:50 GMT
Del:

A new era dawns.  Old questions become quaint and historical.  Is the whole community ready?  Or is physical reality too dangerous for the collective understanding at this time? 

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Author Del Rajan replied on May. 15, 2020 @ 11:24 GMT
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: 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

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Member Paul Davies wrote on May. 17, 2020 @ 23:07 GMT
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?

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Author Del Rajan replied on May. 18, 2020 @ 09:01 GMT
Dear Professor Davies,

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

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

Tunnelling time:  Your suggestion is brilliant!!! That would be a very interesting analysis.  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.  I wish I had thought of that!  I will spend some time reading the literature in this area and think about this.

Cheers,

Del

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adel sadeq wrote on May. 19, 2020 @ 00:02 GMT
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

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adel sadeq replied on May. 19, 2020 @ 00:17 GMT
BTW, my system seem to agree with this interpretation, but not exactly in some details.

https://www.physicsforums.com/threads/the-thermal-in
terpretation-of-quantum-physics.967116/

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Author Del Rajan replied on May. 19, 2020 @ 11:16 GMT
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. 

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

Cheers,

Del

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MARCO CIRO BORRELLI wrote on Jul. 1, 2020 @ 19:18 GMT
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

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MARCO CIRO BORRELLI wrote on Jul. 2, 2020 @ 03:57 GMT
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!

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Author Del Rajan replied on Jul. 11, 2020 @ 10:48 GMT
Dear Marco,

Sorry about the delayed response.  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.  However this is merely a heuristic argument which I emphasized is underdeveloped: I assume that the 'time compression' has the 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).  Analogous to typical and atypical sequences/states, one can then look at typical and atypical time intervals.  In the endnotes, this is also extended to the spatial case with some comments made on the Lorentz transformations.

Cheers,

Del

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