Self-similarity, conservation of entropy/bits and the black hole information puzzle by Douglas Singleton, Elias Vagenas, & Tao Zhu

Doug, et al,

This is a copy of my respond to Doug Singleton on my essay blog.

I have read several papers by Vladimir Dzhunshaliev on octonion field theory, and Merab Gogberashvili is a familiar name as well. Trying to understand how nonassociative mathematics of operators fits into physics is really the hard part. I think that quantum mechanics is purely complex, or C. Of course classical mechanics is R. Gauge theory can be written according to quaternions H. A lot of gauge theory is done though in standard vector form without quaternions. It is interesting though that Maxwell formulated electromagnetism, the first gauge field theory, in quaternions. Field operators in a second quantization act on a Fock space basis to give quantum amplitudes. So we have a relationship that might be heuristically written as π:H --- > C. The question is then whether there is some sort of higher level structure π:O --- > H.

Spacetime I think offers a clue. A black hole horizon has some quantum uncertainty on a scale near the string or Planck length. There will then be an associative uncertainty with three quantum fields, where one of those fields is identified near the horizon. The standard approach to QFT is to assign a harmonic oscillator at every point in space, impose equal time commutators on that spatial surface with the Wightman criterion for commutation, and work from there. Yet that spatial surface on a small scale will have some noncommutative structure and this will lead to a host of uncertainties in assigning QFT operators. If there are event horizons this should lead to an associative uncertainty.

The above "maps" between C, H and O, where a similar map π:C --- > R would be the relationship between quantum mechanics and classical mechanics, are really just forms of the Hopf fibration. The relationship between quantum and classical mechanics is of course a difficult subject in its own right. With each of these "ladders" on the Hopf fibration there is some increased uncertainty. Quantum mechanics saved physics from the UV divergence that classical mechanics predicted with the hydrogen atom. Similarly this may protect physics from divergences with black holes, such as the singularity and maybe with the current big problem of firewalls.

Thanks for the good word. I had a computer crash (virus attack etc) that erased my voting code. I also had it written down on a paper that also went missing. I have not been able to vote on papers for about a week. The FQXi people have so far not serviced my request that it be retransmitted. I have also been a bit slow in reading papers this contest cycle. I see that you have a paper in the list. I seem to remember that last year your paper was riding fairly high, where mine in contrast tanked.

Cheers LC

Dear Douglas Elias & Tao,

I enjoyed your essay and agree that "energy conservation and the tunneling picture of black hole radiation allow us to show how the original "bits" of black hole information encoded in the horizon were transformed into the "its" of the outgoing correlated Hawking photons, thus providing a potential all orders in ~ solution to the black hole information loss puzzle".

It makes perfect sense and was were I was going with my essay, but omitted some further detail which agrees with this. It would have taken another 10 pages in my case to add this aspect.

However, part of the process is apparent when we note that both sides of 0 of the Fibonacci sequence, 2 remains positive. My representation of how Hawking Radiation releases energy is the -1, such that information sits evenly at the horizon and is maintained there. But also in 1-dimensional string like structures that may become Hawking radiation.

Anyway please take a look, and I'm delighted to see such a fantastic essay doesn't contradict mine!

Best wishes and kind regards,

Antony

Dear Doug,

Very nice essay. Not that I dont have reservations about the black hole idea but your thoughts were well presented. So a good score from me.

On the Planck length, what likelihood that it is physically real? My essay is here you may take a look.

Best regards,

Akinbo

Hi Doug

Richard Feynman in his Nobel Acceptance Speech (http://www.nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-lecture.html)

said: "It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but with a little mathematical fiddling you can show the relationship. And example of this is the Schrodinger equation and the Heisenberg formulation of quantum mechanics. I don't know why that is - it remains a mystery, but it was something I learned from experience. There is always another way to say the same thing that doesn't look at all like the way you said it before. I don't know what the reason for this is. I think it is somehow a representation of the simplicity of nature."

I too believe in the simplicity of nature, and I am glad that Richard Feynman, a Nobel-winning famous physicist, also believe in the same thing I do, but I had come to my belief long before I knew about that particular statement.

The belief that "Nature is simple" is however being expressed differently in my essay "Analogical Engine" linked to http://fqxi.org/community/forum/topic/1865 .

Specifically though, I said "Planck constant is the Mother of All Dualities" and I put it schematically as: wave-particle ~ quantum-classical ~ gene-protein ~ analogy- reasoning ~ linear-nonlinear ~ connected-notconnected ~ computable-notcomputable ~ mind-body ~ Bit-It ~ variation-selection ~ freedom-determinism ... and so on.

Taken two at a time, it can be read as "what quantum is to classical" is similar to (~) "what wave is to particle." You can choose any two from among the multitudes that can be found in our discourses.

I could have put Schrodinger wave ontology-Heisenberg particle ontology duality in the list had it comes to my mind!

Since "Nature is Analogical", we are free to probe nature in so many different ways. And you have touched some corners of it.

Good Luck,

Than Tin

Dear Doug, Elias and Tao,

I just finished reading your essay. Your starting point is the previous result of Banerjee and Majhi (arXiv:0808.3688, arXiv:0805.2220) for the temperature of a black hole (eqn 7 in your essay) where backreaction is taken into account. The crucial point is your ansatz (eqn 9) for the form of the coefficients in the expansion of the quantum action in a power series in hbar, from which you obtain the regularized form of the entropy (eqn 10).

If correct (and I haven't checked your calculations) then your result is of great importance. It would put on a firm foundation the notion that quantum mechanics and general relativity **can be** reconciled in a self-consistent framework. However, the work remains incomplete in that underlying your calculations is the implicit assumption that the continuous, commutative nature of spacetime remains the same at all scales. As Mittelman noted in previous comments, at some point non-commutative geometry should take over, leading to a black hole remnant as the end result of black hole evaporation. There should be some simple way to reconcile your calculations with those from the NC approach.

Your work also likely has some connections with Ansari's work on black hole radiation in the framework of LQG (hep-th/0607081, arXiv:0711.1879). Overall your essay is very readable (except for the "public" who have a hard time following any mathematical arguments) and arguably deserves a place in the top three - if not at the very top.

Cheers,

Deepak

Dear Douglas,

One single principle leads the Universe.

Every thing, every object, every phenomenon

is under the influence of this principle.

Nothing can exist if it is not born in the form of opposites.

I simply invite you to discover this in a few words,

but the main part is coming soon.

Thank you, and good luck!

I rated your essay accordingly to my appreciation.

Please visit My essay.

Hi Doug,

Thanks for the very helpful and interesting comments over on my page and for the suggested reading here. I really liked your essay and think you deserve to do well, so hope my rating helps.

Best wishes & kind regards,

Antony

Dear Douglas Singleton, Elias Vagenas, & Tao Zhu :

I am an old physician and I don't know nothing of mathematics and almost nothing of physics,

But maybe you would be interested in my essay over a subject which after the common people, physic discipline is the one that uses more than any other, the so called "time".

I am sending you a practical summary, so you can easy decide if you read or not my essay "The deep nature of reality".

I am convince you would be interested in reading it. ( most people don't understand it, and is not just because of my bad English).

Hawking in "A brief history of time" where he said , "Which is the nature of time?" yes he don't know what time is, and also continue saying............Some day this answer could seem to us "obvious", as much than that the earth rotate around the sun....." In fact the answer is "obvious", but how he could say that, if he didn't know what's time? In fact he is predicting that is going to be an answer, and that this one will be "obvious", I think that with this adjective, he is implying: simple and easy to understand. Maybe he felt it and couldn't explain it with words. We have anthropologic proves that man measure "time" since more than 30.000 years ago, much, much later came science, mathematics and physics that learn to measure "time" from primitive men, adopted the idea and the systems of measurement, but also acquired the incognita of the experimental "time" meaning. Out of common use physics is the science that needs and use more the measurement of what everybody calls "time" and the discipline came to believe it as their own. I always said that to understand the "time" experimental meaning there is not need to know mathematics or physics, as the "time" creators and users didn't. Instead of my opinion I would give Einstein's "Ideas and Opinions" pg. 354 "Space, time, and event, are free creations of human intelligence, tools of thought" he use to call them pre-scientific concepts from which mankind forgot its meanings, he never wrote a whole page about "time" he also use to evade the use of the word, in general relativity when he refer how gravitational force and speed affect "time", he does not use the word "time" instead he would say, speed and gravitational force slows clock movement or "motion", instead of saying that slows "time". FQXi member Andreas Albrecht said that. When asked the question, "What is time?", Einstein gave a pragmatic response: "Time," he said, "is what clocks measure and nothing more." He knew that "time" was a man creation, but he didn't know what man is measuring with the clock.

I insist, that for "measuring motion" we should always and only use a unique: "constant" or "uniform" "motion" to measure "no constant motions" "which integrates and form part of every change and transformation in every physical thing. Why? because is the only kind of "motion" whose characteristics allow it, to be divided in equal parts as Egyptians and Sumerians did it, giving born to "motion fractions", which I call "motion units" as hours, minutes and seconds. "Motion" which is the real thing, was always hide behind time, and covert by its shadow, it was hide in front everybody eyes, during at least two millenniums at hand of almost everybody. Which is the difference in physics between using the so-called time or using "motion"?, time just has been used to measure the "duration" of different phenomena, why only for that? Because it was impossible for physicists to relate a mysterious time with the rest of the physical elements of known characteristics, without knowing what time is and which its physical characteristics were. On the other hand "motion" is not something mysterious, it is a quality or physical property of all things, and can be related with all of them, this is a huge difference especially for theoretical physics I believe. I as a physician with this find I was able to do quite a few things. I imagine a physicist with this can make marvelous things.

With my best whishes

Héctor

Dear All

Let me go one more round with Richard Feynman.

In the Character of Physical Law, he talked about the two-slit experiment like this "I will summarize, then, by saying that electrons arrive in lumps, like particles, but the probability of arrival of these lumps is determined as the intensity of waves would be. It is this sense that the electron behaves sometimes like a particle and sometimes like a wave. It behaves in two different ways at the same time.

Further on, he advises the readers "Do not keep saying to yourself, if you can possibly avoid it. 'But how can it be like that?' because you will get 'down the drain', into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that."

Did he says anything about Wheeler's "It from Bit" other than what he said above?

Than Tin

Dear Douglas Singleton, Elias Vagenas, & Tao Zhu :

I am an old physician and I don't know nothing of mathematics and almost nothing of physics,

But maybe you would be interested in my essay over a subject which after the common people, physic discipline is the one that uses more than any other, the so called "time".

I am sending you a practical summary, so you can easy decide if you read or not my essay "The deep nature of reality".

I am convince you would be interested in reading it. ( most people don't understand it, and is not just because of my bad English).

Hawking in "A brief history of time" where he said , "Which is the nature of time?" yes he don't know what time is, and also continue saying............Some day this answer could seem to us "obvious", as much than that the earth rotate around the sun....." In fact the answer is "obvious", but how he could say that, if he didn't know what's time? In fact he is predicting that is going to be an answer, and that this one will be "obvious", I think that with this adjective, he is implying: simple and easy to understand. Maybe he felt it and couldn't explain it with words. We have anthropologic proves that man measure "time" since more than 30.000 years ago, much, much later came science, mathematics and physics that learn to measure "time" from primitive men, adopted the idea and the systems of measurement, but also acquired the incognita of the experimental "time" meaning. Out of common use physics is the science that needs and use more the measurement of what everybody calls "time" and the discipline came to believe it as their own. I always said that to understand the "time" experimental meaning there is not need to know mathematics or physics, as the "time" creators and users didn't. Instead of my opinion I would give Einstein's "Ideas and Opinions" pg. 354 "Space, time, and event, are free creations of human intelligence, tools of thought" he use to call them pre-scientific concepts from which mankind forgot its meanings, he never wrote a whole page about "time" he also use to evade the use of the word, in general relativity when he refer how gravitational force and speed affect "time", he does not use the word "time" instead he would say, speed and gravitational force slows clock movement or "motion", instead of saying that slows "time". FQXi member Andreas Albrecht said that. When asked the question, "What is time?", Einstein gave a pragmatic response: "Time," he said, "is what clocks measure and nothing more." He knew that "time" was a man creation, but he didn't know what man is measuring with the clock.

I insist, that for "measuring motion" we should always and only use a unique: "constant" or "uniform" "motion" to measure "no constant motions" "which integrates and form part of every change and transformation in every physical thing. Why? because is the only kind of "motion" whose characteristics allow it, to be divided in equal parts as Egyptians and Sumerians did it, giving born to "motion fractions", which I call "motion units" as hours, minutes and seconds. "Motion" which is the real thing, was always hide behind time, and covert by its shadow, it was hide in front everybody eyes, during at least two millenniums at hand of almost everybody. Which is the difference in physics between using the so-called time or using "motion"?, time just has been used to measure the "duration" of different phenomena, why only for that? Because it was impossible for physicists to relate a mysterious time with the rest of the physical elements of known characteristics, without knowing what time is and which its physical characteristics were. On the other hand "motion" is not something mysterious, it is a quality or physical property of all things, and can be related with all of them, this is a huge difference especially for theoretical physics I believe. I as a physician with this find I was able to do quite a few things. I imagine a physicist with this can make marvelous things.

With my best whishes

Héctor

Dear All

A standard-issue big city all-glass high-rise stands across the street from my usual bus stop. When I look up the high-rise facade, I can see the reflections of the near-by buildings and the white clouds from the sky above. Even when everything else looks pretty much the same, the reflections of the clouds are different, hour to hour and day to day.

After I boarded the bus, I rushed to get a single seat facing four others on a slightly elevated platorm. From my vantage point, I can't help noticing the shoes of the four passengers across from my seat are not the same, by either the make , the design, or the style, and that is true even when the four passengers happen to be members of the same family.

I could change the objects of my fascination from shoes to something else, to buttons on the dresses for example, but I do not think the result would have been any different. Diversity or Uniqueness would still rule the day! (There is a delightful essay on the subject of uniqueness by Joe Fisher in this contest.)

I am pretty sure people are fascinated by the diversity and the uniqueness in the world, when the other side of it is the inevitable boredom of sameness every time.

However, we have a need to know where all this beautiful and enchanting diversity comes from. Borrowing Wheelerian phraseology of "How come the quantum?", I ask "How come the diversity?" A standard physics answer is "Entropy always increases." (I am not a physicist, and I don't know if that is the final answer.)

Whenever I'm out of my depth, I go back to my theory of everything (TOE), which is a mental brew of common sense, intuition, gut, analogy, judgement, etc. etc. , buttressed when I can with a little thought-experiment.

The thought-experiment is simple. Imagine cutting a circle into two precisely, identical, and equal parts. Practically, there is no way we can get the desired result, because one part will be bigger or smaller in some way.

Physics - especially quantum physics - says it don't matter, do the superposition!

But superposition is fictive, an invention like the Macarena dance, and it has given us a cat, alive and dead at the same time.

I have heard that angels can dance on the tip of the needle, and now I'm finding out some of us can too!

Cheers and Good Luck to All,

Than Tin

Doug,

Many thanks for the suggested reading - I will take a look. No panic about my essay - there are so many to get through - it is an enjoyable, but massive task.

Best wishes,

Antony

Hello again Doug - sorry about the messages above too - going stir crazy trying to touch back with every thread I've commented on.

I certainly will look at this.

Thanks again and best wishes,

Antony

Having read so many insightful essays, I am probably not the only one to find that my views have crystallized, and that I can now move forward with growing confidence. I cannot exactly say who in the course of the competition was most inspiring - probably it was the continuous back and forth between so many of us. In this case, we should all be grateful to each other.

If I may, I'd like to express some of my newer conclusions - by themselves, so to speak, and independently of the logic that justifies them; the logic is, of course, outlined in my essay.

I now see the Cosmos as founded upon positive-negative charges: It is a binary structure and process that acquires its most elemental dimensional definition with the appearance of Hydrogen - one proton, one electron.

There is no other interaction so fundamental and all-pervasive as this binary phenomenon: Its continuance produces our elements - which are the array of all possible inorganic variants.

Once there exists a great enough correlation between protons and electrons - that is, once there are a great many Hydrogen atoms, and a great many other types of atoms as well - the continuing Cosmic binary process arranges them all into a new platform: Life.

This phenomenon is quite simply inherent to a Cosmos that has reached a certain volume of particles; and like the Cosmos from which it evolves, life behaves as a binary process.

Life therefore evolves not only by the chance events of natural selection, but also by the chance interactions of its underlying binary elements.

This means that ultimately, DNA behaves as does the atom - each is a particle defined by, and interacting within, its distinct Vortex - or 'platform'.

However, as the cosmic system expands, simple sensory activity is transformed into a third platform, one that is correlated with the Organic and Inorganic phenomena already in existence: This is the Sensory-Cognitive platform.

Most significantly, the development of Sensory-Cognition into a distinct platform, or Vortex, is the event that is responsible for creating (on Earth) the Human Species - in whom the mind has acquired the dexterity to focus upon itself.

Humans affect, and are affected by, the binary field of Sensory-Cognition: We can ask specific questions and enunciate specific answers - and we can also step back and contextualize our conclusions: That is to say, we can move beyond the specific, and create what might be termed 'Unified Binary Fields' - in the same way that the forces acting upon the Cosmos, and holding the whole structure together, simultaneously act upon its individual particles, giving them their motion and structure.

The mind mimics the Cosmos - or more exactly, it is correlated with it.

Thus, it transpires that the role of chance decreases with evolution, because this dual activity (by which we 'particularize' binary elements, while also unifying them into fields) clearly increases our control over the foundational binary process itself.

This in turn signifies that we are evolving, as life in general has always done, towards a new interaction with the Cosmos.

Clearly, the Cosmos is participatory to a far greater degree than Wheeler imagined - with the evolution of the observer continuously re-defining the system.

You might recall the logic by which these conclusions were originally reached in my essay, and the more detailed structure that I also outline there. These elements still hold; the details stated here simply put the paradigm into a sharper focus, I believe.

With many thanks and best wishes,

John

jselye@gmail.com

Dears Colleagues,

I have just ended to re-read your intriguing Essay. As I previously told you, it is complementary to my one and, in my opinion, it further improves the elegant approach by Zhang, Cai, Zhan and You. Thanks also to have stressed the importance of the black hole information paradox within the theme of this Essay Competition. In fact, there is some guy who strangely claims that it does not address the core questions of this Essay Contest.

In any case, I enjoyed a lot in reading your Essay and I think that your results are of fundamental importance, not only for the core of this Essay Contest, but also for the whole theoretical physics. Thus, I am going to give you the top rate.

Cheers,

Ch.