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

Hi Hector,

Yes there are many ways to approach "time" -- Newtonian time, relativistic time, psychological time (how a person perceives time), etc. One of the most profound (in my opinion) people to deal with how people perceive and "store"/remember time was the French novelist Marcel Proust in his massive work "Remembrance of Things Past" which if one does a more direct rather than poetic translation is "Recovery of Lost Time".

A colleague of mine at CSU Fresno, Bob Levine, has done studies of how people perceive time. He has a thesis which in simplified form (hopefully not so simplified that I misrepresent) is that all/most of what people do is done in order to "buy" more time or make a given amount of time more pleasant, exciting, relaxing etc.

Anyway I will try to have a look at your essay.

Best regards,

Doug

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.

Douglas, Elias, Tao - congratulations on an outstanding essay. I'm glad I managed to read it and get my rating in to help before the end of the contest.

I see a background of time assumption in your equations. I wonder what correlated photons of Hawking radiation would look like under the subtime interpretation?:

http://fqxi.org/data/forum-attachments/Borrill-TimeOne-V1.1a.pdf

(sorry if the fqxi web site splits this url up, I haven't figured out a way to not make it do that).

Kind regards, Paul

    Best of Luck for the Magnificent Eight !

    I am throught the 180 essays, all rated. For me 2/3 of them were poor and other 1/6 curious. The rest (1/6) have I rated over 4/10.

    You are among the authors of the top essays from my sight - alphabetically :

    Corda, D'Ariano, Maguire, Rogozhin, Singleton, Sreenath, Vaid, Vishwakarma,

    and I hope one of you will be the winner. (Please, don't rate my essay.)

    David

    Hi Paul,

    A technical measure of the correlation, C, between photons of energy E_1 and E_2 emitted is given by the somewhat opaque expression

    C(E_1+E_2 ; E_1, E_2) = ln(Gamma(E_1+E_2))-ln(Gamma(E_1)Gamma(E_2))

    where Gamma(X) is the probability for a photon of energy X to tunneling through the horizon and appear as Hawking radiation. Essentially one is comparing emitting one photon with energy E_1+E_2 versus two separate photons E_2 and E_1. This is discussed in more detail in an early articl eon the subject by my co-author Elias. The exact reference is

    "Hawking radiation as tunneling through the quantum horizon",

    Michele Arzano, A.J.M. Medved, Elias C. Vagenas, JHEP 0509 (2005) 037

    e-Print: hep-th/0505266

    For a truly thermal spectrum the correlation function above is zero -- C=0 -- and one says the photons are uncorrelated. If C=/=0 there is some correlation.

    Now the next question how woul done check this experimentally -- until recently I would have said "I don't know" and in fact I still have to say this, but now I know where to look. There is a recent PRD article

    "Towards experimentally testing the paradox of black hole information loss"

    Baocheng Zhang, Qing-yu Cai, Ming-sheng Zhan, Li You (Tsinghua U., Beijing). Phys.Rev. D87 (2013) 4, 044006

    e-Print: arXiv:1302.1341 [gr-qc]

    which from the title and also abstract (the paper is downloaded and sitting on my laptop but still needs reading) promises to give a way to test the correlations of emitted photons. I'm not sure if the proposal is in terms of analogy systems or what but it is interesting and might be address your question about what correlated photons would look like in the lab.

    Best,

    Doug

    Hi David,

    Thanks for reading our essay the kind words and rating.

    Best,

    Doug

    Hi Doug,

    I've just posted the remarks below at my own essay; but because they're so late, you may have stopped looking for them there, so I'm posting them here too.

    I apologize for being so late in responding to your stimulating comments and thoughts; but hopefully, it's still better late than never! I had written a somewhat lengthy response earlier, but for some reason it wouldn't post; so, I'm going to try a condensed version to see if I can get anything posted.

    Taking your "further unrelated question" first, my "N" is related to that of causal set theory, in which N is the total number of causet elements (CEs) in the four-volume constituted by the past light cone of a suitable observer. This number is way too large for each CE to be a degree of freedom (dof), and hence it is not of the same magnitude as the cosmological entropy S. However, on my account, the number of uncanceled volume-fluctuations of CEs, which is on the order of N's square root at any given time t, is roughly comparable to S. (I don't view these uncanceled CEs as actual dof's, but they are, in some ways, "something like" dof's, at least).

    I agree with your point about the desirability of unifying inflation and late-time dark energy, and I find your idea of linking inflation with Hawking radiation very interesting. My own account of dark energy appeals to the nature of discrete spacetime and its fluctuations, which may also be relevant to the explanation of inflation, as your own work suggests. Of course, the particular aspects of discrete spacetime that are crucial to inflation may be (partly) different than those connected with dark energy; but even so, there's still a significant amount of "unification" here.

    Good luck; hope you win a prize!

    -Willard

      Just a couple of addenda to the comments I recently posted: (i) Barrow & Shaw themselves seem to take an agnostic stance about the cause(s) of inflation, which makes some sense in view of the fact that it's simply unclear whether vacuum energy alone can explain, e.g., the origin of intergalactic magnetic fields, as well as being unclear whether such fields should be connected with inflation at all. It's possible, at least, that any inflationary theory that's able to explain a wide range of phenomena will be somewhat lacking with respect to simplicity and "unity."

      (ii) I admit that the idea of nonlocal cancellation of spacetime fluctuations on a cosmological scale, and the related idea of the spacetime causal set of our universe as a kind of "particle," is rather extreme and crazy-sounding (and possibly just downright crazy!). Fwiw, I actually arrived at this idea by trying to address some issues connected with the account of dark energy in Ahmed, Dodelson, Greene and Sorkin's "Everpresent Lambda" paper. In particular, I was concerned about the criticism made by John Barrow ("A strong constraint on ever-present Lambda") regarding this account's conflict with cosmological observations. It may be that the ideas I'm advancing create too many new issues and problems; but I thought it was at least worth making an attempt to articulate and develop such ideas.

      Anyway, thanks for your insightful comments, and for reading my essay. And, again, best of luck.

      Willard

      Hi Willard,

      I missed your original reply. I haven't figure out how to get announcements from other threads I'm involved with. Thanks for the well wishes.

      With the new Planck results there is a lot of papers on inflation trying to match u with this data. Steinhardt and colleagues even published a recent PLB questioning the inflationary picture in light of the Planck data.

      Best,

      Doug

      3 months later

      Dears Colleagues,

      Congrats for the Prize.

      You, Jennifer Nielsen and Cistnel Stoica are the only positive news on the ridiculous and shameful "results" of this Essay Contest.

      Cheers,

      Ch.

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