Dear John,

In cosmology, the speed of light is used as the denominator when you use comformal coordinates. For the sake of simplicity let us consider the case of euclidean sections (k=0) and the x coordinate only. Then, the Friedmann - Lemaître - Robertson - Walker metric reads ds^2=[R(t)]^2[c^2dt^2-dx^2]. Calling 1 the first galaxy and 2 the second galaxy, the condition of null geodesic for the light gives cdt=dx and, in turn, t1-t2=(x1-x2)/c. But this is NOT the proper time which one uses to compute the redshift. It is ONLY a coordinate time. The infinitesimal proper time dT is given by the root square of [R(t)]^2dt^2=[R(t)]^2dx^2/c^2, i.e. dT= R(t)dx/c. You must integrate this last quantity in order to compute the variation of proper time and, in turn, the redshift. In other words, you cannot merely divide for c in order to get the proper time. Instead, you must know the function R(t) and, in order to do this, you must solve Einstein Field Equation by inserting the Friedmann - Lemaître - Robertson - Walker metric components in such an equation. For galaxies which are not too much distant each other, one approximates R(T)= constant=R obtaining T1-T2=R(x1-x2)/c.

Cheers,

Ch.

Christian,

It's not that I doubt space could be described as expanding mathematically, I certainly accept that, mathematically, gravity is described as the contraction of space. Thus originating the need for Einstein's cosmological constant. What I see is that both processes are concurrent and balanced. Those galaxies are not just inert points of measure, but gravity wells, effectively contracting the expansion between them, resulting in overall flat space. It is just that we can only observe the light from ever more distant galaxies that has managed to pass between all the intervening gravity wells and is therefore most affected by this intergalactic effect. So this would presume expanding space, but not an expanding universe. So if you wanted to send a light signal from one galaxy to another, it would have to "walk up the down escalator" and seem to travel further than it objectively does. Much as gravitational lensing doesn't actually move the source of the lensed light, but only bends and magnifies the light enroute, the galaxies are not objectively moving away from one another, only that the space is warped outward in the least gravitationally affected areas, as it is warped inward in the gravity wells. So there is no need to argue they will eventually vanish because the distance the light travels objectively increases. Thus no need to assume two definitions of space in the same equation. This removes the need for the rather enormous fudges of inflation and dark energy, as well as having to explain what caused the singularity. As for dark energy, that could possibly be explained in terms of how the radiation/light recycles back into mass. Consider there is insufficient mass on the perimeters of galaxies, but there are large excesses of cosmic rays and other radiation, so could gravity emerge as a vacuum effect of radiation condensing into mass, rather than just a property of mass alone? Obviously this would require picking apart the entire process of stellar evolution, but Zeeya was nice enough to put me up a blog posting, listing various of the recent observations posing serious problems for current cosmology.

Regards,

John

As for gravity as a vacuum effect of energy condensing into mass, when energy is released from mass, it creates pressure, so wouldn't the opposite process be at least worth considering?

Vacuum, like pressure, can be described geometrically and not need any gravitons or gravity waves. All that is required is that quanta of radiation traveling in space be more diffuse and less dense than such quanta being absorbed into mass. Considering how much radiation permeates space, this effect would also essentially be synonymous with space.

If it does become more diffuse, the further it travels, there would be some potential mechanisms to explain redshift.

Dear Tom,

Do not worry. In fact, I find the diatribe between Mitra and Baez very interesting. My position is indeed intermediate. I think that a Universe without black holes should be less intriguing. On the other hand, I do not like the concept of singularity. It will be fantastic if the correct answer should be an object with the properties of a black hole but without singularities.

Cheers,

Ch.

Dear John,

I am outside office for the weekend. Thus, I am using my i-phone and it is not simple to reply to your comments in detail. I will bring back to you with detailed replies on next Monday.

Cheers,

Ch.

"It will be fantastic if the correct answer should be an object with the properties of a black hole but without singularities."

It surely will, Christian! Isn't it the same result, though, if every singularity is guaranteed to be extinguished in finite time?

All best,

Tom

Christian,

No rush. Phones have their limits.

Regards,

John

Dear Prof. Corda,

I am finally finding some time to get caught up on the essay I should read. Anyway I we each already noticed there is a strong complementarity between your essay and ours. This area right now seems to be very active i.e. BH evaporation and information loss or not. In any case your essay and previous series of papers makes a good and strong contribution to the debate. Also it seems that now most people are moving in the direction that information is conserved it is just a matter of how.

I did have one specific question and one general question in connection with your essay. You study the transition probabilities Gamma (n-->m) (for example your equation (16)) for m>n which I think corresponds to emission and the BH losing mass. One can as well consider the reverse absorption process (this corresponds to the outgoing/ingoing modes of W&P). How is the transition probability altered for this absorption process? If one naively switches m and n in formula (16) one gets a Gamma >1. W&P get that at the semi-classical level Gamma_absorption = 1 as one would expect (but the Painleve coordinates they use are really a bad way to see this). For absorption does one put an absolute value around m-n ?

The second general question (which actually pertains to all work dealing with information leaking out of the BH) is do you have some insight into the recent interest/excitement about the Almheiri, Marolf, Polchinski, Sully work on firwalls -- the idea that in old BHs (BHs that have evaporated away half their mass) have a region near/at the horizon which is/becomes superheated -- i.e. a firewall. My understanding of this is pretty poor so I'm simply looking for some comment/discuss. It does seem (and AMPS mention in the paper) that this is strongly connected with the information loss problem. At first sight it would seem to throw a monkey wrench in all attempts to explain BH information loss without introducing non-local degrees of freedom.

Best,

Doug

    Hi Yuri,

    I am pleasured to re-meet you here in FQXI.

    Actually, I have not yet read your Essay. I will surely read, comment and rate it in next days.

    Cheers and good luck in the Contest,

    Ch.

    Dear Prof. Singleton, dear Doug,

    Thanks for your kind words. I am honoured by them. Concerning your very important questions, at the present time I am outside office for the weekend and I use my i-phone. Thus, it is not simple for me answering your questions in detail. I will bring back to you with detailed answers on Monday. Thanks again.

    Cheers,

    Ch.

    Dear Christian,

    No problem. I understand well the difficulty of sending replies on scientific topics via an I-phone. Anyway I am particularly interested if you have some thoughts in regard to the AMPS paradox which seems to be a sharpening of the BH evaporation/information loss puzzle and thus has possible implications for all work connected with this area. The one thought I had was that the feature of the firewall appearing after half the BH mass has evaporated away may be connected with the idea of measuring entropy via quantum entanglement. Susskind and Lindesay in their technical BH book "BHs, Information and the String Theory Revolution", mention that if one treats entropy as a measure of quantum entanglement than the related information does not leak out until more than half way through the evaporation process i.e. little information leaks out until >=t/2 and then the information "suddenly" rushes out. This is in figure 8.3 of this book which also shows that the normal, thermodynamics definition of entropy gives a different behavior.

    Anyway this is an interesting (but to me) poorly understood new wrinkle to BH evaporation/information.

    Best,

    Doug

    Hello Christian

    I rated this quite highly, though on reflection I am left wondering.

    So, if there are black holes, and if the theory of general relativity and quantum theory have a consistent conjugation (!) and if all the things we guess to be true of black holes which we have never been close enough to observe or do any experiments on is true, then, if a black hole radiates energy and this leads to a perturbation, and this perturbation is not lost in the singularity (!) then it may be that information is not lost down the hole, although the thing that brings radiation from the event horizon relies on a background of virtual particles. How these virtual particles relate to the information that seemingly disappeared into the black hole is not clear, but they do render information, although the information is not completely random...somehow. It may be coming out as kets of pure state, but am I missing something, or is the information that comes out independent of the information that went in? If so, then how is the history retained. If this is so, isn't this the same as random emissions (no pun intended)?

    't Hooft's assumption that Schrödinger equations can be used universally for all dynamics in the universe is a cool assumption, but whenever one reaches for that differential equation in a world that yells discreteness as minimum scale, I am thrown into scepticism. Again, and t'Hooft knows, such assumptions are anathema in a foundational work. Popper would cry and cut him off his Christmas card list.

    Moreover, while this is a lovely piece of mathematics, what worries me is that the solution seems to be all about probabilities, and I don't see how probabilities are any more than probabilities; meaning they make no advancement at a fundamental level.

    That said, if your argument is true, and history is somehow preserved, would this not imply that inside a black hole is just a harmonic state that remains in contact with the outside, with no singularity?

      Christian,

      I am confused. Of course if you write a Schroedinger equation you get unitarity. Even without many calculations. But by writing a Schroedinger equation you are imposing what you want to get out. The point about BH's is precisely that there is no unitary evolution and therefore no Schroedinger equation. In the classical theory, there is no time translation invariance at infinity. Information can fall in, instead than out. If you assume the opposite to start with, you force the math to say what you want. Am I missing something?

      Carlo

        Dear Christian,

        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.

          Dear Carlo Rovelli,

          While I am seeing your objection logically justified, I just tried to express my view concerning unitarity in a reply to Christian's comment on my essay.

          Eckard

          Carlo,

          I agree with you that if one writes a Schroedinger equation one gets in turn unitarity without many calculations (in fact I stressed that my calculations in my Essay are on the same level of university studies on quantum mechanics). On the other hand, the vice versa, i.e. that unitarity permits to ALWAYS write a Schroedinger equation is not so trivial as you claim. I recall you that Maldacena, Susskind and the same Hawking claimed that unitarity is restored in black hole evaporation through the ADS/QFT duality, that Mathur claimed that unitarity is restored through the "fuzzball" approach and that Zhang, Cai, Zhan and You claimed that unitarity is restored through the correlations among Hawking quanta. In any case, neither Maldacena, Susskind and Hawking, nor Mathur, nor Zhang, Cai, Zhan and You wrote down explicitly a Schroedinger equation which permitted them to find a pure final state. In fact, unitarity is also permitted WITHOUT obtaining a Schroedinger equation as in some cases one obtains a final mixed state but information is preserved trough correlations among the subsystems. I did NOT construct the Schroedinger equation by assuming unitarity. I constructed the Schroedinger equation by using my result in Int. Journ. Mod. Phys. D 21, 1242023 (2012), where I have shown that black holes quasi-normal modes can be interpreted in terms of quantum levels. I do not think that such a result automatically implies unitarity, because in that case, I should have won a Prize in the 2012 Gravity Research Foundation Competition rather than a "simple" Honorable Mention as in that case the black hole information paradox was implicitly automatically solved in my Essay Int. Journ. Mod. Phys. D 21, 1242023 (2012)!! On the other hand, you claims that "In the classical theory, there is no time translation invariance at infinity. Information can fall in, instead than out." But here I am not using neither the classical theory nor the full quantum theory. I am using a semi-classical approximation. Maybe time translation invariance at infinity is restored in my result Int. Journ. Mod. Phys. D 21, 1242023 (2012), I have not checked. You can check it if you like.

          Cheers,

          Ch.

          Dear Eckard,

          I am happy to read that you are seeing Carlo's objection logically justified. Why don't you ask Carlo if he, in turn, see your objections against the theory of relativity logically justified too? In any case, I am going to see your view concerning unitarity in a reply to my comment on your Essay in next days.

          Cheers,

          Ch.

          Hi Doug,

          Thanks again for your insightful comments.

          1) Concerning your question on the reverse absorption process, yes, you are correct in saying that equation (16) for m > n corresponds to emission and the BH losing mass. In fact, I have emphasized both between eqs. (9) and (10) and between eqs. (10) and (11) that I assume m > n. On the other and, for an absorption, the sign of the variation of energy changes in both eqs. (11) and (15). This implies that, when one switches m and n in formula (16) also the sign in the argument of the exponential must change and one gets again exp[2pi(n-m])= exp[-2pi(m-n)]. In any case, I am going to read again the paper by W&P to see in detail what concerns the outgoing/ingoing modes.

          2) Concerning the AMPS firewall framework, I must confess that my understanding of this issue is even pretty poorer than your one. But I am pleasured to have some comment/discuss with you. In my knowledge, the idea that information does not leak out until more than half way through the evaporation process i.e. little information leaks out until >=t/2, is originally due to this paper by Don Page. This recent paper by Maldacena and Susskind verbatim claims that "we believe that the AMPS conclusion is unwarranted" and "we claim that there is no convincing argument in favor of firewalls". Recently also Mathur and Turton claimed that there is a flaw in the firewall argument. A point that surprises me is that all these researchers, i.e. Almheiri, Marolf, Polchinski, Sully, Mathur, Turton, Maldacena, Susskind, Van Raamsdonk, Giddings, Page, etc. NEVER consider the correction to the thermal spectrum by Parikh and Wilczek but continue to consider the strictly thermal spectrum of Hawking original computations. It is my personal opinion that, instead, the non-strict thermality is fundamental to solve the paradox. On the other hand, this paper by Braunstein and Pati looks to show that the paradox arises immediately after the black hole starts to emit Hawking quanta. This looks in contradiction with the idea that information does not leak out until more than half way through the evaporation process and, in turn, makes the paradox more severe.

          Although I have read your FQXi Essay some weeks ago, I am going to re-analyse in detail, comment and rate it in next day.

          Good luck in the Contest!

          Cheers,

          Ch.

          Dear Tom,

          Yes, it could be a similar result if every singularity should be guaranteed to be extinguished in finite time. But we must be careful on which "time" we are referring to. In fact, singularities can be time-like too.

          Cheers,

          Ch.