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**Thomas Ray**: *on* 8/14/13 at 13:08pm UTC, wrote Christian, I'm afraid there's some misunderstanding. I think what Peter...

**Christian Corda**: *on* 8/13/13 at 15:36pm UTC, wrote Hi Vladimir, Thank you very much. Have my best congrats and wishes for...

**Christian Corda**: *on* 8/13/13 at 15:33pm UTC, wrote Dear Jonathan, Thank you very much for your congrats and wishes. In the...

**Christian Corda**: *on* 8/13/13 at 15:25pm UTC, wrote Hi Peter, Thanks for your kind congrats. Have the same congrats from me...

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FQXi FORUM

August 26, 2019

CATEGORY:
It From Bit or Bit From It? Essay Contest (2013)
[back]

TOPIC: Time dependent Schrödinger equation for black hole evaporation: no information loss by Christian Corda [refresh]

TOPIC: Time dependent Schrödinger equation for black hole evaporation: no information loss by Christian Corda [refresh]

In 1976 S. Hawking claimed that “Because part of the information about the state of the system is lost down the hole, the final situation is represented by a density matrix rather than a pure quantum state” (Verbatim from ref. 2). This was the starting point of the popular “black hole (BH) information paradox”. On the other hand, during one of his famous quantum field theory lectures at Harvard, S. Coleman claimed that “The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction.” One of the highest levels of abstraction concerning the harmonic oscillator in Nature is surely represented by BH quasi-normal modes (QNMs), which are a countable set of damped oscillations representing the BH's reaction to perturbations. In a series of papers, together with collaborators, I naturally interpreted BH QNMs in terms of quantum levels. Here I explicitly write down a time dependent Schrödinger equation for the system composed by Hawking radiation and BH QNMs. The physical state and the correspondent wave-function are written in terms of an unitary evolution matrix instead of a density matrix. Thus, the final state results to be a pure quantum state instead of mixed one. Hence, Hawking's claim is falsified by an application of Coleman's claim. Information comes out in BH evaporation in terms of pure states in an unitary time dependent evolution. The assumption by 't Hooft that Schröedinger equations can be used universally for all dynamics in the universe is in turn confirmed, further endorsing the conclusion that BH evaporation must be information preserving.

Theoretical physicist, Ph.D in Physics at the Pisa University. I am Professor of Theoretical Physics, Chairman and Founding Father of the Institute for Theoretical Physics and Advanced Mathematics (IFM) Einstein - Galilei, in Prato, Italy. I started to work on gravitational waves. In the last two years my research was focused on black hole thermodynamics. I am also Editor and/or Editor in Chief of various international journals in the fields of Theoretical Physics, Astrophysics and Mathematics

Dear Dr. Corda,

Glad to see you here again.

I have down loaded your essay and soon post my comments on it. Meanwhile, please, go through my essay and post your comments.

Regards and good luck in the contest.

Sreenath BN.

http://fqxi.org/community/forum/topic/1827

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Glad to see you here again.

I have down loaded your essay and soon post my comments on it. Meanwhile, please, go through my essay and post your comments.

Regards and good luck in the contest.

Sreenath BN.

http://fqxi.org/community/forum/topic/1827

report post as inappropriate

Dear Sreenath BN,

Thanks for your interest in my work.

I am going to read your Essay and I will post my comments in your page.

Best wishes and good luck in the contest,

Ch.

Thanks for your interest in my work.

I am going to read your Essay and I will post my comments in your page.

Best wishes and good luck in the contest,

Ch.

Dear Dr. Corda,

Thanks for your well written essay and in which you have tried to solve one of the outstanding problems in black hole (BH) information paradox that the information is not lost in BH evaporation but that it is preserved. I hope your effort sustains and will be rewarded in due course.

Wishing you all the best and I am going to rate your essay with a very good score.

Sreenath

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Thanks for your well written essay and in which you have tried to solve one of the outstanding problems in black hole (BH) information paradox that the information is not lost in BH evaporation but that it is preserved. I hope your effort sustains and will be rewarded in due course.

Wishing you all the best and I am going to rate your essay with a very good score.

Sreenath

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Dear Dr. Corda,

I have pleasure in rating your essay with maximum honors and I have rightly done so.

Wishing you best of luck in the essay contest.

Cheers,

Sreenath

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I have pleasure in rating your essay with maximum honors and I have rightly done so.

Wishing you best of luck in the essay contest.

Cheers,

Sreenath

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Christian,

Great work. The paper by Singleton, Vagenas and Zhu comes to remarkably similar conclusions. It is clear that conservation of quantum information requires that Hawking radiation have some deformation from blackbody radiation when the number of Planck masses that make it up becomes small.

Cheers LC

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Great work. The paper by Singleton, Vagenas and Zhu comes to remarkably similar conclusions. It is clear that conservation of quantum information requires that Hawking radiation have some deformation from blackbody radiation when the number of Planck masses that make it up becomes small.

Cheers LC

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Hi LC,

Thanks for your congrats.

As you know, I have already read your Essay before submitting my one. It is excellent.

Yes, the Essay by Singleton, Vagenas and Zhu is pretty and complementary to my one. I agree that Hawking radiation has deformations from black body radiation and this is exactly what permits information to come out. In my personal opinion, perfect black bodies do not exist in nature. Also CBR is not exactly thermal.

Cheers,

Ch.

Thanks for your congrats.

As you know, I have already read your Essay before submitting my one. It is excellent.

Yes, the Essay by Singleton, Vagenas and Zhu is pretty and complementary to my one. I agree that Hawking radiation has deformations from black body radiation and this is exactly what permits information to come out. In my personal opinion, perfect black bodies do not exist in nature. Also CBR is not exactly thermal.

Cheers,

Ch.

From a non-specialist, I am reading the higher valued community papers as I find them cogent. This paper offers an intriguing approach to the relationship between quantum jumps and the place of information in black-hole emissions and absorptions. It is beyond my technical expertise to evaluate the quality of the assumptions made throughout this paper, but the assumptions are explicitly and clearly stated. The paper is well written, addresses current concerns in physics, and builds on appropriately selected foundations. Its direct relationship to Its from Bits is implied.

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Hello Christian,

Excellent essay! Very readable and nice balance of history and insight! I particularly like that you allow information to be preserved after Black Hole evaporation. I find this ought to be the case in my essay too.

Great work!

Kind regards,

Antony

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Excellent essay! Very readable and nice balance of history and insight! I particularly like that you allow information to be preserved after Black Hole evaporation. I find this ought to be the case in my essay too.

Great work!

Kind regards,

Antony

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Hi Antony,

Thanks for your kind congrats. I am pleasured by your judgement on my Essay.

I am going to read your Essay and I will post my comments on your FQXi page.

Thanks again.

Best regards and good luck in the Contest,

Ch.

Thanks for your kind congrats. I am pleasured by your judgement on my Essay.

I am going to read your Essay and I will post my comments on your FQXi page.

Thanks again.

Best regards and good luck in the Contest,

Ch.

My pleasure & thanks - I hope my essay doesn't disappoint.

Best wishes,

Antony

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Best wishes,

Antony

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Thanks for the very kind comments over on my page. As I've replied there, I thoroughly enjoyed your essay and will score it highly :)

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Dear Christian,

Very interesting essay, and I should say, your approach is one of the most natural ones. I fully agree that unitary evolution remains true in any circumstances. I think is great that the state vector of the Hawking radiation plus the black hole evolves unitarily. As you know, in my research concerning singularities in general relativity, I advocate the viewpoint that singularities don't block the evolution equations (including the unitary evolution). This may be complementary to your results. (I also work for many years, in parallel, to show that unitary evolution is not broken by quantum measurement. I mean that the so called wavefunction collapse is truly unitary, not just when we consider all universes in the multiverse, or decohered branches etc. There are some huge difficulties here, but at least I could show that this is not impossible in principle, if we admit delayed initial conditions.)

Congratulations for your essay.

Best regards,

Cristi Stoica

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Very interesting essay, and I should say, your approach is one of the most natural ones. I fully agree that unitary evolution remains true in any circumstances. I think is great that the state vector of the Hawking radiation plus the black hole evolves unitarily. As you know, in my research concerning singularities in general relativity, I advocate the viewpoint that singularities don't block the evolution equations (including the unitary evolution). This may be complementary to your results. (I also work for many years, in parallel, to show that unitary evolution is not broken by quantum measurement. I mean that the so called wavefunction collapse is truly unitary, not just when we consider all universes in the multiverse, or decohered branches etc. There are some huge difficulties here, but at least I could show that this is not impossible in principle, if we admit delayed initial conditions.)

Congratulations for your essay.

Best regards,

Cristi Stoica

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Hi Cristi,

Nice to see you here, and thanks for your kind congrats.

I am pleasured to read that you think my approach is one of the most natural ones. In fact, I think that the correspondence between emitted radiation and proper oscillation of the emitting body is a fundamental Principle of Nature. If this is correct, the production of Hawking radiation should be no different than the production of any other type of radiation. If one wants to produce electromagnetic radiation, say at 1 KHz, one needs to take electric charges and vibrate them at 1 KHz. The same should hold for Hawking radiation; waves of a certain frequency should be produced when the characteristic time for the black hole to shift about (i.e. the quasi-normal oscillations) is comparable to the period of the waves.

I surely agree with your viewpoint that singularities don't block the evolution equations, including the unitary evolution. Yes, it is complementary to my results. Also your ideas on the intrinsic unitarity of the wave-function collapse, implying that unitary evolution should not be not broken by quantum measurement, look very interesting.

I am going to read your Essay in order to better deepen my knowledge on your interesting research.

Thanks again and good luck in the Contest.

Cheers,

Ch.

Nice to see you here, and thanks for your kind congrats.

I am pleasured to read that you think my approach is one of the most natural ones. In fact, I think that the correspondence between emitted radiation and proper oscillation of the emitting body is a fundamental Principle of Nature. If this is correct, the production of Hawking radiation should be no different than the production of any other type of radiation. If one wants to produce electromagnetic radiation, say at 1 KHz, one needs to take electric charges and vibrate them at 1 KHz. The same should hold for Hawking radiation; waves of a certain frequency should be produced when the characteristic time for the black hole to shift about (i.e. the quasi-normal oscillations) is comparable to the period of the waves.

I surely agree with your viewpoint that singularities don't block the evolution equations, including the unitary evolution. Yes, it is complementary to my results. Also your ideas on the intrinsic unitarity of the wave-function collapse, implying that unitary evolution should not be not broken by quantum measurement, look very interesting.

I am going to read your Essay in order to better deepen my knowledge on your interesting research.

Thanks again and good luck in the Contest.

Cheers,

Ch.

Christian,

sorry if I cannot sincerely express my congratulations, since your paper is technical (in the sense that it uses formulas from other papers, which I should take from granted, and I cannot use my own judgement).

However, apart from this I made an automatic search in your pdf, and I couldn't find a single instance of the word "Bit"! There is some slight relation with the theme of the competition (but essentially any paper in physics would have it).

My candid question is now: It from bit or Bit from It?

Thank you

Mauro

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sorry if I cannot sincerely express my congratulations, since your paper is technical (in the sense that it uses formulas from other papers, which I should take from granted, and I cannot use my own judgement).

However, apart from this I made an automatic search in your pdf, and I couldn't find a single instance of the word "Bit"! There is some slight relation with the theme of the competition (but essentially any paper in physics would have it).

My candid question is now: It from bit or Bit from It?

Thank you

Mauro

report post as inappropriate

Dear Mauro,

Thanks for your comments.

Actually, formulas from other papers are used only in equations from (1) to (8). Such formulas essentially arise from my published papers (only eqs. (1) and (2) are by Hawking and Parikh and Wilczek, which are obviously and properly cited). The other formulas are completely new and proper of this Essay although, after a rigorous definition of...

view entire post

Thanks for your comments.

Actually, formulas from other papers are used only in equations from (1) to (8). Such formulas essentially arise from my published papers (only eqs. (1) and (2) are by Hawking and Parikh and Wilczek, which are obviously and properly cited). The other formulas are completely new and proper of this Essay although, after a rigorous definition of...

view entire post

Dear Christian Corda,

Did Wheeler really already coin "the phrase "It from bit or Bit from It?" in the 1950s"?

If so I have to correct my essay and perhaps also my tendency to see the pendulum of my judgment that has so far swung in favor of Shannon's view.

If you are a coward, just join those who scored me one without taking issue in public.

Regards,

Eckard

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Did Wheeler really already coin "the phrase "It from bit or Bit from It?" in the 1950s"?

If so I have to correct my essay and perhaps also my tendency to see the pendulum of my judgment that has so far swung in favor of Shannon's view.

If you are a coward, just join those who scored me one without taking issue in public.

Regards,

Eckard

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Dear Eckard,

Actually, I did not know when Wheeler coined the phrase "It from Bit or Bit from it". Also, you can check that I do not use it in my Essay. Thus, I think that you should ask your question to the lots of people that use Wheeler's phrase in this Essay Contest.

I do not usually score Essays without reading them before. Thus, I will surely read and rate your Essay on next week when I will return at home from my holidays.

Cheers,

Ch.

Actually, I did not know when Wheeler coined the phrase "It from Bit or Bit from it". Also, you can check that I do not use it in my Essay. Thus, I think that you should ask your question to the lots of people that use Wheeler's phrase in this Essay Contest.

I do not usually score Essays without reading them before. Thus, I will surely read and rate your Essay on next week when I will return at home from my holidays.

Cheers,

Ch.

Dr. Corda,

I find your paper to be interesting, especially if it is confirmed that Hawking's prediction is proven false. However, I feel that it does not address the core questions of this competition.

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I find your paper to be interesting, especially if it is confirmed that Hawking's prediction is proven false. However, I feel that it does not address the core questions of this competition.

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Dear Stuart Heinrich,

Thanks for your comments and for finding interesting my Essay.

As I explained above, in the reply to Dr. D'Ariano, I do not think that my Essay does not address the core questions of this competition. I rewrite here my reply to Dr. D'Ariano almost verbatim. Although "It From Bit or Bit From It" is the title of the Contest, you can easily check that topics...

view entire post

Thanks for your comments and for finding interesting my Essay.

As I explained above, in the reply to Dr. D'Ariano, I do not think that my Essay does not address the core questions of this competition. I rewrite here my reply to Dr. D'Ariano almost verbatim. Although "It From Bit or Bit From It" is the title of the Contest, you can easily check that topics...

view entire post

Christian,

I not only agree your thesis conceptually, but also consider that if all essays stuck rigidly to the narrowest interpretation of the subject question then we'd be bored to death reading the essays. There would also certainly be more limited value in terms of understanding emergent from the competition.

Both our essays are alike in this respect, evidencing important and new findings and understandings which have a direct effect on the answer to the question. To me yours beautifully provides the mathematical solution in terms of the present doctrine but consistent with my own apparently 'off doctrine' argument of a recycling model, where the information accretion and (re-ionization as) radiation is the hub of the cyclic process. For me then the importance of the task makes the maths essential, though I'd be intrigued by your view on my conceptual 'Dirac Line' distinguishing mathematics from reality.

In fact I again set a tall order for my own essay, identifying a higher order of variations within the qubit and showing how these can resolve the EPR paradox. Perhaps too high as many don't fully understand Bell's case. I look forward to your own views on it (see also Gordon Watson's close mathematical analogy of it).

I hope the value of yours emerges. Well done, including for hitting the front even with my score yet to come! The annual roller coaster ride starts again.

Peter

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I not only agree your thesis conceptually, but also consider that if all essays stuck rigidly to the narrowest interpretation of the subject question then we'd be bored to death reading the essays. There would also certainly be more limited value in terms of understanding emergent from the competition.

Both our essays are alike in this respect, evidencing important and new findings and understandings which have a direct effect on the answer to the question. To me yours beautifully provides the mathematical solution in terms of the present doctrine but consistent with my own apparently 'off doctrine' argument of a recycling model, where the information accretion and (re-ionization as) radiation is the hub of the cyclic process. For me then the importance of the task makes the maths essential, though I'd be intrigued by your view on my conceptual 'Dirac Line' distinguishing mathematics from reality.

In fact I again set a tall order for my own essay, identifying a higher order of variations within the qubit and showing how these can resolve the EPR paradox. Perhaps too high as many don't fully understand Bell's case. I look forward to your own views on it (see also Gordon Watson's close mathematical analogy of it).

I hope the value of yours emerges. Well done, including for hitting the front even with my score yet to come! The annual roller coaster ride starts again.

Peter

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Dear Peter,

Nice to see you here in the Contest again.

Thanks for agreeing with my point of view and for appreciating my Essay.

I am going on holidays for about a week. When I will return to home, I will surely read your Essay. In fact, I am very curious concerning your conceptual 'Dirac Line' distinguishing mathematics from reality and your way to solve the EPR paradox. I will read Gordon Watson's Essay too.

I wish you good look in the Contest.

Cheers,

Ch.

Nice to see you here in the Contest again.

Thanks for agreeing with my point of view and for appreciating my Essay.

I am going on holidays for about a week. When I will return to home, I will surely read your Essay. In fact, I am very curious concerning your conceptual 'Dirac Line' distinguishing mathematics from reality and your way to solve the EPR paradox. I will read Gordon Watson's Essay too.

I wish you good look in the Contest.

Cheers,

Ch.

Resp Prof Christian,

Thank you for elaborating Black hole physics and math with your nice essay. I want to ask you some thing:

Black holes are mathematical singularities. They were not found even after 100 years of their proposal. Thousands probably millions of scientist and astronomers searched in vain to find them. They wasted their energy, time and much more valuable brain power...

view entire post

Thank you for elaborating Black hole physics and math with your nice essay. I want to ask you some thing:

Black holes are mathematical singularities. They were not found even after 100 years of their proposal. Thousands probably millions of scientist and astronomers searched in vain to find them. They wasted their energy, time and much more valuable brain power...

view entire post

report post as inappropriate

Dear Satyavarapu Naga Parameswara Gupta,

Thanks for your kind comments and for reading my Essay.

Your questions are surely interesting, but they need time to be replied in detail. Now, I am going on holidays for about a week. When I will return to home, I will surely answer your stimulating questions in details and I will also read your Essay.

Kind regards and good luck for the Contest,

Ch.

Thanks for your kind comments and for reading my Essay.

Your questions are surely interesting, but they need time to be replied in detail. Now, I am going on holidays for about a week. When I will return to home, I will surely answer your stimulating questions in details and I will also read your Essay.

Kind regards and good luck for the Contest,

Ch.

Dear Christian,

Why to waste our brain power on just mathematical singularities, they are not real?

I am asking you this as you did not get time to reply my question....

Best

=snp

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Why to waste our brain power on just mathematical singularities, they are not real?

I am asking you this as you did not get time to reply my question....

Best

=snp

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Dear Satyavarapu Naga Parameswara Gupta,

Actually, I did not forget your interesting questions. As I told you, they need time to be replied in detail. I will surely restart this interesting discussion with you after the vanishing of the deadline of Community Rating. In the meanwhile, I will surely read, comment and rate your Essay before such a deadline.

Cheers,

Ch.

Actually, I did not forget your interesting questions. As I told you, they need time to be replied in detail. I will surely restart this interesting discussion with you after the vanishing of the deadline of Community Rating. In the meanwhile, I will surely read, comment and rate your Essay before such a deadline.

Cheers,

Ch.

Dear Readers,

I would like to thank all the people who have read and have rated my Essay. Today, I am going on holidays for some days. I will bring my i-phone with me in order to follow the Contest's evolution, but it will be very difficult for me to read pdf files with such an i-phone. In any case, when I will bring back at home on next week, I will restart to read and rate all the various Essays for which I have been requested to give my own views on.

I wish good luck in the Contest to all of view and I hope that you will continue to enjoy with this intriguing FQXi Competition.

Cheers,

Ch.

I would like to thank all the people who have read and have rated my Essay. Today, I am going on holidays for some days. I will bring my i-phone with me in order to follow the Contest's evolution, but it will be very difficult for me to read pdf files with such an i-phone. In any case, when I will bring back at home on next week, I will restart to read and rate all the various Essays for which I have been requested to give my own views on.

I wish good luck in the Contest to all of view and I hope that you will continue to enjoy with this intriguing FQXi Competition.

Cheers,

Ch.

Christian,

Your conclusion, 'The assumption by 't Hooft that Schröedinger equations can be used universally for all dynamics in the universe is in turn confirmed, further endorsing the conclusion that BH evaporation must be information preserving." I find fascinating.

You speak of states as commonly understood in physics, but I was unable to find 'how' you determined such states came to be? I believe the findings from the 12 year experiment I have recently concluded will be of interest to you and may also substantiate your conclusions. I hope you find time to review my findings at:

http://fqxi.org/community/forum/topic/1809

Best wishes,

Manuel

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Your conclusion, 'The assumption by 't Hooft that Schröedinger equations can be used universally for all dynamics in the universe is in turn confirmed, further endorsing the conclusion that BH evaporation must be information preserving." I find fascinating.

You speak of states as commonly understood in physics, but I was unable to find 'how' you determined such states came to be? I believe the findings from the 12 year experiment I have recently concluded will be of interest to you and may also substantiate your conclusions. I hope you find time to review my findings at:

http://fqxi.org/community/forum/topic/1809

Best wishes,

Manuel

report post as inappropriate

Dear Christian

I am admire your expertise, but I do not specialize in this field to be able to discuss with you more, hope that do not therefore that you ignore the assessment of my essay.

To change the atmosphere "abstract" of the competition and to demonstrate for the real preeminent possibility of the Absolute theory as well as to clarify the issues I mentioned in the essay and to...

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I am admire your expertise, but I do not specialize in this field to be able to discuss with you more, hope that do not therefore that you ignore the assessment of my essay.

To change the atmosphere "abstract" of the competition and to demonstrate for the real preeminent possibility of the Absolute theory as well as to clarify the issues I mentioned in the essay and to...

view entire post

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Christian,

If given the time and the wits to evaluate over 120 more entries, I have a month to try. My seemingly whimsical title, “It’s good to be the king,” is serious about our subject.

Jim

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If given the time and the wits to evaluate over 120 more entries, I have a month to try. My seemingly whimsical title, “It’s good to be the king,” is serious about our subject.

Jim

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Hello, Christian Corda,

Thank you for a very informative and physics based essay. I'm very interested in black holes and their use in developing the Holographic Principle. I may wish to email you in the future after I fully digest all this. Thank you for sharing your teaching,

Matthew

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Thank you for a very informative and physics based essay. I'm very interested in black holes and their use in developing the Holographic Principle. I may wish to email you in the future after I fully digest all this. Thank you for sharing your teaching,

Matthew

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Dear professor Cristian Corda:

I am a physician specialized as a psychiatrist. I’m clarifying this point, just to also make understandable that I don’t know almost nothing of physics and also of mathematics. But when I read the title of your essay: “Time dependent Schrödinger equation for black hole evaporation: no information loss” I ask...

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I am a physician specialized as a psychiatrist. I’m clarifying this point, just to also make understandable that I don’t know almost nothing of physics and also of mathematics. But when I read the title of your essay: “Time dependent Schrödinger equation for black hole evaporation: no information loss” I ask...

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Dear Héctor Daniel Gianny,

Don't blame Christian Corda for using the notion time as it has been understood in physics so far.

I expect him merely taking issue concerning my question on Wheeler. He might read this as a reminder.

If you are interested in what I consider Newton's almost correct distinction between the two notions of time, you might just look at Fig. 1 of my previous essay.

I personally share the suspicion by many that his holistic approach, while appealing, is not feasible for all past and future time, even if Schwarzschild's solutions to Einstein's equations exhibit time before and after the end of time.

Eckard

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Don't blame Christian Corda for using the notion time as it has been understood in physics so far.

I expect him merely taking issue concerning my question on Wheeler. He might read this as a reminder.

If you are interested in what I consider Newton's almost correct distinction between the two notions of time, you might just look at Fig. 1 of my previous essay.

I personally share the suspicion by many that his holistic approach, while appealing, is not feasible for all past and future time, even if Schwarzschild's solutions to Einstein's equations exhibit time before and after the end of time.

Eckard

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Dear Hèctor,

Thanks for your kind comments with the interesting point on time.

Hawking claimed in his book "Brief history of time" that we do not know what time is. In Special Relativity it depends on observer's motion. In General Relativity it also depends on the presence of a gravitational field. Yes, in general we use the motion of bodies to measure it. An extremely precise way to measure time is by using bouncing photons in interferometry.

For further information I suggest you to give a look to the first FQXI Essay Contest dedicated to time.

Best wishes,

Ch.

Thanks for your kind comments with the interesting point on time.

Hawking claimed in his book "Brief history of time" that we do not know what time is. In Special Relativity it depends on observer's motion. In General Relativity it also depends on the presence of a gravitational field. Yes, in general we use the motion of bodies to measure it. An extremely precise way to measure time is by using bouncing photons in interferometry.

For further information I suggest you to give a look to the first FQXI Essay Contest dedicated to time.

Best wishes,

Ch.

Dear professor Christian Corda:

Thank you for your answer, you remind me Hawking book 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...

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Thank you for your answer, you remind me Hawking book 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...

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Dear Héctor,

Thanks for your interesting comments on the intriguing mystery of time.

I will surely read and comment your Essay in next days. I will also check your 16 or 17 lines demonstration which in your opinion should prove that with the clock one measures motion rather than time.

Cheers,

Ch.

Thanks for your interesting comments on the intriguing mystery of time.

I will surely read and comment your Essay in next days. I will also check your 16 or 17 lines demonstration which in your opinion should prove that with the clock one measures motion rather than time.

Cheers,

Ch.

Hello Dr Corda

I found your essay very challenging due to the dense equation set with (necessarily due to page constraints) insufficient description of what prompted each equation. What was unfortunately not clear to me was the reasoning behind each step made. My own work had to recreate mathematics from the ground up, and placed natural constraints on physics that would question the possibility of a singularity (not shown in my essay, but follows immediately from it) and for that matter, the Schrodinger equation as a differential (rather it ought to align with CDT). As such, one wonders at the effect the absence of a singularity within a black hole would have on information that would otherwise be lost within a finite time.

I would love to know your line of thinking that gave you the approach to this problem, and guided you through the application of the equations used.

PS. Is there a typo in equation (20) or (22) exp - (...) rather than exp(-...)?

PPS. I would be keen to receive critical feedback on my essay: http://fqxi.org/community/forum/topic/1904

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I found your essay very challenging due to the dense equation set with (necessarily due to page constraints) insufficient description of what prompted each equation. What was unfortunately not clear to me was the reasoning behind each step made. My own work had to recreate mathematics from the ground up, and placed natural constraints on physics that would question the possibility of a singularity (not shown in my essay, but follows immediately from it) and for that matter, the Schrodinger equation as a differential (rather it ought to align with CDT). As such, one wonders at the effect the absence of a singularity within a black hole would have on information that would otherwise be lost within a finite time.

I would love to know your line of thinking that gave you the approach to this problem, and guided you through the application of the equations used.

PS. Is there a typo in equation (20) or (22) exp - (...) rather than exp(-...)?

PPS. I would be keen to receive critical feedback on my essay: http://fqxi.org/community/forum/topic/1904

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Dear Stephen,

Thanks for your comments. Yes, page constraints limits description of what prompted each equation. On the other hand, after a rigorous definition of the quantum problem, I used a standard method of calculation in quantum mechanics following the textbook by Sakurai. Concerning the line of thinking that gave me the approach to this problem, and guided me through the application of the equations used, actually, I started to work on the problem of black hole quantum levels from two years. I had the intuition to replace the Hawking temperature with the effective temperature in order to take into account the non-strictly thermal character of the radiation spectrum in my paper JHEP 1108, 101 (2011). After this, I refined my results in my Essay Int. Journ. Mod. Phys. D 21, 1242023 (2012), which received an honorable mention in the 2012 Essay Competition of the Gravity Research Foundation, by discussing in detail the correspondence between Hawking radiation and BH QNMs. This winter, I had another intuition, i.e. that energies of Hawking quanta should be proportional to the effective temperature instead of to the Hawking temperature in case of deviation from the strict thermality of the radiation spectrum. At that point, by interpreting the absolute values of the QNMs in terms of total emitted energies, and, in turn, in terms of quantum levels, I developed my Essay by using standard techniques of quantum mechanics.

Cheers,

Ch.

P.S.

I checked eq. (22), it should be the same writing exp - (...) rather than exp(-...), or not?

P.P.S.

I am going to read your Essay in next days.

Thanks for your comments. Yes, page constraints limits description of what prompted each equation. On the other hand, after a rigorous definition of the quantum problem, I used a standard method of calculation in quantum mechanics following the textbook by Sakurai. Concerning the line of thinking that gave me the approach to this problem, and guided me through the application of the equations used, actually, I started to work on the problem of black hole quantum levels from two years. I had the intuition to replace the Hawking temperature with the effective temperature in order to take into account the non-strictly thermal character of the radiation spectrum in my paper JHEP 1108, 101 (2011). After this, I refined my results in my Essay Int. Journ. Mod. Phys. D 21, 1242023 (2012), which received an honorable mention in the 2012 Essay Competition of the Gravity Research Foundation, by discussing in detail the correspondence between Hawking radiation and BH QNMs. This winter, I had another intuition, i.e. that energies of Hawking quanta should be proportional to the effective temperature instead of to the Hawking temperature in case of deviation from the strict thermality of the radiation spectrum. At that point, by interpreting the absolute values of the QNMs in terms of total emitted energies, and, in turn, in terms of quantum levels, I developed my Essay by using standard techniques of quantum mechanics.

Cheers,

Ch.

P.S.

I checked eq. (22), it should be the same writing exp - (...) rather than exp(-...), or not?

P.P.S.

I am going to read your Essay in next days.

Hi Dear professor,

It is nice to see you on the leading position.

I see here nothing strange because your work one of best among professionals! I wish you luck on completing this intellectual battle in the same position as you are at the moment!

Best wishes,

George

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It is nice to see you on the leading position.

I see here nothing strange because your work one of best among professionals! I wish you luck on completing this intellectual battle in the same position as you are at the moment!

Best wishes,

George

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Hi Dear George,

Thanks for your kindness. Actually, some guy recently gave me a 1. Thus, now I am #4. In any case, I am very satisfied by this partial result.

Thanks again!

Cheers,

Ch.

Thanks for your kindness. Actually, some guy recently gave me a 1. Thus, now I am #4. In any case, I am very satisfied by this partial result.

Thanks again!

Cheers,

Ch.

Professor Corda,

A fascinating essay (treatise, really) that will take me some time to read and study in depth. You made a difficult topic understandable to a physics/math savvy audience who is not necessarily specializing in your interest area, and also integrated some humor, which I always appreciate (I chuckled at your "increasing abstractions" quote).

"The assumption by 't Hooft that Schröedinger equations can be used universally for all dynamics in the universe is in turn confirmed, further endorsing the conclusion that BH evaporation must be information preserving." The preservation of information here is undoubtedly crucial to a complete physical interpretation of the it-bit debate (a connection I immediately see is that it's quite difficult to describe a universe entirely with info if some of that information is lost to the universe itself). Do you feel that your research here supports "it from bit" ?

Cheers,

Jennifer Nielsen in a Little House on the Prairies of Kansas (KU)

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A fascinating essay (treatise, really) that will take me some time to read and study in depth. You made a difficult topic understandable to a physics/math savvy audience who is not necessarily specializing in your interest area, and also integrated some humor, which I always appreciate (I chuckled at your "increasing abstractions" quote).

"The assumption by 't Hooft that Schröedinger equations can be used universally for all dynamics in the universe is in turn confirmed, further endorsing the conclusion that BH evaporation must be information preserving." The preservation of information here is undoubtedly crucial to a complete physical interpretation of the it-bit debate (a connection I immediately see is that it's quite difficult to describe a universe entirely with info if some of that information is lost to the universe itself). Do you feel that your research here supports "it from bit" ?

Cheers,

Jennifer Nielsen in a Little House on the Prairies of Kansas (KU)

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Dear Jennifer,

Thank you very much for your kind comments. I am very happy to read that you like my Essay. In particular, I am honoured by your congrats concerning the issue that I achieved to make my work accessible even to a non-specialist audience, which is one of the most important goals of this Essay Contest. I am also pleasured that you individuate and appreciated the humor within the Essay. Based on your beautiful signature, I see that you also use humor. By the way, I am fascinated by the Prairies of Kansas. At the present time, I have seen them only by TV and photos, but I hope to travelling and staying in such beautiful lands in the future.

Concerning "it from bit", I think that the relation between "bits", i.e. information and "its", i.e. physical objects, should be similar to the one between matter and space curvature. Curiously, the better formulation of this latter relation, which was, in my opinion, the greatest intuition by Einstein, is again by Wheeler, who also coined "It from Bit or Bit from it". Such a formulation states that "Matter tells space how to curve. Space tells matter how to move". In the same way, I think that "bits" and "its" are complementary, i.e. "Information tells physics how to work. Physics tells information how to flow". In my work, the recovered information should save physics and, in a complementary way, physics shows as information flows through a unitary evolution.

I read in your interesting biographic informations that you work also on galaxy evolution. You could be interested on a recent paper of mine on dark matter, see 10.1016/j.astropartphys.2011.08.009. Maybe we can collaborate in the future.

I am also going to read your Essay. Good luck in the Contest!

Cheers,

Ch.

Thank you very much for your kind comments. I am very happy to read that you like my Essay. In particular, I am honoured by your congrats concerning the issue that I achieved to make my work accessible even to a non-specialist audience, which is one of the most important goals of this Essay Contest. I am also pleasured that you individuate and appreciated the humor within the Essay. Based on your beautiful signature, I see that you also use humor. By the way, I am fascinated by the Prairies of Kansas. At the present time, I have seen them only by TV and photos, but I hope to travelling and staying in such beautiful lands in the future.

Concerning "it from bit", I think that the relation between "bits", i.e. information and "its", i.e. physical objects, should be similar to the one between matter and space curvature. Curiously, the better formulation of this latter relation, which was, in my opinion, the greatest intuition by Einstein, is again by Wheeler, who also coined "It from Bit or Bit from it". Such a formulation states that "Matter tells space how to curve. Space tells matter how to move". In the same way, I think that "bits" and "its" are complementary, i.e. "Information tells physics how to work. Physics tells information how to flow". In my work, the recovered information should save physics and, in a complementary way, physics shows as information flows through a unitary evolution.

I read in your interesting biographic informations that you work also on galaxy evolution. You could be interested on a recent paper of mine on dark matter, see 10.1016/j.astropartphys.2011.08.009. Maybe we can collaborate in the future.

I am also going to read your Essay. Good luck in the Contest!

Cheers,

Ch.

Dear Professor Corda,

Your essay is an awesome contribution and cornerstone in theoretical physics - in a very well formulated and lucid manner you spell out how black hole evaporation still preserves information. I'm going to reread it to fully incorporate all the technical analysis, perhaps with some friends in a discussion group. I appreciate your originality in your approach...

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Your essay is an awesome contribution and cornerstone in theoretical physics - in a very well formulated and lucid manner you spell out how black hole evaporation still preserves information. I'm going to reread it to fully incorporate all the technical analysis, perhaps with some friends in a discussion group. I appreciate your originality in your approach...

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Dear Steve,

I have no words to thank you for your high judgement on my Essay. I am strongly honoured by that judgement, even if I am not sure to deserve it. Ley me know if you will organize a discussion group on my Essay, I will be pleasured to discuss with you and your friends if you agree.

I am surely going to read, comment and rate your Essay in next days.

Thanks again!

Cheers,

Ch.

I have no words to thank you for your high judgement on my Essay. I am strongly honoured by that judgement, even if I am not sure to deserve it. Ley me know if you will organize a discussion group on my Essay, I will be pleasured to discuss with you and your friends if you agree.

I am surely going to read, comment and rate your Essay in next days.

Thanks again!

Cheers,

Ch.

Professor Corda,

Your essay approaches the density of a BH and doesn't evaporate.

"The physical state and the correspondent wave-function are written in terms of an unitary evolution matrix instead of a density matrix."

So the "heat death" prediction by some physicists after billions of years is off? What does your pure quantum state concept do with Big Bang prediction literature, considering the relationship oft made between BHs and the BB? And is there a difference between super-massive black holes and solar black holes?

Jim

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Your essay approaches the density of a BH and doesn't evaporate.

"The physical state and the correspondent wave-function are written in terms of an unitary evolution matrix instead of a density matrix."

So the "heat death" prediction by some physicists after billions of years is off? What does your pure quantum state concept do with Big Bang prediction literature, considering the relationship oft made between BHs and the BB? And is there a difference between super-massive black holes and solar black holes?

Jim

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Dear Jim,

Thanks for your kind comments with interesting questions.

Actually, the unitary evolution discussed in my Essay does not imply that the BH does not evaporate, but only that the evaporation process is information preserving. Avoiding evaporation is usually claimed when one invokes the Generalized Uncertainly Principle which should stop evaporation at the Planck scale.

I did not yet work on potential consequences of the paradox solution on the Big Bang, but they could be intriguing. Mathur recently started to work on this issue. I suggest you to read his paper Awarded in the 2012 Gravity Research Foundation Competition that can be easily download in the Foundation web-site.

My analysis works for both solar and super massive BH. The difference is that for the latter the evaporation time is much longer.

Let me know if my replies are OK or if you need more details.

Thanks again.

Cheers,

Ch.

Thanks for your kind comments with interesting questions.

Actually, the unitary evolution discussed in my Essay does not imply that the BH does not evaporate, but only that the evaporation process is information preserving. Avoiding evaporation is usually claimed when one invokes the Generalized Uncertainly Principle which should stop evaporation at the Planck scale.

I did not yet work on potential consequences of the paradox solution on the Big Bang, but they could be intriguing. Mathur recently started to work on this issue. I suggest you to read his paper Awarded in the 2012 Gravity Research Foundation Competition that can be easily download in the Foundation web-site.

My analysis works for both solar and super massive BH. The difference is that for the latter the evaporation time is much longer.

Let me know if my replies are OK or if you need more details.

Thanks again.

Cheers,

Ch.

Christian,

Your response was quite adequate. Being somewhat of a neophyte in physics and cosmology, I marvel that I can begin to understand some of the issues. Thank you for your research reference.

Jim

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Your response was quite adequate. Being somewhat of a neophyte in physics and cosmology, I marvel that I can begin to understand some of the issues. Thank you for your research reference.

Jim

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Dear Christian,

Your interesting essay provides a thorough and clear description of the developments on the paradox. I always had doubts about Hawking’s results, but my arguments are altogether different: The

quantization of the right hand side of Einstein’s equations, in a given spacetime, has yielded the interesting effects of the Hawking radiation [SW Hawking, Comm. Math. Phys. 43, 199, 1975]. (However, even here the role of back reaction has not been fully understood.) Recently it has been shown that the right hand side of Einstein’s equations, i.e., the energy-stress tensor T^ik, has serious problems [arXiv:1204.1553]. Hence, the results obtained by using it also become doubtful.

Your essay makes important contribution to this subject. I rated your essay high and wish you best of luck in the contest.

___Ram

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Your interesting essay provides a thorough and clear description of the developments on the paradox. I always had doubts about Hawking’s results, but my arguments are altogether different: The

quantization of the right hand side of Einstein’s equations, in a given spacetime, has yielded the interesting effects of the Hawking radiation [SW Hawking, Comm. Math. Phys. 43, 199, 1975]. (However, even here the role of back reaction has not been fully understood.) Recently it has been shown that the right hand side of Einstein’s equations, i.e., the energy-stress tensor T^ik, has serious problems [arXiv:1204.1553]. Hence, the results obtained by using it also become doubtful.

Your essay makes important contribution to this subject. I rated your essay high and wish you best of luck in the contest.

___Ram

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Hi Ram,

Thanks for your kind comments and for the high rate you gave to my Essay.

You know that I have a high opinion on your ideas concerning the deletion of the stress-energy tensor in the right hand side of Einstein Field Equation. It could be interesting to develop your approach in the framework of the gravitational collapse in order to see if Hawking's prevision of black hole radiation is again confirmed.

Thanks again.

Cheers,

Ch.

Thanks for your kind comments and for the high rate you gave to my Essay.

You know that I have a high opinion on your ideas concerning the deletion of the stress-energy tensor in the right hand side of Einstein Field Equation. It could be interesting to develop your approach in the framework of the gravitational collapse in order to see if Hawking's prevision of black hole radiation is again confirmed.

Thanks again.

Cheers,

Ch.

Some definitions.

Dear professor Corda ,

because FQXi contest is not pure scientific forum, I’d like to introduce some common definitions on BHIP ( may be, for readers - poets and philosophers if You agree )

Following Hawking, the black hole (BH) information paradox started in 1967 when Werner Israel showed that the Schwarzschild metric was the only static vacuum black...

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Dear professor Corda ,

because FQXi contest is not pure scientific forum, I’d like to introduce some common definitions on BHIP ( may be, for readers - poets and philosophers if You agree )

Following Hawking, the black hole (BH) information paradox started in 1967 when Werner Israel showed that the Schwarzschild metric was the only static vacuum black...

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Dear Michael,

Thanks for your particular approach to the BHPI. The metaphor of an encyclopaedia works in my case too. Here, the difference with Hawking's approach is that the emitted radiation is not strictly thermal. Now, the encyclopaedia is not more burned. Instead, one can think as its internal pages have been cutted and cutted and cutted. .. an enormous number of times. Inother words, the encyclopaedia becomes an enormous puzzle. My mathematical solution permits to reconstruct the puzzle. Thus, it also a final solution of your pseudo-problem.

I am going to read your Essay in next days.

Cheers,

Ch.

Thanks for your particular approach to the BHPI. The metaphor of an encyclopaedia works in my case too. Here, the difference with Hawking's approach is that the emitted radiation is not strictly thermal. Now, the encyclopaedia is not more burned. Instead, one can think as its internal pages have been cutted and cutted and cutted. .. an enormous number of times. Inother words, the encyclopaedia becomes an enormous puzzle. My mathematical solution permits to reconstruct the puzzle. Thus, it also a final solution of your pseudo-problem.

I am going to read your Essay in next days.

Cheers,

Ch.

Hi Christian,

Great essay and completely in line with the intent of the contest.

Could I over simplify your work by saying BHs evaporate via quantum jumps with no blackbody

radiation involved?

Don Limuti

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Great essay and completely in line with the intent of the contest.

Could I over simplify your work by saying BHs evaporate via quantum jumps with no blackbody

radiation involved?

Don Limuti

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Hi Don,

Thanks for your kind congrats. Concerning your question, we can say that BHs evaporate via quantum jumps generating a quasi-thermal radiation.

I will surely read your Essay in next days.

Cheers,

Ch.

Thanks for your kind congrats. Concerning your question, we can say that BHs evaporate via quantum jumps generating a quasi-thermal radiation.

I will surely read your Essay in next days.

Cheers,

Ch.

Hi Christian,

There is something about your work that reminds me of a though I had about black body radiation and emission spectra of gases. Your work is very different, but there is something about it that may apply to other areas of physics besides BHs. It is just a hunch but take a look at:

http://www.digitalwavetheory.com/DWT/31_Thermodynamics.html

A

nd please forgive my unsophisticated techniques, but quasi thermal kinda fits.

Don L.

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There is something about your work that reminds me of a though I had about black body radiation and emission spectra of gases. Your work is very different, but there is something about it that may apply to other areas of physics besides BHs. It is just a hunch but take a look at:

http://www.digitalwavetheory.com/DWT/31_Thermodynamics.html

A

nd please forgive my unsophisticated techniques, but quasi thermal kinda fits.

Don L.

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Hello Christian,

The main task of contests FQXi - new fundamental ideas. You are fine, revolutionary ideas on the fundamental issues of the Universe, primarily in «one of the most famous and intriguing scientific controversies in the whole history of Science is the so called BH information paradox». You had a brilliant analysis of the problem in the spirit of Descartes: "has come under question." You made sweeping conclusions. They provide an opportunity to take a fresh look at the nature of the information and its essence, a deeper understanding of the concepts of 'matter' and 'energy' and their limits and states.

I wish you every success and respect,

Vladimir

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The main task of contests FQXi - new fundamental ideas. You are fine, revolutionary ideas on the fundamental issues of the Universe, primarily in «one of the most famous and intriguing scientific controversies in the whole history of Science is the so called BH information paradox». You had a brilliant analysis of the problem in the spirit of Descartes: "has come under question." You made sweeping conclusions. They provide an opportunity to take a fresh look at the nature of the information and its essence, a deeper understanding of the concepts of 'matter' and 'energy' and their limits and states.

I wish you every success and respect,

Vladimir

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Much pleased to have discussions with you, dear Prof. Corda,

Hawking radiation itself is indicative of the continuum nature of information, in that we may differentiate information paradox in general from specified BH information paradox. This implies that in particle scenario the observational information is not observational in continuum, which has been defined as information paradox in general. Thus we recommend an alternative cosmological model in a scenario of eigen-rotational segments of string-matter continuum is expressional to resolve these information paradoxes, in that the relationship of Planck constant with energy and frequency is not been altered though the Reduced Planck constant is not applicable. Thus time dependent Schrödinger equation is not descriptive in this paradigm, yet unitary matrix is much germane in describing the observational information continuum, in that discrete incident time from linear flow of time may be quantised for near-reality observations.

With best wishes

Jayakar

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Hawking radiation itself is indicative of the continuum nature of information, in that we may differentiate information paradox in general from specified BH information paradox. This implies that in particle scenario the observational information is not observational in continuum, which has been defined as information paradox in general. Thus we recommend an alternative cosmological model in a scenario of eigen-rotational segments of string-matter continuum is expressional to resolve these information paradoxes, in that the relationship of Planck constant with energy and frequency is not been altered though the Reduced Planck constant is not applicable. Thus time dependent Schrödinger equation is not descriptive in this paradigm, yet unitary matrix is much germane in describing the observational information continuum, in that discrete incident time from linear flow of time may be quantised for near-reality observations.

With best wishes

Jayakar

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Dear Jayakar,

Thanks for your comments. Yes, you are absolutely right. The issue that in particle scenario the observational information is not observational in continuum is exactly the core of the information paradox. I am surely going to read your Essay in next days. Thanks again.

Cheers,

Ch.

Thanks for your comments. Yes, you are absolutely right. The issue that in particle scenario the observational information is not observational in continuum is exactly the core of the information paradox. I am surely going to read your Essay in next days. Thanks again.

Cheers,

Ch.

Dear Christian,

It was a happy moment for me, among others, when Hawking reversed himself on the issue of black hole information loss.

What I could never make sense of, is why the transition from initial to final state in black hole thermodynamics (ground to excited state) should be equivalent to a quantum jump -- where we lose information of the time evolution -- because if Hawking radiation exists at all, it should be a classical map t --> T, for the reason that the extreme condition of the black hole horizon gives us a perfect t = 0 potential that is lacking when we choose t arbitrarily.

So I am all in favor of 't Hooft's efforts to unite classical determinism with quantum mechanics, and I so appreciate your careful argument from pure potential to pure kinetic state. I'm always impressed with your essays and as usual wish you the best in the compeitition! You can count on a high score from me.

Tom

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It was a happy moment for me, among others, when Hawking reversed himself on the issue of black hole information loss.

What I could never make sense of, is why the transition from initial to final state in black hole thermodynamics (ground to excited state) should be equivalent to a quantum jump -- where we lose information of the time evolution -- because if Hawking radiation exists at all, it should be a classical map t --> T, for the reason that the extreme condition of the black hole horizon gives us a perfect t = 0 potential that is lacking when we choose t arbitrarily.

So I am all in favor of 't Hooft's efforts to unite classical determinism with quantum mechanics, and I so appreciate your careful argument from pure potential to pure kinetic state. I'm always impressed with your essays and as usual wish you the best in the compeitition! You can count on a high score from me.

Tom

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Dear professor Christian Corda:

Thank you for reading my essay as you promise and rating my essay so high. I am glad you enjoy reading it. Well I am convince you would enjoy reading Dr. Elliot McGucken self conscious essay, “Where is the Wisdom we have lost in Information? Returning Wheeler’s Honor and Philo-Sophy—the Love of Wisdom—to Physics”. as you know he was a good John Wheeler student at Princeton, maybe after reading it, you would like to read again mine. Personally and probably without the necessary authority, I agree to many things he said about modern physics, I agree with many of his concepts about , to me , the so called “time”, also that is not the fourth dimension, but I disagree with the Moving Dimension Theory, being the so called “time” the moving dimension. The so called “time” is just a remnant word, don’t have physical existence, is not a physical entity, is not an expanding dimension, the fourth dimension is just as Einstein said an imaginary dimension. The so called “time” Is not a moving dimension, but “motion itself ” I think like him that this new position can make a big difference, and knowing that the so called “time” in fact is “motion” can change many things. Probably the contest itself is the less important thing we are doing here.

With my very best wishes

Héctor

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Thank you for reading my essay as you promise and rating my essay so high. I am glad you enjoy reading it. Well I am convince you would enjoy reading Dr. Elliot McGucken self conscious essay, “Where is the Wisdom we have lost in Information? Returning Wheeler’s Honor and Philo-Sophy—the Love of Wisdom—to Physics”. as you know he was a good John Wheeler student at Princeton, maybe after reading it, you would like to read again mine. Personally and probably without the necessary authority, I agree to many things he said about modern physics, I agree with many of his concepts about , to me , the so called “time”, also that is not the fourth dimension, but I disagree with the Moving Dimension Theory, being the so called “time” the moving dimension. The so called “time” is just a remnant word, don’t have physical existence, is not a physical entity, is not an expanding dimension, the fourth dimension is just as Einstein said an imaginary dimension. The so called “time” Is not a moving dimension, but “motion itself ” I think like him that this new position can make a big difference, and knowing that the so called “time” in fact is “motion” can change many things. Probably the contest itself is the less important thing we are doing here.

With my very best wishes

Héctor

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Hi Héctor,

Thanks for signalling McGucken's Essay. I am going to read it in next days. Yes, I remember that he was a "Wheeler boy" and now he has various interests on arts science and technology. I appreciate your statement that "Probably the contest itself is the less important thing we are doing here". On the other hand, thing we are doing here ennoble the Contest in the same way!

Cheers,

Ch.

Thanks for signalling McGucken's Essay. I am going to read it in next days. Yes, I remember that he was a "Wheeler boy" and now he has various interests on arts science and technology. I appreciate your statement that "Probably the contest itself is the less important thing we are doing here". On the other hand, thing we are doing here ennoble the Contest in the same way!

Cheers,

Ch.

Dear professor Christian Corda:

Thanks for your nice essay, well done, i enjoyed reading it very much

I am not expert about black hole, i have two questions:

1The assumption by 't Hooft that Schröedinger equations can be used universally for all dynamics in the universe is in turn confirmed,

why not use relativistic dirac equation?

2 BH evaporation must be information preserving.

then information is preserved for other system? for what kind of system? for the whole universe? how to define it like energy to the symmetry of time

Anyway, I believe BH evaporation is a very important issue, which deserve more future research

Thanks for your nice essay, i rated it with high mark

and from a different point view, my essay may interest you

Bit: from Breaking symmetry of it

http://fqxi.org/community/forum/topic/1906

While symmetry is kind of redundancy which means loss of information, breaking of symmetry gives rise to information.

Hope you enjoy it

Regards,

Xiong

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Thanks for your nice essay, well done, i enjoyed reading it very much

I am not expert about black hole, i have two questions:

1The assumption by 't Hooft that Schröedinger equations can be used universally for all dynamics in the universe is in turn confirmed,

why not use relativistic dirac equation?

2 BH evaporation must be information preserving.

then information is preserved for other system? for what kind of system? for the whole universe? how to define it like energy to the symmetry of time

Anyway, I believe BH evaporation is a very important issue, which deserve more future research

Thanks for your nice essay, i rated it with high mark

and from a different point view, my essay may interest you

Bit: from Breaking symmetry of it

http://fqxi.org/community/forum/topic/1906

While symmetry is kind of redundancy which means loss of information, breaking of symmetry gives rise to information.

Hope you enjoy it

Regards,

Xiong

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Dear Xiong,

Thank you very much for your kind comments with interesting questions and for rating my Essay with high mark. Concerning your questions:

1 Dirac equation describes relativistic fields which correspond to fermions, i.e. elementary particles with half-integer spin. Elementary relativistic particles with integer spin, i.e. bosons, instead obey to the Klein-Gordon equation. Black hole physics is extremely difficult, thus, at the present time, it is impossible to give a complete description of it by considering the full quantum and relativistic effects. Then, by invoking Bohr's correspondence principle, one argues that a semi-classical description should be adequate for large values of the principal quantum number even without considering such full quantum and relativistic effects. In my Essay I have shown that a semi-classical description for the system composed by Hawking radiation and quasi-normal modes can be achieved through a time dependent Schröedinger equation.

2 The principle of the conservation of information, i.e. the claim that "in both classical and quantum world, information cannot appear or disappear" is in general considered a fundamental principle in the evolution of all physics systems in our Universe. The information loss paradox claimed that such a principle is questioned for black hole evaporation.

Thanks again, I am going to read your Essay in next days.

Cheers,

Ch.

Thank you very much for your kind comments with interesting questions and for rating my Essay with high mark. Concerning your questions:

1 Dirac equation describes relativistic fields which correspond to fermions, i.e. elementary particles with half-integer spin. Elementary relativistic particles with integer spin, i.e. bosons, instead obey to the Klein-Gordon equation. Black hole physics is extremely difficult, thus, at the present time, it is impossible to give a complete description of it by considering the full quantum and relativistic effects. Then, by invoking Bohr's correspondence principle, one argues that a semi-classical description should be adequate for large values of the principal quantum number even without considering such full quantum and relativistic effects. In my Essay I have shown that a semi-classical description for the system composed by Hawking radiation and quasi-normal modes can be achieved through a time dependent Schröedinger equation.

2 The principle of the conservation of information, i.e. the claim that "in both classical and quantum world, information cannot appear or disappear" is in general considered a fundamental principle in the evolution of all physics systems in our Universe. The information loss paradox claimed that such a principle is questioned for black hole evaporation.

Thanks again, I am going to read your Essay in next days.

Cheers,

Ch.

Mr. Christian Corda hello,

I read Your essay and it is very interesting but very heavy and full of equation. It will take a lot of time.

I used a very low quantity of equation into My essay. Can I have Your opinion Mr. Corda ? Or at least some impressions ?

http://fqxi.org/community/forum/topic/1903

My Best Regards.

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I read Your essay and it is very interesting but very heavy and full of equation. It will take a lot of time.

I used a very low quantity of equation into My essay. Can I have Your opinion Mr. Corda ? Or at least some impressions ?

http://fqxi.org/community/forum/topic/1903

My Best Regards.

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Dear Giacomo,

Thanks for finding my Essay very interesting and also for taking your time to analyse details of equations. I will surely read, comment and rate your Essay in next days.

Cheers,

Ch.

Thanks for finding my Essay very interesting and also for taking your time to analyse details of equations. I will surely read, comment and rate your Essay in next days.

Cheers,

Ch.

Greeting Christian,

I wanted to let you know that I am happy to see your entry, and that it is doing well in the contest, as I intend to read it this weekend. It appears you have attempted to grapple with a foundational information Physics question, rather than deal with the "It from Bit" paradigm head-on, but that appears to be germane here. Should you have time, my humble effort bears inspection, and I invite your comments.

All the Best,

Jonathan

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I wanted to let you know that I am happy to see your entry, and that it is doing well in the contest, as I intend to read it this weekend. It appears you have attempted to grapple with a foundational information Physics question, rather than deal with the "It from Bit" paradigm head-on, but that appears to be germane here. Should you have time, my humble effort bears inspection, and I invite your comments.

All the Best,

Jonathan

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Hi Jonathan,

Nice to meet you here in the Contest again.

Thanks for your kind comments. Although the statement "It from bit or bit from it" is the title of the Contest, the object is more general as it concerns the general role of information in physics. On the other hand, the black hole information paradox was a fundamental issue for the popolarization of the connection between physics and information within the Scientific Community.

I will be pleasured to read, comment and rate your Essay in next days.

Thanks again and good luck in the Contest.

Cheers,

Ch.

Nice to meet you here in the Contest again.

Thanks for your kind comments. Although the statement "It from bit or bit from it" is the title of the Contest, the object is more general as it concerns the general role of information in physics. On the other hand, the black hole information paradox was a fundamental issue for the popolarization of the connection between physics and information within the Scientific Community.

I will be pleasured to read, comment and rate your Essay in next days.

Thanks again and good luck in the Contest.

Cheers,

Ch.

Dear Dr. Corda -

My view is that we need to be able to think in physical (less-abstract) terms about these issues: Our assumptions need to be revisited before we can venture to ask whether or not information is lost when energy-mass enters a BH. This is not to take away anything from your achievement - but no doubt many will say that the debate continues, and so we should check if, under the assumptions that have prevailed for the last several generations, we can possibly achieve a concrete answer?

Energy conservation enters into our ideas about BH's, for instance. In my essay, I describe a paradigm consisting of energy vortices that are correlated in a larger (omni-dimensional) energy field. The law of conservation is then amended into a perpetual energy exchange between the field and the Cosmos. If you agree with the logic, then you will see that BH's do not need to shrink when radiation is emitted - since they must be energy portals between the Cosmos and the greater energy field.

Stated in such an abbreviated fashion the paradigm acquires a science fiction flavor, I know, but the argument is entirely logical, and clearly shows how the Correlation of distinct energy vortices must be the unifying element of the cosmos.

It then becomes explicable (and no doubt the math needs to be evolved) that Information going into a black hole is scrambled, and that radiation re-emerging from it is also scrambled - but then orders itself as it is distributed between the principal vortices that form the Cosmos.

I believe you will be interested by the Vortex System I describe - and I look forward to your feedback. I have rated your essay, of course, and I wish you the best of luck in the contest -

John

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My view is that we need to be able to think in physical (less-abstract) terms about these issues: Our assumptions need to be revisited before we can venture to ask whether or not information is lost when energy-mass enters a BH. This is not to take away anything from your achievement - but no doubt many will say that the debate continues, and so we should check if, under the assumptions that have prevailed for the last several generations, we can possibly achieve a concrete answer?

Energy conservation enters into our ideas about BH's, for instance. In my essay, I describe a paradigm consisting of energy vortices that are correlated in a larger (omni-dimensional) energy field. The law of conservation is then amended into a perpetual energy exchange between the field and the Cosmos. If you agree with the logic, then you will see that BH's do not need to shrink when radiation is emitted - since they must be energy portals between the Cosmos and the greater energy field.

Stated in such an abbreviated fashion the paradigm acquires a science fiction flavor, I know, but the argument is entirely logical, and clearly shows how the Correlation of distinct energy vortices must be the unifying element of the cosmos.

It then becomes explicable (and no doubt the math needs to be evolved) that Information going into a black hole is scrambled, and that radiation re-emerging from it is also scrambled - but then orders itself as it is distributed between the principal vortices that form the Cosmos.

I believe you will be interested by the Vortex System I describe - and I look forward to your feedback. I have rated your essay, of course, and I wish you the best of luck in the contest -

John

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Dear John,

Thanks for your kind comments. Actually, I do not see contradiction between theoretical physics and abstractions. Abstractions and conjectures arises from intuition which is the basis for constructing theoretical physics. Hence, I totally agree not only with the statement by Coleman on the "ever-increasing levels of abstraction", but also with the famous aphorism by Einstein that "Information is more important than knowledge".

I am going to read, comment and rate your Essay in next days.

Cheers,

Ch.

Thanks for your kind comments. Actually, I do not see contradiction between theoretical physics and abstractions. Abstractions and conjectures arises from intuition which is the basis for constructing theoretical physics. Hence, I totally agree not only with the statement by Coleman on the "ever-increasing levels of abstraction", but also with the famous aphorism by Einstein that "Information is more important than knowledge".

I am going to read, comment and rate your Essay in next days.

Cheers,

Ch.

Hello Dr. Corda -

On the subject of abstractions, I think we are essentially in agreement. My meaning is that we need to rigorously question our assumptions - know which ones we are employing, and justify their inclusion in our emerging paradigm; only then can we attempt to proceed logically and empirically.

In short, before we can answer ultimate questions, we must define the foundational assumptions.

I think my reason for saying this will become clearer once you've had a chance to look over my essay - something I am very much looking forward to!

Best regards,

John.

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On the subject of abstractions, I think we are essentially in agreement. My meaning is that we need to rigorously question our assumptions - know which ones we are employing, and justify their inclusion in our emerging paradigm; only then can we attempt to proceed logically and empirically.

In short, before we can answer ultimate questions, we must define the foundational assumptions.

I think my reason for saying this will become clearer once you've had a chance to look over my essay - something I am very much looking forward to!

Best regards,

John.

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Dear Professor Corda,

I have read your essay but unfortunately I am not properly qualified to make a judgment on it, sorry.

I was reading through your blog and I was pleased to see that you are kind enough to reply to everyone and also curious enough to read everyone's essays.

It is my first time in this contest and I am completely a non-specialist. I have written an essay but so far I haven't received a proper feedback from a professor of theoretical physics.

I would be delighted if you would accept to take a look at it (I have also written a complete theory here, but I don't want to abuse your kindness).

Best regards and good luck with the contest.

Patrick

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I have read your essay but unfortunately I am not properly qualified to make a judgment on it, sorry.

I was reading through your blog and I was pleased to see that you are kind enough to reply to everyone and also curious enough to read everyone's essays.

It is my first time in this contest and I am completely a non-specialist. I have written an essay but so far I haven't received a proper feedback from a professor of theoretical physics.

I would be delighted if you would accept to take a look at it (I have also written a complete theory here, but I don't want to abuse your kindness).

Best regards and good luck with the contest.

Patrick

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Dear Patrick,

Thanks for your kind comments. Yes, I think that the spirit of this Essay Contest is to stimulate discussions, as much as possible, among various authors on the various issues that can emerge from various Essays. Thus, in my opinion is important to reply to everyone and to read everyone's essays. I will be happy to read, comment and rate your Essay in next days. I will also take a look to your The 3D Universe Theory.

Thanks again an good luck in the Contest!

Cheers,

Ch.

Thanks for your kind comments. Yes, I think that the spirit of this Essay Contest is to stimulate discussions, as much as possible, among various authors on the various issues that can emerge from various Essays. Thus, in my opinion is important to reply to everyone and to read everyone's essays. I will be happy to read, comment and rate your Essay in next days. I will also take a look to your The 3D Universe Theory.

Thanks again an good luck in the Contest!

Cheers,

Ch.

Dear Prof. Corda

I read with great interest your essay (the parts that I could understand, you loose me in math). The issue of information and BH is essential in science and I try to follow all the evolvements in this area.

The latest information I got was from New Scientist of 22 june 2013 (www.newscientist.com/article/dn23611-quantum-gravity-takes -singularity-out)

where Juan Maldacena and leonard Susskind come up with a new kind of wormhole, they pose that there is no singularity in the "center" of a BH, this perception is endorsed by Abhay Ashtekar who couples this view with LQG where space-time after the Planck Length 10^-35m is rendered to "chunks". The center of a BH should so be the threshold to another "universe" and information coming in would never be lost because it just "goes" to that other dimension.

I am curious what is your opinion about this theory .

This theory is touching my own perception as is written in my essay "THE QUEST FOR THE PRIMAL SEQUENCE". I should be very obliged if you could eventually read, comment and/or rate my view.

respectfully

Wilhelmus

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I read with great interest your essay (the parts that I could understand, you loose me in math). The issue of information and BH is essential in science and I try to follow all the evolvements in this area.

The latest information I got was from New Scientist of 22 june 2013 (www.newscientist.com/article/dn23611-quantum-gravity-takes -singularity-out)

where Juan Maldacena and leonard Susskind come up with a new kind of wormhole, they pose that there is no singularity in the "center" of a BH, this perception is endorsed by Abhay Ashtekar who couples this view with LQG where space-time after the Planck Length 10^-35m is rendered to "chunks". The center of a BH should so be the threshold to another "universe" and information coming in would never be lost because it just "goes" to that other dimension.

I am curious what is your opinion about this theory .

This theory is touching my own perception as is written in my essay "THE QUEST FOR THE PRIMAL SEQUENCE". I should be very obliged if you could eventually read, comment and/or rate my view.

respectfully

Wilhelmus

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Dear Wilhelmus,

Thanks for your kind comments. Actually, I have not yet read the paper by Maldacena and Susskind. By reading the abstract, I think that their approach to solve the BH information paradox concerns the framework of the "AMPS" firewall, which is a hypothesis of quantum gravity. In general, the approach by Maldacena and Susskind on quantum gravity is the one of String Theory while the approach by Ashtekar is the one of LQG, as you correctly emphasize. I am not an expert neither of String Theory, nor of LQG. In my Essay the approach is different and completely semi-classic. In any case, I agree with them that there should be no singularity in the "center" of a BH. I worked on this issue again at the classical level in my paper C. Corda and H. J. Mosquera Cuesta, Removing black hole singularities with nonlinear electrodynamics, Mod. Phys. Lett. A 25, 2423-2429 (2010). I will surely read, comment and rate your Essay in next days.

Thanks again and good luck in the Contest!

Cheers,

Ch.

Thanks for your kind comments. Actually, I have not yet read the paper by Maldacena and Susskind. By reading the abstract, I think that their approach to solve the BH information paradox concerns the framework of the "AMPS" firewall, which is a hypothesis of quantum gravity. In general, the approach by Maldacena and Susskind on quantum gravity is the one of String Theory while the approach by Ashtekar is the one of LQG, as you correctly emphasize. I am not an expert neither of String Theory, nor of LQG. In my Essay the approach is different and completely semi-classic. In any case, I agree with them that there should be no singularity in the "center" of a BH. I worked on this issue again at the classical level in my paper C. Corda and H. J. Mosquera Cuesta, Removing black hole singularities with nonlinear electrodynamics, Mod. Phys. Lett. A 25, 2423-2429 (2010). I will surely read, comment and rate your Essay in next days.

Thanks again and good luck in the Contest!

Cheers,

Ch.

Dear Christian,

I read and reread your essay with great interest. Although I did not comprehend all of the mathematics and am unfamiliar with some of the references (I am an attorney, but deeply interested in the subject of information, physics, and reality), I think I understood the basics of your essay and was impressed with your depth of knowledge and direction of your thinking.

I have a question that I hesitate to ask (out of concern that my ignorance is such that the question may appear nonsensical to you), but I will ask it anyway. In your technical endnotes, you stated, “In other words, QNMs frequencies are the eigenvalues of the system. The Hawking quanta are then interpreted as the ‘jumps’ among the levels.” My question is this: are the ‘jumps’ among the levels perhaps somewhat analogous – in principle – to the jumps in levels or ‘shells’ of atomic orbitals? Again, I apologize if my question makes no sense, but I wondered, after reading your essay, if such might be the case.

Thank you for your contributions to the subject. I’m going to attempt to learn more about some of the things you mentioned.

Best,

Ralph

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I read and reread your essay with great interest. Although I did not comprehend all of the mathematics and am unfamiliar with some of the references (I am an attorney, but deeply interested in the subject of information, physics, and reality), I think I understood the basics of your essay and was impressed with your depth of knowledge and direction of your thinking.

I have a question that I hesitate to ask (out of concern that my ignorance is such that the question may appear nonsensical to you), but I will ask it anyway. In your technical endnotes, you stated, “In other words, QNMs frequencies are the eigenvalues of the system. The Hawking quanta are then interpreted as the ‘jumps’ among the levels.” My question is this: are the ‘jumps’ among the levels perhaps somewhat analogous – in principle – to the jumps in levels or ‘shells’ of atomic orbitals? Again, I apologize if my question makes no sense, but I wondered, after reading your essay, if such might be the case.

Thank you for your contributions to the subject. I’m going to attempt to learn more about some of the things you mentioned.

Best,

Ralph

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Dear Ralph,

Thanks for your kind words and also for appreciating my Essay. Do not worry, your question is indeed very reasonable and it permits me to give more explanations. The analogy that you cited is very profound although we must be very careful in discussing it. I try to explain this issue. It is a general conviction that black holes should result in highly excited states...

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Thanks for your kind words and also for appreciating my Essay. Do not worry, your question is indeed very reasonable and it permits me to give more explanations. The analogy that you cited is very profound although we must be very careful in discussing it. I try to explain this issue. It is a general conviction that black holes should result in highly excited states...

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Ch,

There's a side that I am not aware of being argued with the info-being-lost paradox where because info goes beyond a boundary, it is just completely gone when the black hole evaporates and gets small like a puddle. Mainly, I see a case for information, which has a energy or heat equivalent, going into a black hole being analyzed by the same method that information leaving a universe...

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There's a side that I am not aware of being argued with the info-being-lost paradox where because info goes beyond a boundary, it is just completely gone when the black hole evaporates and gets small like a puddle. Mainly, I see a case for information, which has a energy or heat equivalent, going into a black hole being analyzed by the same method that information leaving a universe...

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Dear Amos,

Thanks for your kind comments.

Actually, we do not know if the final result of the black hole evaporation is a puddle (having dimensions of order of the Planck scale) or if, instead, the black hole completely evaporates. In fact, avoiding evaporation is usually claimed when one invokes the Generalized Uncertainly Principle which should stop evaporation at the Planck...

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Thanks for your kind comments.

Actually, we do not know if the final result of the black hole evaporation is a puddle (having dimensions of order of the Planck scale) or if, instead, the black hole completely evaporates. In fact, avoiding evaporation is usually claimed when one invokes the Generalized Uncertainly Principle which should stop evaporation at the Planck...

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Ch,

Thanks for the detailed response, the length of which is quite impressive! I'll get that Gravitation book.

Amos.

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Thanks for the detailed response, the length of which is quite impressive! I'll get that Gravitation book.

Amos.

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Hi Christian,

Without stretching too much I think our viewpoints are the same. Here goes:

1. Start with: "Information tells physics how to work. Physics tells information how to flow"?

2. Change physics to "it" and change information to "Bit" and you get:

"Bit tells "it" how to work. "It" tells Bit how to flow"?

3. Lastly change tells to determines and we get:

"Bit determines "it" how to work. "It" determines Bit how to flow"?

4. This is a little awkward so we make it smooth:

"Bits determine how "it" acts. "It" determines how Bits respond.

5. This is close enough for me to say we are saying the same thing. IT and BIT are two side of the same coin.

What do you say will "Russell and Whitehead" accept this logic? Siri says the logic is OK!

Don L.

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Without stretching too much I think our viewpoints are the same. Here goes:

1. Start with: "Information tells physics how to work. Physics tells information how to flow"?

2. Change physics to "it" and change information to "Bit" and you get:

"Bit tells "it" how to work. "It" tells Bit how to flow"?

3. Lastly change tells to determines and we get:

"Bit determines "it" how to work. "It" determines Bit how to flow"?

4. This is a little awkward so we make it smooth:

"Bits determine how "it" acts. "It" determines how Bits respond.

5. This is close enough for me to say we are saying the same thing. IT and BIT are two side of the same coin.

What do you say will "Russell and Whitehead" accept this logic? Siri says the logic is OK!

Don L.

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Dear Dr. Corda,

(Google translation)

You are deservedly at the top of this competition for a number of reasons. Solution "black hole (BH) information paradox" is a very important issue. Aside from that I think that the production of paradoxes, then to be solved wrong way. Just so because my completely different approach to your, I was grateful to get a comment on my article from you. Negative comment is also welcome as positive (ignore the two errors in typing in formulas). Thus, the formulas (2) is:

gamma = 2 ^ {[cy / 2 + p / 2 +3 * log (2pi, 2) / 2] / [1 +137.035999074 ^ 2 * log (I, 2)]} = 1.00137841920431

Rating is irrelevant.

Regards,

Branko

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(Google translation)

You are deservedly at the top of this competition for a number of reasons. Solution "black hole (BH) information paradox" is a very important issue. Aside from that I think that the production of paradoxes, then to be solved wrong way. Just so because my completely different approach to your, I was grateful to get a comment on my article from you. Negative comment is also welcome as positive (ignore the two errors in typing in formulas). Thus, the formulas (2) is:

gamma = 2 ^ {[cy / 2 + p / 2 +3 * log (2pi, 2) / 2] / [1 +137.035999074 ^ 2 * log (I, 2)]} = 1.00137841920431

Rating is irrelevant.

Regards,

Branko

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Dear Prof. Corda,

Its my privilege to comment on your essay.

Regarding your arguments on BH information restorations, I like to add some thing here which may support yours, and equally I invite you in my essay http://fqxi.org/community/forum/topic/1855)to have some comments.

It is well known that basic problem for not receiving any information from the opposite end of an event horizon of BH is due to its superluminal range of escape velocity. Special Relativity restricts the superluminal speeds of particles to emerge out of that event horizon. If in any way we can get the superluminal speeds to overtake that range of high escape velocities around the BH, the information sharing issues with the BH by penetrating the event horizon to the outside world could be instantly resolved.

That is why I sincerely like to invite you in my essay, particularly I request in Eqs.(28)-(31)and paragraph no.5.2 there, where we can get such superluminal speeds of particles in the same frames of special relativity (which is now we have respect to c).

With my regards

Dipak

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Its my privilege to comment on your essay.

Regarding your arguments on BH information restorations, I like to add some thing here which may support yours, and equally I invite you in my essay http://fqxi.org/community/forum/topic/1855)to have some comments.

It is well known that basic problem for not receiving any information from the opposite end of an event horizon of BH is due to its superluminal range of escape velocity. Special Relativity restricts the superluminal speeds of particles to emerge out of that event horizon. If in any way we can get the superluminal speeds to overtake that range of high escape velocities around the BH, the information sharing issues with the BH by penetrating the event horizon to the outside world could be instantly resolved.

That is why I sincerely like to invite you in my essay, particularly I request in Eqs.(28)-(31)and paragraph no.5.2 there, where we can get such superluminal speeds of particles in the same frames of special relativity (which is now we have respect to c).

With my regards

Dipak

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Dear Dipak,

Thanks for your kind comments. Actually, the quantum tunnelling framework which supports the emission of Hawking quanta can overtake the range of high escape velocities around the BH. This is the argument that, not only myself, but various other authors usually invoke. In any case, it will be my pleasure to read, comment and rate your Essay in next days.

Cheers,

Ch.

Thanks for your kind comments. Actually, the quantum tunnelling framework which supports the emission of Hawking quanta can overtake the range of high escape velocities around the BH. This is the argument that, not only myself, but various other authors usually invoke. In any case, it will be my pleasure to read, comment and rate your Essay in next days.

Cheers,

Ch.

Dear Professor Corda

Richard Feynman in his Nobel Acceptance Speech (http://www.nobelprize.org/nobel_prizes/physics/laureates/19

65/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...

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Richard Feynman in his Nobel Acceptance Speech (http://www.nobelprize.org/nobel_prizes/physics/laureates/19

65/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...

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Thanks for your kind comments, dear Than. I am honoured that you think that I have touched some corners of Nature. Like you, I have a strong admiration for Richard Feynman, and I completely agree with your and his point of view on the simplicity of nature. It will be my pleasure to read, comment and score your Essay in next days.

Cheers,

Ch.

Cheers,

Ch.

Christian,

Can I offer a completely different scenario?

Energy manifests information. Information defines energy. Medium/message. Since energy is conserved, in order to create new information, old information is erased. This is the "arrow of time." It is not a vector from past to future, but the dynamic process in which future becomes past. Potential becomes actual. Tomorrow becomes yesterday. The cat lives or dies based on what physically happens. Clocks run at different rates because they are individual processes.

To the extent black holes actually physically exist, they do eject out enormous amounts of radiation. Either the quasar jets out the poles of galaxies, or binary stars going supernova. The energy is conserved, in a cosmic convection cycle of expanding radiation, contracting mass and the structure is consumed, radiated back out.

Information can only do what energy allows it to do. Reductionism is intellectually essential, but much is lost/radiated and when you finally reach the point of all message and no medium, it is delusional illusion. Not a black hole of infinite density, but simply the eye of the storm. There is no gravity at the center, only pressure. There is no platonic realm. Unmanifest structure is a multiple of zero. A dimensionless point is no more real than a dimensionless apple.

The discipline of physics seems all encompassing and unstoppable, but it is only a matter of which of its many fudges and patches proves to be the Achilles heel.

Rant over. Pardon my impropriety, but I just had to get that out.

Regards,

John

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Can I offer a completely different scenario?

Energy manifests information. Information defines energy. Medium/message. Since energy is conserved, in order to create new information, old information is erased. This is the "arrow of time." It is not a vector from past to future, but the dynamic process in which future becomes past. Potential becomes actual. Tomorrow becomes yesterday. The cat lives or dies based on what physically happens. Clocks run at different rates because they are individual processes.

To the extent black holes actually physically exist, they do eject out enormous amounts of radiation. Either the quasar jets out the poles of galaxies, or binary stars going supernova. The energy is conserved, in a cosmic convection cycle of expanding radiation, contracting mass and the structure is consumed, radiated back out.

Information can only do what energy allows it to do. Reductionism is intellectually essential, but much is lost/radiated and when you finally reach the point of all message and no medium, it is delusional illusion. Not a black hole of infinite density, but simply the eye of the storm. There is no gravity at the center, only pressure. There is no platonic realm. Unmanifest structure is a multiple of zero. A dimensionless point is no more real than a dimensionless apple.

The discipline of physics seems all encompassing and unstoppable, but it is only a matter of which of its many fudges and patches proves to be the Achilles heel.

Rant over. Pardon my impropriety, but I just had to get that out.

Regards,

John

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Dear John,

Thank for offering your completely different scenario. You could be interested on a framework in which all the mass-energy has been lost/radiated during the gravitational collapse developed by the Indian physicist Abhas Mitra. Dr. Mitra published such a scenario in various important mainstream peer reviewed journals. On the other hand, John Baez claimed that "Mitra's work is based on some serious misunderstandings of this subject, and is full of mistakes."

Cheers,

Ch.

Thank for offering your completely different scenario. You could be interested on a framework in which all the mass-energy has been lost/radiated during the gravitational collapse developed by the Indian physicist Abhas Mitra. Dr. Mitra published such a scenario in various important mainstream peer reviewed journals. On the other hand, John Baez claimed that "Mitra's work is based on some serious misunderstandings of this subject, and is full of mistakes."

Cheers,

Ch.

Christian,

Thank you for the response and the links. I have to say my thoughts on black holes are arrived at tangentially, as a consequence of the conclusion that gravity already balances expansion in a concurrent, convective-type cycle. (Sort of as if the rubber sheet analogy were placed over water and wherever the ball is not, the sheet is pushed up by an equal amount.)

Rather than take up your thread with the entire argument, I will point out what I see as a conceptual fallacy incorporated into the cosmological model; 1)According to Einstein, "Space is what you measure with a ruler." 2) Space expands. 3) This will eventually result on distant galaxies disappearing, as the light takes ever longer to reach us.

So in this description of expanding space as measured in terms of lightspeed, which is the denominator? Presumably it is lightspeed, yet that would mean space as measured by the ruler of C is not expanding. But if the expanding space were the denominator, what metric would provide and sustain a stable speed of light? If C is the denominator, then it would be an expansion IN space, not OF space and that would mean we are at the center of the universe.

Of course this perception would be quite reasonable if redshift is due to an optical effect, but that would mean light does not travel as a point particle, but is only absorbed as one.

So; How does intergalactic space expand, yet our most basic metric of it remain constant?

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Thank you for the response and the links. I have to say my thoughts on black holes are arrived at tangentially, as a consequence of the conclusion that gravity already balances expansion in a concurrent, convective-type cycle. (Sort of as if the rubber sheet analogy were placed over water and wherever the ball is not, the sheet is pushed up by an equal amount.)

Rather than take up your thread with the entire argument, I will point out what I see as a conceptual fallacy incorporated into the cosmological model; 1)According to Einstein, "Space is what you measure with a ruler." 2) Space expands. 3) This will eventually result on distant galaxies disappearing, as the light takes ever longer to reach us.

So in this description of expanding space as measured in terms of lightspeed, which is the denominator? Presumably it is lightspeed, yet that would mean space as measured by the ruler of C is not expanding. But if the expanding space were the denominator, what metric would provide and sustain a stable speed of light? If C is the denominator, then it would be an expansion IN space, not OF space and that would mean we are at the center of the universe.

Of course this perception would be quite reasonable if redshift is due to an optical effect, but that would mean light does not travel as a point particle, but is only absorbed as one.

So; How does intergalactic space expand, yet our most basic metric of it remain constant?

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Dear John,

Sorry, but I do not see your conceptual fallacy incorporated into the cosmological model. Yes, distant galaxies disappears as the light takes ever longer to reach us, but this merely implies that the universe has an horizon. Where is the problem? Stable speed of light enters in the well known Friedmann - Lemaître - Robertson - Walker metric which evolution is governed by Einstein Field Equation. This does not imply that we are at the center of the universe. It is exactly the opposite which works. Friedmann - Lemaître - Robertson - Walker metric is founded on the Cosmological Principle which states that "Viewed on a sufficiently large scale, the properties of the Universe are the same for all observers". When intergalactic space expands, our most basic metric of it does not remain constant. It is only the curvature which remains constant, the universe scale factor increases.

Cheers,

Ch.

Sorry, but I do not see your conceptual fallacy incorporated into the cosmological model. Yes, distant galaxies disappears as the light takes ever longer to reach us, but this merely implies that the universe has an horizon. Where is the problem? Stable speed of light enters in the well known Friedmann - Lemaître - Robertson - Walker metric which evolution is governed by Einstein Field Equation. This does not imply that we are at the center of the universe. It is exactly the opposite which works. Friedmann - Lemaître - Robertson - Walker metric is founded on the Cosmological Principle which states that "Viewed on a sufficiently large scale, the properties of the Universe are the same for all observers". When intergalactic space expands, our most basic metric of it does not remain constant. It is only the curvature which remains constant, the universe scale factor increases.

Cheers,

Ch.

Christian,

If the speed of light is not our most basic metric, why is it used as the denominator?

Consider normal doppler effect; The train moving away doesn't stretch the tracks, or the spacing of the telegraph poles, or the length of the train. Only the distance between it and the person hearing the whistle changes. So say the train goes from 1 telegraph pole away, to 10. That would be 1/1 to 10/1.

Now consider galaxies moving apart, as the universe expands; Two galaxies go from x lightyears apart, to 2x lightyears apart. x is the denominator, so the distance goes from 1/x to 2/x. Like the length between telegraph poles, a lightyear doesn't get longer. Like the train moving away, these galaxies grow further apart in terms of lightyears. How is it that we can have this constant measure as a denominator, when the very fabric of space is expanding?

(A lightyear is approx. a trillion miles, so the distance in miles increases as well.)

Regards,

John

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If the speed of light is not our most basic metric, why is it used as the denominator?

Consider normal doppler effect; The train moving away doesn't stretch the tracks, or the spacing of the telegraph poles, or the length of the train. Only the distance between it and the person hearing the whistle changes. So say the train goes from 1 telegraph pole away, to 10. That would be 1/1 to 10/1.

Now consider galaxies moving apart, as the universe expands; Two galaxies go from x lightyears apart, to 2x lightyears apart. x is the denominator, so the distance goes from 1/x to 2/x. Like the length between telegraph poles, a lightyear doesn't get longer. Like the train moving away, these galaxies grow further apart in terms of lightyears. How is it that we can have this constant measure as a denominator, when the very fabric of space is expanding?

(A lightyear is approx. a trillion miles, so the distance in miles increases as well.)

Regards,

John

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Dear professor Christian Corda:

The only things about of which I wrote, are the positive ones, my find is of not use for me, practically its only use are for theoretical physicists. I make it really short, about the subject can be written thousands pages, but this is the nut of it, this are the things were everybody get confuse and confuse everybody else....

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The only things about of which I wrote, are the positive ones, my find is of not use for me, practically its only use are for theoretical physicists. I make it really short, about the subject can be written thousands pages, but this is the nut of it, this are the things were everybody get confuse and confuse everybody else....

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Dear Héctor,

Thanks for your historical reconstruction on "the concept of "time". Notice that, when you claim that "men measured "time" since 30.000 years ago" you are using "time", i.e. the 30.000 years. I agree with your positivism to write only positive things. You can easily convert "time" in "motion" by using the speed of light c. In fact, in natural units "time" and space ("motion" is space covered) have the same unit. I have no doubts that “motion” is a quality or property of every physical existing thing, and as such can relate to every physical existing thing. Uncertainty Principle is a proof of these statements.

Cheers,

Ch.

Thanks for your historical reconstruction on "the concept of "time". Notice that, when you claim that "men measured "time" since 30.000 years ago" you are using "time", i.e. the 30.000 years. I agree with your positivism to write only positive things. You can easily convert "time" in "motion" by using the speed of light c. In fact, in natural units "time" and space ("motion" is space covered) have the same unit. I have no doubts that “motion” is a quality or property of every physical existing thing, and as such can relate to every physical existing thing. Uncertainty Principle is a proof of these statements.

Cheers,

Ch.

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...

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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...

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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.

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

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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

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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...

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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...

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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?

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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?

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Hi Stephen,

Thanks for your comments and for rating my Essay quite highly. I well understand your perplexities on the issue that information remains, in a certain sense, random. I think that such perplexities can be generalized to the whole quantum theory and this was exactly the reason for which Einstein claimed that quantum mechanics should not be definitive. I am not an expert on Popper. Did he claim something concerning the determinism/indeterminism issue and concerning the discrete/continue issue? My idea on black holes is that they are exactly harmonic states that remains in contact with the outside, with no singularity!

Cheers,

Ch.

Thanks for your comments and for rating my Essay quite highly. I well understand your perplexities on the issue that information remains, in a certain sense, random. I think that such perplexities can be generalized to the whole quantum theory and this was exactly the reason for which Einstein claimed that quantum mechanics should not be definitive. I am not an expert on Popper. Did he claim something concerning the determinism/indeterminism issue and concerning the discrete/continue issue? My idea on black holes is that they are exactly harmonic states that remains in contact with the outside, with no singularity!

Cheers,

Ch.

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

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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

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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

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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

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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...

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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...

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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.

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.

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.

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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.

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Hello Christian,

I enjoyed your essay greatly, and I think you are insightful to point out a subtle duality between the inhaling and exhaling modes of the Black Hole, which are modulated by variations upon its surface. I note that the condition of n being much greater than 1 is probably easily met any time the BH is feeding, because there would of course be higher harmonics to the...

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I enjoyed your essay greatly, and I think you are insightful to point out a subtle duality between the inhaling and exhaling modes of the Black Hole, which are modulated by variations upon its surface. I note that the condition of n being much greater than 1 is probably easily met any time the BH is feeding, because there would of course be higher harmonics to the...

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T'was I, who commented above.

I thought I was still logged in, but it appears not. However, the words in the comment above are mine.

All the Best,

Jonathan

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I thought I was still logged in, but it appears not. However, the words in the comment above are mine.

All the Best,

Jonathan

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Dear Jonathan,

I wrongly replied to your comments by writing a new post below. Hence, I will copy and past here my reply:

Dear Jonathan,

Thank you very much for your kind words and compliments and for giving a well written "referee report" on my paper. In particular, I am grateful to you to be returned on Professor Rovelli's comment. At the end of such a comment, Professor Rovelli asks if he is missing something. The answer to this question is yes, he is missing what you correctly emphasize, i.e. I supply missing terms without which a true unitary equation could not be written. Such missing terms arise from my previous research work, published in various important international peer review journals, which are correctly cited in my Essay. I strongly suspect that Professor Rovelli have ONLY read the abstract of my work, and this generated to him the misunderstanding that I derived the Schrödinger equation based on an abstract and constructed on air assumption of unitarity. Instead, I derived it by using such missing terms which arise from my previous research work. In other words, in my Essay I did NOT made an abstract assumption of unitarity, but I finalized my previous research work by constructing a Schrödinger equation for a well defined system that I discussed and analysed in my previous papers. I will further bring back on this issue in detail in next days, in order to remove all potential misunderstanding, but here I thank you again to have raised this point. Thanks also for signalling the paper by Barrau et al. which looks connected to my work. I will surely read it in next days.

Cheers,

Ch.

I wrongly replied to your comments by writing a new post below. Hence, I will copy and past here my reply:

Dear Jonathan,

Thank you very much for your kind words and compliments and for giving a well written "referee report" on my paper. In particular, I am grateful to you to be returned on Professor Rovelli's comment. At the end of such a comment, Professor Rovelli asks if he is missing something. The answer to this question is yes, he is missing what you correctly emphasize, i.e. I supply missing terms without which a true unitary equation could not be written. Such missing terms arise from my previous research work, published in various important international peer review journals, which are correctly cited in my Essay. I strongly suspect that Professor Rovelli have ONLY read the abstract of my work, and this generated to him the misunderstanding that I derived the Schrödinger equation based on an abstract and constructed on air assumption of unitarity. Instead, I derived it by using such missing terms which arise from my previous research work. In other words, in my Essay I did NOT made an abstract assumption of unitarity, but I finalized my previous research work by constructing a Schrödinger equation for a well defined system that I discussed and analysed in my previous papers. I will further bring back on this issue in detail in next days, in order to remove all potential misunderstanding, but here I thank you again to have raised this point. Thanks also for signalling the paper by Barrau et al. which looks connected to my work. I will surely read it in next days.

Cheers,

Ch.

Thank you Christian,

I have no axe to grind with Carlo Rovelli, and I respect his work highly, but after a careful review I find no fatal flaws to your reasoning, and it appears you aptly address the caveats of your findings in comments - such as the conciliatory remark regarding Mitra's work and the possibility an event horizon would never be formed. One must make some standard assumptions to proceed with answers to questions like the information loss paradox, and carefully vary a few analytic parameters to reveal something others have not.

It appears you have done this. But graphs contrasting the spectra of pure Hawking radiation with the emanations from QNMs, as in the paper cited, would be extremely helpful. As luck would have it; I met Aurelien Barrau at FFP11 in Paris, and the work cited (then still in preparation) came up in answer to a question. I'll comment further after a bit.

Regards,

Jonathan

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I have no axe to grind with Carlo Rovelli, and I respect his work highly, but after a careful review I find no fatal flaws to your reasoning, and it appears you aptly address the caveats of your findings in comments - such as the conciliatory remark regarding Mitra's work and the possibility an event horizon would never be formed. One must make some standard assumptions to proceed with answers to questions like the information loss paradox, and carefully vary a few analytic parameters to reveal something others have not.

It appears you have done this. But graphs contrasting the spectra of pure Hawking radiation with the emanations from QNMs, as in the paper cited, would be extremely helpful. As luck would have it; I met Aurelien Barrau at FFP11 in Paris, and the work cited (then still in preparation) came up in answer to a question. I'll comment further after a bit.

Regards,

Jonathan

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Christian,

I do not fully understand the connection between the broad universal theme of this contest and this precise, technical essay about a phenomenon limited to black holes. It would be helpful to link the nature of information in a black hole to information in the rest of the universe.

The evaporation of a black hole due to Hawking radiation creates particles and the wavefunctions of associated with those particles. I did not see how the wavefunctions going into the black hole are the same as the ones going out. I did not see anything about wavefunctions going in. As an example, an electron beam travels through a double slit then into a black hole. Would we see a double slit pattern radiating from the black hole when it evaporates?

Thank you for this essay.

Jeff

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I do not fully understand the connection between the broad universal theme of this contest and this precise, technical essay about a phenomenon limited to black holes. It would be helpful to link the nature of information in a black hole to information in the rest of the universe.

The evaporation of a black hole due to Hawking radiation creates particles and the wavefunctions of associated with those particles. I did not see how the wavefunctions going into the black hole are the same as the ones going out. I did not see anything about wavefunctions going in. As an example, an electron beam travels through a double slit then into a black hole. Would we see a double slit pattern radiating from the black hole when it evaporates?

Thank you for this essay.

Jeff

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Dear Jeff,

Thanks for your interesting comments/questions. Concerning the connection between the broad universal theme of this contest and this precise, technical essay about a phenomenon limited to black holes, this criticism has been previously raised by D'Ariano and Heinrich. I rewrite here my reply to them almost verbatim. Although "It From Bit or Bit From It" is the title of the...

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Thanks for your interesting comments/questions. Concerning the connection between the broad universal theme of this contest and this precise, technical essay about a phenomenon limited to black holes, this criticism has been previously raised by D'Ariano and Heinrich. I rewrite here my reply to them almost verbatim. Although "It From Bit or Bit From It" is the title of the...

view entire post

Thank you for your response.

I do not look at the other posts before I post because I want to see if I can understand an essay on my own. Sorry that I made you repeat past statements.

I do find the topic of this contest is not clear. Your theme is clear and concise. My trouble making the connection has more to do with contest theme than your essay theme.

All the best,

Jeff

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I do not look at the other posts before I post because I want to see if I can understand an essay on my own. Sorry that I made you repeat past statements.

I do find the topic of this contest is not clear. Your theme is clear and concise. My trouble making the connection has more to do with contest theme than your essay theme.

All the best,

Jeff

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Dear Jonathan,

Thank you very much for your kind words and compliments and for giving a well written "referee report" on my paper. In particular, I am grateful to you to be returned on Professor Rovelli's comment. At the end of such a comment, Professor Rovelli asks if he is missing something. The answer to this question is yes, he is missing what you correctly emphasize, i.e. I supply missing terms without which a true unitary equation could not be written. Such missing terms arise from my previous research work, published in various important international peer review journals, which are correctly cited in my Essay. I strongly suspect that Professor Rovelli have ONLY read the abstract of my work, and this generated to him the misunderstanding that I derived the Schrödinger equation based on an abstract and constructed on air assumption of unitarity. Instead, I derived it by using such missing terms which arise from my previous research work. In other words, in my Essay I did NOT made an abstract assumption of unitarity, but I finalized my previous research work by constructing a Schrödinger equation for a well defined system that I discussed and analysed in my previous papers. I will further bring back on this issue in detail in next days, in order to remove all potential misunderstanding, but here I thank you again to have raised this point. Thanks also for signalling the paper by Barrau et al. which looks connected to my work. I will surely read it in next days.

Cheers,

Ch.

Thank you very much for your kind words and compliments and for giving a well written "referee report" on my paper. In particular, I am grateful to you to be returned on Professor Rovelli's comment. At the end of such a comment, Professor Rovelli asks if he is missing something. The answer to this question is yes, he is missing what you correctly emphasize, i.e. I supply missing terms without which a true unitary equation could not be written. Such missing terms arise from my previous research work, published in various important international peer review journals, which are correctly cited in my Essay. I strongly suspect that Professor Rovelli have ONLY read the abstract of my work, and this generated to him the misunderstanding that I derived the Schrödinger equation based on an abstract and constructed on air assumption of unitarity. Instead, I derived it by using such missing terms which arise from my previous research work. In other words, in my Essay I did NOT made an abstract assumption of unitarity, but I finalized my previous research work by constructing a Schrödinger equation for a well defined system that I discussed and analysed in my previous papers. I will further bring back on this issue in detail in next days, in order to remove all potential misunderstanding, but here I thank you again to have raised this point. Thanks also for signalling the paper by Barrau et al. which looks connected to my work. I will surely read it in next days.

Cheers,

Ch.

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...

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If I may, I'd like to...

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Who deleted several posts here and at 1793 and why? For instance, I criticized that Christian Corda first wrote that Wheeler dubbed the phrase it from bit in the 1950, after I questioned this, he admitted he did not know when, and nonetheless he reiterated his old text without providing a reference he referred to.

More importantly, we disagreed about the notion unitarity, and I tried to further explain my also missing post belonging to R. Kastner's paper "The Broken Symmetry of Time" in the blog "What can't be sensed?". I argued that it might be more natural to consider time as an abstraction from measurable elapsed time and future time as a continuation of it than ad hoc assuming time as given a priori from minus infinity to plus infinity, sharing Einstein's worry about the now and bother to explain why elapsed time is a special case of abstract time. I see the border between past and future the only natural border. My position might be unwelcome. Is it a sign of strength if belonging posts are brutally deleted?

Eckard Blumschein

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More importantly, we disagreed about the notion unitarity, and I tried to further explain my also missing post belonging to R. Kastner's paper "The Broken Symmetry of Time" in the blog "What can't be sensed?". I argued that it might be more natural to consider time as an abstraction from measurable elapsed time and future time as a continuation of it than ad hoc assuming time as given a priori from minus infinity to plus infinity, sharing Einstein's worry about the now and bother to explain why elapsed time is a special case of abstract time. I see the border between past and future the only natural border. My position might be unwelcome. Is it a sign of strength if belonging posts are brutally deleted?

Eckard Blumschein

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Dear Dr. Corda. I enjoyed your paper very much. An original idea and very competent description. In my view, this is one of the best papers in the contest.

It was perhaps an accident that I read your paper back to back with the essay by Carlo Rovelli, in which he says something very similar (to your description in the technical endnotes). I mentioned this to him on his site. You might...

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It was perhaps an accident that I read your paper back to back with the essay by Carlo Rovelli, in which he says something very similar (to your description in the technical endnotes). I mentioned this to him on his site. You might...

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Dear Paul,

Thanks for your kind words. Your idea on a “background free” conceptualization of time looks quite intriguing. I am going to surely read, comment and score your Essay in next days. Thanks also for signalling me the Essay by Rovelli. I will read it in next days too.

Cheers,

Ch.

Thanks for your kind words. Your idea on a “background free” conceptualization of time looks quite intriguing. I am going to surely read, comment and score your Essay in next days. Thanks also for signalling me the Essay by Rovelli. I will read it in next days too.

Cheers,

Ch.

Dear Christian,

I risk to be naive, but I must ask you. I'm skeptical, what's going on Schwarzschild radius. All just talk about gravity. As if on that radius, repulsion indifferently waiting, what do attraction? Acording Rudjer Bošković maby there are chaingin of atraction/repulsion not only once.

Regards,

Branko

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I risk to be naive, but I must ask you. I'm skeptical, what's going on Schwarzschild radius. All just talk about gravity. As if on that radius, repulsion indifferently waiting, what do attraction? Acording Rudjer Bošković maby there are chaingin of atraction/repulsion not only once.

Regards,

Branko

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Hi Branko,

Do not worry, you are not naive. This question is indeed interesting but it requests some time to be answered in detail. I will bring back to you after the vanishing of the Community Rate's deadline which is exactly today. In fact, today I am very busy in order to review all the Essays I promised to read, comment and rate.

Cheers,

Ch.

Do not worry, you are not naive. This question is indeed interesting but it requests some time to be answered in detail. I will bring back to you after the vanishing of the Community Rate's deadline which is exactly today. In fact, today I am very busy in order to review all the Essays I promised to read, comment and rate.

Cheers,

Ch.

Dear Christian,

Congratulations on maintaining a clear lead as the number one essay. I've read your essay and had several questions which have been covered in comments above, so I will simply convey my congratulations. I did very much appreciate your summary of the problem and recent results on pages 2 and 3. In light of Coleman's remark, I find it fascinating that it has taken until now to perform a QNM analysis of the problem. Again congratulations on formulating the Schrodinger approach.

I found the comments on this page very stimulating and enlightening and add very much to your essay. I've read Susskind and many other papers (including Susskind and Maldecena's latest on the "firewall") but have no expertise in, or strong opinion on, black holes. I do rather have an interest and theory of non-linearity of gravito-magnetism and a new approach as outlined in my current essay, which I hope you find the time to read.

Best regards,

Edwin Eugene Klingman

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Congratulations on maintaining a clear lead as the number one essay. I've read your essay and had several questions which have been covered in comments above, so I will simply convey my congratulations. I did very much appreciate your summary of the problem and recent results on pages 2 and 3. In light of Coleman's remark, I find it fascinating that it has taken until now to perform a QNM analysis of the problem. Again congratulations on formulating the Schrodinger approach.

I found the comments on this page very stimulating and enlightening and add very much to your essay. I've read Susskind and many other papers (including Susskind and Maldecena's latest on the "firewall") but have no expertise in, or strong opinion on, black holes. I do rather have an interest and theory of non-linearity of gravito-magnetism and a new approach as outlined in my current essay, which I hope you find the time to read.

Best regards,

Edwin Eugene Klingman

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Hi Edwin Eugene,

Thanks for your comments with kind congrats. I worked and still work on gravito-magnetism, see here for example. Thus, I am interested on your Essay and I will surely read, comment and rate it before the vanishing of the Community Rate's deadline.

Cheers,

Ch.

Thanks for your comments with kind congrats. I worked and still work on gravito-magnetism, see here for example. Thus, I am interested on your Essay and I will surely read, comment and rate it before the vanishing of the Community Rate's deadline.

Cheers,

Ch.

Dear Corda,

We are at the end of this essay contest.

In conclusion, at the question to know if Information is more fundamental than Matter, there is a good reason to answer that Matter is made of an amazing mixture of eInfo and eEnergy, at the same time.

Matter is thus eInfo made with eEnergy rather than answer it is made with eEnergy and eInfo ; because eInfo is eEnergy, and the one does not go without the other one.

eEnergy and eInfo are the two basic Principles of the eUniverse. Nothing can exist if it is not eEnergy, and any object is eInfo, and therefore eEnergy.

And consequently our eReality is eInfo made with eEnergy. And the final verdict is : eReality is virtual, and virtuality is our fundamental eReality.

Good luck to the winners,

And see you soon, with good news on this topic, and the Theory of Everything.

Amazigh H.

I rated your essay.

Please visit My essay.

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We are at the end of this essay contest.

In conclusion, at the question to know if Information is more fundamental than Matter, there is a good reason to answer that Matter is made of an amazing mixture of eInfo and eEnergy, at the same time.

Matter is thus eInfo made with eEnergy rather than answer it is made with eEnergy and eInfo ; because eInfo is eEnergy, and the one does not go without the other one.

eEnergy and eInfo are the two basic Principles of the eUniverse. Nothing can exist if it is not eEnergy, and any object is eInfo, and therefore eEnergy.

And consequently our eReality is eInfo made with eEnergy. And the final verdict is : eReality is virtual, and virtuality is our fundamental eReality.

Good luck to the winners,

And see you soon, with good news on this topic, and the Theory of Everything.

Amazigh H.

I rated your essay.

Please visit My essay.

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Professor Corda,

Thanks so much for your kind words on my essay (http://www.fqxi.org/community/forum/topic/1914 ), I am very encouraged that the author of your wonderful paper finds my paper likeable! I am working through the mathematical presentation in yours and am learning much -- thank you for presenting it here and sharing and thank you for sharing your comments on my thread!

Cheers and Best of Luck in the Contest -- you should not need it !

Jennifer Nielsen

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Thanks so much for your kind words on my essay (http://www.fqxi.org/community/forum/topic/1914 ), I am very encouraged that the author of your wonderful paper finds my paper likeable! I am working through the mathematical presentation in yours and am learning much -- thank you for presenting it here and sharing and thank you for sharing your comments on my thread!

Cheers and Best of Luck in the Contest -- you should not need it !

Jennifer Nielsen

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Hi Jennifer,

Thank you very much for your kind words. I am honoured that you are working through the mathematical presentation of my paper. I see that you are among the Finalists. Congrats and let us cross the fingers for the final judgement by the FQXi expert panel of judges.

Cheers and Best of Luck in the Contest to you too,

Ch.

Thank you very much for your kind words. I am honoured that you are working through the mathematical presentation of my paper. I see that you are among the Finalists. Congrats and let us cross the fingers for the final judgement by the FQXi expert panel of judges.

Cheers and Best of Luck in the Contest to you too,

Ch.

Christian: I am so impressed to see another author tackle a long-held concept and challenge it, instead of just writing more feel-good metaphysics. (Not only that, but to take on an icon like Hawking! Good for you, we should not be idolators.) I too have challenged a long-held assumption in my paper: that quantum mixtures of the same density matrix are indistinguishable. In my essay (/1610) I propose an empirical way we could distinguish such mixtures (e.g., mix of H and V linear polarized photons from mix of R and L circular states.) It should be of particular interest to you because of the significance of the DM in both our papers. I hope you have time to read it over and perhaps comment. PS to everyone: voting ends at 11:59 tomorrow night EDT (presumed from "ET" in FQXi update.)

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Dear Neil,

Thanks for your comments. Yes, it looks that your Essay is connected to my one. If you really find a way to distinguish quantum mixtures of the same density matrix this is also of fundamental importance for the black hole information paradox. I am going to read, comment and rate your Essay before the vanishing of the Community Rate's deadline.

Cheers,

Ch.

Thanks for your comments. Yes, it looks that your Essay is connected to my one. If you really find a way to distinguish quantum mixtures of the same density matrix this is also of fundamental importance for the black hole information paradox. I am going to read, comment and rate your Essay before the vanishing of the Community Rate's deadline.

Cheers,

Ch.

Dear Christian,

Thank you very much for your encouragement.

You saw very fair.

Actually I insist, as I know now, the first principle of all is duality.

You'll find out, hopefully in a few months.

Regarding the third point:

« 3) What do you think on my Statement Regarding the duality betweens and bit it, ie" Information physics tells how to work. Physics tells how to information flow "? »

If you permit, there is what I think:

« Information tells Energy how to flow. Energy carries Information. »

Here's how I see it, but not exactly. : Energy is the horse, the rider is Information.

Because Information is organised Energy.

In other words. All things in the Universe are information, even the space. Then, what information is ? It is the organized Energy.

Ok, what is the Energy then?

We know how it manifests itself, but we do not know what it is. This is the first reality, impossible to fundamentally explain or define.

Good luck and best wishes,

Amazigh H.

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Thank you very much for your encouragement.

You saw very fair.

Actually I insist, as I know now, the first principle of all is duality.

You'll find out, hopefully in a few months.

Regarding the third point:

« 3) What do you think on my Statement Regarding the duality betweens and bit it, ie" Information physics tells how to work. Physics tells how to information flow "? »

If you permit, there is what I think:

« Information tells Energy how to flow. Energy carries Information. »

Here's how I see it, but not exactly. : Energy is the horse, the rider is Information.

Because Information is organised Energy.

In other words. All things in the Universe are information, even the space. Then, what information is ? It is the organized Energy.

Ok, what is the Energy then?

We know how it manifests itself, but we do not know what it is. This is the first reality, impossible to fundamentally explain or define.

Good luck and best wishes,

Amazigh H.

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This contest is about whether reality can be represented in a binary fashion, not about information in general disappearing down a black hole. I don't see the relevancy to the topic. This is a typical equation heavy science paper that would lose most readers past the first two pages. I can't see this being an article in Scientific American, so I don't see it as being of general interest.

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Dear Mr. Hu,

Your criticism has been previously raised by other people. I rewrite here my reply to them almost verbatim. Although "It From Bit or Bit From It" is the title of the Contest, one easily checks that topics like "How does nature (the universe and the things therein) "store" and "process" information?" and "How does understanding information help us understand physics, and...

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Your criticism has been previously raised by other people. I rewrite here my reply to them almost verbatim. Although "It From Bit or Bit From It" is the title of the Contest, one easily checks that topics like "How does nature (the universe and the things therein) "store" and "process" information?" and "How does understanding information help us understand physics, and...

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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

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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

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Resp Prof Christian Corda,

I am giving my answer to your post in my essay here also, as FQXi does not inform you about my posting there...

Thank you for all the time and trouble you have taken for this.

Thank you for giving me an opportunity to clear up such confusions and puzzling situations.

Thank you for quoting my words from the blog and reading the blog. ...

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I am giving my answer to your post in my essay here also, as FQXi does not inform you about my posting there...

Thank you for all the time and trouble you have taken for this.

Thank you for giving me an opportunity to clear up such confusions and puzzling situations.

Thank you for quoting my words from the blog and reading the blog. ...

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Christian,

First of all thank you for your enthusiastic comments here and at my own essay (/1610). I am flattered to get kudos from the current top-rated essayist. (That BTW is not surprising to me, considering that your essay most resembles a journal paper proposing an advance.) Sadly I have a bit of visual trouble reading your essay, perhaps my older pdf SW did not render it right (it has...

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First of all thank you for your enthusiastic comments here and at my own essay (/1610). I am flattered to get kudos from the current top-rated essayist. (That BTW is not surprising to me, considering that your essay most resembles a journal paper proposing an advance.) Sadly I have a bit of visual trouble reading your essay, perhaps my older pdf SW did not render it right (it has...

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Hi Neil,

Thanks for your kind words. I see that you are among the Finalists. Congrats and let us cross the fingers for the final judgement by the FQXi expert panel of judges. I agree with your point of view that your Essay could have important implications on the BH information paradox because its distinguishing mixtures within the density matrix.

Cheers and good luck in the Contest,

Ch.

Thanks for your kind words. I see that you are among the Finalists. Congrats and let us cross the fingers for the final judgement by the FQXi expert panel of judges. I agree with your point of view that your Essay could have important implications on the BH information paradox because its distinguishing mixtures within the density matrix.

Cheers and good luck in the Contest,

Ch.

Thank you again, Christian. I hope that judges appreciate the importance of papers proposing empirical tests, even if they remain thought experiments due to practical difficulties. Overall I found quite a variety of perspectives and levels of communication here. I do regret not participating in discussions as much as I maybe should have. Being busy and a spell of eye trouble slowed me down but I could have done more. (I did leave a detailed response to your questions at my own page.) Well I keep my fingers crossed too and also hope I get some kind of "amateur" recognition as the administrators were talking about. Yes, despite some significant study and handle on the subjects I am not a pro.

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Congratulations on your placement in the contest! It is refreshing to see a rigorously argued contribution within accepted physical theory that bears on such broad issues.

My own essay was much more philosophically and generally focused, inquiring into the intersection of the foundations of mathematics, computer science, and physics, noting that often the laws of physics themselves seem to be implied by redundancies in information (gauge theories), which are unavoidable.

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My own essay was much more philosophically and generally focused, inquiring into the intersection of the foundations of mathematics, computer science, and physics, noting that often the laws of physics themselves seem to be implied by redundancies in information (gauge theories), which are unavoidable.

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Christian,

My most sincere congratulations on your win. Now it's perhaps the judges turn to be under scrutiny. For such different essays it's astonishing the insight of the Coleman statement; "The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction." was central for us both.

You also know from my AGN (BH) galaxy cyclic sequence work that I'm overjoyed by your cutting through the dense nonsense talked about black holes in recent decades. In fact I hope I can now convince you to cut deeper still to reach a simpler reality where all the matter/information accreted is simply accelerated, re-ionised and blasted back out as quasar jets, condensing fresh fermions from the QV to start the next cycle. The problems of re-ionisation, galaxy mass growth, kinetic decoupling etc. thereby also explained. I propose Coleman's statement then also applies to BH's.

FQXi has never had a better opportunity to fulfil it's remit and enable a (Q?) leap in the understanding of nature. So many theses agreed where the solutions lay, many not even in the top 40, that a major correlation job is required. Do you agree Tom Ray's (excellent I think) idea to compile a 'set of self similar sets'? The term 'herding cats' comes to mind, but is it beyond the wit of man? If the FQXi trustees retreat to doctrine then perhaps one of the title you edit?

Very best wishes for the final assessment.

Peter

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My most sincere congratulations on your win. Now it's perhaps the judges turn to be under scrutiny. For such different essays it's astonishing the insight of the Coleman statement; "The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction." was central for us both.

You also know from my AGN (BH) galaxy cyclic sequence work that I'm overjoyed by your cutting through the dense nonsense talked about black holes in recent decades. In fact I hope I can now convince you to cut deeper still to reach a simpler reality where all the matter/information accreted is simply accelerated, re-ionised and blasted back out as quasar jets, condensing fresh fermions from the QV to start the next cycle. The problems of re-ionisation, galaxy mass growth, kinetic decoupling etc. thereby also explained. I propose Coleman's statement then also applies to BH's.

FQXi has never had a better opportunity to fulfil it's remit and enable a (Q?) leap in the understanding of nature. So many theses agreed where the solutions lay, many not even in the top 40, that a major correlation job is required. Do you agree Tom Ray's (excellent I think) idea to compile a 'set of self similar sets'? The term 'herding cats' comes to mind, but is it beyond the wit of man? If the FQXi trustees retreat to doctrine then perhaps one of the title you edit?

Very best wishes for the final assessment.

Peter

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Hi Peter,

Thanks for your kind congrats. Have the same congrats from me also on your great result. I am going to have a deeper reading of your model of the AGN (BH) galaxy cyclic sequence after the end of my vacations, i.e. in September. I did not know Tom Ray's idea to compile a 'set of self similar sets'. I am going to read it in detail.

Very best wishes for the final assessment also to you,

Ch.

Thanks for your kind congrats. Have the same congrats from me also on your great result. I am going to have a deeper reading of your model of the AGN (BH) galaxy cyclic sequence after the end of my vacations, i.e. in September. I did not know Tom Ray's idea to compile a 'set of self similar sets'. I am going to read it in detail.

Very best wishes for the final assessment also to you,

Ch.

Christian,

I'm afraid there's some misunderstanding. I think what Peter is referring to, is my proposed experiment to catalog a set of results dependent on the orientation of an apparatus emulating a primordial initial condition. This is basically the experimental interpretation of a scale invariant solution to the time-dependent Schrodinger equation. Annihilation of particle pairs which conserves angular momentum, without producing gamma radiation, implies a primary role for wavefunction in particle creation, with no loss of information.

Best,

Tom

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I'm afraid there's some misunderstanding. I think what Peter is referring to, is my proposed experiment to catalog a set of results dependent on the orientation of an apparatus emulating a primordial initial condition. This is basically the experimental interpretation of a scale invariant solution to the time-dependent Schrodinger equation. Annihilation of particle pairs which conserves angular momentum, without producing gamma radiation, implies a primary role for wavefunction in particle creation, with no loss of information.

Best,

Tom

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Congratulations for coming out on top!

Your essay certainly deserves kudos, Christian. I hope the expert judges agree with my assessment (and the accolades of the community) that it is indeed worthy of a prize.

Good Luck!

Jonathan

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Your essay certainly deserves kudos, Christian. I hope the expert judges agree with my assessment (and the accolades of the community) that it is indeed worthy of a prize.

Good Luck!

Jonathan

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Dear Jonathan,

Thank you very much for your congrats and wishes. In the same way, I send you my best congrats and wishes for your excellent position in the final ranking of the Community Rate. Now let us cross the fingers for the final judgement by the FQXi experts panel. All the best for the final result.

Cheers,

Ch.

Thank you very much for your congrats and wishes. In the same way, I send you my best congrats and wishes for your excellent position in the final ranking of the Community Rate. Now let us cross the fingers for the final judgement by the FQXi experts panel. All the best for the final result.

Cheers,

Ch.

Dear Christian,

I congratulate you with all my heart with the first place in the first phase of the V International FQXi Essay Contest 2013!

I wish you continued success in your research and extensive organizational work for the good of the World Science!

Good summer holiday!

With great respect,

Vladimir

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I congratulate you with all my heart with the first place in the first phase of the V International FQXi Essay Contest 2013!

I wish you continued success in your research and extensive organizational work for the good of the World Science!

Good summer holiday!

With great respect,

Vladimir

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Hi Vladimir,

Thank you very much. Have my best congrats and wishes for your excellent position in the final ranking of the Community Rate and let us my best congrats and wishes for your excellent position in the final ranking of the Community Rate.

Good summer holiday also to you and all the best for the final result.

Cheers,

Ch.

Thank you very much. Have my best congrats and wishes for your excellent position in the final ranking of the Community Rate and let us my best congrats and wishes for your excellent position in the final ranking of the Community Rate.

Good summer holiday also to you and all the best for the final result.

Cheers,

Ch.

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