Time dependent Schrödinger equation for black hole evaporation: no information loss by Christian Corda

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 would. You know both apparently vanish, so I would think that makes them equivalent for analysis and thinking about then. Which brings up another question I'm not sure about. Do light rays, which have info, go indefinitely outwards from the view of quantum mechanics? I ask because in General Relativity, since gravity is king at long distances, everything loops back on itself, if you will. So getting down the behavior of data as it goes into a black hole incident is important before even getting to the rest of the issue presented in this pap.

Also, boundaries seem unnatural to exist in reality when the goal of science is to make the most complete picture. The same thing goes for points. Here is another question. What in science is a singularity. I could guess a point where no existence, no mass or distance or grounds for rates, took place, or even a minute region where everything is localized on a very small scale. But beyond guesses, I like most people, am clueless. And since the speed of light is not constant in G.R., could a black hole not yet have adequate conceptual understanding? It seems like since info can go not faster than light in curved spacetime, and since there is a point where the grid just curves too much, that a new description is in order geometrically. Something has to give in this uncharted territory eventually.

Does your paper go on the idea that info hangs out on the outside of the B.H. by that weird 1/4 area to volume rule? I would see evaluating extreme or end behavior near the "edge" of the universe as only appropriate if the case is that info somehow gets past the point of no return around a black hole.

A lot of the information deals with heat theory which has developed quantum mechanically from the starters of it like Boltzmann. Is there attempted generalizations of relativity applied to thermodynamics which might shed new light on the issue here. For all the math here, it seems a little one-sided, the other side maybe not even existing! I read more abstract math here than pictorial verbiage, which vaguely results because some maths just don't condense to easy imaging. One last point is that the reason black holes evaporate didn't poke out at me. In fact, I'm still not entirely sure if they are presented here as giving off info because non is lost and thus shrinking, or rather if info just chills and shifts about like little grains or units and is exchanged, but the real radiation is due to some thermal process that does not fit thermal ideas so is called "non-thermal" behavior. Please clarify my mix up.

The mass equations are quite interesting.

Best,

Amos.

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.

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

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

Dear Professor Corda

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

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

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

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

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

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

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

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

With regards

Than Tin

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

Ch,

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

Amos.

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. You know people think that because for two thousand years the problem of "time" was not solve, can't be solve, this is not true as you can see here.

Anthropologist tell us men measured "time" since 30.000 years ago basically recording celestial bodies "constant" "motion" which was used as a system of measurement by people, for practical daily uses, as agriculture, hunting seasons, commerce.

Civilizations learn from primitive men its use, but with it, acquired the incognita of what they were measuring?, that now days we call the experimental meaning of "time", since their beginnings they ask themselves for that and still do, but in that epoch, they were especially interested in better and more precise ways of measurement.

Long 20.000 years after, science began a very slow beginning and as part of natural science was born a primitive physics no more than 2000 years ago, since the beginning physics included "time" a basic part, a foundational one, during those millenniums there was curiosity about its meaning but not a serious need to know the experimental one. The real need for physics was to improve precision of measurement.

All the above is the most probable.

Now on there is no hypothesis it is only an explanation using only proved facts.

Centuries old proved facts, like earth rotation and its consequence the day, also a prove of an earth complete rotation of "constant" "motion", which last from one sunrise to the next one.

This period of "constant" "motion" the day, it was divided in equal parts in 24 equal hours by Egyptians, the hour in 60 equal minutes and the minute in 60 equal seconds by Sumerians.

If "motion" does not have those characteristics, still could be a variable but can't be divided in equal parts, so can't be use to measure any other "motion".

For practical reasons men copy the "constant" "uniform" celestial bodies "motion" designing clocks. When the hour hand rotate twice around the clock dial, it represents an earth complete "constant" "uniform" rotation "motion".

Looking at the clock dial we will know at what hour of the day we are which is the same that knowing, on what part of the earth complete "constant" rotation "motion" we are.

With the clock dial hands "constant" "motion", representing earth rotation motion, comparatively we measure all "no constant" "motions" which are part of every change or transformation occurring to us, or everything around us.

The real definition of Duration: Is the period of change or transformation allowed by "motion" and limited by men.

Change, transformation and motion, none of the concepts can exist without the other two.

Above it is proved that what theoretical physicists needed for the last 50 years, the experimental meaning of "time" it is "motion".

That with a "constant" "uniform", "regular" "motion" we measure all the rest of "motions" without those characteristics.

Also it is proved that "motion" is a quality or property of every physical existing thing, and as such can relate to every physical existing thing.

Within those "motion" can be affected and affect, gravity, inertia, mass

Etc. etc..............

Héctor

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?

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