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

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

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.

Wow ... I found myself engrossed in that vitriolic exchange of 2004. Sounds exactly like the mess we got into with Joy Christian's result, and for the same reasons. I mean, it appears that when someone -- anyone, it seems -- proposes a purely classical framework (which both Mitra's and Christian's are), it's like waving a red cape in the face of a bull.

I respect John Baez's knowledge and skill in mathematical physics; however, I think he may have been a bit unfair to say things like, "Starting from the solution which describes a black hole of mass m, he attempts by a calculation to show that m = 0. It's a bit like taking an arbitrary prime number and proving that it must equal 37."

However, Mitra didn't assume a black hole of mass M (it should be M in this context). So Baez's criticism amounts to saying that Mitra made an erroneous assumption, not that the calculation is wrong. Nevertheless, Baez then uses what he regards as the erroneous assumption to show that Mitra makes the elementary mathematical error of dividing by zero.

Baez quotes Mitra: "For the benefit of the serious readers, I give below the essence of my proof: In Lemaitre coordinates, the radial geodesic (angular part=0), the metric of a test particle around a BH is ds^2 = dt^2 - g_rr dr^2 (1)"

To which Baez replies, " ... the phrase 'the metric of a test particle' makes no sense. The metric is something on spacetime, and it applies to all particles moving in spacetime, so one never speaks of the metric 'of a test particle'."

While this is exactly true, I think it's ungenerous and a bit condescending. I get the impression that Mitra is using the word metric to mean "trajectory." This would have to be so, in order to fix time coordinates for the endpoints of a geodesic. That is, a particle trajectory on the event horizon traces a metric; it doesn't define a metric. My suspicions is confirmed later on when John says:

"Somehow M = 0 has popped out. It's popped out because in equation (10) he gets ds^2 = 0 at R = 2M, 'following the radial geodesic'. He's not very clear about (what) that means ...

(Well, it's quite clear to me that Mitra means the metric trace of a massless particle, for which t = 0 both at the event horizon *and* for a distant observer.)

" ... but interpreting him generously I'd say he's concluding the change in proper time vanishes for a test particle freely falling into a black hole as it crosses the horizon."

(Mitra's test particle never crosses the horizon.)

"This would indeed be a contradition since general relativity (quoting Mitra here) 'demands that the geodesic must remain timelike there and we should have had ds^2 > 0.'

"So, his mistake may lie in his derivation of ds^2 = 0. Where does this come from? He says it comes from ds^2 = dt^2 - dr^2 at R=R_g (6) and (dr/dt)^2 = 1 at R = R_g (9) I've already said I see no flaw in (6) so probably the flaw is in (9). And indeed, (9) is false for a test particle freely falling into the black hole: in LeMaitre coordinates, r is constant for such a particle, so dr = 0 contradicting (9).

"The rest is a mopping-up operation ..."

Only with John's assumptions. And those assumptions make his criticism look suspiciously like a straw man argument to me, another common characteristic of the Joy Christian controversy. Ah, well.

Professor Corda, if you find this diatribe irrelevant to your forum discussion, please just pull the plug on it.

All best,

Tom

Christian,

"the curvature which remains constant, the universe scale factor increases."

Yes, the curvature remains constant, much as a circle is always 360 degrees, but you have this scale that allows you to say it is larger, or smaller and that scale is the speed of light.

If the universe was the scale and "the light takes ever longer to reach us," wouldn't it be necessary to say it must be the light that is slowing down, if space is the universe?

The scale is the stable base line, not what is changing. If you need to say the speed of light is constant and the universe expands relative to this constant, it just seems to me that you have already defined space in terms of the speed of light.

Christian

Do you like my essay?

Yuri

Christian,

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

Regards,

John

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

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

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