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

Christian,

I know gravity is described as the curvature of spacetime, but does that explain it, or just model it?

One problem I have with spacetime is that it is based on treating time simply as a measure of duration, which is based on the perception of time as a vector from past to future, along which this point of the present moves/exists, depending on your interpretation. Yet it seems much more rational to consider time as an effect of action, so it is the changing configuration of what is, that turns future potential into past circumstance. For example, rather than the earth traveling/existing along some dimension from yesterday to tomorrow, it is that tomorrow becomes yesterday because the earth rotates. This makes time an effect of action, similar to temperature. In essence, time is to temperature what frequency is to amplitude.

Duration does not transcend the state of the present, but is what is presently occurring between events, like the wave cycling between peaks.

Therefore there is no metaphysical "fabric of spacetime" and so no conceptual basis for an expanding universe, or blocktime, or wormholes, or multiverses, or any of the other speculative fantasizing arising from this conjecture.

Spacetime is simply correlation of measures of duration and distance and is mathematically accurate for the same reason epicycles are mathematically accurate; Perspective is inherently relative. There is no such thing as objective perspective. One could, with sufficient complexity, create a self-centric cosmology, for the quite logical reason we are the center of our view of the universe, but that wouldn't mean there are Titans pushing the entire universe in the other direction, every time one walks across the room, just as there is no giant cosmic gear wheels, or fabric of spacetime, pushing and pulling.

If time were a vector from past to future, logically the faster clock would move into the future more rapidly, but the opposite is true. Since it thermodynamically ages/burns quicker, it recedes into the past more rapidly.

Now the temporal vector is the basis of both narrative and linear logic, which are the basis of civilization, so it isn't an easy idea to put in context and I understand why it would be incorporated into foundational theories, but then we still see the sun as moving across the sky and it was only five hundred years ago we began to understand it is the earth spinning the opposite direction.

According to measurements of background radiation, overall space appears flat. This was proposed decades ago and measured by COBE and WMAP. The explanation given is that Inflation initially blew the universe up so much larger than is visible, it only appears flat on local scales, much as a local area of the earth's surface appears flat.

I could speculate as to the various relations between radiation and mass, but I will stop with the above observations as to why current theories may have to be reconsidered, not just continually patched.

Looking at the literature appearing in the popular press, Smolin et al, it might be worth your while to consider thinking about alternatives. I'm just offering some suggestions.

Again, pardon the rant.

Regards,

John

Hi Christian,

In regard to the excitation/de-excitation or ingoing/outgoing modes W&P find at the semi-classical level that for ingoing modes Gamma~1 which they equate with there being unit probability for an ingoing photon to "tunneling into" the BH since there is no barrier at the semi-classical level for something to fall into the BH. However this statement they make is based on their semi-classical approximation.

I'll have to look at the use of thermal spectra by these researcher. It seems "obvious" that due to back reaction the spectrum will have to deviate from thermal/Planckian. I put obvious is in scare quotes since there are examples where due to a collaboration of factors a dynamic/changing space-time can have a Planckian spectrum. The FRW Universe is such an example since there the way in which the photon frequency and temperature come into play works in such a way that as the Universe expands the spectrum remains Planckian just at an ever lower temperature. But this feature depends on an interplay of f and T which may not occur in general. Thus I agree with you - I am puzzled that the assumption is the spectrum remains thermal as the evaporation proceeds. Especially at the end stages it is hard to believe (modulo some specific calculation to the contrary) that the spectrum will remain thermal. And certainly the W&P result indicates that at some level the spectrum should wander away from pure thermal. Also it is a bit puzzling how little attention the work by Zhang, Cai, Zhan and You has received (at least initially). There is a question of what happens to their mechanism at the very end stages of the evaporation since they ignore QG corrections and these are thought to play some role in this regime. But overall their result is very suggestive.

By the way there was an earlier work by Zurek which obtained the same (or maybe only similar?) deviation of thermality of BH radiation using entropy arguments. The paper is

"Entropy Evaporated by a Black Hole", W.H. Zurek, Phys.Rev.Lett. 49 (1982) 1683-1686

It makes sense one could obtain that deviation of the spectrum from entropy arguments since as W&P show there is a close connection between the tunneling rate Gamma and the entropy, S.

Anyway interesting stuff.

Best,

Doug

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 Quasinormal Mode vibrations as soon as the energy is high. But I am assuming that lower values of n correspond to a resting BH in a space devoid of matter to feed upon, and are indistinguishable from thermal or Hawking radiation.

I guess it only matters to consider what goes in when feeding takes place, in terms of information loss, but it seems there would be a ramping up of higher n modes. Regardless; I think that on the whole your analysis is sound, and I respectfully disagree with Professor Rovelli about it being trivial to write a Schrödinger equation and declare the evolution is therefore unitary, as I think what you have done is supplied missing terms, without which a true unitary equation could not be written. You are assuming that any emanation from the BH must be a quantized vibration so that QNMs provide a way to encode things rather than having them be lost, and that the QNM variations then modulate what comes out.

You have done something clever, by taking Coleman's advice seriously, and treating the BH QNM vibrations as a kind of harmonic oscillator, but then you took things a step further - which is nice. It appears that what you did was recast the oscillator problem in Hamiltonian form, and in effect Hamiltonized the variables to put the QNM term in Schrödinger equation format. I first read about this trick in a paper by Steven Kauffmann, but you use it here to great effect - in order to supply the missing term of the full equation. It would be nice to see a graph of how QNM radiation might be distinguishable from pure Hawking radiation, as in the paper by Barrau et al Probing Loop Quantum Gravity with Evaporating Black Holes.

An excellent paper overall.

Regards,

Jonathan

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

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

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

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

Hi Christian,

"But we must be careful on which 'time' we are referring to. In fact, singularities can be time-like too."

Exactly so. Which is the precise reason I pointed out that Baez is wrong to dismiss Mitra's "metric of a test particle" on the event horizon of a black hole. For if the trajectory of a massless particle traces a timelike curve of measure zero on that trapped surface, and a distant free observer receives back a frozen image -- the observer's time relative to the test particle is also measure zero. Thus the singularity {0,0} is a complex point between the observer's spacelike state and the timelike curve on the event horizon -- a pure quantum spacetime relation.

As Hawking explained many years ago, imaginary time in complex space is just as real as the linear time we experience under our ordinary low energy conditions. At the extremis of black hole dynamics, time becomes space and -- because the observer cannot go "north of the North Pole" as Hawking so elegantly put it -- all singularities are extinguished in finite time. The freely falling observer will eventually join the 1-dimension information channel (Bekenstein-Mayo) described by the metric trace, and all information of observer interaction with the test particle trajectory will fall into an ordered line.

All best,

Tom

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

Dear Christian,

On Jul. 2 you wrote to Stuart Heinrich: "the great scientist who coined the phrase "It from bit or Bit from It?" in the 1950s, i.e. John A. Wheeler, was the same scientist who popularized the term "black hole" in the 1960s.

On Jul. 4 I asked you: 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 ..."

On Jul. 7 you wrote to me: "Actually, I did not know when Wheeler coined the phrase It from Bit or Bit from it.

On Aug. 1 you wrote again to Jeffrey Schmitz: "the great scientist who coined the phrase It from bit or Bit from It? in the 1950s, i.e. John A. Wheeler ..."

Well, there are many other reasons for me do distrust the Wheeler glorification, and I appreciate your courage to try and defend his idol against my endnotes. In particular I am waiting for your reply concerning unitarity.

When you did not take issue concerning Gupta's question concerning singularity, I see this justified because he equated black holes with singularities. However, don't singularities have measure zero like anything that does not exist?

By the way, did you read Schroedinger's reasoning in the fourth of his original papers? He made a trick that reduced an equation of fourth order to second order. And he got famous because this correctly described the spectrum of hydrogen - without Einstein's relativity.

Cheers,

Eckard

Having read so many insightful essays, I am probably not the only one to find that my views have crystallized, and that I can now move forward with growing confidence. I cannot exactly say who in the course of the competition was most inspiring - probably it was the continuous back and forth between so many of us. In this case, we should all be grateful to each other.

If I may, I'd like to express some of my newer conclusions - by themselves, so to speak, and independently of the logic that justifies them; the logic is, of course, outlined in my essay.

I now see the Cosmos as founded upon positive-negative charges: It is a binary structure and process that acquires its most elemental dimensional definition with the appearance of Hydrogen - one proton, one electron.

There is no other interaction so fundamental and all-pervasive as this binary phenomenon: Its continuance produces our elements - which are the array of all possible inorganic variants.

Once there exists a great enough correlation between protons and electrons - that is, once there are a great many Hydrogen atoms, and a great many other types of atoms as well - the continuing Cosmic binary process arranges them all into a new platform: Life.

This phenomenon is quite simply inherent to a Cosmos that has reached a certain volume of particles; and like the Cosmos from which it evolves, life behaves as a binary process.

Life therefore evolves not only by the chance events of natural selection, but also by the chance interactions of its underlying binary elements.

This means that ultimately, DNA behaves as does the atom - each is a particle defined by, and interacting within, its distinct Vortex - or 'platform'.

However, as the cosmic system expands, simple sensory activity is transformed into a third platform, one that is correlated with the Organic and Inorganic phenomena already in existence: This is the Sensory-Cognitive platform.

Most significantly, the development of Sensory-Cognition into a distinct platform, or Vortex, is the event that is responsible for creating (on Earth) the Human Species - in whom the mind has acquired the dexterity to focus upon itself.

Humans affect, and are affected by, the binary field of Sensory-Cognition: We can ask specific questions and enunciate specific answers - and we can also step back and contextualize our conclusions: That is to say, we can move beyond the specific, and create what might be termed 'Unified Binary Fields' - in the same way that the forces acting upon the Cosmos, and holding the whole structure together, simultaneously act upon its individual particles, giving them their motion and structure.

The mind mimics the Cosmos - or more exactly, it is correlated with it.

Thus, it transpires that the role of chance decreases with evolution, because this dual activity (by which we 'particularize' binary elements, while also unifying them into fields) clearly increases our control over the foundational binary process itself.

This in turn signifies that we are evolving, as life in general has always done, towards a new interaction with the Cosmos.

Clearly, the Cosmos is participatory to a far greater degree than Wheeler imagined - with the evolution of the observer continuously re-defining the system.

You might recall the logic by which these conclusions were originally reached in my essay, and the more detailed structure that I also outline there. These elements still hold; the details stated here simply put the paradigm into a sharper focus, I believe.

With many thanks and best wishes,

John

jselye@gmail.com

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 find it useful to review his essay also.

My favorite paragraph in your essay:

"In principle, a process in which pure states evolve in completely mixed states does not contradict the laws of quantum mechanics because the apparent information loss is instead hidden by quantum entanglement. The term entanglement means that the quantum state of a quantum system composed by two (or more) subsystems depends on the quantum state of each subsystem even if they are spatially separated. When one sums up the information in the two subsystems the result will be less than the information in the original system. The apparent information loss results hidden inside correlations between the subsystems."

In my essay I introduced a very similar idea that the apparent information loss is hidden by quantum entanglement. I described a "background free" conceptualization of time where subtime flows only down the 1-dimensional path, e.g. The flow of a photon between an emitter and absorber atom. And that this subtime will be reversed in all ontological respects if the energy/information in that photon is now returned to the original atom.

A trapped photon bouncing back and forth between two atoms will therefore trap energy/information and for all intents and purposes will be "dark"; i.e. outside of (classical) time. It appears to me that this description is capable of yielding similar measured results of entanglement, and I have thus described it so (even though I imagine I may endure the wrath of a conventional quantum mechanic).

I believe there may be congruence between our ideas, and I would thus be honored by your comments on my essay if you have time.

Kind regards, Paul