it appears that information and spacetime go hand in hand e.g. the black hole horizon and the growth of its entropy. one could argue that whatever energy is 'stored' in spacetime (i.e. vacuum, gravitational etc.) or its mere combinatorial arrangement (i.e. of events, light cones etc.) builds in a notion of information or entropy. according to the second law of thermodynamics entropy has to grow. it appears that spacetime is copiously produced on cosmological scale (in particular via inflation). yet however space time can fall into a singularity too. is it possible to imagine that 'beginnings', from a singularity and therefore 'endings' decouple/diverge the time from the other spatial dimensions (as per the Hartle-Hawking state) causing a sort of conversion between space into time and vice versa? what appears to be a singularity then in space or time converts into a complementary dimension which doesn't allow the vanishing of the geodesics (into zero). in other words time and space convert to each other while conserving information. what do you experts think?
"Entropy" was invented/discovered as part of the the branch of physics called "thermodynamics" to account for the many ways that thermal energy can be distributed among the constituents or states of a system in nominal thermal equilibrium. The connection of the concept of entropy with information systems was a later construct.
Is "space" conserved, is "time" conserved, is "information" conserved? I would argue that a notion of "conservation of space and time" has no meaning. Space and time are essential attributes of the Universe in which we live and without them would not live. They are given structural elements of the Universe and our concepts of these two enitities likely are not well advanced but I doubt that they are subject to the conservation "laws" that we associate with other entities.
On the other hand, "information" is our construct and we give to it a status that is within the Universe but is not essential to the Universe although a Universe without information is dificult to imagine since it would be empty. Like entropy information is accumulative and additive and not conserved.
If you consider that GR treats the coordinates we call "space" and "time" as an arbitrary overlay on a 4D manifold, I think the first thing you would need to consider is how (or even whether) you could identify an invariant distinction between the concepts.
"Entropy" was invented/discovered as part of the the branch of physics called "thermodynamics" to account for the many ways that thermal energy can be distributed among the constituents or states of a system in nominal thermal equilibrium. The connection of the concept of entropy with information systems was a later construct.
Is "space" conserved, is "time" conserved, is "information" conserved? I would argue that a notion of "conservation of space and time" has no meaning. Space and time are essential attributes of the Universe in which we live and without them would not live. They are given structural elements of the Universe and our concepts of these two enitities likely are not well advanced but I doubt that they are subject to the conservation "laws" that we associate with other entities.
On the other hand, "information" is our construct and we give to it a status that is within the Universe but is not essential to the Universe although a Universe without information is dificult to imagine since it would be empty. Like entropy information is accumulative and additive and not conserved.
If "information" is data like the charge of an electron (and several other quantum numbers), it is a conserved quantity. That is why evaporation of black holes is such a contentious issue.
Dear George,
I have not delved much into "information theory" and so may not be using "information" in accordance with whatever be current thinking but I consider it to be on a par with entropy as a kind of mega-entity that encompasses the state of the Universe as a whole. Thus the charge of the electron as well as the other quantum numbers are pieces of information within the whole body of information. And, yes, there is the issue of the nominal loss of information inescapabably swallowed up in black holes to be, as the song goes, "lost and gone forever, dreadful sorry, Clementine."
@George Dishman, GR is only a (low energy/mass/curvature etc.) approximation, albeit a very good one to spacetime. I think that "time" divergence/decoupling from "space" is seen already on a quantum level in the uncertainty relations. there already is "a bit of information" in a fluctuation occurring, a particle being created/annihilated, its path from point to point etc. all of these cannot happen without a spacetime history (path).
AK: GR is only a (low energy/mass/curvature etc.) approximation, albeit a very good one to spacetime.
That is true but the regimes where it fails are extreme to say the least. The recent LIGO observations found no discrepancy even in the merger of two black holes. The SNR will no doubt improve for future measurements and some deviation may yet be found but it is already a tough test.
AK: I think that "time" divergence/decoupling from "space" is seen already on a quantum level in the uncertainty relations
Not really, our current theories based on QED and QFT are entirely written assuming a local Minkowski background in which space and time are merely a coordinate choice.
DH: [I] may not be using "information" in accordance with whatever be current thinking but I consider it to be on a par with entropy
Well entropy has to have a specific definition if it is to be used in scientific laws so the same must go for "information" where it is used in the QM sense. If you are just using it in a hand-waving sense then you can assume what you like but it won't carry over into any scientific formulation.
Anyway, this is what the Physics FAQ from Usenet (linked) said on the matter:
- In order to understand why the information loss problem is a problem, we need first to understand what it is. Take a quantum system in a pure state and throw it into a black hole. Wait for some amount of time until the hole has evaporated enough to return to its mass previous to throwing anything in. What we start with is a pure state and a black hole of mass M. What we end up with is a thermal state and a black hole of mass M. We have found a process (apparently) that converts a pure state into a thermal state. But, and here's the kicker, a thermal state is a MIXED state (described quantum mechanically by a density matrix rather than a wave function). In transforming between a mixed state and a pure state, one must throw away information. For instance, in our example we took a state described by a set of eigenvalues and coefficients, a large set of numbers, and transformed it into a state described by temperature, one number. All the other structure of the state was lost in the transformation.
https://en.wikipedia.org/wiki/Entropy_(classical_thermodynamics)#Definition
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/info_loss.html
@George, i am aware of a covariant generalization/formulation of the uncertainty about measurement but i doubt that this can be carried over to a setting that concerns a "beginning" (as per Hartle-Hawking) or inflation.
Asher, nothing I said relates to uncertainty or inflation, it is about "information" as the term is used in this specific context.
Dear George,
I have not studied Hawking radiation and the notion that such radiation is of thermal origin and that one can associate a temperature meaningfully with a black hole. I also question the notion of "throwing" the quantum system directly into the maw of a black hole; the system would have "equilibrated" with its environment in passing through the event horizon and thus would be "thermalized" before entering the black hole proper. But in principle I suppose one could "throw" the system into the sun where it would undergo irreversible equilibration with the solar environment with a corresponding increase of entropy. With regard to information loss, is it not the case that a passing information-laden comet falling into the sun gives up its information store irreversibly as it is consumed within the swirl of the solar atmosphere? I don't regard "information" to be a conserved entity but an entity that can be used to characterize the internal state and configuration of a system.
I haven't studied it in any detail either, it is an advanced topic based on the Bogoliubov Transformation and that is far beyond my understanding.
DH: With regard to information loss, is it not the case that a passing information-laden comet falling into the sun gives up its information store irreversibly as it is consumed within the swirl of the solar atmosphere?
No, the interactions move the information into the bulk of the Solar material but it is still there.
DH: I don't regard "information" to be a conserved entity
In QM it is but it has a very specific meaning, if you use a layman interpretation then the question has no definite answer other than "it depends on what you mean by information."
If you burn a book, the words are lost but the number of protons, neutrons and electrons on the planet remains the same, that "information" is conserved.
Suppose a single neutron falls into a BH increasing its mass by 939MeV, then that mass is lost in the form of 939 million photons with an average energy of 1ev each, what happened to the baryon number?
https://en.wikipedia.org/wiki/Bogoliubov_transformation
George,
we are talking past each other because It is obvious that I don't understand "information" in the sense that you are using it. I need to do more homework. But if mass can be converted into energy and thus is not conserved, why should baryon number be conserved, if that is what you mean?
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