So I've been watching some documentaries involving black holes and the information paradox involved with quantum mechanics which says information can never be destroyed... I had an idea to this theory involving black holes and thermal or 'hawking' radiation that doesn't contain information as its released, in a sense it's blank data...

I understand everything we see can be traced back in some way to show all its "lifelong information" so I ask anyone to take a recycled water bottle, and give me a detailed description of everything the atoms in that bottle ever were before they were a scrap bottle. Not just scraps of plastic remolded into another bottle, but according to the theory, anyone should be able to trace and describe everything those particles ever were since their inception into existence...

So can anyone follow the particles of a recycled water bottle (or anything) back through time on this planet, time in a nebula, time in a star, and where they all were billions of years ago? Or just simple the information we see today? And I mean- dates, times, matter, everything for the past 10 billion years? Or just oh it was here, then there, now here... according to the theory, you should be able to trace it all back to its inception with details and tell me exactly what it is... can anyone do that? Or can we accept there are ways information can be 'wiped' and brand new with a clean slate? If if not, explain... cause I feel if nobody can, than in information paradox is just another way of saying 'we have no clue'

41 minutes ago, Alenruffneck said:

So can anyone follow the particles of a recycled water bottle (or anything) back through time on this planet, time in a nebula, time in a star, and where they all were billions of years ago? Or just simple the information we see today? And I mean- dates, times, matter, everything for the past 10 billion years? Or just oh it was here, then there, now here... according to the theory, you should be able to trace it all back to its inception with details and tell me exactly what it is... can anyone do that? Or can we accept there are ways information can be 'wiped' and brand new with a clean slate? If if not, explain... cause I feel if nobody can, than in information paradox is just another way of saying 'we have no clue'

The information paradox is not about our ability to trace back the microscopic history of a system. The microscopic history of a big-enough system can never be followed exactly. The initial state of the 10²⁴ or so molecules in a sample of an ideal gas in equilibrium cannot be traced back, and it never will. This is a consquence of molecular chaos.

The arguable loss of information from the information paradox is a more serious problem, if it responded to an actual phenomenon. It would imply that infinitely many microscopic states would evolve towards one and the same microscopic state. It would be, not a matter of us not having a clue, but of a clue not being there at all, so to speak.

41 minutes ago, joigus said:

The arguable loss of information from the information paradox is a more serious problem, if it responded to an actual phenomenon. It would imply that infinitely many microscopic states would evolve towards one and the same microscopic state. It would be, not a matter of us not having a clue, but of a clue not being there at all, so to speak.

I watched a documentary on this, the debate between Leonard Susskind and Stephen Hawking.

I never understood why the conditions of a black hole are applied to the rest of the universe.

If information is lost via Hawking radiation from the mass of a black hole why does that mean particles elsewhere could go through the same process?

Would they not need BH extreme conditions?

The description of Hawking radiation in his book was along the lines of a pair of virtual particles created at the event horizon, one can be sucked in and the other released as radiation. (Forgive me if this is sloppy, it was popsci and years since I read it)

I later read that virtual particles are more of a mathematical tool not an actual physical thing, like Feynman's backwards in time positrons.

So I think I even less sure of any of it now.

1 hour ago, joigus said:

It would imply that infinitely many microscopic states would evolve towards one and the same microscopic state.

I meant "infinitely many different microscopic states..." The "different" bit is essential.

53 minutes ago, pinball1970 said:

I never understood why the conditions of a black hole are applied to the rest of the universe.

I'm not sure what you mean by this. The conditions of a BH are not applied to the rest of the universe AFAIK. Black holes are very special systems. Although it's true that there are so many. They're not rare objects by any means.

The problem with the BH is that while incoming particles carry distinctions, as Susskind likes to call them, and gives back always the same boring thermal state = one "distinction". A "distinction" is a particular choice of initial conditions (position and momentum). In the parlance of classical mechanics, different choices of initial conditions (so-called points in the phase space) always end up being sent to different points in this space of dynamical states (final conditions.) This, in classical mechanics, is called Liouville's theorem, and is understood to imply conservation of information.

In quantum mechanics, the generalisation of this law is called unitarity. And the picture of particle-antiparticle pairs is basically right from what I know. Virtual particles are something of a mathematical artifact, but if given the right energy by the appropriate interaction, they "become real", which means the vacuum (virtual loops appearing and disappearing) gets promoted to the first excited state (actual particles that can be seen by a detector).

I hope that was helpful. Quantum fields + gravitation are kind of a jerry-built machine, with no proper theory to be sure about anything.

The unitarity condition of Quantum theory dictates that the time evolution of a quantum state, as per the Schrodinger equation, is represented by a unitary operator.
This implies the total probability of all possible outcomes must always sum to 1, meaning probability is preserved in time, and information is conserved.

Everything that goes into a Black hole is/has information; when the BH evaporates through Hawking Radiation, that information is randomized as thermal radiation, and the ability to follow the time evolution of the information vanishes.

That is a problem/paradox according to Quantum theory

Thanks to @joigus and @MigL appreciated

It's worth noting that to an observer outside the blackhole, nothing ever actually falls into the event horizon, not even the collapsing star itself.