[pdonis]

> The information isn't gone, its right -there- in the black hole

No, it isn't; it hits the singularity inside of the hole and gets destroyed. At least, that's what Hawking's original model, the one he used to predict that black holes evaporate, says.

One way of seeing why Hawking's model had to say this is to combine the following facts about the evaporating black hole and the Hawking radiation in Hawking's model:

(1) The hole itself cannot contain any information other than its mass, charge, and spin (because of the "black holes have no hair" theorem), which is far too little information to describe everything that fell into the hole.

(2) The Hawking radiation cannot contain any information about what fell into the hole because it is thermal, black-body radiation, i.e., the only information it contains is its temperature, which is related to the mass of the hole.

So the information can't be stored either inside the hole or outside the hole, which means it must be destroyed, and the only place it can be destroyed is by hitting the singularity inside the hole.

The black hole information loss problem is that the above is inconsistent with quantum unitarity. So Hawking's original model can't be right; but nobody knows what model should replace it.

[BMSmnqXAE4yfe1]

Except that later Hawking came to the conclusion that black holes do have hairs.

[pdonis]

> later Hawking came to the conclusion that black holes do have hairs

Reference, please?

[cthalupa]

https://arxiv.org/abs/1810.01847

"Soft hair", so not exactly enough to resolve the information loss problem.

[effie]

> The hole itself cannot contain any information other than its mass, charge, and spin... which is far too little information

Maybe the information gets encoded in digits of value of mass expressed in some unit. There is enough digits to store any finite number of bits.

[pdonis]

> Maybe the information gets encoded in digits of value of mass expressed in some unit.

No, it can't, not all the information. Two objects of the same mass but different internal composition would add the same mass to the hole, but would be described by different information. So the hole can't store in the value of its mass which of the two objects fell in.

More generally, a hole of, say, ten Solar masses could have gotten that mass by an infinite number of possible combinations of things falling in. The mass itself can't distinguish between any of those possibilities; all it can tell you is that ten Solar masses total of stuff fell in.

[effie]

But why do you assume two objects of same mass but different composition will add the same mass to the black hole? Different composition means different interactions during the fall and different amount of radiated energy. Infinite number of bits can be encoded in single real number. It is hard to measure more than few digits of it, but so it is hard to measure all the information.

[pdonis]

> why do you assume two objects of same mass but different composition will add the same mass to the black hole?

Because that's what the physics says. See below.

> Different composition means different interactions during the fall and different amount of radiated energy.

All of that can be taken into account before the object falls into the hole; the observer outside can measure it all and deduct it from the mass he expects to be added to the hole.

We are talking about the mass that gets added after all that; and for any given mass added to the hole after all those things are taken into account, there are many different possible combinations of objects falling into the hole that can add that mass.

> Infinite number of bits can be encoded in single real number.

We are not talking about math, we are talking about physics. The number of bits that can be stored in an object of finite size is finite as far as physics is concerned.

[effie]

> "for any given mass added to the hole after all those things are taken into account, there are many different possible combinations of objects falling into the hole that can add that mass."

Approximately, sure, best scales can do around 5 significant digits and null measurements can get us few more digits. But we can't verify equality of mass to arbitrary precision. For elementary particles of same kind, we can assume their masses are the same. But there is infinity of digits available. Perhaps there are no two differently composed bodies that have the same real number as mass (too many options to be different). Then maybe any mass addition to mass of the black hole can encode all the information there is about the body.

[pdonis]

> Approximately, sure

This is irrelevant to the argument; our finite ability to measure masses is not what we are talking about. We are talking about what masses are physically possible, whether or not we can measure all of them with unbounded accuracy.

> there is infinity of digits available

You can't have it both ways. If it is physically true that there are an infinite number of digits available to specify an object's mass, then it is also physically true that there are multiple possible combinations of objects whose masses can sum to that same mass (in fact there will be an infinite number of them).

Conversely, if it is not physically true that there are multiple possible combinations of objects whose masses can sum to a given mass, there cannot be an infinite number of digits available to specify an object's mass: there must be only a finite number of possible masses, and the numbers specifying the possible masses must be such that no two such numbers add up to another such number.

[yyyk]

Imagine a 2t object falls into the hole and then a 3t object. Can that be differentiated than what would have happened had there been only one 5t object using mass alone?

Only if mass conservation is broken, and current theory does not predict this (where does the extra mass go to?). Same applies for the other 'no-hair' theorem properties - spin and charge.

[SmooL]

Sure, and the point of this video is that while that may be _mathematically and theoretically_ sound, there's no way you can realistically make any measurements or any observations to confirm or deny your particular idea. What we have a lot of these ideas, with no way to discern between theories which accurately represent nature and theories which are merely mathematically correct.

[pdonis]

> while that may be _mathematically and theoretically_ sound

The particular idea suggested in the GP actually isn't. See my post upthread.