The Black Hole information loss problem is unsolvable

> Hossenfelder's argument is that there are many equally plausible (and equally speculative) ways

This is just not true. Most of the resolutions of the past required new conjectures like EP=EPR, whereas recent solutions rely on newer sort of uses of a path integral, but are still built up from basic QFT+GR.

Claiming agnosticism between those two theories is discarding Occam's Razor entirely, as the latter relies on constructing way less strong of assumptions and provides a believable mechanism for information preservation.

>> Hossenfelder's argument is that there are many equally plausible (and equally speculative) ways

> This is just not true. Most of the resolutions of the past required new conjectures like EP=EPR, whereas recent solutions rely on newer sort of uses of a path integral, but are still built up from basic QFT+GR.

As far as I can tell, what I wrote here seems to reflect what Hossenfelder is saying in the article. Here, for the first time, you seem to be making a reasonable argument that the specific hypotheses are not, in fact, all alike, and that they may differ in a way that at least opens up the possibility of applying Occam's razor correctly - i.e. by rejecting any that make unnecessarily broad or strong assumptions.

This brings us to Hossenfelder's follow-on point: we're going to need more data in order to figure out which, if any, is correct [1]. Without more data, neither Occam's razor nor any other principle (and certainly not subjective simplicity) is sufficient to do this - the most you can do is have a preference, based possibly on which you think is least likely to run into problems with Occam's razor. That's not enough to turn a hypothesis into a theory.

This is the point that you started this thread by objecting to, and I do not think you have yet made a strong enough case to overthrow it, though you are now making better arguments than before.

[1] I'm not sure about Hossenfelder's apparent claim that this data can only come from observing black-hole decay, but that's a separate matter.

Not quite. When Hawking radiation is included, it becomes possible in principle for information to escape the hole. That's not the main issue.

The main issue is that any information carried by an object that falls into the hole and hits the singularity inside the black hole gets destroyed. So either that information is lost, which violates QM unitarity, or the information has to get copied into the Hawking radiation that gets emitted, which violates the QM no cloning theorem.

> One suggestion have been that the information actually never enters the black hole in the first place, it's just spread out over the surface of the event horizon.

This doesn't really help, because the information can't just stop at the horizon; if an object falls in, it carries its information with it. So "spread out over the surface of the event horizon" really has to mean the information gets copied there, which, as above, violates the QM no cloning theorem. Some physicists, such as Susskind, claim that this actually isn't an issue because no single observer will ever observe both copies of the information, but this argument strikes me as contrived (and I don't think it's been proven that it must be the case).

Two possible resolutions that seem to me to at least avoid the problems I stated above are:

(1) Quantum gravity effects change the singularity inside the black hole to something else: one commonly suggested possibility is that a "baby universe" is born there, and that baby universe carries the information that fell into the hole. In other words, the information stays inside the hole and doesn't come out in the Hawking radiation, but it doesn't get destroyed either.

(2) Quantum gravity effects prevent a true event horizon and a true black hole from ever forming in the first place. That means there is never any singularity or any place where information ever gets destroyed; quantum gravity effects end up converting all of the objects that fell into the "hole" (which is now not a true black hole, but will still look like one to us on the outside, at least for a very long time) into the Hawking radiation that the hole emits as it evaporates. So no information ever gets destroyed and no information ever gets cloned.

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.