Why does anyone think gravity might collapse wave function?

[martinbn]

Wald in the book General Relativity discuses it at page 155. Essentially, take a late state of the black hole and in this state replace all future oriented vectors (velocities etc.) by the opposite past oriented ones. If you take this as initial state, you get a white hole.

He discusses Schwartzschild, where nothing forms. If you have a formation of a black hole, and then reverse "time" you get a white hole, but it will violate some energy conditions.

 

[Demystifier]

He discusses Schwartzschild, where nothing forms. If you have a formation of a black hole, and then reverse "time" you get a white hole, but it will violate some energy conditions.

No, time reversal does not violate energy conditions. Take for example the energy condition that $T_{\mu\nu}V^{\mu}V^{\nu}>0$ for all time-like future oriented vectors $V^{\mu}$. Now consider $V'^{\mu}=-V^{\mu}$. Since $V^{\mu}$ is future oriented, it follows that $V'^{\mu}$ is past oriented. In other words, a transformation $V^{\mu}\to V'^{\mu}$ involves a time reversal. However, this does not violate the energy condition because we still have $T_{\mu\nu}V'^{\mu}V'^{\nu}>0$. That's because the vector $V^{\mu}$ appears quadratically in the energy conditions, so the sign of $V^{\mu}$ doesn't matter.

The energy in Einstein equation appears only as a second-rank tensor $T_{\mu\nu}$, which is a deeper reason why the relevant energy conditions are always quadratic in the vectors, which is why the theory is invariant under time reversal.

 

[PeterDonis]

The first one was by Penrose, it was for black holes only. The second one was by Hawking, it was for cosmology only.

I know this is the way the theorems are usually described, because, IIRC, that's the way Penrose and Hawking advertised them, so to speak. But mathematically, it's not correct. Both theorems are time reversible and neither one is restricted to a particular spacetime geometry; they only require that a trapped surface is present and that the spacetime satisfies an appropriate causality condition (in the original theorems I think that was global hyperbolicity, but I believe later extensions have relaxed that somewhat). So Penrose's theorem, by time reversing, could also be applied to an initial singularity such as the Big Bang, and Hawking's theorem, by time reversing, could also be applied to a final singularity such as a black hole.

The difference between the theorems is in the energy condition they assumed: Penrose's theorem used the weak energy condition; Hawking's used the dominant energy condition. I believe a similar theorem has also been proved using the strong energy condition.

 

[PeterDonis]

If you have a formation of a black hole, and then reverse "time" you get a white hole, but it will violate some energy conditions.

This is not correct. For example, you can time reverse the Oppenheimer-Snyder 1939 idealized model for gravitational collapse to a black hole, and obtain a model where a white hole "expands" into an ordinary object. Since the original O-S model does not violate any energy conditions, the time reverse of it won't either.

 

[martinbn]

No, time reversal does not violate energy conditions. Take for example the energy condition that $T_{\mu\nu}V^{\mu}V^{\nu}>0$ for all time-like future oriented vectors $V^{\mu}$. Now consider $V'^{\mu}=-V^{\mu}$. Since $V^{\mu}$ is future oriented, it follows that $V'^{\mu}$ is past oriented. In other words, a transformation $V^{\mu}\to V'^{\mu}$ involves a time reversal. However, this does not violate the energy condition because we still have $T_{\mu\nu}V'^{\mu}V'^{\nu}>0$. That's because the vector $V^{\mu}$ appears quadratically in the energy conditions, so the sign of $V^{\mu}$ doesn't matter.

The energy in Einstein equation appears only as a second-rank tensor $T_{\mu\nu}$, which is a deeper reason why the relevant energy conditions are always quadratic in the vectors, which is why the theory is invariant under time reversal.

This is not correct. For example, you can time reverse the Oppenheimer-Snyder 1939 idealized model for gravitational collapse to a black hole, and obtain a model where a white hole "expands" into an ordinary object. Since the original O-S model does not violate any energy conditions, the time reverse of it won't either.

Yes, I souldn't write without thinking.

But i do believe, although now i should be cautious, that you cannot get a white whole formation without violating an energy condition.

 

[Demystifier]

But i do believe, although now i should be cautious, that you cannot get a white whole formation without violating an energy condition.

You could be right in a practical sense, that without violating an energy condition one cannot get a white hole with physically reasonable initial conditions expected to be possible in practice. But if you just explore the space of mathematical solutions of the Einstein equations, white hole solutions that do not violate energy conditions certainly exist.

 

[martinbn]

No, time reversal does not violate energy conditions. Take for example the energy condition that $T_{\mu\nu}V^{\mu}V^{\nu}>0$ for all time-like future oriented vectors $V^{\mu}$. Now consider $V'^{\mu}=-V^{\mu}$. Since $V^{\mu}$ is future oriented, it follows that $V'^{\mu}$ is past oriented. In other words, a transformation $V^{\mu}\to V'^{\mu}$ involves a time reversal. However, this does not violate the energy condition because we still have $T_{\mu\nu}V'^{\mu}V'^{\nu}>0$. That's because the vector $V^{\mu}$ appears quadratically in the energy conditions, so the sign of $V^{\mu}$ doesn't matter.

The energy in Einstein equation appears only as a second-rank tensor $T_{\mu\nu}$, which is a deeper reason why the relevant energy conditions are always quadratic in the vectors, which is why the theory is invariant under time reversal.

This is not correct. For example, you can time reverse the Oppenheimer-Snyder 1939 idealized model for gravitational collapse to a black hole, and obtain a model where a white hole "expands" into an ordinary object. Since the original O-S model does not violate any energy conditions, the time reverse of it won't either.

Yes, I souldn't write without thinking.

You could be right in a practical sense, that without violating an energy condition one cannot get a white hole with physically reasonable initial conditions expected to be possible in practice. But if you just explore the space of mathematical solutions of the Einstein equations, white hole solutions that do not violate energy conditions certainly exist.

Yes, but i mean a solution that does not have a white hole at an ealry stage, but forms later. For black holes you have that.

 

[Demystifier]

Yes, but i mean a solution that does not have a white hole at an ealry stage, but forms later. For black holes you have that.

In that sense you are right, provided that you work with purely classical gravity. For black holes, you don't have black hole solutions which are not black holes at late stages. By time inversion of that, it follows that you don't have white hole solutions which are not white holes at early stages.

But if you include quantum effects, then there is Hawking radiation, so a black hole may not longer exist at late stages. Assuming that Hawking radiation is a unitary process (which is something that we don't actually understand very well with current understanding of quantum gravity), by time inversion of that it follows that white hole may form from initial configuration of Hawking "anti-radiation" without white hole.

To get to the main topic of this thread, I think Penrose does not believe that Hawking radiation is unitary. If so, then quantum gravity is not time-inversion invariant, which is a hint that quantum gravity can be related to a fundamentally irreversible collapse of the wave function.

So I think now I can answer the initial question of @HomesliceMMA . Semi-classical gravity predicts Hawking radiation which violates unitarity, which implies violation of time-inversion invariance. Some people believe that this violation persists also in full quantum gravity. On the other hand, some people also believe that wave function collapse is fundamentally irreversible. So if both quantum gravity and wave function collapse are fundamentally irreversible, it seems natural to assume that they are related.

 

[martinbn]

So I think now I can answer the initial question of @HomesliceMMA .

What about my follow up question. What are the shortcomings of Penrose's idea? Other than it is not fully developed.

 

[Demystifier]

What about my follow up question. What are the shortcomings of Penrose's idea? Other than it is not fully developed.

The idea is motivated by two assumptions, that:
(i) Hawking radiation is fundamentally irreversible,
(ii) wave function collapse is fundamentally irreversible.
From my (somewhat subjective) point of view neither of the assumptions is very convincing. About (i), most approaches to the black hole information paradox restore unitarity and reversibility at the fundamental level. About (ii), the collapse is widely believed to be somehow emergent from decoherence, and decoherence is based on assumption that fundamental dynamics is unitary and time reversible.

 

[martinbn]

The idea is motivated by two assumptions, that:
(i) Hawking radiation is fundamentally irreversible,
(ii) wave function collapse is fundamentally irreversible.
From my (somewhat subjective) point of view neither of the assumptions is very convincing. About (i), most approaches to the black hole information paradox restore unitarity and reversibility at the fundamental level. About (ii), the collapse is widely believed to be somehow emergent from decoherence, and decoherence is based on assumption that fundamental dynamics is unitary and time reversible.

These are alternatives, that may be more convinsing, but they are not shortcomings of his idea. I am interested if anyone has any objections based only on what Penrose proposes.

 

[gentzen]

These are alternatives, that may be more convinsing, but they are not shortcomings of his idea. I am interested if anyone has any objections based only on what Penrose proposes.

About (ii), the collapse is widely believed to be somehow emergent from decoherence, ...

Independent of the supposed physical mechanism (like decoherence) behind the collapse, the non-local collapse that Einstein called "spooky action at a distance" is an artifact of a "first person in the moment" description of what happens. The description is not wrong per se, but a very subjective description, very much in the spirit of the Bayesian interpretation of probability. This is also what I meant when I wrote that

QBism is indeed only a "more honest" version of the interpretation put forward by defenders of the old Cohenhagen orthodoxy

But the objection remains the same, namely that an artifact of a certain description should better not be promoted to a real physical process.

 

[Demystifier]

But the objection remains the same, namely that an artifact of a certain description should better not be promoted to a real physical process.

I agree, but Penrose and some other guys think that collapse is not merely an artifact of a first person description, but a real non-local physical process. In fact, in some works Penrose goes even further and argues that the first person experience itself is physical and related to fundamentally non-deterministic collapse. More precisely, from the fact that humans can see that the Godel sentence is true, while the Godel sentence is a self-referential statement saying that it cannot be proved by an algorithm, Penrose argues that human intelligence is fundamentally not algorithmic and hence requires a fundamentally non-deterministic process such as collapse.

 

[PeterDonis]

i do believe, although now i should be cautious, that you cannot get a white whole formation without violating an energy condition.

A white hole "formation" is not possible because a white hole contains an initial singularity--there can't be anything "before" it, by definition. If there is, it's not a white hole.

 

[PeterDonis]

from the fact that humans can see that the Godel sentence is true, while the Godel sentence is a self-referential statement saying that it cannot be proved by an algorithm, Penrose argues that human intelligence is fundamentally not algorithmic

It should be noted that many others have raised objections to this argument (and Penrose is not the only one to have made an argument along these lines). See, for example, Dennett's review of The Emperor's New Mind:

https://ase.tufts.edu/cogstud/dennett/papers/penrose.htm

 

[Demystifier]

A white hole "formation" is not possible because a white hole contains an initial singularity--there can't be anything "before" it, by definition. If there is, it's not a white hole.

Not exactly. The definition of black or white hole involves the existence of future or past event horizon. The singularity is not a part of the definition of black or white hole. Instead, the singularity is a result of a theorem, which assumes an energy condition. So if energy condition is not assumed, it is possible to have a black or white hole without singularity.

 

[PeterDonis]

The definition of black or white hole involves the existence of future or past event horizon.

Yes, that's true; a better statement of the required initial condition for a white hole would be that a past horizon has to exist. But a past horizon also can't be brought into being (i.e., there can't be anything "to the past" of it--in more technical terms, it must go all the way back to past timelike infinity), so white hole formation is still ruled out.

the singularity is a result of a theorem, which assumes an energy condition.

Yes, but note that the theorem does not connect a singularity with an event horizon. It connects a singularity with a trapped surface. They're not the same in general, although they happen to coincide in the idealized case of maximally extended Schwarzschild spacetime.

if energy condition is not assumed, it is possible to have a black or white hole without singularity.

No, if the energy condition is not assumed, it is possible to have a trapped surface without a singularity. But this tells us nothing about whether or not it is possible to have a black or white hole without a singularity, since those are defined in terms of event horizons, not trapped surfaces.

 

[Demystifier]

No, if the energy condition is not assumed, it is possible to have a trapped surface without a singularity. But this tells us nothing about whether or not it is possible to have an event horizon without a singularity.

Maybe the theorem itself does not imply it, but explicit black hole solutions (such as the Bardeen black hole) without singularity are known when energy condition is not required. The simplest way to construct such a solution is to write down by hand a regular black hole metric that you want, compute the Einstein tensor for that metric, a finally use the Einstein equation to find the needed energy-momentum tensor.

 

[PeterDonis]

the Bardeen black hole

Do you mean the metric described in equation (1) of this paper?

https://arxiv.org/abs/2007.09408

 

[Demystifier]

Do you mean the metric described in equation (1) of this paper?

https://arxiv.org/abs/2007.09408

Yes.

 

[PeterDonis]

the Bardeen black hole

From what I can gather, the maximal extension of this looks like Reissner-Nordstrom, the only difference being that there is just a regular timelike line at $r = 0$ instead of a timelike singularity. However, $r = 0$ is still behind a Cauchy horizon, meaning that this idealized solution is probably not physically realizable for the same reason as Reissner-Nordstrom is not: the Cauchy horizon (inner horizon) is unstable against small perturbations and would probably be replaced by something spacelike, looking more like the $r = 0$ singularity in Schwarzschild. Ultimately all this probably won't get resolved unless and until we have a confirmed theory of quantum gravity.

 

[PeterDonis]

From what I can gather, the maximal extension of this looks like Reissner-Nordstrom, the only difference being that there is just a regular timelike line at $r = 0$ instead of a timelike singularity. However, $r = 0$ is still behind a Cauchy horizon

To expand on this somewhat, based on some numerical investigations I have been making (and on what is said in some other papers I have found), there is a critical value of $g$ at which the horizon is degenerate (outer and inner horizons merge). For smaller values of $g$, there are two horizons and what I said in the quote above applies. The degenerate case corresponds to the similar case with Reissner-Nordstrom. For larger values of $g$, there is no horizon at all; this corresponds to the "naked singularity" case of Reissner-Nordstrom, but there is no singularity at $r = 0$ so this case corresponds to a static object that is supported against gravity by a sort of "magnetic repulsion" near the center.

 

[Demystifier]

To expand on this somewhat ...

Since you seem to be very interested in this stuff, here are some more papers you might be interested in.
https://arxiv.org/abs/gr-qc/0506126
https://arxiv.org/abs/1911.01020

 

[PeterDonis]

Since you seem to be very interested in this stuff, here are some more papers you might be interested in.
https://arxiv.org/abs/gr-qc/0506126
https://arxiv.org/abs/1911.01020

Thanks! These look interesting.

 

[PeterDonis]

https://arxiv.org/abs/gr-qc/0506126

The Penrose diagram in Fig. 5 of this paper is very interesting. What it is saying is, if you include evaporation in your model as well as formation, there is no true black hole any more. That is, there is no region of spacetime that cannot send light signals to future null infinity, and thus no event horizon (which would be the boundary of such a region).

Another way of putting this is that this paper gives a "semi-classical" model of how gravitational collapse would work in the presence of quantum fields that, when "compressed" enough, can violate energy conditions (and we already know quantum fields can do that) and thereby evade the conclusions of the singularity theorems and have regions of spacetime containing trapped surfaces without having a singularity. It also neatly avoids the issues involved with the inner (Cauchy) horizon in the non-evaporating case (illustrated in Fig. 1 of this paper, which matches the description I gave in post #56).

As the paper notes (p. 4, second paragraph in right column), this thing still looks like a black hole to outside observers, since stuff falls into it and doesn't come out for a time comparable to the Hawking radiation time (something like $10^{70}$ years for a mass of 10 solar masses), and the light from infalling objects gets redshifted by unbounded amounts as the objects approach the outer trapping horizon (which "looks like" an event horizon for a very long time, even though, considering the full spacetime, it isn't).

A key question that this paper doesn't mention is what a merger of two of these things would look like in terms of gravitational wave emission. Would it look similar enough to the waveforms LIGO has detected?