Collapse and unitary evolution

In summary, Susskind's book "The Black Hole War" discusses the concept of unitarity in quantum mechanics and how it relates to the issue of information loss in black holes. He argues that information cannot be lost in quantum mechanics because of unitarity, but this raises questions about the collapse interpretation of quantum mechanics. Susskind favors the many-worlds interpretation and believes that collapse never occurs. However, the issue of information loss in black holes remains even in no collapse interpretations like the many-worlds interpretation. Susskind also discusses the AdS/CFT correspondence and its role in solving the paradox of information in black holes. There is some bias in his conclusion, as the AdS/CFT correspondence is still unproven and may
  • #141
martinbn said:
No, I'll ask if there is such a result about the approximation, or is it just expected. What about stubility?
It's expected by my physical intuition, but maybe I should add that I expect it for ##r>2M(t)##. I'm sure that someone made explicit calculations and haven't obtained anything very surprising, because otherwise I would already heard about that. After all, the mass of the Sun is not constant, yet the Schwarzschild metric describes the motion of planets around Sun very well.
 
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  • #142
Demystifier said:
It's the usual radial coordinate in the Schwarzshild metric.

Or, to make clear that this ##r## labels a geometric invariant, it is the "areal radius" of the 2-sphere on which a given event lies, i.e., if the 2-sphere's area is ##A##, then ##A = 4 \pi r^2##, so ##r = \sqrt{A / 4 \pi}##.
 
  • #143
Demystifier said:
It's about uncharged nonrotating black hole, with a possibly non-constant mass. If the mass changes sufficiently slowly, then the metric can be approximated by Schwarztschild metric with ##M\rightarrow M(t)##.

martinbn said:
I'll ask if there is such a result about the approximation

The Vaidya metric is an exact solution describing a non-rotating, uncharged black hole either emitting or absorbing null dust (basically incoherent EM radiation emitted or absorbed isotropically, equally in all directions). See here:

https://en.wikipedia.org/wiki/Vaidya_metric

Note that the usual way of writing this metric is in the equivalent of Eddington-Finkelstein coordinates, where there is a null coordinate ##u## or ##v## (depending on whether you are looking at the outgoing--emitting radiation--or ingoing--absorbing radiation--case) instead of the Schwarzschild ##t##. For this case, ##M## is a function of ##u## or ##v## only, as shown in the article, and this is true regardless of the rate of change of ##M## with respect to ##u## or ##v##.

I believe what @Demystifier is referring to is an approximation in which (for the ingoing case) ##dM / dv## is small enough that you can transform into standard Schwarzschild coordinates and still have ##M## be a function of only ##t## (instead of both ##t## and ##r##, as it would be in the general case with unrestricted rate of change) for the duration of the process he is analyzing.
 
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  • #144
Demystifier said:
the mass of the Sun is not constant, yet the Schwarzschild metric describes the motion of planets around Sun very well

The usual treatment of the Solar System is basically the order by order PPN expansion of the Schwarzschild metric for the case of small ##M / r##, yes. But this works well because the mass loss (from radiation, solar wind, etc.) is so small compared to ##M## that its effects are negligible. It's not because the solution explicitly uses an ##M## that is changing with time (at least, that's my understanding).
 
  • #145
Demystifier said:
It's expected by my physical intuition, but maybe I should add that I expect it for ##r>2M(t)##. I'm sure that someone made explicit calculations and haven't obtained anything very surprising, because otherwise I would already heard about that. After all, the mass of the Sun is not constant, yet the Schwarzschild metric describes the motion of planets around Sun very well.
But the Sun is very far from a black hole. I think it requires more justification than intuition to extrapolate. It would be interesting to see a theorem.
PeterDonis said:
Or, to make clear that this ##r## labels a geometric invariant, it is the "areal radius" of the 2-sphere on which a given event lies, i.e., if the 2-sphere's area is ##A##, then ##A = 4 \pi r^2##, so ##r = \sqrt{A / 4 \pi}##.
Which two sphere?
PeterDonis said:
The Vaidya metric is an exact solution describing a non-rotating...
My exclamation wasn't about which solution describes the scenario but about the fact that it is one solution that he had in mind. The statement seems to be about black holes in general, then it turns out that when physicists say "black hole" they mean the Schwartzschild solution or Vaiday, or something else but just one solution. Demystifier said that it should be a good enough approximation, which is probably true, but it would be interesting to see a precise statement.
 
  • #146
martinbn said:
Which two sphere?

Whichever 2-sphere the particular event you are interested in (the one labeled with a given value of ##r##) lies on. The entire spacetime is spherically symmetric, which means every event in the spacetime lies on some 2-sphere with a definite area.
 
  • #147
PeterDonis said:
Whichever 2-sphere the particular event you are interested in (the one labeled with a given value of ##r##) lies on. The entire spacetime is spherically symmetric, which means every event in the spacetime lies on some 2-sphere with a definite area.
Ah, ok, so there is an assumption that the space-time is spherecally symmetric.
 
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  • #149
Fra said:
new interactions does emerge as complexity increases, that was physically impossible at lower complexity.

Fra said:
But this is not a viable strategy for one human interacting with other humans. Instead the complex systems develops behaviour that due to chaos can not be inferred from knowledge of interaction of parts.

Example; altruistic attitudes.
 
  • #150
PeroK said:
I'm not sure who said people weren't made of particles.

Indeed.
 
<h2>1. What is the difference between collapse and unitary evolution?</h2><p>Collapse refers to the collapse of a quantum state into a definite state when it is observed or measured. Unitary evolution, on the other hand, is the continuous and deterministic evolution of a quantum state according to the Schrödinger equation.</p><h2>2. How does collapse occur in quantum systems?</h2><p>Collapse occurs when a quantum system interacts with a classical measuring apparatus, causing the superposition of states to collapse into a definite state. This is known as the measurement problem in quantum mechanics.</p><h2>3. Can unitary evolution and collapse coexist?</h2><p>Yes, they can coexist in the Copenhagen interpretation of quantum mechanics. In this interpretation, quantum systems evolve unitarily until they are observed, at which point collapse occurs. However, there are alternative interpretations that do not involve collapse, such as the Many-Worlds interpretation.</p><h2>4. How does the concept of entanglement relate to collapse and unitary evolution?</h2><p>Entanglement is a phenomenon where two or more quantum systems become correlated in such a way that their individual states cannot be described independently. This can lead to collapse when one of the entangled systems is observed, causing the other system to also collapse. Unitary evolution can also preserve entanglement between systems.</p><h2>5. Can collapse and unitary evolution be tested experimentally?</h2><p>Yes, there have been numerous experiments that have tested the predictions of quantum mechanics, including the concepts of collapse and unitary evolution. These experiments have confirmed the validity of quantum mechanics, but the exact mechanism of collapse is still a subject of debate and ongoing research.</p>

1. What is the difference between collapse and unitary evolution?

Collapse refers to the collapse of a quantum state into a definite state when it is observed or measured. Unitary evolution, on the other hand, is the continuous and deterministic evolution of a quantum state according to the Schrödinger equation.

2. How does collapse occur in quantum systems?

Collapse occurs when a quantum system interacts with a classical measuring apparatus, causing the superposition of states to collapse into a definite state. This is known as the measurement problem in quantum mechanics.

3. Can unitary evolution and collapse coexist?

Yes, they can coexist in the Copenhagen interpretation of quantum mechanics. In this interpretation, quantum systems evolve unitarily until they are observed, at which point collapse occurs. However, there are alternative interpretations that do not involve collapse, such as the Many-Worlds interpretation.

4. How does the concept of entanglement relate to collapse and unitary evolution?

Entanglement is a phenomenon where two or more quantum systems become correlated in such a way that their individual states cannot be described independently. This can lead to collapse when one of the entangled systems is observed, causing the other system to also collapse. Unitary evolution can also preserve entanglement between systems.

5. Can collapse and unitary evolution be tested experimentally?

Yes, there have been numerous experiments that have tested the predictions of quantum mechanics, including the concepts of collapse and unitary evolution. These experiments have confirmed the validity of quantum mechanics, but the exact mechanism of collapse is still a subject of debate and ongoing research.

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