Unruh and Hawking Radiation Paradoxes?

In summary: In my opinion, it is a paradox if you have a reason to believe that particles exist even when nobody observes them. If you don't have a reason to believe that, then there is no paradox.However, if the observers are in different frames of reference (accelerated vs. inertial), then the particles do "exist" according to the observers.One does not have to imagine some acceleration and deceleration story, in order to suppose that particle number is not invariant. It is simply, of itself, poorly defined in curved geometry.Unfortunately, in curved spacetimes there is no general global definition of energy. Here are a couple of nice FAQs on the topic:
  • #1
craigi
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Does the existence of observer dependent particles as predicted by the Unruh effect and Hawking radiation lead to paradoxes?
 
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  • #2
craigi said:
Does the existence of observer dependent particles as predicted by the Unruh effect and Hawking radiation lead to paradoxes?
Interesting question!
In my opinion, it is a paradox if you have a reason to believe that particles exist even when nobody observes them. If you don't have a reason to believe that, then there is no paradox.
 
  • #3
I don't think it has anything to do with observation. There would be a paradox if particle number is invariant. But why should it be?
 
  • #4
martinbn said:
I don't think it has anything to do with observation. There would be a paradox if particle number is invariant. But why should it be?

So suppose we accept that particle number isn't invariant under relative acceleration.

In order to conserve energy and avoid a paradox upon deceleration, do we require that free Unruh radiation is absorbed back into the vacuum and that particles that have absorbed Unruh radiation, at least statistically, release it back into the vacuum too?
 
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  • #5
Demystifier said:
Interesting question!
In my opinion, it is a paradox if you have a reason to believe that particles exist even when nobody observes them. If you don't have a reason to believe that, then there is no paradox.

craigi said:
So suppose we accept that particle number isn't invariant under relative acceleration...

AFAIK particle number is simply not an invariant. If the geometry is curved (as realistically speaking it always is, in nature) the particle number is poorly defined, ambiguous. Isn't that right?
Particles only "exist" as detection events.

So I would follow Demystifier's reasoning and say that there is no paradox.

One does not have to imagine some acceleration and deceleration story, in order to suppose that particle number is not invariant. It is simply, of itself, poorly defined in curved geometry.

There was a 2003 paper by Colosi and Rovelli about this which referred to an earlier paper by Paul Davies, but I think it is simply well-known and a reference is unnecessary.
 
  • #7
craigi said:
So suppose we accept that particle number isn't invariant under relative acceleration.

In order to conserve energy and avoid a paradox upon deceleration, do we require that free Unruh radiation is absorbed back into the vacuum and that particles that have absorbed Unruh radiation, at least statistically, release it back into the vacuum too?

I don’t see the paradox, but I do see what you are saying about energy conservation. If the body heats up during acceleration, it seems reasonable to expect that it would either cool back down after deceleration, or leave the volume of space from which it came a little cooler. Whether or not it's possible to specify parameters for energy conservation in this situation is unclear. Here’s what DaleSpam has recently said in a different thread.

DaleSpam said:
Unfortunately, in curved spacetimes there is no general global definition of energy. Here are a couple of nice FAQs on the topic:

http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html
https://www.physicsforums.com/showthread.php?t=506985
 
  • #8
I recall the "paradox" stemming from the fact that an accelerated particle detector will detect quanta (and an inertial detector will not), while both accelerated and inertial observers agree that the local stress-energy tensor vanishes: [itex]\langle 0_M|:T_{\mu \nu}:|0_M\rangle = \langle 0_M|:T'_{\mu \nu}:|0_M\rangle = 0[/itex]. (Here [itex]T_{\mu \nu}[/itex] is the inertial tensor and [itex]T'_{\mu \nu}[/itex] is that in the accelerated frame, the ':' denotes normal ordering, and [itex]|0_M\rangle[/itex] is the Minkowski vacuum.)
 

1. What is the Unruh effect and how does it relate to Hawking radiation?

The Unruh effect is a theoretical prediction that an accelerating observer will perceive a thermal bath of particles, even in the absence of an external source of radiation. This effect is closely related to Hawking radiation, which is the predicted thermal radiation emitted by black holes due to the Unruh effect near the event horizon.

2. How does the Unruh effect and Hawking radiation challenge our understanding of black holes?

The Unruh effect and Hawking radiation challenge our understanding of black holes because they suggest that black holes are not truly black but emit radiation, which goes against the classical view of black holes as objects with only a gravitational pull.

3. Have the Unruh effect and Hawking radiation been observed?

The Unruh effect and Hawking radiation have not been directly observed yet, but there is ongoing research and experiments to detect and measure them. However, their effects have been indirectly observed through various phenomena such as the evaporation of black holes.

4. How do the Unruh effect and Hawking radiation impact our understanding of the universe?

The Unruh effect and Hawking radiation have significant implications for our understanding of the universe, as they provide a way to bridge the gap between quantum mechanics and general relativity. They also challenge our understanding of black holes and suggest that they may not be completely isolated objects, but rather interact with their surroundings through radiation.

5. Are there any proposed solutions to the Unruh and Hawking radiation paradoxes?

There are several proposed solutions to the Unruh and Hawking radiation paradoxes, including modifying the equations of general relativity, incorporating new theories such as string theory, and considering the role of quantum gravity. However, these proposed solutions are still being studied and debated in the scientific community.

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