# Unruh Effect and Temperature Differentials

## Main Question or Discussion Point

Hello!

I've only just come across the Unruh Effect...so please bear with me!

Say you have a long pole, and you spin the pole around its center. The ends of the pole would then be accelerating but the center of the pole wouldn't be. The Unruh Effect would seem to be saying the ends of the pole would experience a higher temperature than the center.

What would happen if you could tap into this energy differential? Would it be available to do work?

Imagine a long thermocouple...would it produce electric power?

## Answers and Replies

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If you could get energy out of the system...would the spinning pole slow down? Would it take more energy to spin the pole than you would ever get out of it?

Bump...anyone? Is this the right forum?

Hello!

I've only just come across the Unruh Effect...so please bear with me!

Say you have a long pole, and you spin the pole around its center. The ends of the pole would then be accelerating but the center of the pole wouldn't be. The Unruh Effect would seem to be saying the ends of the pole would experience a higher temperature than the center.

What would happen if you could tap into this energy differential? Would it be available to do work?

Imagine a long thermocouple...would it produce electric power?
I was trying to solve a similar problem recently and my conclusion was that there is more incident radiation in the direction opposed to the acceleration, which acts as a retarding force on the object. In effect, to maintain the same level of acceleration as if the Unruh effect wasn't present, requires a greater amount of energy. I also concluded that this difference in energy must be equal to the amount on energy gained as heat. Further, I concluded that a deceleration, independent of velocity, must involve an equal and opposite effect.

I don't have a reference for it, and it might be plain wrong, but I can see no other way to conserve energy. There may be quirks to relativistic energy conservation that I'm not aware of that means that this isn't entirely true.

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Bill_K
Science Advisor
I was trying to solve a similar problem recently and my conclusion was that there is more incident radiation in the direction opposed to the acceleration, which acts as a retarding force on the object.
Does not really apply to the OP's situation, does it, since for circular motion the acceleration is radially inward, and a retarding force would need to be tangential.

Unruh radiation is usually discussed as an effect accompanying linear acceleration. It is a matter of some dispute whether or not it occurs also for circular motion. At least some authors have concluded that it does not.

For example, see this review, which argues (Sect III.7) that the vacuum seen by an observer in circular motion is just the Minkowski vacuum, hence the Unruh radiation is absent.

Does not really apply to the OP's situation, does it, since for circular motion the acceleration is radially inward, and a retarding force would need to be tangential.
I think it must apply. More centripetal force must be applied to maintain a circular path if there is another force acting in the opposite direction.

For example, see this review, which argues (Sect III.7) that the vacuum seen by an observer in circular motion is just the Minkowski vacuum, hence the Unruh radiation is absent.
Many thanks for this link. Hopefully, it'll clarify things.

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