Unruh Effect: When Does an Object Receive Radiation?

[tzimie]

When an object starts accelerating, when does it receive Unruh radiation?

1. After some delay, because it takes time for the photons to travel from the Rindler horizon
2. Immediately, because an object instantly "assumes" an accelerating frame, which is already filled with Unruh radiation.

Thanks.

 

[Demystifier]

Number 2.

 

[tzimie]

Number 2.

So we detect Unruh radiation even if Rindler horizon is not visible - say, is obscured by something?

 

[Vanadium 50]

That's logically the same as "Can I still see something when my hands are covering my eyes?"

 

[tzimie]

That's logically the same as "Can I still see something when my hands are covering my eyes?"

What if your hands (screen) are far enough from you - almost at Rindler's horizon?
Then saying that distant screen blocks Unruh radiation is the same as claiming #1 in my first post.

 

[Demystifier]

So we detect Unruh radiation even if Rindler horizon is not visible - say, is obscured by something?

That's correct. The horizon is not essential for the Unruh effect. See e.g.
http://lanl.arxiv.org/abs/gr-qc/0103108 [Mod.Phys.Lett.A16:579-581,2001]

 

[marcus]

Thanks Demy! It's good to have that point clarified!
So (and please correct this if it's wrong) the temperature arises locally in the vacuum just from acceleration---and the Rindler horizon is a nonessential descriptive parameter of the acceleration?

Thanks also to Tzimie for asking the right question to elicit the clarification.

 

[Demystifier]

So (and please correct this if it's wrong) the temperature arises locally in the vacuum just from acceleration---and the Rindler horizon is a nonessential descriptive parameter of the acceleration?

That's almost correct, with a caveat that the effect is local in space (a very small detector can see the effect) but not completely local in time (in order for the detector response to have a thermal spectrum, the acceleration must exist for a long time).

Incidentally, today a new paper appeared which discusses these things in more detail:
http://lanl.arxiv.org/abs/1501.00119

 

[marcus]

That's almost correct, with a caveat that the effect is local in space (a very small detector can see the effect) but not completely local in time (in order for the detector response to have a thermal spectrum, the acceleration must exist for a long time).

Incidentally, today a new paper appeared which discusses these things in more detail:
http://lanl.arxiv.org/abs/1501.00119

Yes! I saw that and logged it on the biblio thread! Nicolaevici "Unruh effect without Rindler horizon"! just what you were talking about (and wrote about several years ago.

 

[tzimie]

Thank you, and I am happy because my intuition was right :)
What's about radiation from the cosmological horizons in our expanding Universe? Do we need to see cosmological horizons or not?

 

[Demystifier]

Thank you, and I am happy because my intuition was right :)
What's about radiation from the cosmological horizons in our expanding Universe? Do we need to see cosmological horizons or not?

Unlike Rindler horizon, the cosmological horizon (similarly to the black hole horizon) is quite relevant for the radiation.

 

[tzimie]

I was also wondering

During the inflation era when the expansion was so rapid --> cosmological horizons were so close --> radiation from them was so intense --> average density of energy could be significant to influence and even to cancel the inflation?