Exploring the Origin of Unruh Temperature: Theories and Implications

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In summary: The Rindler energy of the ith state of the thermometer is ρεi where εi are the proper rest energy levels. So if the Rindler temperature is 1/2π, then the probability of the ith level is ~ e-2πρεiThis means the thermometer registers a proper temperature `1/2πρ = a/2π
  • #1
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A uniformly accelerating observer registers a temperature

T = 1/2π

Or an observer hovering near a black hole. According to current understanding, what are the best ideas about the origin of this temperature?
 
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  • #2
PrashantGokaraju said:
According to current understanding, what are the best ideas about the origin of this temperature?

Mine is that you miswrote something. The title doesn't match the message, there are no units for your temperature, and what you wrote is independent of acceleration. Maybe you miswrote more than one thing.
 
  • #3
The dimensionless character of this temperature is due to the fact that the Rindler time is dimensionless.

A conventional temperature with units of energy or inverse length would be recorded by a thermometer, and this is

T = a/2π

where a is the acceleration.
 
  • #4
PrashantGokaraju said:
A uniformly accelerating observer registers a temperature

Are you perhaps referring to the so-called Unruh effect?

If not, is there a reference to your assertion that describes what you are referring to in more detail?
 
  • #5
Yes, unruh effect. For example if you observe a black hole by it's unruh radiation, you always get a blurry image.
 
  • #6
PrashantGokaraju said:
For example if you observe a black hole by it's unruh radiation, you always get a blurry image.

Huh? "observe a black hole by it's unruh radiation" is a non-sequitur.
 
  • #7
PrashantGokaraju said:
According to current understanding, what are the best ideas about the origin of this temperature?
The Wikipedia article on “Unruh effect” will be a pretty good starting point.
 
  • #8
PrashantGokaraju said:
The dimensionless character of this temperature is due to the fact that the Rindler time is dimensionless.

First, you didn't just write a dimensionless number, you wrote a constant, ##T = 1 / 2 \pi##. The Unruh temperature is not a constant; it varies with acceleration. When you write the temperature correctly, as you did in post #3, of course it has units of acceleration, i.e., inverse length.

Second, Rindler time is not dimensionless; it has units of time, since it's just proper time along the worldline of the Rindler observer at ##x = 1## in Rindler coordinates.
 
  • #9
This is a hard subject to explain. How is your handle on QFT?
 
  • #10
PeterDonis said:
First, you didn't just write a dimensionless number, you wrote a constant, ##T = 1 / 2 \pi##. The Unruh temperature is not a constant; it varies with acceleration. When you write the temperature correctly, as you did in post #3, of course it has units of acceleration, i.e., inverse length.

Second, Rindler time is not dimensionless; it has units of time, since it's just proper time along the worldline of the Rindler observer at ##x = 1## in Rindler coordinates.

The Rindler hamiltonian is

H = ∫ ρT00

The Rindler energy of the ith state of the thermometer is ρεi where εi are the proper rest energy levels. So if the Rindler temperature is 1/2π, then the probability of the ith level is ~ e-2πρεi

This means the thermometer registers a proper temperature `1/2πρ = a/2π
 
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  • #11
DarMM said:
This is a hard subject to explain. How is your handle on QFT?

I do know the basic ideas of canonical quantization and path integrals, feynman diagrams etc. mostly in the special case of scalar fields. Did not study too much other field theories like QCD etc. I want to know for example, what does string theory say about the Unruh temperature and the entropy, microstates etc? Also the various other facts about black holes, like the blurry image, visibility of space behind them, etc. What is the most current understanding of these things, in string theory, or any other modern ideas
 
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  • #12
The origin of the Temperature is that the decomposition of a quantum state into particles is not unique.

A particle is associated with positive and negative frequency modes of solutions to the free field equation. Thus note: particles are intrinsically associated with free quantum fields and only emerge as asymptotic concepts in interacting theories.

The time coordinate of an accelerating observer produces a completely different set of functions as the positive and negative frequency decomposition of solutions to the free field equation. This gives rise to a different notion of particle, Rindler particles say. The Unruh effect is due to the vacuum containing no intertial particles, but being a Thermal bath of Rindler particles.
 
  • #13
Vanadium 50 said:
Huh? "observe a black hole by it's unruh radiation" is a non-sequitur.
Not a non-sequitur. Just bloody difficult. Bryce DeWitt derives the temperature of a black hole, observed at infinity, from the surface Unruh temperature, in General Relativity: an Einstein Centenary.
 
  • #14
PrashantGokaraju said:
The Rindler hamiltonian

Where are you getting this from?
 

1. What is Unruh temperature?

Unruh temperature is a theoretical concept proposed by physicist William Unruh in 1976. It suggests that an accelerating observer in a vacuum will experience a temperature due to the presence of virtual particles in the vacuum.

2. How is Unruh temperature related to the origin of the universe?

Unruh temperature is related to the origin of the universe because it is a key component of the theory of cosmic inflation, which explains the rapid expansion of the universe in the first fractions of a second after the Big Bang.

3. What are some theories that attempt to explain the origin of Unruh temperature?

Some theories that attempt to explain the origin of Unruh temperature include the Hawking effect, which proposes that the temperature is caused by the emission of virtual particles near the event horizon of a black hole, and the Unruh-DeWitt detector model, which suggests that the temperature is a result of the interaction between an accelerating observer and the vacuum.

4. What are the implications of Unruh temperature for our understanding of the universe?

The implications of Unruh temperature for our understanding of the universe are significant. It provides a possible explanation for the observed temperature of the cosmic microwave background radiation and supports the theory of cosmic inflation. It also has implications for our understanding of black holes and the behavior of matter in extreme environments.

5. How can we test the existence of Unruh temperature?

There are several proposed methods for testing the existence of Unruh temperature, including using particle accelerators to simulate the conditions of an accelerating observer and measuring the temperature of the cosmic microwave background radiation. However, due to the extremely small temperature predicted by Unruh's theory, further research and technological advancements are needed to confirm its existence.

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