Unruh effect and conservation of energy

In summary, the Unruh effect states that a uniformly accelerating observer will perceive a thermal bath with particles at a temperature determined by the acceleration. This can lead to a non-zero probability for certain interactions, such as proton decay, to occur. However, for an inertial observer, the energy required for these interactions may not be sufficient if the acceleration is small or the duration is short. This raises questions about energy conservation and the possibility of a Rindler horizon forming in such scenarios. Overall, there is confusion about the validity of these ideas and what may be missing from the current understanding.
  • #1
asimov42
377
4
Hi all,

I have a question about the Unruh effect and energy conservation; I'd originally asked part of this in another forum, but I thought it might be more appropriate to post here.

I understand that, as per the Unruh effect, a uniformly accelerated observer and an inertial observer will see different vacua, i.e., the notion of 'particles' end up being observer-dependent. A uniformly-accelerating observer will see a thermal bath at some temperature T depending on the magnitude of the acceleration. The bath will contain all types of particles with some probability, even though that probability may be vanishingly small is certain cases.

Now my question: consider, say, proton decay (to a neutron, positron and neutrino). Once he proton is uniformly accelerated (by, e.g., a linear accelerator), according to the Unruh effect there should be a non-zero probability that the proton will interact with a Rindler electron in thermal bath and 'decay' to produce a neutron.

From the inertial observer's perspective, the energy required for the decay comes from whatever is powering the acceleration.

Here's where I become confused: if the magnitude of the acceleration is small, and/or the duration is short, the energy imparted to the proton *may not be sufficient* for the decay process to occur.

So in the accelerated frame there is a non-zero transition probability, and in the inertial frame the probability is zero because insufficient energy was supplied. And energy overall must be conserved.

Clearly, this can't be right - I'm wondering what I'm missing?

If the duration of the acceleration is finite, does the alter the description of the process in the accelerated frame (i.e., in Rindler coordinates)?
 
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  • #2
Perhaps a different question - can a Rindler horizon form if the particle is only accelerated uniformly for a finite period of time? Does this imply that the situation described in the previous post cannot occur?

I'm fairly lost on this one...
 

What is the Unruh effect?

The Unruh effect, named after physicist William Unruh, is a theoretical phenomenon in quantum field theory where an accelerating observer perceives a vacuum state as a thermal bath of particles. In other words, an observer that is constantly accelerating in empty space will experience a temperature and see particles that are not observed by an inertial observer.

How does the Unruh effect relate to the conservation of energy?

The Unruh effect does not violate the conservation of energy. Although an accelerating observer may perceive particles and experience a temperature, the total energy of the system remains constant. This is because the energy of the particles perceived by the accelerating observer is balanced by the negative energy of the gravitational field that is required to accelerate the observer.

Is the Unruh effect experimentally proven?

Currently, there is no direct experimental evidence for the Unruh effect. It is a theoretical concept that has not been observed in experiments due to the difficulty of creating the necessary conditions of constant acceleration in a vacuum. However, indirect evidence has been found in various experiments, including the Hawking radiation phenomenon.

Can the Unruh effect be observed in everyday life?

No, the Unruh effect is only significant in extreme conditions such as very high accelerations and vacuums. In everyday life, the effects of the Unruh effect are negligible and cannot be observed.

How does the Unruh effect affect our understanding of the universe?

The Unruh effect is a fundamental concept in quantum field theory and has implications for our understanding of gravity and spacetime. It also helps to reconcile the principles of quantum mechanics and general relativity. However, further research and experimentation are needed to fully understand the complexities of this phenomenon and its implications for our understanding of the universe.

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