Temperature , tensors, and the unruh effect

[pervect]

Given that an unaccelerated detector detects no Unruh radiation, and an accelerated detector does, it seems to me that whatever the detector is measuring, it can't (by definition) be a tensor, as it doesn't transform properly.

I was wondering if there were anything in the literature that went into this in more detail.

 

[TrickyDicky]

Given that an unaccelerated detector detects no Unruh radiation, and an accelerated detector does, it seems to me that whatever the detector is measuring, it can't (by definition) be a tensor, as it doesn't transform properly.

I was wondering if there were anything in the literature that went into this in more detail.

AFAIK from the literature it seems clear that particles are described by the stress-energy tensor, besides detected particles are observables, wikipedia says: "Physically meaningful observables must also satisfy transformation laws which relate observations performed by different observers in different frames of reference. "

 

[Mentz114]

I found this interesting, not sure if it addresses your question

http://arxiv.org/abs/0709.4101v1

 

[Bill_K]

Quoting Birrell and Davies on this point. (They are actually talking about a very closely related situation - radiation from a moving mirror.)

"One trajectory of interest is uniform acceleration... it follows that <T_μν>_ren = 0, which implies that no energy at all is radiated... Clearly the mirror emits particles... and it is also clear that a particle detector would respond to the presence of quanta. Nevertheless no energy is radiated. This example beautifully illustrates the looseness of the relation between particles and energy-momentum. The presence of quanta need not imply the presence of energy.

There appears to be a paradox concerning how the particle detector can, in the absence of field energy, absorb quanta and make a transition to an excited state. The resolution is that in so doing, the detector emits negative energy into the field to compensate. The emission of negative energy by mirrors and detectors is not without precedent in quantum field theory..."

Elsewhere they say:

"The emission of negative energy is a purely quantum phenomenon. It opens up the possibility of unusual new physical processes not encountered in classical theory. Negative energy fluxes play a role in the quantum evaporation of black holes. It might be supposed that a moving mirror could be used to violate the second law of thermodynamics by radiating negative energy into a hot body, thereby cooling it. However, if [the flux] is integrated over time between periods of stasis, it is always positive definite."

 

[atyy]

Perhaps it's somethings like "relative velocity", or g(u,v), which is a scalar, dependent on observers u and v?

There's a discussion on p109 of https://1e47a410-a-62cb3a1a-s-sites...4uL4u5lL22g3Hk6pw8VfivJboz9ck=&attredirects=0.

 

[TrickyDicky]

Quoting Birrell and Davies on this point. (They are actually talking about a very closely related situation - radiation from a moving mirror.)

"One trajectory of interest is uniform acceleration... it follows that <T_μν>_ren = 0, which implies that no energy at all is radiated... Clearly the mirror emits particles... and it is also clear that a particle detector would respond to the presence of quanta. Nevertheless no energy is radiated. This example beautifully illustrates the looseness of the relation between particles and energy-momentum. The presence of quanta need not imply the presence of energy.

There appears to be a paradox concerning how the particle detector can, in the absence of field energy, absorb quanta and make a transition to an excited state. The resolution is that in so doing, the detector emits negative energy into the field to compensate. The emission of negative energy by mirrors and detectors is not without precedent in quantum field theory..."

Elsewhere they say:

"The emission of negative energy is a purely quantum phenomenon. It opens up the possibility of unusual new physical processes not encountered in classical theory. Negative energy fluxes play a role in the quantum evaporation of black holes. It might be supposed that a moving mirror could be used to violate the second law of thermodynamics by radiating negative energy into a hot body, thereby cooling it. However, if [the flux] is integrated over time between periods of stasis, it is always positive definite."

Those authors seem to postulate the existence of something called "negative energy" to explain something related to the OP problem, according to wikipedia, leaving aside the esoteric and fiction plot device meanings, it is the energy associated to negative mass.
Is emission of particles with negative mass something not considered highly speculative anymore?

 

[Bill_K]

Is emission of particles with negative mass something not considered highly speculative anymore?

Not negative mass particles, negative field energy. Meaning T₀₀ < 0. As the rest of the quote indicates, such a concept is acceptable only with strong limitations.

One of the common explanations of how Hawking radiation can be emitted "when nothing can escape from a black hole" is that as the particles are emitted, the mass of the black hole decreases because of an inward flux of negative energy.