1. Oct 11, 2005

### marcus

in case anyone is interested
Unruh radiation is somewhat like Hawking radiation, a quantum gravity thing----so I will post it here
http://www.arxiv.org/abs/hep-th/0510089
Unruh Radiation in Atomic and Nuclear Systems
Shahar Hod
2 pages
"We analyze the Unruh radiation effect experienced by an accelerated particle in atomic and nuclear systems. For atomic systems, the effect is shown to be negligible as compared to the characteristic energy of the system. On the other hand, we find that a quark inside a nucleon may experience Unruh radiation whose energy is comparable with the quark's own mass. We discuss the implications of these results."

Shahar Hod already provoked a disturbance with his conjecture about BH seminormal vibration modes and the relation to Hawking radiation. Always looking for excitement.

2. Oct 12, 2005

### Mike2

What is the energy per unit volume, the energy density, of a space with a given temperature? I wonder because due to the equivalence principle, there's no distinction between acceleration and gravitation. So if an accelerating reference frame has a certain Unruh radiation and associated temperature for any body in that accelerated reference frame, then by the equivalence principle so does a body in a graviational field feel an Unruh temperature. So if there is a temperature in space alone simply because it is in an accelerated reference frame due to gravity, then there is an energy density of that space due to that temperature. Could it be that this energy density which might surround a galaxy be enough to produce the dark matter effects? For that matter, since there is a gravitational field associated with the entire universe, perhaps this Unruh effect due to the accelerated reference frames of gravity might actually be the cosmological constant. And perhaps this cosmological constant is not evenly distributed but is more dense around galaxies so that we see its effects as dark matter. Anybody want to do the math and get a Nobel prize?

Last edited: Oct 12, 2005
3. Oct 13, 2005

### Chronos

I think Hod missed the boat on that one, marcus. Relativity does not work at atomic scales... e.g., electrons do not experience relativistic mass increase while 'orbiting' an atomic nucleus.

4. Oct 13, 2005

### marcus

I think I should wait to see whether or not he missed the boat, and if he did then for what reason.

I would agree that thinking of the electron as "orbiting" the nucleus is of limited usefulness (maybe a wave slopping around is better) but if you DO then I believe a typical speed for an electron in a bohr H atom is 1/137 of the speed of light. At that speed there wouldnt be much relativistic mass increase, would there?

I think I will keep my powder dry on this one, and see if there is any response to Hod.

5. Oct 13, 2005

### Chronos

This is the first time I have totally disagreed with you, marcus. I greatly appreciate your enthusiasm and sincerity. It's inspirational, but, I think you missed the boat on this one. Hod's assumptions are just plain wrong, IMHO.

Last edited: Oct 13, 2005
6. Oct 13, 2005

### Spin_Network

The effects of local enviromental change (for instance here) :http://www.physlink.com/News/050920SpinProtonsNeutrons.cfm

makes as a good scale example?

The internal working of material may be constant for all matter and observers contained?..example the:http://csep10.phys.utk.edu/astr162/lect/gclusters/attractor.html

the effects we observe being external to the portion of space known as the Great Attractor, may not be existing for any observers "contained" inside the actual area/volume of space?

7. Oct 13, 2005

### Hans de Vries

You would probably like to rephrase this to: SR works perfectly at atomic scales
but QM makes it harder to apply classical relativistic mechanics.

-----------------------------------------------

Going to the extreme:

A classical particle spinning with a frequency corresponding to Plancks mass (E=hf)
at a Compton radius corresponding to Planck's length has an acceleration of:

5.56078 1051 meter/s2

and thus observes Unruh radiation with a temperature of:

$$T_U \ = \ \frac{\hbar a}{2 \pi c k_B} \ = \$$ 2.25489 1031 degrees.

Which is exactly Planck's Temperature divided by $2\pi$

(odd factor $2\pi$ Mr. Unruh? ....)

But then to put things into perspective:

Our classical particle with Planck's mass would feel a centrifugal force at
a (Compton) radius of Planck's length of:

1.2102755 1044 kg m / s2

Which is enough to accelerate the Earth (5.9742 1024 kilograms)
to it's orbiting velocity around the Sun of circa 30,000 m/s in a time of:

1.5 10-15 seconds or 1.5 femtoseconds....

Well it's not so strange that classical mechanics gives up somewhere.

Regards, Hans

Last edited: Oct 13, 2005
8. Oct 13, 2005

### marcus

thanks for such a nice rephrasing of Chronos' point, Hans! If that is what he is saying I can agree fully---would have no reservations at all.

BTW I recognize that force as the Planck force c4/G
and the acceleration you mentioned is the unit acceleration in the Planck system of units

9. Dec 16, 2005

### marcus

I don't think anyone disposed of this issue raised by Hod.

Shouldnt we keep track of it a bit longer? Apparently the quarks inside the nucleon are being jerked around a lot and experiencing a lot of gees like 10^50 gees, which must make them see lots of Unruh radiation----a kind of hallucination which people can get from abruptly accelerating

shall we say that this is not our problem---just something that the quark feels. Hod says the energy density in this Unruh radiation is comparable to the mass of the quark. Is there some reason that this does not matter? Did Hod make a mistake?