When I was at Birkbeck College, University of London in 1971, David Bohm once said to me that "General Relativity has a complete theory of measurement, while quantum theory doesn't." I think he meant the Wheeler approach that is detector-centric. If you cannot formulate the GR in terms of small detectors in a gedankexperiment you quickly get lost in the opium fog of pure mathematics leading you off the true path to Paradiso in Dante's sense.
Midway upon the journey of our life
I found myself within a forest dark,
For the straightforward pathway had been lost.
On Jan 30, 2011, at 4:49 PM, Paul Zielinski wrote:
Look I understand what Gibbons and Hawking are trying to do. They are working from a formal thermodynamic analogy between black hole and cosmological event horizons, and are proposing a quantum theoretic model for the thermodynamics of cosmological horizons which involves the detector-dependent creation of particles.
ok
My question is about whether such an acceleration-dependent model for the thermodynamics can be given a generally covariant description GCD within the framework of GTR. What do you think?
Tricky question because GCD assumes a unique vacuum classically, which is not true quantum mechanically. Look at Susskind's horizon complementarity. The real on-mass-shell particle content is a function of the covariant tensor acceleration of the detector. One must use Bohr type approach in GR as well as in QM i.e. "total experimental arrangement" as soon as quantum effects like Unruh effect become important. There is too much formal math in GR without any real anchoring in experiment. Not enough Bridgman operationalism. The Wheeler-Thorne school is the exception to this of course.
On Jan 30, 2011, at 4:43 PM, Paul Zielinski wrote:
Well of course I think *you* still don't get it. The effect is reciprocal. :-) Of course the Unruh phenomenon depends on the acceleration of the detector. The question is whether such effects are objective and can be thus separated from frame artifacts.
The effect is objective. In my model, which may not work BTW, the virtual electron-positron pair is the accelerating detector because its stuck at the event horizon, whether objective or observer-dependent won't matter.
In the de Sitter observer-dependent case the photon emitted from the observer who is always at r = 0 when g00 = 1 - / ^2 sees a stuck e+-e- pair (static LNIF) at distance H from its (the photon's) horizon.
http://www.npl.washington.edu/npl/int_rep/tiqm/TI_toc.html
past emitter is at r = 0, future absorber is at tiny H from r = /^-1/2 Your MTW "LNIF" is a chimera, since it bundles objective acceleration-dependent effects (represented by tensor invariants) with frame artifacts (represented by the *components* of 4-tensors).
Nonsense Z the acceleration I use is completely covariant with a tensor invariant. Your statement is wrong because
(The minus sign on σ0 ensures that is future pointing.) This is the frame that models the experience of static observers who use rocket engines to "hover" over the massive object. The thrust they require to maintain their position is given by the magnitude of the acceleration vector
This is radially outward pointing, since the observers need to accelerate away from the object to avoid falling toward it. On the other hand, the spatially projected Fermi derivatives of the spatial basis vectors (with respect to ) vanish, so this is a nonspinning frame.
http://en.wikipedia.org/wiki/Tetrad_(general_relativity)
The corresponding formula in the de Sitter case is
[c^2(/^1/2 + / ^2) (1 - / ^2)^-1/2)e1
note that the /^1/2 term is like the hf/2 zero point term in the quantum oscillator - call it the horizon surface gravity Hawking radiation term missing from Einstein's classical calculation.
Similarly in the black hole case we must use
c^2/rs + rs/2r^2 in the Newtonian coefficient
in these units rs = 2m
On Jan 30, 2011, at 8:45 PM, Paul Zielinski wrote:
There are a number of papers arguing that there is no actual Unruh radiation, and that the Unruh temperature seen by an accelerating detector is an effective temperature, but otherwise the physical situation is exactly the same as that experienced by a non-accelerating observer at the elevated temperature.
For example:
http://arxiv.org/abs/quant-ph/0509151
What impact if any would that have on your Wheeler-Feynman model for cosmological horizons?
It would destroy it obviously. That is a good thing. My model is Popper falsifiable, unlike many archive papers. There is another reason that my model may not work, but I am not sure yet.