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Clearly the geodesic paths are tensor invariant as are the relative disclinations of neighboring light cones in curved spacetime. We cannot make global Fourier transforms like in special relativity for qft propagators.
The measured energy of test particles eg photons depends on state of motion of the detectors relative to the local invariant gmd field ds^2. Therefore, in a typical gravity redshift calculation
dt = ds/(gtt(r))^1/2 = ds'/(gtt(r'))^1/2
For the measured time distortion ds - ds' for a null geodesic connecting events r & r'.
guv must be in same detector representation for r & r'!
Eg for SSS gtt = 1 - rs/r both r & r' have static lnif detectors
Key issue is
A photon is exchanged between coincident lif & lnif, will there be a frequency shift or not?
Remember lnif sees black body real unruh photons whilst coincident lif sees only virtual zpe photons as dark energy!
On Jul 18, 2010, at 5:34 PM, JACK SARFATTI wrot
PS I mean to say that if we track signals from geodesic probe falling into a black hole, we will not see any redshift at all! We will see a sharp cut off of signal when probe passes through horizon of course.
The usual argument only works for a transmitter adiabatically lowered on a steel cable from a hovering rocket at fixed distance from the event horizon.
There is no paradox only an inconsistent violation of the equivalence principle in the text book argument that incorrectly erases the absolute difference between coincident lif & lnif.
On Jul 18, 2010, at 5:21 PM, JACK SARFATTI wrote:
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Curvilinear metric e.g.
gtt = 1 - rs/r
Is for static lnif
A coincident lif should be like static lnif at r --> infinity
When v ~ 0
Pound Rebka experiment Harvard Tower clearly both lnif
Atoms in sun & supernovae lnif from pressure gradients
What about Gps satellites in lif orbits? Is precision good enough to distinguish satellite finite r from r infinite?
Problem is with probe falling freely into black hole. One can argue signal from geodesic probe near event horizon should blue shift to us far away not redshift! Of course signal from hovering rocket near horizon will redshift.
Assuming lif same as coincident lnif seems inconsistent with equivalence principle. Also Unruh effect shows absolute physical difference between coincident lif and static lnif near horizon of black hole whose g force is
g(lnif) = (rs/r^2)(1 - rs/r)^1/2
Compared to
g(lif) = 0
When they are momentarily coincident at fixed r
Am I only one to notice this?
Where is my error?