From: *spinozalens via Free Thinkers Physics Discussion Group*
<atvoi...@googlegroups.com <mailto:atvoi...@googlegroups.com>>
Δ
No, Susskind makes clear that the Hawking radiation is blue shifted
near the Horizon, and every other source I have on this agrees. You
can't get a detectable photon for the outside observer if the photon
wasn't at a very much higher energy near the horizon.
We have argued this back and forth many times. But the answer is very
clear. Hawking radiation is produced just above the BH horizon with
exactly the energy with which it is observed by the stationary observer
at infinity. The apparent divergence in energy near the horizon occurs
*only* for a fiducial observer, held at rest there. The photon does not
lose energy climbing through the gravitational field. There is no
gravitational potential energy. All that changes with distance from the
horizon is the clock rate.
This is explained very clearly in MTW. Einstein used energy conservation
to deduce the red shift, but Schild improved this argument to show that
the red shift is in fact caused by spacetime curvature (MTW, pp187-189).
In their discussion of the Pound-Rebka-Snider red shift experiment, MTW
make an even clearer explanation. On page 1058 they explain in detail
that if one views a photon as a sequence of wave crests, then each
successive wave crest sees exactly the same gravitational field,
"...therefore the crest of each electromagnetic wave that climbs upward
must follow a world line t(z) identical in form to the world lines of
the crests before and after it.... Hence, expressed in /coordinate/
time, the interval between reception of successive wave crests is the
same as the interval between emission. Both are ΔΔ/t/." (MTW p1058).
Atomic clocks (and stationary observers) measure proper time, not
coordinate time. Hence the difference as given by the Killing factor.
Bruce
You seem to want to exclude high energy photons near the horizon and
you can't do this. That's why AMPS predicted a firewall. Only a highly
red shifted photon approaches the wavelength you describe. You're
ignoring how a photon red shifts as it climbs out the gravity field.
In GR this takes the form of time dilation of course.
Bob Zannelli
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