Hawking radiation vs GR1915 vs GR
Eric Baird wrote:
But there's a potential loophole in the usual argument that a general
theory must reduce to the physics of SR over small regions, in that we
still have to consider whether or not a situation involving particles
whizzing past each other at significant relativistic velocities
//should// count as a flat-spacetime problem.
The issue does not directly involve the speed of the particles, merely
the size of the region of spacetime involved and the strength of gravity
there. For instance, at the CDF detector at Fermilab, protons and
antiprotons moving at 0.999999 c collide head on, and their interactions
produce many secondary and tertiary particles moving at speeds 0.9 c.
The detector fits inside a sphere that is 20 meters in radius, so the
maximum duration of an event in the detector is about 100 ns (not
counting electronic delays, which are not subject to gravity). In order
to analyze an event in a locally inertial frame, that frame must be in
freefall; the simplest one to use is at rest relative to the detector at
the start of the event.
Exercise: compute how far that frame will fall during 100 ns,
and compare to the resolution of the detectors (take this as
~1 micron, which is smaller than their actual resolution but
will do).
Exercise: do the same for the rotation of the earth during
the event.
These experimenters are fully justified in neglecting gravity and
rotation, and using SR to analyze their events.
If we think that it should, then we get special relativity.
If we think that it shouldn't, [...]
There's no sensible way to "think that it shouldn't".
BTW in attempting to distinguish between "GR1915" and "GR", you attempt
to make a distinction without a difference. We have learned A LOT since
1915, but the theory is still that of Einstein in 1915.
Tom Roberts
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