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Mathematician


May
5
comment Can the equivalence principle be tested to high precision in a human-sized lab falling through the horizon of a black hole, in principle?
My post tried to explain why it is pointless to try to stick a "human sized lab" everywhere you can and measure the deviation of dynamics from flat space dynamics by reducing measurement error. For any fixed scale of experiment and any precision your experimental devices can discern, there is a mass limit below which, at the apparent horizon, the fuzziness built-in to the statement of EP is already bigger than your experimental error, so your experiment can't confirm EP more than a less precise experiment.
May
5
comment Can the equivalence principle be tested to high precision in a human-sized lab falling through the horizon of a black hole, in principle?
Without seeing the fine prints of those test that you found, I cannot say whether they are valid or not. You seem to be missing the point of my post, so let me say it again. There are two spots which will cause a disagreement between your measurement and the dynamics as predicted in flat space. First is due to unavoidable experimental error (and I assume when you say "high precision" you mean to try to minimize this as much as you can). The second is due to the inherent fuzziness in the statement of the equivalence principle. This fuzziness comes from local curvature effects.
May
5
revised Can the equivalence principle be tested to high precision in a human-sized lab falling through the horizon of a black hole, in principle?
fixed spelling and some computations.
May
5
comment Can the equivalence principle be tested to high precision in a human-sized lab falling through the horizon of a black hole, in principle?
@finbot: and I claim the question is meaningless with regards to the absolute horizon in general, since the absolute horizon is not locally definable. For stationary black holes, the two horizons coincide, and so there is no difference. But for dynamical black holes the issue of searching in local measurements for gravitational artifacts only makes sense if you are speaking about apparent horizons.
May
5
answered Can the equivalence principle be tested to high precision in a human-sized lab falling through the horizon of a black hole, in principle?
May
5
comment Can the equivalence principle be tested to high precision in a human-sized lab falling through the horizon of a black hole, in principle?
The comments about large versus small blackholes, however, is something altogether different yet again. At the apparent horizon, the area radius $r$ is roughly the same as the (Hawking) mass $M$, while the curvature is roughly $M/r^3$ on a (slowly evolving) blackhole spacetime. So at the apparent horizon you expect a curvature of about $1/M^2$, hence that for large black holes, even at the apparent horizon, the curvature effects may be weak.
May
5
comment Can the equivalence principle be tested to high precision in a human-sized lab falling through the horizon of a black hole, in principle?
This horizon is not that horizon. As the event horizon is teleologically determined, you can have the event horizon experiencing no curvature whatsoever. (Imagine the gravitational collapse of a spherical shell of matter, when the shell becomes sufficiently compact, there can be regions inside the shell that is completely flat, yet inside the event horizon.) The apparent horizon is (almost; statement is true in spherical symmetry) locally determined, and its presence necessarily signals non-flat geometry (again, spherical symmetry blah blah blah by considering the Hawking mass).
Apr
27
comment What exactly is meant by the “Gaussianity” of CMBR?
@Ted: very nice read. Thanks for the write-up!
Apr
27
comment Which Mechanics book is the best for beginner in math major?
@John JFYI, I didn't receive a notification for the comment you just wrote. I suspect it is because you put a comma immediately after my name and the @-notification system choked.
Apr
27
comment What is meant by positive and negative gravity/energy/spactimecurvature?
Do you have a reference? It may be easy to interpret the meaning that way.
Apr
27
comment Which Mechanics book is the best for beginner in math major?
Ah! How could I have forgotten this one.
Apr
27
comment Which Mechanics book is the best for beginner in math major?
Did you just say Arnold lacks the soul of a physicist? :-)
Apr
27
awarded  Editor
Apr
27
comment Sewing together flat spacetime pieces = flat spacetime?
@Deepak: ah, I see, you were referring to the last sentence I wrote in my answer. Sorry I wasn't being clear: I meant "sew it back up" in the sense of surgical removal of something, you sew up whatever is left. I changed the wording now and hope it is clearer.
Apr
27
revised Sewing together flat spacetime pieces = flat spacetime?
added 9 characters in body
Apr
27
comment Sewing together flat spacetime pieces = flat spacetime?
@Deepak: My interpretation of the query is not that the you remove a piece and put it back, I interpret it as a generalization of "making a cone": you remove the "pizza slice", eat it, and try to force the remainder together to look like a whole pizza.
Apr
27
comment Which Mechanics book is the best for beginner in math major?
If you are a math major, you maybe able to just start with Arnold's Mathematical methods of classical mechanics
Apr
27
answered Sewing together flat spacetime pieces = flat spacetime?
Apr
27
comment Sewing together flat spacetime pieces = flat spacetime?
@David: You don't even need Jerry's construction. Your statement is only true if every loop is homotopic to zero. So non trivial topologies will give you easy candidates.
Apr
25
comment What exactly is meant by the “Gaussianity” of CMBR?
+1 I've heard a whole semester's worth of seminars on nongaussianity, and no one explained it as nicely.