On GR and Interstellar exploration

owenhbrown
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Hello folks,

I was wondering about a possible probe sent to alpha centauri which would be able to do a deep scan of the system, maybe for a month, and then send back results.

I then wondered, that if the probe was exposed to different gravitational conditions, let's say favourbly, would information come back sooner than we expected because of a difference in time perception?
 
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Alpha centauri is 4.3 light years away. A signal sent back to Earth from a probe near that star would take 4.3 years to get here.
 
My question is regarding time spent scanning the system, not time traveling there or back.

I am asking that if the probe is given a month to scan the system, is it possible that, because of relative time, it may require less or more than an Earth month to complete the scan, because the same length of time time near Alpha Centauri moves faster or slower relative to us.

So you see, the issues of interstellar travel were not brought up.
 
Time runs slower for clocks deeper in a gravity well, so the only situation in which an observer measures a distant clock to run faster due to gravitational time dilation is if the observer is closer to a source of gravity than the clock. I'm pretty sure the gravitational time dilation from the Earth and Sun is too small to make any significant difference in the rate of local clocks vs. distant clocks, but if you imagine an observer on a ship very close to a black hole who is receiving signals from a probe far from the black hole, she could see the signals appreciably sped up.
 
To give an idea of how small the effect would be, if the probe were to land on the surface of a very small and dense neutron star we might find that it takes 2 months to complete its scan.
 
OK, so this has bugged me for a while about the equivalence principle and the black hole information paradox. If black holes "evaporate" via Hawking radiation, then they cannot exist forever. So, from my external perspective, watching the person fall in, they slow down, freeze, and redshift to "nothing," but never cross the event horizon. Does the equivalence principle say my perspective is valid? If it does, is it possible that that person really never crossed the event horizon? The...
ASSUMPTIONS 1. Two identical clocks A and B in the same inertial frame are stationary relative to each other a fixed distance L apart. Time passes at the same rate for both. 2. Both clocks are able to send/receive light signals and to write/read the send/receive times into signals. 3. The speed of light is anisotropic. METHOD 1. At time t[A1] and time t[B1], clock A sends a light signal to clock B. The clock B time is unknown to A. 2. Clock B receives the signal from A at time t[B2] and...
From $$0 = \delta(g^{\alpha\mu}g_{\mu\nu}) = g^{\alpha\mu} \delta g_{\mu\nu} + g_{\mu\nu} \delta g^{\alpha\mu}$$ we have $$g^{\alpha\mu} \delta g_{\mu\nu} = -g_{\mu\nu} \delta g^{\alpha\mu} \,\, . $$ Multiply both sides by ##g_{\alpha\beta}## to get $$\delta g_{\beta\nu} = -g_{\alpha\beta} g_{\mu\nu} \delta g^{\alpha\mu} \qquad(*)$$ (This is Dirac's eq. (26.9) in "GTR".) On the other hand, the variation ##\delta g^{\alpha\mu} = \bar{g}^{\alpha\mu} - g^{\alpha\mu}## should be a tensor...
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