Quote:
Originally Posted by billdan
Hi Steven,
I'm not questioning your formula that you used, but I find it hard to believe it takes nearly 2 Billion years for an observed object to travel 20Km falling into a black hole.
If you had said it was 20 Sec's vs 16 Sec's, I would have said that sounds reasonable.
I understand that it is from a close observers point of view where time slows down, but its still mind boggling.
Regards
Bill
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Bill,
The result looks quite incredulous but at or near the event horizon, time literally stands still to an observer outside the gravitational well.
To this observer photons emitted from the object are infinitely red shifted, and if it was possible to observe the object it would be forever stuck on the event horizon without passing through it.
The falling object on the other hand would freely pass through the horizon.
If the object is a clock and assuming it is not destroyed by tidal forces, the maximum proper time elapsed during the 20 km fall is given by the equation.
http://members.iinet.net.au/~sjastro...propertime.gif
This works out to being about 6.67 X 10^-5 seconds.
Over this distance in the vicinity of the event horizon the object is travelling at around 0.995c.
The differences are quite staggering when comparing the clock's proper time to the elapsed coordinate time of 1.94 X 10^9 years when measured by an outside observer
On a much more subtle scale we observe these effects in our own backyard.
The
Shapiro time delay is one such example.
Steven