• #### Re: Fast pennies

From J. J. Lodder@21:1/5 to wugi on Sat Jan 20 13:20:15 2024
wugi <wugi@brol.invalid> wrote:
[from spr]
Op 15/01/2024 om 22:10 schreef Stefan Ram:
What would happen if a penny with a mass of 0.003 kg and a speed of

0.99999999999999999999999999999999999999 c

from outer space would hit the earth (being directed at its center)?

[[Mod. note --
There are 38 9's in that speed, i.e., the speed is (1 - 1e-38)*c.
That implies a Lorentz gamma factor of (1 - v^2/c^2)^(-1/2) = 7e18,
so the penny's total relativistic energy is gamma*m*c^2 = 2e33 Joules. That's rather a lot of energy. :) In fact, it's about 8 times the
Earth's gravitational binding energy (2.5e32 Joules according to the all-knowing Wikipedia).

So, the tricky question is, how much of the penny's energy would go
into disrupting the Earth, versus how much would go into kinetic energy
of whatever came out the other side?

And finally, I'll note that (IMHO not superb, but still an enjoyable read) the 1993 science-fiction novel "Flying to Valhalla", by Charles Pellegrino,
is based on a similar question.
-- jt]]

Wouldn't it pass almost unnoticed through the Earth? The reaction time
with whatever obstacles it encounters would exceed largely its time of passing by, so there would be hardly "explosive information" passed on
to them, or would there?

Au contraire, it would hardly penetrate, at first.
The localised explosion it produces will destroy all of the Earth
though, in a few milliseconds. (at the speed of light)

All this is utterly unrealistic of course
Conditions like these could have been found
very early in the Big Bang perhaps,
at energies that are many orders of magnitude out of experimental range.
We don't know the laws of physics that would apply,

Jan
(sorry, not posting in spr)

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