From: Lee Corbin (firstname.lastname@example.org)
Date: Sat Apr 19 2003 - 10:59:29 MDT
> In special relativity, I view myself as still always. I see the other
> guy as moving. Since I see him as moving, I view him as having
> kinetic energy. (I must admit I'm not entirely clear on the notion of
> measuring space without reference to objects within the space...)
In your frame of reference, he *does* have kinetic energy. This is
sort of compensated for by the fact that physical processes take
more time to complete than they would if they weren't moving relative
> BTW, this is why in special relativity, if I have two objects that
> have time bombs on them that will blow them up after ten seconds
> (relative to the local frame of reference), and we send one of them at
> high speed past the other, the observer on each of the objects
> perceives himself as still, and therefore sees time as dilated for the
> other guy, so both think the other blows up first.
Actually, each "thinks" that the other blows up *after* his. Bertrand
Russell used to say that one problem with special relativity was that
the other man's cigar appeared to last longer than one's own. I put
"thinks" in quotation marks, because sometimes people suppose that there
is some sort of error involved, or that it's subjective. No, the
processes really do slow down, there is no "thinks" about it, nor
is there anything subjective about it. There are just different
frames of reference, which isn't really the same thing.
> Ah, but I was under the impression that the average geometry of the
> expanding universe we're in is flat...
I wish I knew. But I'm all for it! ;-)
> Under General Relativity spacetime is not flat; it can be curved
> and, in fact, can be expanding. [Right] Imagine a balloon covered
> in raisins. As you blow up the balloon, the raisins get farther
> apart; this is inflation.
Well, this is really known as the expansion of the universe. The
term *inflation* is usually reserved for a peculiar era early in
the history of the universe when expansion was unbelievably rapid.
> The local speed of any raisin can never exceed c, but it's
> also possible that if two raisins start out 186,000 miles
> apart and motionless relative to each other, a ray of light
> starting from one raisin to the other will not have reached
> the second raisin one second later because of the expansion
> of space in the meanwhile. If you pick two sufficiently
> distant points on the balloon, it may be that even if the
> two raisins are motionless relative to each other, a ray
> of light from one can never reach the other because the
> balloon is inflating too fast.
That's exactly correct. But the phrasing raises a new question
for me. Are we simply forbidden to ask what is the relative
velocity independent of expansion of two remote objects? I mean,
is there some subtle sense in which the question is not supposed
to make sense?
The best guess I have goes like this. Claim: you can measure
(approximately) your velocity with respect to the big bang.
You just average out the frequencies in the various directions
of the Cosmic Background radiation. Then you might be able to
assert that you are at rest with respect to the big bang. Then
suppose that the other party over the horizon (i.e. light can
never reach you from him unless the universe starts to contract)
is also at rest relative to the big bang, but the space is
expanding between you and him at so many light-years per second.
Then he is also at rest relative to you (except for expansion).
Then is there a combined, unified frame of reference so that
your clock and his run at the same rate!? That is, is there
Special Relativity at a distance?
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