west@sdcsla.UUCP (Larry West) (11/05/84)
mhuxt!js2j asked: "Could someone explain why FTL is illegal? In small words?"
I sent a mail response, but it occurs to me that others may be interested;
also, I'd be interested in criticism of my reply: is it clear? convincing?
correct? And if not, why not? [Reply by mail, please.] (I know this
is a little long-winded, but my intention is to make it easy to follow.)
References: <327@mhuxt.UUCP> <8130@watarts.UUCP> <333@mhuxt.UUCP>
Einstein's Special Relativity (1905) was founded on two postulates:
1) Absolute uniform motion cannot be detected;
2) The speed of light is independent of the motion of
the source.
The postulates were inspired by the fact that light waves propagate in
a vacuum (as predicted by Maxwell's equations), which is really a fairly
strange thing for waves to do -- normally waves are simply disturbances
(compression/expansion) of the media through which they propagate.
This lack of a medium means there's no absolute reference to compare
the speed of light against (as verified by Michelson & Morley (1887)).
Contrast this with sound waves, which can always be compared to the medium
in which they travel.
The second postulate is the most direct blow against Faster Than Light
motion, so let's do a little thought experiment to see why it is
reasonable.
So (without relativity), if you have two observers moving relative to
each other, and they measure different speeds of light, which would be
correct? For example, if observer "A" (female) is moving toward Earth
at 100,000 km/sec, and observer "B" (male) is on Earth, and they each
(simultaneously) shoot a 1-second laser pulse at the other:
A--> <--B (approaching at 100,000 km/sec)
[Presumably they have synchronized their watches and agreed beforehand
on when to fire their lasers, and they time the interval between when
they fire and when they receive the other's light pulse.]
A would (in non-relativistic Universes) see the light from B moving
at a speed greater than the speed of the light which she sent to B.
A: "My light pulse left at 300,000 km/sec, but I measure B's
pulse as approaching me at 400,000 km/sec."
B: (ditto)
So A would expect her pulse to reach B after B's pulse reached her.
And likewise, B would see A's light moving faster than B's own pulse.
A: "Since B's pulse left at the same time as mine, and his
pulse is traveling faster, he must have received my pulse
after I received his."
B: (ditto, change gender of pronouns)
When they meet, each believes the other's light was travelling
faster, and thus that the other one will have recorded a longer
time-interval between firing and detection.
Thus we arrive at a contradiction, and hence one (or more) of our assumptions
is incorrect. And the best way of resolving this (and other problems
which arise from similar thought experiments) is Special Relativity, which
posits those two postulates given above.
Note that this contradiction would not occur with sound waves, because the
medium (air, water, whatever) enters into the matter [so to speak], and
essentially provides an absolute frame of reference (and the easiest one to
calculate in).
{Of course, a relativistic explanation of the above would not be nearly
as simple, since simultaneity and synchronization are out, and so forth.}
So, no faster than light travel, unless you can find some other
assumption (besides "speed of light is relative to observer/source")
to give up -- and if you do, no need to broadcast it to the net --
let's talk it over, and I'll make the plane reservations to Stockholm.
Hope this was worth your time in reading through it.
-- Larry West, UC San Diego, Institute for Cognitive Science
-- UUCP: {decvax!ucbvax,ihnp4}!sdcsvax!sdcsla!west
-- ARPA: west@NPRDC {{ NOT: <sdcsla!west@NPRDC> }}
--
-- Larry West, UC San Diego, Institute for Cognitive Science
-- UUCP: {decvax!ucbvax,ihnp4}!sdcsvax!sdcsla!west
-- ARPA: west@NPRDC {{ NOT: <sdcsla!west@NPRDC> }}mike@amdcad.UUCP (Mike Parker) (11/10/84)
> > > So (without relativity), if you have two observers moving relative to > each other, and they measure different speeds of light, which would be > correct? For example, if observer "A" (female) is moving toward Earth > at 100,000 km/sec, and observer "B" (male) is on Earth, and they each > (simultaneously) shoot a 1-second laser pulse at the other: > > A--> <--B (approaching at 100,000 km/sec) > > [Presumably they have synchronized their watches and agreed beforehand > on when to fire their lasers, and they time the interval between when > they fire and when they receive the other's light pulse.] > > A would (in non-relativistic Universes) see the light from B moving > at a speed greater than the speed of the light which she sent to B. > > A: "My light pulse left at 300,000 km/sec, but I measure B's > pulse as approaching me at 400,000 km/sec." > B: (ditto) > > So A would expect her pulse to reach B after B's pulse reached her. > And likewise, B would see A's light moving faster than B's own pulse. > > A: "Since B's pulse left at the same time as mine, and his > pulse is traveling faster, he must have received my pulse > after I received his." > B: (ditto, change gender of pronouns) > > When they meet, each believes the other's light was travelling > faster, and thus that the other one will have recorded a longer > time-interval between firing and detection. > > > -- Larry West, UC San Diego, Institute for Cognitive Science Ah, Excuse me, but, you see, I'm new to the net and I don't understand. All this talk about boys and girls ( men and woman, if you insist ) and how fast their pulses are. I thought I was reading net.singles but this shooting at each other with lasers sounds rather aggressive. Is there a group for S&M?????? Mike at AMD