js2j@mhuxt.UUCP (sonntag) (10/31/84)
It seems to be well known that Einstien's theories disallow relative
velocities higher than lightspeed. It also seems to disallow passing infor-
mation faster than lightspeed. I would greatly appreciate it if someone
could explain why in language that someone with a couple of years of
college physics and lots of calculus could understand.
I never did like speed limits.
Jeff Sonntag
ihnp4!mhuxl!mhuxt!js2jupen@watarts.UUCP (Li Pen) (11/01/84)
to put it short: Einstein assumed that nothing could move faster than the speed of light. From there he deduced his theories. He redefined simultanuity to the measurable simultanuity, meaning that two events happen at the same time for an observer if he receives the information at the same time at the speed of light. Thus, if something moved faster than the speed of light, it would effectly move backward in time according to Einstein's universe, since the observer could now know something before the event occured in his reference frame. (I'm not going to go into the mathematics of his hyperbolical space-time, but that is the jist of it). Since Einstein's equation seem to be supported by experimental evidence, we assume them to apply in which case FTL would lead to logical contradictions. (moving backwards in time is not very logical). Ue-li Pen Math Undergrad @ University of Waterloo
js2j@mhuxt.UUCP (sonntag) (11/02/84)
> to put it short: Einstein assumed that nothing could move faster than > the speed of light. From there he deduced his theories. He redefined I thought that he concluded, on the basis of the results of the M-M experiment, that observers in ANY inertial frame of reference would measure the same value for the speed of light. Am I totally wrong? > simultanuity to the measurable simultanuity, meaning that two events happen > at the same time for an observer if he receives the information at the same > time at the speed of light. > Thus, if something moved faster than the speed of light, it would > effectly move backward in time according to Einstein's universe, since > the observer could now know something before the event occured in his > reference frame. (I'm not going to go into the mathematics of his Why would an observer knowing something about an event before he received the information via a slow medium like light imply that something had moved backward in time? Could I hear from some other people on this one? The above explanation sounds rather circular: Einstien assumes that nothing can move faster than the speed of light, and is then able to prove that nothing can move faster than C. Jeff Sonntag ihnp4!mhuxl!mhuxt!js2j
herbie@watdcsu.UUCP (Herb Chong, Computing Services) (11/03/84)
The Michealson-Morley (sp?) experiment was not a proof but a confirmation
of the validity of Einstein's hypothesis about the speed of light to the
accuracy of the experiment. There have been at leastfive experiments since
then that have improved the accuracy of this hypothesis several orders of
magnitude. BTW, his hypothesis was that the speed of light was invariant
when observed from any inertial frame of reference. The consequence that
nothing can move faster than the speed of light is a conclusion of several
"thought" experiments that Einstein did whose results are bizarre unless
nothing can move faster than the speed of light. It's been a few years
since I've had to do this so I would have to look in my old physics texts
to remember the details. I believe the experiments had to do with the
concept of simultaneaity and it's interpretation in special relativity.
Incidentally, I know of frame of reference which meets all the criteria
of an inertial one precisely. One can come very close though. Most
problems involving relativity that I've ever had to do needed only special
relativity. General relativity deals with what happens in a reference
frame that has gravity.
Herb Chong...
I'm user-friendly -- I don't byte, I nybble....
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CSNET: herbie%watdcsu@waterloo.csnet
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BITNET: herbie at watdcs,herbie at watdcsurecovert@ihuxf.UUCP (recovert) (11/05/84)
<----->>>> FTL is impossible due to the following: 1) As your velocity increases, your mass also increases. As you approach the speed of light (SOL), your mass approaches infinity. At the SOL, your mass would be infinite. Since, your mass can not be infinite, you can not reach the SOL. Since you cann't reach the SOL, you can not exceed the SOL. 2) Since you mass increases with your speed, the energy required to accelerate also increases. Since (1) says that your mass approaches infinity, therefore the energy required would also approach infinity. 3) As your velocity approaches the SOL, the time elapsed between your world (i.e. your spaceship) and the outside world increases. As the SOL no time would elapse in your ship while infinite time would elapse in the outside world. Carl Sagan had a good series on PBS (in the US anyway), that explained the relativistic effects of moving at speeds approaching the SOL. P.S. I hope that someone would someday discover a way to exceed the SOL, but that would require refuting Einstein's theories. A possible way is the sf-lover's hyperspace (an imaginary space/time continum where you can exceed the SOL). But I leave that solution to the student. -- Richard E. Covert (312) 979-4428 ihuxf!recovert (BTL,Indian Hill)
upen@watarts.UUCP (Li Pen) (11/06/84)
sorry, I forgot to mention that the Michelson-Morley experiment implied constant velocity of light independent of the observer which in turn implies that nothing moves faster than the speed of light. And I admit that using Special Relativity to disprove FTL is like proving that sin(x) lim ------ = 1 x->0 x using l'hopital's rule, which my calculus prof actually did. (you have to know the limit before you can take the derivative of sin(x)) (of course, once you accept special relativity, faster than light travel brings many contradictions)
jlg@lanl.ARPA (11/07/84)
> > to put it short: Einstein assumed that nothing could move faster than > the speed of light. From there he deduced his theories. He redefined > simultanuity to the measurable simultanuity, meaning that two events happen > at the same time for an observer if he receives the information at the same > time at the speed of light. > Thus, if something moved faster than the speed of light, it would > effectly move backward in time according to Einstein's universe, since > the observer could now know something before the event occured in his > reference frame. (I'm not going to go into the mathematics of his > hyperbolical space-time, but that is the jist of it). > Since Einstein's equation seem to be supported by experimental evidence, > we assume them to apply in which case FTL would lead to logical contradictions. > (moving backwards in time is not very logical). > > Ue-li Pen > Math Undergrad @ University of Waterloo He didn't ASSUME that nothing could move faster than light. He assumed that the speed of light was the same in all reference frames. (That is, if you move toward a light source, the light still seems to be arriving at the same speed.) From there he derived special relativity (the form of which had been around for years - but not rigorously developed from first principles). In turn, special relativity implied that something with rest mass (that is, something traveling slower than light) would require infinite energy just to accelerate to c. To go faster than c would require more than infinite energy! If something is found which travels faster than light, it will have imaginary rest mass - whatever THAT means.
gjphw@iham1.UUCP (11/09/84)
Just would like to make two comments about the FTL topic under
discussion. The first is about what changes, or doesn't change, with
velocity and the other is about the origin of the Lorentz
transformation.
One biographer of Einstein wrote that Albert's primary interest in
exploring relativity was to discover which properties remained
invariant at high speeds. He was interested more in what does not
change than what does change with velocity (reflecting most physicists'
interest in constants of nature). If you consider that theories in
physics can be organized in a hierarchy, from the very concrete such as
electrons to the very abstract such as unified field theories,
Einstein's special theory is an example of a theory formulated
primarily by considering the concepts surrounding an issue and not by
appeal to experiment. The special theory resolves a conflict between
Maxwell's equations for electrodynamics and Newton's laws of dynamics.
Albert said that he was not aware of the Michelson-Morley experiments
(doubtful) but rather concentrated on resolving conflicts and seeking
invariants.
In Maxwell's equations, electric charge is invariant and other
properties (e.g., magnetism) are velocity dependent. Similarly, from
Newton's dynamics, mass is the invariant quality with momentum and
energy being velocity dependent (above the Newtonian expressions).
With this convention, as it is being used in the search for grand
unification theories, mass does not change with velocity but momentum
does. Even with mass being a constant, the velocity of light in a
vacuum still remains a limit for motion as has been amply described in
many recent submissions.
Related to the faster-than-light discussion is the origin of the
Lorentz transformations. Lorentz, the foremost physicist at the time,
was deeply interested the properties of light at different velocities.
The behavior of light traveling through lengths of rapidly flowing
water was carefully studied for many years before Lorentz wrote down
his equations governing contractions and transformations. These
equations depended upon the speed of light in the medium and the motion
of the medium.
Virtually at the same time, Einstein wrote his special theory and
named the transformation equations after Lorentz thinking that they
had already been derived. In fact, the equations had been derived for
light traveling through a medium, did not reference the speed of light
in a vacuum, and did not include time as a variable parameter. Today,
with the outstanding success of Einstein's formulation, we often
overlook how close Lorentz (from an experimental perspective) and
Poincare (from a mathematical-conceptual perspective) were to
formulating special relativity.
--
Patrick Wyant
AT&T Bell Laboratories (Naperville, IL)
*!iham1!gjphwgwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (11/09/84)
> And I admit that using Special Relativity to disprove FTL is like > proving that > sin(x) > lim ------ = 1 > x->0 x > > using l'hopital's rule, which my calculus prof actually did. (you have > to know the limit before you can take the derivative of sin(x)) Oh, really? I thought all you had to know to take the derivative of sin() was the sine-of-sum-of-angles formula.