kenv@dartvax.UUCP (Ken Varnum) (01/11/84)
With all this discussion about the speed of light, I would like to throw in my own question: Does time slow down as as you approach the speed of light, and go backwards if you should invent an FTL drive and go for a quick trip to Proxima Centauri? I would appreciate an answer to this. Ken Varnum (...!decvax!dartvax!kenv)
giles@ucf-cs.UUCP (Bruce Giles) (01/14/84)
No matter what you do, you will not notice any change in how fast time passes for you. However, to an observer who is in another frame of reference, *subject to the condition that both of your frames are inertial* (that is, you are both free from all acceleration and gravity fields), you will appear to be <1>: shorter by a factor of L' = L * sqrt(1-v^2/c^2) <2>: having time dilation by a factor of t t' = -------------- and sqrt(1-v^2/c^2) What this means is that if you (in the first frame) flash a light every second, the other observer will see it every 1/sqrt(1-v^2/c^2) seconds. Similarily, if you pass through a number of `electric eyes' (see below), a length of 1 meter in the first frame will appear to be sqrt(1-v^2/c^2) meters long in the other frame. LIGHT SOURCES * * * * * * * * | | | | | | | | | | | | | | | | | | ============= ->| | | | | | meterstick | | | | | | | | | | v v v v v v v v DETECTORS A very important fact is that these equations are symmetrical. That is, while the second observer sees *you* (the first observer) undergoing length contraction and time dilation, you observe *her* undergoing length contraction and time dilation also. And to each of you, you seem to be perfectly normal. A few of you have probabily heard of the twin paradox, and wonder how it can be reconciled with the above information. In fact, it is an improperly posed question in *special relativity* because in order for the question to have meaning, acceleration must occur. Yet special relativity does not allow for acceleration. --> You must use general relativity to fully understand the solution. (For those of you who think that is a cop-out, when did you stop beating your wife?) Finally, the question concerning FTL cannot be answered in the context of relativity. The theory does not even pretend to be accurate for such conditions, and there is absolutely no experimental data. If you want to claim that everyone turns into toads whenever they use a FTL drive, I won't argue because the discussion is of the form false premise --> any conclusion and such statements are always true in conventional logic. Gimmicks in stories such as Larry Niven's `Known Space' series (i.e., a ship cannot enter hyperspace within a certain (variable) distance from a major mass) may quite possibily be true, but are presently conjecture only. For those with a fairly good mathematical background, I would recommend Wheeler's *Spacetime Physics*. It can be difficult at times, but it covers most of the paradoxes, and (for the masochistic) can be used to lead into Misner/Wheeler/Thorne 's *Gravitation*, a very complete book on general relativity. However, *Gravitation* is at the graduate level, and can easily take several years to understand without help. Bruce Giles --------------------------------------------- UUCP: decvax!ucf-cs!giles cs-net: giles@ucf ARPA: giles.ucf-cs@Rand-Relay Snail: University of Central Florida Dept of Math, POB 26000 Orlando Fl 32816 ---------------------------------------------