carroll@uiucdcsb.CS.UIUC.EDU (11/13/85)
For math types, the important quantity is sqrt(1-(v/c)**2). If we call that R, then time, mass, and length change as follows, from the viewpoint of someone on EARTH! Please note, everything depends on who is the observer. T' = T * R M' = M / R L' = L * R Where T',M',L' are what you see while the voyagers are traveling rapidly, and T,M,L are what they were just before they left. So, when v is close to c, one hour on Earth (T) becomes a very small amount of time on the ship (T'). The inevitable question is: "I thought it was all relative, why don't the voyagers see Earth as running slow in time?", or the Twins Paradox. The answer is that someone (the voyagers) accelerated, and the other people didn't, and that distinguishes them. Accleration and gravity slow down clocks too, just like high speeds.
bl@hplabsb.UUCP (11/14/85)
> > For math types, the important quantity is sqrt(1-(v/c)**2). If we call that > R, then time, mass, and length change as follows, from the viewpoint of > someone on EARTH! Please note, everything depends on who is the observer. > T' = T * R > M' = M / R > L' = L * R > > Where T',M',L' are what you see while the voyagers are traveling > rapidly, and T,M,L are what they were just before they left. So, when v > is close to c, one hour on Earth (T) becomes a very small amount of time > on the ship (T'). The inevitable question is: "I thought it was all relative, > why don't the voyagers see Earth as running slow in time?", or the Twins > Paradox. The answer is that someone (the voyagers) accelerated, and the other > people didn't, and that distinguishes them. Accleration and gravity slow > down clocks too, just like high speeds. OK, lets rephrase the question. The two twins get into identical space ships and accelerate at the same amount but in opposite directions. What do they observe about the other?
jabusch@uiucdcsb.CS.UIUC.EDU (11/16/85)
The twins don't observe anything about each other, because they can't see through spaceships :)
carroll@uiucdcsb.CS.UIUC.EDU (11/17/85)
They see the same thing as the equations describe, if you assume that they don't spend much of their time accelerating. Each sees the other as "running" slower than he is, based on their relative velocity (which would be twice that of a "stationary" observer). You may say, "Wait, that's not possible. They can't both see the other as running slower", but it is, if you realize that there is NO universal "present". The "present" for each of the twins has is different in different regions of space. The only time people can agree on what time it is is when they are both in the same inertial frame, i.e. at rest with respect to each other and not-accelerating. There is a good book by Einstein about this, I will try to find the name of it, but I think it's just entitled "Relativity". Please note: There are two theories of relativity. The Special case deals only with relative motion in inertail frames (non-accelerating (so called "inertial" because Newton's laws (of inertia) are accurate in one)). General Relativity deals with acceleration, gravity, and other things, but is widely complex. (In fact, my friend the physics major tells me that it has only been tested to first order approximations, because the effects are hard to compute and very hard to test).
henry@utzoo.UUCP (Henry Spencer) (11/17/85)
> OK, lets rephrase the question. The two twins get into identical space ships > and accelerate at the same amount but in opposite directions. What do they > observe about the other? When and how do they do the observing? Special Relativity states firmly that "simultaneous" is a meaningless word at any distance. To get the twins to agree on timing, you will have to get them back together again. -- Henry Spencer @ U of Toronto Zoology {allegra,ihnp4,linus,decvax}!utzoo!henry
mcgeer@KIM (Rick McGeer) (11/18/85)
>> >> For math types, the important quantity is sqrt(1-(v/c)**2). If we call that >> R, then time, mass, and length change as follows, from the viewpoint of >> someone on EARTH! Please note, everything depends on who is the observer. >> T' = T * R >> M' = M / R >> L' = L * R >> >> Where T',M',L' are what you see while the voyagers are traveling >> rapidly, and T,M,L are what they were just before they left. So, when v >> is close to c, one hour on Earth (T) becomes a very small amount of time >> on the ship (T'). The inevitable question is: "I thought it was all relative, >> why don't the voyagers see Earth as running slow in time?", or the Twins >> Paradox. The answer is that someone (the voyagers) accelerated, and the other >> people didn't, and that distinguishes them. Accleration and gravity slow >> down clocks too, just like high speeds. >OK, lets rephrase the question. The two twins get into identical space ships >and accelerate at the same amount but in opposite directions. What do they >observe about the other? If their roles are symmetric, then clearly neither twin is preferred: when they meet again, *so long as their roles have been prefectly symmetric* (identical accelerations, identical velocity vectors (in magnitude) wrt to a third observer, identical trip times, again wrt a third observer) they will be the same age. Let's consider the following: let's suppose that the twins (call them Harold & Maude) leave from Earth and head for planets P & Q, each of which are 8 light years from Earth in radially opposite directions. Harold & Maude travel at .8 c, and acceleration and deceleration times are negligible and can be ignored. They return immediately. OK. For each, 1-v^2/c^2 = .36, hence tau = .6. Hence the distance for each of them are foreshortened by an identical amount, namely to 4.8 light years. At a velocity of .8c, they reach the planets in six years, by their own clocks, return in an identical time, and have each (according to their own clocks) aged 12 years. According to an observer of earth, 20 years have passed. But while their roles have been symmetric, each believes the other has been aging very strangely. Suppose H & M, before they leave, agree to send a signal to the other at the end of each year. Since their roles are symmetric, we need only consider Harold. Maude's velocity relative to him is 1.6c/1.64 ~= .975c Hence, by the Doppler effect, Harold will receive .113 flashes/year on the outbound trip. Hence (according to Harold) Maude has aged only .678 years on his outbound trip... Then Harold turns around. He still hasn't received 5.322 of Maude's outbound flashes. Now, he's moving with speed zero relative to Maude *when she fired the flashes*. Hence, 0 doppler effect. Hence, for the first 5.322 years of his return voyage he gets a flash a year. Now Harold starts to pick up the flashes Maude sent on the inbound journey. Her velocity relative to him is -.975c, which means that the frequency of the flashes is now 1/.113 flashes * year, or 8.84 flashes/year, which means that over the last .678 years of his trip Harold picks up six flashes from Maude. Of course, Maude perceives exactly the same phenomenon... To summarize: Harold thinks Maude aged .678 years though the first six years of his trip. Harold thinks Maude aged 5.322 yrs. through the next 5.322 years Harold thinks Maude aged 6 years during the last .678 years of his trip. and Maude thinks the reverse. Who's right and who's wrong? Well, neither and both: the key thing is that events separated by space can't be temporally compared. -- Rick.
john@frog.UUCP (John Woods, Software) (11/21/85)
>>OK,lets rephrase the question. The two twins get into identical space ships >>and accelerate at the same amount but in opposite directions. What do they >>observe about the other? >When and how do they do the observing? Special Relativity states firmly that >"simultaneous" is a meaningless word at any distance. To get the twins to >agree on timing, you will have to get them back together again. > Henry Spencer @ U of Toronto Zoology > To use the standard example, each twin has a radio transmitter that emits a tick every second. Each twin has a receiver which counts the times between the other twin's ticks. Because the twins are separating, you expect a certain increase in time between ticks, because the radio pulse has slightly farther to travel each time. However, Relativity predicts that after you take that into account, each twin will perceive the other twin's ticks as being slower than the clock of the receiving twin. I recently read Bertrand Russell's book, "Relativity", and enjoyed it quite a bit. Though I already knew the equations of Relativity (the simpler ones, anyway, I didn't delve deeply into it in college), his book gave me a great deal more insight into *why* the equations really work. -- John Woods, Charles River Data Systems, Framingham MA, (617) 626-1101 ...!decvax!frog!john, ...!mit-eddie!jfw, jfw%mit-ccc@MIT-XX.ARPA Out of my way, I'm a scientist! War of the Worlds