art@ACC.ARPA (11/19/85)
>> As one approaches the speed of light, the rate that time passes in one >> frame of reference (like a spaceship) as "observed" from the other >> (say on Earth) approaches zero. >What happens if two ships leave with opposite vectors, and they both approach >the speed of light relative to their initial frame. The v above, relative to >each other, would approach 2*c, giving a non-real answer. Where am I goofing? >(Or is it time to invest in a FTL ship? :-) ) [I'll try my best, but I'm not a physicist] Here one has to examine which frame of reference that the velocities are measured in. If two ships leave the Earth in opposite directions, then both ships will be "seen" to travel at some speed less than "c" in their respective directions by an Earthbound observer. The Earthbound observer will also "see" the clocks on each ship slow down due to time dilation. If we change the frame of reference to be on either ship, then the other ship will be "seen" to be traveling at a somewhat greater velocity than "seen" from Earth, but STILL LESS THAN "c". As seen from Earth, each ship's clock is slow, and will therefore measure a lower velocity for the other ship than the Earth based clock. As seen from a ship, the velocity of the other ship, measured using the Earth based clock is also lower, because the Earth based clock is perceived to be slower. From what I've read, the "Twin Paradox" is most properly dealt with in General Relativity, because at least one of the frames of reference is ACCELERATED. Special Relativity really deals with relationships between Inertial (non accelerated) frames of reference. In the case of the "Twin Paradox", for two observers to agree, they must both have experienced the same measurable "Events". An Earthbound Twin only experiences the ship departure and return. The spacefaring twin also experiences the acceleration event, and therefore the situations are not symetric. For two spacefaring twins who take identical but opposite trips, I believe that their ages will agree. Finally think about what "Measuring velocity" entails. How does one establish the "distance" between any two remote points? "When" does a ship pass such a point (any signal telling us is limited to speed of light)? On the cosmic scale, one cannot deal with time and distance independently. Art@ACC.ARPA ------