In theory of relativity two events that happen at the same time in one system do not necessarily happen at the same time in another system. For example: if I see that you are much younger than me, it does not mean you see me much older, because the two events (A: me watching and B: you being observed) are not simultaneous in your system.The guy at rest will see the watch of the moving guy running slow. But each has to age according to his own clock, so the moving guy is seen as aging slower. But how to do the comparison of ages? See the "twin paradox" in ZapperZ's reference.
Now, think about the fact that each guy sees the other as moving, so each sees the other's watch as running slow. But how can they both see the other as aging slower?
It's a perfectly valid question. You need to use the relativistic addition of velocity formula, explained here: http://www.phys.ncku.edu.tw/mirrors/physicsfaq/Relativity/SR/velocity.html" [Broken])Can I as a follow-up (dummie) question?
Simply put - If I stand at a point in space and send my friend A East at 60% the speed of light (.6c), and then send my friend B West at .6c - both of these seem feasible for me. What speed are they travelling relative to each other?
Is this even a valid question?
Whenever you mention distance or time you must specify the frame in which the measurements were made. In this case the frame is that of one of the moving ships. According to ship A, after 1 year ship B will have traveled 0.88 light years with respect to ship A.i guess im still not getting it, but if 2 objects depart in opposite directions both objects are moving at .6c from origin; how can there only be a distance of .88 light years between them after one year of travel?
If you measure their travel with respect to the original frame (the frame in which the ships travel at 0.6c), then according to that frame the ships will each travel 0.6 light years in 1 year.if you only recorded the distance of one of those objects after a years time would it still have traveled .6 lightyears?
Right. According to the outsider's observations, the ball separates from the thrower at a rate of 0.175c.So if the train goes at a speed X, and you throw a ball at Y, you see the ball going away from you at Y, but the outsider not on the train does NOT see the ball moving away from you at Y, but at a value (slighlty) less than Y because you and the ball are both moving relative to the person outside the train (and time dilates some for you and the ball relative to the observer). Indeed if your train moves at .8c relative to me, and you throw at .8c relative to you, I see the ball moving away from you at much less than .8c (if I calculate correctly, it would be seen to be moving away from you at 0.175c)... yeh?
The clocks are synchronized in the frame of the road, but not according to the frame of the moving car. And the distance between those clocks is less according to the frame of the car.Suppose we have a long road. every 150,000 km (93,000 miles) along the road there is a clock, and above it a high resolution camera. The clocks are numbered, 1, 2, 3....100. All clocks are synchronized.
OK: Both car clock and road clock #1 read exactly 9am when they pass each other.A car is riding along the road, at half the speed of light (150,000 km/sec) relative to the road. On its roof a big clock, and a high resolution camera.
Every time the car pass by a clock, the cameras in the car and on the road takes a picture of both clocks: the one on the road and the one in the car.
The question is: If at clock #1 on the road, both pictures from the cameras, the one on the road and the one on the car, will show exactly 09.00.0000000, what will they show in clock 2, and 3?
Of course there is time dilation. Each frame views the other's clocks as running slow. The car sees the road clocks as running slow and the road frame observers see the car clock as running slow. What's the problem?If you think that there is time dilation, remember that relative to the car, the road is the one which is moving, and since unlike the twin paradox, no acceleration is involved, which clock will slow down?
At clock number n the clock on the road will show 09:00 plus [tex]n\,1\,s[/tex]The question is: If at clock #1 on the road, both pictures from the cameras, the one on the road and the one on the car, will show exactly 09.00.0000000, what will they show in clock 2, and 3?
Your question has been answered but maybe you should have also asked how that answer adheres to time dilation (and length contraction). Although this was pointed out, it didn't "click" with you so let me try to explain it in more detail.Thanks for the answer, but I do not believe you answered what I asked.
The question was: "what will the pictures from both cameras, the one in the car, and the one on the road will show?"
An answer could be: At clock 1, the picture from the camera above the clock will show 090001 at the road's clock, and 09000086 at car's clock. and at clock 1, the picture from the car will show 0900001 at the car's clock and 09000086 at the road's clock.
try to answer it, and see if you do not run into a problem.
I did answer. Both photos will show the same, of course. (Sorry if that wasn't clear.) As I said, the time on road clock #2 will show 1 sec after 9 (or 9:00:01 if you prefer) and the time on the car clock will show 0.866 sec after 9 (or 9:00:00866).Thanks for the answer, but I do not believe you answered what I asked.
The question was: "what will the pictures from both cameras, the one in the car, and the one on the road will show?"
An answer could be: At clock 1, the picture from the camera above the clock will show 090001 at the road's clock, and 09000086 at car's clock. and at clock 1, the picture from the car will show 0900001 at the car's clock and 09000086 at the road's clock.
Obviously I had no problem answering it. Where do you see a problem?try to answer it, and see if you do not run into a problem.
Rather than play mindreading games, I like to answer the actual question asked as directly as possible. (And then see what that leads the questioner to ask next.)On a side note, every question isn't an opportunity to flex intellectual muscle. Second, something like the following exchange :
OP: "Thanks for the answer, but I do not believe you answered what I asked."
Reply: "I did answer. Both photos will show the same, of course. (Sorry if that wasn't clear.) As I said, the time on road clock #2 will show 1 sec after 9 (or 9:00:01 if you prefer) and the time on the car clock will show 0.866 sec after 9 (or 9:00:00866)."
It's as if you two are working from two different "frames" lol. Of course, (and sorry if I'm not clear) the one answering the question, doesn't know if the question has been answered. Only the one asking does. It's almost as if the one answering the question has to put themsleves in the same "frame" as the one asking. In not so many words, put yourself in their shoes. This is particularly obvious for a question pertaining to relativity.
Just because the one asking the question does not understand the answer does not mean that the question was not answered.Of course, (and sorry if I'm not clear) the one answering the question, doesn't know if the question has been answered. Only the one asking does.
Nothing unclear about that. (Im guessing we're talking about the books that clocks read after passing a certain school grade)Rather than play mindreading games, I like to answer the actual question asked as directly as possible. (And then see what that leads the questioner to ask next.)
Like so:
Question: What do the clocks read when they pass?
Answer: One clock reads XXX, the other reads YYY.
What's unclear about that?
(Note that the first part of your post was a response to a question asked over three years ago.)