# Relative speed question

From all of the literature that I have read, I’ve gathered that as a person travels faster, other people will perceive time more slowly. For example, if a person goes close to the speed of light and comes back to earth, everyone there will be much older than when the person left.

So lets say a person goes to the moon (or another set distance) and back at close to the speed of light. When he comes home, everyone there has aged a lot. How fast in mph was he really going? I’m confused.

Or are sci-fi books full of s***

The faster you go, the more time slows down for you (relative to things which are not moving so fast) - so it’s not that the people at home would age faster, it’s that you would experience time more slowly (i.e. less of it) than the non-travellers; so they will seem older than they should be when you return.

It’s not actually possible to travel at the speed of light, but if you could, you would experience no time at all during the journey.

Travelling to the moon and back at the speed of light would only take a few seconds; ignoring the practical complications of this, the most time you could ‘lose’ from doing this would be those few seconds; you might have to reset the second hand on your wristwatch, nothing more.

I’m still confused. Say you travel near the speed of light for fifty years, and then return home. You’d experience very little time, while the people on earth would experience fifty years. So your speed would vary in mph between you and earth, because from your perspective you’ve covered distance x in a few minutes, while from earth’s perspective you’ve covered distance x in 50 years. So the speed changes.

Yes. Speed is distance over time, and time is different for the traveller and the observer. So the “miles per hour” speed is dependent on who’s hour you’re talking about.

It all goes back to Einstein, who says that there are no privileged reference frames. IOW, the reference frame you are inhabiting is true but so is the reference frame in which people are moving at a different speed. It’s only when you put the two back together that you discover that there is a discrepancy in the way that elapsed time is perceived. The discrepancy is real; there is no way that it can be reconciled. Even so people in each reference frame experienced time moving at the standard one second per second at every instant. This is one major reason it is called relativity theory. Time and space are relative to the one absolute, the Einstein contant C, the theoretical absolute speed of light.

Expano Mapcase mentioned this but I think it bears being pointed out again.

If you travel for fifty years at very near the speed of light you will have aged 50 years. From your perspective in the spaceship everything seems normal. Time moves at 1 second per second. Everything works just as you see things work now. What will surprise you is when you return to earth 50 years (from your persepctive) later. The folks on Earth will have experienced hundreds (or more…someone would have to do the math) of years passing. To them you are ancient history.

Note that this time dilation is not in the realm of sci-fi. This has been experiementally verified. IIRC the astronauts aboard the Mir spacestation for six months clocks were 3 seconds behind those on earth upon their return (that was not the experiment but gives you a sense of these things). Also note that time dilation only becomes really noticeable when getting very close to the speed of light. 50% light speed does not see a 50% time dilation. Someone who understands the math better can maybe explain that better.

Actually, relative speed is one of the few things both frames can agree on. What you don’t agree on is distance X. For instance, suppose you travel from here to Vega and back, at 99% the speed of light. Observers on Earth would measure the distance you travel as 52.8 lightyears, and would time the trip as taking 53.3 years. From your persepective, though, the trip only takes 7.52 years, and you only cover a distance of 7.45 lightyears. In both cases, though, your speed relative to Earth (or Earth’s speed relative to you), is .99c .

Einstein was a lot smarter that I thought he was, I’ll give him that. But he’s got nothing on my hair :). Thanks for the replies. I think I understand better now.

As best as I recall, relatavistic speeds / times involve SQRT ( 1 - v[sup]2[/sup]/c[sup]2[/sup] ), where v is your speed in your reference frame, and c is lightspeed in free space. As Exapno Mapcase noted, Einstein’s theory of relativity holds (in part) that c is a constant in all reference frames.

I’d suspect that they were actually ahead, although 3 seconds doesn’t seem too many orders of magnitude off.

Because there’s another time-dilation effect: gravity also slows down time. Mir station experiences less gravity so time speeds up for her: this effect dwarfs the effects of non-relativistic speeds.

Here is a page from my website:
http://www.1728.com/reltivty.htm
It has the formula and a calculator for determining the time dilation amount.
For example, if you are travelling at 50% the speed of light (which is very fast), 1 year to you is like 1.1547… years to your friends back on Earth.

It doesn’t actually dwarf the speed effect; as I recall, it’s exactly twice as large. But yes, it is significantly larger, and in the opposite direction.

Minor but meaningful nitpick: It’s not like 1.1547… years to them, it is 1.1547… years to them. There’s nothing subjective about relativity.

Chronos
Like you are right. (You certainly are worthy of that SDSAB title).

I stand corrected … and thanks.

Since the OP has been answered, I hope this hijack will be excused:
What determines which time runs slower? If I move away from earth at 0.99c, everybody tells me that my time runs slower. But what determines that I move and the earth stays put if no reference frame is special? Why can’t my time be the “correct” one and earth’s time run slower?

Just as there’s no fixed frame of reference, there’s no universal clock, no “correct” absolute time. As far as you’re concerned, you left Earth a year ago. As far as the people on Earth are concerned, you left fifty years ago. It’s all good.

AFAIK, it is which frame is doing the acceleration that determines which time runs slower relative to the other. Sure, you might be in the fast spaceship and to you it looks like Earth is accelerating away from you, but you are the one experiencing the acceleration (i.e. pulling some major G’s – it would take around a year to accelerate to around C at one G!) Earth on the other hand is not experiencing that acceleration.

I can understand how that argument applies during the acceleration, but doesn’t the effect last as long as you move, even if you don’t accelerate any more?

If it helps the discussion, there’s a decent treatment of the Twin Paradox from several conceptual angles in the Sci.physics FAQ.

If you just leave Earth at high speed never to return, then you’ll say Earth’s clocks are running slow, and the Earthlings will say that your clock is running slow, and you will both be equally correct: In your reference frame, the Earth clocks are running slow, and in Earth’s reference frame, your clocks are running slow. This may be counterintuitive, but unless you actually meet up again to compare, there’s no contradiction.

And if you do meet up again, that means that at least one of you must have changed reference frames. In the typically-discussed case, the astronaut flies off to Alpha Centauri and returns. In this case, you can’t just talk about “the astronaut’s reference frame”, because the astronaut doesn’t have a reference frame, he has (at least) two. The fact that the astronaut changed reference frames, but the Earthlings didn’t, introduces an asymmetry into the problem.