# Close to the speed of light relative to what?

1. Dec 23, 2014

### Tiago

Hi,

We know that gravity affects time and the presence of big masses such as planets will cause big distortions in spacetime wich slows things down (if I'm floating in space, won't I be distorting spacetime for.. say.. an ant? Won't the ant gravitate towards me?).

Anyway. we know that velocity also affects time, and if I'm travelling very close to the speed of light, time would go slower for me than people on Earth. But only the speed of light is constant, everything else is relative to another frame of reference. So if I say the Earth is travelling at N km/h, that would have to be relative to something (perhaps the Sun). So, in order for me to be travelling at 99% of the speed of light, what reference frame am I using? Earth? I need to be going at the speed of the Earth, plus the 99% of the speed of light? And wich velocity of Earth? Relative to what?

Thanks

2. Dec 23, 2014

### ShayanJ

Hi
The presence of any kind of any energy, by any amount, distorts spacetime. Its just that the amount you and an ant distort spacetime, is very very very very small so people just forget about it.
Uniform motion is relative. So if we consider the frame A to be at rest and frame B to be moving with speed v w.r.t. A, we can also consider B to be at rest and A to be moving with velocity -v w.r.t. B. Then A sees that B's time slows down and B sees that A's time slows down and both of them are right.

3. Dec 23, 2014

### phinds

No, it would not. Time always passes locally at one second per second. What is observed by a remote observer is not what happens locally.

4. Dec 23, 2014

### Tiago

Ok, but if I'm going close to the speed of light for 10 years, when I'd return to Earth, 20 years (or so) would have passed and I only aged 10. So time went slower for me than time of people on Earth. What's confusing me is at what speed should I go to do that. Einstein says it should be very close to the speed of light, but relative to what? To the velocity of the Earth?

5. Dec 23, 2014

### Staff: Mentor

Relative to ANY inertial frame whatsoever (this is the first postulate of relativity). You can pick any inertial frame that you like, do that calculation, and come out with the same result. It doesn't have to be the inertial frame where the earth is at rest or anything.

6. Dec 23, 2014

### phinds

No, time progressed for you at exactly the same rate as it did for the people on Earth, one second per second. The fact that you traveled along a different world line mean you AGED by a different amount while the time passed at the same rate. This is a confusing concept but it is the way it is.

7. Dec 23, 2014

### A.T.

Kinetic time dilation has nothing to do with local vs. remote, just with relative motion. A moving clock runs slower than a resting clock, even when they pass close to each other, and are observed locally.

8. Dec 23, 2014

### phinds

DOH ! I knew that

9. Dec 23, 2014

### Staff: Mentor

Yes, you and the ant will be drawn towards one another. You don't even need any general relativity; Newton's law of gravitation $F=Gm_1m_2/r^2$ and $F=ma$ is adequate for this job. It's a good exercise to try calculating the force between a 100 kg person and an ant weighing a few milligrams.

10. Dec 23, 2014

### nitsuj

I am confused by this concept. It implies clocks don't measure time, but merely "age".

11. Dec 23, 2014

### Staff: Mentor

Clocks measure the amount of time that has passed between two events - the successive ticks of the clock. "Age" is just another word for the amount of time that has passed since two events (in the case of a human, birth and right now when you and the human in question are colocated). Thus, we can use a human body as a clock, although not an especially useful and well-calibrated one - the greyer the hair and the more wrinkled the skin, the more time has passed since the birth event.

On all paths through spacetime, you will age at one second per second. All clocks (and any time-dependent process can be used as a clock - human ageing, your wristwatch, sand in an hourglass, superbly accurate atomic clocks, the decay of a sample of radioactive material, ...) moving along that path will tick at that rate and therefore report the same amount of elapsed time between any two points on that path.

However, if I take two clocks, separate them, and then move them back together they will have followed different paths through spacetime between the first "they were together" event and the second. It is possible (and this is the essence of the twin paradox) that the amount of time elapsed on these two paths is different.

12. Dec 23, 2014

### nitsuj

I agree; clocks measure time, and don't "age". In the case of a "clock" it is idealized to be a perfect measure of time.

13. Dec 23, 2014

### Staff: Mentor

I would say that clocks measure the derivative of age, also called proper time and usually denoted by $d\tau$. You can integrate proper time from "birth" to get age: $\tau = \int d\tau$. I don't know if there is an authoritative standard terminology, but that would be mine.

14. Dec 23, 2014

### nitsuj

I agree; clocks measure time, and don't "age". In the case of a "clock" it is idealized to be a perfect measure of time.

15. Dec 24, 2014

### ghwellsjr

I always thought $d\tau$ was a differential.

16. Dec 24, 2014

### nitsuj

I re-read an old thread where I thought thoroughly about time & age and more less came to the conclusion that "age" is sequenced accumulation of physical occurrence to a "body/object" (or the display on an imperfect clock), and time is a component of spacetime geometry. As phinds said "rate" is distinctly different from age.

In that case only an idealized perfect clock measures time, and for example my mechanical watch that gains 2 minutes per day ages, the hourglass ages, and the most consistent measures of the "rate" c (such as a light clock) is a measure of strictly time, not merely an accumulation of "change" but the rate.

If I understand the concepts right, I am saying a proper clock measures lightlike intervals. Our "biological" clock, hour glass ect can be a measure of proper time, timelike intervals, which of course different from coordinate time and the lightlike intervals of a perfect clock.

So with coordinate time I see the light clock in motion has the same rate of c, but the accumulation of "ticks" (different from rate) takes longer (different path).

17. Dec 24, 2014

### Staff: Mentor

Oops, yes you are right. It is a differential line element on a timelike world line. I was sloppy above.

18. Dec 25, 2014

### Tiago

So to go back to my initial question, Stephen Hawking says that a good way to travel to the future would be to go on a rocket and travel very close to the speed of light and come back to Earth in a few years (ok, so far so good). But when he says "travel very close to the speed of light", we'd be travelling at that speed relative to what frame? The Earth? So we'd need to picture the Earth at rest and the rocket at 99% of the speed of light? So that would mean, we'd traveling at the speed of the Earth plus 99% the speed of light?

19. Dec 25, 2014

### nitsuj

Yes there would be a frame where it is observed that you were in motion prior to going (according to your frame) 0.99 of c relative to Earth.

However it is not a simple sum, according to the frame that observed Earth (and you the time traveler) in motion, your rulers and clocks were contracted/dilated prior to you deciding to go 0.99 of c relative to Earth. So to that observer you never reached 0.99 of c relative to Earth, but your measures/observations/calculations tell you you have, again this is because your rulers 'n clocks are not making the same measurements as the frame that observed Earth in motion.

So just as your rulers and clocks aren't making the same measurements (in turn calculation of velocities) we cannot simply add velocities as x+y.

The concept is more easily understood with a car and it's headlights. First the posit c is invariant; regardless of comparative motion every observer calculates light to have the velocity of c. So when a car is driving down the road with it's lights on, the driver calculates the light emitted from the headlights to be c, and the observer at rest to the road also calculates the light from the headlights to be c, not simply the car velocity + c. The "mechanics" is the car driver's rulers and clocks were contracted/dilated compared to yours (from your frame) to a point where he/she calculates the lights velocity to be c and not the car velocity + the headlight light velocity...note according to the driver he/she is at rest and your rulers and clocks are contracted/dilated.

20. Dec 25, 2014

### ghwellsjr

Usually, when we say that something is traveling at a particular speed, we mean with reference to a particular Inertial Reference Frame (IRF). So you could say that in your chosen IRF, the earth is traveling at some speed, say, 10% of the speed of light (we'll call that 10%c) in some particular direction, and then you could say that the rocket is traveling at 99%c according to that same IRF in the same direction (or any other direction). Then the speed of the rocket relative to the earth will not be 99%c. It won't generally be a speed that you could easily calculate off the top of your head but it can be determined based on your specification of your scenario.

But we can also specify a scenario by saying that something is traveling at a particular speed with reference to some other object and then we don't care what the speed of that object is with reference to any other object or IRF. We just use that second object as the definition for an IRF in which it is at rest.

So in your example, if you just say that the rocket is traveling at 99%c with respect to the earth, it doesn't matter if the earth is also traveling at some particular speed with respect to the sun or any other object, as long as you aren't interested in determining anything that is happening on that other object or what observers on that other object see or determine that is happening on the earth or on the rocket.

So when Stephen Hawking says that we can travel into the future by taking a rocket at 99%c and returning, he is assuming the IRF in which the earth is at rest. At that speed, the Time Dilation Factor is 7.1 so if you say that the rocket is gone for 10 years, you have to tell us if you meant 10 years on earth or 10 years on the rocket. If you meant 10 years on earth, then you would have aged only 10/7.1 by the time you got back which is equal to 1.4 years so you would have traveled 8.6 years into the future of earth which isn't very much. If you meant 10 years of the rocket's time then the earth would have aged 10 times 7.1 or 71 years by the time you got back so you would have traveled 61 years into the future of earth and you would see a huge difference.

By the way, when considering speeds close to that of light, the Time Dilation due to gravity can generally be ignored since its contribution to the problem is so slight.

So the bottom line is that you get to set up your scenario any way you want and if all you care about is the relative aging between the people on earth and the people on the rocket, then you don't have to take into account any other objects or their relative speeds to either the earth or the rocket. The only thing that matters is the speed of the rocket relative to the earth.

Does that make sense to you?