1. Feb 25, 2015

### arsenal1607

Sorry i put this in the wrong forum so reposted it here:
[Mentor's note: Please don't do this. We end up with responses in both threads and straightening out the resulting mess is a tedious and error-prone task. Next time, just report your own misplaced post and any of us mentors will be happy to move it for you]

Hi everyone, just joined simply to ask these following questions but before I do, just want to make a few things clear:
- I have read numerous topics/pages/articles/forums on this subject, and i'm still unclear about things.
- I am useless at maths, i can't even do the most basic of equations so please try not to answer using equations

So here are the things i'm really struggling to comprehend in my head, and i've not found anything that gives me the answers:

1. I know time slows down as you move faster, but I don't understand this. I've read that if my same age friend (say we're both 25) hypothetically went into space at 99% speed of light, came back 30 yrs later when i'm 55, he'd only be 35? Would he look 35? Or something along those lines. How can this possibly be? Surely no matter where he is in the universe, 30 earth years have still passed for me, he is alive during those 30 years, so surely he would have aged 30 years as well? Are we saying that while i'd look like an old man he will still look young - even though we were both the same age before he went?

2. I know light has no concept of time, but surely it's still travelling through time as opposed to getting from a to b in a instant? If we were able to observe the universe from afar in space, we would see light leaving a star millions of miles away and travelling towards earth. Obviously it doesn't get to earth instantly as some light can take thousands/millions of years. IF we could observe this, it means light is still travelling and taking x amount of time to get there - regardless of whether the light particles themselves realise this or not. I don't understand how time could be 0 for light, even when it's travelling millions of miles and taking years to get there.

3. If you were travelling in a car at the speed of light in space, turn on your headlights, the light will move forward from you at the speed of light. This is what i've read, but if the car is already going at light speed or say 99% of it for arguments sake, wouldn't that make the light go faster then light speed?

Sorry for these questions which might be basic to you, i have a genuine real fascination with this stuff but unfortunately not the mind to go with it to be able to work it out or understand some of the stuff i've read!

Last edited by a moderator: Feb 26, 2015
2. Feb 25, 2015

### phinds

You have pretty much the same misunderstandings/confusion that most of us have when first studying this stuff. I'm about to close down for the night and won't give much of an answer.

Here's one thing though. It is NOT true that the traveler ages at a different RATE but it is true that the traveler ages by a different AMOUNT. We all age at one second per second regardless of our path through space-time but different paths through space-time can have different results for the ending point vs the starting point of two paths. So I can age 30 years while traveling and you age 55 years staying at home and when we meet up, I'm 30 years older and you're 55 years older and we've both been aging at one second per second.

3. Feb 25, 2015

### Staff: Mentor

Yes, he would age only ten years while you aged thirty years. (Although you wouldn't look like an old man, you'd only be 55 and that's not old ). He travelled one path through spacetime between when you separated and when you met again, you travelled a different path, and those two paths had different lengths in spacetime so less time passed on one than on the other. It's as if you and he both drove your cars between point A and point B - if you take different routes you may find that you drive a different number of miles.

You'd think so, wouldn't you? That's consistent with all our experience observing things moving at speeds that are small compared with the speed of light. I can throw a ball at 20 meters/second, I'm standing on a car moving down the road at 100 meters/second, I throw the ball ahead, you'd expect it to be moving at 100+20=120 meters second relative to the road. It's not. The actual rule for adding the speeds (if $u$ is the speed that I can throw the ball at and $v$ is the speed of the car) is not $u+v$, it is $(u+v)/(1+uv/c^2)$. You can't tell the difference with speeds that are small compared to that of light, but if you try it with $v=c$ you'll see that we can't get the light to go faster than $c$ no matter how fast the car moves. Google for "relativistic velocity addition" for more information.

Time isn't zero for light, it is totally undefined. For anyone else, the time it takes a light signal to cover a distance $d$ is $d/c$, just as you'd expect.

Last edited: Feb 25, 2015
4. Feb 25, 2015

### Staff: Mentor

What you're asking in those simple questions is to explain a whole course in special relativity which could take quite some time.

The first stop is the thought experiment that Einstein used of two people one on the train platform and one on the train speeding by both timing an event of light leaving a lamp bouncing off a mirror and then returning to the starting point.

Anyway, this book by Benjamin Crowell may be helpful in your studies:

http://www.lightandmatter.com/sr/

5. Feb 26, 2015

### Fredrik

Staff Emeritus
1. Your friend would be $25+30\sqrt{1-0.99^2}=29.2$ years old when you're 55. Yes, he would look 29.2 and feel like only 4.2 years have passed. SR doesn't really tell you why this happens. It only tells you how to calculate the age.

2. The time it takes for light (or any massless particle) is undefined, not zero. However, the time it takes for a massive particle is small when the velocity is high, and goes to zero as the velocity goes to c. So there's no limit to how small the time "experienced" by a massive object can be.

3. "Addition" of velocities in SR is more complicated than that. The velocity of that light in the coordinate system in which the car has velocity 0.99c isn't c+0.99c =(1+0.99)c. It's
$$\frac{1+0.99}{1+1\cdot 0.99}c=\frac{1.99}{1.99}c =c.$$ More generally, if u is the velocity of the car and v is some object's velocity relative to the car, that object's velocity in the coordinate system where the car has velocity u is
$$\frac{u+v}{1+\frac{uv}{c^2}}.$$

6. Feb 26, 2015

### harrylin

I'm afraid that each question could be a thread on its own; but -happily- 1. and 2. can be combined.
Hi Arsenal, welcome to PF!

You and your friend will have lived 30 more years according to your clock, but his clock will have advanced for example only 10 years (but note the calculation of Fredrik). In fact, all natural processes in his spaceship will have progressed less than on Earth, and that includes his aging process. So, he'll look only 35 years old (if the voyage wasn't too stressful!).

The speed of light can never be reached by any material thing, but in principle natural processes would "freeze" at the speed of light. Of course that doesn't change the fact that light and objects at very nearly the speed propagate or move at almost 300'000 km/s through space (note that light moves through space as function of time).
Light is not really a particle, but you could imagine a clock (for example a radioactive particle) that is quickly accelerated to nearly the speed of light; If it travels millions of miles it will hardly count any time (it will not or hardly have decayed any further).
SR models light as a wave and this is reduced to the second postulate as follows: "light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body."
As a consequence, according to measurements on the ground (and also GPS including the one in your car), the light only advances relatively to you at a speed of 3000 km/s.

Note that if you would set up a reference system of your own, related to your car, then you would assign different distant clock times ahead of you (the technical term for that is "relativity of simultaneity"); and next you will measure that the light advances relatively to you at a speed of 300'000 km/s. Fredrik gave you the formula's for that. As a consequence you can just as well hold that you are standing still, and the ground is moving.

Last edited: Feb 26, 2015