# Special relativity and time dilation

1. Oct 8, 2013

### DanPease

I was just looking for a basic explanation of special relativity in relation to an object with mass accelerating towards the speed of light. And with reference too time dilation can v and c be referred too as a percentage or decimal depending on the units in the equation used??

Many Thanks

2. Oct 8, 2013

### Staff: Mentor

Welcome to PF!

1. Thread moved to the Relativity section.
2. Could you please be more specific about what you want explained? What resources have you used so far?
3. Yes, in some contexts, C can just be 1 (1C) and velocity can be a fraction of it.

3. Oct 8, 2013

### DanPease

Well I wanted too know why an object with mass can't travel at the speed of light with reference to SR.

4. Oct 8, 2013

### phinds

Because it would take infinite energy to get it go c

5. Oct 8, 2013

### Noyhcat

Right, because as I understand it, it's because when you apply the Lorentz factor ("with reference to SR") to things like $F=ma$, you actually get $F = \gamma ma$. Which is:

$F= \frac{ma}{\sqrt{1-\frac{v^2}{c^2}}}$.

As you can see, when velocity increases, the amount of force required to accelerate it approaches infinity.

6. Oct 9, 2013

### dauto

That's not right. You only get $F = \gamma ma$ if the acceleration is perpendicular to the velocity. If they are parallel to each other you'll get $F = \gamma^3 ma$, and if it is neither parallel nor perpendicular, you get the more general $\vec F = \gamma m[\vec a + \frac{\gamma^2}{c^2}(\vec a \cdot \vec u)\vec u]$ which means the force and the acceleration won't even be parallel to each other.

7. Oct 9, 2013

### DanPease

Sweet guys thanks for the help. Would anyone be kind enough too explain length contraction??

8. Oct 9, 2013

### dauto

Yes, moving objects will have their length contracted by a $\gamma$ factor. Of course from an object's own point of view it is never moving so there is no contraction. But other observers will see the object contracted according with how fast the object is moving from their point of view.

9. Oct 9, 2013

### DanPease

Brilliant, cheers buddy.

10. Oct 9, 2013

### Noyhcat

Figured I'd start simple for clarity and go with the $\perp$.

11. Oct 10, 2013

### DanPease

Ok guys, why does time dilation happen?? What is it about the speed of light that warps time???

12. Oct 10, 2013

### bapowell

Because the speed of light is the same for all observers. Time dilation results from this fact. Why is the speed of light constant for all observers? Who knows...ask the Flying Spaghetti Monster.

13. Oct 10, 2013

### phinds

It's a bit of a mistake to think of it as "warping time". What happens is that from one inertial frame of reference X, the time for a fast-moving object (fast-moving relative to X) appears to be slower than it appears for the clock that is traveling along with the fast-moving object.

The hitch is that the clock that is moving along with the "fast-moving" object is NOT moving relative to itself and so it ticks at the same one second per second that the clock in X does, and it does not experience any time dilation.

So time dilation is an artifact of remote observation, not a physical reality.

BUT ... to further complicate things, if the two clocks are brought back together (which requires the "fast moving" one to accelerate) they WILL show different times because they have traveled along different world-lines to arrive at the even which is their reunion.

This is discussed at length with the "twin paradox".

14. Oct 10, 2013

### A.T.

It has nothing to do with remote observation. A moving object will age slower even when it is very close.

15. Oct 10, 2013

### phinds

But only in the reference frame of the person making the measurement, which is why I say it IS an artifact of remote observation.

For example, if you have X1 taken as a base-line frame of reference and you have X2 moving at some speed away from X1 and you have X3 moving at that same speed away from X2 (and thus at [almost] double the speed relative to X1) then the time passage in X3 will be seen as one thing in X3, a slower amount in X2 and a still slower amount in X1.

Which of these is right? They are all correct, but only in their own reference frames. They are not absolute and the "slower" measurements of X1 and X2 are just as correct as the measurement in X3. Thus, I say that the "slowness" of X3 is an artifact of remote observation and have no effect on the time measurements taken in X3.

Last edited: Oct 10, 2013
16. Oct 10, 2013

### dauto

Couple quibbles: X3 will not be seen at double of the speed from X1 point of view. Also, while what you said is essentially correct, the word artifact is a poor choice because it is often used to describe effects that aren't actually real. Time dilation is real.

17. Oct 10, 2013

### yuiop

It is just unfortunate that we do not have a rigorous definition of real in this context. If by real we mean a coordinate independent measurement that all observers agree on, then the relative time dilation between two strictly inertial reference frames is not real.

18. Oct 10, 2013

### phinds

Yeah, I was over-simplifying.

Hm ... I'll have to think about that one.

19. Oct 10, 2013

### dauto

Good thing that's not what's meant by real uh?

20. Oct 10, 2013

### DanPease

So with reference too time dilation is it only the clocks that are affected not the physical effects of time?