# Special relativity

1. Jan 31, 2012

### DataGG

1. The problem statement, all variables and given/known data
A beam of unknown particles travels at a speed of 2.5 x 10^8 m/s. When the particles are moving at this speed, their average lifetime is found to be 7,3 x 10^-8 s. What is their average lifetime when at rest?

2. Relevant equations

Well, Lorentz transformation for time is an obvious one: t = t'*$\gamma$

3. The attempt at a solution

Well, I really have no idea where to pick this from. I know that when v = 0 => t = t'.

I'm missing something here...

2. Jan 31, 2012

### Staff: Mentor

you have the info to calculate the gamma right? as they gave you the particle's speed.

what is the t and what is the t' in the equation you posted?

3. Jan 31, 2012

### DataGG

I believe i know how to solve it now, I'll try it out after posting this. Sorry for not defining my letters, but t = time measured on a frame with V = 0, and t' = time measured on a referencial frame with v >> 0. (the usual stuff).

Yes, I do have the info the calcullate gamma

EDIT: No, i still don't know how to solve this

Last edited: Jan 31, 2012
4. Jan 31, 2012

### DataGG

I edited my last post, I still don't know how to solve this, damn.

5. Jan 31, 2012

### BruceW

I think you've got it the wrong way round. But the first thing to do is to calculate gamma, and this will give the ratio of the time according to the two frames.

6. Jan 31, 2012

### DataGG

What's wrong? why? And what do I do with gamma? (I already calculated it, but I don't know how's that gonna help me)

7. Jan 31, 2012

### BruceW

t and t' are the wrong way round, according to the way you defined them. You can tell this because the time according to the lab frame should be greater (which is why it is called time dilation).

8. Feb 1, 2012

### DataGG

Are you sure? I'd say that the time particles experience is greater than the lab-frame. Well, I believe it depends on what we define the "proper-time" to be, right? When it says that the life-time is 7,3x10^-8, is it measured on S' or S?

Anywho, eitherway, I've no idea how to solve this.

9. Feb 1, 2012

### DataGG

EDIT: I've just reread what i wrote and all I said was that t = time read on S frame (at rest relative to earth), and t' = time read on S' frame (which is moving relative to earth). That is correct. How is that wrong?

10. Feb 1, 2012

### Staff: Mentor

I have this particle it lives for 10 secs. it goes whizzing by this observer at near light speeds. The observer says the particle lives for 100 secs. The time equation you have converts time in the particles frame to time in the observers frame. right?

so what is stopping you from solving this problem?

11. Feb 1, 2012

### DataGG

I may be missing something here, I've done all the other problems but I can't seem to do this one. I can easily convert time in the particles frame to time in the observers frame. However, that's not what it's asking. I need to know its lifetime when v = 0. Seriously, sorry if i'm really missing something right in front of me, but wow, I simply can not see it.

EDIT: lol... I just re-read the question, I've done it. Note to self: re-read the question.