# Homework Help: Time Dilation in the same frame of referance?

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1. Oct 9, 2016

### Klairence Leitch

1. The problem statement, all variables and given/known data
A rocket ship is accelerating through space. Clocks P and Q are at opposite ends of the ship. An astronaut inside the rocket ship is beside clock P and can also observe clock Q.

Note: There is a diagram given in the question and clock P is at the top ('north') of the rocket ship and Q is at the other end. The rocket is accelerating in towards 'north'.

2. Relevant equations

3. The attempt at a solution
I don't think there would be a difference in time at the clocks are accelerating with the same magnitude/ direction, so although clock Q is accelerating towards the astronaut at P, the astronaut and clock P are being accelerated away from clock Q.

Would they both occupy the same frame of reference? I'm not very confident in my answer and I feel as though I might be missing something? This is an advanced higher question (equivalent to English A level) and it's worth 2 marks.

2. Oct 9, 2016

### phinds

No, you're not missing anything. If you take a frame of reference in which a part of the ship is stationary, then everything in the ship is in stationary in that frame of reference including both clocks and the astronaut. Well, things like the HANDS of the clock and stuff like that are moving but you get the picture.

You are incorrect however in saying that either of the clocks is accelerating relative to the astronaut since they are all stationary in the same frame of reference.

3. Oct 9, 2016

### jbriggs444

A frame of reference is not something that can be occupied.

It would be proper to say that there is a[n accelerating] frame of reference in which the astronaut and both ends of the spacecraft are continuously at rest.

4. Oct 9, 2016

### phinds

Better yet, why not just do what I suggested and consider a frame of reference in which the ship is stationary?

5. Oct 9, 2016

### PeroK

Have you been studying the equivalence principle and/or the relativistic Doppler effect?

6. Oct 9, 2016

### Klairence Leitch

Thank you for helping, I understand where I went wrong with my logic.
Thank you for your help, I'll keep this in mind for next time.

I have recently been taught the equivalence principle and the relativistic Doppler effect, though my knowledge of the latter is limited.

7. Oct 9, 2016

### Carrock

A mass at P has more potential energy than one at Q.
Think of the work required to move a mass from Q to P.
The situation is much the same as a tower on earth experiencing 1G acceleration.
How would a clock at the top of the tower run, compared to one at the bottom?

8. Oct 9, 2016

### phinds

You are bringing in gravitational time dilation which, I believe, is not relevant to the heart of the OPs question who appears to be asking about time dilation due to motion.

@Klairence Leitch, jump in if I am wrong.

9. Oct 9, 2016

### Klairence Leitch

I don't think the question is asking about gravitational time dilation - it does not mention anything about a gravitating mass that would cause there to be a gravitational potential, so I'm assuming that it is just time dilation.

Though it is accelerating through space, so I don't know if I am to assume that the acceleration is due to the rocket being in a gravitational field (linking in to the equivalence principle)? I'm not very sure. I'm sorry if I'm not being very clear.

10. Oct 9, 2016

### Carrock

The OP's question appears to be about clocks with different potential energy.
There is no mention of motion in the original post.
Assuming the acceleration is 1G, the same result could be obtained (apart from tidal effects etc) if the rocket was still sitting on the launchpad.
I see no harm in hinting that in the OP 'A rocket ship is accelerating through space.' could be replaced with 'A rocket ship is accelerating.'

11. Oct 9, 2016

### Carrock

I cross posted.
The equivalence principle means you can't tell without looking outside the spaceship, so thinking about such experiments on earth would give you the answer.
i.e.
'Though it is accelerating through space, so I don't know if I am to assume that the acceleration is due to the rocket being in a gravitational field (linking in to the equivalence principle).'
- you can assume either and still get the right answer.

12. Oct 9, 2016

### Klairence Leitch

So, looking back at the question, Clock Q would be observed to show time moving faster as it has a weaker gravitational potential (because it is further from the source of gravitation). Is that right? Or am I missing something?

13. Oct 9, 2016

### phinds

Yes. My original answer was wrong overall because I was distracted by your discussion of RELATIVE acceleration so was only considering motion, not the equivalency principle, which others have correctly brought into the analysis.

14. Oct 9, 2016

### Klairence Leitch

Okay, thank you very much for your help. Despite not being part of the homework question, I feel a lot more confident about frames of reference from your post.

Thank you for all of your help!

15. Oct 9, 2016

### Carrock

I think you understand but got mixed up.
P has greater potential energy and runs faster. (You have to add energy to a mass to move it from Q 'up' to P.
Don't say 'gravitational potential' unless you know it is as you lose generality - the whole point of equivalence.
Do look up atomic clocks in a tower and try to see why the tower's equivalent to a spacecraft accelerating in a negligible gravitational field.
x-posted again... goodnight!

16. Oct 9, 2016

### phinds

@Klairence Leitch it seems like I am destined to do nothing but contribute to your confusion in this thread. Listen to @Carrock instead

I assumed you got it right this time and didn't go back to see which one was higher in the equivalent gravitational well. Carrock has been paying attention. It's good that one of us has.

17. Oct 9, 2016

### David Lewis

The astronaut would observe Clock P to be ticking at the correct rate (neither fast nor slow) because the astronaut is standing next to it.

18. Oct 9, 2016

### phinds

Which is correct but irrelevant as to which clock is running fast relative to the other.

19. Oct 11, 2016

### David Lewis

As long as both Clocks P and Q are ticking at the correct rate (neither fast nor slow), and if the observation interval lasts long enough, all observers will agree that a different amount of time has passed at Point P than has passed at Point Q.

20. Oct 17, 2016