## Time dilation

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Duncan
Posts: 9
Joined: Tue Mar 20, 2012 6:21 pm

### Time dilation

Hi,
I used to think I understood time dilation, but the more I read the less it seems I know!
Hoping you can clarify the following.

1). If you reduce the speed of the light beam, say replace it with a mechanical pointer moving back and forth across the car , and reduce the speed of the car in proportion, don't you get the same length hypotenuse and the same time dilation?

2). When the car is stationary, the actual light beam is still moving across the car. Why is their no time dilation relative to the stationary observer?

3). If the light beam is at the start fired at an angle in the same direction as the car moves, the car's motion causes the beam to straighten, giving a shorter , not longer, path, so time speeds up with motion. Any ideas?

Cheers
Duncan
joe
Posts: 755
Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

### Re: Time dilation

1). If you reduce the speed of the light beam, say replace it with a mechanical pointer moving back and forth across the car , and reduce the speed of the car in proportion, don't you get the same length hypotenuse and the same time dilation?
Yes. However, there is nothing special about the speed of a pointer or whatever you use in that clock. Further, different observers would see the pointer travelling at different speeds. The speed of light is special: different observers (experimentally) see it travelling at the same speed. So c is special: it really relates time and space.

Running out of length: go to the next message.
Joe
joe
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Location: Sydney

### Re: Time dilation

2). When the car is stationary, the actual light beam is still moving across the car. Why is their no time dilation relative to the stationary observer?
Both see this light clock ticking at the same rate: (width of car)/c. It's a good clock: when frames are not in relative motion, it measures the same time. But with relative motion, there is time dilation.
3). If the light beam is at the start fired at an angle in the same direction as the car moves, the car's motion causes the beam to straighten, giving a shorter, not longer, path, so time speeds up with motion. Any ideas?
When the observer outside the car sees the light going in the same direction as the car, he sees a slower tick. When it goes towards the back of the car the tick is slower. The two do not cancel out* and the dilation for this clock comes out to exactly the same factor.

Joe

* the maths is just the same as swimming against the current and with it - imagine when swim speed and current are almost the same
Duncan
Posts: 9
Joined: Tue Mar 20, 2012 6:21 pm

### Re: Time dilation

Thanks Joe,
Re.Q.1. So if the " beams " speed could be reduced by half and the cars speed by half, the time dilation wouldn't alter as their relative motion would be the same for both sets of speed?

Re. Q. 2. I agree both observers see the stationary clock ticking at the same rate. But if there was a theoretical clock on the light beam, wouldn't it run slow from both observers view because the beam is in relative motion to them even if the clock's box isn't?

Re. Q. 3. I don't believe I framed this question clearly before, so I'll try again. If the light beam is switched on at an angle to the mirrors other than 90 degrees, and in the same direction as the movement of the car, the beam's initial deflection caused by the car's motion, is to 90 degrees. i.e. a shorter not longer path!
Regards,
Duncan.
joe
Posts: 755
Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

### Re: Time dilation

Re.Q.1. So if the " beams " speed could be reduced by half and the cars speed by half, the time dilation wouldn't alter as their relative motion would be the same for both sets of speed?
The time dilation in all cases is that calculated for the light clock, because only light has the same speed in all frames. So the time dilation would be substantially less if the car speed were less. And the speed of the pointer beams is irrelevant to the time dilation because their speed is not the same in all frames.

Joe
joe
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Location: Sydney

### Re: Time dilation

Re. Q. 2. I agree both observers see the stationary clock ticking at the same rate. But if there was a theoretical clock on the light beam, wouldn't it run slow from both observers view because the beam is in relative motion to them even if the clock's box isn't?
As objects travel at speeds closer and closer to the speed of light, their time dilation gets greater and greater. Sometimes people say that 'the clocks would stop if accelerated to the speed of light'. But this is hypothetical because clocks cannot be accelerated to the speed of light.

However, high speed particles travelling at close to the speed of light do have lifetimes very much longer than they have in their own frame.

So yes, a high speed particle travelling at close to the speed of light across the car, or in any direction, would have a very high time dilation.

Joe
joe
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Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

### Re: Time dilation

Re. Q. 3. I don't believe I framed this question clearly before, so I'll try again. If the light beam is switched on at an angle to the mirrors other than 90 degrees, and in the same direction as the movement of the car, the beam's initial deflection caused by the car's motion, is to 90 degrees. i.e. a shorter not longer path!
I don't understand the question: I don' know what you mean by initial deflection caused by the car's motion.

However, for the observer on the ground, the fastest path from one side of the car to the other is the one at right angles to the car's velocity, in the frame of the ground. Hence all moving frames have time dilation.

Joe
Duncan
Posts: 9
Joined: Tue Mar 20, 2012 6:21 pm

### Re: Time dilation

Hi Joe,
Re. Q.3. Let me re-explain,
The car, light clock thought experiment, starts with a light beam moving at 90 degrees between two mirrors. Introduce motion of the car/clock relative to the observer and the beams path becomes a zig zag. However if instead the beam starts by being fired at an angle, and in the direction of the cars motion, the cars motion changes the angled beam to a vertical ( 90 degree ) beam.This would mean the beams path is shorter, not longer, and time speeds up?
Thanks,
Duncan.
joe
Posts: 755
Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

### Re: Time dilation

Car stationary, light beam traces a zigzag path between sets of mirrors on either side. Both observers agree on the clock time: it is slow, because light travels along the hypotenuse. Now the car accelerates until its speed is so great that, to the driver, the light beam appears to be going at right angles to the car. So the driver in the car sees the clock to be fast and the observer on the ground still sees it to be slow. Is that it?

This is very similar to the arrangement shown in the animation in
http://www.phys.unsw.edu.au/einsteinlig ... lation.htm
The driver sees the clock moving with the car tick at w/c and the observer on the ground sees it tick more slowly: the observer on the ground sees the clock moving with the car to have time dilation.

Joe
Duncan
Posts: 9
Joined: Tue Mar 20, 2012 6:21 pm

### Re: Time dilation

Joe,
I'm trading in the car for a train, complete with a set of 2 light clock and a two observers .
The light clocks are activated with their beam fired at a 45 degree angle to the mirrors, producing a zig zag path. Both observers see this path with the train standing still. One clock goes on the train, and the other on the platform.
So the train moves off left to right which is the same direction as the light beam is zig zagging. This causes the light beam to straighten from the platform observers view, while the observer on the train, being in motion with the train continues to see the zig zag on their clock.
So the moving clock has a has a shorter path between mirrors ( vertical beam ), while the stationary clock has a longer path ( zig zag beam ), how come?
Regards,
Duncan
joe
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Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

### Re: Time dilation

Here are two symmetric cases: perhaps you mean the second.

1. with respect to the platform, the (diagonal) light beam has a velocity component v to the East and the train moves to the East with v, then the path of the light beam in the train frame (Tic = w/c) will be shorter than in the platform frame. The platform observer sees the train clock running slow. This is the result shown in
http://www.phys.unsw.edu.au/einsteinlig ... lation.htm

2. with respect to the train, the light (diagonal) beam has a velocity component v to the West and the train moves to the East withv. Now we have a clock at rest with respect to the platform (Tic = w/c) and the observer in the train sees that clock running slow. Time dilation is completely symmetrical, as explained in
http://www.phys.unsw.edu.au/einsteinlig ... lation.htm

If you mean neither, then
3. you have a clock (system with repeated cycles) moving with respect to both observers. In that case each sees that it has a different time dilation.

Joe
Duncan
Posts: 9
Joined: Tue Mar 20, 2012 6:21 pm

### Re: Time dilation

Hello Joe,
Let me condense this down. If you start with a light beam at 90 degree to the mirrors,, lateral motion obviously lengthens the beams path, but if you start with an angled beam in the direction of the train/cars motion, lateral motion shortens the beams path. Contradictory results. Can you explain?
Regards,
Duncan.
joe
Posts: 755
Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

### Re: Time dilation

The result is symmetric, rather than contradictory.

A clock is something that uses repeated cycles: an event that recurs at the same position. Like a pendulum, oscillating crystal, discharging capacitor, escapement... or light beams between two (or some other number or) mirrors, and then repeating.

1. So, if an observer sees the light beam travelling between the same pair of mirrors, then that clock is at rest in his frame, and that observation will be the fastest that that clock ever ticks.

2. For an observer who sees the light beam tracing a zig-zag path, this is not a set of repeated events in her rest frame of reference: it requires a large number of stationary mirrors and the events are never repeated. These light beams can only repeatedly strike the same 2 mirrors if the mirrors travel at v where v is the component of velocity of the beams at right angles to the mirrors. So, she sees that this moving clock run slow. Observers see clocks moving with respect to his own frame running slow.
Joe
Duncan
Posts: 9
Joined: Tue Mar 20, 2012 6:21 pm

### Re: Time dilation

Hi Joe,
Re. the Jasper & Zoe car animation .
When Jasper sees the light pulse heading for, call it mirror A, Zoe could see it heading for Mirror B, as the animation shows.If the car is stopped both see the same pulse path, 90 degrees to the mirror, but where will the pulse be on that path?
Cheers,
Duncan.
joe
Posts: 755
Joined: Fri Aug 29, 2003 11:57 am
Location: Sydney

### Re: Time dilation

Gday Duncan

in that animation
http://www.phys.unsw.edu.au/einsteinlig ... n.htm#time
both observers see the light pulse going towards the same mirror.

If you want to see where the pulse is in that animation, you could make a screen shot.

Joe