# B Time dilation and 2 identical clocks

1. Nov 25, 2017

### Ross Arden

Hi

Couldnt figure this out

U have 2 identical clocks where a pulse of light goes from a light source (a), reflects off a mirror (b) and goes to the end (c)

A person is stationary wrt one clock and another clock is in a space ship moving, relative to the observer, in the direction v at velocity v

The clock in the space ship is shown at time t1, t2 and t3

Theory says the observer should see the clock in the space ship ticking slower than the clock at rest wrt the observer.

If the height of the clock is H and its length is L the observer will deduce the clock in the space ship ticks at 2H/c. The observer will deduce the stationary clock will tick at some time greater than 2H/c ...is that right?

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2. Nov 26, 2017

### Ibix

You can't make a clock with a pendulum that swings one way and then stops. So that isn't a clock, unless you put a mirror at point c so that the light comes back to point a, in which case more analysis of the return tick is needed.

If you aren't aware of the relativity of simultaneity, you should google that term.

3. Nov 26, 2017

### Ross Arden

its not a pendulum clock!

4. Nov 26, 2017

### Ross Arden

there is no pendulum in an hour glass

5. Nov 26, 2017

### Ibix

It's not a clock full stop, unless it has a mirror at c. It doesn't complete a cycle so there's no way to compare any other clock to it without invoking a simultaneity convention.
True. But it measures one unit of time at a point (the neck of the glass). If you want to measure any more than that you need to turn it over, then turn it over, then turn it over. And there you have your cyclic motion.

Your design does not measure time at a point because a and c are not co-located. So it doesn't work as a sand timer since it mixes up space and time, and interpreting its results depends on your simultaneity convention (did you google the relativity of simultaneity?). And it doesn't work as a regular clock because it doesn't cycle.

6. Nov 26, 2017

### Sorcerer

Ibix, what you're saying is that it only works as a clock if the start of the cycle ends at the same location in space with respect to the person using it to measure time, correct?

7. Nov 26, 2017

### PeroK

Ah, I see what you have done. The light clock is supposed to fire light vertically upwards and be reflected vertically back down. This is what happens when the clock is at rest with respect to an observer. The distance travelled by the light is $2H$; hence the time for an up and down light trip is $2H/c$.

But, if the light clock is moving with respect to an observer, then the light will travel in a triangle, hence further. And, since the speed of light is invariant, this will take longer and the observer will conclude that the moving light clock is running slow.

But, to an observer moving with the light clock, the light will be going up and down vertically and the clock will be running normally.

8. Nov 26, 2017

### Ibix

Yes - that's a clearer way to phrase it. So you can just about get away with calling a sand timer a clock because you can talk about the proper time between the events of the sand starting to slide through the neck of the glass and finishing sliding through. You can also talk about the proper time between the events "light leaves a" and "light arrives at c", but this doesn't correspond to the proper time of anyone at rest with respect to the device.

So I suppose one could argue that it's a clock (in the narrow sense of a one-shot sand timer) for a very specific observer, one who happens to be passing a at the time the light is emitted and happens to be passing c at the time the light is received. And time dilation will work out as usual if this frame is used as the rest frame. But that's a bit odd - that isn't the rest frame of the device.

On balance, I stand by "that is not a clock". A lot of highly specific caveats must apply to regard it as a clock.

9. Nov 26, 2017

### Sorcerer

As suspected. Then, correct me if I'm wrong, it makes no sense to talk about measuring time unless you are either next to both the clock and the event or have some means of synchronization with the clock that is next to the event. In other words the interval of space through which the event transpires should be zero as you measure the time (unless there is some method of synchronization).

Nor does it make any sense to talk about a length unless the interval of time through which the object moves is zero as you measure the length (unless you again have some method of synchronization).

Yes? No? In the ball park?

10. Nov 26, 2017

### Mister T

If two events occur at the same location then the time that elapses between them is called a proper time. To an observer moving relative to these two events they will of course not occur in the same place. He can measure the time that elapses between them, but he will need two clocks, one at the location of the first event and one at the location of the second event. If he synchronizes them (this is where the convention that @Ibix mentioned comes in) then he will indeed be able to measure the time that elapses between them, and he will find that elapsed time to be larger than the proper time. This is what's called time dilation.

The twist is that to an observer present at both events those two clocks that the moving observer uses will not be properly synchronized.

11. Dec 5, 2017

### Ross Arden

the purpose of a clock is to measure time whether that be eternity or cooking an egg .... in the scenario I depicted the egg timer in the space ship would time the cookig of the egg faster than the egg time external to the space ship...is that right?

12. Dec 5, 2017

### Ross Arden

there are many natural, and probably unnatural, phenomena that can be used to measure time, ie the rotation of a neutron star, atomic phenomena, but do not have a feed back loop such as a pendulum. Where it is cast in stone that a device used to measure time must have a "feed back" mechanism such as a pendulum?

another one would be the half life of radioactive materials, time measurement with no feed back mechanism

In the scenario I depicted even if there was only one tick of the clock, say the guy doing the experiment was testing the clock to see if it worked. Even after only a single "tick" of the clock they would have to conclude the clock in the space ship was going to run fast

13. Dec 5, 2017

### Ibix

You can't use the setup described in your OP to time an egg. Let’s assume the pan is at the "start" end of your tube. You send out the light pulse and start cooking your egg. But when do you stop? It can't be when the light reaches the far end of the tube because you can't know when that happens. You must either have a real clock to tell you when you predict that the light pulse has reached the other end, or you must use a telescope to watch the far end and turn off the pan when you see the light arrive. In the first case your v-tube is not acting as a clock. In the second case you need to factor in the light travel time between "light arrives at end of tube" and "you see it arrive". In either case you will find normal time dilation applies.
But all of these work at a single point and can be used as a clock at that point. Yours doesn’t, unless you add a telescope or some other kind of return leg, so you can't use it as a clock (at least, not in its rest frame) because you can't tell when the end of a tick happens.

14. Dec 5, 2017

### Ross Arden

put the pan at the detector end of the tube. An egg timer is placed at the light source. Each time a grain of sand falls thru the egg time a light pulse is triggered. The egg timer has 500 grains of sand. A counter is placed at the pan. when the counter gets to 500 the heat is tuned off. the egg timer is oriented with the direction of movement of the space ship

If the experiment is conducted million of times the counter in the space ship will turn off consistently quicker than the one external to the space ship

15. Dec 5, 2017

### Ibix

So you turn on the heat when you get the flash corresponding to "first grain falls" and turn it off when you get the flash corresponding to "last grain falls"? This is basically watching a standard egg-timer through a telescope. The egg-timer is the only clock in this setup.

16. Dec 5, 2017

### Ross Arden

the counter located in the space ship turns off/on the heat. As the timer in the space ship turns off the heat early the egg in the space ship is not fully cooked , where as the egg external to the space ship is

l

17. Dec 5, 2017

### Ross Arden

the set up external to the space ship is identical to the setup internal to the spaceship

18. Dec 5, 2017

### Ibix

I think you need to explain clearly where you have egg timers and where you have pans, and which ones are moving with the rocket and which ones are moving with the stick man.

19. Dec 5, 2017

### Ross Arden

see pic

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20. Dec 5, 2017

### Ross Arden

the setup next to the stick man is identical, minus the rocket of course