# Time dilation and the photon clock

1. Dec 20, 2007

### Stellar1

Hello,
I just baught my next set of textbooks and started reading about relativity. In one of the books it uses the example of a two clocks who "tick" every time a photon it emitted hits the mirror and returns to the sensor. It demonstrated that, if the box containing this clock is moving, it will tick slower than one that is stationary. I understand this and why, but I dont understand how this is supposed to show time dilation? If I perform the same experiment but with a clock that shoots a tennis ball, while fixing the tennis ball's speed at a constant value, the moving clock, even at speeds far below the speed of light, will still tick slower than the stationary one, yet there would not really be time dilation.

2. Dec 20, 2007

### jcsd

The second postulate of relativity is that the speed of light (i.e. the speed of a photon) is the same in all inertial (non-acclerated) frames of reference. There is no equivalent postulate for tennis balls :)

3. Dec 20, 2007

### Riogho

Of course, the speed of a photon isn't constant :P It's just constant in a vacuum, and that is given as c

4. Dec 20, 2007

### Stellar1

Yes, I know its not constant everywhere, but thats what I meant, in a vacuum.

Never the less, I still do not see how this test actually displays any time dilation.

jcsd: if the tennis ball were held at a constant speed, the speed of the tenis ball would also be the same in all inertial frames of reference.

Can anyone simply explain to me how this whole example shows time dilation, rather than the mechanism of the clock simply being affected by the movement? That's all I see happening, the mechanism of the clock is made such that the clock is only accurate when it is stationary.

5. Dec 20, 2007

### Staff: Mentor

Why do you say that the moving tennis-ball clock will tick slower than a stationary tennis-ball clock even at speeds far below light speed?

And why do you think that with a tennis-ball clock there "would not really be time dilation"?

All moving clocks will be observed to slow down by the same factor, whether made of light beams, tennis balls, or the ticking of a human heart. Of course, analyzing the tennis-ball clock from first principles would be much harder since--as jcsd stated--there's no simple principle about the speed of a tennis ball being the same in all frames.

6. Dec 20, 2007

### jcsd

Yes, simply put in relatvity all motion is relative (whence relativity). There is no absolute way to distinguish betwen a stationery and a moving observer (assuming both observers are inertial). Someone who was moving with the 'moving' photon clock would view the same time dialtion effect on a 'stationery' photon clock.

Last edited: Dec 20, 2007
7. Dec 20, 2007

### jcsd

The speed of a tennis ball (unless they are travelling at c, which it is safe to assume they are not unless otherwise stated), cannot be the same in all inertial frames of reference.

8. Dec 20, 2007

### Stellar1

Because if the speed of the tennis ball is constant, then the stationary clock's tennis ball has only a vertical component for velocity. The moving clock has both a vertical and horizontal component for it's tennis ball's velocity, and the speed can not exceed that of the stationary one's vertical velocity therefore the moving clock's tennis ball's vertical velocity is slower than that of the stationary one, thus the clock ticks slower.

Because it is moving at speeds far below that of the speed of light, yet the ticks can still differ greatly. The clocks will be far out of sync, but it isnt due to time dilation, it is due to the way the clocks were constructed.

Not at all, not if the tennis ball's speed is maintained at a constant and equal level between the two clocks. One clock's tennis ball will have a faster vertical velocity than the other, therefore the one that's moving will tick slower.

Ok, but how does this whole example prove time dilation? It simply shows the inexactitude of the mechanism of the clock, does it not?

If it was constant, then why not?

9. Dec 20, 2007

### Staff: Mentor

Ah, I see what you were doing. You were assuming that the tennis ball speed would be constant in all frames (like for photons), which is not true. (Only things that move at lightspeed can have the same speed in all frames.)

An ordinary tennis ball clock (if there's such a thing) would behave like any other clock. All clocks exhibit the same "slowing down" affect due to relative motion. It has to be this way, otherwise the laws of physics would depend on one's arbitrary speed, which they do not.

The reason why the light clock is used as an example is that it is easy to analyze and deduce the time dilation factor. As I stated earlier, analyzing the behavior of the tennis ball clock to predict the time dilation factor would not be simple--but it could be done. (Since the tennis ball does not have the same speed in all frames, you would have to use the relativistic transformation for velocity to predict its speed in various frames.)

10. Dec 20, 2007

### Stellar1

I know thats not true, but lets make that assumption. It doesnt change the laws of physics. If need be, lets say its not a tennis ball but a device that will exert the appropriate amount of thrust in the appropriate direction in order to maintain that constant speed.

I know it will. But I'm not asking about that, I'm asking about how the experiment/example itsself shows time dilation. I dont see that it does, I just see a flawed design of the clock.

But as I see it, it is not time dilation that is occuring... time still goes by at the same rate, its just the clock that records things differently depending on how fast the clock is travelling.

But if we use a tennis ball, the time dilation, according to the clocks, will be much greater than according to the photon clocks.

11. Dec 21, 2007

### Janus

Staff Emeritus
In order for that to work, the thrust would only be exerted as seen in one frame, and that would involve a change in the law of Physics between the two frames.
We are talking about a difference between identical clocks.
Imagine that you have a "tennis ball" clock running next to each photon clock. An observer next to each set of clocks notes that the photon clock ticks x times for every one tick of the tennis ball clock next to it. This must be true for any observer watching the pair of clocks. Thus if the photon is seen as ticking twice as slow due tot he fact that the motion of the clock, the tennis ball clock must also tick half as slow in order to maintain that x to 1 ratio. The tennis ball clock and the photon undergo the same time dilation.

12. Dec 21, 2007

### Stellar1

How would it involve a change in the law of physics? In any case, it is irrelevant because I was just using it as an example to better convey my question "how do we know that it is time dilation that occurs rather than inaccuracy in the equipment?"

Indeed they are identical; however, the accuracy of it is dependent on the speed of the clock. It seems to me that, rather than time dilation occuring in the example, it is simply inaccuracy in the equipment that's responsible for time being different.

Indeed, I understand that. My point is, however, that the time dilation measured by the difference of the clock's values for the tennisball is different than that of the photon clock...

13. Dec 21, 2007

### Ich

Instead of concentrating only on the second postulate, you should remember the first.
That means that it does not matter whether the clock is moving and the observer is stationary, or the clock is stationary and the observer is moving.
This implies that the photon in a stationary clock is moving at the same speed as seen by every observer moving at arbitrary speed relative to the clock. How you achieve that with thrusters?

14. Dec 21, 2007

### Staff: Mentor

Unfortunately that does require a change in the laws of physics. Unless the tennis balls are moving at light speed (not possible), they will have different speeds depending upon who's doing the observing. And there's no possible device that could ensure the same speed for all observers.
Why do you keep saying this? Time dilation measured by any kind of clock will be the same.

15. Dec 21, 2007

### neopolitan

What orientation does the tennis ball clock have? That is, do the tennis balls travel parallel with the frame's velocity or transversely to that velocity.

This seems to make a difference.

Say we have two observers with a tennis ball clock each. One we consider to be stationary and the other we consider to be in motion. We set the clocks in motion when the observers are collocated. At the end of one tick and one tock, where are the tennis balls?

Doesn't it all rely on what we mean by set the "clocks in motion"? If we think that the operating speed of the tennis ball in each clock is vtb then setting the clocks in motion means bestowing enough momentum to each tennis ball such that it attains this speed. The amount of moment transferred may be lorentz invariant, but in the moving frame you have to overcome a little inertia as well as setting the tennis ball in motion (or possibly give the tennis ball insufficient momentum to account for the frame's motion, depending on the orientation of the clock, the effect is the same either way). The tennis ball in moving frame will move more slowly.

It doesn't seem valid to compare this to the operation of a light clock (where we don't actually need to provide the photon with momentum, we just release it).

That said, the light clock derivation has its own problems, specifically when you orient the clock such that the photon travels parallel with the frame's motion.

cheers,

neopolitan

16. Dec 21, 2007

### Janus

Staff Emeritus
As Ich has already pointed out, you are missing an important part of this whole scenerio.

It doesn't matter which photon clock is considered as "moving". You have two identical photon clocks, each with an observer at rest with repect to it. The photon clocks have a relative velocity to each other. Each observer notes that his clock ticks once every sec. Each observer will also note that the other clock will take longer than one sec between ticks. IOW, the two observers do not measure the same amount of time as elapsing between two given events (such as the ticking of one particular clock).

17. Dec 21, 2007

### Staff: Mentor

Nonsense. When the light clock is oriented parallel to the direction of motion the derivation is a bit different, but it still works just fine.

18. Dec 21, 2007

### Stellar1

Hmm, let me start this from scratch.
Forgetting about the whole tennis ball clock analogy, what is it about the photon-clock that proves time dilation? Maybe thats the fundamental point I'm missing.

19. Dec 21, 2007

### Stellar1

Alright, one sec. I just lied down in bed for a while and just thought about the whole situation. So I see what you are saying now and what you mean by the tennis ball not being the same speed between the two inertial frames of reference.

So, what you are saying is that, since the speed of light is maxed at c, the stationary clock's photons are moving vertically at c. From the perspective of the moving clock, however, the photons of the stationary clock would also have a horizontal component for velocity, which would put their speed above c, which is impossible, therefore it is time that must slow down to maintain the speed at c, correct?

20. Dec 21, 2007

### paw

Bingo. That's the whole point.

IF we lived in a universe where tennis balls always moved at a specific speed in a vacuum AND if the speed they move was always the same for all inertial observers THEN the tennis ball clock would also demonstrate time dilation in exactly the same manner.

Since we don't live in a universe where tennis balls behave this way the tennis ball clock cannot demonstrate time dilation. It will, of course, slow down like any other mechanical clock when viewed from a different inertial frame but because tennis balls can have any velocity < c there's no way to calculate delta t using tennis balls.