Understanding Light Clock & Time Dilation

[Shark 774]

Hi guys,

I am having trouble getting my head around the light clock scenario which demonstrates time dilation. I can't help but intuitively feel that it seems like a fault of the clock, rather than time dilation. I hope you can understand what I'm getting at. If someone could try to give an explanation that's not too complicated that would be great, cheers.

 

[bobc2]

Hi guys,

I am having trouble getting my head around the light clock scenario which demonstrates time dilation. I can't help but intuitively feel that it seems like a fault of the clock, rather than time dilation. I hope you can understand what I'm getting at. If someone could try to give an explanation that's not too complicated that would be great, cheers.

Perhaps one way of looking at it is to consider two observers moving in opposite directions at the same speed with respect to the black rest coordinates (In the normal 3-D world of the black coordinates the red and blue guys move horizontally in opposite directions).

Now look at the four dimensional world as sketched below. All objects are static four dimensional objects (including the physical structure of the observers). A red observer (leaving aside the metaphysics), while moving along the horizontal black axis is also moving along the red X4 (4th dimension) coordinate at light speed while the blue observer moves along the blue X4 coordinate at light speed as well. The red guy carries a light clock with him. Special relativity theory has the red and blue observers actually living in two different 3-D cross-sections of a 4-D universe at any given instant. The two different worlds for the two observers incude two different 3-D cross-section views of the 4-dimensional light clock. The photon of light here is depicted as a 4-dimensional filament zigzagging along its 4-D world line at 45 degree angles to the black coordinates (corresponds to 3-D motion along X1 coordinates, with respect to all three coordinates) at the speed of light.

So, fundamentally, the time dilation results from the different 3-D cross-section "NOWs" for different observers moving at relativistic speeds (simultaneous events are different for different moving observers). Notice below that when blue is at station no. 10 along his world line (blue "NOW"), his simultaneous 3-D space includes the red guy (and clock) at red station no. 8. And when red is at his station 10 (red "NOW"), his 3-D world at that instant has the red guy (and clock) at the red station no. 8. That's time dilation.

 

[ghwellsjr]

Hi guys,

I am having trouble getting my head around the light clock scenario which demonstrates time dilation. I can't help but intuitively feel that it seems like a fault of the clock, rather than time dilation. I hope you can understand what I'm getting at. If someone could try to give an explanation that's not too complicated that would be great, cheers.

Usually, when a light clock is explained, it is made up of just two mirrors with a single flash or beam of light bouncing back and forth between them. But I like to demonstrate it using a circle of mirrors because that can demonstrate both time dilation and length contraction at the same time. Here is an animation that illustrates it:



You will note that both observers have their own circle of mirrors and to start with, both of them are looking at the same flash of light. You will note that it takes longer for the light to make the round trip from the traveler to his mirrors and back to him compared to the observer who is stationary in the frame in which we are depicting the two observers.

For more explanation, see my posts (starting with #7) on this thread where I used the same animation to illustrate a question about measuring the speed of the same light flash:

https://www.physicsforums.com/showthread.php?t=482534

Let me add that if you want to blame a moving clock for ticking slowly as compared to another clock to which it has relative motion, then you have this problem that the first clock will blame the other one for ticking slowly. They each will see the other one as ticking more slowly compared to themself so which clock do we blame?

Or do you just mean that it is only light clocks that we can blame, as if other clocks don't behave the same way?

 

[bobc2]

Usually, when a light clock is explained, it is made up of just two mirrors with a single flash or beam of light bouncing back and forth between them. But I like to demonstrate it using a circle of mirrors because that can demonstrate both time dilation and length contraction at the same time. Here is an animation that illustrates it:



You will note that both observers have their own circle of mirrors and to start with, both of them are looking at the same flash of light. You will note that it takes longer for the light to make the round trip from the traveler to his mirrors and back to him compared to the observer who is stationary in the frame in which we are depicting the two observers.

For more explanation, see my posts (starting with #7) on this thread where I used the same animation to illustrate a question about measuring the speed of the same light flash:

https://www.physicsforums.com/showthread.php?t=482534

Let me add that if you want to blame a moving clock for ticking slowly as compared to another clock to which it has relative motion, then you have this problem that the first clock will blame the other one for ticking slowly. They each will see the other one as ticking more slowly compared to themself so which clock do we blame?

Or do you just mean that it is only light clocks that we can blame, as if other clocks don't behave the same way?

Very nice animations, ghwellsjr. Thanks.

 

[bobc2]

Or do you just mean that it is only light clocks that we can blame, as if other clocks don't behave the same way?

Any good clock (moving at some relativistic speed) would appear to be ticking slower. But I wouldn't blame the clocks at all. I would blame that strange quirk of nature (as revealed in Einstein's relativity theory) that has two different observers living in different instantaneous 3-dimensional worlds. Those different worlds contain two different 3-D pieces of the same 4-dimensional clock. A mysterious feature of nature for sure, but, amazingly, it does result in the laws of physics working the same for all observers and gives us a uniform manifestation of photons for all observers (photons move at 186,000 mi/sec for all observers).

Or, you might prefer to say that because physics works the same for all observers, the observers naturally seek out the continuous sequence of instantaneous cross-section views that are initelligible to them (3-D cross-section views that manifest the order associated with the rules of physics).

 

[TobyC]

Hi guys,

I am having trouble getting my head around the light clock scenario which demonstrates time dilation. I can't help but intuitively feel that it seems like a fault of the clock, rather than time dilation. I hope you can understand what I'm getting at. If someone could try to give an explanation that's not too complicated that would be great, cheers.

I know exactly what you're getting at but the reason it can't be a fault of the clock is all to do with the privileged position of light (or anything which travels at the speed of light) in special relativity. Every observer, whatever their velocity, must see a light beam travel at the same speed relative to them.

A typical way of setting up a light clock is to have light traveling vertically between two mirrors, over and over again. It's probably a good idea to ignore relativity to start with and imagine that you could set the same experiment up with a bouncing ball, endlessly bouncing vertically between two 'mirrors'. If this 'bouncing ball clock' was placed inside a spaceship moving horizontally, then relative to an observer on the spaceship the ball would have a certain speed and the period of the clock (the time it takes to bounce between each 'mirror') would depend on this speed.

However, if the clock was viewed through a window by an observer outside the spaceship, the ball would be traveling a greater distance between each bounce because of the motion of the ship (the 'mirrors' will have moved horizontally by the time the ball reaches them again) but the period of the clock must still be the same for this outside observer (because in non-relativistic physics everyone agrees on the time intervals between events). The outside observer explains this by observing that the speed of the ball is greater than what the observer inside the ship measures (because from the point of view of the outside observer the ball has a horizontal component to its motion as well).

When you try to repeat this same scenario for light, things get more complicated because the speed of light must be measured as the same for all observers. The observer outside the ship still sees the light beam traveling a greater distance between 'bounces' than the observer inside the ship, but he no longer sees the light beam as having a greater speed, because of the fundamental postulates of relativity. The fact that the light beam has the same speed as it does from the point of view of someone inside the ship, combined with the fact that it is traveling a greater distance within each period, therefore means that the period of the clock must be measured as different by the two different observers.

Finally, the remaining postulate of special relativity, which says that the laws of physics are the same for all inertial observers, means that this time dilation not only occurs for light clocks, but must occur for all clocks, because otherwise by measuring the discrepancy between your light clock and your normal clock you could tell that you were moving.

 

[Shark 774]

I know exactly what you're getting at but the reason it can't be a fault of the clock is all to do with the privileged position of light (or anything which travels at the speed of light) in special relativity. Every observer, whatever their velocity, must see a light beam travel at the same speed relative to them.

A typical way of setting up a light clock is to have light traveling vertically between two mirrors, over and over again. It's probably a good idea to ignore relativity to start with and imagine that you could set the same experiment up with a bouncing ball, endlessly bouncing vertically between two 'mirrors'. If this 'bouncing ball clock' was placed inside a spaceship moving horizontally, then relative to an observer on the spaceship the ball would have a certain speed and the period of the clock (the time it takes to bounce between each 'mirror') would depend on this speed.

However, if the clock was viewed through a window by an observer outside the spaceship, the ball would be traveling a greater distance between each bounce because of the motion of the ship (the 'mirrors' will have moved horizontally by the time the ball reaches them again) but the period of the clock must still be the same for this outside observer (because in non-relativistic physics everyone agrees on the time intervals between events). The outside observer explains this by observing that the speed of the ball is greater than what the observer inside the ship measures (because from the point of view of the outside observer the ball has a horizontal component to its motion as well).

When you try to repeat this same scenario for light, things get more complicated because the speed of light must be measured as the same for all observers. The observer outside the ship still sees the light beam traveling a greater distance between 'bounces' than the observer inside the ship, but he no longer sees the light beam as having a greater speed, because of the fundamental postulates of relativity. The fact that the light beam has the same speed as it does from the point of view of someone inside the ship, combined with the fact that it is traveling a greater distance within each period, therefore means that the period of the clock must be measured as different by the two different observers.

Finally, the remaining postulate of special relativity, which says that the laws of physics are the same for all inertial observers, means that this time dilation not only occurs for light clocks, but must occur for all clocks, because otherwise by measuring the discrepancy between your light clock and your normal clock you could tell that you were moving.

Great! Elegantly simple, thanks a lot.

 

[vinven7]

" because otherwise by measuring the discrepancy between your light clock and your normal clock you could tell that you were moving."

This is the part that I have trouble understanding. Now, I am on the spaceship with an ordinary clock as well as the light clock. Both the clocks are at rest wrt me. So the light clock and the ordinary clock should then show the same time? (as there is no relative motion between them?) Why would the two clocks show different times?

 

[A.T.]

Now, I am on the spaceship with an ordinary clock as well as the light clock. Both the clocks are at rest wrt me. So the light clock and the ordinary clock should then show the same time? (as there is no relative motion between them?) Why would the two clocks show different times?

If only the light clock was affected by time dilation, other observers moving relative to you would see them out of sync. But if the clocks remain synced for you, they must remain synced for every other observer. So for an observer moving relative to you it can't be just the light clock that goes slow, but every physical process.