# Time dilation

1. Jun 15, 2006

### delerious121

This question is not directly related with time dilation as much it is with the light clock that is so often used to improvise the concept of time dilation. This clock consists of two mirrors placed parallel to each other, a light blip that bounces between the mirrors. The light blip is periodically intensified to account for the absorption by the photo detector placed on one of the mirrors.

Now let’s assume for the sake of clarity that the clock is moving along the x axis and the mirrors are placed parallel to xy plane at some distance z’ from each other. Also let’s assume that the motion is non-accelerated and that it can be represented by vector v

Which of these should be correct?

1) Due to the motion of the clock there will be an x component of velocity imparted to the blip and now the sum of two component c in z direction and v in x direction will be equal to c in xz plane. (My guess is that its most unlikely because the motion of source does not affect the speed of light.)

2) There will no horizontal component of light and that will require mirrors to be of infinite length for this arrangement to work as otherwise the blip will continue to shift in –x direction and eventually fall off the clock.

2. Jun 15, 2006

### actionintegral

You need to specify the initial motion of the "blip"

3. Jun 15, 2006

### pervect

Staff Emeritus
None of the above, really.

Let us set up two frames of reference: the Earth frame, in which the light clock is moving, and the clock frame, in which the light clock is standing still.

Then in the Earth frame, the light beam will not be bouncing "straight across", but at an angle. The speed of light will still be 'c', of course, so there will be an x component of the velocity, and the z component of the velocity will be lower than 'c'.

The mirrors do not need to be infinitely long. If we mark a specific sppot on the mirror with an 'x' (on the backside of the mirror, so it doesn't interfere with reflection) where the light pulse hits, the light pulse will always hit the same spot, it will always hit the spot marked with the 'x'.

Hence, in the Earth frame, the light clock will apear to tick more slowly than it should, because the z component of the velocity is not equal to 'c'.

Another way of saying this - in the Earth frame, the light in the light clock will be aberrated.'

see for example
http://en.wikipedia.org/wiki/Astronomical_aberration

Your #1 comes the closest to being right, but you apparently somehow did not realize that the light, in the Earth frame, willl not be at right angles to the mirror.

In the clock frame, the light beam will be bouncing straight across - it will not be "at an angle" (aberrated) in the clock frame.

Therfore the light clock will appear to keep normal time in the clock frame.

This demonstrates that in the Earth frame, the light clock ticks more slowly than it does in its own frame.

It does not (yet) get into other aspects of relativity, such as length contraction and the relativity of simultaneity. These other aspects are important for understanding how relativity is self-consistent and resolving the so-called "twin paradox".

The "light clock" does, however, motivate the existence of relativistic time dilation, though it is not yet a complete description of relativity.

4. Jun 15, 2006

### robphy

This "circular light clock" http://www.phy.syr.edu/courses/modules/LIGHTCONE/LightClock/ [Broken] also does reveal length contraction, relativity of simultaneity, and the doppler effect.

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