Horizontal spacetime clock and horizontal motion

If I am in a moving reference frame according to some outside observer and I have a light beam clock oriented horizontally, shouldn't I notice that the light beam travels faster in one direction than in the other?

For example if I then had a horizontal clock, could I not use the horizontal clock to show that the duration of the horizontal ticks are different in the each direction?

• Light travels at the same speed in all directions. Jul 27, 2017 at 23:32
• Is this speed limit enforced by time dilation? Jul 28, 2017 at 1:38

This is actually what one would expect intuitively. But it turns out that the speed of light is the same in any inertial frame of reference, i.e. any frame of reference moving at constant speed.

Let's say you're moving very swift to the left relative to another observer. You have a 'light clock', i.e. a device reflecting a light impulse back and forth between two parallel mirrors. Furthermore, suppose that clock is horizontally aligned to the direction of your motion relative to the other observer.

Both of you will measure the same speed of light, whereas classically you would expect the speed of light to be slower when the light impulse is reflected in your direction of motion and faster when it is reflected in the opposite direction.

Special relativity sort of 'buys' the invariance of the speed of light in inertial frames of reference at a cost. That is, time and space can no longer be treated separately from one another when switching between frames of reference.

Let me give you an example: Let's say you're moving at 50% of the speed of light relative to another observer. While both of you measure the same speed of light for the light impulse in your light clock, there are two special effects.

In your inertial frame of reference everything that is not moving along with you is contracted in length in the direction of your motion. For example your light clock will still have the same length as it had at rest but the houses and trees you pass by will be contracted in length. On the other hand, the other observer will see you and your light clock contracted in length because in his inertial frame of reference you are moving relative to him and everything else is at rest. This phenomenon is called Lorentz contraction.

The other effect is called time dilation. While you in your inertial frame of reference do not notice anything weird about the passing of time, the other observer in his inertial frame of reference will say that time for you passes slower because you are moving at a very high speed relative to him. Conversely, you will say the same about him. After all, he is also moving relative to you in you inertial frame of reference, just in the opposite direction.

• I'am very confused with your last paragraph about time dilation. Time passes slower for me or for the "outside observer" ??? From @Steeven Profile : "If you can't explain it simply, you don't understand it well enough" - Albert Einstein. Jul 28, 2017 at 8:37
• The other observer will say time passes slower for you in your inertial frame of reference. His own clock ticks just fine. The same goes for you though: You will say time for him passes slower, in his inertial frame of reference. Jul 28, 2017 at 9:01
• I apologize:If two events 1 and 2 are by a time interval $\Delta t = t_{2}-t_{1}=10\,\text{sec}$ apart for ME and I am moving with $v=0.60c$ with respect to the OO (Outside Observer), then for OO this time interval is dilated to $\Delta t' = t'_{2}-t'_{1}=\gamma \Delta t=1.25 \times 10 =12.5\,\text{sec}$ and in turn since OO is moving with $v=0.60c$ with respect to ME (in the opposite direction), then for ME this time interval is dilated to $\Delta t = t_{2}-t_{1}=\gamma \Delta t'=1.25 \times 12.5 =15.625\,\text{sec}$ and so on an infinite sequence tending to $\infty$. Where is the truth ??? Jul 28, 2017 at 9:36
• Both observers are correct. Think of a light clock aligned vertically to your motion. While you will see the light Impulse being reflected back and forth in a straight line between the mirrors, the other observer will see the clock moving along with you. That means for him the light travels in a zic-zac path between the mirrors. Thus, for him the light has to cross a larger distance. So for the speed of light to be the same the time has to pass slower for you from the other observer's inertial frame of reference. Jul 28, 2017 at 10:23