# Why does light travel in a diagonal in the time dilation experiment? [duplicate]

According to the typical though experiment to derive the time dilation:

a stationary observer would see that light travels more distance, and since light speed is constant, it must follow that time must slow down.

What I am having a hard time understanding is not the conclusion, but rather the premise:

Why/how does the light emitted "know" to travel in a diagonal from the point of view of the stationary observer?

Why doesn't the stationary observer see the light go straight "north" from his/her own frame of reference?

Where is light getting its "west" - "east" velocity component from (if velocities don't add up when dealing with light)?

What would happen if the light was emitted from a stationary light source instead? Would the moving observer see the photon miss the mirror in a diagonal in the other direction?

How does a photon "know" it was emitted from a source in a train and thus has to move in a diagonal (from the pov of the stationary observer), and to move straight "north" if emitted from a source in the stationary frame of reference?

Image by: By Sacamol - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=48778704

## marked as duplicate by Alfred Centauri, ZeroTheHero, Yashas, John Rennie special-relativity StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Apr 28 '17 at 5:58

• It doesn't. This picture is seen from a frame where the source is moving. – ZeroTheHero Apr 27 '17 at 23:11
• @ZeroTheHero The picture shows both the moving frame of reference and stationary frame of reference. The question is precisely why does stationary frame the see light moving "west". – pakman Apr 28 '17 at 2:56
• There is really nothing more to say here... – ZeroTheHero Apr 28 '17 at 4:58
• One way to look at it would be to stand in the middle of a room and mount a stationary laser in a perfect vertical position, so that it hits a mirror at the ceiling directly above it, and then gets back to the center of the laser again. Moving it even a slightest bit, and it shouldn't hit the target. Now might be a good time to admit I cheated -- the laser cannot be "stationary"! The Earth, along with the Milky Way, is actually drifting through space at millions of km/h relative to some other galaxy. Seen from some distant alien, the light will surely go diagonally? – Lou Aug 21 '17 at 23:12
• So, the point is that the person in the train is you, standing on Earth. From your perspective (i.e. your inertial frame), the rest of the universe is running away, and your laser is the only one which emits its photons vertically. Some distant alien looking through a telescope will, however, see a different picture. – Lou Aug 21 '17 at 23:14

It has absolutely nothing to do with the light knowing anything.

Consider somebody running and dribbling a basketball. In their frame, the basketball is going straight up and down; in yours, it's going diagonally. It's not that the basketball 'knows' to move diagonally. There's one motion it's doing, and it just happens to look diagonal in your frame. The situation with the light is exactly analogous.

• What? Light is not a basketball; you cannot add the speed of the source. – pakman Apr 28 '17 at 0:31
• @pakman No, you can't just add the speeds, but again, this is irrelevant. The basketball has to be going diagonal because it keeps bouncing between the floor and the person's moving hand. The same goes for the light. It's not like the same light ray can hit the mirror in one frame, but not hit it in another. – knzhou Apr 28 '17 at 0:33
• The point is that two people can see the same thing in two different ways, even without special relativity. Consider a basketball sitting on the floor. A person standing next to it sees it as stationary. A person walking by see it moving - the ball started out near him and keeps getting farther behind him. If the stationary person was dribbling the ball, he would see it moving up and down, like the first picture. A person walking by would see the ball going up and down, and getting farther behind. It would follow a path like the second picture. – mmesser314 Apr 28 '17 at 1:04
• @knzhou The basketball moves horizontally because a force was exerted upon it which gave it a horizontal velocity. What gave light it's horizontal velocity? The basketball is a nice analogy, but It breaks down with massless photons. – pakman Apr 28 '17 at 3:10
• @pakman Do you understand in the steady state why there's no issue? The dribbler exerts no horizontal force while dribbling, in both frames. – knzhou Apr 28 '17 at 3:14

Here is how I think of it.

For an inertial light-clock, treat the first emission as a set (a spray) of light-signals in all spatial directions. Only one of those light-signals will strike that particular light-clock's distant mirror at the spot across from the source...(or think of very short mirrors), then continue to reflect back and forth between the mirrors of that particular light-clock.

Here's my video of it: https://www.youtube.com/watch?v=1-K3VDKjMdM

• Yes, I thought about that too, but imagine it is a laser, or better, the source emits a single photon. – pakman Apr 28 '17 at 2:45