# Is it best to look at light as a particle when trying to understand special relativity?

So my course about special relativity explains time dilation using a moving train, where one sends up (i.e. perpendicular to the direction of movement) a light pulse which gets reflected etc. (a similar example is to be found here so you guys know what I'm talking about)

Let's say the source of the light pulse is a flash light. In the moving frame of reference, it is pointed upwards, and thus only has an upward component. Everything fine so far.

The thing is, that when you look at it from the outside ("the train station"), I picture the flash light to still be pointed directly upward, but somehow when the pulse leaves the flash light, it gets a horizontal component. This does not make sense if you think of it in terms of some stationary ether (which is also wrong as Michelson & Morley showed).

The problem is that I can't seem to get my mind around the fact that it somehow seems that the flash light is pointed at an angle in the outside frame of reference. Except if I think of light as photons (particles), then it seems intuitively correct that they get a horizontal component (compare it to a skater throwing up a tennis ball). So, when trying to understand SR, do you have to think of light as particles?

My course states this nowhere explicitly so I'm not sure.

I might have answered my own question again by formulating it in a more or less ordered fashion, as happens so often when I post it here :P

## 1 Answer

With a particle it's obvious what a velocity is. Since the velocity is a vector it's obvious how to add another velocity to get the resultant velocity, and I'd guess this is why you're thinking that maybe we should consider the light as particles.

However for a plane wave we can define a wave vector that points in the same direction as the velocity of the wave (mostly). In fact the Wikipedia article I've linked to discusses how this can be represented as a four vector. The point is that we can define a velocity of the wave as a vector and it can be added to other velocities just like the velocity of a particle. There is no need to consider the light as particles to understand why it moves at an angle in your observer's frame.

• Wow, spot on answer that removes the problem of the wave-particle duality all together. Thanks! – Jan M. Aug 21 '12 at 20:25
• Take the "problem" part in the above comment with a grain of salt :P I meant that your answer made it so that I don't even have to involve the fundamental nature of light, I just have to look at the mathematical representation. – Jan M. Aug 21 '12 at 20:50