# Components of speed of light

I'd like to start off by saying this may be totally wrong; thus I would like some help clarifying this.

Suppose you are in a vacuum, and a beam of light is travelling at, say, a N$$45°$$E bearing. The light ray has a velocity $$c=3\cdot10^8$$. Now, we can split this velocity up into North-South and East-West components.

I could calculate the velocity of this component, which is just $$v_{\text{component}}=c\sin{45°}$$.

Here's my question: for someone who is living in one dimensional space, someone who can only see things along the North-South axis, the speed of light is no longer $$3\cdot10^8$$. For them, since they don't even know that the East-West axis exists, they measure the speed of light as roughly $$2.12\cdot 10^8$$. So, can the speed of light can be inconsistent depending on your perspective? Even though this is only a component of the speed of light, should the people on the North-South axis still measure it as $$c$$?

• But the actual beam of light only crosses the N-S axis at one point; there is nothing physically moving either N-S or E-W. If there was a cousin of your creature living on the NE line, they'd see the beam moving at c. Jul 25, 2019 at 13:59
• Your last paragraph doesn't make sense. If someone is "living in a one-dimensional space," everything in that space (including light) would be constrained to moving in that one dimension. Jul 25, 2019 at 14:39
• The person in the one dimensional space sees an instantaneous light flash, not a beam. Jul 25, 2019 at 22:35

Newton's laws remain valid when you project out one or two of the spatial dimensions. What you've described is an example of the fact that this does not hold in general, for all our laws of physics.

I'm not sure what you mean by one dimensional, because one dimensional is a literal point, but the closest we can get to one dimensional to explain this is a line.

Let's say there is a two dimensional space, the xy plane, but you can only see along the y axis, and your position is (0, 0) facing the North. The light beam is travelling parallel to the x axis at y=5, lets say. BUT since you're unable to see anything to your left and right you only see when the light beam intersects your line of sight, x = 0. It intersects at the point (0, 5). So the time t at this intersection you will see a flash of light. There is no velocity because there is no distance for it to travel. The formula for velocity is v = d/t. The d is zero so v = 0. You just see a flash for some duration t (also AT a time t, but since there really is no way to measure time without space, its meaningless to define t)

This holds true for a light beam with the equation y = x + 5. So it is 45 degrees with the x axis and 45 degrees with the y axis. It will still intersect your line of sight at (0, 5) and will have no velocity because it is not travelling any distance in your point of view.

So to answer your question, the reason we can measure velocity is because we have an x and a y direction. Without our standard definition of space in xy or xyz you can't measure velocity because there's no distance. It's just a flash in space (read the note at the end, because it's not really a flash). If the light beam was travelling in your line of sight away or towards you, you would measure it as a velocity c, BECAUSE it can travel a measurable distance between you and itself. If it was completely one dimensional, appearing at a POINT, you couldn't measure anything. :) Hopefully that answers your question.

Note: technically, with your line of sight, you can only see points in front of you. And points are zero width and zero height, so you shouldn't even be able to see the light cross. BUT for the sake of the thought experiment, lets say you can see the light.

• one dimensional is a literal point - zero dimensional is a point. One dimensional is a line. Sep 28, 2019 at 6:45

First of all, Electromagnetic waves cannot be split into components like vectors because Electromagnetic waves aren't vectors. Secondly, According to Einstein's theory of Special Relativity, Speed of light is constant from whichever point u observe it from. And thirdly, If a beam of light would be observed by someone who could see only one axis, then As soon as the light crosses that axis, (from POV of the observer) a single dot would appear for them(since they would be able to see only a single axis

You have confused yourself by confusing issues concerning the speed of light with issues concerning its direction. The best way I can conceive to dispel your confusion is as follows. Imagine you live somewhere upon a y axis. A friend is at the origin with a torch. The y component of the speed of the light from the torch can take any value between +c and -c depending upon the direction in which your friend shines the torch. If your friend shines the torch along the x axis the component of light's speed in your direction will be zero.

The speed of light does not change when your friend moves the torch from one angle to another. The component in your direction is simply that, a component. Physically the speed of light is the sum of the components- you cannot simply ignore one of them.

In the example you give you would be correct to say 'The component of the speed of light from the beam in my direction is csin(45)'. You would be wrong to say 'The speed of light is csin(45)'.