# Distinguishing inertial reference frames

As described in Wikipedia as well as this entry here, "being at rest on the surface of the Earth is equivalent to being inside a spaceship (far from any sources of gravity) that is being accelerated by its engines." Even more fundamentally, in an elevator in space, how do you know you are moving at a constant speed or are stationary?

I am confused about something. Consider the following situation:

An alien with spectacular vision (that can resolve time differences on the order of 10^-12 seconds) is in a train that is stationary and is looking at a light that is switched on about a meter away from his eye. The light is switched on at time t1 and he perceives it at t2. Now consider the situation when the train starts to move.

The alien sees the same event. There are no windows and there is no way the alien can get information from outside the cabin. According to the fact that the train is not accelerating but moving at a constant velocity, nothing the alien can do should tell him that he is moving. But consider which photons the alien is seeing.

When the light is switched on, the photons go in all directions. In a stationary train, the alien sees the photon going straight up, but in the moving train, the photon that reaches his eye, is the one that takes off from the light at an angle.

Now make a stencil with numbers cut out on it like so:

and put it over the light like so:

When the train is stationary, the alien sees the number '1' but when the train is moving he sees the number '5'. Please forgive the scale. I wanted to make the numbers readable so I made the mask very large. You might be tempted to say that by the time the oblique ray reached the mask, the mask will have moved so the alien will really see a different number (2 maybe?). But make the mask really small so it is really close to the source. And make the stenciling really small so you can resolve small differences.

So it seems to me that such a 'light speedometer' can tell us how fast our frame of reference is moving even without any information from outside our frame. It relies on the fact that we know the speed of light is constant in all inertial reference frames. This seems to suggest that we can distinguish inertial frames of reference. It goes all the back to the idea of Newton who spoke about absolute reference frames here

Please note, I have not made any claims about time or the concept of simultaneity. I am not discussing special relativity. Yet the concept of the space elevator introduced by Einstein now bothers me. With such a 'light speedometer' shouldn't I be able to know how fast I am going in an absolute sense?

• If you use a "mask" like that for light or an inertial projectile, then the projectile will be emitted from the source, go through the 1 exactly, and then hit the observer. This can be visualized in a Newtonian sense fairly easily, because all three are in a line, and they will remain in a line at every point in time. From his perspective, the projectile would have to bend to the left to hit the 2, then bend back to go into his eye. At least, that is the case if the mask moves with him. If it isn't moving with him, then you're just measuring speed between two reference frames. Mar 21, 2016 at 19:49
• Maybe you can clarify in the question which things (lightbulb, stencil, alien) are supposed to be moving, and which are supposed to be still? I think if you do this the answer might be clearer to you (and if it isn't it will still make the question much easier to answer). If all three items are on the "moving" train then the alien of course sees the light beam pass through 1, exactly as if the train were still.
– AGML
Mar 21, 2016 at 20:33
• Moving at a constant speed relative TO WHAT????? Mar 22, 2016 at 0:28
• @agml why are you confused? The drawing is clear- everything is on the train. As I said - in the moving train, the photon that reaches his eye, is the one that takes off from the light at an angle. The reason he ONLY sees the oblique Ray is because his head has moved away from where the vertical Ray will impact. To make it clearer, imagine that the light is only briefly pulsed at t1. By t2, there is no light being emitted. The only light being detected is from the pulse at t1. Mar 22, 2016 at 3:32
• @CuriousOne constant relative to itself,i.e., no acceleration=> inertial reference frame Mar 22, 2016 at 3:38