0
$\begingroup$

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.

enter image description here

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?

$\endgroup$
  • 1
    $\begingroup$ 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. $\endgroup$ – Lacklub Mar 21 '16 at 19:49
  • $\begingroup$ 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. $\endgroup$ – AGML Mar 21 '16 at 20:33
  • $\begingroup$ Moving at a constant speed relative TO WHAT????? $\endgroup$ – CuriousOne Mar 22 '16 at 0:28
  • $\begingroup$ @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. $\endgroup$ – aquagremlin Mar 22 '16 at 3:32
  • $\begingroup$ @CuriousOne constant relative to itself,i.e., no acceleration=> inertial reference frame $\endgroup$ – aquagremlin Mar 22 '16 at 3:38
2
$\begingroup$

The answer, of course, is that when the train is moving the person sees the '1' signal in exactly the same way they do when the train is still, because the stencil is moving with the train.

$\endgroup$
  • $\begingroup$ The alien's head has moved away by the time the light has traveled the 1 meter distance from the bulb to his head's original position. Instead, the only light reaching his head is the oblique ray. The stencil is very small and very close to the light bulb so it carries the label of light Ray very early in the light ray's life. A vertical light Ray has a different label than an oblique one. The alien would see the same number only if the stencil was close to his eye. $\endgroup$ – aquagremlin Mar 22 '16 at 3:27
  • $\begingroup$ 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. $\endgroup$ – aquagremlin Mar 22 '16 at 3:34
  • $\begingroup$ @aquagremlin: the stencil also moves by the time the light reaches it, and it is very easy to see that, however large it us, it has moved just enough that the light passes through the '1'. $\endgroup$ – tfb Mar 22 '16 at 7:51
  • $\begingroup$ that is correct, the stencil is moving. so when the vertical ray from the light pulse reaches it, the cutout numbers have moved ahead so no light penetrates. the faster the train(and stencil) are moving, then progressively more rays are blocked. Only the ray of light that is sufficiently oblique to traverse the distance to the stencil will pass. $\endgroup$ – aquagremlin Mar 23 '16 at 1:47
  • $\begingroup$ @aquagremlin and that ray (which is oblique from the point of view of a stationary observer, vertical from the point of view of an observer in the train) will pass through the '1'. And now make the observation that the two observers differ about the time that ray takes to reach the observer in the train and special relativity drops out. $\endgroup$ – tfb Mar 23 '16 at 8:39

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.