Is a blinking pole moving through a barn at relativistic speeds striped?

Question

I am working on a hypothetical to better demonstrate length contraction and I want to verify that the hypothetical is correct.

Let's start with the classic pole-through-the-barn scenario. We have a barn that is slightly longer than 0.8667 light-seconds. We also have a 1 light-second long pole that is moving at 0.5C relative to the barn.

From the pole's frame of reference, the 'front door' and the 'back door' of the barn must be open at the same time in order for the pole to pass through it, since the pole is longer than the barn.

From the barn's frame of reference, however, the pole is contracted by alpha=0.866 and therefore small enough to be enclosed in the barn. Therefore, from the barn's frame both the front and back doors of the barn can be closed for an instant while the pole fits inside the barn.

I want to show that the reason the pole is contracted from the barn's reference frame is the barn's reference frame sees the different parts of the pole at different times (or moments). In particular, the barn's reference frame sees the end of the pole at an earlier time that the front of the pole. The other parts of the pole fall in between those two times/moments.

So, I am adding the idea that the pole is going through a series of color changes. That is, the pole is running through a sequence of four different colors every second. This is happening in the pole's reference frame.

EDIT: The color of the entire pole is changing all at once in the reference frame of the pole. The pole is not striped in the pole's reference frame, but changing color entirely.

I am interesting in what the barn's reference frame 'sees'. I believe it will see a striped pole, in that a series of observers in the barn's reference frame will claim the pole is a different color.

I would also like to ignore doppler, as is the case in almost every special relatively example ever discussed.

In this thought experiment, I believe the barn's frame would see the pole as being striped - comprised of the four colors at any given time. Additionally, the colors would be moving across the pole in kind of a barber-shop fashion. This is because the two ends of the pole would be at a different times/moments in the barn's reference frame and this would correspond to the ends of the pole being different colors than the front or middle.

I think this really helps give a better understanding of what is happening during length contraction and the difference in the perspective of the two frames of reference.

Is there anything wrong with this example that I need to be concerned about? Is there anyway you can think to improve it?

Thanks.

Answer 1

The forward direction of the barn / pole thought experiment is that the pole is length contracted, as you state.

Resolution of the reverse direction (the frame of reference of the pole) is a matter of simultaneity. In the classic version of the experiment, the barn sees the exit open just as the entrance closes, so the pole can fit through, since it is contracted to be short enough to instantaneously fit in the barn. In the pole's frame, there obviously must still be no collision. This is resolved by the fact that the pole sees the barn exit open long before the barn entrance closes. Thus, the pole says "the reason I fit through is the barn neglected to wait until I fully entered before opening the exit, I was never totally fit into the barn." The breaking of simultaneity between the exit open and entrance close is how the pole sees itself fit through.

Just as simultaneity is broken for the doors from the pole's perspective, simultaneity for your light is broken from the barn's perspective. Your light experiment can be done by placing infinitesimal multicolor lights along the length of the pole that are synchronized in the pole frame. They switch RYGBRYGB together in lock step. Each light changing color is an "event" in relativity. When you transform those events to the barn frame of reference with the Lorentz transform, the barn will not see them at simultaneous. The exact pattern of "stripes" will be speed dependent. This is ignoring doppler of course, but the doppler can be accounted for by the barn anyway. The barn frame can mathematically "unblueshift" the light to figure out what it was emitted as, but it will still see the color changes as not simultaneous.