A big, circular room

#1

Imagine you were in a circular room, basically inside of a cylinder. In the center of the room is a small turntable with a laser-pointer sitting on it.

If the circumference of the room is 100 feet, and the turntable rotates at one revolution per second, if the laser-pointer is powered on, you will see the laser dot appear to move across the wall at 100 feet per second.

Now what if the room were expanded to be 1,000 feet in circumference? Presuming that the laser-pointer is powerful enough to reach the wall, the dot will appear to move at 1,000 fps. How about a room that is 10,000 feet in circumference? You get the idea.

Now, imagine a room that is 186,000 MILES in circumference - yes that’s a big room - but now, would the dot appear to move at 186,000 miles per second? The speed of light? What if we made the room even bigger, say 200,000 miles in circumference. The pointer still rotates at 1 revolution per second. How fast does the dot appear to move to a viewer at the wall? Yes, it will take about a sixth of a second for the light to reach the wall, but that doesn’t matter.

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#2
My answer and a question for you

Nothing physical is actually moving along the wall, it’s only a visual pattern. A pattern like that can “propagate” faster than the speed of light as it’s not actually physically propagating - there is no causal link between the photon hitting one part of the wall and any other. So, at least theoretically, an observer could watch the light appear to move essentially continuously along the wall faster than the speed of light. But I think there is a practical problem - your laser is too puny. Most of the wall won’t see any light at all.

A similar question I thought about recently is how the light from the sun might be seen from the surface of a large sphere with the sun at its center. The sun makes a hell of a laser! But the energy it outputs is still finite, and photons quantized. So even large areas of a sphere with sufficient radius would see a photon very rarely.

So which points would see light? I think it must be a probability distribution, but would it be uniform everywhere? Or concentrate in patches (even points?) which become more disjoint as the radius of the sphere increases? It’s an issue of how light is emitted from the atoms in the sun.

For the same reason, much of the wall of your room might see no light at all. The questions of which points the light reaches is now an issue of the pointer’s rotation. Even a planck length angle change of the pointer would cast a large arc on the wall. Again would the probability distribution of the area the light reaches be uniform? Constant, possibly in patches? Or would it oscillate with successive rotations?

#3

Continuing the discussion from A big, circular room:

Well the actual, practical limitation is a room with a diameter greater than 4x that of Earth.

The correct answer is as you state, which is that an image can appear to move faster than the speed of light.

The question of the sun as viewed from a sphere surrounding it is basically the question of how spot and flood lights (of similar lumens) differ in intensity and focus.

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#4

:rofl:

Also it looks like lasers are pretty powerful… You’d need a much bigger room to start having problems. I didn’t check the math, but you’d probably need a bigger universe to deal with my problem.

I guess the word focus might encompass this, but here is my real concern. I commissioned an artist to depict my scenario:

image
image.jpg1743Ă—2523 135 KB

It looks like the answer is that the probability is uniform across the sphere. Light really is a wave after all and expands in every direction. Hard to reconcile…. I need to learn QFT.

#5

the weird thing for me is that the image would be moving faster than the light bouncing off the wall into your eyes.

thought about it for a while and decided it doesn’t change the fact that you’d see the image moving faster than the speed of light. cool.

#6

well I think the speed you perceive it to be moving might change the further it gets from you. The slower speed of light would slow things down if the ending point you’re using to measure the speed of the image is further from you than the starting point is.

#7

:thinking: What are the starting and ending points? Do you mean if you aren’t at the center of the room?

#8

Yeah, he said “how fast does the dot appear to move to a viewer at the wall?”. For starting and ending points, I’m saying that if you tried to measure not just how long one revolution takes, but how long it takes the image to get from one point to another and calculate the speed that way. You’d get different answers based on the points you choose thanks to the slower speed of light.

#9

Ah I missed that completely. I thought the viewer was at the center.

So you mean it would appear to move at different speeds at different parts of the circle as the ratio between the rpm and the delay of the light reaching you changes. I need to think more about it. I could make a little visualization.

#10

this oversimplification is how I thought about it.

Say you’re one meter away from where the light first hits, and you measure the time it takes the image to go one meter, and let’s just say that that end point is then 2 meters away from you.

Now pretend it takes light 3 seconds to go one meter, and it takes the image 2 seconds to move one meter.

When the light from the first spot hits your eyes, the light from the second spot is one second into its 6 second journey to your eyes, so you would measure that it took 5 seconds for the image to go one meter, rather than 2.

Obviously these units are ridiculous and it’s not accounting for the curve of the wall/your position with respect to the wall but hopefully you get the idea.