# Moving fairground light, thought experiment

1. Mar 26, 2014

### delsaber8

Ok, I have an experiment, well actually it is more of a question than an experiment. I have a very elementary background when it comes to relativity.

So anyway, here is what I am wondering: Picture an extremely long line of those lights you see on the fair grounds (the ones that are timed to light up one at a time to make it look like the light is moving along the track of bulbs). Now picture the timing of the lights where it is so precise that it could simulate the light moving along the track of bulbs to be faster than light. What would this light look like? would it experience relativistic effects or would: if for example it was set up say beside a laser and the two raced, it would win.

Sorry if this sounds a little vague I'm having great difficulty explaining what I am thinking. Please do not hesitate to ask for clarification.

2. Mar 27, 2014

### Staff: Mentor

Since nothing is actually moving in the direction the lights are lighting up, there would be no relativistic effects. This is similar to sweeping a laser beam across the Moon from here on Earth. The spot could easily move faster than light because the photons are not traveling across the Moon, but towards it. You could make the lights light up at any speed if you set them up correctly, even FTL. (Again, nothing is actually moving FTL. It's only a question of timing the lights to light up at the right time)

3. Mar 27, 2014

### A.T.

Yes it is basically the same issue. Here the laser thing explained:

4. Mar 28, 2014

### ghwellsjr

Before we can deal with the simulation looking faster than light, we need to specify what looking like the speed of light might be. If it were a string of lights spaced one foot apart and since the speed of light is one foot per nanosecond, shouldn't we see each successive bulb light up one nanosecond after the previous one? So what does it take to make that happen? This may surprise you, but it requires all the bulbs to light up simultaneously (as defined by their mutual rest frame). Then if you were located at the beginning of the line of lights stretching off to the right, you would see the second bulb light up 1 nanosecond after the first one (colocated with you). You would see the third bulb light up one nanosecond after the second one and so on. The lights would appear to be moving away from you to the right at the speed of light.

What about a person standing at the far end of the line of lights? Well, he is going to see the bulbs lighting up in the opposite direction, going away from him toward the left, back in your direction.

Or consider a long line of lights stretching away from you in both directions. You will see the bulbs lighting up going away from you in both directions. In fact, no matter where anyone is standing along the line of lights, they will see the lights appear to be moving away from them in opposite directions at the speed of light.

This may be a surprise to you again, but a laser would actually appear to be traveling at one half the speed of light. That's because when you turn it on, although it takes one nanosecond for the light to get 1 foot away from you, it takes another nanosecond for its reflection off an object one foot away to get back to you. So even though the bulbs are timed to look like they are turning on at the speed of light, they would win against a laser, they don't have to be timed to look like they are faster than the speed of light, they are already twice as fast.

I think you did a very fine job.

But you ought to consider that if you wanted to make the lights appear to go faster than the speed of light, although you could do this for a person situated at a particular place along the line of bulbs, people at other locations would see it completely differently. Better to stick with the simple arrangement of making all the lights flash simultaneously.

5. Mar 28, 2014

### pervect

Staff Emeritus
Lets consider two lights in this string. In the frame of the light string, suppose A flashes first, then B flashes next. There will be some frame (moving relative to the light stirng) in which A and B will flash at the same time. There will be another (moving) frame in which B will flash first and A will flash last.

There is a jargon-y name to describe the situation, which is that the lights are "space-like separated".

6. Mar 28, 2014

### ghwellsjr

That isn't always true but what is always true is if A and B flash at the same time in their mutual rest frame, then in other moving frames they can flash in either order. But what has this to do with the OP's question?

Let's be clear, it's not the two lights in the string that are "space-like separated", it's the two events of them flashing at the same time in their mutual rest frame that are "space-like separated".

7. Mar 28, 2014

### delsaber8

By the sounds of it, we are dealing with relativity of simultaneity, similar to the classic train problem. Now I've always had a bit of trouble understanding this concept. I understood the one with the car crashes on separate sides of the world. Now I know what happens in this case but I don't truly understand why. Unfortunately I have only a small understanding of calculus, so if a proper explanation requires the math, it will most likely go in one ear out the other. However if someone could clear this up that would be great.

8. Mar 28, 2014

### ghwellsjr

There's no relativity of simultaneity since no one is traveling at high speed, certainly not your fair-goers and we're only considering one frame.

It's simply a matter of the speed of light. If a flash occurs 1 foot away from you, you will see it 1 nanosecond later (according to your rest frame). If it's two feet away, you will see it 2 nanoseconds later, three feet away, you will see it 3 nanoseconds later. That doesn't take any math at all, does it?

So if all the lights flash at the same time, you will see them flash one by one from the closest to the farthest and it will look like a flash of light moving away from you at the speed of light.

Would a spacetime diagram help clear it up?

9. Mar 28, 2014

### delsaber8

I see, so then why exactly could different observers, observe the flashes of light in a different series? Again my apologize my background is little to nothing in this field.

10. Mar 29, 2014

### ghwellsjr

We're talking about different stationary observers at different locations along the string of light bulbs (not different observers traveling at high speeds). If you see the lights flash away from you to the right, someone already to the right of you at the other end of the string will see them flash away from him to the left. Someone in the middle will see them flash away from him to the right and the left. All appearing to be traveling at the speed of light.

Maybe I don't understand what you mean by "a different series".

11. Mar 29, 2014

### delsaber8

My apologize for the confusion, I completely agree that is not relativity of simultaneity. I was referring to pervect's post, in which he talks about the lights flashing in different orders, which is more or less what I meant by a different series.

12. Mar 29, 2014

### ghwellsjr

He wasn't talking about what any observers actually see, which is what you said was your concern, but rather what the Coordinate Times are of the flashes of light according to different reference frames. But these different reference frame have no bearing on what any observers would see. I have no idea why he brought up this irrelevant subject.

13. Mar 29, 2014

### pervect

Staff Emeritus
If you think about it. you'll realize that there is always some frame in which two spacelike separated events are simultaneous.

In addition, with certain additional constraints that amount to a uniform (pseudo) velocity, the OP's original scenario is equivalent to one where all the lights flash simultaneously - in some different/moving inertial frame. This would represent the case of an infinite (pseudo) travel velocity in that particular frame. I think that's worth pointing out to the OP.

Yes, the flashes are what are space-like separated.

Last edited: Mar 29, 2014
14. Mar 29, 2014

### ghwellsjr

That's true but that's not what you said. You said:
That statement is not always true.

I have no idea what you are talking about. I doubt the OP does either. If you think it's worth pointing out, could you please explain in more precise detail?

Look, I pointed out that there are ways to flash the lights so that a particular observer (stationary at some point along the string) will see the lights flash so that they appear to him be traveling at faster than the speed of light, but other stationary observers at other locations will see something totally different. The only way to flash the lights so that everyone at the fair sees the same thing, no matter where they are along the string of lights is to flash them simultaneously in their mutual rest frame.

15. Mar 29, 2014

### ghwellsjr

I decided to make some spacetime diagrams depicting how two observers at either end of a string of simultaneously flashing lights will see the flashing lights as moving away from them at the speed of light, no matter where they are along the string and no matter what frame we use to depict the scenario. Here is the rest frame of the observers and the string of lights:

Let's assume that you are represented by the blue line with your clock ticking at 1-nanosecond intervals as marked by the blue dots. The flashes of each bulb are depicted by the red dots at the Coordinate Time of 0 and the images of them are depicted by the thin red lines propagating in both directions at the speed of light. The other observer is depicted in green at the far end of the string. Each observer cannot see the bulbs when they flash, they have to wait for the propagation of the different images to reach them.

What do you see? At your clock time of zero, you see the flash of the first bulb colocated with you. At your clock time of 1 nsec, you see the flash that was emitted by the bulb that was 1 foot away from you. At your clock time of 2 nsec, you see the flash that was emitted by the bulb that was 2 feet away from you and so on for the remainder of the string. It looks to you like the light is traveling away from you to the right at 1 foot per nsec which is the speed of light.

What does the green observer see? At his clock time of zero, he sees the flash of the tenth bulb which is colocated with him. At his clock time of 1 nsec, he sees the flash that was emitted by the ninth bulb which is 1 foot to his left. At his clock time of 2 nsecs, he sees the flash from the bulb that is 2 feet to his left and so on for the entire string. It looks to him like the light is traveling away from him to his left at 1 foot per nsec which again is the speed of light in the opposite direction.

So you both see the same thing, the light appears to be traveling away from both of you at the speed of light.

We could also consider another observer at the midpoint of the string, colocated with bulb 5. He will see the light appearing to move away from him in both directions at the speed of light.

Now let's transform the coordinates of this scenario to a frame that is moving at -0.2c:

This is what pervect was talking about: in this frame the lights are not flashing simultaneously but rather each one comes on a little later than the previous one. But this new frame doesn't in any way change what each observer sees. You (the blue observer) still see the light appearing to move away from you to the right at the speed of light (according to your clock and ruler) and the green observer sees the light appearing to move away from him to the left at the speed of light according to his clock and his ruler and another observer at the midpoint sees the light appearing to move away from him in both directions at the speed of light according to his clock and his ruler.

Transforming the original frame to a speed of 0.2c, we get this diagram:

Now we see that the lights flash in a different order, each one coming on a little earlier than the one before but still, all observers continue to see the light appearing to move away from them at the speed of light.

Hope this helps.

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Last edited: Mar 29, 2014
16. Mar 29, 2014

### delsaber8

Thank you, I see how this works now, a little tricky to think about at first but the diagrams really helped.