Theoretical problem with an empty seat going faster than light

[conquest]

Hi everyone,

Recently I randomly thought of a thought experiment of something going faster than light, along the lines of a shadow or some other "non-information carrying object". In this case it would be an empty seat.

The idea is to take 800 million and one chairs of half a meter breadth and put them in a row. Then take 800 million people and make them sit on the first 800 million chairs. Then the trick is to get them to simultaneously stand up and move to the seat next to them in 1 second. The idea is that the empty seat now traveled 400 million meters in 1 second.

Hopefully the general idea is clear. I was discussing the idea with some people and it seemed they had a serious (theoretical) problem with the set up. Basically their question was about how one gets everyone to switch seats at the same time. I proposed giving everyone a clock before going to their seats (synchronized clocks) then everyone moving to their seats and performing a calculation to re-synchronize their clock with the clock of the person on the first chair. Then everyone switches seats at a particular time.

This argument was not convincing, but time constraints made it so the people I was discussing with could not explain the exact obstruction to me.

So I guess my question is if you could explain what the problem with this thought experiment is. More clearly, I want to know why this experiment is really theoretically flawed?

Of course if you think it is possible and can maybe fix the problem (that I do not quite see) then that would also help.

I hope the question is at least clear, thanks in advance.

 

[mathman]

Assuming synchronizing watches can be resolved, there is nothing wrong, but what is the point? You start wit one empty chair and one second later you have a different empty chair - so?

 

[Grinkle]

One thought and one question.

The thought -
Describe your observer who reports all participants changed seats simultaneously.

I don't think the participants would agree with this observer that they moved simultaneously.

The question -
Why is this equivalent to an actual chair moving faster than c?

 

[conquest]

The thought -
Describe your observer who reports all participants changed seats simultaneously.

I don't think the participants would agree with this observer that they moved simultaneously.

There is not really an observer involved, right. After they are seated the participants are always in the same inertial frame, so they should all agree on the simultaneity of events, right?

Assuming synchronizing watches can be resolved, there is nothing wrong, but what is the point? You start wit one empty chair and one second later you have a different empty chair - so?

Why is this equivalent to an actual chair moving faster than c?

Let me clarify that I obviously don't claim that any chair would be moving faster than the speed of light. The point is that the empty seat, i.e. the vacancy, moves faster than the speed of light. It is similar to the well-known example of a bug passing in front of a light and casting a shadow on a screen. If the screen is far enough away than the shadow moves faster than the speed of light, see:

https://en.wikipedia.org/wiki/Faster-than-light#Light_spots_and_shadows

How about the problem about synchronizing clocks?

 

[PeterDonis]

the empty seat now traveled 400 million meters in 1 second.

Yes, this is true, and there is nothing wrong with this thought experiment as long as you are not claiming that it somehow shows a "paradox" or a violation of relativity. It doesn't.

 

[PeterDonis]

Describe your observer who reports all participants changed seats simultaneously.

I don't think the participants would agree with this observer that they moved simultaneously.

Sure they would, at least to a good enough approximation. The participants each have to shift position by just one chair, which means they have to move at roughly 1 meter per second. This speed is negligible as far as relativistic effects are concerned, so it is perfectly fine to consider all the participants at rest relative to the chairs and do things in the reference frame in which the chairs are all at rest. Then we just need to synchronize all clocks in this frame (which is easily done, look up "Einstein clock synchronization"), and the participants all agree to shift chairs at the same instant as seen on the clocks.

 

[conquest]

Yes, this is true, and there is nothing wrong with this thought experiment as long as you are not claiming that it somehow shows a "paradox" or a violation of relativity. It doesn't.

Of course I do not claim that it shows any such violation, I thought it would simply supply a cute example of "something" going faster than the speed of light. But, to come back to my question, are you saying there is no problem with the thought experiment at all?

 

[PeterDonis]

the empty seat, i.e. the vacancy, moves faster than the speed of light. It is similar to the well-known example of a bug passing in front of a light and casting a shadow on a screen. If the screen is far enough away than the shadow moves faster than the speed of light

All of these are fine, and none of them show any "paradox" or violation of relativity either.

 

[PeterDonis]

are you saying there is no problem with the thought experiment at all?

Yes. Do you think there is? If so, what is it?

 

[conquest]

Yes. Do you think there is? If so, what is it?

Actually I don't see any problem either, but it seemed the people I was discussing with did! So I assumed there was some subtlety that I was not seeing somehow.

 

[PeterDonis]

it seemed the people I was discussing with did!

Did they give any details about what they thought the problem was?

A common misconception about such scenarios is that they somehow violate the rule that "nothing can go faster than light". The short answer to that is that the empty seat is not a "thing" to which that rule applies. But this being an "I" level thread, I'll give a somewhat longer and more technical answer.

The actual rule is that any two events that are causally connected must be timelike or null separated--i.e., the "effect" must be within the future light cone of the "cause". In the scenario you describe, the empty seat starts out at one end and ends up on the other end; but the cause of the empty seat at the end is not the empty seat at the start. It's the participant who moved from that seat, now empty, to the adjacent one. That participant moved much more slowly than light (about a meter per second), so there is no problem with causality: the seat that ends up empty is well within the future light cone of the event that caused it to be empty, the participant moving out of it. (And, similarly, the cause of the seat that was originally empty now being full is not the empty seat at the other end; it's the adjacent participant moving into it, much more slowly than light.)

A slightly more sophisticated objection is that the participants all moved simultaneously, which means that the events of them moving are spacelike separated, so somehow there is still an issue. But the cause of any given participant moving is not the other participants moving: it's the previous arrangement that they all made to move at the same instant by the synchronized clocks. All of that (the arrangement and the synchronization) took place at or below the speed of light, so again there's no issue.

 

[Dale]

I agree with Peter's response. There is no theoretical problem here, causality is not violated.

 

[conquest]

Did they give any details about what they thought the problem was?

Let me provide some details. The problem was definitely not with the misconception you point out. The problem was about how you make sure that all the participants move at the same time. This is necessary since otherwise people cannot switch seats because they bump into one another and so on and the whole thing is a big mess. A lot of this kind of "congestion" would really matter for the eventual speed of the vacancy. I proposed simply agreeing on a time to stand up and move beforehand synchronizing 800 million clocks and giving one to each participant. The objection at this point was that once the participants arrive at their respective seats the clocks would not be synchronized any more. The people I was discussing with thought this would be a big problem, but to me it seems to be fixed with relative ease.

 

[conquest]

I agree with Peter's response. There is no theoretical problem here, causality is not violated.

To reiterate, I also agree about that. In fact also the people I was discussing with agree about that. In fact the idea is basically to give a cute example of something going faster than light without violating causality. The problem is really just to determine if it is possible to get 800 million people sitting in a line of 400 million meters to stand up at the same time.

 

[conquest]

A slightly more sophisticated objection is that the participants all moved simultaneously, which means that the events of them moving are spacelike separated, so somehow there is still an issue. But the cause of any given participant moving is not the other participants moving: it's the previous arrangement that they all made to move at the same instant by the synchronized clocks. All of that (the arrangement and the synchronization) took place at or below the speed of light, so again there's no issue.

Thank you! This is what we were really talking about. For some reason I didn't see it the first time I read your post (sorry for the previous post).

 

[Dale]

The objection at this point was that once the participants arrive at their respective seats the clocks would not be synchronized any more.

You can do Einstein synchronization once they are all in their respective seats each with their clock.

 

[conquest]

Thank you Dale and mostly Peter for completely answering my question

 

[PeterDonis]

The objection at this point was that once the participants arrive at their respective seats the clocks would not be synchronized any more.

If the clocks don't move (they each stay with the seats they started with), then they will stay synchronized. Clocks that start out at rest in a seat, but move along with the participant in that seat to the next seat over, will, in principle, get out of synchronization with clocks that stay at rest relative to their seat of origin. But, as I noted in a previous post, the amount by which they will get out of synchronization is negligible.

 

[georgir]

As long as you consider the empty chair a "thing", there can be "things" moving faster than light, no problem. More traditional examples along the same idea are the bright spot a light beam makes on a far away screen, or the crossing point of a guillotine, etc.
In neither case is it an actual object or information moving faster than c. Even though it might create the illusion of it from some reference frames, from others it may very well seem to be moving in the other direction or even be at multiple places at once, etc.

 

[Maxila]

The idea is to take 800 million and one chairs of half a meter breadth and put them in a row. Then take 800 million people and make them sit on the first 800 million chairs. Then the trick is to get them to simultaneously stand up and move to the seat next to them in 1 second. The idea is that the empty seat now traveled 400 million meters in 1 second.

I don’t see how you can conclude anything other than; the empty seat at one end traveled at ½ meter per second relative to the people and became an occupied seat and the occupied seat at the other end traveled at the same rate and became an empty seat?

The only way to come to your conclusion is if the specific seat moved the 400 million meters relative to the people, which it does not; each individual seat only moves ½ meter per second relative to the people.

 

[Ibix]

I think the OP was going for something like a Mexican wave effect. A Mexican wave done spontaneously works by each person reacting to the person to their left (or right). But there's nothing stopping you from pre-planning one - everyone in a stadium one light minute long agrees in advance that the people at one end will stand up at 12:00:00 and the other end at 12:00:30, and everyone in between at the appropriate time by linear interpolation. Then the Mexican wave travels at 2c.

But the point is that nothing is actually travelling; nothing is being communicated faster than light. It's just the human mind's way of abstracting what it sees that proposes that the wave is one entity (particularly if you know how they happen in real life). It's a very convenient view in a lot of respects, but it is totally betraying us here.

 

[Maxila]

Exactly, there is no cause and effect and the "faster than light" is an illusion. Its as if I pre-arranged a time for someone 1 light hour away to send me a message "help is on the way" then 59 minutes after that time I send out to them an SOS. It would appear we communicated faster than light (they responded in under a minute even though they were 1 light hour away) but there was no cause and effect, just two prearranged communications that gave the illusion of one.

Other than reminding us how easy it is to give the illusion a physical impossibility is real, or as a puzzle to solve, I don't see scientific value in this type of thought discussion?