High School Paradox of Simultaneous Flashing in a Moving Triangle of Lights

[O Great One]

TL;DR

Triangle of lights.

There are 3 lights in the form of a triangle...
A, B, and C are lights and are stationary with respect to each other. S1, S2, S3 are spaceships.

                                    B

                        S1                      S2

              A                     S3                    C

S1 is moving from A towards B. S2 is moving from B towards C. S3 is moving from C towards A. A, B, and C flash simultaneously in their frame of reference. So in the frame of reference of S3, A flashes first followed by C flashing. In the frame of reference of S2, C flashes first followed by B flashing. In the frame of reference of S1, B flashes first followed by A flashing. So the sequence of flashing is A, C, B, A. But wait! A flashed first. How can it flash last? How can A flash both first and last?

 

[hutchphd]

You do not need all the complications of the triangle to state this problem. Einstein's train with lightning flashes in 1D is equivalent. See "relativity of simultaneity" wherever such things are considered. A before B, B before A, A and B simultaneous is the stuff of Einstein's original paper. No news here.

 

[PeterDonis]

How can A flash both first and last?

It doesn't. It flashes first in one frame and last in another. There is no frame in which it flashes both first and last.

 

[Dale]

Summary:: Triangle of lights.

How can A flash both first and last?

Indeed. How can it?

It can because the order of the flashes is physically irrelevant. None of the flashes caused the others. You may care which order they occurred, but nature simply does not care.

The order of non causally related events is simply not a matter of physical fact. You are free to choose any order you like and adopt an arbitrary convention to make it so.

 

[O Great One]

Can anyone describe what happens then and in what order the lights flash?

If A flashes before B and B flashes before A are both possible and just depends on the frame of reference and all frames of reference are equally valid then how can the light from B be both simultaneously traveling and not traveling through space at the moment that A flashes?

 

[A.T.]

If A flashes before B and B flashes before A are both possible and just depends on the frame of reference and all frames of reference are equally valid then how can the light from B be both simultaneously traveling and not traveling through space at the moment that A flashes?

Simultaneity also depends on the frame of reference.

 

[russ_watters]

How can A flash both first and last?

How are different signals traveling different distances in different amounts of time confusing?

As far as I can tell, this scenario has nothing to do with Relativity. The problem works the same for a marching band.

A, B, and C flash simultaneously in their frame of reference.

The way you said that is impossible, but presumably they have some synchronization convention for the flashing.

 

[Dale]

Can anyone describe what happens then and in what order the lights flash?

Yes, anyone can describe it. And each description is equally valid.

how can the light from B be both simultaneously traveling and not traveling through space at the moment that A flashes?

Again, because simultaneity doesn’t matter. There is no physical fact about what B is doing when A flashes. Nature simply doesn’t care, regardless of how much you think she should.

 

[anuttarasammyak]

Summary:: Triangle of lights.
So the sequence of flashing is A, C, B, A. But wait! A flashed first. How can it flash last? How can A flash both first and last?

I could follow you all the text before this sentence. You should pay attention to make a sequence from the event sequences observed in different inertial frames of reference.

 

[Ibix]

A flashed first. How can it flash last? How can A flash both first and last?

According to S1, A is behind it. According to S3, A is infront of it. A is behind. How can it be infront? How can A be both infront and behind?

Some things are relative and the description depends on the observer. More things are observer dependent in Einsteinian relativity than Galilean relativity, including the order of spacelike separated events. In my first paragraph in the italicised part that parodies your question, note that I've stripped out the observers who are describing A as infront or behind, and that's actually the only thing that makes the question confusing. Put "if S1" and "of S3" in the appropriate place and the question becomes trivial.

This is a good rule of thumb for any relativity problem: always state who is making any measurement. We gave a good instinct for when we need to specify the observer in Newtonian physics, from everyday experience. But relativity is more complex and our Newtonian intuition betrays us - more things are relative, and specifying the observer or frame used helps to remind us to check our assumptions.

Your particular problem here seems to be failing to recognise the more complicated causal structure in relativity. In Newtonian physics an event can only be before, after, or at the same time as another. In relativity, an event can be timelike or lightlike separated from and after another, timelike or lightlike separated from and before it, or spacelike separated from it. In the latter case, order is frame dependent. This doesn't matter because the events cannot directly affect each other due to the finite maximum speed in relativity: they are too far apart.

 

[PeroK]

So the sequence of flashing is A, C, B, A. But wait! A flashed first. How can it flash last? How can A flash both first and last?

You might be interested in question 3 from Chapter 1 of "Spacetime and Geometry" by Sean Carroll:

3. Three events, A, B, C, are seen by observer $O_1$ to occur in the order A-B-C. Another observer, $O_2$ sees the events occur in the order C-B-A. Is it possible that a third observer sees the events in the order A-C-B?

Note that what you interpret as a radical departure from simple common sense has been part of modern physics for over 100 years. If relativity had basic, fundamental flaws, these would have been identified a hundred years ago.

 

[Ibix]

If relativity had basic, fundamental flaws, these would have been identified a hundred years ago.

To forestall likely comments on this, we are all aware that relativity is probably only an approximation to a more complete theory. However, it is not internally inconsistent, and consistency is the only thing you can check for with thought experiments. Hence PeroK's comment.

I strongly recommend learning to draw spacetime diagrams. Once I did, and once I saw how to transform one into another, I realized that I had a clear visualisation of special relativity's self-consistency.

 

[A.T.]

So the sequence of flashing is A, C, B, A. But wait! A flashed first. How can it flash last? How can A flash both first and last?

I think what you might be attempting here is to apply the Einstein synchronization convention globally for objects moving along a closed loop. This synchronization convention is not very useful for that.

If you increase the number of points from 3 to N, your spaceships are approaching a spinning circular space station. We had many threads here about rotating frames, and synchronization of clocks attached the circumference of a spinning loop.

 

[robphy]

Here's a visualization. I think I rendered it correctly.

A,B,C with colors R,G,B
S1 from A to B (i.e. R to G) is Yellow, etc...
The smaller disk is has a larger t-component in that frame.

Of course, events A,B,C are acausally related.
So, there is no invariant causal ordering of these events.

(There is transitivity among a causally-related set of events, but not among an acausally-related set.
A little off-topic:
simultaneity [in special relativity] isn't a transitive relation.
Friendship isn't a transitive relation.
)

https://www.geogebra.org/m/mu7fpa6s

 

[Dale]

Oooo, pretty picture!

Nice work, it looks correct to my eye

 

[jbriggs444]

How can A flash both first and last?

How can rock be both best and worst? Paper and scissors want to know!

 

[Herman Trivilino]

Can anyone describe what happens then and in what order the lights flash?

The order doesn't have to be same in each frame if the events have a spacelike separation.

Your mind is stuck. The only way to get it unstuck is to work through numerical examples that involve specific positions, times, and speeds.

 

[Vanadium 50]

The only way to get it unstuck is to work through numerical examples that involve specific positions, times, and speeds.

This is good advice. While I am impressed with your stamina and that you have been posting on this topic for seventeen years, you would gain a lot of clarity by working out the algebra with real numbers.

 

[PeterDonis]

Since the OP is now taking a vacation from PF, this thread can be closed.