# Lightning Bolts / Relativity of Simultaneity

• MattRob
In summary, it seems that the example may be illustrating something about relativity of simultaneity that goes beyond simply the effects of light-lag.f

#### MattRob

So, I think most of the folks here are familiar with Einstein's thought experiment that illustrates the relativity of simultaneity by using two lightning bolts and how the light reaches an observer on a moving train; that an observer on the ground observers the strikes simultaneously, but an observer on the train sees one before the other.

But, something that kinda gets me about this, is this seems to imply that relativity of simultaneity only comes as a result of light-lag, rather than the events actually occurring at different times in the coordinate system.

For example, if we're in a fluid, and two sound sources beep simultaneously, then an observer on the ground would hear them both at once, but an observer on a moving train would hear one before the other. This doesn't mean that simultaneity is relative based upon the speed of light of the fluid; it's merely a relic of the fact that sound has a finite speed. If the observer on the train properly takes this into account, then he'll realize that the two beeps really were simultaneous in his reference frame.

So what sets the lightning bolt example apart? Light goes the same speed in every reference frame, true, but why does that make that difference?

I do understand that it's not merely due to light-lag, but rather that SR truly effects how space and time flow; I'm just trying to make sense of the lightning bolt / train thought experiment in light of that knowledge (pun not intended, but relished nonetheless). Also for this reason, I do prefer the ladder-barn paradox to illustrate simultaneity rather than the lightning bolt illustration.

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To re-iterate and better illustrate; let's say you could teleport instantly to a given point. Now let's say we replace the lightning bolts with lights that are white, but then flash blue. Let's say someone argues; "Well, that doesn't mean that simultaneity is truly relative. As soon as you see the blue flash from the source in front of you, if you were to teleport to it, you would see it's white; ergo; you're merely seeing into the object's past because it took its light awhile to reach you; not because simultaneity is truly relative."

While I know in reality, that relativity of simultaneity means that if you could teleport instantly to that object in your frame of reference; you'd arrive there and find it blue(?) (or rather, at least that less time passes for that object than if the above argument were correct). So what would be the correct response to the above argument?

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We are doing the same lag analysis in the case of the light signal and the sound signal in a moving medium: "the signal reaches us at time ##T## after traveling at speed ##v## over a distance ##d##; therefore the signal was emitted at time ##T_e=T-d/v##".

With light everyone uses the same value of ##v##, so the different ##d## values imply different ##T_e## values for different observers. With sound in a medium we also have different ##v## values and it turns out when we do the calculation the the ##T_e## values come out the same.

A good exercise, which will go a long ways towards clarifying this effect, is to try working through an analogous thought experiment using sound signals instead of light... But because there is a constant breeze, both the platform observer and the train observer are moving relative to the medium.

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So, I think most of the folks here are familiar with Einstein's thought experiment that illustrates the relativity of simultaneity by using two lightning bolts and how the light reaches an observer on a moving train; that an observer on the ground observers the strikes simultaneously, but an observer on the train sees one before the other.

But, something that kinda gets me about this, is this seems to imply that relativity of simultaneity only comes as a result of light-lag, rather than the events actually occurring at different times in the coordinate system.

For example, if we're in a fluid, and two sound sources beep simultaneously, then an observer on the ground would hear them both at once, but an observer on a moving train would hear one before the other. This doesn't mean that simultaneity is relative based upon the speed of light of the fluid; it's merely a relic of the fact that sound has a finite speed. If the observer on the train properly takes this into account, then he'll realize that the two beeps really were simultaneous in his reference frame.

So what sets the lightning bolt example apart? Light goes the same speed in every reference frame, true, but why does that make that difference?

I'd encourage you to work through the logic of the lightning bolt as presented by Einstein - or perhaps one of the alternate versions in Scherr's paper "The challenge of changing deeply held student beliefs about the relativity of simultaneity".

As far as your examples go:

Sound in a material is different from the speed of light because the speed of sound waves in a moving media is not the same in both directions, while the speed of light is.

"Instantaneous" teleportation isn't something that physically exists. An important part of relativity is the existence of a universal speed limit, "c". And part of the point of Einstein's thought experiment is to show that the very notion of "instantaneous" is dependent on the frame. You'll have to follow the logic to understand this. In this case bringing up more and different scenarios serves only to shift your focus away from deeply appreciating the argument Einstein and others make about the relativity of simultaneity. In particular, assuming in advance that ideas contrary to relativity are true (ideas such as no universal speed limit) will simply lead either to inconsistencies (if you also assume the tennents of relativity) - or a consistent theory that's not relativity (if you just make up your own ideas without making the assumptions relativity makes).

So my suggestion is to stick with the original "lightning bolt and train" thought expierment and try to understand it, rather than to drag up different scenarios.

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