# Simultaneity in Special Relativity

## Main Question or Discussion Point

So I've been doing some review on special relativity and I realized that I never fully understood how simultaneity is relative in special relativity. Taking the thought experiment about a lightbulb being turned on in a train, I get that the observer in the middle of the train will see light hitting both sides of the train simultaneously and that the observer at rest will not.

What I'm wondering about is whether this is because there is a lag between when the events happen and between when the observer on the train observes them which is different for the two events. Let's say the train is moving east. Will the light moving west actually impact the wall before the light moving east but simply take longer to reach the observer since on the return trip, it would take longer due to the light now facing east?

Essentially, on the return trip, since the direction of the train now works against the light moving west, it seems that you could have the light impact the west side of the train before the east side and still observe them to be simultaneous, hence actual simultaneity would be preserved between the moving frame of reference and the stationary one despite the observations being different.

My intuition is that this isn't the case and that it's just the example used which isn't entirely illustrative, otherwise this thought experiment doesn't seem to be as significant as it should be. I guess what I want to ask is in the train example above, if you had two people at each end of the train (moving with the train) observe when the light hits them, would they record the events as simultaneous (assuming they could instantly communicate the result to each other as such). Or alternatively, if two lightbulbs at different ends of the train were turned on at the same time, would the observer in the middle see the light from both lightbulbs hit them simultaneously?

Sorry for the long winded question I'm having some difficulty wrapping my head around this and any help/confirmation is appreciated!

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## Answers and Replies

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Nugatory
Mentor
What I'm wondering about is whether this is because there is a lag between when the events happen and between when the observer on the train observes them which is different for the two events....
No. Relativity of simultaneity and all other relativistic effects are what's left over after you've accounted for the lag from the light travel time. It's really pretty straightforward: if the light from two equidistant events hits your eyes at the same time, you know they had to have been simultaneous. The events are equidistant, so the time lag was the same; the light hit your eyes at time T so you know the events both happened at time T-L, where L is time lag you get by dividing the distance by the speed of light. If the light hits your eyes at different times, then you know the events happened at different times so weren't simultaneous.

Or alternatively, if two lightbulbs at different ends of the train were turned on at the same time, would the observer in the middle see the light from both lightbulbs hit them simultaneously?
If by "at the same time" you mean at the same time according to clocks set up and calibrated on the train, yes. But then the two flashes will not be simultaneous according to ground-based observer. That's relativity of simultaneity at work.

You might be tempted to say that the ground guy is seeing what's "actually" simultaneous because he's at rest and the train is moving so his observations aren't confused by the train's motion. But we could just as easily say that the train is at rest and the ground is moving backwards.

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assuming they could instantly communicate the result to each other as such
If we had way to exchange information infinitely fast, we would have absolute simultaneity: just check real-time what a clock reads at distant place. Relative simultaneity wouldn't make much sense then. You can check for example Andromeda paradox (http://en.wikipedia.org/wiki/Rietdijk–Putnam_argument) and imagine how it would look like if we had infinitely fast signals in use.

Relative simultaneity is very interesting subject and I guess that there are lots of opinions how "real" it is. I personally tend to think that relative simultaneity isn't physically real, because we cannot test it anyhow. Such a test would need infinitely fast signals (i.e. real-time check what clock shows at distant place) and we don't have those.

For me, relative simultaneity is something like an optical illusion caused by strange properties of light speed. If "optical illusion" sounds bad, one can translate it to "subjective calculations that are based on certain assumptions and can be disputed by other observers" which is essentially the same in this case.

The simultaneity calculations that are made in relativity are valid in the sense that they cannot be proven wrong (or right, for that matter). So you can use the relative simultaneity as it's defined, and it will work together with other relativity machinery so that there are no contradictions. There is nothing wrong with using relative simultaneity, we just need to remember it's not absolute fact but just one way to look at things.

ghwellsjr
Gold Member
For me, relative simultaneity is something like an optical illusion caused by strange properties of light speed. If "optical illusion" sounds bad, one can translate it to "subjective calculations that are based on certain assumptions and can be disputed by other observers" which is essentially the same in this case.
Yes, "optical illusion" sounds bad because it is bad and wrong because Relativity of Simultaneity is not optical so how could it be an optical illusion? And your translation is also wrong because of the word "subjective". Relativity of Simultaneity is an objective process that is based on certain assumptions (actually called postulates). I'm not sure when you say "disputed by other observers" you mean other theories or explanations, or you mean other Inertial Reference Frames. If the latter, then you are just restating the Relativity aspect of Simultaneity. If the former, there is no other theory or explanation that is any more objective than that of Special Relativity and it is simpler than any other theory or explanation which is why it has become the preferred theory.

ghwellsjr
Gold Member
So I've been doing some review on special relativity and I realized that I never fully understood how simultaneity is relative in special relativity. Taking the thought experiment about a lightbulb being turned on in a train, I get that the observer in the middle of the train will see light hitting both sides of the train simultaneously and that the observer at rest will not.
Which train thought experiment is it that has a single lightbulb being turned on? Einstein's famous train thought experiment had two light sources (lightning strikes) hitting both ends of the train.

In your thought experiment you could have two trains side by side in relative motion and two observers in the center of each with a common light bulb going off between them when the observers coincide and both observers will see the reflections from the two ends of their respective trains simultaneously. However, this scenario doesn't elucidate the issue of Relativity of Simultaneity. It just illustrates the Principle of Relativity, Einstein's first postulate. You also need his second postulate to get his theory of Special Relativity in which the Relativity of Simultaneity comes out.

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Yes, "optical illusion" sounds bad because it is bad and wrong because Relativity of Simultaneity is not optical so how could it be an optical illusion? And your translation is also wrong because of the word "subjective". Relativity of Simultaneity is an objective process that is based on certain assumptions (actually called postulates). I'm not sure when you say "disputed by other observers" you mean other theories or explanations, or you mean other Inertial Reference Frames. If the latter, then you are just restating the Relativity aspect of Simultaneity. If the former, there is no other theory or explanation that is any more objective than that of Special Relativity and it is simpler than any other theory or explanation which is why it has become the preferred theory.
By "subjective" and "disputable" I just wanted to emphasize the fact that relative simultaneity does not mean simultaneity in the concrete "if we could check what time is at Andromeda right now by using infinitely fast signals" sense.

Different observers have different opinions about distances, clock rates and times. Two persons meet at street, one walking towards Andromeda and other walking away from it. The calculations about Andromeda time are subjective in the sense that both persons have their own, disputable because they disagree about it (although both can understand why the other person calculates differently).

I know this is a bit touchy subject and I'm not trying to offend on purpose. I admit that relativity works in practice, I just hate it and don't think that the philosophical basis (e.g. concerning relative simultaneity) is very strong.

ghwellsjr
Gold Member
What I'm wondering about is whether this is because there is a lag between when the events happen and between when the observer on the train observes them which is different for the two events. Let's say the train is moving east. Will the light moving west actually impact the wall before the light moving east but simply take longer to reach the observer since on the return trip, it would take longer due to the light now facing east?
Which one trip takes longer is "up in the air" but the sum of the two trips for the two round-trip light signals will be equal. This is also true if the signals propagated in a fixed medium, either light in an absolute ether, or sound in air, or waves on water.
Essentially, on the return trip, since the direction of the train now works against the light moving west, it seems that you could have the light impact the west side of the train before the east side and still observe them to be simultaneous, hence actual simultaneity would be preserved between the moving frame of reference and the stationary one despite the observations being different.
Yes, the observation of the reflected light will always be simultaneous for inertial trains but this has nothing to do, by itself, with the light hitting both ends of the train simultaneously.
My intuition is that this isn't the case and that it's just the example used which isn't entirely illustrative, otherwise this thought experiment doesn't seem to be as significant as it should be.
Your intuition is correct, that's why I asked you in the previous post where you got that thought experiment from
I guess what I want to ask is in the train example above, if you had two people at each end of the train (moving with the train) observe when the light hits them, would they record the events as simultaneous (assuming they could instantly communicate the result to each other as such). Or alternatively, if two lightbulbs at different ends of the train were turned on at the same time, would the observer in the middle see the light from both lightbulbs hit them simultaneously?
As has been pointed out, there's no instant communication nor any point in speculating about it. But the two lightbulbs going off at the two ends of the train are essentially what Einstein proposed in his thought experiment, except that by using lightning strikes, we don't have to worry about whether the light source is stationary with respect to the train or the ground. Now it is simply a matter of defining simultaneity. If the observer at the midpoint on the train sees them simultaneously, then they are defined to be simultaneous.
Sorry for the long winded question I'm having some difficulty wrapping my head around this and any help/confirmation is appreciated!

Chestermiller
Mentor
Suppose that, by coincidence, there are two observers on the train, each of whom is physically present at one or the other of the two spatially separated flashes. These observers have pre-synchronized clocks (synchronized in their frame of reference), and record the time that they see the flashes at their respective locations in notebooks. Suppose further that, by coincidence, there are two observers on the ground, each of whom is physically present at one or the other of the same two spatially separated flashes. These observers also have pre-synchronized clocks (synchronized in their frame of reference), and record the time that they see the flashes at their respective locations in notebooks. After the flashes have occurred, the four observers convene a meeting to compare results on the times that they recorded in their notebooks. The two observers on the train report that they observed the two flashes at the same time according to their synchronized clocks. The two observers on the ground report that they observed the two flashes at significantly different times, according to their synchronized clocks. Do you believe this? I hope so because this is what the Lorentz Transformation predicts.

Chet

Dale
Mentor
I admit that relativity works in practice
That is all that is required for scientific verification of a theory.

I just hate it and don't think that the philosophical basis (e.g. concerning relative simultaneity) is very strong.
Neither your emotional reaction nor your philosophical opinion are scientifically relevant.