Simultaneity: how can all observers be right?

[DAC]

In Einstein's train/lightning strike thought experiment, the embankment and train observers disagree on the simultaneity of the events.
But let's alter the experiment so that if the strikes are seen to be simultaneous, ( embankment observer ), the combined strikes blow up the entire experiment. The train observer will say the strikes were not simultaneous so there was no explosion. How can both observers views be correct?

 

[Dale]

All observers will agree if the mechanism activating the detonator triggers. Only one will say that the mechanism detects simultaneous strikes. Other observers will say that the mechanism detects non simultaneous strikes.

 

[Herman Trivilino]

But let's alter the experiment so that if the strikes are seen to be simultaneous, ( embankment observer ), the combined strikes blow up the entire experiment. The train observer will say the strikes were not simultaneous so there was no explosion. How can both observers views be correct?

By what mechanism is the explosion triggered? The reason I ask is because it seems the strikes would have to be simultaneous and in the same place to trigger an explosion. In that case all observers will agree that the strikes are simultaneous and that an explosion is triggered.

On the other hand, if the strikes are separated along the train platform then you'd have to specify what you mean by simultaneous. You mean simultaneous to the platform observer, right? If so, then as Dale pointed out, the train observer will agree that to the platform observer the strikes are simultaneous and that therefore an explosion is triggered. But the train observer will not agree that the strikes are simultaneous. He'll claim there was an explosion because in order for the strikes to be simultaneous to the platform observer, they'd have to be not simultaneous to him, the train observer.

 

[Ibix]

It was a dark and stormy night...

Let's mount lightning rods at each end of the embankment. How are we going to tell that they were struck simultaneously? The fastest way to do it is to set up cameras in the middle of the embankment pointing at the detectors. If both cameras see a flash at the same time then the strikes were simultaneous - but we can't see this happen until $L/2c$ after the strikes, where $L$ is the length of the platform.

If we set up an identical pair of cameras on the train, then they cannot be next to our embankment ones at the time(s) of the strikes and also at the time our detector triggers - the train has moved in the interim. So they won't agree on the simultaneity of the flashes.

In short, you can't build a simultaneity detector because you can't react to a remote event until the light from it reaches you. You can only build a simultaneity-in-some-frame detector.

 

[sdkfz]

The animations in this post by Janus shows it well.
https://www.physicsforums.com/threads/struggling-with-the-special-relativity-and-simultaneity.834339/page-3#post-5243619

They show clearly how the observers can disagree whether or not according to them the two flashes were simultaneously emitted, yet they can agree that the flashes reached one of the observers at the same time. i.e. in the bottom animation, from the point of view of the train observer, the two flashes reach the embankment observer at the same time.

 

[A.T.]

if the strikes are seen to be simultaneous, ( embankment observer ), the combined strikes blow up the entire experiment.

If by "seen" you mean visually registered by a person, then all frames will agree that this person saw them simultaneously and blew up the experiment. They will just disagree if the distant strikes themselves happened simultaneously.

 

[russ_watters]

Only one will say that the mechanism detects simultaneous strikes. Other observers will say that the mechanism detects non simultaneous strikes.

Er - either it does or it doesn't: the mechanism only detects one thing and everyone should know what it detected. So the way you said that sounds funny: A remote/moving observer would say "the detonator saw simultaneous strikes, but *I* didnt."

 

[A.T.]

the mechanism only detects one thing and everyone should know what it detected.

True for the local part of the mechanism, which makes the decision based on receiving signals from distant events. But frames will disagree what that means for the simultaneity of those distant events.

 

[Dale]

Er - either it does or it doesn't: the mechanism only detects one thing and everyone should know what it detected. So the way you said that sounds funny: A remote/moving observer would say "the detonator saw simultaneous strikes, but *I* didnt."

Sure, you can say it that way. However, if you say " the mechanism only detects one thing" then in my opinion that thing must be an invariant quantity. That would automatically exclude statements like the OP.

 

[russ_watters]

Sure, you can say it that way. However, if you say " the mechanism only detects one thing" then in my opinion that thing must be an invariant quantity. That would automatically exclude statements like the OP.

It is invariant. That's why the wording of the OP doesn't work:
"The combined [simultaneous strikes] strikes blow up the entire experiment." is not an accurate description of the criteria. The actual criteria was:
The combined [simultaneous] strikes measured by the detector blow up the entire experiment.

Everyone agrees that the detector detected the strikes simultaneously.

The reason I think this matters is the OP's wording implies that it should really be true that the bomb both does and doesn't go off...which is what the OP was asking about. People are always harping on the importance of specifying reference frames and in this case the reference frame that matters should be specified.

 

[pervect]

In Einstein's train/lightning strike thought experiment, the embankment and train observers disagree on the simultaneity of the events.
But let's alter the experiment so that if the strikes are seen to be simultaneous, ( embankment observer ), the combined strikes blow up the entire experiment. The train observer will say the strikes were not simultaneous so there was no explosion. How can both observers views be correct?

If we imagine one mechanism set up in the embankment frame with an explosive charge that blows up the mechanism on simultaneous strikes, and another mechanism set up in the train frame with a similar explosive charge, everyone in both frames will agree that the bomb in the embankment frame goes off - destroying it's mechanism - while the bomb in the train frame doesn't go off, leaving it's mechanism intact.

"The challenge of changing deeply-held student beliefs about the relativity of simultaneity" http://arxiv.org/abs/physics/0207081 may be helpful. The observation you made is good, and avoids one of the pitfalls mentioned in the paper:

Failure to recognize that events
that occur in one frame occur in all
frames

So you've recognized and avoided that pitfall, but have apparently fallen into another one. What seems to be missing is recognizing that in the moving frame, a bomb attached to the train with an identical mechanism (but different sensors and wires, sensors and wires which are fixed to the train and hence are moving in the embankment frame) will not go off. Why you are missing this, I can't say as of yet.

Note that in the paper above, the "bomb" was replaced with a less dramatic tape player, that starts on one signal and stops on the other, and the question asked is "does the tape player play in the embankment frame" and "does the tape player play in the train frame". The other difference is that the only mechanism considered is a mechanism on the train. There is no reason you can't introduce another mechanism on the ground if you wish, but it's not really terribly relevant. If you do introduce such an additional mechanism, it confirms that the events were in fact simultaneous in the embankment frame. But you still need to address the question of what happens to the mechanism attached to the train. And you're not really considering that, you're focussing on the wrong mechanism (one attached to the embankment).

 

[DAC]

All observers will agree if the mechanism activating the detonator triggers. Only one will say that the mechanism detects simultaneous strikes. Other observers will say that the mechanism detects non simultaneous strikes.

Thanks for all your replies. But, the explosion only happens if there are simultaneous strikes. Non simultaneous strikes therefore don.t result in an explosion. Which appears to leave the explosion happening in one frame and not in the other.

 

[A.T.]

But, the explosion only happens if there are simultaneous strikes.

That is an ill defined condition, as already explained to you.

You can have a trigger that fires, if the flashes reach it simultaneously. Then all frames will agree that they did. But they will disagree on whether the strikes happened simultaneously.

 

[Dale]

Thanks for all your replies. But, the explosion only happens if there are simultaneous strikes. Non simultaneous strikes therefore don.t result in an explosion. Which appears to leave the explosion happening in one frame and not in the other.

There is no such mechanism. You cannot build a device which works like that.

 

[Herman Trivilino]

Thanks for all your replies. But, the explosion only happens if there are simultaneous strikes. Non simultaneous strikes therefore don.t result in an explosion. Which appears to leave the explosion happening in one frame and not in the other.

As in the thread that involved the dispensing of beer bottles, or the one that involved what eventually came to be called the "DAC clock", you are refusing to engage in the thought processes necessary to address your misconceptions.

Just as in the case of the beer dispenser, there is confusion over the relationship between events called "lightning strikes" and the events called "arrival of the signals that notify the observer of the lightning strikes". Let us call the lightning strikes themselves $L$ and the arrival of the information $A$. The essential point of confusion here is that events $L$ are spatially separated but events $A$ are not. Simultaneous events $L$ cannot be used to trigger an explosion or dispense a beer or do anything of the sort because they occur at different locations. Simultaneous events $A$ can be used to dispense beer or trigger explosions, or do any number of other things we might imagine. Different observers may disagree on whether or not events $L$ are simultaneous. They in fact must do so if the Principle of Relativity is valid. Just as in the case of this thought experiment where the Principle of Relativity is being tested, there are real processes that also test it. There are engineers, technicians, and scientists witnessing these prcesses every minute of every day across the world as they work with such things as high speed electronic computer circuits, high speed particles such as those used in proton therapy, and high precision clocks such as those used in the GPS.

On the other hand, if events $A$ are seen as simultaneous according to one observer, they will be simultaneous to all observers.

 

[PeterDonis]

The essential point of confusion here is that events $L$ are spatially separated but events $A$ are not.

The usual terminology of relativity would use the word "event" (singular) for $A$, not "events" (plural), because the word "event" refers to a point in spacetime. The condition being described is that the light signals from two spatially separated lightning strikes arrive at some detector at the same point in spacetime. So there are two signals, but only one arrival event.

 

[Ibix]

I don't know if this will help you, but you could try my interactive Minkowski diagram tool to visualise what's going on. Go to www.ibises.org.uk/Minkowksi.html , scroll down to where it says "Einstein's train" and click the "Make Einstein's train" button. The graph at the top of the page should now display a graph showing the train experiment.

The vertical axis is time and the horizontal axis is position along the track. We're initially set up in the embankment frame. The three blue lines (there's one along the vertical axis that's a bit hard to see) represent the ends and the middle of the embankment. The lines are vertical - this is because the position of the embankment along the track does not change. An object that is moving will make a tilted line, because its position does change with time. For example, the three green lines represent the position of the front, middle, and rear of the train. It is traveling left-to-right, so the lines are sloped so that at later times (higher up the screen) the train is further to the right.Things that happen simultaneously in this frame lie on the same horizontal line (they have the same time coordinate). You can see that the rightmost green line crosses the rightmost blue line at the same time the middle green crosses the middle blue and the leftmost green crosses the leftmost blue. That is to say, the front of the train exits the embankment at the same time as the middle of the train passes the middle of the embankment and the rear enters the embankment. Where the front lines cross, you also see the start of a yellow line sloping to the left. This is the light from the lightning strike propagating backwards. Similarly, there's light moving forwards from the event where the rear green and blue lines cross. You can see that these pulses meet in the middle of the platform. But you can also see that the pulses do not cross the middle of the train at the same time - in fact, the forward-going pulse reaching the midpoint of the train is not shown.

This is the map of spacetime that the embankment observer draws. To him, the pulses came from the same distance infront and behind and arrived at the same time. They must have been emitted at the same time. But he does not expect the train observer to receive the pulses at the same time because she is moving towards the front pulse and making the back pulse play catch-up.

Now, click on one of the green lines (it should acquire a grey highlight) and click the "Boost to selected line rest frame" button in the panel to the right of the graph. The computer executes a smooth transition to the frame where the train is at rest. Now look at the blue lines - they slope to the left because in this frame the embankment is moving right-to-left. Look at the green lines - they are vertical because in this frame the train does not change position. Look at the yellow lines - they have not changed slope because light speed is invariant.

Now look at the intersections between the green and blue lines. They are still in a line, but it is not a horizontal line. So these things do not occur at the same time. Nevertheless, you can see that the times and positions conspire so that the two yellow lines cross the green one at the same time.

This is the map of spacetime that the train observer draws. She agrees that the pulses cross in the middle of the embankment, and that the backward traveling pulse reaches her first. However, she interprets this as being because the front pulse was emitted first and played catch-up to the embankment observer while he moved towards the pulse from the back.

The observer on the train can easily build a detector for simultaneity in the embankment frame - she just places it where this map tells her to, three quarters of the way along the train, for the parameters I set. But this is not detecting simultaneity in her frame. She agrees that the embankment observer will see the pulses simultaneously but disagrees with the reasoning he uses to draw his map.

Finally, take a look at the spacing between the green lines compared to the blue in this frame. How could the pulses be emitted simultaneously? The train is too long to fit alongside the embankment.

The key point to realize here is that neither of these maps is righter than the other. Both are valid interpretations of the evidence. But they are not consistent with an absolute notion of simultaneity.