Simultaneity, does it confuse causality?

[Brin]

I came up with a sort of thought experiment to help me ask this question. It goes as such:

Jack, Jill, and Joe sit near two buttons (Button A, and Button B). Joe sits directly in the middle of the two buttons, and is to push the buttons at the appropriate time. Jack and Jill sit on the left (closest to Button A) and right (closest to Button B), respectively.

When Joe pushes the button, three events are possible of happening: Event A, Event B and Event C. If Joe pushes Button A first, Event A happens. If Joe pushes both buttons simultaneously, Event B happens. If Joe pushes Button B first, then Event C happens.

Because of the positioning of everyone (so the light reaches them appropriately): Jack perceives Joe pushing Button A, and as such, would expect Event A. Joe knows he pushes both buttons simultaneously and expects Event B. Jill perceives Joe pushing Button C, and expects Event C.

Which one actually happens?

I have read that because of the principle of relativity, absolute simultaneity is thought to not exist - but I figured that the result of some event occurring would reflect that there is absolute simultaneity. Could someone help me reflect on this?

Thanks.

P.S. the idea regarding causality here is that the ordering of the button presses causes the corresponding event.

 

[Doc Al]

Because of the positioning of everyone (so the light reaches them appropriately): Jack perceives Joe pushing Button A, and as such, would expect Event A. Joe knows he pushes both buttons simultaneously and expects Event B. Jill perceives Joe pushing Button C, and expects Event C.

But Jack, Joe, and Jill are all in the same reference frame, so they all agree that Joe pushed the buttons simultaneously (in their reference frame). They must take light travel time into account to properly interpret their observations, of course.

The thought experiment would be more interesting if multiple frames were involved, for example if Jack and Jill viewed the button pushing while traveling past Joe at high speed. In that case you'd have to physically define what you mean by events A, B, and C and how they would come about. (Just saying that event B happens when the buttons are push "simultaneously" is not physically meaningful--since simultaneity is frame dependent--unless you just mean simultaneously according to Joe.)

 

[Brin]

Doc, if I read you correctly I made the following error:
I assumed that the simultaneity was merely a trick of light, so to speak, and that the velocity of observers had nothing to do with it. So, if the three amigos there share a frame of reference, they need only to account for the 'trick of light,' right?

Which means that, in order to make this thought experiment more meaningful, and yet still maintain the question, we should set Jack and Jill in motion relative to each other, and Joe. Just in case the comfortable vagueness of Event A, B and C is troublesome, I will instead set the buttons rigged to detonate one of three cars.

So, to correct this:
Joe sits in a vast, vast, vast parking lot, facing two buttons (Button A on the left, Button B on the right), both in equidistant arms length.

Jack is riding in a high-high-speed car approaching Button A from Joe's left. Jill, too, is riding in a high-high-speed car approaching Button B on the right. From Joe's reference frame, he presses both buttons simultaneously.

The buttons are connected to a machine, rigged to detonate Car A, Car B, or Car C depending on how the buttons are pressed (i.e. Car A detonates if Button A is pressed first, Car B detonates when both buttons are pressed simultaneously, and Car C detonates when Button B is pressed first).

Jack, still, sees Button A pressed first and expects Car A to detonate. Jill sees the opposite, and expects to see Car C detonate. Joe knows he pressed the buttons simultaneously and expects Car B to detonate.

So, what happens from each person's point of view?

 

[neopolitan]

The buttons are connected to a machine, rigged to detonate Car A, Car B, or Car C depending on how the buttons are pressed (i.e. Car A detonates if Button A is pressed first, Car B detonates when both buttons are pressed simultaneously, and Car C detonates when Button B is pressed first).

The problem is in here.

Unfortunately you have to specify the frame.

So you have to say "Car A detonates if Button A is pressed first in Joe's frame, Car B detonates when both buttons are pressed simultaneously in Joe's frame, and Car C detonates when Button B is pressed first in Joe's frame".

Note that I am assuming an arrangement like this:

Jack......Button A..Joe..Button B........Jill

If the arrangement in the middle is more like:

Button A
...Joe...
Button B

Then with some careful arrangement, your scenario would work as advertised, even without referring to frames.

cheers,

neopolitan

 

[Brin]

Well, I am trying to figure out if simultaneity can confuse causality. Not necessarily one that turns cause->effect into effect->cause, but one that shows a "forking" in what we perceive.

So one of the results I sort of predicted is one where Jack and Jill somehow perceive two different entire events. It doesn't sound plausible, so I am trying to figure out where I am going wrong. So far this forum topic is going great, but now you are all aware of my motives.

Here is the final (?) thought experiment iteration:

Joe sits in a vast, vast, vast parking lot, facing two buttons (Button A on the left, Button B on the right), both in equidistant arms length.

Jack is riding in a high-high-speed car approaching Button A from Joe's left. Jill, too, is riding in a high-high-speed car approaching Button B on the right. From Joe's reference frame, he presses both buttons simultaneously.

The buttons are connected to a machine, rigged to detonate Car A, Car B, or Car C depending on how the buttons are pressed (i.e. Car A detonates in Joe's frame if Button A is pressed first in Joe's frame, Car B detonates in Joe's frame when both buttons are pressed simultaneously in Joe's frame, and Car C detonates in Joe's frame when Button B is pressed first in Joe's frame).

Jack, would see Button A pressed first and would expect Car A to detonate in his own frame. Jill sees the opposite, and expects to see Car C detonate in her frame. Joe knows he pressed the buttons simultaneously and expects Car B to detonate in his frame.



From what I gather, if Joe detonates Car B in his frame due to his simultaneous pushing of the buttons, than others will perceive the detonation of car B as well, but will have seen Joe push Button A, or Button C respectively. This would then mean that certain frames ARE more correct than others, right? Because, what they saw (i.e. Joe pushing button A or C) would be incorrect! Right? Am I off my rocker?

 

[Fredrik]

Note that it's only possible for two inertial frames to disagree about the time ordering of two events A and B if they are "spacelike separated": (x(A)-x(B))² > c²(t(A)-t(B))². That means that a light signal emitted at one of the events won't reach the location of the other event before it happens.

Note also that being spacelike separated is a propery of the events, and is completely independent of the coordinate system used.

 

[neopolitan]

Jack and Jill should not expect simultaneous pushing of the buttons in their rest frames to cause Car B to explode. They will both expect simultaneous pushing of the buttons in Joe's rest frame to cause Car B to explode.

They just will know (or find out) that events that are simultaneous in Joe's frame are not necessarily simultaneous in their frame.

cheers,

neopolitan

 

[jambaugh]

Well, I am trying to figure out if simultaneity can confuse causality. Not necessarily one that turns cause->effect into effect->cause, but one that shows a "forking" in what we perceive.

This may already be clear to you but let's review the general causal structure of events in SR.
Given an event A there will be a past and future light cones and the region of space-time outside both light-cones. (Excluding the boundary) I'll call this region simply the "Outer Region".

Point I: All observer frames will see the same light-cones. They are invariant under Lorentz transformations about the event A.

Point II: An event B occurring in the outer region with respect to A there are a set of inertial frames wherein event B and event A appear to occur simultaneously. There are also frames wherein A occurs before B and frames wherein B occurs before A.

Point III: An event which causes A must occur in the past light-cone of A and an event caused by A must occur in the future light-cone of A. (In each case we include the boundaries)

Now understanding that simultaneity is a frame dependent concept but cause and effect are not. You cannot formulate a well defined thought experiment werein different observers see qualitatively different causal events. They may only see variations in quantitative frame dependent relationships (such as the duration as measured by an observers clock between two events which may be positive, negative, or zero=simultaneity).

As you formulate your thought experiments it may help to go into detail as to how outcomes are decided. For example you button pushing fellow with simultaneity dependent outcomes would we suppose use a simple logic circuit connected to the two buttons. Focus then on how the observers moving relative to the button pusher see the signals from (as they see it) non-simultaneous button presses reach the same central control circuit. I think you'll see they all agree that the signals themselves must reach the control circuit simultaneously.

Assume speed of light signals for example and note that the control circuit lies on the intersection of two light-cones with vertices at the two button press events. Each observer will see a different relationship for the button events but the intersection sets for all observers will agree. They will see different distances traveled by each signal. This because they all see the signals travel at speed c but different relative motion between signal and the button-control circuit pairs since in their frames these are not stationary.

 

[Saw]

Jack and Jill should not expect simultaneous pushing of the buttons in their rest frames to cause Car B to explode. They will both expect simultaneous pushing of the buttons in Joe's rest frame to cause Car B to explode. They just will know (or find out) that events that are simultaneous in Joe's frame are not necessarily simultaneous in their frame.

Yes, a fundamental principle of SR is that all observers agree on which events happen and which do not. Certainly, they disagree on which events are simultaneous and which aren’t, as well as on other things (for example, duration and length), but all those discrepancies do not lead to disagreement on what happens.

One hint: Einstein’s idea was that one should not define concepts aprioristically and dogmatically (I can look for the quotation if anyone wishes), but on the basis of how they work in real life with real life instruments.

In this case, the real process would be as follows. To start with, Joe’s brain had to send orders to his muscles to move his hands and push the buttons simultaneously. This will be done through electric signals traveling through the nervous system. We choose that at that time Joe and observers located in Jack and Jill’s frame synchronize their clocks. So the start of the show, the departure of the electric signals, is simultaneous for the three frames. For Joe the signals reach his two hands simultaneously and so his hands push the buttons simultaneously. For Jack, for example, this is not so: the signal to the left arrives to the target (Joe’s left hand) earlier than the signal to the right. Why? Because in Jack’s frame, Joe’s left hand is traveling to the right, heading towards the electric signal, while Joe’s right hand is escaping from it. But then new signals have to be transmitted from the buttons to a detector that interprets whether they were simultaneous or not. Let us say that the detector is placed mid-way between buttons A and B. This detector is programmed so that if it receives one signal, it sends the order for the corresponding car to explode and gets blocked so as not to blow out another car; instead, if it receives two signals simultaneously, it orders the explosion of both cars. Joe judges that the two signals reach the detector at the same time. And so does Jack! It is true that for Jack the left hand pushed its button earlier, because it was heading towards its own signal, but then the opposite must be also true: the signal coming from Joe’s left hand, now moving in the opposite direction, was facing an escaping target and so it took more time to do its job. It woke up earlier, but it also had to do a tougher job. One thing compensates the other. So Jack agrees that the detector will receive the two signals simultaneously and blow the two cars.

One could draw a spacetime diagram where all relativistic effects (relativity of simultaneity, time dilation and length contraction) are taken into account and the result is as described. It is easier if the signals were light signals, a little more complicated if they are electric signals, because the latter do not have the same speed in all frames (in Joe’s frame, they would; in Jack’s, you would have to apply the relativistic law for the addition of velocities), but the system would work anyhow: all frames agree that the detector should blow the two cars.

Conclusion: Was what Joe measured incorrect? No, it wasn’t, as long as Joe does not think that it is the final clue, as if his relative judgment on simultaneity directly provided the solution. If it were absolute, it could. But in reality, observers do not coincide in their judgments of simultaneity. So they are relative. That entails that you have to combine them with other judgments in order to reach the same solution as other observers. You can say, however, if you wish, that if the observer located where the detector is judges that the first signals reach his hands simultaneously, that is a final clue as to whether the new signals will reach the detector simultaneously…

 

[Doc Al]

Doc, if I read you correctly I made the following error:
I assumed that the simultaneity was merely a trick of light, so to speak, and that the velocity of observers had nothing to do with it. So, if the three amigos there share a frame of reference, they need only to account for the 'trick of light,' right?

Right. The relativity of simultaneity is no "trick of light". (If it was, it would be rather trivial and uninteresting.) Relativistic effects are what's left after you account for light travel time.

Which means that, in order to make this thought experiment more meaningful, and yet still maintain the question, we should set Jack and Jill in motion relative to each other, and Joe. Just in case the comfortable vagueness of Event A, B and C is troublesome, I will instead set the buttons rigged to detonate one of three cars.

Good, but you'll need to define just how those buttons are rigged.

So, to correct this:
Joe sits in a vast, vast, vast parking lot, facing two buttons (Button A on the left, Button B on the right), both in equidistant arms length.

Jack is riding in a high-high-speed car approaching Button A from Joe's left. Jill, too, is riding in a high-high-speed car approaching Button B on the right. From Joe's reference frame, he presses both buttons simultaneously.

The buttons are connected to a machine, rigged to detonate Car A, Car B, or Car C depending on how the buttons are pressed (i.e. Car A detonates if Button A is pressed first, Car B detonates when both buttons are pressed simultaneously, and Car C detonates when Button B is pressed first).

Again, you must physically define how those cars are detonated. One way is this. Let the pushing of each button trigger an electrical signal. Set up a coincidence detector midway between the two buttons. If the detector sees two signals within some time interval it declares the buttons to have been pushed "simultaneously". Otherwise, the detector detects one signal arriving first and blows up the appropriate car.

This would again be more "realistic" (for a thought experiment!) if the buttons were miles and miles apart, so that there would be some significant disagreement about which was pushed first in the various reference frames. You could have Joe at one button and his twin brother John at the other. Then Joe and John could push the buttons simultaneously (in their frame) or not.

Jack, still, sees Button A pressed first and expects Car A to detonate. Jill sees the opposite, and expects to see Car C detonate. Joe knows he pressed the buttons simultaneously and expects Car B to detonate.

So, what happens from each person's point of view?

Everyone, of course, sees the same car detonate. Note that Jack, who travels in the A to B direction, observes button B (not A) to have been pressed first (after correcting his observations for light travel time, of course). But Jack agrees--everyone agrees--that the signals from the two buttons arrived simultaneously at the coincidence detector--so he fully expects car B to explode, given how this arrangement was made.

From what I gather, if Joe detonates Car B in his frame due to his simultaneous pushing of the buttons, than others will perceive the detonation of car B as well, but will have seen Joe push Button A, or Button C respectively. This would then mean that certain frames ARE more correct than others, right? Because, what they saw (i.e. Joe pushing button A or C) would be incorrect! Right? Am I off my rocker?

Realize that for physically unconnected events--the pushing of the two buttons, in this case--the time order depends on the frame doing the observing. So an absolute statement such as "if buttons A and B are pressed simultaneously" has no physical, frame-independent meaning.

Again:
Joe presses the buttons simultaneously in his frame; the signals arrive at the detector simultaneously, car B detonates.

Jack observes button B pressed first followed by A, but agrees that the signals arrive at the detector simultaneously anyway (since the detector is moving), so he fully expects car B to explode.

Jill observes button A pressed first followed by B, but agrees that the signals arrive at the detector simultaneously anyway (since the detector is moving), so she fully expects car B to explode.

 

[Brin]

Wow. I don't think you guys can know how grateful I am right now. After reading (and re-reading) all the posts above, then thinking about the problem a bit more, I am left with little doubt as to what would happen.

Even, as jambaugh and Doc Al reminded, if I rigged the experiment with some sort of electric circuit, I'm guessing that the very motion of the circuit would be affected enough such that, the electric signal being processed by Button A (BA) and Button B (BB) would be matched in Jack and Jill's frames such that the trigger would be considered simultaneous. I even thought about if the signal sent out by the buttons was some sort of light signal, say, if BA is pressed first, there is a red light. Simultaneous button presses equate to a green light, and BB being pressed first would equate a blue light. The circuit which detects which color light to show, would be moving as well, and so we would be left in a very similar situation as some sort of other logic circuit.

Jambaugh, your lesson was more tutorial than reminder, since I have not been taught about that stuff yet. But I will study up and keep it all in mind for the next thought experiment.

EVERYONE said something that triggered "Ah, interesting," thoughts in my head, so I am, again, grateful.