# Violation of simultaneity - real of frame-dependent perception?

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1. Oct 29, 2012

### arindamsinha

I am trying to understand what 'violation of simultaneity' really means, and whether it has any real importance (i.e. why was it introduced?).

The Wikipedia note on this (Topic: Relativity of Simultaneity):
"... the relativity of simultaneity is the concept that simultaneity–whether two events occur at the same time–is not absolute, but depends on the observer's reference frame.

According to [SR], it is impossible to say in an absolute sense whether two distinct events occur at the same time if those events are separated in space, such as a car crash in London and another in New York ... in some reference frames the two accidents may happen at the same time, in other frames (in a different state of motion relative to the events) the crash in London may occur first, and in still other frames the New York crash may occur first. If the two events are causally connected ("event A causes event B"), then the relativity of simultaneity preserves the causal order (i.e. "event A causes event B" in all frames of reference)..."

My questions are as follows:
- Assuming that signals from the crash events travel at the speed of light, I can understand that different observers (at different distances and/or moving with different speeds) somewhere between New York and London may 'perceive' the events happening in different order. Is this not a matter of perception of different observers only, while in reality there is really a specific order in which the events actually happen, even if not causally connected? Why would it be impossible to say which crash actually happened earlier in an absolute sense?
- Secondly, what is the importance of this concept of simultaneity violation, if any?

2. Oct 29, 2012

### A.T.

Signal delay has nothing to do with this or other relativistic effects. They are what is left after you have already accounted for signal delay.
Instead of concentrating on separate effects you should try to grasp the transformation between reference frames as a whole. The rest follows from that.

3. Oct 29, 2012

### Staff: Mentor

I would second A.T.'s comment. All of the relativistic effects are what is left over after accounting for the finite propagation of light.

In relativity, the important effects occur because c is invariant, not because we can send signals at c.

4. Oct 29, 2012

### Staff: Mentor

I'm going to answer these questions in reverse order.
What is the importance of relativity of simultaneity? Relativity of simultaneity (Please don't call it "simultaneity violation" - nothing's being violated here) is what underlies time dilation, length contraction, the impossibility of truly rigid objects, and most other interesting SR effects. Some relevant posts are here, here, and here.

The first question is a bit harder to answer without asking a few rhetorical questions. What do you mean by an "absolute sense"? Suppose I said to you "This frame is the 'real' frame, and if two events are not simultaneous in that frame they are 'really' not simultaneous even if they appear to be in other frames".... How would you test the truth of that statement, and how would this frame behave differently than any frame? Why, if I cannot test the truth of that statement should I take the apparent simultaneity in one frame more seriously than the apparent non-simultaneity in another frame?

When the wikipedia article says it is impossible to say in an absolute sense whether time-like separated events are simultaneous, it's really saying that it is impossible to satisfactorily answer these questions.

5. Oct 29, 2012

### arindamsinha

Indulge me in asking this in a slightly different manner:
- Let us have a situation where exactly between New York and London there is a 'crash signal detector' which records the receipt of the two crash signals. Since all the locations are at rest w.r.t. the others, I think we can establish a clear chronology of the events depending on the time of receipt of the signals. Does this not mean that any others observes who detect a different chronology of the events are only 'perceiving' them to be so because of their state of motion, while there really is an actual chronology of the events? All observers should be able to accept the decision of the 'crash signal detector' as the actual chronology of events, no matter how they perceived it?

Or is this not even a valid way of trying to look at the relativity of simultaneity?

6. Oct 29, 2012

### PAllen

Let's add to your scenrio: what happened in London is a meteorite crashing into an fast moving train. Same in New York, train moving so at rest compared to London train. There are also a hovercraft co-moving with the trains, spaced half way between them. Now, if the meteorites strikes are simultaneous per the hovercraft, they are not simultaneous per the 'floating' crash detector; and vice versal.

Who is right? Suppose, instead of earth and train, we just have different rockets in space with similar arrangement?

7. Oct 29, 2012

### Staff: Mentor

No. If the observers in the other frames of reference also had identical crash signal detectors situated exactly half way between the locations at which the two crashes were observed to occur (as reckoned by observers in their frames of reference), they would determine a different time interval between the crashes, and might even determine a different order for the crashes, even though their clocks are identical to the ones used in the "stationary" (earthbound) frame of reference.

8. Oct 29, 2012

### PAllen

I have a sense of 'biggest object's frame wins' in your perception. As discussed in another thread, you can pick one frame and do all your calculations in this frame. You can compute, using this frame, how all other (moving) clocks and signals will behave. If you insist, you can call this frame the 'true frame' (and its simultaneity, the true simultaneity). As long as you use the correct SR formulas, you will not go wrong with this procedure. What you can't do is stop me from saying, no, my frame (I am moving rapidly relative to you, and vice versa) is the true frame, because I can do all the same things, and get the right answers as well, so I must be right.

9. Oct 29, 2012

### Staff: Mentor

Why should I consider the crash signal detector that's at rest with respect to New York and London as any more "actually right" than a crash signal detector that's not at rest with with respect to New York and London?

Before you respond to that question, consider how you'd answer if the events were not happening on the ground in New York and London, but were instead happening on jetliners flying east over those two cities at 500 mph. Would you now say that the signal detector that is "actually" right is one that's midway between the cities, but also moving east at 500 mph? That's the one that will be at rest relative to the two jetliners and exactly halfway between them.

To elaborate a bit... Say we have two jetliners. Both are flying due east at 500 mph. One of them is over New York and the other is over London. In the middle of the Atlantic (hey, you're the one who chose New York and London - it's not my fault that there's an ocean in the middle) we have a ship carrying a detector, carefully maintaing its position to be at rest halfway between the two cities. We also have a third aircraft carrying another detector, flying due east at 500 mph over the ship.

The people on the ship and the people on the ground in the two cities have synchronized their watches (and straightened out the time zone differences between London, New York, and the middle of the Atlantic) so they all agree about what "at the same time" means. The people on the three aircraft have done the same.

People on the ground in London and New York signal the aircraft overhead at the same time (easy to do, they've synchronized their watches). The detector on the ship will see both signals to have happened at the same time. But the people on the two airplanes will say that the two signals happened at different times, the detector on the airplane in the middle of the ocean will record the two signals as happening at different times, and they have their synchronized watches to prove it.

Then the two airplanes over the two cities try signaling the ground at the same time according to their synchronized watches. The detector on the airplane in the middle of the ocean will also receive both signals at the same time. But the detector on the ship will receive the signals at different times, and when the people on the ground compare the times (synchronized watches, so they can compare times) that they received the signals, they will agree with the detector on the ship that the signals were issued at different times.

So why should I prefer one group's notion of "at the same time" over the other group's?

10. Oct 29, 2012

### Staff: Mentor

Here is a concept that you need to get used to when working with SR. If the clocks throughout a given inertial frame of reference (say frame S) are all synchronized with one another, and the clocks within a second inertial frame of reference (say frame S') are also all synchronized with one another, observers in the S frame of reference will ascertain that, according to their reckoning, the clocks in the S' frame of reference are out of synchronization, and observers in the S' frame of reference will ascertain that, according to their reckoning, the clocks in the S frame of reference are out of synchronization. Which team of observers is correct? They both are. Each inertial frame of reference has its own unique synchronized time.

11. Oct 30, 2012

### arindamsinha

This is good stuff, more like what I was looking for to extend my thinking and understanding.

I think what you are saying is that, it is not simultaneous per the 'floating' crash detector because the hovercraft remains at rest w.r.t. the trains, while the crash detector can be considered to have moved, and therefore gets the two signals in a different order than the hovercraft? Is this understanding correct? (I suspect I may still missing be something here, but will ask some further questions if my understanding is correct)

Yes, agreed. If I am not mistaken, this is essentially the same thing as PAllen is stating in the above post. If so, my question to you is the same as above.

I think you have got my perception thing absolutely right. Also understand your reasons for the comparison between the frames, and why both of them might consider themsleves to be right.

I still have this feeling that any disagreement about the order of events stems from the different distances of the two observers from the source of the events at (a) when the events happen, and (b) when light signals reach the observers telling them about the events. Meaning, this is a pereception issue, rather than an actual order of events based on some 'coordinate clock' (I realize I am getting into thorny territory here). So, what am I getting wrong here?

Your detailed explanation is helpful, and in essence similar to what PAllen has stated, and my follow up questions are also to you.

This I understand from an SR theory perspective. I am trying to figure out whether there is a frame-based perception involved here that gives these different orders of events, or there really is no such thing as simultaneity.

12. Oct 30, 2012

### PAllen

This is correct. So, now what would you say of the universe consisted only of two similar solar systems moving rapidly passed each other (but not too close). Who wins the contest for being the true frame?

Note, in our universe, you cannot get away with saying the CMB represents a frame. This is because two galaxies each seeing the CMB as isotropic, see the other receding at high speed. Each galaxy actually has its own effective 'rest frame', and they are completely different in their decisions about simultaneity. So our universe really does have the above scenario.

13. Oct 30, 2012

### arindamsinha

Thanks for confirming that my understanding is correct, so I will get on to the follow up question I mentioned.

Before I proceed further, let me say that the scenario in our Universe you are talking about is very interesting and exciting, and I would very much like to discuss some of that with you at a later stage. The one paragraph on CMB etc. brings in horde of things that I have been thinking about, and would like to have some light shed on, but I will do that in other threads later. Let me first clear up the points in this thread.

My thoughts were these:
• A. We agree that the event is simultaneous as per the hovercraft but not as per the floating crash detector (and vice versa).
• B. Now, the movement of the trains keeps them 'at rest' w.r.t. each other, as well as only one of the frames - the hovercraft. Does this not make the hovercraft the 'preferred' or 'true' frame for observations? All other frames suffer from the deficiency of having the signals travel different distances, I think.
• C. If the trains had actually been at stations and not moving, it is the hovercraft which would have considered the events non-simultaneous, while the crash detector would have considered them simultaneous
• Question: So does it not mean that the non-simultaneity of the same events in different frames is a 'frame-dependent perception' rather than a true chronology of events?

14. Oct 30, 2012

### Staff: Mentor

The non-simultaneity is frame-dependent - there's no question about that.

The question you raised in your initial post, based on the wikipedia article, is whether it is possible to construct a single "true chronology" of events after the frame-dependent effects (different travel times for signals and the like) have been allowed for.

So let's completely remove the frame-dependent signal propagation effects from the thought experiment...
Return to my example of the airplanes, but take away both mid-ocean detectors. All we have is the two cities with two airplanes flying above them. Of course without the mid-ocean detectors, we have no way of following events as they unfold, but because of the synchronized clocks we can reconstruct the chronology after the fact. For example, if the people in London say "At noon GMT X happened in the streets of London" and the people in New York say "At noon GMT Y happened in the streets of New York", someone constructing a chronology would able to say that X and Y happened "at the same time".

But look at what happens when we try to construct a "real" chronology in my example:

The people in London and Paris report that they sent signals from the ground to the aircraft overhead at the same time. They also report that they received signals from the aircraft overhead at different times.
The people in the airplanes report that they both sent signals to the ground at the same time. They also report that they received signals from the ground at different times.

So where's the one true chronology?

Last edited: Oct 30, 2012
15. Oct 30, 2012

### Staff: Mentor

The distance is immaterial. Suppose that instead of having two hovercraft you have three, all travelling the same speed in the same direction. These three hovercraft are all at rest in the same inertial frame and will therefore agree about the simultaneity of any pair of events, regardless of the different distances. Remember, all relativistic effects are what is left over after they intelligently account for the finite speed of light. So the distance is unimportant, only the velocity.

It certainly is frame dependent, but "true chronology" is undefined. The problem is that there is no experimental way to distinguish a "true chronology" from any other chronology. So you can, by fiat, assert that "the true chronology is X", but then I can assert that "the true chronology is Y" and there is no way to justify or contradict either of our statements.

In my opinion, the universe simply doesn't "care" about simultaneity, all it "cares" about is causality. Simplistically, if A caused B then A came first and B came second, if A did not cause B then the universe has no prefered ordering.

16. Oct 30, 2012

### bossman27

I'll admit to only fully reading about half of the previous comments, but I didn't see anyone adress an issue which might help the OP to understand the relativity of simultaneity: The distinction between space-like intervals, time-like intervals, and light-like intervals.
The invariant interval is defined as follows:
$s^{2} = (c \Delta t)^{2} - \Delta r^{2}$
-- You could think of $\Delta x = \Delta r$ if we only think about 1 dimension of motion along the line connecting the events.
-- You can also define it in the reverse way. That is: $s^{2} = \Delta r^{2} - (c \Delta t)^{2}$
---------- (Wikipedia defines it this way, and we can just reverse the sign of s^2 in this case, when looking to see whether it's positive or negative.)
---------- In any case, the equations below hold.
This quantity $s^{2}$ is invariant for all frames of reference, meaning every reference frame will agree on it. Qualitatively, you can think of it as the difference between the spacial separation between the two events and the distance light could travel between the occurrences of the two events in time, though that's not exact because of the squares.

There are three types of possible invariant intervals for two events:
1) Time-like Interval (causal): $(c \Delta t)^{2} > \Delta r^{2}$
-- This means that enough time passes that light could leave the first event, and reach the second event before it happens. That means that, in theory, A could have caused B. In this case there are no possible reference frames would record that B happened before A. Everyone will agree that A happened before B.
-- However, there are possible moving reference frames that would record that the spacial order of the events is reversed, or that they occurred at the same point in space.

2) Space-like Interval (non-causal): $\Delta r^{2} > (c \Delta t)^{2}$
-- This means that light could not have left one event and reached the second event before it happened. Every reference frame would record that the events are located spatially in the same order.
-- However, there are reference frames which will record the events happening at different orders in time, or at the same time.
*** Note that this is the case for your example with two crashes happening simultaneously (in the earth's rest frame), at two different locations. The order of events will depend on your velocity with respect two the two cities; but, it might make you feel better to note that all observers would at least agree on the relative locations of NY and London, i.e. their "order" in space.

3) Light-like Interval: $\Delta r^{2} = (c \Delta t)^{2}$
-- Only light could traverse the distance between two events in the time between them. That is, if light left the event A it would reach the location of event B exactly as B occurred.
-- In this case, all observers, while they will disagree about the time/distance between the events, they will all agree on the order of events, both spatially and temporally.

It helps to understand all of this more thoroughly if you work with Minkowski Diagrams, and using the concept of a light-cone (though I preferred just drawing some axes for super-relativistic frames and seeing what could happen).

Also, just for fun, think about how much the events would have to be separated in time, in the rest frame, to be time-like seperated...

Well, we have $\Delta r = 5586 kilometers = 5.586 \times 10^{6} m$

We want: $c \Delta t > \Delta r$

$\Delta t > \frac{5.586 \times 10^{6}}{3 \times 10^{8}} = .01862 sec$

Thus if the the crash in New York happened at least .01862 seconds before the one in London, as measured by an observer at rest with respect to both events, we would have a time-like interval, and then all observers would agree that the New York crash happened before the London crash.

Last edited: Oct 30, 2012
17. Oct 30, 2012

### bossman27

To address this question more directly: This is a matter of the perceptions of different observers, but the key here is that there is no "absolute" frame of reference. That is precisely the basis of relativity -- that no frame of reference is an "absolute frame".

From any reference frame, it is possible to use the Lorentz transformations and boost to the rest frame of these two events, i.e. the stationary earth-bound observer's frame, and reconstruct the simultaneity of the crashes for that observer. The point here is just that the rest observer's perspective is not more "real" or "absolute" than any other perspective.

18. Oct 30, 2012

### Staff: Mentor

I have a few more comments about this discussion. What we are really talking about here is the same old relativistic train problem (in sheep's clothing) involving lightning strikes. Imagine that there is a team of observers strung out along the railroad track on the ground (S frame of reference), and a second team of observers strung out along the "moving train" (S' frame of reference). The S coordinates are x and t, and the S' coordinates are x' and t'. All the clocks on the ground are synchronized with one another, and all the clocks on the train are also synchronized with one another. Unfortunately, even though the clocks on the ground are synchronized with one another, the ground observers reckon from their frame of reference that the set of clocks on the train are not in synchronization. Similarly, even though the clocks on the train are synchronized with one another, the train observers reckon from their frame of reference that the set of clocks on the ground are not in synchronization. The observers on each of the two teams arrive at these conclusions by observing only the clock in the adjacent frame of reference that is directly opposite them at any given moment.

At any arbitrary value of t on the ground clocks, the set of ground observers can, together in combination, view the entire train all at once (i.e., some ground observers are situated adjacent to the front of the train at time t, some ground observers are situated at the middle of the train at time t, and some ground observers are situated at the rear of the train at time t). But, according to the observers on the train, the ground observers are not seeing all parts of the train at the same time t’ displayed on the train synchronized clocks; the ground observers are, at time t, seeing some parts of the train at earlier values of t’, and some parts of the train at later values of t’. If the ground observer at x = 0 and t = 0 is directly opposite the train observer at x' = 0 at time t' = 0, then some observers on the ground are seeing certain parts of the train (i.e., are immediately adjacent to certain parts of the train) in x' = 0 observer's future (i.e., t' > 0), and some observers on the ground are seeing parts of the train ( i.e., are immediately adjacent to certain parts of the train) in x' = 0 observer's future (t' < 0). This is an example of how events that are simultaneous in one frame of reference (observers on the ground viewing the train at time t) are not simultaneous in another frame of reference.

Here is an interesting through experiment that I dreamed up (it probably isn't original). Suppose at time t = 0, each of the observers in the ground frame of reference simultaneously switch on a light bulb at their individual locations. How would the observers in the train frame of reference perceive what has happened?

19. Oct 30, 2012

### Austin0

They would see them come on sequentially beginning at some point ahead at the limit of vision and moving toward the train.

20. Oct 30, 2012

### Staff: Mentor

Yes. The "wave" would move right up to, through, and past the train into its wake. Next, how fast would the wave front between the lit bulbs and the not-yet-lit bulbs be traveling?