Doubt in Relativity of Simultaneity

[Dale]

That is in some reference frames where event at A happens first the ambulance will receive call from A first and will go to street A while in reference frames where event at B happens first ambulance will go to street B (ambulance responds to the call it receives first). So in two different reference frames the ambulance is at two different sites and so two different sets of victims die which appears to be physically impossible.

Yes, this is physically impossible, and it does not happen according to relativity. The outcome depends on the ordering of C and D, not A and B. C and D are timelike separated, so their ordering is invariant.

The problem is that you are thinking that "A happens first" implies "C happens first", but it doesn't. The ordering of C and D depends not only on the ordering of A and B, but also on the distances and the motion of the ambulance. Those other dependencies work to ensure that the ordering of C and D is invariant, despite the fact that the ordering of A and B is not.

 

[Nugatory]

I don't get how you clubbed two distinct events into a single event just because they happened at the same place and time.

That's the definition of an "event" in relativity: a single point in spacetime, identified by a time and place. More than one thing can happen at a single event: for example two people bumping into one another can be described as "Joe was at point X at time T and Bob was at point X at time T" or "The Joe-Bob collision happened at point X at time T". This is different than the comonplace English usage of the word.

It just about has to be that way, because otherwise we would have appalling logical inconsistencies that are never observed in nature. For example... Suppose that the two telephones are wired to a trigger mechanism that sets off a bomb if and only if both phones ring at once. Surely all observers, regardless of their state of motion, must agree that either the call center is blown up or it is not?

To be more clear, suppose in the traincar experiment signals are sent from either ends of the traincar towards a sensor present in the middle of the traincar just as the train passes a platform. Then by relativity of simultaneity for the observer in the traincar the sensor would receive the two signals at the same place at the same time(simultaneously) while for the observer standing on the platform the reception of the two signals(two different events) would happen at the same place but at different time.

You are misunderstanding the train experiment and where relativity of simultaneity comes in. If two signals arrive at either central detector at the same time (one event - "two flashes of light hit the central detector at time T") both the train and platform observer will agree on that fact. They will disagree about whether the emissions of the two light flashes (lightning strikes in Einstein's original version of the thought experiment) were simultaneous; the two lightning strikes at different points are separate spacelike-separated events. Note that they will also disagree about the distance that each light signal has traveled - that's how they can find different emission times yet agree that the flashes arrived at the detector together.

 

[Vitro]

See as far as I know for two events which are timelike separated there can be no reference frame where the two events are simultaneous.

That's correct.

While in the above case if A and B are simultaneous in a reference frame and the center is equidistant from A and B then center will receive signals from A and B at the same time and C and D will be simultaneous,

They will be more than that, happening at the same place and the same time makes them identical meaning it's a single event in spacetime, like Nugatory also mentioned. This is a very particular case, the ambulance center need not be equidistant in the frame where A and B are simultaneous, but regardless, this now single call center event is also invariant, it's a single event in every frame regardless of the order of A and B. If you refer back to my original reply where I said you can try a numeric example I explicitly stated "two distinct events C and D" so that the scenario is more general. You can also try an example where C and D coincide, since you brought it up.

so I don't think the center will follow a timelike worldline.

Every observer follows a timelike worldline. Always.

Also if the signal is made to a moving ambulance directly then events C and D would happen at different place and time, i.e. separated in space and time

Not necessarily, the moving ambulance can very well happen to be in a place where both calls arrive simultaneously. It doesn't change the scenario in any way. The moving ambulance also has a timelike worldline and if C and D are distinct they would have the same order in every frame and if they coincide they would do so in every frame as well.

 

[PeterDonis]

Two events are causally connected when one event causes the other to happen.

Yes, and that's true for events C and D, because the ambulance (or call center) is involved in both. Events don't have to have a single cause; different causes can contribute. As long as at least one cause is common to both, they are causally connected (at least in the sense that's relevant for this discussion).

More generally, the relevant concept here is not "causal connection" but "timelike separation". Events C and D are timelike separated, and that is what requires their time ordering to be invariant. We know they must be timelike separated because they are both on the worldline of the same object (the ambulance/call center).

In the above case events B or D does not cause event C to happen or A or C does not have a role in cause of D.

This is false, because C does have a role in the cause of D; see above. D won't happen unless the ambulance is there, and the ambulance has to pass through C first, so what happens at C does cause what happens at D, in the relevant sense.

can't we come up with any example/experiment where the order of happening of events A and B affects event C.

No. In order for what happens at events A and B to affect what happens at event C, some kind of signal must travel from A and B to some object of interest (the ambulance/call center in your example) whose worldline passes through C. What happens at C depends on the order at which signals arrive at that object. That order is invariant because the object's worldline is timelike. The fact that the order of A and B themselves is not invariant (because they are spacelike separated) is irrelevant; what matters is the order in which signals arrive at the object to be affected, and that object's worldline will always be timelike, so distinct signal arrivals will always be timelike separated and their order will always be invariant.

 

[Stephanus]

There's something I'd like to add here.

Two events are causally connected when one event causes the other to happen.

For one event (A) causes the other (B) to happen, A and B must be TIME LIKE
But a two- time like events DOESN'T CAUSE causality, forgive the pun
Example 1: A causality events must be time like.
Watching live CNN financial (or politic?) channel, showing Greece bankrupts and pick up your phone to call your broker to sell EURUSD (sorry for the futures; ever wonder why forex trading is called "future" ; trader) must be time like. Selling EURUSD is the causality of watching Greece bankrupt.
The signal reaches your TV from Greece (or CNN studio) travels at the speed of light should be less than 1/7 seconds, more likely more. It's impossible for the signal from Greece to arrive at your TV less then 1 miliseconds. That's why this must be time like.
Example 2: A two time like events but doesn't cause causality.
You miss your boy/girl friend, and one hour later he/she knocks at your door. This is definitely time like, but it's not a causality.
And if you insist that these two events (think about your lover; knock at your door) are causality, you might want to visit mystic forum.
I hope you understand the difference between time like and causality.
Causality MUST BE time like
Time like DOESN'T have to cause causaility.

 

[Stephanus]

You are misunderstanding the train experiment and where relativity of simultaneity comes in. [..]

Perhaps I should show you the train experiment.
I'm an (very) amateur, too in SR. But it's this simulation that leads me to discover Lorentz Length contraction, Lorentz Time dilation and relative simultaneity of events. (Tough Hendrik had devised it more then 120 years ago!)

Consider Einstein's Train example.
https://www.physicsforums.com/threads/length-contraction.817911/page-2#post-5135255
You have a train with an observer at the midpoint between the ends. you also have an observer standing along the tracks. Lightning strikes the end of the trains when, according to the track-side observer the train observer is passing him. Thus he sees the light from the strikes at the same time and determines that the strikes occurred simultaneously. Thus, according to the frame of the tracks, events look like this:

ANIMATION 1

Now consider how things look from the frame of the train. The lightning strikes the ends of the train, and each lightning strike has to happen when the respective end of the train is next to the same red dot as it was according to the track frame. The light from each flash must also arrive at the track-side observer at the same time just like in th efirst animation. The light from either flash must also hit the train observer when he is next to the same point of the tracks as it does according to the track frame. (In other words, any event that happens in any frame must happen in the other frame.)

Now here is where you have to take length contraction into account. In the track frame as shown above, the train is moving so it is length contracted. So it is the length contracted train that fits between the two red dots that mark where the lightning strikes occur. In the train frame, the train is its non-contracted proper length, and it is the tracks that are length contracted. Thus the distance between the red dots is shorter than the length of the train and the ends of the train do not align with these dots at the same time. Since the event of the lightning striking an end of the train when it is next to a red dot is common to both frames, this means the lighting strikes cannot occur at the same time in the train frame. And in order for the light from each strike to reach the track observer at the same time and to meet the requirements of all the other common events between frames, the light must expand outward at a constant speed from the points of the strikes. Thus from the frame of the train events look like this.

[PLAIN]http://home.earthlink.net/~jparvey/sitebuildercontent/sitebuilderpictures/trainsimul2.gif[SIZE=7][COLOR=#ff0000][B]ANIMATION 2[/B][/COLOR][/SIZE]

Supposed the velocity is 0.6c.
The length of the platform is 120c. Let's use a 8 * 3 * 5 number for rounds result.
Lets say the back of the platform is PB the front if PF
The back of the train: TB, front = TF.
See Animation 1: Platform rest frame. Platform will see
The length of the train is (of course) 120ls, remember the front and the back of the train fits the platform.
The length of the platform; 120 ls
The distance of the observer (R) from the back of the platform; halfway or 60ls.
(PB meets TB) and (PF meets TF) event happen at the same time. For the light reaches the observer (R) at the sametime.
Dividing the speed of light and distance, the light will reach the observer (R) at 60 seconds.
Supposed if (R) regardless of frame of reference receives the signal AT THE SAME TIME, R will shine a GREEN light. If not R will shine a Red light.
In this case, we see that the lights reach R AT THE SAME TIME. So R will show Green.

--- And remember. The speed of light is INVARIANT. So PB and PF will see that they are at the CENTER of the LIGHT CONE.
| --------------------------------------------------------
|
| Now let's take a look from the train frame, see animation 2
|
-->And remember. The speed of light is INVARIANT. So TB and TF will see that they are at the CENTER of the LIGHT CONE.
So, when TF reaches PF the light shines, but the train, sorry the platform also moves at 0.6c back ward. So, the light will reaches R at 60/(1-0.6) = 150 seconds.
When TB reaches PB the light shines, so the light will reaches R at 60/(1+0.6) = 37.5 seconds.
No, this CAN'T be right. The light have to reach R AT THE SAME TIME. The proof? R lights Green lamp remember?
Let's study this picture.

Remember, all calculation below does NOT use Relativity, it uses ALGEBRA. So you shouldn't be afraid with SR.
Okay, let define L, first
L is the distance from the observer (R) or half the platform size. Platform = 2L
Let's see the above diagram first.
L3 and L
R has already at L length from TF/PB traveling at 0.6c when the light shines at c.
So, what is L3 so that the light catches up R?
$L3 = V(L3+L); L3 = 0.6(L3+L); L3 = \frac{3}{2}L; \frac{L3}{L3+L} = V$
See below
What is L1 so that the light will meet R?
$(1+V)L1 = L; 1.6L1 = L; L1 = \frac{5}{8}L; L2 = \frac{3}{8}L; again \frac{L2}{L1} = V$
So at TF/PF, R has to travel along L4 distance before TB meets PB
$L4+L2 = L3; L4 = \frac{9}{8}L$
Let's add all length
$L_{Train} = L + L4 + L = \frac{25}{8}L; L_{Train} = \frac{25}{16}L_{Platform}$
Conclusion: The length of the train at rest must be $\frac{25}{16}$ length of the platform at rest.
No, that is wrong!
Conclusion: The length of the train at rest must be $\frac{25}{16}$ length of the platform at traveling!
The length contraction works both ways.
Conclusion: The length of the train at rest is $\sqrt{\frac{25}{16}} = \frac{5}{4} = 1.25$ length of the platform at rest.
Where in Lorentz factor $\gamma=\frac{1}{\sqrt{1-V^2}} = \frac{1}{\sqrt{0.64}} = 1.25$
How much time that TF takes when it meets PB until it meets PF?
$T_{Train} = L_{Platform, traveling}/V = \frac{120 / 1.25}{0.6} =160 seconds$
At platform frame, how much time that TF takes when it meets PB until it meets PF?
$T_{Platform} = L_{Platform, rest}/V = \frac{120}{0.6 } = 200 seconds$

So in this example you'll see that
1. The length is contracted for moving object
2. There's a relativity simultaneity of event.
- Where in platform frame TF/PF happens at the same time as TB/PB,
- In train frame TF/PF happens first, then TB/PB.
3. Time dilation. 160 secods for train frame = 200 seconds for platform frame.
That's all. I didn't want to mislead the OP. I hope the honorable mentors/advisors will immediately correct me if I'm wrong.

 

[Rohit Solanki]

Yes, this is physically impossible, and it does not happen according to relativity. The outcome depends on the ordering of C and D, not A and B. C and D are timelike separated, so their ordering is invariant.

The problem is that you are thinking that "A happens first" implies "C happens first", but it doesn't. The ordering of C and D depends not only on the ordering of A and B, but also on the distances and the motion of the ambulance. Those other dependencies work to ensure that the ordering of C and D is invariant, despite the fact that the ordering of A and B is not.

I think I understand your point.Tell me if I'm getting this right: Because it would lead to logically inconsistent results otherwise, all the dependencies in all the reference frames must always work in a way to ensure that order of C and D( which causes the inconsistency ) is invariant. That is we'd never come up with any experiment or numeric example where those dependencies fail to do so and C and D are not invariant.

Also I wanted to know, had C and D happened at different place, i.e. the calls would have been made to different centers then can the order of C and D be not invariant.

 

[Stephanus]

Can I answer?

I think I understand your point.Tell me if I'm getting this right: Because it would lead to logically inconsistent results otherwise, all the dependencies in all the reference frames must always work in a way to ensure that order of C and D( which causes the inconsistency ) is invariant.

It seems so, but it doesn't have to be.
Consider this diagram:

Consider 3 events
A, B and AB. They're just arbitrary events. Nothing triggers A and B.
Even without dependencies, the order of event AB and A is invariant. AB happens first then A. Even if you move the world line anywhere you like.
Note: The order of AB and B in both pictures vary. In Pic 1. AB first, then B. Pic 2: B then AB.

Also I wanted to know, had [Edit] C and D AB and A happened at different place, i.e. the calls would have been made to different centers then can the order of C and D AB and A be not invariant.

Have to edit your question. I already draw AB and A. Needs much effort to change the letters.
Okay, so C and D AB and A happened at different place. But now matter where the calls were made, the order of AB and A can't be vary.
Why? Because AB and A are time like.
See, AB and B, the order varies if you look at different frames. Why? Because they are space like.

Perhaps you should understand the terms "space like" and "time like". Btw, I just knew these terms about a week ago, but I think I understand it
Two events are called time like, if the angle more than 45⁰
Why? Because theoretically there will be an object that can travel from AB to A in time when A happens.
Two events are called space like, if the angle less than 45⁰
Why? Because it's physically impossible for an object to travel from AB to A in a given time. That's why it's not time like, but space like.
Light ray angle always 45⁰ or -45⁰.
So any events above light ray are always time like, below are space like.

That is we'd never come up with any experiment or numeric example where those dependencies fail to do so and C and D are not invariant.

Experiment? I think no with our current technology.
Numeric example? Well, yes. You can study Lorentz transformation and plug any numbers you like, it will show you that the order of any time like events are invariant.
Like I said before, forget relativity, forget common sense. Just algebra-ing Lorentz. Study the easy Lorentz transformation, boost in 1 dimension until you can do it intuitively.

 

[Stephanus]

Btw, we live in a better world than in early 20th century. Or even at the late 19th century.
Hendrik Lorentz, Minkowski and other. They didn't have computers, even the ST plotter software. If you want it, I could give you the software. Someone wrotes this software not me. And someone in this forum gives me the software. Every draw you saw are generated by that software.
I think the tactic to understand relativity is this.
Study Lorentz transformation (in 1 dimension), and length contraction. Algebra those numbers, until you can do it intuitively. Then try to imagine the universe as shown by the numbers not as our common sense. Then, you'll realize that actually our "common sense" is wrong. .

 

[Dale]

That is we'd never come up with any experiment or numeric example where those dependencies fail to do so and C and D are not invariant.

Also I wanted to know, had C and D happened at different place, i.e. the calls would have been made to different centers then can the order of C and D be not invariant.

Yes to both of these. On the second one, for the ordering to be not invariant requires that the events be spacelike separated meaning that a signal from one to the other cannot travel at c or less.

 

[Rohit Solanki]

It just about has to be that way, because otherwise we would have appalling logical inconsistencies

The thing was I didn't focus on that. I mean there was a time when people thought that the idea of relativity of simultaneity or time dilation was logically inconsistent or against our "common sense". But because it was based on experimentally verified fundamentals (principle of invariance of speed of light) and well-sought thought experiments, that we accepted it no matter how appalling the end results sound at the time. But as one of the mentors pointed out earlier, that's outside the scope of this forum. So I'd stop here and go do more study and research.
And thanks everyone for your comments, it really helped.

 

[Nugatory]

I mean there was a time when people thought that the idea of relativity of simultaneity or time dilation was logically inconsistent or against our "common sense".

"Logically inconsistent" and "against common sense" are very different things. There has never been a time when anyone who knew what time dilation and relativity of simultaneity were believed that they were logically inconsistent, although many people have and still do find logical inconsistencies in things that they mistakenly call "time dilation" and "relativity of simultaneity".

"Against common sense"... Now that's a different matter altogether :-)