Doubt in Relativity of Simultaneity

[Rohit Solanki]

Hey everyone, I have this doubt for quite some time now. So could somebody please help me and explain where I am going wrong with this.

According to the relativity of simultaneity, 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. The question of whether the events are simultaneous is relative: 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.

Now what happens if outcome of an event or the consequence of two distinct events depend upon the simultaneity of the two events.

For example, let us suppose that two different car crashes took place in two different streets('A' & 'B') of New York, which are not causally connected. Both are serious cases where victims need immediate medical attention. Now assume there is only one ambulance present in that region which responds to the call made first. Now in some reference frames the accident at street 'A' would have happened first and victims at street 'A' would have been saved while victims at street 'B' would have died. However, in some other reference frames the accident at street 'B' would have happened first and victims at street 'A' would have died.
So the two different observers observing the same events from two different reference frames would record two conflicting observations.

PS: Thanks in advance...

 

[Orodruin]

The events when the ambulance personal receives the calls from either accident are causally connected and therefore have a fixed time ordering.

 

[PeterDonis]

what happens if outcome of an event or the consequence of two distinct events depend upon the simultaneity of the two events.

It can't; this is physically impossible.

assume there is only one ambulance present in that region which responds to the call made first.

The ambulance is not responding to which call is made "first" in the sense of simultaneity. It's responding to which call it receives first. That is an invariant; it doesn't depend on which frame you choose.

 

[cpsinkule]

to alert an ambulance you have to send a signal to the ambulance.for the signal to affect the ambulance it has to be in the lightcone of the ambulance. events within the lightcone are timelike separated and the order cannot change by lorentz transformation

 

[Rohit Solanki]

The events when the ambulance personal receives the calls from either accident are causally connected

I'm sorry I don't get how those events are causally connected. Let us call the event when personnel receive call from accident at street A as event C and that from B as event D. So shouldn't C solely depend on A and not on B, Also A and B are not causally connected

 

[Orodruin]

That A and B are not causally connected does not mean that their light cones are disjunct. C and D must be causally connected, the ambulance call center is present at both of them!

 

[cpsinkule]

I'm sorry I don't get how those events are causally connected. Let us call the event when personnel receive call from accident at street A as event C and that from B as event D. So shouldn't C solely depend on A and not on B, Also A and B are not causally connected

for anything to affect an observer it must enter the lightcone of the observer. all events occurring in a lightcone of an observer cannot have their order changed

 

[PeterDonis]

shouldn't C solely depend on A and not on B

Yes, but C and D both also depend on the ambulance/call center, since they are both on its worldline. As Orodruin says, C and D must be causally connected because of that latter dependence, not because of anything about A and B.

 

[Orodruin]

all events occurring in a lightcone of an observer cannot have their order changed

This is not true, given any light cone, there are events inside it which are spatially separated, take the light cone of the event (0,0) and consider the events (1,-0.6) and (1,0.6), which are both in its light cone. What you probably meant to say is that events along an observer's world line cannot have their order changed, since they are time-like separated.

 

[Rohit Solanki]

And referring to your above point.

It can't; this is physically impossible.

Could you elaborate...I mean can simultaneity or order of two distinct events affect a third event.

 

[Orodruin]

And referring to your above point.

Could you elaborate...I mean can simultaneity or order of two distinct events affect a third event.

In order to know the answer to this question, you need to specify in which frame the distinct events should be simultaneous or not.

 

[cpsinkule]

This is not true, given any light cone, there are events inside it which are spatially separated, take the light cone of the event (0,0) and consider the events (1,-0.6) and (1,0.6), which are both in its light cone. What you probably meant to say is that events along an observer's world line cannot have their order changed, since they are time-like separated.

yes, i meant their order according to the ambulance

 

[PeterDonis]

can simultaneity or order of two distinct events affect a third event.

No. If two events are simultaneous in any reference frame, they must be spacelike separated. The ordering of two spacelike separated events cannot affect what happens at any other event.

 

[Stephanus]

Perhaps these can answer your question. About simultaneity of events.
But I still can't understand what "at the same time means".

 

[Stephanus]

No. If two events are simultaneous in any reference frame, they must be spacelike separated. The ordering of two spacelike separated events cannot affect what happens at any other event.

I should have tried it with ST diagram, but... I just like an easy answer.
Are you trying to say that if two events are timelike separated (E1 and E2), it is geometrically/mathematically or event physically impossible for the two event to connect to a third event (E3) no matter where we draw E3 at the ST diagram?

 

[PeterDonis]

Are you trying to say that if two events are timelike separated (E1 and E2), it is geometrically/mathematically or event physically impossible for the two event to connect to a third event (E3) no matter where we draw E3 at the ST diagram?

I didn't say anything about timelike separated events at all. I'm not sure what you mean by "connect", but if you mean "connect via a light signal", obviously it depends on the events. One thing that is true of all pairs of timelike separated events is that their time ordering is invariant, the same for all observers.

 

[Stephanus]

I didn't say anything about timelike separated events at all. I'm not sure what you mean by "connect", but if you mean "connect via a light signal", obviously it depends on the events. One thing that is true of all pairs of timelike separated events is that their time ordering is invariant, the same for all observers.

Oh, okay. If they are spacelike separated, the light intersection can happens both in the future or both in the past.
If they are timelike separated. One is in the future, one is in the past.

 

[Stephanus]

[..]Now in some reference frames the accident at street 'A' would have happened first and victims at street 'A' would have been saved while victims at street 'B' would have died. However, in some other reference frames the accident at street 'B' would have happened first and victims at street 'A' would have died.

I once read something about Schrodinger cat, is it caused by simultaneity of ordering events? Perhaps when something travels faster than the speed of light?

 

[pervect]

For example, let us suppose that two different car crashes took place in two different streets('A' & 'B') of New York, which are not causally connected. Both are serious cases where victims need immediate medical attention. Now assume there is only one ambulance present in that region which responds to the call made first. Now in some reference frames the accident at street 'A' would have happened first and victims at street 'A' would have been saved while victims at street 'B' would have died. However, in some other reference frames the accident at street 'B' would have happened first and victims at street 'A' would have died.
So the two different observers observing the same events from two different reference frames would record two conflicting observations.

PS: Thanks in advance...

You just specified that there was "one and only one ambulance". The sort of ambulances we can build cannot "know" when an accident occurs until it receives a radio signal (or some other signal, which must travel at less than or equal to the speed of light by the laws of relativity). Given a specific ambulance, with a specific state of motion, and a specific receiver, the ambulance will either receive one signal first (and go to that accident), or receive both signals at the same time and make an on-the-spot decision as to which accident scene to plot a course for. It will never (by the problem statement) be able to be in two places at once.

If you are imagining an ambulance that "knows" instantly at a distance when something happens, this is not directly compatible with special relativity, so you are imagining something that's not possible in the context of relativity and asking what happens according to relativity. Relativity can't answer this question. It is not, so far as I know, necessarily logically impossible to imagine "different physics" governing the operation of the receiver that are not special relativity, but the details of what sort of physics you might imagine and how you make this imaginary physics compatible with the experimental results to date (which all support SR) are perhaps outside the scope of this forum. Specifically, one would need to find a peer reviewed paper on the topic before it would be suitable for discussion at PF, as the policy is to only discuss peer-reviewed theories at PF and not any sort of "theory" one might be able to imagine. I did a little digging to see what might be out there, the closest thing I found was https://en.wikipedia.org/wiki/Test_...rtson.E2.80.93Mansouri.E2.80.93Sexl_framework. But this is hardly an exhaustive literature search.

 

[PeterDonis]

I once read something about Schrodinger cat, is it caused by simultaneity of ordering events?

No. Schrodinger's cat is a completely separate issue. If you want to ask about it, the proper place is the Quantum Physics forum (but please search the forum first as there are many threads already there discussing it).

 

[Vitro]

I'm sorry I don't get how those events are causally connected. Let us call the event when personnel receive call from accident at street A as event C and that from B as event D. So shouldn't C solely depend on A and not on B, Also A and B are not causally connected

You where on the right track to figuring it out but then you took a wrong turn. Let's trace back to where you had just defined events C and D. Now, what can you say about events C and D, what important property do they have that's different from A and B?

Events C and D are both experienced by the ambulance center which has a timelike worldline, meaning they are timelike separated. Two timelike separated events have the same chronological order in all reference frames, if the ambulance center got call C before call D (or vice-versa) in one frame then it did so in every other frame regardless of the order of events A and B.

Try a numeric example, take two simultaneous events A and B and two distinct timelike events C and D such that C is in the future of A and D is in the future of B. Now do a few transforms to other frames and compare the time orders of the events.

 

[PeterDonis]

If they are spacelike separated, the light intersection can happens both in the future or both in the past. If they are timelike separated. One is in the future, one is in the past.

This is a garbled description, but your diagram clarifies what you are getting at. Here is a better way of stating it:

If two events are spacelike separated, their future light cones intersect somewhere to the future of both events, and their past light cones intersect somewhere to the past of both events.

If two events are timelike separated, the future light cone of one intersects the past light cone of the other, and this intersection is "between" the two events (to the future of one and to the past of the other).

Note that in both of the above cases, explicitly stating where the intersection is located (future or past) relative to the two events is redundant; that is already determined by which light cones are intersecting.

 

[Stephanus]

No, no, SR first not quantum. It's just that I read the sentence, in case 1 victim A dies, in case 2 victim 2 dies. Sounds like in case 1 the cat dies, in case2 the cat lives.
Thanks, I'll stop right here.

 

[Stephanus]

This is a garbled description, but your diagram clarifies what you are getting at. Here is a better way of stating it:

If two events are spacelike separated, their future light cones intersect somewhere to the future of both events, and their past light cones intersect somewhere to the past of both events.

If two events are timelike separated, the future light cone of one intersects the past light cone of the other, and this intersection is "between" the two events (to the future of one and to the past of the other).[..]

And I could add

Two timelike separated events have the same chronological order in all reference frames

And also two spacelike separated events experience relative simultaneity. Good conclusion here! I've tried with Minkowski space time plotter. Easy.

 

[Rohit Solanki]

Sorry Pervect, I wasn't imagining an ambulance where signal reaches instantly. I was making the point you mentioned here...

a specific ambulance, with a specific state of motion, and a specific receiver, the ambulance will either receive one signal first (and go to that accident)

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.

If you see our above discussion, Peter and Orodruin suggested that events C(ambulance receiving call from A) and D(ambulance receiving signal from B) are causally connected. (And Peter I'd like your thought on the following point...)
Two events are causally connected when one event causes the other to happen. The logic behind the invariance of order of happening of events which are causally connected is that cause comes before effect.So if one event causes or affects happening of other event then the latter must always happen after the former. 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. The effects of events C and D(where ambulance goes to, as it cannot be at A and B at the same time) are however connected. So while the effects of events C and D are related but C and D are not causally connected and hence the order of C and D should not be invariant.

And thanks Peter, pervect and Orodruin for your insightful comments...

 

[Rohit Solanki]

The ordering of two spacelike separated events cannot affect what happens at any other event.

See Peter that's what's bothering me, I mean why can't it happen...
Let us say 3 events A, B and C happen in a spaceship X. For an observer in another spaceship say Y events A and B(which are distinct and not causally connected) are simultaneous. Now can't we come up with any example/experiment where the order of happening of events A and B affects event C. If we can then how are we making the pre-supposition that event C is invariant while the order of happening of A and B is relative to choice of reference frame.

 

[Nugatory]

See Peter that's what's bothering me, I mean why can't it happen...
Let us say 3 events A, B and C happen in a spaceship X. For an observer in another spaceship say Y events A and B(which are distinct and not causally connected) are simultaneous. Now can't we come up with any example/experiment where the order of happening of events A and B affects event C. If we can then how are we making the pre-supposition that event C is invariant while the order of happening of A and B is relative to choice of reference frame.

If events A, B, and C all happened in spaceship X then they are necessarily timelike-separated, because there exists a frame (in this case, the frame in which X is at rest) in which they happened at the same place but different times. Because they are timelike-separated, the order in which they occurred will be the same in all frames; there is no way that A and B can be simultaneous for Y.

The only way that there can be any disagreement about whether two events happened at the same time or which one happened before the other is if they are spacelike-separated. That requires that they happened at different places but so close to one another in time that a light signal from one could not have reached the other. The two car crashes at the start of this thread were this way; events A, B, and C happening on the same spaceship are not.

 

[atyy]

See Peter that's what's bothering me, I mean why can't it happen...
Let us say 3 events A, B and C happen in a spaceship X. For an observer in another spaceship say Y events A and B(which are distinct and not causally connected) are simultaneous. Now can't we come up with any example/experiment where the order of happening of events A and B affects event C. If we can then how are we making the pre-supposition that event C is invariant while the order of happening of A and B is relative to choice of reference frame.

Perhaps a simpler way to understandis to realize that "simultaneous" is not a meaningful concept. For example, when you have a video conference with someone on the other side of the world, when he speaks, do you simultaneously hear what he says? You don't, because the signal takes time to be transmitted. Because the speed of light is a universal speed limit, this places this means that there is a spatially separated people cannot hear what the other person is saying "simultaneous",

 

[Rohit Solanki]

Events C and D are both experienced by the ambulance center which has a timelike worldline, meaning they are timelike separated.

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

 

[Nugatory]

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

If the two signals are received at the same place (the call center) at the same time, then their reception is a single event: "Both phones in the call center rang at midnight". What makes the world line of the call center timelike is that all observers will agree that the event "Call center clock read midnight and both phones rang" happened after the event "Call center clock read 23:59" and before the event "Call center clock read 00:01".

 

[universal_101]

Hey everyone, I have this doubt for quite some time now. So could somebody please help me and explain where I am going wrong with this.

According to the relativity of simultaneity, 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. The question of whether the events are simultaneous is relative: 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.

Now what happens if outcome of an event or the consequence of two distinct events depend upon the simultaneity of the two events.

For example, let us suppose that two different car crashes took place in two different streets('A' & 'B') of New York, which are not causally connected. Both are serious cases where victims need immediate medical attention. Now assume there is only one ambulance present in that region which responds to the call made first. Now in some reference frames the accident at street 'A' would have happened first and victims at street 'A' would have been saved while victims at street 'B' would have died. However, in some other reference frames the accident at street 'B' would have happened first and victims at street 'A' would have died.
So the two different observers observing the same events from two different reference frames would record two conflicting observations.

PS: Thanks in advance...

This is a very clear scenario you presented.

Except you end up drawing a wrong conclusion, Let me try to clear your doubt.

So long the ambulance itself is in the different frames which are observing the two events A & B, the ambulance will respond to the calls depending on which frame the ambulance itself is in. Whereas, if the ambulance is in a particular reference frame which is not changing, it doesn't matter from which frame you observe the response of the ambulance, it'll always be the same.

I hope it clears your doubt.

 

[Stephanus]

See Peter that's what's bothering me, I mean why can't it happen...
Let us say 3 events A, B and C happen in a spaceship X. For an observer in another spaceship say Y events A and B(which are distinct and not causally connected) are simultaneous. Now can't we come up with any example/experiment where the order of happening of events A and B affects event C. If we can then how are we making the pre-supposition that event C is invariant while the order of happening of A and B is relative to choice of reference frame.

I think for you to understand all the answers here (Nugatory, Vitro and PeterDonnis), you have to understand what "space like" and time like" mean. And also space time diagram.

Two events are called "space like" when light can't go to that place in the speed of light.
Event_0: Goa, at time: 0 seconds
Event_1: Jakarta, at time: 10 miliseconds after Event_0
Event_2: New Delhi, at time: 20 milliseconds after Even_0
For example. the distance between Jakarta and New Delphi is (very close to)5000 km (ignoring the Earth curvature). It takes 16.7 miliseconds for light to reach New Delphi and Jakarta. So if there's an Event_2 happens at New Delhi at 20 seconds and Event_1 happens at Jakarta 10 miliseconds, we called the two events are space like. Light from New Delhi can't reach Jakarta at 10 miliseconds.
Event_0 from Goa and Event_2 from Delhi we call them time like. The distance between Goa and New Delhi is 1500 km, it takes 5 miliseconds for light to travel from Goa to Delhi. So Event_0 and Event_2 are timelike. Here the summary.
Event_0 and Event_1: space like
Event_0 and Event_2: time like
Event_1 and Event_2: space like
See the graph. The angle for space like event is less than 45⁰. Time like angle more than 45⁰
The space time diagram that I upload contains 1 spatial dimension, and 1 time dimension.

 

[Stephanus]

I think it's better to draw space time diagram for these events:
Pic 1 as seen from the victim A and B

Pic 2 as seen from other observer (Green) not related with the ambulance and the victims.

Pic 3 as seen from the ambulance:

[..]If you see our above discussion, Peter and Orodruin suggested that events C(ambulance receiving call from A) and D(ambulance receiving signal from B) are causally connected. (And Peter I'd like your thought on the following point...)

Now I beg to differ here.
Altough events C and D are time like. Altough mathematically (and physically posible) correct that event D happens first after event C. We all both know that the phone call at event C doesn't trigger the phone call at event D.
The phone call from C is triggered by A and the phone call from D is triggered by B.
According to real world scenario
A and C is causally connected
B and D is causally connected
According to physics:
A and C are time like, so A can trigger C
B and D are time like, so B can trigger D
D and C are time like, so D can trigger C altough it's illogical one phone call triggers another!
A and B might/might not be time like. But as the pictures that I uploaded suggest: A and B are not time like they are space like

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

Of course, that goes without saying. And that also implies that the events are time like.

The logic behind the invariance of order of happening of events which are causally connected is that cause comes before effect.So if one event causes or affects happening of other event then the latter must always happen after the former. 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. The effects of events C and D(where ambulance goes to, as it cannot be at A and B at the same time) are however connected. So while the effects of events C and D are related but C and D are not causally connected and hence the order of C and D should not be invariant.[..]

Now I think it's not right. Because event C and D happens at the ambulance call center if I might say. So C and D are time like, so C and D must be invariant. Altough A and B might vary, depending on the reference frame. See the picture for blue, green and red.

 

[Rohit Solanki]

If the two signals are received at the same place (the call center) at the same time, then their reception is a single event

I don't get how you clubbed two distinct events into a single event just because they happened at the same place and time. If we had established that both phones would ring simultaneously in all reference frames, then the worldline of the center would be timelike and all observers would agree that the event(both phones rang simultaneously) happened after 23:59 and before 00:01. But we didn't establish that the events would happen simultaneously in all reference frames.

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.
So just because two events happened at same place and time in one frame, I don't think it makes them a single event or consider it timelike and declare that all observers would agree that two events always happen at the same place and same time.

PS: I apologize for the confusion caused by the poor example of the spaceship. Events A and B are to be spacelike separated. Right now I am thinking of a better example to illustrate my point

 

[Mentz114]

I don't get how you clubbed two distinct events into a single event just because they happened at the same place and time.
''
''
So just because two events happened at same place and time in one frame, I don't think it makes them a single event or consider it timelike and declare that all observers would agree that two events always happen at the same place and same time.

The mapping from coordinates to spacetime must be 1:1 so it would invalidate most of SR if you allow two different events to have the same coordinates.
By definition they are the same.

Our common experience is that no two material things can be at the same place at the same time exactly.