# Doubt in Relativity of Simultaneity

1. Jul 23, 2015

### 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.

2. Jul 23, 2015

### Orodruin

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

3. Jul 23, 2015

### Staff: Mentor

It can't; this is physically impossible.

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.

4. Jul 23, 2015

### 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

5. Jul 23, 2015

### Rohit Solanki

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

6. Jul 23, 2015

### Orodruin

Staff Emeritus
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!

7. Jul 23, 2015

### cpsinkule

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

8. Jul 23, 2015

### Staff: Mentor

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.

9. Jul 23, 2015

### Orodruin

Staff Emeritus
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.

10. Jul 23, 2015

### Rohit Solanki

And referring to your above point.
Could you elaborate.....I mean can simultaneity or order of two distinct events affect a third event.

11. Jul 23, 2015

### Orodruin

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

12. Jul 23, 2015

### cpsinkule

yes, i meant their order according to the ambulance

13. Jul 23, 2015

### Staff: Mentor

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.

14. Jul 23, 2015

### Stephanus

But I still can't understand what "at the same time means".

15. Jul 23, 2015

### Stephanus

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?

16. Jul 23, 2015

### Staff: Mentor

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.

17. Jul 23, 2015

### Stephanus

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.

18. Jul 23, 2015

### Stephanus

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?

19. Jul 23, 2015

### pervect

Staff Emeritus
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.

20. Jul 23, 2015

### Staff: Mentor

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).

21. Jul 23, 2015

### Vitro

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.

22. Jul 23, 2015

### Staff: Mentor

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.

23. Jul 23, 2015

### 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.

24. Jul 24, 2015

### Stephanus

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

25. Jul 24, 2015

### Rohit Solanki

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