Relativity of Simultaneity and Time

  • #1

Main Question or Discussion Point

Hey guys,

i am not a science guy by any means so any answer written for the layman would be much appreciated. i may not be understanding this right but here it goes:
In einstein's relativity of simultaneity we talk about how events A,B, and C are simultaneous for one observer (lets call him O1). For another observer A comes first then B then C (O2). For another it goes C, B, A.(lets call him O3).

For O2 C is in the past of B, for O3 A is in the past of B. They cant both be in the past of B can they?

Maybe I am not understanding this correctly.
 

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  • #2
Orodruin
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In order for the time ordering of events to be ambiguous, they need to have space-like separation (in layman terms, you cannot send any sort of signal from one event to the other - they are not within each other's light cones). What would be called the "past" of event A is just its past light cone and its interior and what is in the "future" of A is just its future light cone and its interior. Any other events are "elsewhere" and the time ordering of A with respect to those events will depend on the reference frame.

Apart from this terminology issue, it would depend on the events whether it is possible to find a frame where A and C both occur earlier than B.
 
  • #3
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For O2 C is in the past of B, for O3 A is in the past of B. They cant both be in the past of B can they?

Maybe I am not understanding this correctly.
You are understanding correctly.

A, B, and C cannot be causally related (none of them can cause any of the others), so their ordering is not important.
 
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  • #4
Orodruin
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You are understanding correctly.

A, B, and C cannot be causally related (none of them can cause any of the others), so their ordering is not important.
But if you read carefully, this is not the actual question. The actual question is whether you can find any ordering or whether ABC in one frame implies simultaneity or ABC or CBA in all other frames. The answer to this is that it depends on the events. I can easily find a set of events where the order can be made arbitrary by changing the frame. I can also find a set of events which do satisfy the statement.
 
  • #5
In a nutshell what confuses me is the future for one is the past for another. Past and future are relative. Doesn't the universe move forward in time or am i missing something?
 
  • #6
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The answer to this is that it depends on the events.
Yes, I agree. I may have misread the question so I don't think that there is a conflict between our answers, they are just answers to slightly different questions.
 
  • #7
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In a nutshell what confuses me is the future for one is the past for another. Past and future are relative. Doesn't the universe move forward in time or am i missing something?
If you take any event (specific point in space and moment in time) then you can divide the universe into three regions.

One is the interior of the past light cone, this is the region that can send signals to the event at light speed or less. Things within this region can be causes of the event.

The second is the interior of the future light cone. This is the region that can receive signals from the event at light speed or less. Things within this region can be effects of the event.

The third region is everywhere else, also called the exterior of the light cone. There are no signals to or from the event in this region since such signals would have to go faster than c. This region cannot cause the event nor be an effect of the event.

In all reference frames causes preceed and effects follow an event. The only region where the ordering is frame dependent is in the exterior where there can be no cause and effect relationship. Causes always preceed effects, and for the rest the order doesn't matter.
 
  • #8
Orodruin
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In a nutshell what confuses me is the future for one is the past for another. Past and future are relative. Doesn't the universe move forward in time or am i missing something?
I suggest you read what I said in post #2 about the future and the past of an event. In order for it to be possible to change the time-order of two events between frames, it is necessary that the events are not within each other's light cones. If they are, then one event can influence the other and you can objectively say that one happened before, but if they are not they are independent events.

In classical mechanics, there are generally three options. If you have two events A and B, B can be in the future of A, in the past of A, or simultaneous to A. If B is in the past of A, B can influence A and vice versa. It is the same in relativity with the correction that simultaneous must be expanded. If the events are separated enough, they cannot influence each other even if they occur at different times (i.e., if the separation in space is larger than the separation in time multiplied by the speed of light). We say that event B is "elsewhere" from A. Only if B is elsewhere from A can you change their time order.
 
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  • #9
So I drop an apple and an orange at the same time. I see they land at the same moment. Observer 2 else sees me drop the apple first, the orange second. And observer 3 sees me drop the orange and the apple. The apple or the orange did not cause the other to drop. For observer 2 the dropped apple is in the past of the orange being dropped. observer 3, the dropped orange is in the past of the apple. If the universe is moving forward in time. Past to the future. Which is in the absolute past. This is my real question. Is there no such thing as an absolute past?
 
  • #10
Orodruin
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As was explained to you by both me and Dale, yes there is a past for each event, it is the set of events inside the past light cone - not the set of events with smaller time coordinate. The point is that you do seem to use the word "past" in the same meaning as in classical mechanics. This is not how it will generally be used in relativity.
 
  • #11
Ibix
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There is rather more flexibility around simultaneity and ordering in relativity than in Newtonian physics - but there are limits. If you are holding the apple and orange three feet apart and you drop them simultaneously, people will disagree about the ordering. But they will never disagree by more than three nanoseconds either way, which is the time it takes light to cross the three feet between the apple and orange.

If there's more than three nanoseconds between the drops then light has time to cross the distance and the fall of the first object could affect the fall of the second - by minute radiation pressure effects if nothing else. In that case, everyone will agree on which happened first, although they may disagree on the amount of time between the drops.

So we have three possible situations.

1 - the orange drops more than 3ns before the apple. Everyone agrees that the orange dropped first - in technical language, the orange drop is in the past light cone of the apple drop.

2 - the orange drops more than 3ns after the apple. Everyone agrees that the orange dropped second - in technical language, the orange drop is in the future light cone of the apple drop.

3 - the orange drops within 3ns of the apple. This is the complicated case. It is always possible to find a (possibly hypothetical) observer who says that the two drops happened simultaneously. It is always possible to find (possibly hypothetical) observers who say that the orange dropped first. It is always possible to find (possibly hypothetical) observers who say that the orange dropped second. Everyone will agree that the time difference between the drops was less than 3ns. This doesn't have a formal technical name, except "outside the light cones". Some people call it "elsewhere", if that's a help.

In Newtonian physics there's no upper speed limit. No matter how far apart two events are in space and how close in time they could (in principle) influence one another. That's why there's no third case (no "elsewhere") in Newtonian physics and no ambiguity over "past" and "future".

This is a less general and less technical version of what Dale and Orodruin have written - hope it helps.
 
  • #12
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This is my real question. Is there no such thing as an absolute past?
For any given event, there is a past (everything in the past light cone of that event), a future (everything in the future light cone of that event), and a third set of events that are in neither light cone. All observers, regardless of their state of motion, will agree about which events are in each of these three categories; this is sufficient to guarantee that there are no paradoxes or logical contradictions in which effects happen before their causes.

However, something may be in the past light cone of one event but not another, so there's no way of saying "this happened in the past" without saying what it is in the past of.
 
  • #13
Sorry for all these questions! i really appreciate all the help, yet I am very confused and would like to understand more
Ok in this animation A and C are outside the light cones https://en.wikipedia.org/wiki/File:Relativity_of_Simultaneity_Animation.gif.
How can it take place neither in the past or future. Maybe I am getting things confused. I seem to have this idea of relativity showing that nothing is absolute.
So I seem to think that I spilled my milk when I was 5 but that is going on in my future according to some alien moving far away in the universe.
 
  • #14
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So I seem to think that I spilled my milk when I was 5 but that is going on in my future according to some alien moving far away in the universe.
Not so. Everything that happened to you after you spilled your milk at age five is the future light cone of that milk-spilling event. Thus all observers including that fast-moving and far-away alien will agree that it is in your past. Equivalently, we could say that we can divide your life history into two segments: before you spilled the milk, and after you spilled the milk. Everything in the "before" segment is in the past of everything in the "after" segment, everything in the "after" segment is in the future of everything in the "before" segment, and all observers agree about this.

If you haven't already studied Einstein's thought experiment on the relativity of simultaneity (Google for "Einstein train simultaneity") do so. Note that neither lightning strike is in the past or future light cone of the other. If you try restructuring the experiment so that one flash is in the future light cone of the other you will find that both observers will agree about the relative ordering of the two lightning strikes.
 
  • #15
Mister T
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In einstein's relativity of simultaneity we talk about how events A,B, and C are simultaneous for one observer (lets call him O1).
These events could occur in a different order for different observers.

You spilling your milk at age 5 and you reading this message are two events with a relationship fundamentally unlike the relationship between A, B, and C. There is no frame of reference in which you spilling your milk at age 5 is simultaneous with you reading this message.
 
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  • #16
PeterDonis
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what confuses me is the future for one is the past for another.
The way to avoid this confusion is to recognize that, in SR, spacetime is divided into three regions, not two. You don't just have the future and the past. You have the future, the past, and the spacelike separated region, which is neither. Your future at a given event is your future light cone; your past at a given event is your past light cone. Events that are spacelike separated from you are in neither your past nor your future. That's why their ordering with respect to you can be arbitrary without making any difference to you.
 
  • #17
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You are understanding correctly.

A, B, and C cannot be causally related (none of them can cause any of the others), so their ordering is not important.
So, any spacelike events ordering can be rearanged?
Any timelike events cannot be rearranged?
I try to do that with Minkowski software, I can't rearrannge timelike but I can rearrange spacelike.
So it's a proof that spacelike events can be rearranged.
But is there a proof that timelike events CAN'T be rearranged? I mean it's mathematically impossible for any two timelike events:
A then B.?
Even if we see those events from anyframe, it can't be B then A?

Thanks.
 
  • #18
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The third region is everywhere else, ... the only region where the ordering is frame dependent is in the exterior where there can be no cause and effect relationship. Causes always preceed effects, and for the rest the order doesn't matter.
It's been answered. So from the original point. The third region is what we call spacelike?
 
  • #19
Orodruin
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The third region is what we call spacelike?
No, spacelike is a property of the separation. We call the region the "exterior of the light cone" or "elsewhere" (see previous posts in the thread).
 
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  • #20
Samy_A
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But is there a proof that timelike events CAN'T be rearranged? I mean it's mathematically impossible for any two timelike events:
A then B.?
Even if we see those events from anyframe, it can't be B then A?
Isn't that a direct consequence of the invariance of proper time?
 
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  • #21
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Isn't that a direct consequence of the invariance of proper time?
So there is really a rule that states "invariance of proper time". Okay...
 
  • #22
Samy_A
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So there is really a rule that states "invariance of proper time". Okay...
Invariant under Lorentz transformation, yes.

I'm not sure about the terminology: is that a "rule", or simply a property of the Lorentz transformation that proper time is an invariant?
 
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  • #23
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No, spacelike is a property of the separation. We call the region the "exterior of the light cone" or "elsewhere" (see previous posts in the thread).
Perhaps spacelike is the distance from the tip of the cone to any coordinates in the third region. I understand the concept, but can't express myself clearly. Thanks
Isn't that a direct consequence of the invariance of proper time?
So there really is the term "Invariance of proper time". I thought it was just a consquences, but it's explicitly stated. Okay, thanks.
 
  • #24
Mister T
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So, any spacelike events ordering can be rearanged?
Any timelike events cannot be rearranged?
We're talking about the interval between events, also called the separation of events. Not the events themselves.

I try to do that with Minkowski software, I can't rearrannge timelike but I can rearrange spacelike.
So it's a proof that spacelike events can be rearranged.
That would be a demonstration, not a proof.

But is there a proof that timelike events CAN'T be rearranged? I mean it's mathematically impossible for any two timelike events:
A then B.? Even if we see those events from any frame, it can't be B then A?
Depends on what you mean by "proof". Yes, it's a consequence of the two postulates, so in that sense it's a proof. In other words, if both postulates are valid, then the ordering of events with timelike separation is the same for all observers.
 
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  • #25
Ok guys so I think I am starting to understand this a little better. Heres one quick question. Lets say the apple and the orange about are dropped and hit the ground simultaneously in one frame. Now lets freeze time. In one frame they are on the ground at the same time at the second they have dropped. Another frame the apple is on the ground but the orange is still midair. Another frame the apple is on the ground, but the orange has been on the ground for sometime. Is this the case?
 
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