Relativity of Simultaneity and Time

[Banksyboy88]

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 can't both be in the past of B can they?

Maybe I am not understanding this correctly.

 

[Orodruin]

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.

 

[Dale]

For O2 C is in the past of B, for O3 A is in the past of B. They can't 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.

 

[Orodruin]

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.

 

[Banksyboy88]

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?

 

[Dale]

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.

 

[Dale]

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.

 

[Orodruin]

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.

 

[Banksyboy88]

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?

 

[Orodruin]

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.

 

[Ibix]

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.

 

[Nugatory]

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.

 

[Banksyboy88]

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.

 

[Nugatory]

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.

 

[Mister T]

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.

 

[PeterDonis]

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.

 

[Stephanus]

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.

 

[Stephanus]

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?

 

[Orodruin]

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).

 

[Samy_A]

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?

 

[Stephanus]

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...

 

[Samy_A]

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?

 

[Stephanus]

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.

 

[Mister T]

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.

 

[Banksyboy88]

Ok guys so I think I am starting to understand this a little better. Heres one quick question. Let's say the apple and the orange about are dropped and hit the ground simultaneously in one frame. Now let's 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?

 

[Mister T]

Lets say the apple and the orange about are dropped and hit the ground simultaneously in one frame. Now let's freeze time.

Not sure what you mean by that last sentence. But in the previous sentence you are simply stating that two events are simultaneous in one frame of reference. This means the interval between them is spacelike. Therefore they can occur in a different order in different frames of reference.

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?

Yes. There are also frames of reference where the orange is on the ground at the same time the apple is still in midair.

But since the events have a spacelike separation it's impossible for observers on the apple to know whether or not the orange has yet landed, and vice-versa. In other words, the events are causally disconnected.

This is the reason why faster-than-light communication is unacceptable. Having it would mean an effect could precede its cause. No one can accept such a thing.

 

[Stephanus]

Ok guys so I think I am starting to understand this a little better. Heres one quick question. Let's say the apple and the orange about are dropped and hit the ground simultaneously in one frame. Now let's 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?

Yes, I think it's like that, but... it should be observed by an observer who moves relative to the planet.
Perhaps I can elaborate a little.
Supposed:
The distance between the apple tree and the orange tree is 300m.
The time difference between the apple dropped and the orange dropped must be less then 1 micro second in apple/orange frame.
Let's say the dropping of the apple we call it event A1 and the dropping of the orange is event O1.
Event A1 and O1 must be observed by an outside observer who travels at some significant speed to see that A1 happens BEFORE O1, and from another angle/frame it is A1 AFTER O1.
It can happen if apple and orange tree is 300m and less than 1 micro second.

 

[Stephanus]

That would be a demonstration, not a proof.

Sorry, it's a foolish statement. Yes it's the proof of the demonstration of the software not the universe itself. Perhaps I'm too occupied with this software that I forget perhaps it's not how the universe works. But that software helps me much in understanding SR, although very basic SR. . You're right

 

[Dale]

But is there a proof that timelike events CAN'T be rearranged?

Yes. I won't do the whole proof rigorously, but the key concept is that the set of all events for fixed $s^2=-t^2+x^2+y^2+z^2$ forms a hyperboloid of two sheets for $s^2<0$. So you cannot smoothly transform an event on the future sheet into an event on the past sheet, they are disconnected regions.

 

[pervect]

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).

So far I agree

For O2 C is in the past of B, for O3 A is in the past of B. They can't both be in the past of B can they?

Maybe I am not understanding this correctly.

I wouldn't put things the way you did, though I'd stop short of saying that it's wrong - it's just not entirely clear what you mean. Past, present, and future imply causality relationships, and in relativity casual relationships are represented by light cones. Every event has its own past and future, represented by a light cone - there is no universal "past" or universal "future".

So for your events A,B,C which are simultaneous according to some observer O1, all of the events have different light cones and no event is in either the past light cone or the future light cone of any other event.

But it's perfectly correct to note that in the coordinate system $O_1$, events A,B, and C all might have the same time coordinates. If we represent the time coordinate of event A in coordinate system $O_1$ by $t_1(A)$, then we could say $t_1(A)=t_1(B)=t_1(C)$. In some other coordinate system $O_2$, the events A, B, and C might have different time coordinates, such that $t_2(A) < t_2(B)<t_2(C)$. The coordinates have no direct physical significance, because they depend on the observer, but the light cones do have physical significance, they are observer independent and can be taken to represent the causal relationships between events.

 

[Grimble]

Let me take this idea of causality a step further and ask what you think about it. This is not trying to rewrite anything but merely posing an interesting(?) logical line of thought...

Let us take another event P when the Apple and Orange are picked up from a basket on a table and then taken to where they will be dropped.
In the light cone from this event the dropping and landing of the apples will be causally connected and lie in Event P's future light cone - however far apart those later events might be; even in different galaxies if need be. Or a similar previous event for A,B and C in that thought experiment - let us say that A,B and C are guns firing and the Event P in this case is the loading of the three guns (or rather the act of picking up the three bullets.

Now in addition to our non causally connected events we have larger light cones that do connect all our events. A,B and C or the dropping and landing of the fruit, are in the light cone of the appropriate events P.

This means that the invariant Spacetime Interval between P and each of the others, being invariant has an absolute value. And must be the same for every other frame of reference (FoR), whether that interval is space-like, time-like or light-like in that frame.

The spatial distance between the events will be the same for each FoR as spacetime is stationary as mapped in any FoR.

If those subsequent events are fixed in time relative to event P, how can they then be reordered in another FoR - relative to another observer.

To take this a step further, every event in Spacetime is in the light cone of the Big Bang and must therefore be causally connected to the Big Bang and therefore have invariant spacetime intervals relative to the big bang and therefore be fixed in time.

 

[PeterDonis]

every event in Spacetime is in the light cone of the Big Bang and must therefore be causally connected to the Big Bang and therefore have invariant spacetime intervals relative to the big bang

This is sort of true. The part you left out is that the invariant interval between the big bang and a particular event depends on which curve between the two you pick. There are an infinite number of possible timelike curves between the big bang and a given event, which can have different intervals between the two events.

(This is a special case of the more general point that the "interval" between two events depends on which curve between them you pick. You can't talk about "the" unique interval between two events; you have to specify which curve the interval is evaluated on. In SR this is often glossed over because inertial frames pick out a unique curve between any pair of events, and the "interval" is assumed to be the interval along that curve. But even in SR that's not always the curve you want to focus on.)

In cosmology, it is common to pick one particular timelike curve from the big bang to a given event, which is the one that is the worldline of a "comoving" observer--an observer who always sees the universe as homogeneous and isotropic. The interval along the "comoving" worldline from the big bang to a given event is indeed unique.

and therefore be fixed in time.

This is not true. What is true is that we can choose coordinates in such a way that the "time" coordinate assigned to each event is the same as the interval along some chosen worldline--the usual choice in cosmology is the "comoving" worldline. But that choice is for convenience; nothing in the physics requires it. When cosmologists talk about "time", they are (in almost all cases) implicitly using the definition of "time" as the interval along comoving worldlines. They talk about "time" without qualification not because that is the unique physical definition of "time", but because it's the most convenient one.

 

[Dale]

The spatial distance between the events will be the same for each FoR as spacetime is stationary as mapped in any FoR.

This is not true.

If those subsequent events are fixed in time relative to event P

They are not, your premise is false.

 

[Grimble]

(This is a special case of the more general point that the "interval" between two events depends on which curve between them you pick. You can't talk about "the" unique interval between two events; you have to specify which curve the interval is evaluated on. In SR this is often glossed over because inertial frames pick out a unique curve between any pair of events, and the "interval" is assumed to be the interval along that curve. But even in SR that's not always the curve you want to focus on.)

So are you saying that the invariant spacetime interval between two events is not invariant?

 

[Grimble]

This is not true.
.

OK, it is the Spacetime interval, not the Spatial interval Every Frame of Reference maps spacetime as at rest relative to that spacemap - as Minkowski stated:
"The substance existing at any world point can always be conceived to be at rest, if time and space are interpreted suitably."