Why is Time Relative? - Understand the Concept

[onestarburns]

this may be posted in the wrong place, but can sombody help me understand why time is relative? why should it not be absolute?

 

[Jimmy Snyder]

this may be posted in the wrong place, but can sombody help me understand why time is relative? why should it not be absolute?

The line of reasoning that ends with "time is relative", starts with the postulate that the speed of light is the same for all observers. This postulate was itself based on the failure of certain experiments that were supposed to measure differences in the speed of light between observers.

This behavior of light is different from that of a baseball thrown by someone on a moving train. The speed of the ball depends upon the situation of the observer. Someone on the train would give one speed for the ball, while someone on the ground watching the train go by would give a different speed.

Speed is the ratio of space to time. If space and time are absolute, then the speed of light must be relative, depending upon the speed of the observer. The speed of light is absolute and does not depend upon the speed of the observer, therefore, either space or time must be relative. A more detailed algebraic calculation will show that both must be relative.

 

[Farsight]

You need to look up Einstein, Special Relativity, and Michelson-Morley. These two guys measured the speed of light in different directions, expecting a difference due to the Earth's motion through space. They didn't find any. And since velocity is distance over time, if the velocity didn't change but the distance did, the time had to change as well.

 

[axawire]

For a detailed explanation do what farsight said. But as a quick thought experiment ignoring most of the aspects of Einstein’s theories. First we synchronize our wrist watches. Suppose you stand 100m away from someone with a flash light and as soon as you see the person turn on the flash light you record the time on your watch. I will stand 200m away and will record the time from my watch when I see the flash light turned on. Assuming we were super accurate with our fast reflexes etc… when we compare times we do not agree on when the flash light was turned on. This is because light had to travel twice as far to reach me as it did to reach you. So time is relative to the observer. But light is so fast in reality we don’t notice that in our everyday lives as well as the other bizarre stuff that Einstein’s special relativity predicts.

 

[Rach3]

Simultaneity does not exist. Two events may seem simultaneous in one inertial frame, and not simultaneous in other; in fact observers will not generally agree on the order of events, depending on their relative motions.

See, e.g. http://en.wikipedia.org/wiki/Relativity_of_simultaneity

Another feature of SR - observers will not agree on elapsed time intervals. For instance, a fast plane circling the earth, returning to its starting point, will experience a slightly shorter time interval than an observer who never moved from the starting point. This is a feature of the geometry of Minkowski spacetime; the longest interval between any two spacetime points is a straight line! Exactly the opposite of Euclidean geometry. The crucial point is: obsevers do not agree on elapsed time interval, because their measurement of elapsed time depends on what trajectory they took in the meanwhile.

 

[Gelsamel Epsilon]

this may be posted in the wrong place, but can sombody help me understand why time is relative? why should it not be absolute?

S = D / T

Speed and distance are both variable, and hence time is too :tongue2:

A cop out explination but an explination nonetheless.

 

[MeJennifer]

Simultaneity does not exist. Two events may seem simultaneous in one inertial frame, and not simultaneous in other; in fact observers will not generally agree on the order of events, depending on their relative motions.

Well isn't this a bit to broad?
It is true that observers may not agree on the order of events but that does not imply that simultaneity does not exist.
It really comes down to how you define it.

For instance would we say, length does not exist since observers may not agree on the length of something, or duration does not exist since observers may not agree on the duration of something?

 

[BoTemp]

Well isn't this a bit to broad?
It is true that observers may not agree on the order of events but that does not imply that simultaneity does not exist.
It really comes down to how you define it.

It does come down to how you define it. What they meant was that universal simultaneity does not exist. Two events which are simulataneous in one frame will not, in general, be simultaneous in all frames. Simultaneity is subjective.

Time is relative because the speed of light is constant. If one works out the consequences of the speed of light being measured the same in any frame, no matter the velocity, one finds that time and length must contract, and mass must increase. In fact, Einstein only postulated that the speed of light was independent of the speed of the emitter, but the constancy of the speed of light in any reference frame directly follows from that. Certain things in the universe are relative, and certain constant. It would be more intuitive for time to be constant, but it just isn't the case.

Michelson & Morley is the most famous experiment which backs up relativity. I believe there was an astronomer which determined observationally that the speed of light as measured on Earth is independent of the speed of the emitter, but I haven't been able to find anything more specific.

 

[Rach3]

I meant simultaneity in the usual sense - for two events (t1, x1), (t2, x2), there is no consistent statement of the form "t1 = t2" except in the trivial case in which it holds in only one Lorentz frame (or else x1=x2, also trivial).

The point of "does simultaneity 'exist'" seems entirely semantic to me. It is not uniquely defined, and has no usefullness, so in my narrow, pragmatist worldview I'm not concerned.

 

[MeJennifer]

I meant simultaneity in the usual sense - for two events (t1, x1), (t2, x2), there is no consistent statement of the form "t1 = t2" except in the trivial case in which it holds in only one Lorentz frame (or else x1=x2, also trivial).

The point of "does simultaneity 'exist'" seems entirely semantic to me. It is not uniquely defined, and has no usefulness, so in my narrow, pragmatist worldview I'm not concerned.

It is obvious that simultaneity exists in the universe because otherwise the universe could not have a causal structure.

 

[JesseM]

It is obvious that simultaneity exists in the universe because otherwise the universe could not have a causal structure.

There is still a single objective truth about whether one event lies in a second event's past light cone, that should be enough to give the universe an objective "causal structure", I don't see why simultaneity (which involves events with a spacelike separation that cannot possible affect one another) is relevant to this.

 

[MeJennifer]

There is still a single objective truth about whether one event lies in a second event's past light cone, that should be enough to give the universe an objective "causal structure", I don't see why simultaneity (which involves events with a spacelike separation that cannot possible affect one another) is relevant to this.

Feel free to explain why you think simultaneity involves only events with a spacelike separation. To me that simply does not make any sense.

 

[JesseM]

Feel free to explain why you think simultaneity involves only events with a spacelike separation. To me that simply does not make any sense.

Because there is no inertial reference frame where two events with a timelike or lightlike separation happen at the same time-coordinate, whereas for any pair of events with a spacelike separation, there is always an inertial frame where they are simultaneous.

 

[Rach3]

Feel free to explain why you think simultaneity involves only events with a spacelike separation. To me that simply does not make any sense.

Huh? Simultaneous MEANS "at same time". Timelike-seperated events occur at DIFFERENT time coordinates, in all frames. SR has a causal structure - things are either in the past lightcone, or the future lightcone, or causally seperated. Simultaneity has nothing to do with this.

 

[MeJennifer]

Timelike-seperated events occur at DIFFERENT time coordinates, in all frames. SR has a causal structure - things are either in the past lightcone, or the future lightcone, or causally seperated. Simultaneity has nothing to do with this.

Two space-time events X and Y can be timelike separated and many worldlines can travel between it, which means that they are arriving at Y simultaneously. What their individual proper times indicate is really irrelevant!

 

[JesseM]

Two space-time events X and Y can be timelike separated and many worldlines can travel between it, which means that they are arriving at Y simultaneously. What their individual proper times indicate is really irrelevant!

Perhaps this is just a terminological issue, but that's not what physicists are talking about when they use the word "simultaneity". They are only talking about whether the two different events have the same time-coordinate in a given reference frame, the question of a signal going from one event to the other doesn't enter into it. Obviously if two signals converge at the same point in space and time they do so simultaneously (in all reference frames), but then the two events that you're saying happened simultaneously both occurred at Y (meaning there is no separation between them, timelike or spacelike), you aren't even talking about the event X of either signal being emitted.

 

[Rach3]

Two space-time events X and Y can be timelike separated and many worldlines can travel between it, which means that they are arriving at Y simultaneously. What their individual proper times indicate is really irrelevant!

Worldlines have nothing to do with this! X and Y are not simultaneous; one happened before the other, and that is consistent in all frames. That is what "timelike seperated" means.

'they are arriving at Y simultaneously"
Yes, the event Y is simultaneous with itself. That's all that means.

 

[MeJennifer]

Worldlines have nothing to do with this! X and Y are not simultaneous; one happened before the other, and that is consistent in all frames. That is what "timelike seperated" means.

I don't think it is true that X has happened before Y in all frames. In flat space-time yes, but not in curved space-time.
It seems to me that in curved space-time it is all but guaranteed that X happens before Y in all frames.

 

[JesseM]

I don't think it is true that X has happened before Y in all frames. In flat space-time yes, but not in curved space-time.

Even in curved spacetime, there is still an objective coordinate-independent truth about whether X lies in the past light cone of Y. Still, perhaps you could design a weird coordinate system where X and Y happen at the same time-coordinate, I'm not sure what the limits on allowable coordinate systems are for GR.

It seems to me that in curved space-time it is all but guaranteed that X happens before Y in all frames.

Wait, isn't that the opposite of what you just said above?

 

[RandallB]

Posted by Rach3
Worldlines have nothing to do with this! X and Y are not simultaneous; one happened before the other, and that is consistent in all frames. That is what "timelike seperated" means.

I don't think it is true that X has happened before Y in all frames. In flat space-time yes, but not in curved space-time.
It seems to me that in curved space-time it is all but guaranteed that X happens before Y in all frames.

I suspect you’re contradicting yourself by not staying clear on the difference between "spacelike separated" and "timelike separated".
To make what Rach has said clearer, remember if X and Y are only "timelike separated" then there exists a reference frame moving fast enough that X and Y will occur at the same PLACE in that frame. Note that frame also sees the time between X and Y to be the largest - all other frames will see shorter time intervals but always in the same order. As he said if they are "timelike separated" they cannot be simultaneous in any valid reference frame.

But if X and Y are “spacelike separated” there is no reference frame where X and Y are measured as being in the same place, but they can be simultaneous. Example you and a friend snap fingers simultaneously across a room – not even a reference frame moving at the speed of light from your fingers to their fingers can put them those events at the same place.
But all other frames other then you and our snap partner’s will disagree about who snapped first and by how much.

RB

 

[MeJennifer]

Even in curved spacetime, there is still an objective coordinate-independent truth about whether X lies in the past light cone of Y.

Quite correct, and that is exactly my point!
The observations from an observer perspective (e.g. frames of reference) are Lorentz transformed, always. So what for observer A is simultaneous is not necessarily so for observer B.

If we consider space-time event X and several particles approaching it is only those who will reach that event that we can talk about an interaction, or simultaneity. Think about it what else is simultaneity than two or things happening at the same space-time event!

Wait, isn't that the opposite of what you just said above?

No, the argument was made that X happens before Y in all frames of reference. I wrote I disagreed with that. It would be nice if someone could demonstrate it is impossible! But anyway it seems completely irrelevant.

I suspect you’re contradicting yourself by not staying clear on the difference between "spacelike separated" and "timelike separated".

Well to me spacelike separated is outside the null cone, timelike separated is inside. So let me look at your arguments:

To make what Rach has said clearer, remember if X and Y are only "timelike separated" then there exists a reference frame moving fast enough that X and Y will occur at the same PLACE in that frame.

Of course because they are timelike separated. No disagreement.

Note that frame also sees the time between X and Y to be the largest - all other frames will see shorter time intervals but always in the same order. As he said if they are "timelike separated" they cannot be simultaneous in any valid reference frame.

Well in flat space-time no disagreements. I am not convinced at all for curved space-time. Feel free to demonstrate that it is impossible for curved space-time.

But if X and Y are “spacelike separated” there is no reference frame where X and Y are measured as being in the same place, but they can be simultaneous.

Well that is were we disagree, two different events in space-time cannot possibly be simultaneous.

Example you and a friend snap fingers simultaneously across a room – not even a reference frame moving at the speed of light from your fingers to their fingers can put them those events at the same place.

Well off course not, since they are spacelike separated. No disagreement.

But all other frames other then you and our snap partner’s will disagree about who snapped first and by how much.

The only thing that the other frames can assert is when they got a signal from both events. Their statement on who snapped first is completely dependent on their location and direction in space-time.

 

[JesseM]

Quite correct, and that is exactly my point!
The observations from an observer perspective (e.g. frames of reference) are Lorentz transformed, always. So what for observer A is simultaneous is not necessarily so for observer B.

Agreed. But since you brought up the issue of curved spacetime, would you agree that it only makes sense to talk about "frames of reference" which are Lorentz transformations of one another in flat spacetime, or in local neighborhoods of curved spacetime?

If we consider space-time event X and several particles approaching it is only those who will reach that event that we can talk about an interaction, or simultaneity. Think about it what else is simultaneity than two or things happening at the same space-time event!

Again, this is not what physicists mean by the word "simultaneity", they don't use it as a synonym for "interaction", they just use it to mean "at the same time-coordinate". Look at http://casa.colorado.edu/~ajsh/sr/simultaneous.html for example, which defines simultaneity as "the notion of events ocurring at the same time at different places", or the wikipedia page on the relativity of simultaneity which says "Relativity of simultaneity means that events that are considered to be simultaneous in one reference frame are not simultaneous in another reference frame moving with respect to the first."

No, the argument was made that X happens before Y in all frames of reference. I wrote I disagreed with that. It would be nice if someone could demonstrate it is impossible! But anyway it seems completely irrelevant.

In special relativity, it's certainly true that if X happens in the past light cone of Y in one inertial frame, then X will have a smaller time-coordinate than Y in any inertial frame obtained by a Lorentz transform on the first--are you disagreeing with this? In GR there are very few restrictions on what types of coordinate systems you can use, so I'm not sure whether or not you could use a coordinate system where X happened at a time coordinate greater than or equal to Y's time coordinate if X was in Y's past light cone.

 

[MeJennifer]

But since you brought up the issue of curved spacetime, would you agree that it only makes sense to talk about "frames of reference" which are Lorentz transformations of one another in flat spacetime, or in local neighborhoods of curved spacetime?

Well in general relativity there are two aspects. First there is the curvature and then there is the Lorentz transformation. But curvature or not, one always need the Lorentz transformation to compare from one frame to another.

Again, this is not what physicists mean by the word "simultaneity", they don't use it as a synonym for "interaction", they just use it to mean "at the same time-coordinate".

Well in space time we have events right? So if two particles meet there they are synchronized right? I don't see the problem.

Look at http://casa.colorado.edu/~ajsh/sr/simultaneous.html for example, which defines simultaneity as "the notion of events occurring at the same time at different places",

Well I understand what they mean but that is certainly not a property of space-time. In fact you cannot observe two spacetime separated events at the same time. In fact you can't observe either one of them!

One can only derive that the event happened by examining light or sub lightspeed information that arrived at your location. Furthermore one can not actually know the distance of the event unless one has full information about the curvature at the event and the curvature of the complete worldline of the signal coming to you.

An example is the examination of far away objects in the universe. We can make educated guesses about their distances, using things like material composition and redshift but it cannot be exact.

In special relativity, it's certainly true that if X happens in the past light cone of Y in one inertial frame, then X will have a smaller time-coordinate than Y in any inertial frame obtained by a Lorentz transform on the first--are you disagreeing with this?

Not at all, in fact I would go one step further, the frame does not have to be inertial at all, accelerated frames apply as well.

In GR there are very few restrictions on what types of coordinate systems you can use, so I'm not sure whether or not you could use a coordinate system where X happened at a time coordinate greater than or equal to Y's time coordinate if X was in Y's past light cone.

It is not so much a matter of coordinate systems but a matter of the direction of the null cones.

 

[JesseM]

Well in general relativity there are two aspects. First there is the curvature and then there is the Lorentz transformation. But curvature or not, one always need the Lorentz transformation to compare from one frame to another.

I don't know too much about general relativity, but I was under the impression that diffeomorphism invariance meant you were allowed to use pretty much any coordinate system you like (maybe with the exception of badly-behaved ones that assign the same event multiple coordinates or things along those lines), which would presumably include coordinate systems that are not related to each other by a Lorentz transformation.

Again, this is not what physicists mean by the word "simultaneity", they don't use it as a synonym for "interaction", they just use it to mean "at the same time-coordinate".

Well in space time we have events right? So if two particles meet there they are synchronized right? I don't see the problem.

This seems like a non sequitur to me. "Simultaneity" as defined by physicists deals with the question of whether multiple events happen at the same time-coordinate, period. The meeting of particles is a single event, not multiple events...I suppose you could consider it to be two events which happen at the same point in spacetime, but the important thing is that simultaneity does not exclusively deal with the trivial case of two events at the same point in spacetime, physicists usually talk about simultaneity in the context of two events at different points in spacetime with a spacelike separation.

Also, what does it mean to say two particles are "synchronized"? Usually it's only clocks that are said to be "synchronized" in a given frame, which means that at any given time-coordinate in that frame both clocks read the same time...again, you seem to be using physics terminology in a nonstandard way here.

Look at this page for example, which defines simultaneity as "the notion of events occurring at the same time at different places"

Well I understand what they mean but that is certainly not a property of space-time. In fact you cannot observe two spacetime separated events at the same time. In fact you can't observe either one of them!

The point is that "simultaneity" as the word is defined by physicists doesn't deal with objective properties of spacetime, it is a completely coordinate-dependent notion, like velocity. Also, in SR "observe" usually means how you reconstruct events to have happened in your inertial reference frame rather than what you actually see at a given moment with light signals--for example, if I see the light from an event 10 light years away in 2006, and the light from another event 20 light years away in 2016, I obviously did not see the events at the same time but physicists would often say I "observed" them to happen at the same time. For example, see jtbell's post on this thread where he says:

In relativity, you have to distinguish between what the twins see which is affected by the time it takes light or radio/TV signals to travel between them, and what they observe, i.e. what they infer is actually happening to the other twin after correcting for the signal-propagation time.

 

[MeJennifer]

I agree, but the point is that "simultaneity" as the word is defined by physicists doesn't deal with objective properties of spacetime, it is a completely coordinate-dependent notion, like velocity.

True, but we are discussing special and general relativity here correct?

 

[JesseM]

True, but we are discussing special and general relativity here correct?

Yes, and simultaneity is a coordinate-dependent concept which is introduced in the context of inertial reference frames in special relativity. There is no objective, coordinate-independent notion of "simultaneity", just like there is no objective, coordinate-independent notion of "velocity", but both concepts are useful in SR.

 

[MeJennifer]

There is no objective, coordinate-independent notion of "simultaneity", just like there is no objective, coordinate-independent notion of "velocity", but both concepts are useful in SR.

There is, it is called an event!

 

[JesseM]

There is, it is called an event!

No, again, you're misusing the terminology here. Physicists do not treat the word "simultaneity" as being synonymous with "event" or "interaction" or any other such coordinate-independent aspect of relativity. To physicists, "simultaneity" has only one meaning: two or more distinct events with the same time-coordinate in a given coordinate system.

edit: I guess I should add that it would be correct to say a single event is simultaneous with itself, but as Rach3 says this is just a trivial case of the general definition.

 

[Rach3]

An event is simultaneous with itself! How many worldlines or particles that event involves is irrelevant - an 'event' is merely a fixed location in spacetime - a specification of location, and time (in SR). It certainly occurs at the same time as itself, in all frames, that is a tautology. There is no other simultaneity except this trivial one.

Incidentally, I explicitly mentioned this trivial case in post #9:

(or else x1=x2, also trivial)

 

[MeJennifer]

An event is simultaneous with itself! How many worldlines or particles that event involves is irrelevant - an 'event' is merely a fixed location in spacetime - a specification of location, and time (in SR). It certainly occurs at the same time as itself, in all frames, that is a tautology. There is no other simultaneity except this trivial one.

Well it seems what is trivial for one is of great significance for an other.

In fact all particle interactions are nothing more than a crossing of wordlines, in other words, events.

Remember Rach3 this discussion was triggered by your statement that:

Simultaneity does not exist. Two events may seem simultaneous in one inertial frame, and not simultaneous in other; in fact observers will not generally agree on the order of events, depending on their relative motions.

 

[JesseM]

Remember Rach3 this discussion was triggered by your statement that:

Simultaneity does not exist. Two events may seem simultaneous in one inertial frame, and not simultaneous in other; in fact observers will not generally agree on the order of events, depending on their relative motions.

Do you disagree with Rach3's statement here? It's true that in the special case of two events at the same point in spacetime, all frames will agree that they are simultaneous, but Rach3 said that "Two events may seem simultaneous in one inertial frame, and not simultaneous in other" and "observers will not generally agree on the order of events". Both these statements would be true if you pick any two events that do not occur at the same point in spacetime, so as general statements they are correct, even if there is a special case where all frames agree on simultaneity.

Analogously, if I said "a clock that is running slower than another clock in one inertial frame may be running faster in another inertial frame", or "observers will not generally agree on which of two clocks is running slower", these statements would be correct as well, even though in the special case where the two clocks are at rest with respect to each other, all inertial frames would say they both tick at the same rate.

 

[Rach3]

Well it seems what is trivial for one is of great significance for an other.

It is trivial! It's a logical tautology! An event is simultaneous with itself, because it is itself, what is so amazing about this?

In fact all particle interactions are nothing more than a crossing of wordlines, in other words, events.

How do you think this is relevant to simultaneity of two events?

 

[MeJennifer]

Do you disagree with Rach3's statement here?

Yes, two colliding particles is simultaneity!

If you and I meet at the same time and at the same Starbucks for a coffee tomorrow then we have simultaneity. We are both at the same time and at the same place.

"Two events may seem simultaneous in one inertial frame, and not simultaneous in other" and "observers will not generally agree on the order of events". Both these statements would be true if you pick any two events that do not occur at the same point in spacetime, so as general statements they are correct, even if there is a special case where all frames agree on simultaneity.

The whole concept of simultaneity for spacelike events is a rather mute point, pretty meaningless, since there is no causal relationship possible.

So what that the spacelike "3D plane of simultaneity" or the "tilt of space" for a wordline is different from frame to frame? That's why it is called relativity.

Analogously, if I said "a clock that is running slower than another clock in one inertial frame may be running faster in another inertial frame", or "observers will not generally agree on which of two clocks is running slower", these statements would be correct as well, even though in the special case where the two clocks are at rest with respect to each other, all inertial frames would say they both tick at the same rate.

Well, in my opinion, the whole idea of "clocks running slower" and "rods getting smaller" is really a misconception of what is happening.
Clocks and rods don't change just because someone else measures them from another frame!

For object A and B in relative and constant motion with each other, nothing factually happens whatsoever with their clocks and rods, nothing! It is simply due to the fact that they are in relative motion with each other which causes them to travel through a tilted space.
For an accelerated frame versus an inertial frame it is the case that the object in the accelerated frame acquires less time than the object in the inertial frame.

 

[JesseM]

Yes, two colliding particles is simultaneity!

It is a single event, which like all single events is simultaneous with itself. But two separate events with a spacelike separation that have the same time-coordinate in a given frame is also an example of simultaneity, and it is this sort of example, not a single-event example, that you will invariably find in any physics textbook which discusses the issue of simultaneity--do you disagree?

The whole concept of simultaneity for spacelike events is a rather mute point, pretty meaningless, since there is no causal relationship possible.

But this is what physicists mean when they use the word simultaneity! You can't just make up your own definitions of words that have an accepted meaning in physics! If you think the concept is pointless, that's your opinion, but the fact is that that's what the word is understood to mean. If you want to invent a new term to deal exclusively with events that happen at a single point in spacetime, then go right ahead, but don't call it "simultaneity", that term is already taken.

Well, in my opinion, the whole idea of "clocks running slower" and "rods getting smaller" is really a misconception of what is happening.
Clocks and rods don't change just because someone else measures them from another frame!

Of course not, but the phrase "clocks running slower" does not imply they do. All it means is that the number of clock-ticks per coordinate time is smaller for a clock with a higher velocity in that coordinate system. It's a coordinate-dependent concept, just like velocity itself.

Do you have a problem with any discussion of coordinate-dependent concepts? Would you also reject the statement "the speed of light is the same for all observers", for example, since speed itself is a completely coordinate-dependent notion?

 

[Rach3]

It is really frustrating that you persist in using your own, non-standard terminology to the confusion of everyone else including yourself.

Yes, two colliding particles is simultaneity!

If you and I meet at the same time and at the same Starbucks for a coffee tomorrow then we have simultaneity. We are both at the same time and at the same place.

No, you're several meters apart over a very extended time interval measured in minutes or hours. You're trying to force colloquial usage of words over their exact, well-defined physics usage.