- #1
onestarburns
- 12
- 0
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.onestarburns said:this may be posted in the wrong place, but can sombody help me understand why time is relative? why should it not be absolute?
onestarburns said:this may be posted in the wrong place, but can sombody help me understand why time is relative? why should it not be absolute?
Well isn't this a bit to broad?Rach3 said: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.
MeJennifer said: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 is obvious that simultaneity exists in the universe because otherwise the universe could not have a causal structure.Rach3 said: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.
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 said:It is obvious that simultaneity exists in the universe because otherwise the universe could not have a causal structure.
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 said: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.
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.MeJennifer said:Feel free to explain why you think simultaneity involves only events with a spacelike separation. To me that simply does not make any sense.
MeJennifer said:Feel free to explain why you think simultaneity involves only events with a spacelike separation. To me that simply does not make any sense.
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!Rach3 said: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.
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.MeJennifer said: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!
MeJennifer said: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!
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.Rach3 said: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.
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.MeJennifer said: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.
Wait, isn't that the opposite of what you just said above?MeJennifer said:It seems to me that in curved space-time it is all but guaranteed that X happens before Y in all frames.
MeJennifer said: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.
Quite correct, and that is exactly my point!Even in curved spacetime, there is still an objective coordinate-independent truth about whether X lies in the past light cone of Y.
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.Wait, isn't that the opposite of what you just said above?
Well to me spacelike separated is outside the null cone, timelike separated is inside. So let me look at your arguments:I suspect you’re contradicting yourself by not staying clear on the difference between "spacelike separated" and "timelike separated".
Of course because they are timelike separated. No disagreement.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.
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.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 that is were we disagree, two different events in space-time cannot possibly be simultaneous.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 off course not, since they are spacelike separated. No disagreement.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.
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.But all other frames other then you and our snap partner’s will disagree about who snapped first and by how much.
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?MeJennifer said: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.
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."MeJennifer said: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!
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 said: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.
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.JesseM said: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 space time we have events right? So if two particles meet there they are synchronized right? I don't see the problem.JesseM said: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 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!JesseM said: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",
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.JesseM said: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?
It is not so much a matter of coordinate systems but a matter of the direction of the null cones.JesseM said: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.
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.MeJennifer said: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.
JesseM said: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".
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.MeJennifer said:Well in space time we have events right? So if two particles meet there they are synchronized right? I don't see the problem.
JesseM said:Look at this page for example, which defines simultaneity as "the notion of events occurring at the same time at different places"
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:MeJennifer said: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!
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.
True, but we are discussing special and general relativity here correct?JesseM said: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.
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 said:True, but we are discussing special and general relativity here correct?
There is, it is called an event!JesseM said: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.
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.MeJennifer said:There is, it is called an event!
Rach3 said:(or else x1=x2, also trivial)
Well it seems what is trivial for one is of great significance for an other.Rach3 said: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.
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.MeJennifer said: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.
MeJennifer said: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.
Yes, two colliding particles is simultaneity!JesseM said:Do you disagree with Rach3's statement here?
The whole concept of simultaneity for spacelike events is a rather mute point, pretty meaningless, since there is no causal relationship possible.JesseM said:"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.
Well, in my opinion, the whole idea of "clocks running slower" and "rods getting smaller" is really a misconception of what is happening.JesseM said: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.
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?MeJennifer said:Yes, two colliding particles is simultaneity!
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.MeJennifer said:The whole concept of simultaneity for spacelike events is a rather mute point, pretty meaningless, since there is no causal relationship possible.
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.MeJennifer said: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!
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.MeJennifer said: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.