Age Relative? Time, Speed and Paradox Explored

[russ_watters]

Russ:
I like your addition to my flat-earth analogy. You have told the same story that everyone was saying back in the Middle Ages.

I knew when I posted it that you wouldn't understand it, but I posted it anyway to illustrate a point. The piece you are missing is the evidence. In my hypothetical example there really was evidence that the world is flat. In the real world, there isn't - but there is evidence for SR. That is why your analogy (and your analysis) fails. You don't see or refuse to accept this.

 

[jcsd]

Russ:
I like your addition to my flat-earth analogy. You have told the same story that everyone was saying back in the Middle Ages. Just as it turned out then the Earth was not flat and today the theory of SR is not the end of the story. All the observations that prove SR also apply to my GST-07 drawing. I have asked before, where is the GST space-time wrong with respect to observation or experiment.

Just as the laws of Newton still apply so also does SR. SR is just a part of the whole picture. It is the view of the egocentric observer just like the farmer of the Middle Ages. The farmer at that time could prove to you by thousands of measurements that the sun went around the earth.

R.G.

Out of interest the idea that people in the middle ages thought the Earth was flat (some may of, but an eductaed person would not of thought this) is a 19th century myth.

 

[robphy]

Sorry for jumping in late. But I don't understand GST-07. Although it claims a resemblance to http://physics.syr.edu/courses/modules/LIGHTCONE/LightClock/ , GST-07 has some errors (as Fredrik points out)... the most serious is the absence of length contraction along the x-direction. Without length contraction, event K is not the intersection of the reflected rays from J and from H (assuming the constancy of the speed of light). In addition, GH should be congruent to HK... which means that the center of the second cyan ellipse should be halfway between G and K.

Additionally, it's not clear to me what 4Newton's position is and how GST-07 tries to support it.

 

[Fredrik]

Most of the solutions of Einsteins equation are not as easy to visualize as Minkowski space. Fortunately, there is one solution with a "big bang" that is easy to draw. Remember that in a spacetime diagram that represents Minkowski space, horizontal lines represent space at different times, and their vertical position indicates what time that is. Later times are drawn above earlier times. In a spacetime diagram that represents a homogenous and isotropic universe with positive constant curvature, "space at different times" are drawn as circles with different radii. (If you would like to visualize two spatial dimensions, replace the circles with spheres). In this spacetime diagram, increasing time is not "up". It's "outward".

4Newton, I had not yet looked at your drawing GST-8 when I wrote this. The drawing is exactly what I'm talking about, except that the light cones are drawn wrong. The world lines of light rays should not be drawn as straight lines here. They should be drawn as curves that make a 45 degree with every straight line through the big bang (lines like CA and CB) that it crosses. In other words, the light cones should be somewhat V-shaped, but the top of the V should be bent outward.

If you understand that the blue circle represents space at a certain time, and that A and B are the same two points in space as A' and B', then you should already know that the big bang didn't happen at some point in space. What point would that be? What point on the blue circle would represent the position where the big bang happened?

 

[Fredrik]

Object A takes the path C-A’-A and object B has the path of C-B’-B. At any time a light pulse may be sent from either object to the other. This is shown by light lines A’ to B and B’ to A. The length of each light path must be equal. Therefore from the point of any simultaneous events on either objects the light must arrive at the same time on the other object. The start of the simultaneous event may be all the way back to the BB. The point of the BB must be simultaneous for all events in the universe. By this method it is shown that at all times all events in the universe are simultaneous and that all objects in the universe have the same normal, or proper time.

This is an interesting argument, but is it correct? Let's find out.

"Object A takes the path C-A’-A and object B has the path of C-B’-B"

You should have explained what this drawing represents before you started talking about the path of objects. I will do it for you. We started out by attempting to find solutions of Einstein's equation that describe spacetimes that can be "sliced" into one-parameter families of spacelike hypersurfaces that are homogeneous and isotropic. The drawing is a spacetime diagram that represents one such solution. In this particular solution, the spacelike hypersurfaces are 3-spheres.

The easiest way to construct a coordinate system on a spacetime that is a one-parameter family of 3-spheres is to take the parameter that labels the 3-spheres to be the 0th coordinate (i.e. the "time" coordinate) and use a coordinate system that's appropriate for a 3-sphere to define the other three coordinates. (This is not the only way however).

With this choice of coordinates, any two points on the same 3-sphere (from this one-parameter set of 3-spheres) are simultaneous in the sense that they have the same time coordinate.

We can think of these 3-spheres as "space" at a different times, but it's important to realize that this "time" is just a parameter that labels the different 3-spheres. We can't just assume that e.g. A and B are simultaneous in any kind of "absolute" way. We can however be certain that any two clocks that are stationary in this frame will tick at the same rate. This is obvious because of the symmetries we have imposed on these solutions (homogeneity and isotropy). Because of this, it is natural to choose the value of the time parameter to be the time displayed by a clock (any clock) that's stationary in this frame.

"At any time a light pulse may be sent from either object to the other. This is shown by light lines A’ to B and B’ to A."

There are two things you could mean by "at any time":

1. At any value of the parameter that labels the 3-spheres (i.e. "on anyone of the 3-spheres")
2. At any "real" time, where you have assumed that the parameter represents some kind of "real" time

The second alternative is pretty much what you're trying to prove, so you wouldn't want that to be one of your assumptions, would you? You probably meant 2, but I'm going to try to find a way to make sense of your proof, so I'll pretend that I believe that you meant 1.

The light lines are drawn incorrectly. See my earlier post about this.

"The length of each light path must be equal."

OK. (You should have explained why, but since I already know why, it doesn't really matter to me).

"Therefore from the point of any simultaneous events on either objects the light must arrive at the same time on the other object."

Do you think anyone understands what you're trying to say here? I have no idea what "from the point of any simultaneous events on either objects" is supposed to mean. You're not making sense.

"The start of the simultaneous event may be all the way back to the BB. The point of the BB must be simultaneous for all events in the universe."

You're still not really making sense. When you say stuff like "simultaneous for all events ..." it really sounds like you have absolutely no idea what you're talking about.

"By this method it is shown that at all times all events in the universe are simultaneous and that all objects in the universe have the same normal, or proper time."

This is a bizarre claim. "By this method it is shown..." No, it isn't.

It's hard to tell what you're thinking, but I can make a guess, based on what I've read here, and in your previous posts. This is what I believe you're trying to say:

"If the big bang happened N seconds ago to the observer at A whose world line is GA'A, it must also have happened N seconds ago to the observer at B whose world line is GB'B. Since A and B are just two arbitrary points in space, this means that every stationary observer at a point on the same 3-sphere (i.e. on the blue circle) will agree that the big bang happened N seconds ago. This proves that all points in space are simultaneous, in an absolute sense, and that anyone who says that it makes just as much sense to think of two events that are not on the same 3-sphere as simultaneous is just wrong".

The last sentence is OK until the first comma, but not after that. I would agree that it makes sense to think of two points on the same 3-sphere as simultaneous, but this is not a very profound statement. It's kind of like saying that "bald guys have no hair".

There is nothing in your analysis that justifies the conclusion that simultaneity is absolute.

 

[4newton]

Fredrik and all:
My little story is only to illustrate that we are all affected by preconditioned ideas as we come together here. Russ I am sorry. I could not help myself when I turned your thought around a little. It’s a weakness I have.

I have never said that SR is wrong just as you cannot say that Newton’s laws are wrong. Both are right in within their context. They are not, however the total stories. Einstein did not have any knowledge of the BB and could see no relationship beyond the observer. His total theory is the relationship of observer to observer. His one great exception was the speed of light. He recognized the speed of light as a constant and invariant, or absolute, for all observers.

We seem to have a problem with the idea of dimensions. I thought it is recognized by all that there is a time dimension and a spatial dimension. It may be necessary to go into more detail on the nature of dimensions.

The idea of time distance is simply the conversion of time into the same units as the spatial dimension by multiplying time (in seconds) by the speed of light (meters per second) with the result of time distance in meters. ( ct ) I thought you were familiar with this concept.

You are starting to see my point. How do we know what real space-time is? At this time Minkowski space-time looks like a better starting point than SR, in light of the BB and a dynamic universe. It is important not to take a dogmatic approach in favor of any theory but to examine the theories point by point in view of observation and experiment. Just as with Einstein and SR the pieces are all there it how you put them together that makes the difference.

I will skip your thoughts on GST-07 at this time in light of your comments on GST-08.

You are correct on the drawing not representing the true light path. I did not want to complicate the drawing and be misunderstood. It was not important to understanding the concept I am trying to convey. It is also difficult to draw. If you understand that concept you must also understand that all objects including light in transition must transition outward from the BB together independent from any spatial transition. As the curve you describe indicates. You now need to ask the question. What is the difference between the outward transition from the BB and our transition in the time dimension? If every hypersurface is a segment of time then the transition outward from the BB must be the time dimension.

The BB is not just a point in space. You have two choices. The universes started at some point in an absolute frame of all dimensions or all the dimensions of the universe are the result of the BB. There is no way to tell the difference at this time. In either case all actions, of the smallest and shortest possible, occur at the same time at the point of the BB. All objects, including radiation… transition outward in the expansion direction. From you thoughts before you seem to think that is the time dimension and I agree with you. As you agreed before all actions that are simultaneous on any hypershpere will remain simultaneous on all hypershere’s.

 

[4newton]

Alkatran:

Well of course if you pick two objects which have the same speed they're going to agree about the amount of time passed!

Consider this:
Let's say, hypothetically, that the moon and Earth agree on how much time since the big bang. The moon is moving relative to the earth, and accelerating around us, so it's proper time != Earth proper time. That means a moment later, they WILL NOT AGREE on how much time since the big bang!

Ok, let's say the center of the 3d sphere is the center. How does that mean ANYTHING to the 2d people restricted to the surface area of the balloon? There's no point in their 2d space which is the center of the sphere, so THERE IS NO CENTER IN THEIR SPACE. Just as THERE IS NO CENTER IN OUR SPACE (according to the big bang theory).

The point is that all objects in the universe are in transition outward from the BB. That is the basic idea of the expansion of the universe, this is verified by observation, red shift…

The transition outward from the BB is not a spatial dimension. Also verified by the same above observation. It is also agreed by most that all clocks that transition without any spatial motion will tick at the same rate and will accumulate the same total time. All clocks on every hypersphere as illustrated by the blue line in GST-08 will tell the same time from the BB. This expansion transition is also a convenient candidate for what we recognize as the time dimension. The same behavior of clocks is observed when no spatial transitions are taking place and only time is passing even when the clocks are separated in space.
Clocks only change rate and accumulation of time when they are in transition in the spatial dimension.

 

[4newton]

Robphy:

Sorry for jumping in late. But I don't understand GST-07. Although it claims a resemblance to http://physics.syr.edu/courses/modu...ONE/LightClock/ , GST-07 has some errors (as Fredrik points out)... the most serious is the absence of length contraction along the x-direction. Without length contraction, event K is not the intersection of the reflected rays from J and from H (assuming the constancy of the speed of light). In addition, GH should be congruent to HK... which means that the center of the second cyan ellipse should be halfway between G and K.

Additionally, it's not clear to me what 4Newton's position is and how GST-07 tries to support it.

The whole thread is about simultaneous events in space-time. The discussion revolves around the idea of simultaneity being relative to the observer or referenced to a universal event.

My drawing is not correct. Just my poor 3d drawing technique. The website is correct.
The drawing is to show that the one way time to reflection is different dependent on direction of transition.

If you add contraction in the x direction only then the light pulse will not arrive back at the same point that the light does from the path in the y direction. See the MM experiment. If you contract the entire ring then you will not have a clock difference when you bring the moving clock back to the static clock. (The twin paradox)

Please feel free to give your opinion on the concept of simultaneity.

R.G.

 

[Fredrik]

I have never said that SR is wrong

Yes you have. You claim that there are paradoxes in SR, which would be a much more serious problem than a mere disagreement with experiment. You also claim that only one of the infinitely many ways to split spacetime into space and time is correct, but it's obvious from the mathematics of SR (and GR) that it isn't so.

Einstein did not have any knowledge of the BB

Wrong. Of course he did. The big bang theory is based on solutions of Einstein's equation that were found a long time ago, in the 1920's I think.

At this time Minkowski space-time looks like a better starting point than SR, in light of the BB and a dynamic universe.

SR is the theory of Minkowski space, and nothing more, so you're really saying that SR looks like a better starting point than SR, which is a pretty strange thing to say.

There is no big bang in Minkowski space.

I will skip your thoughts on GST-07 at this time in light of your comments on GST-08.

In other words, you will ignore the fact that your GST-07 is incorrect and (more importantly) pointless, and proceed as if it wasn't.

If every hypersurface is a segment of time then the transition outward from the BB must be the time dimension.

Yes, but these spheres are not the only spacelike hypersurfaces that can be called "a segment of time". Any spacelike hypersurface will do. This means that there are many ways to split spacetime into space and time, just as in SR.

I really think that you should focus on SR (i.e. Minkowski space) instead of GR. You will not understand stuff like simultaneity in GR until you understand it in SR.

 

[4newton]

Yes you have. You claim that there are paradoxes in SR, which would be a much more serious problem than a mere disagreement with experiment. You also claim that only one of the infinitely many ways to split spacetime into space and time is correct, but it's obvious from the mathematics of SR (and GR) that it isn't so.

You seem to be unable to grasp the concept that a theory may be valid within defined limits and totally wrong outside of those limits. If SR or GR were correct in all cases Einstein would not have failed to find unification. SR is a fine little theory and describes very well what an observer will see in most cases. It has the same problem that all egocentric views have, they are always wrong on the large scale. The bad result of theories like SR is they become accepted in dogmatic way and close off the thought process to the larger view. You have accepted SR as a religion and are willing to distort the real world in favor of your belief.

It should be obvious even to you that if SR and GR are able to produce an infinite number of space-times that are different when only one is required to explain all things there must be something wrong with the theories of SR and GR on the large scale.

Wrong. Of course he did. The big bang theory is based on solutions of Einstein's equation that were found a long time ago, in the 1920's I think.

To what equation are you referring? Do you remember something about a static universe and a correction factor?

SR is the theory of Minkowski space, and nothing more, so you're really saying that SR looks like a better starting point than SR, which is a pretty strange thing to say.
There is no big bang in Minkowski space.

I think you should learn about Minkowski space-time. Minkowski space-time is time distance (ct) and space (s) that does not change with the observer. Time is absolute and space is absolute, as is the speed of light in Minkowski space-time. Minkowski treats space and time as two independent dimensions. All objects including light move at the same rate in the time dimension and the rate is not affected by transition in the spatial dimension.

If you look at the similarities of the spatial dimension and the time dimension you may start to realize the nature of dimensions. You may transition in the spatial dimension an infinite number of possible directions but you can only move in one spatial direction at a time and you can not exceed the speed of light. The same is true in the time dimension. You can transition outward from the Big Bang in an infinite number of directions but you can only move on one time line at a time and the rate of the transition is always equal to the speed of light. Any time you transition in the spatial dimension your vector sum of the transition in space-time always exceeds the speed of light since your transition in the time dimension is always equal to the speed of light.

Of course there was no BB in Minkowski space-time, but there is now. All normal time lines are known now not to be parallel and space is not a horizontal line. Space is a curve with a radius equal to the distance out from the BB. Our entire present universe is on this curved hypershpere.

If you think this is the same as SR and GR great.

If you don’t think this is Minkowski space-time then you may give me credit for it and call it Green space-time.

In other words, you will ignore the fact that your GST-07 is incorrect and (more importantly) pointless, and proceed as if it wasn't.

I have no intentions of ignoring GST-07 , you should realize this of me by now. I just think that if we move on to more observations the concept of GST-07 will start to resolve themselves much easier.

Yes, but these spheres are not the only spacelike hypersurfaces that can be called "a segment of time". Any spacelike hypersurface will do. This means that there are many ways to split spacetime into space and time, just as in SR.

There is only one hypersurface that is our universe. It is the hypersurface that is 15 billion years from the Big Bang.
There may be an unlimited number of hypersurfaces, each one a universe but they would be at a different time then our universe. We have no knowledge of these other hypersurfaces if they exist. If you have not noticed we are unable to move froward or backward outside of our current position on any time line.

I really think that you should focus on SR (i.e. Minkowski space) instead of GR. You will not understand stuff like simultaneity in GR until you understand it in SR.

It seems to me from your comments that you are the one that is lacking in understanding. If you must resort to insults to enhance your position you only broadcast you inability to deal with the subject. If your position is correct simply state it clearly. You have been all over the map, half-agreeing half-insulting and always obtuse in understanding. You have not shown where SR is right, with proof, compared to the statements made here. You just hold up your understanding of SR and GR as gospel and make dogmatic statements that ideas presented here don’t agree with SR or GR and therefore must be wrong. Then you state that if I , or I would guess anyone, understand SR and GR as you do we would agree with you. These are methods of control to avoid results that may prove you wrong.

 

[russ_watters]

You seem to be unable to grasp the concept that a theory may be valid within defined limits and totally wrong outside of those limits.

"The Twins Paradox," which (1) you erroneously believe is a paradox in SR (as has been said, its a paradox resolved by SR), (2) goes right to the heart of of the domain of applicability of SR. Since both 1 and 2 are mutually exclusive, you can't be right about both points - however, you can and are wrong about both points. This should be a clear red-flag to you that you are missing something pretty basic about SR.

It seems to me from your comments that you are the one that is lacking in understanding.

How many times, by how many people, in how many different places, all saying the same thing does it take for you to accept that it is you who has the misunderstanding? Is there any point at which you will reconsider?

You just hold up your understanding of SR and GR as gospel and make dogmatic statements that ideas presented here don’t agree with SR or GR and therefore must be wrong. Then you state that if I , or I would guess anyone, understand SR and GR as you do we would agree with you. These are methods of control to avoid results that may prove you wrong.

Try saying that to your mirror and see what response you get.

 

[Gamish]

Under bounds of relativity, paradoxes don't exist. Now, if one were to bend the "classic" veiws of SR and Gr, one cound create many paradoxes. But, I believe that age is not relavent, only time.

"Im the master at time!"

I finally found a group I like

 

[Alkatran]

Under bounds of relativity, paradoxes don't exist. Now, if one were to bend the "classic" veiws of SR and Gr, one cound create many paradoxes. But, I believe that age is not relavent, only time.

"Im the master at time!"

I finally found a group I like

Age reflects time so it is relevant. What do you mean by 'classic' views of SR and GR? The ones incorrect ones?

 

[Fredrik]

We seem to have a problem with the idea of dimensions. I thought it is recognized by all that there is a time dimension and a spatial dimension.

What is recognized by physicists is that spacetime is a 4-dimensional manifold with a metric of -+++ signature (or +--- if you prefer that convention). What it doesn't mean is that there's only one way to "slice" spacetime into a one-parameter family of spacelike hypersurfaces, or that there are several such slicings but one of them is more real than the others. That's just an assumption that you have made, without any good reason.

It may be necessary to go into more detail on the nature of dimensions.

Books about differential geometry do that. I suggest you get one of them and read the parts where they define concepts like "manifold", "coordinate system", "tangent space", "tensor field", "metric", "geodesic" and "isometry". It's impossible to really understand GR without some knowledge about these things. You will not even understand the concept of "frames" (i.e. coordinate systems) fully until you've read at the least the first chapter of a book on differential geometry. (This stuff is also explained pretty well in some books on GR, like "General Relativity" by Wald).

How do we know what real space-time is?

The only way to find out if a particular solution of Einstein's equation is an accurate model of our universe is to do experiments and make astronomical observations.

However, I suspect that you actually meant to ask "How do we know which spacelike hypersurface really is space?". The answer to that question is that there is no reason to believe that one of them is "space" and the others aren't.

You seem to be unable to grasp the concept that a theory may be valid within defined limits and totally wrong outside of those limits.

You're still missing the point. You claim that there are paradoxes in SR, which would mean that it's not valid within it's own limits.

If SR or GR were correct in all cases Einstein would not have failed to find unification.

That's probably true. But we already know what the problem is with GR. It's not a quantum theory.

SR is a fine little theory and describes very well what an observer will see in most cases. It has the same problem that all egocentric views have, they are always wrong on the large scale. The bad result of theories like SR is they become accepted in dogmatic way and close off the thought process to the larger view. You have accepted SR as a religion and are willing to distort the real world in favor of your belief.

That's ridicilous. SR is a perfect model of a fictitious universe where there is no gravity and no quantum phenomena whatsoever. It's nothing more than that, and nothing less. Because of that, it will only agree with experiments in situations where gravity and quantum effects can be ignored.

It should be obvious even to you that if SR and GR are able to produce an infinite number of space-times that are different when only one is required to explain all things there must be something wrong with the theories of SR and GR on the large scale.

There's only one spacetime in SR. It's called Minkowski space. GR however describes many possible spacetimes (different solutions of Einstein's equation). As I said before, only experiments and observations can determine if anyone of them has the same large-scale properties as our own universe.

To what equation are you referring?

There's only one equation in GR. It's called Einstein's equation.

I think you should learn about Minkowski space-time.

Thanks for making me laugh.

Of course there was no BB in Minkowski space-time, but there is now.

What are you talking about? Minkowski space is flat. The big bang is a singularity, a point of infinite curvature.

If you don’t think this is Minkowski space-time then you may give me credit for it and call it Green space-time.

GST-07 looks like a spacetime diagram that represents Minkowski space. GST-08 looks like a spacetime diagram that represents a closed http://en.wikipedia.org/wiki/Friedmann-Lema%EEtre-Robertson-Walker spacetime. I don't know what Green spacetime would be. Would you like to define it?

I have no intentions of ignoring GST-07 , you should realize this of me by now. I just think that if we move on to more observations the concept of GST-07 will start to resolve themselves much easier.

Actually it has made it easier to understand what it is that you have misunderstood, and why you have misunderstood it. In the closed FLRW model (i.e. in GST-08), one choice of spacelike hypersurfaces does stand out from the rest. A 3-sphere is the only shape that has a constant curvature. Perhaps this is why you believe that only they can be called "space".

There is only one hypersurface that is our universe. It is the hypersurface that is 15 billion years from the Big Bang.

You have not given us any good reason to believe that it would make less sense to call e.g. a spacelike 3-ellipsoid "space".

If your position is correct simply state it clearly.

That's what I have done, and that's what you should do.

You have not shown where SR is right, with proof, compared to the statements made here.

What you don't seem to understand is that SR is a theory of mathematics as well as a theory of physics. The mathematics of the theory can't be wrong unless pretty much all of mathematics is wrong. Suppose e.g. I define a theory that consists of the set of real numbers and the function f, defined by f(x)=2x. Is there any way this theory can be wrong? SR is not very different from this. Minkowski space is just a set, with a bunch of functions and stuff defined on it. This can't possibly be wrong. And if it were, the burden of proof would definitely be on you.

The physics of SR is just the simple statement that physical space and time can be accurately represented by Minkowski space. That statement can't be proved. It can only be disproved, and the only way to do that is by experiment.

 

[ramollari]

The discussion has got out of hand for me. I don't understand very well spacetime coordinates, Minkowski spaces, etc. I just know that two inertial frames of reference move at constant speed relative to each other and that speed of light c is the same for both observers. With these two conditions it is enough to show that both observers reach contradictory conclusions that throw doubt upon the validity of physical laws. I also think that age is a relevant indicator of time, because it is directly observable and cannot be relative.

 

[Fredrik]

I just know that two inertial frames of reference move at constant speed relative to each other and that speed of light c is the same for both observers.

This is correct.

With these two conditions it is enough to show that both observers reach contradictory conclusions...

This is wrong.

 

[ramollari]

This is wrong.

Ok let me clarify something. If each of the observers correctly concludes that the other's clock runs slower does this necessarily mean that there's a contradiction/paradox? This conclusion results from the fact that the frames move relative to each other at constant speed and c is the same for both observers.
Will be any of the observers ever be able to deduce the other's age without the need to return to Earth?

 

[Fredrik]

Ok let me clarify something. If each of the observers correctly concludes that the other's clock runs slower does this necessarily mean that there's a contradiction/paradox?

This is not a paradox. The reason is that these guys actually make the same prediction about spacetime, and SR is a theory of spacetime, not of space and time separately.

Will be any of the observers ever be able to deduce the other's age without the need to return to Earth?

They will be able to calculate the other observer's age at any point in spacetime.

 

[Fredrik]

They will be able to calculate the other observer's age at any point in spacetime.

This answer isn't very good, so I'll provide a better one. All observers will agree about a person's age at any point on his world line, but not at other points in spacetime. They can calculate the person's age at any point in spacetime, but in general they will not get the same result. The reason is that they may disagree about which point on the world line is simultaneous with the point they're considering (the point at which they're supposed to calculate this person's age).

This comment also answers the question that started this thread. Age is relative at most points in spacetime, but not on the world line (which is the set of events that this person is experiencing).

 

[4newton]

Ramollari:
You have the right idea in the first place. Don’t be put off by convoluted answers.
As proved by experiment. It is a fact that two clocks do not agree on accumulated time when one transitions away and returns to the first clock. The difference has nothing to do with acceleration or observation. The difference between clocks is only dependent on the rate and length of time of the transition. The answer given has no mechanism of the change.

This answer isn't very good, so I'll provide a better one. All observers will agree about a person's age at any point on his world line, but not at other points in spacetime. They can calculate the person's age at any point in spacetime, but in general they will not get the same result. The reason is that they may disagree about which point on the world line is simultaneous with the point they're considering (the point at which they're supposed to calculate this person's age).

This comment also answers the question that started this thread. Age is relative at most points in spacetime, but not on the world line (which is the set of events that this person is experiencing).

The answer does not address the reason the clock ticks slower. The change of the tick of the clock is not a result of observation. The change is real, as proven when the clocks come back together.

The age of all observers may always be calculated at any point by any observer. Any observer may calculate the reading on any other clock. This is the basic idea of SR. If you deny this ability then SR has no use at all.

 

[4newton]

Fredrik:
Now that we are in TD we can work from observation and develop a theory works in all cases including QM.

A good place to start is the Big Bang. Again I ask you did the BB create all that there is including space, time, spacetime, or is there a basic frame of dimensions that exceeds the universe.

 

[SamCJ]

I found this exhaustive thread in archives because the question interests me. I grew tired of the differences of opinion that confused me. I would like to pose the question a little differently.

Two twins are called Earthbound and Spacestation, each is wearing perfectly accurate radioactivity decay watches and each has a pulsar pulse counter. When Spacestation gets into orbit he believes he is standing still and that Earthbound is spinning at a high rate of speed. Earthbound believes that he is standing still and Spacestation is orbiting at great speed. These respective observations go on for 20 years, after which Earthbound joins Spacestation on the space station in orbit and he takes his perfectly accurate watch and his perfectly accurate pulse counter with him.

Question: When the two compare watches and pulse counters, what will the see? Could Einstein prove your answer is correct using mathematics?
Hasn't this experiment already been done and where can I find the results?

 

[pervect]

The experiment has actually been done as a side-effect of the implementation of the GPS system.

The result is that the satellite clocks run faster than the ground clocks. The type of clock - quartz, atomic, pulse counter, radioactive decay, etc. is totally irrelevant in determining this result, except that the accuracy one can expect from the clock varies significantly among clock types, and some clocks may not be accurate enough to reliably measure the results because of uncontrolled varaitions in how well they keep time. (Pulse counting in particular is subject to large enviromental variation).

The satellite clocks run faster, and not slower, because of a factor that you did not realize was significant but was nonetheless very important - the altitude of the clock. To clarify this a bit, what turns out to be important is the gravitational potential energy of the clock - for more details, see some of the threads on gravitational time dilation.

For more on the GPS clocks, see

http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see Lecture 32). A straightforward calculation using Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate.

Further, the satellites are in high orbits, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see Lecture 20 on Black Holes). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.

The combination of these relativitic effects means that if not accounted for the clocks on-board each satellite would tick faster than clocks on the ground by about 38 microseconds per day (45-7=38)! This sounds small, but the high-precision required of the GPS system requires nanosecond accuracy,

Note that the GPS satellite system isn't necessarily one of the most precise tests of relativity that has been done - the GPS system was not specifically designed to test relativity. Rather, it simply illustrates that relativity is not just for textbooks anymore.

In evaluating the archive responses, you might want to note that the posts by users who eventually wound up being banned (and having their names crossed out) are generally not representative of current scientific thought.

Many times a few users can create a false sense of controversy or uncertanity about results that are really not controversial (mainly in the minds of those who are not aware of the facts, and hence falsely weight every opinion with equal value).

 

[SamCJ]

Thanks. I had not thought of the lesser amount of gravity at the higher altitude. Unfortunately, that oversight made you miss the point I was trying to understand. I have usually read the the ground-based twin will be the older one when they rejoin, but a time or two I read that each twin will think the other is younger. However, I have never read an explanation of how the spaceship twin can be younger when both twins believe that it is the other that is moving faster, and, as I understand relativity, they are correct in thinking that from their own perspective. By adding the watches, I was trying to remove subjective misperception by either twin as a factor. By adding the pulse counter, I was trying to create a time machine that was common to both twins. By having Earthbound join Spacestation in the space station, I was trying to remove acceleration as a factor. (I do not think Einstein mentioned subjective misperception or acceleration as a factor in determining their ages at the end of the trip, and I have not understood any of the discussion of simultanaety and frames of reference.)
I anticipate that you might respond the the space twin may be deceived about which one is moving, but we know it is he and not the earthbound twin because he went through acceleration for a relativity brief time at the beginning of the trip and he must decelerate at the end of the trip. But, if so, I say, Isn't acceleration the same as deceleration except in a different direction? If space twin's spaceship heads in the direction that the Earth came from, he would appear to all earthbound people to be accelerating, but in actuality, he would be decelerating. In that event, earthbound twin really would be moving faster until the space twin tried to turn around and come back, at which time he would really have to hurry.
In any case, my question is essentially the same one that was originally asked in this thread. If there was a good answer to it, I missed it in all the confusion. (Thanks also for the tip about the lines through the names.)

 

[jtbell]

When the two compare watches and pulse counters, what will the see? Could Einstein prove your answer is correct using mathematics?
Hasn't this experiment already been done and where can I find the results?

Time dilation for the "travelling twin" has been incidentally observed in studies of precise timekeeping for military applications (targeting bombs etc.). The required precision is such that relativistic effects are observable even on clocks in airplanes flying around in circles.

tycho.usno.navy.mil/ptti/ptti2002/paper20.pdf[/URL] (PDF file)

This isn't quite the same sort of situation you were asking about, but it's close enough that you might be interested in seeing these results.

 

[pervect]

Thanks. I had not thought of the lesser amount of gravity at the higher altitude. Unfortunately, that oversight made you miss the point I was trying to understand. I have usually read the the ground-based twin will be the older one when they rejoin, but a time or two I read that each twin will think the other is younger. However, I have never read an explanation of how the spaceship twin can be younger when both twins believe that it is the other that is moving faster, and, as I understand relativity, they are correct in thinking that from their own perspective.

I'd recommend doing the problem in flat space-time first, this means imagining that both spaceships are far from any planet and there is no gravity.

In that case, there is a very easy explanation. Each twin is correct in thinking that the other twin is moving faster, and each twin thinks that the other's clock is running slow.

However, in order for the twins to re-unite, one twin must accelerate.

The twin that accelerates is the twin that will experience the shortest amount of time. If you haven't read anything about it, there are only about a zillion articles on the twin paradox. I'd recommend the sci.physics.faq on the twin paradox as a good start

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

To do the problem with gravity involved requires considering the metric of space-time. This is a lot harder job. For starters, even describing the metric of space-time from the perspective of the orbiting satellite would be quite a challenge. The "easy" coordiante system to use to describe the metric of space-time is a coordinate system anchored to the center of mass of the most significant massive body (in this case the Earth). If you have two massive bodies, the problem becomes almost insanely difficult (unless you use pertubative methods, in which case it becomes only extremely difficult). The difficulty/reward ratio is low for the problem with two massive bodies.

If you have only one massive body, though, the metric of space-time to use is the Schwarzschild metric, which you can also read about in the wikipedia

http://en.wikipedia.org/wiki/Schwarzschild_metric#The_Schwarzschild_metric

The process of computing the elapsed time on an observer consists of integrating dtau over the path followed by the body in Schwarzschild coordinates, where dtau^2 is given

dtau^2 =
(1-r/rs)*dt^2 - dr^2/c^2*(r-rs)-r^2/c^2*(dtheta^2+sin^2(theta) dphi^2

(Note dtau is just the metric, ds^2, from the Wikipedia, multiplied by a scaling factor of -1/c^2).

This is actually not that hard to do if you are familiar with basic calculus. If you work out this intergal for the orbiting satellite and for the ground based observer, you'll get the results I described.