# Are causes relative?

1. Jul 13, 2007

### enridp

Hello !
I'm having troubles with the causes of time dilation.
I will to appeal to the twin paradox because it is known for everybody.
A = Earth twin.
B = traveller twin.

We know B is younger than A when he returns.
Now, why? I mean... from the viewpoint of A, he is younger because his time was dilated during his inertial trip (we can neglect the effect of acceleration here). But from the viewpoint of B, A was under the effect of "time dilation" too, but during the acceleration, B sees a uniform pseudo-gravitational field fill the universe. And this field is the cause of the final difference between B and A's clocks.
We have 2 very different "causes" for the same effect. What is the correct?

bye !

2. Jul 13, 2007

### StatusX

B only measures a gravitational field if he decides he is moving inertially, so that whatever acceleration he feels must be due to such a field. Whether he makes this "mistake" or accurately accounts for the fact that he is accelerating is irrelevant, because both are equivalent under Einstein's equivalence principle, and both lead to the same conclusions about the elapsed time on A's clock. In other words, your question is like asking: what caused my hand to burn, the heat of the stove or the molecular motion of its atoms?

Last edited: Jul 13, 2007
3. Jul 13, 2007

### pervect

Staff Emeritus
They are both correct. Both analyses are described in terms that depend on a particular frame or coordinate system, and both describe how that coordinate system acts.

If you'd like an example of a coordinate independent analysis, that would go something like "the observer who follows a geodesic maximizes his proper time. (In GR or SR with a funky topology, one would have to be a bit more careful and say "extremizes his proper time", because it might be possible to draw two different geodesics between two events in space-time, in which case only one of the geodesics would be a true maximum).

Because this analysis is written in terms that don't depend on the coordinate system, some of the extraneous coordinate dependent details are "filtered out". This has the advantage of not having so many different possible explanations, but it's a bit more abstract and it takes some time to learn coordinate independent language and thinking.

It's not necessary to use a coordinate independent analysis, of course, but one then has to be able to deal with the multiplicity of possible "causes".

Another typical example of this is that one observer might describe a force on a charge as being due to an electric field, while a different observer might describe the same force as being due to a magnetic field.

4. Jul 14, 2007

### enridp

thanks StatusX !
At really I think yes, I mean... we can say: my hand was burnt because the heat of the stove which produced the motion of its atoms. They are not "conflicting causes".
But I can't visualize the cause of the real difference between A and B's clocks.
How do you interpret that consequence? (I mean... is the consecuence of what?)

thanks !

PS: I've seen the pervect's answer:
If I understand it correctly, the larger geodesic has the longest proper time, it can be showed mathematically, but the conceptual interpretation is that we are travelling at constant "c" in 4D (space-time), the geodesic is the shorter path in the spatial dimensiones, therefore, we are "wasting" the rest of our 4-velocity in time. Is this correct?
But, from the viewpoint of B (traveller twin), he is seeing his path like a longer or shorter geodesic (with respect to his brother)?

Then, there is an interesting change of the question.
pervect: Can you explain it better? I think It fazed me.
How can we solve it? Or we just accept the relativity of the causes?

thanks again !

5. Jul 14, 2007

### robphy

Try my visualization:
as part of
physics.syr.edu/courses/modules/LIGHTCONE/LightClock/.
In my opinion, it provides a pedagogically attractive mechanism for marking the ticks on a piecewise-inertial worldline.

("It's all done with mirrors [and light-rays and the principle of relativity].")

6. Jul 14, 2007

### StatusX

No, the motion of the atoms just is the heat, one doesn't cause the other. In the same way, the acceleration is the gravitational field and the electric field is the magnetic field. What's relative is not the cause, but the name we assign to it. The different names are just how people with different points of view describe the same physical object.

7. Jul 14, 2007

### enridp

Hi StatusX !
"the electric field is the magnetic field"
But I don't know if we can use it like:
"acceleration is the gravitational field":
From the Earth's viewpoint the acceleration (or gravitational field) is not the cause, actually, we can neglect its effects if the acceleration's time->0.
But from the traveller's viewpoint the acceleration is the cause, we can not neglect it.
I don't know if I'm explaining my doubt in the right way because my english is very poor, I hope you understand it anyway.

Thanks !

8. Jul 14, 2007

### StatusX

In the limit that the time of acceleration gets very short, the magnitude of accelaration, and thus the magnitude of the gravitational field, gets correspondingly large, in such a way that the combined effect on time dilation is the same. It's the analagous to the way we think of a perfect dipole as being the limit two very close, very charged particles of opposite signs. Even though the two charges are (in the limit) right on top of each other, the fact that we've made their charges so large means they don't cancel.

On the other hand, in the acceleration interpretation, what determines time dilation is not the acceleration but the velocity. Thus it is actually simpler to assume the acceleration is instantaneous, since then we only ever have to integrate constant velocity paths.

9. Jul 14, 2007

### pervect

Staff Emeritus
Unfortunately, this is not quite right.

Let's assume that we have two events, A and B, and that B is located inside the light cone of A, so that someone starting at A can reach event B without exceeding the speed of light.

A geodesic is like a straight line. If we restrict ourselves to suitably simple examples in SR, there is only one geodesic (you might also see the phrase time-like geodesic used) between A and B.

Thus there isn't a "longer" or a "shorter" geodesic. There is only one, unique geodesic connecting the two events. This geodesic has the longest elapsed time of any possible path that can be traversed between events A and B.

The whole point of this very abstract approach is to able to talk about the situation without using "viewpoints".

As I said before, it's perfectly OK to use "viewpoints", but then you have to deal with the fact that different "viewpoints" use different language to describe the exact same phenomenon, which is what you were complaining about.

10. Jul 14, 2007

### enridp

Yes, you are right StatusX, and I understand it. I know there's no paradox. What I don't know is how to interpret this result. From the Earth's viewpoint acceleration is not important, only the inertial paths are (we can neglect acceleration in our calculus). From the traveller's viewpoint acceleration is the principal cause. We can't neglect it. Acceleration feels like a gravitational field, and then (from the traveller's viewpoint) the Earth grow older for that reason, I mean, acceleration is the cause for the traveller twin, but is not for the "Earth twin".
I can't understand what is the cause then. I understand the effects, but the causes not, that's my problem :-(

Greets !

PS: robphy: very nice web ! and wonderfull animations, thanks!.
It would be nice if you put some animations from the traveller's viewpoint, to see what he sees when is accelerating...

11. Jul 14, 2007

### robphy

Thanks!

Yes, version 2.0 or 3.0(?) will have that.
(A version of my VPython programs used making the diagrams allow the scene to viewed dynamically from an arbitrary frame. That is, while the animation runs, the user can freely boost into different frame to see the diagrams drawn from that frame. However, it used some non-standard programming techniques that are now broken in the current versions of Python and VPython. When I get back to it, I'll try to fix them up.)

In the diagram from an accelerating frame, one has to confront the nontrivial issue of what the events on that diagram represent (and how they are determined operationally). [This diagram cannot be nicely transformed into one for an inertial observer, without possibly tearing, overlapping, or excluding regions of the diagram... which is an indication that two observers are not symmetrical.]

12. Jul 14, 2007

### enridp

Hi pervect !:
You said:
Maybe that's the problem, I can't visualize what your are saying...
If we can't put the "viewpoint" in our traveller twin, then how can we understand what he is seeing?
Are accelerated frames invalid? I mean... if we are analyzing events from an accelerated frame, our conclusions are invalid?
(maybe it's like the centrifugal force...)

From the traveller's viewpoint, is he following a geodesic?

13. Jul 15, 2007

### StatusX

I don't really know what you mean by something "causing the time difference." Time just travels at different rates for different observers, this needs to be taken as a basic fact in relativity. The best you can do is ask what's causing the clock of another observer to be currently ticking at a different rate than yours, and two ways you might try doing this are 1) by claiming he's moving, or 2) by claiming he's at a different location in a gravitational field.

If you go through this problem in a step by step way, and note what each twin observes of the other at each point, it will turn out that both twins will observe their counterparts to be aging slower at every point of the journey, except at the turning point, where the moving twin (the one who feels acceleration) sees his brother suddenly age at a tremendous rate, which he could attribute to him being higher up in a gravitational potential. The earth twin doesn't experience such a process, so his brother will always appear younger to him.

14. Jul 15, 2007

### pervect

Staff Emeritus
I'm getting a bit burned out on this discussion, but if you'd like to read more of the approach I have been describing, try:

http://www.eftaylor.com/pub/chapter1.pdf

in the section on "the principle of maximal aging".

Here's a short quote:

Sorry if this isn't getting through, I think I may have introduced some concepts that are too advanced for where you're at - and I also may not be doing a great job of writing. If it's the later that's the problem, I'd suggest reading the online artilce above, as Taylor writes much better than I do, at much greater length, and with some very helpful supporting diagrams.

15. Jul 16, 2007

### enridp

Hi StatusX !
Yes, I know that, and that is what I'm asking at really.
The moving twin says the cause is the gravitational field, without this gravitational field his brother will be younger.
And the earth twin says the acceleration has nothing to do here. His brother is younger because he was moving.
Then why cocks walk at different rates?
I always see that effect like an "illusion", I mean, if the traveller twin doesn't back, who is younger? both sees the other is younger. And it's OK to me, time is relative, but when the twin turn back, he is the younger ("absolutely").
Then, if during his 1st leg of the trip the time was an "illusion" (both sees the other is younger), and durint the home coming again, both sees the other is younger, when was the "real" change of the clocks?
Earth twin: during 1st and 2nd legs traveller's clock was running slowly.
Traveller twin: during 1st and 2nd legs earth's clock was running slowsly but during acceleration earth's clock was running very very fast.
I know all the maths works perfectly, but I think physics it's not only maths, maybe I'm wrong, but I need a cause for every effect, here the effect is the difference between the two clocks, and I can't find the cause of that effect.
I know RE is OK, and I know the paradox doesn't exists at all, but I can't find the cause of the final effect, that's my problem :-(
I hope you can help me to understand it.

bye !
PS: pervect: I will read the pdf, thanks !

16. Jul 16, 2007

### StatusX

The whole point of relativity is that there are no absolutes: one observer's interpretation is just as good as another's, even if they are completely different. And the math works out so that all concrete observations are the same.

When the twins are separated, before the first one turns, both will observe the other's clock (by the way, that l is important) running slowly, but it's meaningless to ask who's right, because there's no way to directly compare the clocks. To emphasize: the twin's observation of the other's clock running slow is as real as his observation of his own clock, it is not an illusion. The apparent contradiction is resolved not by claiming the measurements are somehow wrong, but by noticing that there's no way to compare the clocks, and so no way to expose a contradiction.

After one turns around and returns to his starting point, there are a few different interpretations of what happened, as I've explained a few times. But they are all underlied by the fact that one twin has travelled less proper time, according to the metric. The different interpretations are all derived from the metric, which is a tensor, and so independent of coordinate system (ie, frame of reference), and this is why the observations all come out the same.

I'm sorry, I don't think I can explain this any better. All I can say is you need to understand the different nature of the relativistic theory and the Newtonian theory. Specifically, the ambiguity of simultaneity in relativity is one thing I think you're not completely appreciating. It might help to look at this situation from the points of view of various other observers moving relative to both twins.

Last edited: Jul 16, 2007
17. Jul 16, 2007

### JesseM

This type of thing isn't specific to relativity. The fact that there are "uniform gravitational fields" in non-inertial frames in flat spacetime is directly analogous to the fact that there are fictitious forces in non-inertial frames in classical mechanics. If I'm on the edge of a rapidly spinning wheel and I let go of a ball which flies off at a tangent, in an inertial frame this is just because objects move in straight lines when no forces are acting on them, but in a non-inertial frame where the wheel is at rest it's due to some combination of the "centrifugal force" and the "coriolis force". Would you say that this means "causes are relative" in classical mechanics too? It seems to me that this is basically an issue of semantics, it depends on what you mean by "cause".

18. Jul 16, 2007

### enridp

Thanks again StatusX, and don't worry, I understand you, I'm really familiarized with relativity effects like simultaneity and time dilation and I know there's no possible to compare the clocks in two inertial frames. I know we can explain the final effect like a long and shorter way according to the Minkowski metric.
But it's really difficult to me say why. All the maths are OK, they work fantastic and in a really elegant manner. But if you ask to me why my phone is blue and my wall is white, I just answer: because they are made of different materials and atoms, and they reflect in a different way the light.
But I can't find the answer to the rhythm of the clocks. If the movement is not the cause, if the acceleration is not the cause, then, what is the cause?

JesseM:
I think you hit the nail on the head. I think there's no problem with relativity of the causes too... but I'm not sure.
Anyway in newtoninan mechanics you can explain it by "fictious forces" or just because objects move in a straight line (geodesic in GR). That is, it's easy to find the "cause". But I can't see the cause to the rhytms of the clocks... is the longest length (in 4D=>spacetime) a cause? I see it like a method for computing the results, not like a cause, maybe it's only my problem, I don't know...

19. Jul 16, 2007

### robphy

You certainly can compare two clocks in two inertial frames... it just that the result depends on who is making the measurement and what is the nature of that measurement.

I'm curious what "message" you got from the visualizations I linked to earlier.
It may be that my message wasn't clear enough. If so, I'd like to understand better what is unclear.

20. Jul 16, 2007

### StatusX

I really should just give up at this point, but I get obsessed with explaining things clearly. So I'll keep going.

At a certain point you need to take some facts as basic. You seem to be more picky about this in relativity than in the case of atoms reflecting light of different wavelengths because of different internal structure, which you seem to take as a sufficient explanation in itself, even though this question has puzzled scientists for thousands of years.

Here's a situation completely analagous to the twin paradox. Two people are in a field. They are pushing along wheels that measure distance. That is, the wheels are, say, 1 m in circumference, and every time they turn they click off a reading. Now one person travels in a straight line from one point of the field to another, while the other goes a more roundabout way between the two points. When they meet up, the first person will find that his wheel has turne fewer times than the second person's, even though they've travelled between the same two points. Does such a result need a cause, or can't we just say that the second person has travelled a further distance the the first?

Last edited: Jul 16, 2007