# What determines who feels the time dilation?

1. Sep 29, 2008

### nickclarson

Ok so I know the basics of relativity but I keep thinking of one situation that keeps confusing me.

Lets say you and one other person are in empty space with nothing else around you. That person uses their "engine" to accelerate away from you at light speed for some distance then turns around and comes back. Now at this point one person is going to be younger than the other, but I'm having trouble figuring out who will for a couple reasons. What determines who feels the acceleration? As far as I'm concerned, even though I didn't use my engine I still moved away from the other person at the same rate that they moved away from me. What made them feel acceleration and not me? Does it have something to do with being relative to space itself? Would then somehow "the universe" be able to recognize who actually used their engine and decide who actually created the acceleration?

I guess knowing who felt the acceleration would then answer my main question. I suppose I should have entitled the thread a little differently, oh well!

Hope this makes sense, this thought has been bothering me for awhile.

Thanks,
Nick

2. Sep 29, 2008

### JesseM

If it helps, you can tell who really accelerated in a physical sense based on who felt G-forces and who felt weightless. Also, time dilation isn't based on traveling at light speed (which is impossible for any object with mass), it's based on traveling at a large fraction of light speed (although all speed is relative--two non-accelerating observers moving relative to one another will each say the other one is moving relative to them, and therefore the other one's clocks are slowed down relative to their own rest frame).

3. Sep 29, 2008

### nickclarson

even though I didn't use my engine why didn't I feel g-forces? I was still moving away from the other person in the same fashion as they were moving away from me. Why did they feel g-forces and I didn't? Does it have to do with the space around us?

I must be missing something huge... ahh acceleration doesn't even matter to begin with. Time dilation aside though, I'm still wondering about who feels the force of acceleration and why.

ha yea I know I can't go the speed of light... but I wish I could!

4. Sep 29, 2008

### JesseM

Because acceleration is absolute in relativity, and you were accelerating in an absolute sense. I don't think you can answer the question of why inertial motion is relative but acceleration is absolute, it's just how the laws of physics work that all the laws will obey the same equations in different inertial coordinate systems constructed out of rulers and clocks that are experiencing no G-forces, but they'll obey different equations in non-inertial coordinate systems. Physicists can't discover why the laws of physics are what they are, only discover what the laws are.

5. Sep 29, 2008

### Jonathan Scott

It has nothing to do with who feels the force of acceleration, in that for example if you change course by passing close by a star or planet, you will be in free fall all the time, but relative to a Special Relativity inertial frame you will have changed course.

It works like straight and non-straight lines in ordinary space, only in a backwards way (in that the one who travels in the straighter line experiences the LONGER time between events).

The mathematics of the separation of space-time events in Special Relativity works like bits of string (as I said in some other thread recently). If you take the (x,y,z) displacements between the ends of a piece of string as the displacement in space, and take the length as being equivalent to ct, then the amount of slack in the string (the maximum distance you can move the mid point from side to side) is the amount by which something would age when travelling directly from the start event to the end event. If it goes via some other event which is within the same line, the total slack still adds up to the same, but if it goes somewhere else on the way, the total amount of slack is decreased.

6. Sep 29, 2008

### JesseM

If you change course by using gravity while in free-fall (so you feel no acceleration), then you're dealing with motion in curved spacetime and SR is inadequate, no coordinate system in a region of spacetime that's curved can be called an "inertial frame". You must use general relativity to deal with such situations. And as long as you're dealing with a flat region of spacetime without curvature, all changes in velocity will be accompanied by G-forces.

7. Sep 30, 2008

### Jonathan Scott

For purposes of Special Relativity, gravity can simply be treated as a force within flat space-time, provided that fields are weak and speeds are non-relativistic. Even relativistic speeds can be handled reasonably accurately by including extra terms to allow for the curvature of space.

Even if that turn-around was caused by dipping into an extreme potential well, requiring GR to calculate the exact path, the overall effect on a much larger path would simply be a change in direction.

8. Sep 30, 2008

### JesseM

If "speeds are non-relativistic" then you're dealing with Newtonian physics, not special relativity! All laws of physics in SR must be Lorentz-invariant, so they obey the same equations when you transform from one inertial frame to another--the Newtonian equations for gravity are not Lorentz-invariant.

9. Sep 30, 2008

### schroder

Both persons started in the same inertial reference frame. One remained in that frame, while the other person accelerated away and then returned. The original frame is then the reference both for the acceleration and for the time elapsed. The one who remained behind obviously did not undergo any acceleration with respect to the original reference frame, while the other person did. So the one who travelled underwent acceleration as well as a time dilation relative to the one who stayed behind. The traveler is younger. It has nothing to do with the space acting as some sort of ether or master frame and is only a relative relationship between the two personsâ€™ inertial frames. In relativity, there is no master frame, all is relative but one frame can be used as a reference to gauge another.

10. Sep 30, 2008

### JesseM

The "original reference frame" is irrelevant to the problem, you can analyze the problem from the perspective of any inertial reference frame (including one where, say, the inertial twin is moving at relativistic speed while the accelerating twin is at rest during the first phase of the journey and then is moving at an even faster speed than the inertial twin during the second phase after the turnaround) and still get the same answer to how much time has elapsed on each twin's clock when they reunite (I can give a simple numerical example if you like). What you can't do is apply the standard rules of SR in a frame where the twin who accelerated was at rest throughout the journey, since this would not be an inertial frame.

11. Sep 30, 2008

### lightarrow

This is true, but I think that Jonathan Scott however is right, in the sense that it's not the amount of acceleration which causes the amount of time delay between the two twins, and because the twins paradox can be treated in SR even in the presence of a massive body, provided that the spacetime region we are considering is asimptotically flat. I think I read it somwhere, I'm not totally sure.

12. Sep 30, 2008

### Jonathan Scott

What I'm pointing out is that an object which is being accelerated relative to some approximately flat background coordinate system does not necessarily have to "feel" that acceleration, as the change of direction could be caused by a local gravitational field. Conversely, it might "feel" an acceleration while travelling at constant velocity if that was being achieved by using thrusters to oppose a gravitational field.

You can get quite accurate results for gravitational effects anyway using a semi-Newtonian approach within SR, treating space as flat and gravity as a force. For weak fields and non-relativistic speeds this is trivial. For relativistic speeds near central masses, you can use Newtonian gravity plus a (1+v^2/c^2) speed-dependent factor (from GR) for the acceleration, and that for example duplicates the deflection of the light by the sun. You can also apply a Lorentz transformation to the whole system to see what it looks like from some other flat frame of reference. It is only when higher orders of accuracy are needed (for example to allow for the variation in the speed of light between the local observer and the background coordinate system) that GR needs to be used, and even then it can normally be expressed as additional corrections to the Newtonian approach.

For "twin paradox" purposes, the method or rate of acceleration is in any case irrelevant. It is only the overall change in velocity which determines the relationship of two frames of reference.

13. Sep 30, 2008

### JesseM

That's interesting, I didn't know you could get a Lorentz-invariant pseudo-Newtonian gravitational force so easily...if Einstein's original motivation for coming up with the theory of GR was that Newtonian gravity was incompatible with SR, I wonder why he didn't think of coming up with something so simple? With such a theory in hand I don't see why there'd be any obvious theoretical motivation to come up with a new theory of gravity, and it would have taken a while before anyone noticed the theory wasn't accurate experimentally.
Yes, but how can you determine empirically which twin's velocity is changing (relative to all inertial frames) and which twin is moving inertially, if you can't take advantage of the fact that G-forces are measurable?

14. Sep 30, 2008

### Jonathan Scott

It's hard to tell whether you might be serious, but from a theoretical point of view it's fairly easy to show that an attempt to base gravity theory on something like electromagnetism combined with SR is going to fail because of the non-linearity of gravity, and the experimental evidence shows that the bending of light is twice that predicted by Newtonian theory. However, for practical calculations one can take Newtonian theory, add in the (1+v^2/c^2) factor calculated from General Relativity and get quite close.

As for the Lorentz transformations; a force transforms as a force and an acceleration transforms as an acceleration, regardless of the causes behind them, provided that the space is flat enough for that approximation to be useful.

In an SR flat space model where gravity is taken as a force, then a twin being accelerated by gravity is not in an inertial frame of reference (as in GR), but is really accelerating. If there were no windows, then the twin might have practical difficulties in distinguishing acceleration from gravity, but with appropriate external navigation equipment it should be possible. The point is simply that one does not necessarily "feel" one's acceleration accurately, so that word in the title of the thread could cause some confusion.

15. Sep 30, 2008

### JesseM

I don't understand what you mean by "an attempt to base gravity theory on something like electromagnetism combined with SR", I though you were saying we could just add a term to Newtonian gravity to give us a Lorentz-invariant gravitational theory, what does electromagnetism have to do with it? And would the Lorentz-invariant pseudo-Newtonian theory of gravity that you described be "linear" in some sense?
I may have the history wrong, but I had thought that this was not noticed until it was predicted by GR and they decided to test it. I suppose even without a theory that predicts a different bending than Newtonian gravity, someone would eventually think to test this.
I don't see how this comment is supposed to make sense as a response to anything I wrote, I certainly never questioned the notion that "a force transforms as a force and an acceleration transforms as an acceleration".
Even if they can see the gravitating objects, it might still be difficult to judge who was accelerating if there is a possibility that the motion of the gravitating objects themselves is not being determined solely by the gravitational force from other objects--in a thought-experiment one could imagine that these objects were also being accelerated by some other force, and if you didn't know the force law for this other force, you wouldn't be able to use the positions of objects as guideposts to determine who's moving inertially. A simple example would be if this other force was accelerating both myself and the entire Earth at 9.8 m/s^2 in the opposite direction that I am being pulled towards the Earth, in which case I will be moving inertially despite the fact that I'm getting closer to the Earth's center at a rate of 9.8 m/s^2. This may not be a very realistic scenario, but ideally we'd like to have an ironclad physical procedure for determining who's moving inertially that would work in all physically possible situations.
But in the real universe, as opposed to this hypothetical universe where gravity is a force operating in flat space, you do always feel your acceleration accurately--that's implied by the equivalence principle.

Last edited: Sep 30, 2008
16. Sep 30, 2008

### atyy

In both GR and SR the "age" of a twin is the proper time along his path, because atomic clocks measure proper time. It is believed, but not proven, that people "age" like atomic clocks. Neither twin "feels" a time dilation, since each twin always "feels" his own proper time. A proper time clock is not affected by acceleration, so the twin paradox does not depend on acceleration in this sense.

In SR, in a Lorentz inertial frame, we can easily calculate the proper time of any particle along an arbitrary path. If two particles are moving with constant velocity relative to each other, then their proper times are also the time axes of Lorentz inertial frames, and we get the "usual" time dilation formula. If a particle is accelerating, its proper time isn't the time axis of a Lorentz inertial frame, and the "usual" time dilation formula will fail, so the twin paradox depends on acceleration in this sense. The moment of acceleration will be felt by the accelerating twin and measured by an accelerometer. He will know enough not to use the "usual" time dilation formula to calculate the proper time of his twin.

GR, not SR, be used when gravity is present. Each twin still feels his own proper time. Free fall in gravity over a short distance cannot be felt by a person nor measured by an accelerometer. In some cases, we can divide the time dilation into "GR" and "SR" components. A twin cannot calculate his twin's proper time using the pure SR formula, since the two components partially cancel. To get it right, he must measure the curvature of time at the location of his twin. A correct formula for this situation may be almost equally valid in some frames related by Lorentz transformations. The frames of the twins are still not related to each other by Lorentz transformations.

Last edited: Sep 30, 2008
17. Sep 30, 2008

### atyy

Yeah, I found that interesting too. So far I've learnt that other theoretically plausible theories around that time were Nordstrom's and Whitehead's. (Neither are exactly what Jonathan Scott was talking about, and not easy to come up with, at least for me. )

Scalar Gravitation and Extra Dimensions
Finn Ravndal
http://arxiv.org/abs/gr-qc/0405030

On the Multiple Deaths of Whitehead's Theory of Gravity
Gary Gibbons (DAMTP), Clifford M. Will
http://arxiv.org/abs/gr-qc/0611006

Last edited: Sep 30, 2008
18. Sep 30, 2008

### Jonathan Scott

One of the most difficult things about GR is the completely different viewpoint it uses to describe gravity compared with the Newtonian model and its extensions to SR. This leads to confusion when things get mixed up between the two models. In GR, an inertial frame of reference is a free fall one, which locally looks like an SR frame of reference, and gravity affects the shape of space-time. In SR, an inertial frame of reference is one with constant velocity, and gravity looks like a external force.

I'm not saying that there is a Newtonian gravity theory in flat space which is self-consistent and compatible with SR. I'm saying that if you are using SR terminology then gravity is seen as an external force, and to a reasonably practical level of approximation one can use a Newtonian theory for calculation purposes. If the gravitational source is not static, one can Lorentz transform the local events to a frame in which the source is static in order to calculate the effect.

The approximation can be made more accurate by including an extra GR factor of (1+v^2/c^2) for the acceleration of an object moving approximately tangentially at relativistic speeds. An even more accurate approximation can be achieved by using isotropic coordinates and treating c as a scalar variable, in which case space-time is no longer flat but it is not necessary to use tensor calculations. However, the accuracy of the approximation is not relevant to the "twin paradox".

In full GR there is an additional complication that the time dilation along a free fall path locally maximizes proper time, so if two objects are falling in a local field the one which moves at constant velocity between the same two points is the one which ages less! I'm guessing (admittedly without calculating) that for longer paths which only briefly pass near heavy masses, this effect should be completely overwhelmed by the different proper times along the overall paths.

Note that the "twin paradox" doesn't just apply to changes of direction. It also applies to changes of speed. If the twins set off in the same direction, but one keeps a constant speed and the other sometimes goes faster and sometimes slower, then the one which varied in speed will have aged less when they meet up again.

19. Oct 1, 2008

### Al68

For what it's worth, you only "accelerated" relative to the other person. The other person accelerated relative to you, every star, planet, nebula, and rock in the entire universe. According to Mach's principle, the sum of these masses is the source of inertia itself, and the reason that G-forces are felt when someone accelerates relative to them.

Al

20. Oct 1, 2008

### JesseM

Although Einstein initially wished to incorporate Mach's principle into general relativity, from what I've read most physicists think he was unsuccessful in this, and that GR is not a truly "Machian" theory so you can't explain why acceleration is absolute in this way.

21. Oct 1, 2008

### JesseM

OK, so I take it I misunderstood when I thought you were saying we could add some term to the force expression for Newtonian gravity to produce a Lorentz-invariant pseudo-Newtonian theory? It's also not clear to me that the papers atyy references are talking about a Lorentz-invariant force-based theory which works in flat spacetime. Thinking about the fact that both Coulomb's law and Newtonian gravity obey an inverse-square law, I wonder if we could produce a Lorentz-invariant pseudo-Newtonian theory just by modifying electromagnetism so that there is only one type of gravitational "charge" which is proportional to mass, and like gravitational charges attract rather than repel...even if this would produce a mathematically consistent theory, perhaps the resulting theory would have been obviously incompatible with experimental evidence in 1905, not giving correct predictions about basic issues dealt with by Newtonian gravity like planetary orbits.

22. Oct 1, 2008

### Jonathan Scott

The principle of equivalence (gravity is locally like acceleration) leads directly to the conclusion that time rates vary in different gravitational potentials, which means space-time cannot be flat globally. Einstein tried for a while in his initial attempts at GR to let time vary with potential but keep flat space, but eventually realized that for consistency space had to vary as well.

The effects of gravitational forces transform somewhat differently from electromagnetic ones. Note for example that a static gravitational field does not change the total energy of a moving object relative to flat background coordinates, but changes its kinetic energy and effective rest energy (via the potential energy) by a matching amount. In contrast, a static electric field changes the total energy and kinetic energy of a moving charged object but does not change its rest energy.

It is possible to describe a gravitational model which incorporates the GR features of varying time and ruler size but is expressed in terms of a Coulomb-like theory expressed relative to a flat background space. The most convenient coordinate system for this purpose is isotropic coordinates, where rulers are assumed to shrink by a scalar factor regardless of direction. Accurate space navigation within the Solar System usually uses this type of model, although the GR-specific terms are not usually very significant.

23. Oct 1, 2008

### lightarrow

The situation is not symmetric: the one who really accelerates (and feel g-forces) is the one who receives a force from (= interact with) an external element (body, field, ecc.).

24. Oct 1, 2008

### JesseM

But a priori there's no obvious theoretical reason why a relativistic theory of gravity would have to include the equivalence principle--that was a good guess of Einstein's, but if Einstein hadn't been around and other physicists were working on trying to come up with a theory of gravity that wouldn't conflict with SR, I don't think there'd be any clear line of reasoning that would lead them to it. (of course, this question of why physicists didn't suggest a simpler theory to reconcile gravity and SR when SR was first proposed is fairly tangential to the original topic, so we don't have to pursue the issue if you're not interested)
Are you talking about Newtonian gravity here, or GR? I'm not familiar with the notion of "effective rest energy" or how it's related to potential energy (and why it would change in a gravitational field but not an electromagnetic field), perhaps you could elaborate or give me a link?

25. Oct 1, 2008

### Jonathan Scott

Given the success of special relativity and the known properties of gravity, the principle of equivalence (at least in its local form) was a reasonable assumption, although perhaps quite imaginative at the time. Even if it wasn't exact, the idea that gravity is "like" an acceleration would be enough to show that time rates would probably need to vary.

I've personally tried quite hard to understand the limits on representing gravity using semi-Newtonian extensions to SR, because I use a very simple notation to handle SR (known as "complex four-vector algebra" or the "Algebra of Physical Space") and I would have very much liked to handle GR without tensors and curved space. However, in gravity one cannot escape the fact that c varies relative to any global coordinate system, and not even necessarily as a scalar (it could vary by different amounts in different directions), and this messes up many of the neat properties of four-vectors.

I mean the rest energy as observed relative to an isotropic coordinate system or similar, as opposed to the rest energy as locally observed (which is of course constant). The rest energy is multiplied by the time factor of the metric, approximately (1-GM/rc^2) in the usual case, so it decreases by the Newtonian potential energy.