# Relative velocity time dilation question

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1. Feb 18, 2015

Since relative velocity time dilation is due to an increase in velocity, with a person moving faster moves through time slower than those on earth, does it follow that it's possible to move slower than the earth and therefore move through time faster than them? Because the earth is moving through space at incredible speeds, is it possible to slow down relative to the earth?

I assume this wouldn't work because in this scenario, the earth is standing still with no motion. That said, both make sense to me in a non mathematical and ignorant logic.

I don't want to get into the possible, but absurd, scenarios like the earth being closer to a black hole, etc. Just purely velocity based time dilation.

Thanks a bunch.

2. Feb 18, 2015

### Orodruin

Staff Emeritus
In relativity (and Newtonian mechanics) there is no such thing as an object at absolute rest. There will always be reference frames where the object is moving.

3. Feb 18, 2015

I know there's no such thing as absolute rest. I was more meaning that since this is relative velocity, would the person on earth be the reference frame for velocity (i.e his relative velocity is 0 since the other guy started there as well and moved away).

4. Feb 18, 2015

### PeroK

That's exactly what can happen. The Earth is spinning. If a plane flies against the spin, then its velocity (from an inertial frame outside the Earth) is less than someone on the surface. So, an atomic clock on such a plane will run faster than one on Earth. There are also gravitational time dilation effects to be taken into account, which also make the flying clock run faster.

If the plane flies Eastwards, then time does indeed run slower on the plane than on the ground.

You could check out the Hafele-Keating experiment, if you are interested:

http://en.wikipedia.org/wiki/Hafele–Keating_experiment

5. Feb 18, 2015

So if that's correct, would it follow that if a person left earth accelerating in the opposite direction the earth is moving (therefore slowing in velocity relative to the earth), he would be moving steadily slower and slower through time? And then if he stopped, nulled out the velocity, and rapidly sped up to much faster than the earth to return, he could theoretically experience, say, 5 years to earth's 1 year?

6. Feb 18, 2015

### Orodruin

Staff Emeritus
No, the effect is much smaller than that. If you go too fast (relative to the Earth's surface), you will lose the effect. This really should not be handled wih special relativity and the concepts you learned there.

7. Feb 18, 2015

What do you mean if you go too fast? How would increasing the velocity difference cancel out the effects of time dilation?

8. Feb 18, 2015

### Orodruin

Staff Emeritus
As I said, you really should look at this with GR. But let us strip everything down to remove the Earth and any gravitational effect just for the sake of it and imagine the observers are held in place by a cord or similar. The observer moving along with the Earth's surface will then be accelerating and changing inertial frames. If you take someone moving less rapidly this observer is moving "against" the rotation relative to the original observer and if large enough relative velocity, will be at rest with respect to an observer in the middle of the "Earth". Any larger relative velocity and the observer will start getting time dilated again. Proper time computations really is something that you should not hand-wave in all but the simplest cases and definitely not by simply referring to relative velocities.

9. Feb 18, 2015

I'm not sure I'm understanding since you're referring to both people as the "observer"--was confusing which you were talking about. But from what I can gather, you're only talking about the rotation of the earth as being the only velocity through space. You have the velocity of the rotation, then the movement around the sun, then the system around the milky way, then the milky way moving through space--all of that adds up to a very high velocity. So, if you were to move in the opposite direction of that overall velocity, would the answer be the same?

10. Feb 18, 2015

### Orodruin

Staff Emeritus
You simply cannot talk about overall velocities without specifying with respect to what. We can just pick the rest frame of the Earth and analyze everything there. You can analyze it in any different frame as well, but the results will be the same.

11. Feb 18, 2015

I suppose I'm suggesting an overall velocity with respect to the origin point of the expansion of the universe. Wouldn't that be the overall velocity?

Maybe if I explain my scenario it will help give something to refer to to help me understand. I'm wondering about travel between star systems in our local supercluster. If the supercluster is moving in one overall direction (X+) at a high velocity (V) and I'm traveling to a star that is technically behind our system (in terms of direction of velocity) at 10V, therefore moving X-, would time pass faster for me than in the two systems?

So in the same way, would moving to a system ahead of ours in the X+ direction at 10V make time move slower for me than in the systems?

Moving X- would technically slow me down relative to the universal velocity, right?

This is also assuming I'm travelling multiple times faster than the overall velocity of the supercluster.

Or would time dilation or GR happen at all in this scenario?

12. Feb 18, 2015

### Orodruin

Staff Emeritus
This is another common misconception, there is no point of origin of the expansion. It is an expansion of space itself, not that things are having a velocity away from an expansion center. The Big Bang happened everywhere.

13. Feb 18, 2015

### Staff: Mentor

No. At least, not with the obvious interpretation of "time passing", which would be the time it takes you to complete the journey, according to your clock, compared to the time it takes according to clocks at rest in the supercluster--I'm assuming the stars you are traveling between are also at rest in the supercluster. But that's not the only possible interpretation; see below.

It's unfortunate that pop science presentations of relativity reduce all the complexities involved in these scenarios down to one rule of thumb: "moving faster slows time down". This rule happens to work in some very simple scenarios, but it stops working as soon as you go beyond those simple scenarios. The question in your OP assumes that you can apply this rule in all scenarios; but you can't.

The problem with the rule is illustrated by Orodruin's comment in post #10: there is no such thing as "moving" in any absolute sense. "Moving" is always relative. So in order to even apply the above rule of thumb, you have to define what things are "moving" relative to. And in the general case, there is no unique answer to this question; there is no unique choice of something that is "at rest" to which all "motion" can be referred.

It just so happens that in certain special cases, such as the Hafele-Keating experiment referred to in post #4, you can uniquely pick out something that can be considered "at rest" for purposes of analyzing just that special case. In the case of the H-K experiment, the thing that can be considered uniquely "at rest" is an idealized non-rotating Earth whose center of mass follows the same path through spacetime as the center of mass of the actual Earth. This defines an inertial frame to sufficient precision for analyzing the experiment; and we can use motion relative to this inertial frame as our definition of "motion" in that analysis. By that definition, the westbound clock moves slower than the clock on the (rotating) Earth's surface, and the eastbound clock moves faster; so the westbound clock will have more elapsed time than the clock on the (rotating) Earth's surface, and the eastbound clock will have less.

(Actually, in the real experiment, there is also gravitational time dilation due to altitude, as PeroK mentioned. I've left that out of the analysis I just gave because it happens not to change the relative ordering of the clock rates in this case, though of course it does affect the precise numbers.)

In the case of moving between stars in a supercluster, as I said above, there is an obvious interpretation of "moving" according to which the supercluster is at rest and you, in your ship, are "moving", so you have less elapsed time. But there are also other possible interpretations of what is "moving", and in this scenario, because you don't set out from and return to the same place (note that in the H-K experiment, all three clocks start out and end up co-located), there is no unique way to pick one interpretation of what is "moving" as the "right" one.

14. Feb 18, 2015