Velocity time dilatation

[theend3r]

So, this is probably an elemental question for most of you here but please bear with it. I think I quite understand time dilatation as an effect of gravity but not so much with velocity as velocity is always relative. If a ship was moving relative to earth at 1/2 c, that would also mean that earth is moving relative to that ship at the same speed, no? Then how come that the clocks on those two bodies would show different time after their reunion, not taking gravity into account? Would it also work in an isolated system with only earth and that ship since there wouldn't be any difference between them except their mass?

[K^2]

As the ship passes the Earth, from Earth's perspective the ship's time is dilated. From ship's perspective, it's the Earth's time that's dilated, because, as you pointed out, velocity is relative.

However, if the ship slows down to land on Earth, after comparing the two clocks, it will be the ship's clock that's behind. The reason for that is acceleration. Unlike velocity, acceleration is absolute. And acceleration also causes time dilation effects. If you have to describe time dilation from perspective of an accelerated object, you have to use General Relativity.

Since Earth does not accelerate, however, from its perspective, Special Relativity still works. So you can describe ship's time dilation using Earth's frame of reference and the SR time dilation formula.

[theend3r]

If it were only acceleration, then it wouldn't matter how long you orbit earth, the time difference would always be the same. That's not the case though, is it? You age slower in the orbit.

[K^2]

Going around in circles also requires acceleration.

By the way, there is also contribution due to gravity, which also has to do with acceleration, but for LEO, gravitational time dilation is pretty much the same as that on the ground. On a high orbit, however, both velocity and gravitational time dilation are lower. So on GPS satellites, for example, time runs faster than on the ground.

[theend3r]

Going around in circles also requires acceleration.

Really? Even so, what's the difference between you and earth then?

By the way, there is also contribution due to gravity, which also has to do with acceleration, but for LEO, gravitational time dilation is pretty much the same as that on the ground. On a high orbit, however, both velocity and gravitational time dilation are lower. So on GPS satellites, for example, time runs faster than on the ground.

Yeah, I know that, read the opening post.

Also, would the time dilatation be reversed if earth had engines and flew away from the ship and back?

[K^2]

Really? Even so, what's the difference between you and earth then?

Earth is not accelerating. Satellite is. Earth is an inertial frame of reference, and you can use Special Relativity. Satellite is not, and you have to use formulas from GR.

[theend3r]

Just found this:

http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#Clock_Hypothesis

Seems like it IS velocity and not acceleration.

[K^2]

Just found this:

http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#Clock_Hypothesis

Seems like it IS velocity and not acceleration.

The clock hypothesis states that the tick rate of a clock when measured in an inertial frame depends only upon its velocity relative to that frame

Satellite is not an inertial frame of reference, because it is accelerating. Hence, you cannot use Special Relativity to describe the world from perspective of a satellite.

[theend3r]

Makes sense but let's say we have two ships. One moves away from the other in a straight line at high velocity and then returns. Would they experience time dilatation? There is no difference between them, it doesn't matter which one fires engines, they could just be shot from one point in opposite directions.

[K^2]

It does matter which one fires its engines. If you are standing aboard the ship that fires its engines, you can actually tell that it's your ship that accelerated. And the ship on which you can experience an acceleration is not an inertial frame of reference. You cannot use SR from that ship's perspective. The ship that continues drifting at constant speed, however, is an inertial frame of reference. And you can use SR equations to describe time dilation on the other ship. So the ship that accelerated away and then back is the one that's going to age less due to time dilation.

You know what? All of this is covered relatively well in Twin Paradox article.

[theend3r]

Yeah, just found out it's the Twin Paradox:rolleyes:. Anyways, thanks for your help.

Edit: "naive application of time dilation" in the article made me chuckle.

Edited January 15, 2014 by theend3r

[Seret]

Really?

Definitely, your velocity vector is constantly changing,

[theend3r]

Definitely, your velocity vector is constantly changing,

I realised that afterwards but it should've been obvious. Sometimes I'm really disappointed by my stupidity.

[Seret]

I realised that afterwards but it should've been obvious. Sometimes I'm really disappointed by my stupidity.

To be fair circular motion is a bit weird and counterintuitive.

[miracmert]

I realised that afterwards but it should've been obvious. Sometimes I'm really disappointed by my stupidity.

Don't feel stupid, this is science. Doesn't matter how much you know, you will still know too little

I should feel stupid though. As an engineering student, I should have remembered what "centrifugal acceleration" is while taking a physics exam (Well actually I couldn't remember what it was because it was in another language)

Anyways, time dilation is complex yet fun subject to know about, and I would recommend you to learn the basic of the "space-time plane" (I don't know if I said it correct, I don't know the English word for it) such as how mass bends it, and how velocity (therefore acceleration) effects the time vector of the object and more.. It is going to be much easier to understand then.