When the Earth spins

[Vay]

If you are looking at Earth from outer space, you could see Earth spin right? While on Earth we can't feel the spin or the Earth move because time has slowed down for those on Earth. Is the acceleration significant enough for this difference?

 

Also, if time slows down when you move fast, then how are you moving fast if time has slowed down? I remember reading in a book that when driving in a car, time inside the car would be slowed down in respect to the outside, so does it apply to the car itself as well, because if it does, then how does the car move faster and not slower?

Edited March 3, 2011 by Vay

[Schrödinger's hat]

Well, by time slowing down, we mean, 1 second in the car is a number of seconds outside. So it actually feels like you're going even faster (from your point of view you're going less far, everything in the direction you travel is shorter so it takes less time). If you travel at 0.866 times the speed of light, for 0.866 light years, people on earth will see it taking a year. For you it was only half as far, so it took you half a year.

It's quite counter-intuitive to begin with. The problem is that not everyone's clock is measuring the same thing.

If you think of someone with two rulers at right angles, they're measuring height and length, but then if you turn them height and length change.

Time and distance work the same way. If you're moving compared to earth then your clock is measuring a little bit of what someone on earth would consider distance, your ruler measures a bit of time. To you, their clock would measure some distance, and their ruler would measure some time. You only agree if you combine the times and distances you measure together to get something called the interval between two events (a bit like how someone with the two rulers could measure the distance between two objects, then they'd stop disagreeing and arguing about how one event was above the other in one frame, and beside the other in the other frame, they'd both agree that they were one metre apart).

 

 

 

 

With regards to earth, we don't feel it move because we're moving with it. It's making really huge circles, and takes a while to do it, so the Coriolis effect won't make you feel dizzy or like you're spinning. You can 'feel' the spin indirectly by doing an experiment, a really big, symmetric pool of water will spin if you let the plug out -- a lot of the twist of the vortices we see in baths etc is due to hydrodynamics and chaos (sometimes it'll even go the wrong way).

The acceleration also alters how much force things exert on the ground. Local 'gravity' (this includes centrifugal acceleration) varies from the equator to the poles.

None of this has very much to do with relativity.

 

Time in orbit around the sun, and on Earth's surface does travel a little differently, but at these speeds it's only a minute amount. I read a neat result somewhere saying the General Relativistic corrections and the special relativistic corrections on earth's surface almost completely cancelled out, but I can't remember the source.

[swansont]

If you are looking at Earth from outer space, you could see Earth spin right? While on Earth we can't feel the spin or the Earth move because time has slowed down for those on Earth. Is the acceleration significant enough for this difference?

 

Time is slightly slower on the surface of the earth because it's within a gravitational potential well. The spin actually has no effect; the spin means the earth isn't a sphere and the effects cancel. However, this overall effect only about a part in 10^7 as compared to someone in deep space, so we're slow by seconds in a year. Closer to earth, the difference are even smaller.

 

Also, if time slows down when you move fast, then how are you moving fast if time has slowed down? I remember reading in a book that when driving in a car, time inside the car would be slowed down in respect to the outside, so does it apply to the car itself as well, because if it does, then how does the car move faster and not slower?

 

If I measure the speed of a car I use my clock, not the car's. I also use my own meter stick.

 

The slowing is relative to another frame. You never see your own clock slow down.

[IM Egdall]

To expand on Swansont's comments, say you are in a car moving along a highway and I am on the side of the road. To you inside your car, time is running normally. But to me on the side of the road, I see your time running slower. Why? Because you are moving with respect to me.

 

At car speeds, this effect is extremely tiny. But if you were in some future rocket-car traveling at say 87% the speed of light (relative to me), then according to special relativity, I would see your time running slower by 50%. So for every second which ticks off on my watch, only a half second ticks off on yours.

 

However, you inside your rocket-car still see your clock running perfectly normally. Why? Because your clock is not moving with respect to you.

 

This is the wild world of relativity.

Edited March 3, 2011 by I ME

[John Cuthber]

The tangential speed of the Earth is, an most, about 1000 miles an hour. That's a very small fraction of C, so relativistic effects are tiny- too small to notice.

However the effect of the spin of the earth can be measured quite easily, a spring balance calibrated at the equator will give the wrong results if used at the poles. The effect isn't big (about 0.3%), but it's a lot bigger than any relativistic effects.

[lemur]

In reference to the OP: I think you would have to be orbiting the sun parallel to Earth to really see it rotate. If you're orbiting Earth, how can you distinguish between the apparent motion of the Earth due to your rotation and its rotation on its axis? I would pick an orbit as close to Earth's as possible on the sunny side. That way you could watch the day side with backlighting and no glare.

[DrRocket]

 

 

If I measure the speed of a car I use my clock, not the car's. I also use my own meter stick.

 

The slowing is relative to another frame. You never see your own clock slow down.

 

Right, and you don't see your meter stick shrink either.

 

Both you and the driver of the car will agree on the speed of the car relative to you (or of you relative to the car). The time dilation and length contraction effects compensate so that the ratio is the same in both reference frames. Were this not true the resulting asymmetry would allow identification of a preferred frame.

[Vay]

To expand on Swansont's comments, say you are in a car moving along a highway and I am on the side of the road. To you inside your car, time is running normally. But to me on the side of the road, I see your time running slower. Why? Because you are moving with respect to me.

 

At car speeds, this effect is extremely tiny. But if you were in some future rocket-car traveling at say 87% the speed of light (relative to me), then according to special relativity, I would see your time running slower by 50%. So for every second which ticks off on my watch, only a half second ticks off on yours.

 

However, you inside your rocket-car still see your clock running perfectly normally. Why? Because your clock is not moving with respect to you.

 

This is the wild world of relativity.

 

So that means the guy inside the rocket will see the outside world speeding up?

Edited March 7, 2011 by Vay

[swansont]

So that means the guy inside the rocket will see the outside world speeding up?

 

In inertial frames, no. The dilation is symmetric. But when one undergoes an acceleration, then the non-accelerating clock will be seen as speeding up.

[IM Egdall]

Ya, I should have added: To you in the rocket, time is running normally. Why? Because you are traveling in uniform motion (no change in speed or direction). So from your point of view, you and the rocket car are standing still. And you see me moving by you in the opposite direction. This also means that to you see my time running slower than yours.

 

So I see my time running normally and your time running slower. But you see your time running normally and my time running slower. Who is correct? We both are. Time is relative.

 

But say you in your rocket car decide to turn around and return to Earth. Now what? That turn around is key. Your rocket car had to accelerate (change in speed and direction) to turn around. So when you arrive back on Earth, it is you whose time has run slow (compared to me on Earth). Why? Because you experienced acceleration. I did not. (Do you have a headache yet?)

Edited March 7, 2011 by I ME