Relativity - clocks out of sync

TheRingslayer

Reading Hawking's brief history of time atm.

Tbh, a good chunk of it is going over my head especially the sub atomic particle chapter.

Nonetheless, he says that to prove relativity, they placed one clock on the surface of the earth. and a second clock in sync with it, up really high (not sure how high). and that after a while, the clocks went out of sync!

I just don't understand this, and nobody has been able to explain it to me.

I understand the part when he says that to travel forward in time is possible if you travel faster than the speed of light or close to it.

Captain Chaos

It's the fact that time moves slower the faster you travel relative to someone who does not more or moves at a slower rate. They have to correct for this in GPS systems in space relative to Earth time or they would be out of sync.

TheRingslayer

but a clock is programmed to tick once every second. I can't see how the second hand would tick slower the further up in space you go.

SOL

If you accept that the speed of light is the same to everyone who looks at it then the result follows.



Imagine you are looking at a train that is going at 0.6 times the speed of light. Now imagine someone on the train shines a light against the ceiling of the train.

To the person on the train the light goes straight up and straight down so, the speed of light being constant, it takes a fixed ammount of time to cover that distance (distance/speed).

To the person looking at the train go by at 0.6 times the speed of light the beam of light also has to keep up with the train, so it has to cover a longer distance (like in the picture). It is still only travelling at the speed of light (to the observer outside the train), so it just takes longer for the same thing to happen as far as the person looking in from the outside is concerned.


Does that help?

Morbert

TheRingslayer wrote: »

but a clock is programmed to tick once every second. I can't see how the second hand would tick slower the further up in space you go.

According to general relativity, space and time are dynamical and affected by mass. A clock high above the surface of the earth still ticks once per second, but the definition of "1 second" depends on the surrounding mass (among other things).

sbsquarepants

TheRingslayer wrote: »

but a clock is programmed to tick once every second. I can't see how the second hand would tick slower the further up in space you go.

It's because there isn't really any such thing as a second, only a second for a given reference frame. The up high clock is moving quickly relative to the down low one, it's second is a perfectly normal second to someone watching right beside it, but if you were to watch from the point of view of the low down clock it would seem to be running slow.
A simple way to picture it is that space and time are linked together as spacetime - put simply the faster you move through one the slower you move through the other, conserving the overall total. If all your effort is going into moving through space as quickly as possible, the side effect is that you're moving through time more slowly (from the point of view of somebody who isn't moving) This is not exactly how it works, but it's helpful in picturing what is happening. Faster through space means slower through time.

Morbert

sbsquarepants wrote: »

It's because there isn't really any such thing as a second, only a second for a given reference frame. The up high clock is moving quickly relative to the down low one, it's second is a perfectly normal second to someone watching right beside it, but if you were to watch from the point of view of the low down clock it would seem to be running slow.
A simple way to picture it is that space and time are linked together as spacetime - put simply the faster you move through one the slower you move through the other, conserving the overall total. If all your effort is going into moving through space as quickly as possible, the side effect is that you're moving through time more slowly (from the point of view of somebody who isn't moving) This is not exactly how it works, but it's helpful in picturing what is happening. Faster through space means slower through time.

I think in this case, the time dilation is gravitational, rather than kinematic. I.e. Even if the two clocks are stationary with respect to each other, as in Hawking's description, they will fall out of sync.

sbsquarepants

Morbert wrote: »

I think in this case, the time dilation is gravitational, rather than kinematic. I.e. Even if the two clocks are stationary with respect to each other, as in Hawking's description, they will fall out of sync.

See, this is what happens when I try to explain things I don't understand myself!

Is that due to equivalence? Gravitational pull being the same as acceleration?

Morbert

sbsquarepants wrote: »

See, this is what happens when I try to explain things I don't understand myself!

Is that due to equivalence? Gravitational pull being the same as acceleration?

It is possible to understand gravitational time dilation in the context of the equivalence principle. When you change velocity, your line of simultaneity (the line intersecting all events in the "present" according to your reference frame) shifts. A local gravitational field is equivalent to uniform acceleration, which means your line of simultaneity is uniformly shifting. Objects higher higher up in the gravitational field will appear to move faster, while objects further down will appear to move more slowly.

This time dilation is asymmetrical. I.e. Both observers will agree on what clock ticks faster, unlike time dilation due to velocity, where both observers will say their own clock ticks faster than the other's.

SOL

Wait, so are you telling me that the clock in the concord used to show special relativity is a lie?

Morbert

SOL wrote: »

Wait, so are you telling me that the clock in the concord used to show special relativity is a lie?

As in the Helefe-Keating experiment? They categorised the resultant time dilation into gravitational time dilation and kinematic time dilation.

http://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment#Results