Aging related to speed of the Earth

[jiufer]

Hey, I am by no means a physics expert so don't get on my for being somewhat uneducated in the topics of relativity but I have been trying to figure out many seemingly mind boggling questions lately and I was hoping some of you could help.

First of all, as it is commonly stated that time progresses slower as a body's speed increases what is it that determines the progression of time. For instance,if the Earth were to increase its rotational speed (only around its rotational axis) would the people living on Earth experience slower aging than if the Earth had not speed up? Why or Why not? What about if the Earth were to increase the speed at which it rotated the sun? Would the increase in speed cause all things on Earth age slower relative to how fast they would age if it had never increased in speed?

Secondly, since it is supposedly proven that the Earth is gradually slowing (even if by a few milliseconds per year) does that mean all things on Earth are actually aging faster relative to our ancestors millenia ago?

All help is appreciated, I have a few more questions bouncing around but it'll take some time for me to formulate them correctly. Thanks a bunch!

 

[pervect]

You wouldn't notice any difference if the Earth's orbital velocity sped up or slowed down. Living on Earth, you would experience time in exactly the same way - at 1 second per second.

If one had a clock that was stationary with respect to the sun, i.e. without the Earth's orbital velocity, it would have to hover on rockets. If it did so, it would run faster by about 5 parts per billion compared to the Earth clock.

That's because the Earth's orbital velocity is about .0001 c, and 1/sqrt(1 - .00001^2) $\approx 1 - 5*10^{-9}$

So when the Earth came by on its orbit next year, there would be a .15 second difference between the Earth clock and the hovering clock.

 

[Chris Hillman]

Ditto pervect, except that I'd caution against thinking "First of all, as it is commonly stated that time progresses slower as a body's speed increases what is it that determines the progression of time"; search PF for posts challenging the (misleading) notion that "time slows down" in various situations. (It is more correct to say that the world lines of time signals spread apart, or something similar, details depending on the situation.)

 

[pervect]

If you break any statement about "time slowing down" into an actual experiment, you'll eventually have to wind up explaining exactly how the clocks are compared. In some cases, the clocks can be compared when they are at the same position in space-time. However, if one wants to compare clocks remotely (i.e. compare two clocks when they aren't at the same location in space time), one has to specify the comparison method, which will involve some sort of signaling method. In this case one has to analyze the signal propagation in detail to truly understand the situation, one cannot really "take it for granted".

It's definitely true, though, that if two otherwise identical clocks take different paths through space-time (in our example, the orbiting Earth clock and the rocket hovering clock) they will not necessarily read the same when they are reunited.

It might be interesting (though somewhat advanced) to point out in this example that the hovering rocket clock, though it will have a larger time reading than the Earth clock, does not have the largest possible reading for a clock that travels between the two endpoints.

The largest possible reading will be on a clock that does not accelerate, but a coasting clock that starts out and ends up at the same location as both of the clocks in the previoius example. This clock has to start out with a radial outward velocity to be at the same ending location - it moves away from the sun, then falls back to rejoin the other clocks.

The reason this clock has a larger reading is not due to velocity time dilation but "gravitational time dilation".