Time dilation and space contriction doubts

[Okidanokh]

Hi,
I've been with this question in my mind for ages, can somebody, please explain me, if I'm wrong ,and where I'm wrong in my thought's:

-If, the length of any object in a moving frame will appear foreshortened in the direction of motion, or contracted.

-And a clock in a gravitational field runs more slowly according to the gravitational time dilation relationship from general relativity.

Doesn't this mean that if we take an observer into a higher gravitational field where things are closer he wouldn't even notice it because time would be slower for him and distances would seem the same as before?

 

[Garth]

Doesn't this mean that if we take an observer into a higher gravitational field where things are closer he wouldn't even notice it because time would be slower for him and distances would seem the same as before?

Yes!

And welcome to these Forums Okidanokh!

To add a little elaboration.

It depends how you measure any such change in the rate of clocks or the length of rulers.

A clock at the bottom of a gravitational 'well' is observed when compared with a clock at the top to run slowly, a gravitational red shift is observed.

The speed of light is constant by the relativity principle; therefore' if the ruler at the 'bottom of the well' is measured by timing a photon traveling along it, it would appear to an observer at the 'top of the well' to have increased in length. However the observer at the bottom would observe no increase in length or dilation of time. In her frame her clock runs at a regular rate, and the ruler appears to be of its normal length.

In GR, as a consequence of the equivalence principle, atomic masses are constant, rulers are rigid and clocks regular. By definition things are not closer' at the bottom, for if they were, to the observer "distances would seem the same as before".

If however you measure the universe using the photons used to observe it then the story is different...

Garth