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

 

[Entropia]

First of all, it's important to understand that time dilation and space contraction are both consequences of Einstein's theory of relativity. Time dilation refers to the slowing down of time for an object or observer in motion, while space contraction refers to the shortening of distances in the direction of motion. Both of these concepts are based on the idea that the laws of physics are the same for all observers, regardless of their relative motion or position.

To answer your question, let's first consider the example of a clock in a gravitational field. According to general relativity, clocks in a stronger gravitational field will run slower than clocks in a weaker gravitational field. This is because gravity warps the fabric of spacetime, causing time to pass at a different rate. So, if we were to take an observer into a higher gravitational field, they would indeed experience time passing more slowly. However, this does not mean that they would not notice any changes in their surroundings. In fact, the observer would still observe objects appearing to be closer together due to the effects of space contraction.

To understand this, we can think of a simple thought experiment. Imagine two clocks, one in a weaker gravitational field and one in a stronger gravitational field, but both at the same distance from the observer. The clock in the stronger gravitational field will appear to be running slower, but the observer will also see that the space between the two clocks is contracted. This is because the observer is still able to perceive the difference in distances between objects, even if their perception of time is affected by the gravitational field.

In conclusion, time dilation and space contraction are both real phenomena that are predicted by the theory of relativity. They work together to ensure that the laws of physics are consistent for all observers, regardless of their frame of reference. While an observer in a higher gravitational field may experience time passing more slowly, they will still be able to perceive changes in the distances between objects due to the effects of space contraction.