I see your clock as running slow

[michel123456]

Swansont wrote:

"If I am in a different locally flat region, I see your clock as running slow, but I also see your "straight line" as being curved (or, along r, you simply get length contraction)"

 

I am focusing on the "I see your clock as running slow" part.

 

 

For a moving body, the "clock running slower" corresponds also to a change in distance (due to motion) and to a change "in-distance" (due to length contraction)

 

But for an object inside a gravitational potential, where the change due to motion is null, what does that mean?

 

Does that mean that

1, indeed, the other clock runs slower, so that as much I wait, the discrepancy will rise? no matter the fact that distance due to motion remains the same?

or

2, there is a gap between the 2 clocks and this gap will remain the same no matter how long we'll wait?

Edited December 28, 2010 by michel123456

[swansont]

The clocks run at different rates, i/e/ the dilation factor is applied to the frequency of the clock. The lag between the clocks is (frequency difference)*(elapsed time). If the clock deeper in the well is running 1 second slow per day (dilation factor is 1/86400), after 10 days is will be 10 seconds slow. After a year, it will be 365 seconds slow.

[Janus]

Swansont wrote:

 

 

I am focusing on the "I see your clock as running slow" part.

 

 

For a moving body, the "clock running slower" corresponds also to a change in distance (due to motion) and to a change "in-distance" (due to length contraction)

 

 

 

The "change in distance" is not important for time dilation for a moving body. That part of what you see happening to the body's clock rate is accounted for by Doppler shift. If the body was moving towards you, you would "see" his clock running fast, but once you factored out the Doppler shift, his clock would be running slow according to you. Or you could have the body circling you at high speed, maintaining a constant distance, and his clock would still run slow according to you.

Edited December 28, 2010 by Janus

[michel123456]

Still wondering:

 

In gravitational field there are 3 possible situations:

 

1. the 2 bodies are free falling in the direction of the gravity well.(as falling from an airplane,the one at t1, the other at t2, without friction)

 

2. one body is at rest on the external surface and the second body is free falling. (as standing on Earth's surface and observing a stone falling in a well, without friction)

 

3. the 2 bodies are at rest at different altitude (as one standing at sea level and one standing on Mont Everest).

 

I guess equations must be different for the 3 situations.

[Janus]

Still wondering:

 

In gravitational field there are 3 possible situations:

 

1. the 2 bodies are free falling in the direction of the gravity well.(as falling from an airplane,the one at t1, the other at t2, without friction)

The body released later will run faster than the earlier one as it will always be at a high gravitational potential (even though both "feel" no gravity as they are in free fall)

 

2. one body is at rest on the external surface and the second body is free falling. (as standing on Earth's surface and observing a stone falling in a well, without friction)

If the second was released from the same height as the first, it will run slower. Both from moving to a lower potential and from increasing its speed due to the fall.

 

3. the 2 bodies are at rest at different altitude (as one standing at sea level and one standing on Mont Everest).

 

The sea level clock will run slower