Gravitational Dilation of Time

[boyongo]

Im having trouble understanding the gravitational dilation of time concept. I know its states that time go slower on higher gravitational potentials and i know it has to do with light loosing energy (decrease in frequency) as stated in Stephen Hawking's Book "A brief History of Time". How does this related with time?

 

[Mordred]

Not sure how he's inferrring that light losing energy has anything to do with time.


http://www.physast.uga.edu/files/phys4102_fertig/Spacetime%20Physics.pdf

This article may help its a nice informative PDF

 

[bcrowell]

I know its states that time go slower on higher gravitational potentials [...]

It's the other way around: slower at lower potentials.

and i know it has to do with light loosing energy (decrease in frequency) as stated in Stephen Hawking's Book "A brief History of Time". How does this related with time?

I don't know if this helps:
http://www.lightandmatter.com/html_books/genrel/ch01/ch01.html#Section1.5 (subsection 1.5.5)

If you don't understand a particular argument, you'll probably get more helpful replies by outlining your understanding of the argument and spelling out what step or steps you don't understand.

 

[boyongo]

bcrowell: You are right! What i meant to say is that time goes slower in a "strong" gravity field and faster in a weaker one. The argument that I don't understand is why does this effect happen? I am reading the links, let's see if they help.

 

[bcrowell]

bcrowell: You are right! What i meant to say is that time goes slower in a "strong" gravity field and faster in a weaker one.

No, that isn't right either. It depends on the potential, not the field.

 

[pervect]

If you think of time dilation as the relation between coordinate time and proper time (which is true, by the way, but I suspect that not a lot of people think that way) it makes more sense.

Example: think of the relation between the longitude coordinate and distance on the Earth.

The longitude coordinate is a coordinate that tells you are - it's analogous to coordinate time. The distance tells you relative displacement - it's analogous to the sort of time you measure with a clock, proper time.

You can see because of the Earth's curvature that equal changes in the longitude coordinate do not represent equal distances. In our analogy , this would mean that coordinate time does not pass at the same rate as proper time, the time clocks actually measure. In other words, it's a model of time dilation, if you recall that time dilation can be thought of as the relation between coordinate time and proper time.

You can also see that even if you have a very highly curved surface, you won't see any curvature effects on distances for clocks that are close enough together.

There isn't any exact equivalent in this analogy for "potential" but you can see that you need both curvature and distance to get appreciable time dilation.

The same thing happens with clocks. Even in a strong gravitational field, two clocks close together will tick at the same rate (when you compare them via light signals). You need to have clocks that are separated a good ways before you can get appreciable time dilation, even if you have a lot of curvature.

One "gotcha" with this approach- it suggests that if you have no curvature, you expect clocks to run at the same rate. While curvature is associated with "natural" gravity, it's not associated with artifical gravity, like Einstein's elevator. However, we still see time dilation in the accelerating elevator, so unfortunately the analogy isn't quite perfect.