Can anyone to study a simple case of GR.?

[aditya23456]

consider a following situation,where a person A is on Earth and another one B far from Earth where his proper time is not influenced by Earth's gravity field.now what's time flow felt by A wrt A and wrt to B.?
I get the answer for it but i need a explicit explanation..Is there any link where I can get formulae for this using GR.??thanks in advance

 

[harrylin]

consider a following situation,where a person A is on Earth and another one B far from Earth where his proper time is not influenced by Earth's gravity field.now what's time flow felt by A wrt A and wrt to B.?
I get the answer for it but i need a explicit explanation..Is there any link where I can get formulae for this using GR.??thanks in advance

http://en.wikipedia.org/wiki/Gravitational_time_dilation

 

[aditya23456]

what does this mean----
"If a distant observer is able to track the light in
a remote, distant locale which intercepts a time
dilated observer nearer to a more massive
body, he sees that both the distant light and
that distant time dilated observer have a
slower proper time clock than other light which is coming nearby him, which intercepts
him, at c, like all other light he really can
observe. When the other, distant light
intercepts the distant observer, it will come at c
from the distant observer's perspective."

 

[harrylin]

what does this mean----
"If a distant observer is able to track the light in
a remote, distant locale which intercepts a time
dilated observer nearer to a more massive
body, he sees that both the distant light and
that distant time dilated observer have a
slower proper time clock than other light which is coming nearby him, which intercepts
him, at c, like all other light he really can
observe. When the other, distant light
intercepts the distant observer, it will come at c
from the distant observer's perspective."

That's very messy formulation. Gravitational time dilation and length contraction imply that in GR the speed of light is only a local constant.

-> that is also mentioned in par.5 of chapter 22 here:
http://www.bartleby.com/173/22.html

For example, take the measurement of the speed of light of a horizontally propagating light ray at great height, using a standard ruler, a clock and a mirror. For simplicity assume this is done in vacuum and ignore the rotation of the Earth (or have it measured in an airplane that flies against the rotation of the Earth, thus cancelling it).
Then the speed as measured with those local instruments will be c. However, according to a reference system with otherwise identical instruments at sea level, the ruler in the airplane has the same length but the airplane clock is running fast.

BTW, do you understand the equations given in the wiki?

 

[sardar]

Yes, anyone with a basic understanding of general relativity (GR) can study a simple case involving the effects of gravity on time. In this situation, person A is on Earth and person B is located far from Earth where the Earth's gravity field does not have a significant influence on their proper time (the time measured by a clock moving with them). The question is asking for the time flow experienced by person A relative to themselves and person B.

According to GR, time is affected by gravity and the closer an object is to a massive body, the slower time moves for that object. This is known as gravitational time dilation. In this case, person A, who is on Earth, is closer to the massive body (Earth) compared to person B who is far from Earth. Therefore, person A will experience time moving slower compared to person B. This means that person A's proper time will be slower than person B's proper time.

To calculate the exact time flow, we can use the formula for gravitational time dilation, which is given by Δt' = Δt√(1-2GM/rc^2), where Δt' is the proper time, Δt is the coordinate time (time measured by a distant observer), G is the gravitational constant, M is the mass of the massive body, r is the distance from the center of the massive body, and c is the speed of light.

In this case, person A's proper time (Δt') will be slower compared to person B's proper time (Δt). This is because the value of r for person A is smaller compared to person B, due to their proximity to Earth. Therefore, the term √(1-2GM/rc^2) will be smaller for person A, resulting in a slower time flow.

As for finding a link with more information and formulae for this scenario, a simple search for "gravitational time dilation" or "time dilation in general relativity" will provide numerous resources and explanations. Some recommended sources include the general relativity section of the Stanford Encyclopedia of Philosophy and the "Gravitation" book by Misner, Thorne, and Wheeler.