time dilation in gravitational potential

[michel123456]

In any gravitational potential Relativity states that time dilation takes place.

But Relativity states also that Speed Of Light is constant. So I presume that under gravitational potential, not only time is dilated, but space too, in order to preserve the relation c=d/t unchanged.

So, when time contracts, distances contract, and when time expands, distances expand.

Is that correct?

Edited December 27, 2010 by michel123456

[swansont]

Space curves as well, and that also gives you length discrepancies.

[michel123456]

Space curves as well, and that also gives you length discrepancies.

Length discrepancies? Less important than time discrepancies?

 

I don't see any length discrepancy in the following formula (about gravitational time shifts).

 

 

from here

Edited December 27, 2010 by michel123456

[swansont]

Length discrepancies? Less important than time discrepancies?

 

No, exactly compensating for them. Locally, you will always measure c to be the same thing.

 

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)

[michel123456]

No, exactly compensating for them. Locally, you will always measure c to be the same thing.

 

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)

 

And the same goes for a body in gravitational potential. (I will split the thread because there is another interesting point raising from your answer).

 

I don't see any length contraction in the above equation. Distances are untouched.

 

--------------------------------------------------------------------------------

 

_Time discrepancies in the Hafele-Keating experiment are measured in nanoseconds.

_1 nanosecond corresponds to approx 0,3m (calculated by multiplying 1 ns by the speed of light)

_The larger theoretical time discrepancy due to gravitation in this experiment is 179 nanoseconds. (see here)

which corresponds to a distance of 179 x 0,3m = 53,7m.

 

Which is very small in correspondance with the approximations of the experiment:

"This corresponds to an average height of 8900 m, a reasonable flight altitude for a commercial airline."

and

"since to the level of the approximations used, the height of the aircraft does not significantly change the radius R." (from the same link) under Kinematic Time shift calculation" after the "The problem encountered with measuring the difference between a surface clock and one on an aircraft is that(...)"

 

-------------------------------------------------------------------------

 

in this equation (from wiki's article here) under "Gravitation"

"Where c = speed of light, h = height, g=acceleration of gravity, v = velocity, ω = angular velocity of Earth's rotation and τ represents the duration/distance of a section of the flight. The effects are summed over the entire flight, since the parameters will change with time."

 

I see no factor influencing the value of h=height.

Edited December 28, 2010 by michel123456

[swansont]

And the same goes for a body in gravitational potential. (I will split the thread because there is another interesting point raising from your answer).

 

I don't see any length contraction in the above equation. Distances are untouched.

 

No you wouldn't. Because it's an equation for the time dilation. You don't see length contraction in the SR equation for time dilation either. If I am in a flat space and see an area that appears curved, that curved path will be longer that it appears to someone in that space.

 

 

 

_Time discrepancies in the Hafele-Keating experiment are measured in nanoseconds.

_1 nanosecond corresponds to approx 0,3m (calculated by multiplying 1 ns by the speed of light)

_The larger theoretical time discrepancy due to gravitation in this experiment is 179 nanoseconds. (see here)

which corresponds to a distance of 179 x 0,3m = 53,7m.

 

Which is very small in correspondance with the approximations of the experiment:

"This corresponds to an average height of 8900 m, a reasonable flight altitude for a commercial airline."

and

"since to the level of the approximations used, the height of the aircraft does not significantly change the radius R." (from the same link) under Kinematic Time shift calculation" after the "The problem encountered with measuring the difference between a surface clock and one on an aircraft is that(...)"

 

-------------------------------------------------------------------------

 

in this equation (from wiki's article here) under "Gravitation"

"Where c = speed of light, h = height, g=acceleration of gravity, v = velocity, ω = angular velocity of Earth's rotation and τ represents the duration/distance of a section of the flight. The effects are summed over the entire flight, since the parameters will change with time."

 

I see no factor influencing the value of h=height.

 

The accumulated phase from time dilation is not the right comparison. You need to use the dilation factor, which is gh/c^2 close to the earth for the gravitational contribution. Which is about a part in 10^12. Meaning the height is contracted by about 9 nm, and that isn't something one would worry about. Multiplying by c isn't meaningful, because you aren't sending light anywhere.

[michel123456]

Why use SR instead of GR?

[swansont]

I don't understand the question. I used GR. Gravitational time dilation is GR.

[michel123456]

I don't understand the question. I used GR. Gravitational time dilation is GR.

 

You said (emphasis mine)

No you wouldn't. Because it's an equation for the time dilation. You don't see length contraction in the SR equation for time dilation either. If I am in a flat space and see an area that appears curved, that curved path will be longer that it appears to someone in that space.

 

I am confused.

Edited December 28, 2010 by michel123456

[swansont]

Time dilation equations tell you about time dilation. To say that it does not include length contraction in it is meaningless, because it is not a length contraction formula. The SR time dilation formula does not include length in it, so why would you expect the GR equation to? The objection is a non sequitur.

[michel123456]

I am so sorry, but I don't understand why it is meaningless to include length contraction.

 

As i said in post#1

 

when time contracts, distances contract, and when time expands, distances expand.

 

At which you seemed to agree.

 

I don't understand how a theoretical equation about time dilation ignores completely distance contraction.

[IM Egdall]

No you wouldn't. Because it's an equation for the time dilation. You don't see length contraction in the SR equation for time dilation either. If I am in a flat space and see an area that appears curved, that curved path will be longer that it appears to someone in that space.

 

The accumulated phase from time dilation is not the right comparison. You need to use the dilation factor, which is gh/c^2 close to the earth for the gravitational contribution. Which is about a part in 10^12. Meaning the height is contracted by about 9 nm, and that isn't something one would worry about. Multiplying by c isn't meaningful, because you aren't sending light anywhere.

 

Fisrt you say "If I am in a flat space (zero gravity) . . . the cuved path will be longer than it appears to someone in that space." Later you say " . . . the heght is contracted by about 9 nm . . ." Don't these two statements contradict each other. Did I miss something?

 

As I understand it, a radial distance on the surface of the Earth is stretched not contracted by the Earth's mass/energy (as seen from flat space). So your first statement agrees with this, but not the second. Please clarify.

Edited December 28, 2010 by I ME

[swansont]

Sorry. The dilated frame will have shorter lengths. Each local frame will measure the expected value for c. ("path" and "meter stick" aren't the same thing; I mixed them up)

 

It's similar to kinematic dilation where the meter stick is shortened in the moving frame; more of them will fit into the length between two points in the rest frame. e.g. if the points are 10m apart, but the moving meter stick is shortened, 11 of them will fit into the space.