Gravity and Time Dilation: How Do They Relate?

[vector22]

sattelite tick slower than an Earth bound clock. Let's say an atomic clock.

From what I've gathered so far, the clock aboard the GPS sattelite ticks slower

The sattelite is in free fall so the clock aboard the sattelite is in zero G. Is the zero G condition the only condition that cause the sattelite clock to tick slower?

 

[Bill_K]

See the thread https://www.physicsforums.com/showthread.php?t=487230

 

[bcrowell]

http://www.lightandmatter.com/html_books/genrel/ch02/ch02.html

Use your browser's search function to find the text "Let's determine the directions and relative strengths of the two effects in the case of a GPS satellite."

 

[Drakkith]

sattelite tick slower than an Earth bound clock. Let's say an atomic clock.

From what I've gathered so far, the clock aboard the GPS sattelite ticks slower

The sattelite is in free fall so the clock aboard the sattelite is in zero G. Is the zero G condition the only condition that cause the sattelite clock to tick slower?

In one case you have the clocks speeding up since they are experiencing less gravity than clocks on Earth are. On the other hand they are at a high velocity which will slow them down relative to ours here on earth. The two equal out to being a bit slower than Earth clocks i believe.

 

[yogi]

In one case you have the clocks speeding up since they are experiencing less gravity than clocks on Earth are. On the other hand they are at a high velocity which will slow them down relative to ours here on earth. The two equal out to being a bit slower than Earth clocks i believe.

The gravitational affect that detemines the clock rate due to potential (GR) is more significant than the velocity difference due to special relativity - GPS clocks are preset before launch to run faster so they are approximately synchronized with Earth clocks

 

[Drakkith]

The gravitational affect that detemines the clock rate due to potential (GR) is more significant than the velocity difference due to special relativity - GPS clocks are preset before launch to run faster so they are approximately synchronized with Earth clocks

Of course. I meant that the clocks WOULD run slower, but as you pointed out they are corrected to run with the correct time.

 

[harrylin]

The gravitational affect that detemines the clock rate due to potential (GR) is more significant than the velocity difference due to special relativity - GPS clocks are preset before launch to run faster so they are approximately synchronized with Earth clocks

Sorry that is half wrong, the effect of gravitation is just the other way round. For clarity, please allow me to correct your statement:

The effect due to gravitational potential is more significant than the velocity effect - GPS clocks are preset before launch to run slower so that in orbit they run approximately synchronous with Earth clocks.

Without that adjustment they would tick very slightly faster than Earth clocks.
See the already provided references for details.

 

[bcrowell]

Without that adjustment they would tick very slightly faster than Earth clocks.

Yes.

 

[vector22]

So i gather the GPS clocks tick faster than Earth bound clocks - any links to reference materials on that. So evidently, zero gravity (free fall) is not the only condition. The current science suggests that there is more than one condition that can effect a clock's timing . If there is more than one condition, are the conditions dependant on each other?

Oh i found the above link - time dilation looks like pretty exotic stuff

 

[yogi]

Sorry that is half wrong, the effect of gravitation is just the other way round. For clarity, please allow me to correct your statement:

The effect due to gravitational potential is more significant than the velocity effect - GPS clocks are preset before launch to run slower so that in orbit they run approximately synchronous with Earth clocks.

Without that adjustment they would tick very slightly faster than Earth clocks.
See the already provided references for details.

Yes -quite right

 

[Drakkith]

So i gather the GPS clocks tick faster than Earth bound clocks - any links to reference materials on that. So evidently, zero gravity (free fall) is not the only condition. The current science suggests that there is more than one condition that can effect a clock's timing . If there is more than one condition, are the conditions dependant on each other?

Oh i found the above link - time dilation looks like pretty exotic stuff

Free fall has nothing to do with time dilation. The gravitational pull at whatever distance the satellites are at, and their velocity relative to ours here on Earth are the only factors. The satellites further up or lower in orbit have different rates of time dilation due to different gravitational pull and velocities compared to the GPS satellites.

Imagine a spaceship hovering stationary at a height equal to the GPS satellites. It has the same gravitational effects on its time that the GPS satellites have. However, since it is not moving at a high speed, it does not have the same effects from velocity.

 

[bcrowell]

Free fall has nothing to do with time dilation. The gravitational pull at whatever distance the satellites are at, and their velocity relative to ours here on Earth are the only factors. The satellites further up or lower in orbit have different rates of time dilation due to different gravitational pull and velocities compared to the GPS satellites.

Actually it's the gravitational potential that matters, not the gravitational force.

Imagine a spaceship hovering stationary at a height equal to the GPS satellites. It has the same gravitational effects on its time that the GPS satellites have. However, since it is not moving at a high speed, it does not have the same effects from velocity.

Experiments of this type have actually been done with atomic clocks, one in a valley and one at the top of a nearby mountain.

 

[Drakkith]

Actually it's the gravitational potential that matters, not the gravitational force.

Oh. What's the difference?

Experiments of this type have actually been done with atomic clocks, one in a valley and one at the top of a nearby mountain.

Sure. I was just relating it to the current topic of GPS.

 

[bcrowell]

Actually it's the gravitational potential that matters, not the gravitational force.

Oh. What's the difference?

Gravitational potential is potential energy per unit mass.

 

[Drakkith]

Gravitational potential is potential energy per unit mass.

Exactly what does that mean in regards to time dilation?

 

[bcrowell]

Exactly what does that mean in regards to time dilation?

The ratio of the rate of flow of time between two points is equal to e^{\Delta\phi}, where \Delta\phi is the gravitational potential difference.

 

[Drakkith]

The ratio of the rate of flow of time between two points is equal to e^{\Delta\phi}, where \Delta\phi is the gravitational potential difference.

So is using "Force" instead of "Potential" just a bad choice of words for me, or is it just pretty much wrong on all levels?

 

[bcrowell]

So is using "Force" instead of "Potential" just a bad choice of words for me, or is it just pretty much wrong on all levels?

They're different things. One is right and one is wrong.

 

[harrylin]

So is using "Force" instead of "Potential" just a bad choice of words for me, or is it just pretty much wrong on all levels?

To illustrate the difference: it is possible to have the same gravitation force at different heights, for example at ground level and deep below the surface.
- http://en.wikipedia.org/wiki/File:EarthGravityPREM.jpg

The gravitational potentials at those depths are very different.

 

[Cleonis]

So is using "Force" instead of "Potential" just a bad choice of words for me, or is it just pretty much wrong on all levels?

Another way of illustrating the difference:
At each point in space the gravitational force is given by the gradient of the gravitational potential.

You can state the gravitational force for a single point in space and that is a meaningful statement. And you can measure it right there. An accelerometer positioned at some point on the Earth's surface gives you the local gravitational acceleration. There is no outside reference; a state of zero acceleration is defined by the accelerometer giving a reading of zero acceleration.

A statement of potential is by nature stating a relation, it's not about a single point.
For the two inverse square forces, gravity and the Coulomb force, the most common practice is to relate the potential at some altitude to the potential at infinity. It is convenient to designate the gravitational potential at infinity as zero. At all lower altitudes the potential is lower.

Whenever you specify a gravitational potential at a particular altitude you reference this potential to some designated zero point. Another use of potential is that you compare the potential at one altitude to the potential at another altitude. Potential is designed to provide an integral picture. (Quite literally: the mathematical definition of gravitational potential is that it's the integral of work being done by gravitational force.)

 

[vector22]

Cleonis

you said:

(Quite literally: the mathematical definition of gravitational potential is that it's the integral of work being done by gravitational force.)

A sattelite in orbit does no work as energy is not consumed in free fall (conservation of energy) so how does the gravitational potential relate to time dilation for objects in orbit (free fall)?

 

[Cleonis]

[...] how does the gravitational potential relate to time dilation for objects in orbit [...]?

As every introduction to general relativity describes: for an object located at some depth in a gravitational well less proper time elapses than for an object that is not subject to gravitational time dilation. The bigger the difference in gravitational potential the larger the difference in amount of proper time that elapses.

For an object on the surface of the Earth the difference is in the order of tens of microseconds per day.

See also the following 2005 physicsforums post by George Jones about https://www.physicsforums.com/showpost.php?p=731738&postcount=5".