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I found these two consecutive posts on physicsforums.1) The time dilation caused by gravity on the surface of a planet is equal to the time dilation for an object moving at the planet's escape velocity in space. This can be proved using the Schwarzschild metric. GR doesn't explain why this is true. It seems to be an odd coincidence.2) Meaning, I assume, in free space, far away from all gravitating bodies?Is this correct?

Quote from: jeffreyH on 09/03/2015 01:49:50I found these two consecutive posts on physicsforums.1) The time dilation caused by gravity on the surface of a planet is equal to the time dilation for an object moving at the planet's escape velocity in space. This can be proved using the Schwarzschild metric. GR doesn't explain why this is true. It seems to be an odd coincidence.2) Meaning, I assume, in free space, far away from all gravitating bodies?Is this correct?It's really very simple Jeff. Think of this in terms of the black hole. We are all familiar with the escape velocity of a black hole as being equal to c. Understanding this, the fact that escape velocity for any mass in question is caused by the gravitational influence, and as such is directly proportional to the time dilation associated with that mass. That fact should come as no surprise.

This requires a variation in density.

But that all assumes point masses.

We are all familiar with the escape velocity of a black hole as being equal to c.

Quote from: EthosWe are all familiar with the escape velocity of a black hole as being equal to c. If that were the case, wouldn't light escape?

With Ve = SQRT(2gr) if we hold g constant and vary r as in a change in density then we have a differing value for Ve. So gravitational acceleration and escape velocity are not proportional. This means that while for the earth the value of g at the surface is much less than Ve there can be situations in which g is greater than Ve near very dense objects. In theory this can result in superluminal acceleration.

Quote from: jeffreyH on 10/03/2015 11:59:42With Ve = SQRT(2gr) if we hold g constant and vary r as in a change in density then we have a differing value for Ve. So gravitational acceleration and escape velocity are not proportional. This means that while for the earth the value of g at the surface is much less than Ve there can be situations in which g is greater than Ve near very dense objects. In theory this can result in superluminal acceleration.I think you've misunderstood my use of the word proportional Jeff. I was not saying they were equal, Webster's defines proportional as: "to arrange the parts of (a whole) so as to be harmonious. a ratio"

The time dilation caused by gravity on the surface of a planet is equal to the time dilation for an object moving at the planet's escape velocity in space. This can be proved using the Schwarzschild metric. GR doesn't explain why this is true. It seems to be an odd coincidence.

It isn't a function of g, because that denotes the "local slope" of gravitational potential. Gravitational time dilation denotes the depth of gravitational potential. And to escape it, you need to "take a run at it", wherein your escape velocity is related to the gravitational time dilation. Quote from: jeffreyHThe time dilation caused by gravity on the surface of a planet is equal to the time dilation for an object moving at the planet's escape velocity in space. This can be proved using the Schwarzschild metric. GR doesn't explain why this is true. It seems to be an odd coincidence.It's no coincidence. The thing is, GR doesn't actually explain why matter falls down. It doesn't actually say why an object acquires some given speed, which is escape velocity when you flip things round. However it's very easy to understand if you think about the wave nature of matter and stuff electron diffraction and spin. Just simplify the electron to light going round and round, then simplify it further to light going round a square path. The horizontals bend in the gravitational gradient, and the electron falls down. It's similar if you accelerate the electron in gravity-free space. Sadly you never seem to see any texts which combine relativity with the wave nature of matter.

Of course it has to be a function of g.

If you are stationary on the earth you are experiencing time dilation.

You are not accelerating away from it.

The velocity involved in escaping the field is due to kinetic energy.

If the gravitational field were absent the time dilation would be due to the velocity.

At a stationary position on the earth there is still a potential for acceleration. However there is NO potential for escape unless there is an impetus away from the surface. This will INDUCE a time dilation.

Without the impetus there is no dilation due to Ve. Can't you see that?

You only have the value of g operating.

Quote from: jeffreyH on 10/03/2015 21:51:05Of course it has to be a function of g.No it isn't. See this depiction of gravitational potential:CCASA image by AllenMcC, see ...sorry, you cannot view external links. To see them, please REGISTER or LOGIN.The time dilation is represented by the depth of potential, how low in the plot you are, whilst g is the slope of the plot. Note that there's an inflection, so g at one elevation is the same as g at another. You can find two places on the plot where you can draw the same tangent. Quote from: jeffreyH on 10/03/2015 21:51:05If you are stationary on the earth you are experiencing time dilation.Yes. Quote from: jeffreyH on 10/03/2015 21:51:05You are not accelerating away from it.Yes. Quote from: jeffreyH on 10/03/2015 21:51:05The velocity involved in escaping the field is due to kinetic energy.Yes, and in your ascending rocket going faster and faster you are swapping gravitational time dilation for special-relativistic time dilation. Quote from: jeffreyH on 10/03/2015 21:51:05If the gravitational field were absent the time dilation would be due to the velocity.Yes. Quote from: jeffreyH on 10/03/2015 21:51:05At a stationary position on the earth there is still a potential for acceleration. However there is NO potential for escape unless there is an impetus away from the surface. This will INDUCE a time dilation.Yes. And as you ascend away from the surface you reduce the gravitational time dilation. Quote from: jeffreyH on 10/03/2015 21:51:05Without the impetus there is no dilation due to Ve. Can't you see that?Yes. Quote from: jeffreyH on 10/03/2015 21:51:05You only have the value of g operating.The acceleration due to gravity is g, and it is due to the local slope of the potential. That's like the local slope of the gravitational time dilation. If your clock at the ceiling runs at the same rate as your clock at the floor, your pencil doesn't fall down. If your clock at the ceiling runs faster than your clock at the floor, your pencil falls down. If your clock at the ceiling runs much faster than your clock at the floor, your pencil falls down much faster. Note that your clocks might be light clocks, and that g can be expressed as the local slope of your plot of the coordinate speed of light.

It's no coincidence. The thing is, GR doesn't actually explain why matter falls down. It doesn't actually say why an object acquires some given speed, which is escape velocity when you flip things round. However it's very easy to understand if you think about the wave nature of matter and stuff electron diffraction and spin. Just simplify the electron to light going round and round, then simplify it further to light going round a square path. The horizontals bend in the gravitational gradient, and the electron falls down. It's similar if you accelerate the electron in gravity-free space. Sadly you never seem to see any texts which combine relativity with the wave nature of matter.

That's a useful way of looking at things. Where do you get your knowledge from, because I'd like to explore the source.

Jeffrey: David Simmons-Duffin was being overly hostile. Take a look at the picture on the quora page. Then note that the ...sorry, you cannot view external links. To see them, please REGISTER or LOGIN. And note this: that "first light" dates from 300,000 years after the big bang. How can that tell you anything about the first nanosecond after the big bang? The universe was a seething maelstrom of plasma for a third of a million years. It would be like putting those sonic standing waves into a blender.

Quote from: Bill S on 10/03/2015 00:53:33Quote from: EthosWe are all familiar with the escape velocity of a black hole as being equal to c. If that were the case, wouldn't light escape?Yes of course...........I should have said "escape velocity greater than c." But greater by only the smallest degree.

Quote from: Ethos_ on 10/03/2015 01:05:43Quote from: Bill S on 10/03/2015 00:53:33Quote from: EthosWe are all familiar with the escape velocity of a black hole as being equal to c. If that were the case, wouldn't light escape?Yes of course...........I should have said "escape velocity greater than c." But greater by only the smallest degree.Would't escape velocity be proportional to the mass of the black hole, in other words; A very small black hole being very close to c but a super massive black hole very much great than c?If not, why?