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Author Topic: How does gravity affect the speed of light?  (Read 7194 times)

Pmb

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How does gravity affect the speed of light?
« on: 07/12/2013 12:32:20 »
I ran into something that caught me by suprised the other day.

Please consider the derivation of the fact that light slows down in a gravitational field at http://home.comcast.net/~peter.m.brown/gr/c_in_gfield.htm

Eq. (6) defines the Schwarzschild metric. Understanding the derivation means understanding the meaning of the variables in that derivation. In another forum there was an uncomfortably large number of people who didn't understand the derivation. In the end I learned that they didn't understand the physical meaning of the variables. Right now I'm curious about the general understanding of this metric and the meaning of the variables.

If you don't mind me asking, those of you believe yourself knowledgeable of Schwarzschild spacetime geometry what is the meaning of the time parameter, i.e. where is the clock that reads that time located. If it could be at a multitude of places then please describe that multitude. Thank you all! :)
« Last Edit: 02/01/2014 20:28:38 by chris »

Pmb

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Re: Coordinate clock in general relativity
« Reply #1 on: 11/12/2013 01:48:35 »
I ran into something that caught me by suprised the other day.

Please consider the derivation of the fact that light slows down in a gravitational field at http://home.comcast.net/~peter.m.brown/gr/c_in_gfield.htm

Eq. (6) defines the Schwarzschild metric. Understanding the derivation means understanding the meaning of the variables in that derivation. In another forum there was an uncomfortably large number of people who didn't understand the derivation. In the end I learned that they didn't understand the physical meaning of the variables. Right now I'm curious about the general understanding of this metric and the meaning of the variables.

If you don't mind me asking, those of you believe yourself knowledgeable of Schwarzschild spacetime geometry what is the meaning of the time parameter, i.e. where is the clock that reads that time located. If it could be at a multitude of places then please describe that multitude. Thank you all! :)
I haven't recieved a response to this question yet and am wondering why? Anyone? Perhaps those who read this don't understand GR to the extent that they felt comfortable answering the question?

distimpson

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Re: Coordinate clock in general relativity
« Reply #2 on: 11/12/2013 14:36:35 »
Interesting question for me, still learning gr, I knew proper time is different from coordinate time but there's more:
"But the coordinate time is not a time that could be measured by a clock located at the place that nominally defines the reference frame,..."
http://en.wikipedia.org/wiki/Coordinate_time

"The coordinate time tc is the time that would be read on a hypothetical "coordinate clock" situated infinitely far from all gravitational masses (U = (GM/r) = 0), and stationary in the system of coordinates (v = 0)."

http://en.wikipedia.org/wiki/Time_dilation#Time_dilation_due_to_gravitation_and_motion_together

Always more to learn...

jeffreyH

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Re: Coordinate clock in general relativity
« Reply #3 on: 12/12/2013 13:29:41 »
Interesting question for me, still learning gr, I knew proper time is different from coordinate time but there's more:
"But the coordinate time is not a time that could be measured by a clock located at the place that nominally defines the reference frame,..."
http://en.wikipedia.org/wiki/Coordinate_time

"The coordinate time tc is the time that would be read on a hypothetical "coordinate clock" situated infinitely far from all gravitational masses (U = (GM/r) = 0), and stationary in the system of coordinates (v = 0)."

http://en.wikipedia.org/wiki/Time_dilation#Time_dilation_due_to_gravitation_and_motion_together

Always more to learn...

That sounds like a hypothetical universal reference frame without gravitational influence. A see it all position from which everything else is referenced. As a mathematical convenience it could only work if all velocities within a system are known and their various magnitudes which they are not.
« Last Edit: 12/12/2013 13:32:29 by jeffreyH »

Pmb

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Re: Coordinate clock in general relativity
« Reply #4 on: 12/12/2013 13:50:15 »
Question: For those who have looked at the derivation and understand it do you believe I should touch it up so that the reader understands what the dr/dt means? Part of that has to do with the longer distance the light has to travel and that is not the part which contributes to the slowing of light in a gravitational field. What I mean to say is that I know what it means simply by inspection (i.e. the factor in front of dr is not unity and varies with r). I assumed that those who read it understood that too since GR textbooks never mention this fact. However I'm begining to unerstand their confusion better. But perhaps assuming the reader knew this was a mistake on my part? So my question is Did I assume too much from the reader?
« Last Edit: 12/12/2013 14:04:57 by Pmb »

yor_on

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Re: Coordinate clock in general relativity
« Reply #5 on: 12/12/2013 23:15:55 »
Sure you do Pete :)
Break it down as far as you see how.

Pmb

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Re: Coordinate clock in general relativity
« Reply #6 on: 13/12/2013 01:59:43 »
Quote from: yor_on
Sure you do Pete :)
Break it down as far as you see how.
Please restate that. I don't know what you mean by it.
« Last Edit: 13/12/2013 08:25:12 by Pmb »

jeffreyH

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Re: Coordinate clock in general relativity
« Reply #7 on: 13/12/2013 07:10:55 »
Think of it this way. Take a right angled triangle. The hypotenuse will be the direction of travel as seen by an observer looking into a moving train. If we extend the opposite and adjacent sides to equal c then light cannot possibly travel along the hypotenuse in the same time it would have taken to move along in a straight line. This would mean a speed for light greater than c. So there has to be some contraction to compensate. So either the opposite or adjacent side has to contract. At c this would leave a straight line the triangle being compressed flat. Hence the angle of travel flattens with momentum.

yor_on

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Re: Coordinate clock in general relativity
« Reply #8 on: 13/12/2013 09:36:52 »
What I mean is a response to your question. "Did I assume too much from the reader?"

Yes, you do. What you assume is that people will understand the mathematics and the concepts behind that mathematical symbolism. Although that should be be correct with those already familiar with the subject, and symbolism used, you will find that on a site like this, you will need to define each step of the way as far as possible to lead people, including those without mathematics, to your conclusion mathematically. And I guess that is what Jeffery is taking a shot at there too. Interpreting the mathematics into a mind image.

Pmb

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Re: Coordinate clock in general relativity
« Reply #9 on: 13/12/2013 10:28:22 »
Think of it this way. Take a right angled triangle. The hypotenuse will be the direction of travel as seen by an observer looking into a moving train. If we extend the opposite and adjacent sides to equal c then light cannot possibly travel along the hypotenuse in the same time it would have taken to move along in a straight line. This would mean a speed for light greater than c. So there has to be some contraction to compensate. So either the opposite or adjacent side has to contract. At c this would leave a straight line the triangle being compressed flat. Hence the angle of travel flattens with momentum.
Jeff - What are you talking about? I can't understand what you're trying to argue or the poin

Pmb

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Re: Coordinate clock in general relativity
« Reply #10 on: 13/12/2013 10:30:31 »
Quote from: yor_on
What I mean is a response to your question. "Did I assume too much from the reader?"
Why do you believe that? The page is targeted to be read and understood by someone who has some understanding of GR and the math required to learn it.

jeffreyH

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Re: Coordinate clock in general relativity
« Reply #11 on: 13/12/2013 11:28:29 »
Think of it this way. Take a right angled triangle. The hypotenuse will be the direction of travel as seen by an observer looking into a moving train. If we extend the opposite and adjacent sides to equal c then light cannot possibly travel along the hypotenuse in the same time it would have taken to move along in a straight line. This would mean a speed for light greater than c. So there has to be some contraction to compensate. So either the opposite or adjacent side has to contract. At c this would leave a straight line the triangle being compressed flat. Hence the angle of travel flattens with momentum.
Jeff - What are you talking about? I can't understand what you're trying to argue or the poin

It is describing the apparent path of light (diagonal) as seen by a stationary observer of a beam of light directed vertically on a moving train. It is a description to show in layman's terms how time dilation must account for the extra distance the light is perceived to travel. If the two sides of the triangle that make up the right angle were extended to 299,792,458 metres each then the light path down the diagonal cannot take 1 second as this would violate the speed of light as light would have to travel faster than c. This is a good indicator of both time dilation and length contraction.

Pmb

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Re: Coordinate clock in general relativity
« Reply #12 on: 13/12/2013 11:41:44 »
Quote from: jeffreyH
\It is describing the apparent path of light (diagonal) as seen by a stationary observer of a beam of light directed vertically on a moving train. It is a description to show in layman's terms how time dilation must account for the extra distance the light is perceived to travel. If the two sides of the triangle that make up the right angle were extended to 299,792,458 metres each then the light path down the diagonal cannot take 1 second as this would violate the speed of light as light would have to travel faster than c. This is a good indicator of both time dilation and length contraction.
The extra distance traveled is due to the non-Euclidean nature of the space around the sun.

yor_on

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Re: Coordinate clock in general relativity
« Reply #13 on: 13/12/2013 12:58:09 »
Well Pete, TNS also draws people without the mathematics, and then it becomes a question of whom you want this page to be directed too. Personally I prefer the citation where AE is told to have said "You do not really understand something unless you can explain it to your grandmother." On the other hand he also seems to have said "keep it as simple as you can, but no simpler than that." Or something to that matter at least? :)

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Re: Coordinate clock in general relativity
« Reply #14 on: 13/12/2013 13:00:16 »
Quote from: jeffreyH
\It is describing the apparent path of light (diagonal) as seen by a stationary observer of a beam of light directed vertically on a moving train. It is a description to show in layman's terms how time dilation must account for the extra distance the light is perceived to travel. If the two sides of the triangle that make up the right angle were extended to 299,792,458 metres each then the light path down the diagonal cannot take 1 second as this would violate the speed of light as light would have to travel faster than c. This is a good indicator of both time dilation and length contraction.
The extra distance traveled is due to the non-Euclidean nature of the space around the sun.

Yes and this is exactly the point that most people misunderstand. Also things like relativistic beta and gamma are assumed as known in advance.
http://scienceworld.wolfram.com/physics/RelativisticGamma.html
« Last Edit: 13/12/2013 13:14:55 by jeffreyH »

Pmb

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Re: Coordinate clock in general relativity
« Reply #15 on: 13/12/2013 13:11:17 »
Quote from: yor_on
Well Pete, TNS also draws people without the mathematics, and then it becomes a question of whom you want this page to be directed too.
I only show these pages to those whom I believe has the ability to follow them. That's why if you read the opending post I said
Quote
.. those of you believe yourself knowledgeable of Schwarzschild spacetime geometry ...

Otherwise you can't give a mathematical proof to those who can't follow the math. To those who don't know the math I just tell them the way it is. Simple.
« Last Edit: 13/12/2013 13:13:21 by Pmb »

yor_on

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Re: Coordinate clock in general relativity
« Reply #16 on: 13/12/2013 13:12:33 »
I think I could use the idea of a observer, observing the event horizon of a black hole? Saying that for the earthbound observer, according to his clock and ruler, 'time stops' there. If now time 'stops' for the earthbound observer, using his coordinate system to measure it (what happens at the event horizon)  by, then light should stop there too, according to his measurements. Or is that a wrong approach to a 'coordinate clock'? My own take on this is wondering in what situation it becomes a meaningful definition? Locally it is simple, 'c' is 'c' as I think.

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Re: Coordinate clock in general relativity
« Reply #17 on: 13/12/2013 13:44:58 »
Yes it's all in the coordinates Pete.

http://arxiv.org/pdf/1308.0394v1.pdf

Pmb

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Re: Coordinate clock in general relativity
« Reply #18 on: 14/12/2013 02:37:14 »
Quote from: jeffreyH
Yes it's all in the coordinates Pete.
What is all in the coordinates, Jeff?

jeffreyH

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Re: Coordinate clock in general relativity
« Reply #19 on: 14/12/2013 12:10:36 »
Quote from: jeffreyH
Yes it's all in the coordinates Pete.
What is all in the coordinates, Jeff?

Depending upon the coordinate system selected the results can differ. As the article showed some of these are insolvable. I also believe that physics has been plagued with infinities and renormalization problems simply because Schwarzschild died before expanding upon his work. The results hs got contained a fundamental error which would have been corrected in time. I am working on correcting this.
« Last Edit: 14/12/2013 12:15:39 by jeffreyH »

Pmb

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Re: Coordinate clock in general relativity
« Reply #20 on: 14/12/2013 15:20:53 »
Quote from: jeffreyH
Depending upon the coordinate system selected the results can differ.
Of course. That's why it's called relativity.

jeffreyH

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Re: Coordinate clock in general relativity
« Reply #21 on: 14/12/2013 17:12:41 »
Quote from: jeffreyH
Depending upon the coordinate system selected the results can differ.
Of course. That's why it's called relativity.

To me it seems appropriate to consider coordinates at an infinite distance from any gravitational source as a starting point. YMMV

yor_on

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Re: Coordinate clock in general relativity
« Reply #22 on: 15/12/2013 02:30:18 »
To get to different coordinate systems I think you first need to define a 'container', containing them. Then you need a 'system' defining limits as I think. 'c' is a very peculiar limit, as it is valid (locally measured) for/in all uniformly moving frames of reference, no matter what speed you measure something else to have relative yourself. That will give you a multitude of coordinate system, as each observer strictly defined can be assumed to have his own unique coordinate system, depending on mass (energy), acceleration deceleration, and relative motion. That doesn't mean that they aren't applicable, or have a relevance. The problem for me is to to see when they have it :) and I also suspect that Pete has a much better training in defining for what situations they are valid, than I ever will.
=

I should mention a arrow for it too, and, to me, that arrow is locally equivalent to 'c', meaning that is 'constantly there' for you. So whenever I talk about 'c' nowadays I'm also thinking of it as a definition of a arrows 'local and constant property'... Da*n it, I should also mention mass, but I won't :) .. Or i did, maybe? :)
« Last Edit: 15/12/2013 12:33:15 by yor_on »

Pmb

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Re: Coordinate clock in general relativity
« Reply #23 on: 19/12/2013 17:20:53 »
This conversation has gotten so off subject that it now bears little to no resemblance of the original topic.
The topic of this thread is the fact that the speed of light slows down as it passes through a gravitational field.  I was asking those of you here who are knowledgeable of Schwarzschild spacetime geometry.

Who here understands general relativity well enough to understand the derivation which shows that the speed of light slows down as it moves through a gravitational field?

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Re: Coordinate clock in general relativity
« Reply #24 on: 30/12/2013 15:12:56 »
This conversation has gotten so off subject that it now bears little to no resemblance of the original topic.
The topic of this thread is the fact that the speed of light slows down as it passes through a gravitational field.  I was asking those of you here who are knowledgeable of Schwarzschild spacetime geometry.

Who here understands general relativity well enough to understand the derivation which shows that the speed of light slows down as it moves through a gravitational field?

That question is not a simple one. It has to involve both length contraction and time dilation but those properties of gravitation may not be as well understood as people think.

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Re: Coordinate clock in general relativity
« Reply #24 on: 30/12/2013 15:12:56 »