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EM in warped space

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  EM in warped space RichD <r_delaney2001@yahoo.com> - 2015-08-03 13:10 -0700
    Re: EM in warped space John Heath <heathjohn2@gmail.com> - 2015-08-03 15:25 -0700
      Re: EM in warped space John Heath <heathjohn2@gmail.com> - 2015-08-03 15:36 -0700
    Re: EM in warped space Tom Roberts <tjroberts137@sbcglobal.net> - 2015-08-03 20:18 -0500
      Re: EM in warped space Bohuš Matuška <bohu@paranetnet.net> - 2015-08-04 15:50 +0000

#359554 — EM in warped space

I wonder, what happens to the Maxwell eqs., and 
the solutions, in a high gravity gradient, in GR?

A diagram would be better, but anyway... postulate 
a G field which intensifies linearly in the x-direction; 
constant in y and z directions.

Place a linear antenna, with circular symmetry in 
its gain, in this space.  The antenna might be 
oriented along the x axis, or alternatively, along 
the y axis.  What does the radiated wave look like?

It's basically a schoolboy problem.  
Can somebody run out and find me a schoolboy?


--
Rich

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#359572

Hi Richard

Good question. I see this as similar to the position offset of stars close to the sun in the famous Einstein experiment. In this case the photons were falling into the sun's gravity offsetting their perceived position. As this test was successful it can be assumed the same would happen in your experiment. As the g field intensifies linearly in the x-direction a round EM field should be egg shaped with the pointed end in the direction of the increasing gravitational field when viewed at right angles from the X or y direction.The buzz word for an intensifying gravitational field is gravity gradient. This is similar to another question you had regarding time dilation from the center of the earth to outer space. I have a nifty graph that plots this out in detail and including both SR and GR time dilation from the center of earth to well out into space. Will have to find the link in another post so it will come later.   

On Monday, August 3, 2015 at 4:10:59 PM UTC-4, RichD wrote:
> I wonder, what happens to the Maxwell eqs., and 
> the solutions, in a high gravity gradient, in GR?
> 
> A diagram would be better, but anyway... postulate 
> a G field which intensifies linearly in the x-direction; 
> constant in y and z directions.
> 
> Place a linear antenna, with circular symmetry in 
> its gain, in this space.  The antenna might be 
> oriented along the x axis, or alternatively, along 
> the y axis.  What does the radiated wave look like?
> 
> It's basically a schoolboy problem.  
> Can somebody run out and find me a schoolboy?
> 
> 
> --
> Rich

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#359575

There ya go

http://tinyurl.com/pzvvf42

On Monday, August 3, 2015 at 6:25:08 PM UTC-4, John Heath wrote:
> Hi Richard
> 
> Good question. I see this as similar to the position offset of stars close to the sun in the famous Einstein experiment. In this case the photons were falling into the sun's gravity offsetting their perceived position. As this test was successful it can be assumed the same would happen in your experiment. As the g field intensifies linearly in the x-direction a round EM field should be egg shaped with the pointed end in the direction of the increasing gravitational field when viewed at right angles from the X or y direction.The buzz word for an intensifying gravitational field is gravity gradient. This is similar to another question you had regarding time dilation from the center of the earth to outer space. I have a nifty graph that plots this out in detail and including both SR and GR time dilation from the center of earth to well out into space. Will have to find the link in another post so it will come later.   
> 
> On Monday, August 3, 2015 at 4:10:59 PM UTC-4, RichD wrote:
> > I wonder, what happens to the Maxwell eqs., and 
> > the solutions, in a high gravity gradient, in GR?
> > 
> > A diagram would be better, but anyway... postulate 
> > a G field which intensifies linearly in the x-direction; 
> > constant in y and z directions.
> > 
> > Place a linear antenna, with circular symmetry in 
> > its gain, in this space.  The antenna might be 
> > oriented along the x axis, or alternatively, along 
> > the y axis.  What does the radiated wave look like?
> > 
> > It's basically a schoolboy problem.  
> > Can somebody run out and find me a schoolboy?
> > 
> > 
> > --
> > Rich

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#359582

On 8/3/15 8/3/15   3:10 PM, RichD wrote:
> I wonder, what happens to the Maxwell eqs., and
> the solutions, in a high gravity gradient, in GR?

Here are Maxwell's equations in flat spacetime, written in the language of 
differential forms:
	dF = 0
	*d*F = J
Here d is the exterior derivative, * is the Hodge dual operator, F is the 
Maxwell 2-form, and J is the current 1-form. In terms of the electromagnetic 
potential 1-form A:
	F = dA


Here are the corresponding Einstein-Maxwell equations in curved spacetime such 
that the energy density of the EM fields is negligible (compared to other 
mass/energy that determines the geometry):
	dF = 0
	*d*F = J
Yes, they are the same, including the meanings of all the symbols.

This shows the advantages of using advanced mathematics: the usual 4 Maxwell's 
equations become two equations, the two equations relating E and B to A and \phi 
become a single equation, and the equations are valid in curved manifolds.

	
> A diagram would be better, but anyway... postulate
> a G field which intensifies linearly in the x-direction;
> constant in y and z directions.
>
> Place a linear antenna, with circular symmetry in
> its gain, in this space.  The antenna might be
> oriented along the x axis, or alternatively, along
> the y axis.  What does the radiated wave look like?

Assuming that the energy density of the EM source and field is negligible 
compared to the mass/energy that determines the geometry of the manifold, and 
assuming weak gravitation (e.g. as in the solar system), the EM wave will be 
Doppler shifted in frequency and wavelength, in the usual way. As the EM field 
is continuous, this Doppler shift in the wavelength implies a corresponding 
"bending" of the direction of propagation in suitable circumstances.


Tom Roberts

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#359624

Tom Roberts wrote:

> On 8/3/15 8/3/15   3:10 PM, RichD wrote:
>> I wonder, what happens to the Maxwell eqs., and the solutions, in a
>> high gravity gradient, in GR?
> 
> Here are Maxwell's equations in flat spacetime, written in the language
> of differential forms:
> 	dF = 0 *d*F = J
> Here d is the exterior derivative, * is the Hodge dual operator, F is
> the Maxwell 2-form, and J is the current 1-form. In terms of the
> electromagnetic potential 1-form A:
> 	F = dA
> 
> 
> Here are the corresponding Einstein-Maxwell equations in curved
> spacetime such that the energy density of the EM fields is negligible
> (compared to other mass/energy that determines the geometry):
> 	dF = 0 *d*F = J
> Yes, they are the same, including the meanings of all the symbols.

No, they are not the same. The former was Maxwell, the later Einstein is 
added to it: Einstein-Maxwell.
 

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