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Author Topic: Lambert's Cosine Law  (Read 7084 times)

jeffreyH

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Re: Lambert's Cosine Law
« Reply #200 on: 22/01/2015 23:26:03 »
If we increase the distance between the two black holes and consider the central mass to be emitting a synchronized sphere of photons then it should be possible to calculate the deformation of the photon sphere as it moves outwards. The line connecting the two centres of gravity will form a triangle along the line of the perpendicular plane and this would be an interesting situation to study as the spacetime will experience no curvature. The angle at the apex will form a special relationship between the strength of the gravitational field at a particular point and the effect upon the wavelength and frequency of the photons moving in those directions. The change in the waveform can then be calculated for other directions were the gradient of curvature increases.

jeffreyH

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Re: Lambert's Cosine Law
« Reply #201 on: 22/01/2015 23:44:37 »
A note on the two flat spacetimes. The shaft through the sphere is one dimansional being a line through the sphere. Movement away from a straight line path will drift into a curvature in the fabric of spacetime. In the case of the two perfect spheres we have a two dimensional flat spacetime. What is of interest and likely not possible is if we can determine a flat spacetime that is 3 dimensional. If such a spacetime can be determined then we will have either gravity shielding or anti-gravity. Like I just said I don't believe this is possible. We need a third derivative of spacetime that is not at the centre of a mass. This will be a point in spacetime and therefore zero dimensional unless there is some other way of achieving it.

jeffreyH

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Re: Lambert's Cosine Law
« Reply #202 on: 24/01/2015 23:24:08 »
In the model with the flat plane between two equivalent perfect spheres we can say that the centre of gravity of the whole system lies outside of either mass. The equilibrium point coincides with the point on the plane that is positioned on the line between the two individual centres of gravity of the perfect spheres. All particles coincident with the plane and initially stationary at points away from equilibrium will be drawn towards this equilibrium point by the combined gravitational forces and their vector directions.

We can then define situations in which particles that are not stationary may be drawn into orbits around the equilibrium point. This flat spacetime is a unique situation to model and removes the complexity of dealing with curvature of the geometry. This is an ideal model with which to examine the change in the wave function due to the influence of gravitation.

jeffreyH

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Re: Lambert's Cosine Law
« Reply #203 on: 25/01/2015 19:10:31 »
We can introduce something akin to the uncertainty principle into our two perfect sphere model. If we start with an orbit perpendicular to the plane between the masses that passes directly through the equilibrium point this will be our point of uncertainty. At the point of equilibrium in a perfect orbital path there are now two paths the orbit can take. It can either continue around the original mass or go into a figure of eight orbit around the second mass. As all forces are equal at this point there is a degree of uncertainty here. This is in effect a quantum state and binary in nature.

NOTE: An intriguing third option is that the particle continues on the plane away from both masses on its flat spacetime. This now becomes a three choice situation.
« Last Edit: 25/01/2015 19:13:36 by jeffreyH »

jeffreyH

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Re: Lambert's Cosine Law
« Reply #204 on: 25/01/2015 19:33:18 »
If we consider the third choice for the orbital path, then any particle following this type of path will act in a similar manner to a jet expelled from the pole of a black hole. The difference is that instead of a directed jet we get a distribution along a plat plane. Does this have anything in common with the relativistic jet?

jeffreyH

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Re: Lambert's Cosine Law
« Reply #205 on: 28/01/2015 02:22:40 »
Since a particle that is initially at rest on the plane will tend to move towards equilibrium in a straight line path then we can set two out of 3 dimensions to have zero rate of change. This then produces a scalar value for the gravitational force and is analogous to the path of the particle falling down the shaft through a perfect sphere running from one surface to the opposite surface and passing through the centre of gravity. This one dimensional path still has a direction along the plane and a magnitude. The lack of curvature in the spacetime simplifies the change in wavelength of the particle. The slight complication arises due to the vector directions of the forces of the masses above and below the plane. Since these are equal we can sum them since we already have the direction of the vector of the particle.

jeffreyH

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Re: Lambert's Cosine Law
« Reply #206 on: 28/01/2015 02:33:53 »
One reason why it is important to determine how waves may be affected by gravitation is linked to the Penrose Interpretation which is described here:

http://en.wikipedia.org/wiki/Penrose_interpretation

jeffreyH

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Re: Lambert's Cosine Law
« Reply #207 on: 30/01/2015 00:32:57 »
A little speculation now. As the density of the gravitational field increases it is my assertion that not only does the remote observer see an object slowing down but it actually does. This is because the increase in density acts against the acceleration due to gravitation. Once inside the ergosphere this density is likely to also trap light. This then prevents acceleration from violating the speed of light as objects approach a black hole. This will also mean that objects disappear upon entering the ergosphere. A similar situation will occur when approaching light speed since unlike the photon tardyons have non zero rest mass that increases relativistically. Also the speed at which the particles will be traveling, being relativistic, will mimic an increase in density of the gravitational fileds of distant objects in the particles vicinity. This will become more pronounced when in the vicinity of a massive object. The attached image, which was posted previously shows the results of earlier calculations of this. At that time I had put this aside but now feel more confident in this assertion.

 

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