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Author Topic: Lambert's Cosine Law  (Read 983 times)

jeffreyH

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Re: Lambert's Cosine Law
« Reply #25 on: 03/08/2014 23:46:53 »
This entry in wikipedia describes the general direction in which I am going.

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

jeffreyH

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Re: Lambert's Cosine Law
« Reply #26 on: 04/08/2014 20:55:53 »
I think I've found the mass of the photon by finding the point of unity in one of the factors in the functions I am examining. I have no proof that this is correct but I'm posting it here in case it is right and it can be recorded. The value is 2.42169*10^-25. The units are eV/c^2
« Last Edit: 04/08/2014 21:45:05 by jeffreyH »

jeffreyH

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Re: Lambert's Cosine Law
« Reply #27 on: 05/08/2014 20:19:55 »
I am going to ignore the previous post for now as I am not convinced by my methodology. For consistency with standard definitions measurements in the Planck scale will now be donated by lP for Planck length, tP for Planck time and mP for Planck mass. A correction may need to be made to our factor p. It may be that this should possibly be r0/r1^2. Unity may not be the correct scaling for the denominator. It would appear that the former value would produce too high a gravitational field strength. It is known that gravitation is a much weaker force than electromagnetism.

Our partial differential has an implicit time on the z-axis so I need to investigate the implications for the denominator as it is not really momentum that this would represent as such. This uses time like a one dimensional space component that is unidirectional. When applied individually to the x and y axes this would represent a combination of length contraction and time dilation. The z axis should remain unaffected to preserve a direct connection to the speed of light.

If we assume r0/r1^2 as our p function then when r0 = r1 we could simplify this to 1/r1. This may be invalid. Also angular momentum and the vector of forward motion need to be treated independently. The upper limit on 2554a2bb846cffd697389e5dc8912759.gif of 7/44*360 needs a proportionality factor of its own.
« Last Edit: 05/08/2014 21:43:48 by jeffreyH »

jeffreyH

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Re: Lambert's Cosine Law
« Reply #28 on: 05/08/2014 22:52:45 »
When we substitute angular momentum in place of mass-energy then any deviation from a straight line path that the wave takes is due to the stress on the waveform. So we have angular momentum and stress instead of mass energy and stress. This is easier to deal with in a mechanical way. We can effectively add a stress energy tensor into the model at some stage as an angular momentum analogue. As frequency and energy are directly proportional and substituting angular momentum for energy also gives a directly proportional relationship we can put in place the last link between particles, stress-energy and gravity.

jeffreyH

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Re: Lambert's Cosine Law
« Reply #29 on: 05/08/2014 23:10:33 »
One very spooky conclusion that can be reached is the quantization of momentum itself. This would explain the fact that zero point energy remains at absolute zero and could be the basis for this quantization.

jeffreyH

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Re: Lambert's Cosine Law
« Reply #30 on: 06/08/2014 00:47:26 »
If momentum is quantized then there is a relationship between the kinetic energy of a particles motion through space and the angular momentum of the particle waveform. If slowed due to time dilation then there will come a point where the minimum quanta of angular momentum is reached and can no longer slow down any more. If this equates to the speed of light in the direction of travel then the quantization of momentum is the cosmic brake rather than light speed only. There will be a minimum quanta of time dilation that equates to light speed. This would put an end to speculation on FLT travel.

jeffreyH

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Re: Lambert's Cosine Law
« Reply #31 on: 06/08/2014 18:09:56 »

jeffreyH

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Re: Lambert's Cosine Law
« Reply #32 on: 07/08/2014 17:39:49 »
The uncertainty principle has been questioned many times, particularly the Copenhagen interpretation. I find that the uncertainty principle as a concept is quite valid but the number of unknowns involved makes the measurement uncertain. It stems from a seemingly deterministic system. However it is not possible to determine the point in the evolution of the wave equation you will be measuring in advance. It would necessitate knowing the previous states of all other processes that affected the previous states of the wave that led to its current state at point of measurement.

jeffreyH

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Re: Lambert's Cosine Law
« Reply #33 on: 08/08/2014 18:06:56 »
The next step is producing the mathematics for the non-gravitational portion of the wave function. This will necessitate the use of matrices, one for each partial differential initially.

jeffreyH

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Re: Lambert's Cosine Law
« Reply #34 on: 10/08/2014 13:43:53 »
I have attached 3 plots. The first two take no account of gravitation and show the profiles for diverging and converging waves. The profiles differ for each one. The third is a plot that accounts for the waves shift due to gravity. It is important to note that the profile for both under the influence of gravitation are identical and show a curvature in the progression of the angular quanta only when in a gravitational environment. The straight lines connecting one end of the angular progression to the other should be ignored. This marks the transition past 360 degrees on the x axis.

NOTE: No time element is present in the three graphs shown here. Time, if present, would be shown on the y axis as in Minkowski diagrams. However this would not be a simple unit scale and would vary. The function required to plot this scale is linked directly to the equations of time dilation. The plots of curvature would need adjustment to prevent a negative time appearing during wave evolution.
« Last Edit: 10/08/2014 18:50:45 by jeffreyH »

jeffreyH

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Re: Lambert's Cosine Law
« Reply #35 on: 10/08/2014 19:47:36 »
Now back to our time component and the need for this to be incorporated on the y axis. To do this we need to modify e8b40a892f462413b0c8d876775c483b.gif to become 94b6446995be78aa3c87cf13d02ef3c0.gif. We should now have gravitation operating on time and not velocity. Since velocity (momentum) and gravitation can be considered equivalent in particular cases time makes more sense.

jeffreyH

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Re: Lambert's Cosine Law
« Reply #36 on: 10/08/2014 20:09:08 »
It is almost time to examine Lambert's cosine law again.

http://en.wikipedia.org/wiki/Lambert's_cosine_law

How can this be applied, in a modified form, to the gravitational field? The velocity in the case of light is c and in the case of gravitation is also considered to be c. This then fixes the denominator in our modified Maxwell equation. We therefore arrive at 064a0e8d2d117c657660c1de7cbc0ab4.gif. We can now state our equations as de79d85bb6f9d019009d824eecf0327b.gif. Since we have a range of masses for our denominator (photon mass to Planck mass would be the ideal range) We arrive at c9c092f77d9d436c5dc5800bac0593b5.gif. To model any particular particle we substitute its mass for dm. This will model two of the same types of particles ie two electrons interacting. For interaction based on gravitation we must use the Planck mass.
« Last Edit: 10/08/2014 21:19:25 by jeffreyH »

jeffreyH

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Re: Lambert's Cosine Law
« Reply #37 on: 10/08/2014 23:20:13 »
The attached image is a purposely exaggerated view of the evolution of a waveform over time. We now have a time scale on the y axis.

jeffreyH

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Re: Lambert's Cosine Law
« Reply #38 on: 11/08/2014 00:43:37 »
It should be noted that in the previous plots the speed of light is violated as gravitational damping is NOT yet applied. This will have an effect on the curvature inherent in the angular quantization. It also implies a direct link between light speed and gravitation. Without gravitation this limit on photon velocity would not exist. This conclusion is tentative at best. This could also indicate an intimate relationship between the photon and the graviton.
« Last Edit: 11/08/2014 00:48:35 by jeffreyH »

jeffreyH

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Re: Lambert's Cosine Law
« Reply #39 on: 11/08/2014 19:12:01 »
With 592c6c14f5632724e5b255bf0454a4fc.gif being equal to 0877f871cf7ea9b700a1c9b1c97392cd.gif we can simplify further to 14e556ac118387864e8a34fbb102e360.gif. This results in the attached plot. Plot no 2 shows this with a log scale on the y axis. These plots can not reflect the reality of gravitational interaction without more work on the mathematics. It is a tentative step. Maybe they will be of use, maybe not.
« Last Edit: 11/08/2014 19:17:16 by jeffreyH »

jeffreyH

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Re: Lambert's Cosine Law
« Reply #40 on: 11/08/2014 22:51:57 »
I have now been able to reformulate the equations to remove the gravitational component altogether. This may seem like no big deal but in fact it is. This plot is attached.

jeffreyH

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Re: Lambert's Cosine Law
« Reply #41 on: 12/08/2014 05:54:06 »
If we now integrate this with Maxwell's equations we see a looping in the wave as it loops back on itself. Nearer to a source this flattens and exhibits length contraction in the direction of the force of the field. Taking this looping into account we still see the curvature of angular quanta preserved. Uncertainty is due to a variety of factors including the looping nature of the waveform.
« Last Edit: 12/08/2014 05:59:31 by jeffreyH »

jeffreyH

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Re: Lambert's Cosine Law
« Reply #42 on: 16/08/2014 12:26:12 »
The state of the photon wave, evolving symmetrically or with broken symmetry, is dependent upon the Pauli exclusion principle and the exact spin states of electron pairs as the photon is emitted.

jeffreyH

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Re: Lambert's Cosine Law
« Reply #43 on: 16/08/2014 12:30:22 »
The graviton's loop profile is attached. This diverges from the profile of the photon with increasing distance from the source. This indicates a well defined strict density in the gravitational field in order to trap light. The deflection of light may be due to an induced and partial symmetry breaking of the electromagnetic wave due to interaction with the graviton.
« Last Edit: 16/08/2014 12:35:49 by jeffreyH »

jeffreyH

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Re: Lambert's Cosine Law
« Reply #44 on: 16/08/2014 12:52:10 »
This raises the question, if gravitation can bend light then does light bend the gravitational field. If we view this in terms of Newtons third law the answer appears to be yes. Therefore we can ask, can we focus the gravitational force using light?

jeffreyH

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Re: Lambert's Cosine Law
« Reply #45 on: 17/08/2014 11:50:49 »
I now need to go back and add a gamma factor at the Planck scale where v = 0 to represent the conditions at the event horizon of a black hole. This may take me a while.

jeffreyH

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Re: Lambert's Cosine Law
« Reply #46 on: 17/08/2014 13:08:43 »
Attached is an image of the curvature inherent in the graviton with more realistic frequency values.

jeffreyH

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Re: Lambert's Cosine Law
« Reply #47 on: 17/08/2014 13:29:54 »
I am now going down a slightly different path. In another post JP brought up coherent quantum states which I will now be following. The work here shows a deterministic view of the wave equation which is an approximation to reality. The starting point was artificial and considered frequencies that would not exist in the real world. This does give some insights which I will now try to follow.

 

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