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Lambert's Cosine Law
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Lambert's Cosine Law
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Re: Lambert's Cosine Law
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Reply #20 on:
27/07/2014 10:23:50 »
We have a very interesting explanation of how DE Broglie derived his wave equation here:
http://chemwiki.ucdavis.edu/Physical_Chemistry/Quantum_Mechanics/Quantum_Theory/De_Broglie_Wavelength
His starting point was to assume E whilst represented by mc^2 could also equal hv which is Planck's constant times velocity. This term operates for light only so examining equation 5 we see that he ended up with essentially h/mv. If we take angular momentum as a stand in for energy and because we have 2 fields in motion we should be able to derive an equation at the Planck scale that equals De Broglie's. This is dependent upon the radius of a particle.
It has to be understood that we are no longer describing the wavelength here. If we are working in natural units the angular momentum will range between 0 and 1. The velocity is forward momentum and so describes the stretch of the wave with time. Hench this formula describes the rate of change in the wavelength.
Now if we go back to
we also have a mass component. If we have Va as our angular momentum we have h/Va*v as the velocity of a wavelength segment which can then be related to the time over which it evolves. As
describes our wave and
relates this to mass and gravity we should be able to combine these. Remember that the mass was the only true variable in
and in the De Broglie equation it is mass we have modified by replacing it with angular momentum.
Since we are only modifying mass all our calculations are done at a set radials distance as mass dereases. This is because Pl never changes. If we take the earth as an example we need to correlate a change between the surface and twice the radius to our fixed radius. We need to see how the mass should decrease to give us the right gravitational field strength. This factor is important to determine. Because we hold the radius fixed we can then model the wave evolution over a spherical surface as described above. This is not meant to reflect the reality of particles but is a device to determine the relationships.
In our left hand term the mass factor relates to the radial distance the wave travels away from the source. This has to be a density change. It is not only related to the density of the source mass but also the gravitational field density at any radial distance. Our factor will be p with p= 1/r1^2 where r1 is the distance away from the source hence we now have
as our first term. The use of radial distance now connects the permittivity/permeability term directly to the wave evolution via the vector r1. The starting point will have r0 (our static radius) equal to r1. As r1 moves away the density is reduced by our term p. This will produce a gradual blue shift and can be related to time dilation via an implicit time on the z-axis. This does NOT describe the evolution of a light wave. Other factors come into play for light.
From now on the model uses linear algebra.
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Last Edit: 03/08/2014 17:33:53 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #21 on:
03/08/2014 17:50:20 »
At this point I need to state one conclusion I have already reached. The magnetic field force carrier should be a symmetry broken photon. It needs a partner particle which I firmly believe is a symmetry broken graviton. We should be thinking in terms of a gravitomagnetic field as well as an electromagnetic one. Now all I have to do is prove it. [8D]
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Re: Lambert's Cosine Law
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Reply #22 on:
03/08/2014 20:36:37 »
The next posts will be concentrating on examining the effects on the partial differentials for E and H in the Maxwell equations.
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Re: Lambert's Cosine Law
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Reply #23 on:
03/08/2014 21:39:59 »
I have changed the first sentence of paragraph 2 of reply #17 from "The diameter of the unit circle is 2*pi" to "The circumference of the unit circle is 2*pi" as the former was in error and was confusing.
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Re: Lambert's Cosine Law
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Reply #24 on:
03/08/2014 22:15:12 »
At this point 3 things about the De Broglie equations should be understood.
Frequency and Energy are directly proportional.
Wavelength and Energy are inversely proportional.
Wavelength and frequency are inversely proportional.
Angular momentum was substituted for energy above so for our model evolving a wave over a spherically rotating and forward moving surface we can say:
Frequency and Angular Momentum are directly proportional.
Wavelength and Angular Momentum are inversely proportional.
Wavelength and frequency are inversely proportional.
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Last Edit: 03/08/2014 22:21:05 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #25 on:
04/08/2014 00:46:53 »
This entry in wikipedia describes the general direction in which I am going.
http://en.wikipedia.org/wiki/Gravitoelectromagnetism
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Re: Lambert's Cosine Law
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Reply #26 on:
04/08/2014 21:55:53 »
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
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Re: Lambert's Cosine Law
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Reply #27 on:
05/08/2014 21:19:55 »
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
of 7/44*360 needs a proportionality factor of its own.
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Last Edit: 05/08/2014 22:43:48 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #28 on:
05/08/2014 23:52:45 »
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.
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Re: Lambert's Cosine Law
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Reply #29 on:
06/08/2014 00:10:33 »
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.
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Re: Lambert's Cosine Law
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Reply #30 on:
06/08/2014 01:47:26 »
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.
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Re: Lambert's Cosine Law
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Reply #31 on:
06/08/2014 19:09:56 »
An interview with Roger Penrose that any serious physicist should read and absorb.
http://discovermagazine.com/2009/sep/06-discover-interview-roger-penrose-says-physics-is-wrong-string-theory-quantum-mechanics
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Re: Lambert's Cosine Law
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Reply #32 on:
07/08/2014 18:39:49 »
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.
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Re: Lambert's Cosine Law
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Reply #33 on:
08/08/2014 19:06:56 »
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.
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Re: Lambert's Cosine Law
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Reply #34 on:
10/08/2014 14:43:53 »
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.
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Re: Lambert's Cosine Law
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Reply #35 on:
10/08/2014 20:47:36 »
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
to become
. 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.
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Re: Lambert's Cosine Law
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Reply #36 on:
10/08/2014 21:09:08 »
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
. We can now state our equations as
. Since we have a range of masses for our denominator (photon mass to Planck mass would be the ideal range) We arrive at
. 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.
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Last Edit: 10/08/2014 22:19:25 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #37 on:
11/08/2014 00:20:13 »
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.
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Re: Lambert's Cosine Law
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Reply #38 on:
11/08/2014 01:43:37 »
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.
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Last Edit: 11/08/2014 01:48:35 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #39 on:
11/08/2014 20:12:01 »
With
being equal to
we can simplify further to
. 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.
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Last Edit: 11/08/2014 20:17:16 by jeffreyH
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