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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 #40 on:
11/08/2014 23:51:57 »
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.
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Re: Lambert's Cosine Law
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Reply #41 on:
12/08/2014 06:54:06 »
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.
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Last Edit: 12/08/2014 06:59:31 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #42 on:
16/08/2014 13:26:12 »
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.
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Re: Lambert's Cosine Law
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Reply #43 on:
16/08/2014 13:30:22 »
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.
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Last Edit: 16/08/2014 13:35:49 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #44 on:
16/08/2014 13:52:10 »
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?
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Re: Lambert's Cosine Law
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Reply #45 on:
17/08/2014 12:50:49 »
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.
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Re: Lambert's Cosine Law
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Reply #46 on:
17/08/2014 14:08:43 »
Attached is an image of the curvature inherent in the graviton with more realistic frequency values.
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Re: Lambert's Cosine Law
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Reply #47 on:
17/08/2014 14:29:54 »
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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Re: Lambert's Cosine Law
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Reply #48 on:
22/08/2014 00:56:16 »
It may be that the process of photon absorption may be due to wave inter-locking. When both interacting waves are in the right phase this process can happen. When the phases are not aligned we have reflection or refraction. For materials like glass the structure of the medium is important and generally causes a refraction with a precise angle. In wave interlocking the photon would not so much be absorbed as add momentum to the electron and deflect its path to a higher orbital until re-emitted when the waves disengage. This then gets round the problem of Planck length/Planck time and the photon/electron momentum problem at the Planck scale.
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Re: Lambert's Cosine Law
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Reply #49 on:
22/08/2014 23:16:29 »
Wave interlocking can be thought of like the table cloth trick where crockery remains in place if the cloth is removed fast enough. However if this is the actual mechanism of photon absorption then it makes describing the interaction of the graviton much harder to derive. The waveform of the gravitational field must be very strange indeed.
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Re: Lambert's Cosine Law
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Reply #50 on:
24/08/2014 16:13:51 »
The first derivative of g = GM/r^2 is 2GM/r^3 which describes the change in acceleration or jerk. The Schwarzschild metric has 2GM/c^2 and the right hand factor of our wave function has
. The right hand term can be rewritten as
where r is distance of the wave from the source of gravitation. Before getting back to Lambert's Cosine Law it will be necessary to investigate Coulomb's Law with respect to the previous equations. This may seem like a very strange path to take, which it in fact is, but I want to determine certain relationships before proceeding.
A correction to the above.
should be
.
«
Last Edit: 25/08/2014 19:57:25 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #51 on:
25/08/2014 20:08:31 »
Light is affected by gravity which experiment shows is true. A photon leaving a gravitational field is slowed. Where then does the energy come from to restore the loss of kinetic energy whilst leaving the gravitational field? The photon will gain momentum due to the fall off of gravitational effect due to the inverse square nature. Can it be only the fall in gravitational strength that is the cause? Or is it the relationship between forward and angular momentum which is redistributed according to a law of nature? We say this is the conservation of energy. Then energy IS momentum. Conservation of energy thus means conservation of momentum which again suggests quantization of momentum.
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Re: Lambert's Cosine Law
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Reply #52 on:
25/08/2014 23:15:17 »
Attached is a graph of the gravitomagnetic wave of the graviton. Both positive and negative energies are presented. Maxwell's concern about negative energies can be overcome if momentum and energy are considered equivalent. The positive and negative energies are then due to opposing spin in a two component particle. The positive and negative elements cause attraction with both positively and negatively charged particles. This double opposing spin also indicates that the graviton cannot be polarised, unlike the photon. This plot is slightly reminiscent of the amplituhedron. I say slightly as it cannot be said that they are equivalent in any way.
The positive portion of the wave exhibits the loop back inherent in the magnetic field. The positive portion has an altogether different profile.
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Re: Lambert's Cosine Law
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Reply #53 on:
27/08/2014 02:07:30 »
I have come to a conclusion driven by the mathematics that I didn't expect. I had assumed that for any black hole the point at which escape velocity reaches c would be at a greater radius than the point where g equals c. This was not the case. Perpendicular motion, if my math is correct, is overcome before the event horizon is reached. I do need to check this but if correct then any photon is doomed before it actually reaches the event horizon. I am still skeptical about this result as it means black holes should consume mass more aggressively than expected. This is not what happened to the G2 gas cloud.
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Re: Lambert's Cosine Law
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Reply #54 on:
06/09/2014 14:56:10 »
One point to note for anyone even remotely interested in reading this thread. I am breaking mathematical notation in ways that physicists would consider invalid. Don't try this at home because you can't determine why.
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Re: Lambert's Cosine Law
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Reply #55 on:
09/09/2014 22:49:30 »
The reason why there may be a region at a point outside the event horizon that seals a particles fate may be because magnetic field lines first fall beyond the event horizon making it a sink for the field. To maintain the circulation of the field the particle would be doomed to enter the horizon once the field line is trapped.
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Re: Lambert's Cosine Law
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Reply #56 on:
10/09/2014 00:54:45 »
For the first time I have been able to plot the profile of acceleration toward light speed taking gravitational self interaction into account. The plot is attached and shows the view from a frame external to the acceleration. This SOLVES the infinite mass problem due to the time dilation effects. The external observer would initially see the object accelerate and then appear to slow down and become fainter. This is similar to the effects when approaching an event horizon.
NOTE: This profile suggests an intensifying gravity well around the accelerating object.
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Last Edit: 10/09/2014 01:03:24 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #57 on:
10/09/2014 01:17:34 »
This could mean that during the early stages of the universe some black holes were formed during the inflationary period when velocities were much higher and not simply due to collapse. These would be the so called primordial black holes. This would also explain the apparent slow down after the inflationary period. The other strange thing when viewing the plot is that it suggests that things appear to be accelerating away precisely because we are slowing down and the time dilation and length contraction are now reversing.
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Last Edit: 10/09/2014 01:30:02 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #58 on:
11/09/2014 02:09:12 »
Counter to what I stated previously the universe has not actually left its inflationary phase. This is a consequence of gravitation. The gravitational field evolves away from the source into an expanding spacetime. The energy of the field occupies a compressed space near to the source. Gravitation therefore cannot itself be affected by dilation or contraction. The consequence has to be that its propagation is superluminal until it reaches infinity where it will equal the speed of the photon. A consequence of this is that the gravitational field can in fact radiate out of a black hole.
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Last Edit: 11/09/2014 02:10:49 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #59 on:
11/09/2014 02:13:49 »
Another consequence of this is that it must be mass itself that compresses the spacetime and not gravitation. The operation of gravity merely accumulates the mass in the first place. I can currently think of no way that gravitational force can be carried by a boson with such properties. It may be a consequence of the spin 2 nature but how I don't know.
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Last Edit: 11/09/2014 02:17:54 by jeffreyH
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