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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 #160 on:
04/12/2014 22:59:21 »
Contrary to what I may have posted earlier in this thread the gravitational field in fact does lose energy but the equation describing the rate of change is not a simple relationship. More energy is lost nearer the source than further away. In fact the field later regains some of the lost energy from somewhere. This is puzzling. Gravity well is an understatement of the situation. I can now derive the density variations outside the event horizon and the 'no light zone' before the start of the accretion disk..
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Re: Lambert's Cosine Law
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Reply #161 on:
04/12/2014 23:01:57 »
If we consider the energy of the gravitational field as negative then this implies the field is becoming more positive as it moves away from the source. This does not mean that it will ever become a repulsive field but may explain the accumulation of dark energy due to energy conservation.
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Re: Lambert's Cosine Law
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Reply #162 on:
04/12/2014 23:39:28 »
The possibility of gravity giving rise to the dark matter/energy halos comes from the profile of energy loss. Starting low then reaching a peak and dying away again. This would produce such a halo effect with most of the dark material concentrated at the peak of energy loss. The dark matter/energy produced would be even weaker than the gravitational energy and would accumulate over time. A galaxy that has had the material stripped by an encounter with another galaxy could over time re-acquire its halo due to future energy loss from the gravitational field of the central black hole. These anomalies may be detectable and it may be fruitful to find such galaxies.
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Re: Lambert's Cosine Law
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Reply #163 on:
05/12/2014 22:51:30 »
One consequence of the above hypothesis is that the electromagnetic field will lose energy in the same proportions as the gravitational field. This does not apply to the magnetic field itself which loses no energy. This makes sense as it circulates and would be unable to sustain circulation if energy was lost. So the electric portion of the field and the
possibly
photon itself lose this energy the further from the source the position of the field or particle is. I say possibly in the case of the photon as I just don't know for sure.
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Re: Lambert's Cosine Law
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Reply #164 on:
05/12/2014 23:48:31 »
Gravitational lensing should be more pronounced at a set radial distance from the mass generating the gravitational field. This will be within the halo region around the mass at a set radial distance from its surface.
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Re: Lambert's Cosine Law
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Reply #165 on:
06/12/2014 00:16:31 »
The other thing all this finally establishes in my opinion is that gravity does in fact travel at exactly light speed and itself undergoes dilation due to its interactions with the electromagnetic field. They affect each other proportionally. Like the charge of the proton and electron being the same while the mass differs the electromagnetic and gravitational field affect each other proportionally even though their energies are not equivalent. I have no idea how this works.
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Re: Lambert's Cosine Law
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Reply #166 on:
09/12/2014 02:00:45 »
Finally we come to our equation for the wave. If we rearrange the mass equation to be M =
we now have a time dilation component implicit to the function. This includes the velocity of the mass. Applying
to the inverse light speed t/L also relates to the dilation of the photon in a gravitational field. However this form is concerned with velocity alone. Interestingly the square of the radius and the surface value of g also increase. This echoes the thinking of Paul Marmet that the Bohr radius must increase with velocity. The next step is to test the equation for the results it will produce to see if in fact it does reflect the real world experimental data.
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Last Edit: 09/12/2014 02:10:30 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #167 on:
10/12/2014 17:40:25 »
The mass dilation equation has some of the fundamental constants incorporated into it. It would be interesting, although maybe not very informative in its present state, to try values at the Planck scale for radius and g. This can be done using the variation derived for the Planck mass black hole. Using this a fixed reference point can be set at the event horizon.
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Re: Lambert's Cosine Law
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Reply #168 on:
13/12/2014 15:37:07 »
I have found an interesting papaer which may be of interest. I haven't read it yet. It is from December 2011 so is only 3 years old. The title is "Where is hbar Hiding in Entropic Gravity?". This is to do with the proposal of entropic gravity by Erik Verlinde which I also haven't reviewed. This is apparently a classical Newtonian gravity theory with origins in quantum mechanics. The link is:
http://arxiv.org/abs/1112.3078
Just a note from me. Is hbar hiding in the definition of mass as above?
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Last Edit: 13/12/2014 15:41:05 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #169 on:
20/12/2014 16:59:19 »
One concrete proposal has come out of these investigations which I will need to provide the equations for eventually. For a black hole with the mass of the earth with rs set at around 1cm there is a special region which extends outward radially to a distance of 815.4 metres (Approx.).I am not entirely sure if light would be trapped within this zone, probably not. However any other tardyon mass WILL be trapped within this zone. So therefore the event horizon is not the danger zone for the possibility of escape. This already occurs further out. This may in effect prevent the measurement of the mass of black holes with any accuracy.
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Last Edit: 20/12/2014 17:02:17 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #170 on:
21/12/2014 15:41:45 »
The results above had led onto an equation that includes one function for angular momentum and another for specific area. I am not sure what the specific area indicates as it is only indirectly related to specific volume. These equations when viewed with respect to the earlier equations in this thread should provide some new insights on the interaction of mass with gravity. I am working on this now and will post the details when the equations are complete.
EDIT: If a function of angular momentum can be used in the mass equation then this will allow the evolution of the wave due to gravitation to be an inherent property of mass. This may also become a way of describing the action of time dilation.
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Last Edit: 21/12/2014 15:48:29 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #171 on:
22/12/2014 18:22:34 »
In the equation below we can determine the distance traveled during an amount of time t when the gravitational acceleration equals g.
Δy = 1/2*g*t^2
If we then set g to equal
g = 2L/t^2
we can show that in one second due to cancellation of the following
1/2*2L/t^2*t^2
That we will have traveled L distance in one second. Since L is equal to 1 light second of distance this means that we will have reached light speed during this acceleration. Applying this to the parameter for earth gives us an exclusion zone around an earth sized black hole. This is the first step in deriving our new mass equation.
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Last Edit: 22/12/2014 23:55:13 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #172 on:
23/12/2014 00:04:27 »
If we set g = 2L/t*dt we have
2L/t^2 = Gm/r^2
Re-arranging for r
r = SQRT(t*dtGm/2L)
If r = L then
L^2 = t*dtGm/2L
Re-arranging for m
m = 2*L^3/t*dt*G
Setting G equal to the approximation 1/50c
m = 2*L^3/t*dt*50*L/t
Restoring c
m = 100c*L^3/t*dt
And finally re-arranging
Volumetric acceleration
m/100c = L^3/t*dt
Cumec for volumetric flow is in the units m^3/s so here we have the potential volumetric acceleration of gravitation for the whole mass. We need to reconcile this with g at the surface that will be the next step.
The above is equivalent to the following simply formula.
Gm/2
Here the factor of 2 appears again. So if we let a equal this volumetric acceleration we arrive at:
a = Gm/2
EDIT: To cater for length contraction in 1 spatial dimension we would modify the equation thus:
m/100c = L^2*dL/t*dt
Now we can cater for the effects of both relativistic changes with respect to the potential volumetric acceleration.
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Last Edit: 23/12/2014 00:52:34 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #173 on:
23/12/2014 01:09:56 »
The difficulty of reconciling gravitational acceleration with volumetric acceleration lies in the fact that while the first follows a linear geodesic the second represents an infinite number of radial directions in 3 dimensional space. These all emanate from the centre of gravity.
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Re: Lambert's Cosine Law
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Reply #174 on:
23/12/2014 16:46:22 »
So how to reconcile this. Well we saw that y = 1/2gt^2. If we re-express a = Gm/2 as a = Gm/(2r^2) we find the equivalent acceleration for the length y during a 1 second interval. What needs to be determined now is how an expression for angular momentum can be achieved.
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Re: Lambert's Cosine Law
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Reply #175 on:
27/12/2014 02:03:59 »
For a general wave equation we can show the following progression:
m = g*r^2*h*1/(2pi)*(1/c^2)*[1/lP^2*(gamma*t)/L]
P^2 = 2*Ke*g*r^2*h*1/(2pi)*(1/c^2)*[1/lP^2*(gamma*t)/L]
λ = h/SQRT(Ke*g*r^2*h*1/pi*(1/c^2)*[1/lP^2*(gamma*t)/L])
In the final wave equation the velocity v should be considered the only variable. It is a component of both Ke and gamma. Since we have components such as c^2, h and the Planck length squared it would be interesting to review equations containing these combinations to see if this gives us an insight into gravitation, mass and quantum mechanics.
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Re: Lambert's Cosine Law
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Reply #176 on:
27/12/2014 03:17:29 »
As a starting point for an angular momentum formula we need to review the following.
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/qangm.html
Another useful reference is on wikipedia.
http://en.wikipedia.org/wiki/Azimuthal_quantum_number
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Last Edit: 27/12/2014 03:52:56 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #177 on:
28/12/2014 18:15:30 »
To develop our equation of angular momentum we must first review an earlier post.
"Before trying to link the gravitational field to Lambert's Cosine Law I need to take a detour. This starts with the unit sphere and the unit circle. Using the unit sphere and circle shows some interesting relationships and can be scaled up. This can then be used to describe both subatomic and macroscopic domains.
The circumference of the unit circle is 2*pi. To determine the angle of an arc around the circle whose arc length is equal to the radius we can use (1/2*pi)*360 which can be simplified to 7/44*360. This proportionality will become important when viewing interactions at differing scales and relates to wave frequency, length contraction and time dilation effects. The angle we have determined can be converted to radians to use in calculations.
It is interesting to note that the period of sin x is 2*pi. This can be utilized by considering forward motion and angular rotation as it relates to the unit sphere. The relationship between these two properties can describe the evolution of a wave and can be related directly to the gravitational field. When used it can be shown to show the underlying mechanism of the Pauli Exclusion Principle and the difference in energy levels required between electrons.
There are 3 directions of motion under consideration within this model. One motion is forward direction and is considered to be aligned with the poles of the sphere. The two other directions are angular. The first is around the equator and the second follows a longitudinal path intersecting both poles. The maximum unit of motion in unit time in the polar direction is equal to the unit sphere radius. The maximum unit of motion of the angular paths is 7/44*360 as stated above. If viewed at the Planck scale the angular components cannot reach this speed or none of us would be here. Therefore we can deduce that this dampening in angular momentum must be due to gravity which is what the current physical theories state.
If we follow this line of thinking through to its conclusion we can show that when considering the universe as a whole system light might get infinitesimally near to c but will never actually reach it as long as any gravitational field remains. I will demonstrate the reasons for this conclusion as I proceed."
The angle derived above becomes important only when the radius of an object is 1 Planck length. As this will only apply in some string theories we can disregard it. Not only because it relates to string theory but it relates to light speed which angular momentum should never reach. This will be discussed later.
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Last Edit: 28/12/2014 18:27:59 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #178 on:
29/12/2014 15:48:42 »
In examining angular momentum it is not sensible to have Planck units. The best units to select would be nanometres and nanoseconds. Thus the speed of light can be represented by L*1 nanometre divided by 1 nanosecond. We can then apply a factor to L to determine a non-relativistic speed. Now we may have a problem as the angular momentum of a particle is L = r x mv. The two values for L, 1 light second versus L for angular momentum mus NOT be confused. L = r x mv is the cross product mv the linear momentum and r which is the point of rotation. This is best illustrated in the animation on wikipedia.
http://en.wikipedia.org/wiki/Angular_momentum
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Last Edit: 31/12/2014 14:40:53 by jeffreyH
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Re: Lambert's Cosine Law
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Reply #179 on:
01/01/2015 00:12:17 »
I have decided to temporarily suspend posts to this thread until I have reviewed the following.
http://phys.org/news/2013-11-proton-radius-puzzle-quantum-gravity.html
http://arxiv.org/abs/1412.4515
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