# The Naked Scientists Forum

### Author Topic: Lambert's Cosine Law  (Read 48823 times)

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #150 on: 29/11/2014 00:01:10 »
What happens when the value of g = c^2? Then e0/g can be said to be similar to e0/c^2. However it is not an equality. It is an artificial modification. The gravitational acceleration becomes superluminal for a start. The points of interest are the resulting reduced mass term and the mass radius.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #151 on: 29/11/2014 19:27:13 »
The basic problem with the mass and energy equations derived in this thread are their application. They can tell us nothing significant about the particle since the radius is uncertain and variations of mass/energy at that scale are too small to investigate. In the case of a macroscopic mass the equations neglect the nature of the mass as individual particles within molecules which combined together have individual interactions that would invalidate results. This is why the derivation of an equation with an intrinsic wave component is one of the only ways to proceed.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #152 on: 30/11/2014 13:36:30 »
Can we incorporate the wave into the mass equation? Let's start with two equations. The first for kinetic energy and the second for the wavelength itself.

Here KE is kinetic energy, m is the mass and v its velocity.

KE = (1/2)mv^2

For the wave equation we have:

f = h/p

Where f is the frequency, h is Planck's constant and p is momentum. To incorporate kinetic energy into the equation the following steps are required.

KE = (1/2) mv^2

2KE = mv^2

2KEm = m^2v^2

2KEm = (mv)^2

Since momentum equals mv we can derive momentum to include kinetic energy using SQRT(2KEm). Then for the wavelength we have:

f = h/SQRT(2KEm)

We can never have zero kinetic energy because we always have zero point energy. Therefore KE has to be intrinsic to mass which means mass always has momentum. Only  for purposes of mathematical derivation can we use rest mass. Since mv would require velocity to be a numerator we would be multiplying velocity with hbar so no we cannot incorporate the wave equation into a mass equation. The same can be said for the energy equation. This indicates that the wave is merely an effect of the motion of the particle through space. Either in a straight line path or via angular momentum. From this we can reach the conclusion that because the wave is not intrinsic it can be directly affected by the gravitational field. Since the gravitational field will affect trajectory.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #153 on: 30/11/2014 18:03:13 »
Now in a previous post we did see how a wave can be affected by gravitation. The plot is shown again here. This was arrived at by examining Maxwell's equations. It is not a verified equation by any means. What it does attempt to show is the shift in wavelength as a particle moves outward from gravitational field source. As a starting point this needs to be re-examined rigourously.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #154 on: 30/11/2014 18:10:25 »
What the above plot does bring to mind are the discrete energy levels and integer wavelengths of the electron orbitals.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #155 on: 30/11/2014 18:25:39 »
We can develop a 3 particle model to show gravitational interactions as vectors. We have to use 3 since we can describe a plane that all the particles line up with at any point in the evolution of the interactions. Any more particles cannot be assumed to sit on this moving plane. The inherent values of g for each particle can then be described as vectors in the system as it changes over time. Determining how each wave evolves during the interactions will be of interest. Exactly how do they behave?

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #156 on: 03/12/2014 03:03:02 »
A correction to one of the posts above. In the equation f = h/SQRT(2KEm) of course f is wrong as it is the frequency and not the wavelength. In case I confused everybody. It should be λ = h/SQRT(2KEm). If we hold mass as invariant then the kinetic energy determines a change in the wavelength. Since gravitation alters the kinetic energy this can be used to describe the effects of gravitation on the wave. More on this later.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #157 on: 04/12/2014 03:12:00 »
The Kaluza-Klein theory is described here:

http://en.wikipedia.org/wiki/Kaluza–Klein_theory

This is a scalar theory of gravitation. Interestingly from here:

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

We find that:

"Kaluza–Klein theory involves the use of a scalar gravitational field in addition to the electromagnetic field potential  in an attempt to create a five-dimensional unification of gravity and electromagnetism. Its generalization with a 5th variable component of the metric that leads to a variable gravitational constant was first given by Pascual Jordan."

The fact that this leads to a variable gravitational constant is of interest. Only one of the papers appears to have a translation. This theory has some interesting consequences and should be pursued vigorously in my opinion. I will be investigating this in conjunction with the work shown in this thread.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #158 on: 04/12/2014 03:28:37 »
For reasons I will explain when I have worked out the proof, mass can exceed light speed but only when approaching an event horizon. Within a defined region surrounding the horizon nothing will be visible. It is not that things disappear once the horizon is crossed. They will vanish BEFORE the horizon is reached. The innermost point of an accretion disk will mark the extent of the outer visible area. X-ray sources must then emanate from this region as they would not escape the region beyond this.

NOTE: It MAY be possible to achieve superluminal interstellar velocities but only if it is possible to shield against gravitation. This has to be considered with caution since it relies on propositions that are entirely without proof.
« Last Edit: 04/12/2014 03:37:18 by jeffreyH »

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #159 on: 04/12/2014 22:17:12 »
I have discovered a relationship in the gravitational field density. This is shown in the attached graph. I will not be showing how this was derived at the moment as this has far reaching consequences if correct. I will be developing a set of equations around this initial equation.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« 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..

#### jeffreyH

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##### Re: Lambert's Cosine Law
« 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.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« 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.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« 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.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« 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.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« 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.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« 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.
« Last Edit: 09/12/2014 02:10:30 by jeffreyH »

#### jeffreyH

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##### Re: Lambert's Cosine Law
« 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.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« 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?
« Last Edit: 13/12/2014 15:41:05 by jeffreyH »

#### jeffreyH

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##### Re: Lambert's Cosine Law
« 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.
« Last Edit: 20/12/2014 17:02:17 by jeffreyH »

#### jeffreyH

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##### Re: Lambert's Cosine Law
« 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.
« Last Edit: 21/12/2014 15:48:29 by jeffreyH »

#### jeffreyH

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##### Re: Lambert's Cosine Law
« 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.
« Last Edit: 22/12/2014 23:55:13 by jeffreyH »

#### jeffreyH

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##### Re: Lambert's Cosine Law
« 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.
« Last Edit: 23/12/2014 00:52:34 by jeffreyH »

#### jeffreyH

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##### Re: Lambert's Cosine Law
« 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.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« 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
« Reply #174 on: 23/12/2014 16:46:22 »