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Lambert's Cosine Law
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Lambert's Cosine Law
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jeffreyH
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Re: Lambert's Cosine Law
«
Reply #140 on:
09/11/2014 01:50:29 »
Ignoring the hbar for now what of our energy equation e
p
=
. What use is it? We if we consider the g factor to be the gravitational acceleration at the surface indicated by the radius r the we can have an external g
e
value. This value will be the g force from an external mass acting upon the local mass in e
p
=
. We can determine the change in e
p
by using
. If g>g
e
then our potential energy is positive. if g<g
e
then our potential energy is negative. What happens when g=g
e
. This is the situation where the fields are said to cancel. This is equivalent to reducing the potential energy by cancelling g in the equation. So that zero gravity situations will decrease potential energy. Where does it go? Usually we would think of this as becoming kinetic energy. This is one puzzle whose solution will ease our way into a theory of quantum gravity.
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Re: Lambert's Cosine Law
«
Reply #141 on:
09/11/2014 02:49:09 »
Because we have a cancellation of g our kinetic energy must be internal. This indicates a low point in time dilation. So that within a hollow cavity at the centre of a mass time dilation will be at its lowest. Since all the forces of the outer mass cancel then the only g force present is that of any particle at the centre of the cavity. This bears out the theory that an event horizon must start at the centre of mass and work its way outwards. This also indicates that composite particles should merge in order for the cancellation to operate outward. If the particles were still individual then a full cancellation would not apply for all particles. Only a unit mass with a single gravitational force can cause such an inward collapse.
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Re: Lambert's Cosine Law
«
Reply #142 on:
09/11/2014 04:05:12 »
Having sat and thought about this the equation
is not valid at all. While the situation in a hollow cavity would still apply this subtraction of the external value of g
e
in the above is incorrect.
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Re: Lambert's Cosine Law
«
Reply #143 on:
09/11/2014 23:11:38 »
The equation for Planck energy is SQRT([hbar*c^5]/G). This can be derived from the above as [g*h]/[pi*L]. This dispenses with the square root and the gravitational constant and returns the value in joules. Importantly the Schwarzschild radius of the Planck mass is inherent in the equation and so can be rearranged to find g. Our value for g is then 2.77943185E+51. This accelerates mass to superluminal velocities according to this result but does it. Not if we take length contraction into account. The speed of light is never actually violated. Therefore length contraction must exist. This also implies that kinetic energy has a different relationship to gravity than has been thought previously. When moving through a length contracted frame the locally viewed acceleration will appear faster than is apparent to an observer in a remote frame. This will only be noticeable near to a dense massive object with an intense gravitational field. Solving Einstein's field equations in this situation becomes a real challenge. Do we even need to?
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Re: Lambert's Cosine Law
«
Reply #144 on:
10/11/2014 00:29:00 »
The g force works out to be very approximately pi*c^6. What significance this has I have no idea. Except that it must relate to length contraction in intense gravitational fields.
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Re: Lambert's Cosine Law
«
Reply #145 on:
10/11/2014 01:17:47 »
A while ago I came across the work of Paul Marmet. The significance of his work has only become apparent to me very recently. He was an opponent of general relativity so was largely ignored by the mainstream. I hope to vindicate him not by proving general relativity wrong but by modifying it.
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Re: Lambert's Cosine Law
«
Reply #146 on:
14/11/2014 07:54:28 »
I have copied two of my posts from other threads.
1) I don't want to do that. I want an equation of the form
in three dimensions. Here energy is not simple to describe. The components of mass, potential and kinetic energy interact with the gravitational field.
2) If we take the centre of gravity of a perfect sphere and have a plane running through it. We can then define x, y and z axes tilted so each is axis has the same angle to the plane. If we then set a path that when projected onto the intersection of pairs of axes is at 45 degrees all axes that describe the path perpendicular to the plane then change at the same rate. As a baseline for mapping the effects of rates of change this can map a straight line path. This can then be adapted for curved trajectories. Extending this path out to an imaginary spherical surface the mass within the surface can be defined to be of any size with a radius of choice. Comparisons are then easy to make against the baseline straight path. It would be interesting to see what effects we could model on the interchange of energy under various conditions. To include the electric, magnetic and gravitational fields. With an equivalent value for rate of change at equidistant points the effects on energy of multi-mass systems would be fairly straightforward. Just an idea.
Taken together these two ideas can ultimately produce equations of the type derived by Maxwell for the gravitational field. Very early in this thread a gravitational component replaced the permittivity/permeability factor in one of Maxwell's equations.
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Re: Lambert's Cosine Law
«
Reply #147 on:
18/11/2014 23:47:00 »
Just as g can be shown to be an intrinsic part of a mass equation can we include a factor describing the de Broglie wave equation itself? If so maybe then we can show exactly how particles behave in a changing gravitational field.
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Re: Lambert's Cosine Law
«
Reply #148 on:
28/11/2014 23:24:03 »
E
0
= m
0
c^2 relates rest energy to invariant rest mass. We have derived e
p
=
for potential energy. What if we rearrange like this? e
p
/g =
. Here g is the gravitational acceleration AT THE SURFACE of a mass. It cannot be anywhere else. Here g is an acceleration in square seconds, c^2 is a squared velocity. WE can say that e
p
/g = e
x
where we do not know what x represents. We know it must represent a reduced mass and therefore a reduced energy but cannot be separated from the mass from which it was derived. However a change in the dimension of the radius of the mass will change the inherent value of g at its surface. This also means a change in density. If the radius increases so g decreases and the reduced mass value is larger. If the radius decreases then the value of the reduced mass gets smaller. So therefore the proportion of mass that is involved directly in the gravitational force then increases as is shown by other gravitational equations indirectly. This shows directly how density varies the gravitational force via a redistribution in the balance of mass involved in gravitational interactions.
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Re: Lambert's Cosine Law
«
Reply #149 on:
28/11/2014 23:27:55 »
The only 2 values that appear to change in the above equation are mass radius and g at the surface. Here lies the first problem. How do we decide on the radius of a particle? It isn't like a beach ball. In fact how do we really know what it is like or how it is distributed. The only way we can proceed now is via the wave equation that is well defined and experimentally verifiable. Can it be done? At this point I don't know.
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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 e
0
/g can be said to be similar to e
0
/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.
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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.
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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.
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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.
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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.
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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?
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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.
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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.
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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
»
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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.
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