# The Naked Scientists Forum

### Author Topic: Lambert's Cosine Law  (Read 48406 times)

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #125 on: 31/10/2014 00:34:14 »
So we end up with M = -1. Looking at it this way the g force is inherent in the mass with gravity as the catalyst.
« Last Edit: 31/10/2014 00:40:45 by jeffreyH »

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #126 on: 31/10/2014 01:19:17 »
Finally we can rearrange as M = g-1. So now we only need modify g and r to find the mass contained within a radius that will produce a particular g force. We can attempt to apply this to a particle or to a black hole. There is a direct relationship to density inherent in the equation. This neglects time dilation and length contraction but it is straightforward to modify to take these into account. However the complexities rises with four independent variables.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #127 on: 31/10/2014 01:51:26 »
Our mass equation can then be substituted into the momentum equation p = √(2Em) where L/t does matter as this has an effect due to both time dilation and length contraction. It can also be a way of showing the effects on kinetic energy. We have to be careful in the application of this formula as it is the mass energy that changes in order to have an effect on the kinetic energy. Which is the wrong way round. Unless we consider it a change in flux rate.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #128 on: 31/10/2014 20:59:58 »
I think that gravity as a catalyst is unworkable for a variety of reasons.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #129 on: 01/11/2014 01:36:43 »
To get energy Mc^2 we arrive at -1. Which we can rearrange as Mc^2 = -1. The deBroglie wavelength being h/p we should be able to use these equations to model the effect of gravity on particle waveforms. For momentum we get p = √(2kEg/c^2[{lP^2/r^2}{L/hbar}]^-1).
« Last Edit: 01/11/2014 01:44:49 by jeffreyH »

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #130 on: 01/11/2014 03:18:47 »
Having the Planck area lP^2 in the equation is of interest.

http://en.wikipedia.org/wiki/Planck_length
"The Planck area, equal to the square of the Planck length, plays a role in black hole entropy. The value of this entropy, in units of the Boltzmann constant, is known to be given by A/4lP^2, where A is the area of the event horizon. The Planck area is the area by which a spherical black hole increases when the black hole swallows one bit of information, as was proven by Jacob Bekenstein."

The term lP^2/r^2 can therefore link our mass-energy to a density function that relates to the horizon black hole.

"In doubly special relativity, the Planck length is observer-invariant."
So is length contraction valid or are space and time separate.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #131 on: 02/11/2014 15:11:30 »
Upon reading further there are serious problems with double special relativity so I am going to ignore it for now. The energy equation is important as it relates energy to gravitation rather than mass. As the photon is massless this is the only way we can use the equation with the photon wave equation. I will be looking at Pete's relativistic mass page soon to see how it can all be combined.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #132 on: 04/11/2014 23:08:29 »
We can finally rearrange the mass equation from M = g-1 to M = g to remove the reciprocal with units of joule second^2 metres^-2.

Correction the units are joule second metres^-2. And of course 1 (joule second) per (square metre) = 1 kg / s
« Last Edit: 04/11/2014 23:39:19 by jeffreyH »

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #133 on: 05/11/2014 00:06:09 »
So now if we multiply this mass value by 1 second we get our kg value. Since our 1 second value relates to light speed. As time dilation increases our time value increases. Multiplying by the new value gives our increase in mass due to time dilation and increasing velocity.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #134 on: 05/11/2014 01:45:09 »
This of course gives us mass flow rate A.K.A mass flux. This is usually used in fluid dynamics although there is no reason not to use it in other ways.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #135 on: 06/11/2014 00:30:03 »
The mass equation M = g can be rearranged in the same way the energy equation was to become M = g. The term gives us the number of Planck squares in our radial square area and therefore reduces the magnitude to a scalar Planck multiplier. If the value of r were 2lP this would equal the rs value of the event horizon of a Planck mass black hole. The scalar value then becomes 2. Interestingly this is the factor in the rs equation 2GM/c^2. To derive the Planck mass value from this expression would simply require finding the corresponding value for g.
« Last Edit: 06/11/2014 00:36:51 by jeffreyH »

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #136 on: 06/11/2014 00:43:24 »
To hold r at 2lP and simply increase g is the same as increasing mass within a set volume. Therefore increasing density. When we get to the point where instantaneous acceleration equals the speed of light we will have found a value of great interest. This will be the point of no return at which a singularity is inevitable.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #137 on: 08/11/2014 23:07:00 »
We have kinetic energy ek = and potential energy ep = -. These equations balance as energy is converted from potential to kinetic and visa versa. What is not taken into account here is the effect of time dilation due to a changing gravitational field. The derived equations above can however take this into account. Using energy instead of mass in these equations is the only way to proceed when dealing with massive or massless particles.
To verify length contraction an effect upon kinetic energy must be present. This must be equivalent to a loss of energy when viewed from a remote frame. I intend to show that there is no such effect upon the overall kinetic energy of an object moving through a gravitational field. As the kinetic energy reduces there is an equal amount of increase in the potential energy. This can be thought of as the kinetic energy being negative and the potential energy as positive. Kinetic energy becomes positive only when approaching a mass through its gravitational field. Which is why no force is felt. When accelerating outside of a significant gravitational field, a mass carries with it its own gravitational field and so does feel a force as it cannot be moving through its own field. Its kinetic energy is inherently negative.
« Last Edit: 08/11/2014 23:22:50 by jeffreyH »

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #138 on: 09/11/2014 00:20:54 »
So we arrive at ep = . We now need the same form for ek. Here we have m^2 s^-2 but with hbar having joule second units which signify angular momentum. So how do we square this with a kg unit?
« Last Edit: 09/11/2014 01:14:39 by jeffreyH »

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #139 on: 09/11/2014 01:34:42 »
Well one answer from yahoo is:

"Do you really mean m^2/s^2 and not m/s^2, which is just acceleration.

But m^2/s^2 could mean many things. For example, during the recent nuclear disaster in Japan, the radiation dose rate received by workers and citizens was measured in Seiverts/hour. The unit of dose, the Seivert has the dimension m^2/s^2, which is equivalent to Joules (energy) per kg:

Example: Energy(Joules) = force x distance (Nm) = mass x acceleration x distance (kg m^2/s^2)
Energy per mass = Dose (Seivert) = mass x acceleration x distance / mass (m^2/s^2)"

So this could be thought of as energy per mass. What of the hbar in our denominator in joule seconds?

#### 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 ep = . 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 ge value. This value will be the g force from an external mass acting upon the local mass in ep = . We can determine the change in ep by using . If g>ge then our potential energy is positive. if g<ge then our potential energy is negative. What happens when g=ge. 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.

#### jeffreyH

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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.

#### jeffreyH

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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 ge in the above is incorrect.

#### jeffreyH

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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?

#### jeffreyH

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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.

#### jeffreyH

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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.

#### jeffreyH

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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.

#### jeffreyH

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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.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #148 on: 28/11/2014 23:24:03 »
E0 = m0c^2 relates rest energy to invariant rest mass. We have derived ep = for potential energy. What if we rearrange like this? ep/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 ep/g = ex 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.

#### jeffreyH

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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 #149 on: 28/11/2014 23:27:55 »