# The Naked Scientists Forum

### Author Topic: Lambert's Cosine Law  (Read 48585 times)

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #100 on: 16/10/2014 04:30:18 »
One thing that comes out of this is that the radial distance from a source will be affected by length contraction which is not catered for in gravitational calculations such as that for g or escape velocity. For a distant observer this would be important but not an observer local to the frame that the radius refers to. The factor of 50 must vary as the radius varies so any function to adjust for change in apparent length must operate on this factor as well as the radius. This could be one way of integrating gravity with quantum mechanics.

Note: To achieve the integration the starting point to choose would be the imaginary surface of the event horizon where a fixed value exists.
« Last Edit: 16/10/2014 04:34:06 by jeffreyH »

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #101 on: 16/10/2014 04:58:34 »
I have checked the equation (hbar*M)/(lP^2*c^2*L*r^2) and it was a terrible guesstimate. I will go over it again to find out where I went wrong.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #102 on: 16/10/2014 23:01:59 »
Right. L = the distance a photon travels in 1 second. c = the speed of light. lP = the Planck length. hbar is the reduced Planck constant. Our factor of 1 is then [50*L*c^3*lP^2]/hbar. This I have checked and it is near as damn it to 1. So this factor is then applied to M/[50*L*r^2] which is our calculation for g (gravitational acceleration).
« Last Edit: 16/10/2014 23:04:56 by jeffreyH »

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #103 on: 16/10/2014 23:24:30 »
That then gives us [M*c^3*lP^2]/[hbar*r^2] for our gravitational acceleration. What the units are I have no clue so any help would be appreciated. It may be totally invalid.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #104 on: 16/10/2014 23:50:34 »
Since the factor of 50 has canceled what we can say now is there is no energy loss. This means that it is the field density alone that affects its strength. So as in the case of the electromagnetic field the gravitational field must have a force carrier. This will be the spin 2 boson.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #105 on: 18/10/2014 09:23:19 »
Taking 2 candidate galaxies and their central supermassive black holes it should be possible to calculate a time dilation gradient between them. The unknowns are the masses of each black hole and the extent of the event horizons of each one. If these were known then our starting point at each of the galaxies would be the imaginary surfaces of the spherical horizons. This has to be imaginary due to any bulging caused by angular rotation. The effects of recessional velocity and any intervening masses would affect this gradient over time. It would be best to start with an idealized model with known variables. This would be made more difficult due to the velocities of the black holes. This causes the point at the horizons surface to be modified away from a fixed universal value. Isn't relativity fun?

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #106 on: 18/10/2014 09:36:16 »
The solution of course is to have an observer midway between the galaxies and moving relative to both in order to maintain an equal distance from each one. This then becomes our second fixed point and cancels the effects on each event horizon.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #107 on: 18/10/2014 21:57:27 »
I am now going to attempt to put together a theory of quantum gravity. Wish me luck.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #108 on: 21/10/2014 00:19:57 »
Well I thought nobody was paying attention so I'll come clean. Remember [M*c^3*lP^2]/[hbar*r^2]? Well the c^3 isn't really that. It has L tucked away which is a scalar. What it should be is [M*c^2*L*lP^2]/[hbar*r^2]. So we now have Mc^2 in our gravitational equation. Quantum gravity is easier to deal with at lower energies and includes too many infinite variables at higher energies at the Planck scale. What happens if we have energy implicit in our equation and an intimate link to the Planck dimensions?

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #109 on: 22/10/2014 00:31:08 »
We can think of c as being L/1. That is 1 light second. We then end up with (L/1)^2 standing in for c^2. This can be viewed as [L^2*lP^2]/1. Square area over time. Multiplying this result again by L gives us a reduced cubic area over time which includes an energy component implicitly by virtue of the mass in the numerator. This resolves to a spatial containment of energy reduced by a proportionality at the Planck scale. This is exactly what we need to start down the path of quantum gravity. By removing the need for G and replacing this with energy we can more easily integrate this with the wave equation and consequently electromagnetism.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #110 on: 23/10/2014 23:03:38 »
Reviewing the equation [M*c^2*L*lP^2]/[hbar*r^2] can show us some important points. (L/1)^2 can also be viewed as (dL/dt)^2 where t cannot go below 1 as this would make the speed of light superluminal. So dt >= 1 and then dL <= L giving both time dilation and length contraction implicit within this function. Then M(dL/dt)^2 gives us a changing energy profile as the properties of the system change. Our L*lP^2 gives us a volume of space over which the change of properties occur. Having hbar as the denominator seems to indicate a Planck variant scale in changing frames. Which implies a constant Planck scale over which mass density changes. This is why relativity has not been resolved. The curvature has been viewed in the wrong way. So now we can separate the functions into [M(dL/dt)^2]*[(L*lP^2)/(hbar*r^2)]. This is an energy against volume equation relating energy density to gravitation as both time dilation and length contraction vary. It is also directly connected to the effects of gravity on the photon.
« Last Edit: 23/10/2014 23:07:06 by jeffreyH »

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #111 on: 24/10/2014 01:09:01 »
Considering the equation [M(dL/dt)^2]*[(L*lP^2)/(hbar*r^2)] it is apparent that r, the radial distance from the source, has to bear a proportionality to dL/dt as this is the distance from the source of gravitation and therefore relates to the strength of the field. The dilation and contraction must fit with experimental observation. In the case of length contraction this is difficult to achieve.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #112 on: 24/10/2014 01:11:23 »
Once the proportionality is established this then forms the basis of the time dilation gradient between black hole event horizons. This will include a full model of the behavior of light between these fixed points.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #113 on: 24/10/2014 23:03:59 »
There is one more pertinent point to make. To measure in a frame dependent way we would use the form [M(L/t)^2]*[(L*lP^2)/(hbar*r^2)] where L/t does not vary. So that local observers all read the same result. This is equivalent to the form GM/r^2. For observers measuring remote frames then the form is [M(dL/dt)^2]*[(L*lP^2)/(hbar*r^2)].

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #114 on: 25/10/2014 19:02:21 »
To separate out time dilation or length contraction we can vary time whilst keeping distance constant or vary distance whilst keeping time constant. I have attached two graphs showing this. For the time dilation graph the x axis starts at 1 second which is the local frame. Any point away from this shows the decrease in change over time. At the 2 second point, for instance, it will take 2 seconds for an action to happen that would take 1 second in the local frame. This can also be seen in the length contraction graph. The curves are not equivalent and operate differently. We cannot read off equivalent energy values from both graphs and use the time and distance values taken in our original equation as the energy would differ. The next step will be to develop the dilation/contraction equation.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #115 on: 26/10/2014 18:31:28 »
To correct the equation we cannot only vary length or time whilst holding the other constant. We start with E = M(L/t)^2. This can be rearranged to give SQRT(E/M)*t = L. This graph is linear and energy is now constant. This is the time dilation gradient. The graph is attached.
« Last Edit: 26/10/2014 18:34:37 by jeffreyH »

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #116 on: 26/10/2014 18:33:11 »
Since we already removed the factor of 50 earlier this shows conservation of energy in gravitational interactions. NOTE: This is a graph of energy distribution over time and distance. It relates to the speed of energy flux.
« Last Edit: 26/10/2014 18:52:39 by jeffreyH »

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #117 on: 26/10/2014 21:14:32 »
Here again the local observer is at 1 second and the distance is L.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #118 on: 26/10/2014 21:27:21 »
We can see from the graph that if we look at say the 2 second position on the graph and read off the distance we get twice L. This is not length contraction. The speed of light has not changed at all. What does this show us? Well energy MUST vary otherwise gravitation has no effect. The first two graphs separated out time dilation and length contraction and showed a difference in those curves with respect to energy. This means there is a factor missing. This could indicate a negative energy component. This would be our gravitational energy. Without this we cannot validate the effects of the gravitational force. Without it gravity doesn't exist.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #119 on: 26/10/2014 21:44:00 »
I asked a question in the the Physics, Astronomy and Cosmology forum as to whether length contraction exists. The next derivation should prove that it doesn't. This is in fact an error that has caused a stall in relativity.If you look at the graph where length is held constant and time changes we see a curve that looks like an inverse square equation. This is absent when we hold time constant and vary length. I will post this another time.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #120 on: 27/10/2014 01:15:07 »
We can rearrange the equation for g to get the time factor as SQRT([M*L^2]/g*[L*lP^2]/[hbar*r^2]). This graph is also linear and starts at L/1. This can be thought of as the speed of light at an infinite distance from any gravitational source. Moving horizontally right is equivalent to moving into an intensifying gravitational field where light is effectively slowed down as viewed by an observer at infinity.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #121 on: 27/10/2014 01:22:47 »
The time axis in the above graph will reach infinity at the event horizon. Any marked effects represented by the plot will only occur near massive dense objects. The attached plot of earth's g shows no noticeable difference on the time axis as this will be measured in nanoseconds and will be unobservable under normal conditions. This can be considered a linear relationship in a less intense gravitational field.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #122 on: 27/10/2014 08:12:00 »
Kinetic energy is given by E = (1/2) mv^2. E is kinetic energy, m is the mass and v is velocity. We can derive momentum as p = √(2Em). The deBroglie equation for wavelength is λ = h/p where here λ is the wavelength, h is Planck's constant and p is momentum. This can be written as λ = h/√(2Em). Since we have already derived t from the gravity equation then we can also derive m. Then time and kinetic energy will be variables in the wave equation. This can be used to show the evolution of the wave under the influence of gravity. In which case m becomes the mass of the particle with r^2 indicating the particle radius squared. The value of g for the particle is most important. This is our way into quantum gravity.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #123 on: 27/10/2014 20:16:50 »
The most profitable investigation would be into the relationships between mass-energy, kinetic energy and time.

#### jeffreyH

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##### Re: Lambert's Cosine Law
« Reply #124 on: 30/10/2014 23:18:18 »
I am now in the position that I need to derive the mass equation.  This is to test an hypothesis that gravitation is merely a catalyst and not a force in its own right.

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##### Re: Lambert's Cosine Law
« Reply #124 on: 30/10/2014 23:18:18 »