The Shell-Universe and The V-effect - Chapter 2.6 - 2.9


2.6 Einstein's calculation.

Two hundred years after Laplace, Einstein predicted that light bends off, when passing close to the sun. First he got the same value as Laplace, but later he changed to twice that value. Measurements later showed that Einstein was right.

To calculate the influence of gravitation on photons we should use Einstein´s theory of relativity.


2.7 Alternative Law of Gravitation.

Newton's law of gravitation gives the force between two bodies or particles.
It gives the wrong result for photons.

Einstein´s theory of relativity should be used for photons, but then you have to be good at advanced mathematics.

Here is a simple way of making one common law for both particles and photons.
A law, that seems to be valid for these calculations.

Newton´s law of gravitation
Force between particle M1 and particle M2

An alternative law of gravitation
Instead of calculating with masses, we can calculate with kinetic energy.

For ordinary particles we have

This gives an alternative law of gravitation :
[ F2.7a ]
F = 4 * G * Ekin1 * Ekin2 / v12 / v22 / D2 [ F2.7a ]

This is just Newton´s law of gravitation but with other expressions.

I assume it is valid also for photons. This is tested in 2.8.

Effect on ordinary particles
For particles we get back Newton´s Law of Gravitation

Ekin = m * v2 / 2
F1 = G * m1 * m2 / D2 [ F1 ]

Effect on photons
For photons we have

but we also have
Effect between photon and particle
For M1 = photon and M2 = particle we get
Ekin1 = mrel1 * c2
Ekin2 = m2 * v2 / 2
F2 = 2 * G * mrel1 * m2 / D2
or
[ F2.7b ]
F2 = 2 * G * h * Fr1 / c2 * m2 / D2 [ F2.7b ]

Effect between photons
for M1 and M2 = photons we get

[ F2.7c ]
F3 = 4 * G * h2 * Fr1 * Fr2 / c4 / D2 [ F2.7c ]

SUMMARY
Without a real knowledge of Einstein's general law of relativity and knowing that the authors, writing about this law, warn that you should never try to mix the calculations following Newton with those following Einstein, I still take the risk of formulating a "new" law of gravitation , which in these cases seem to apply both for particles of ordinary matter and for photons ,

[ F2.7a ]
STATEMENT :
In these cases an alternative law of gravitation can be used
F = 4 * G * Ekin1 * Ekin2 / v12 / v22 / D2 [ F2.7a ]


2.8 Calculation : One photon passing the sun.

We test the alternative law of gravitation by recalculating 2.2

When light from a star passes close to the sun it bends off.


Figure 2.8

( The figure is calculated with [ F2.7b ] and mB = 100, G = 0.001, Y0 = 1, v0 = 1 )

The complete calculation is shown in the printed paper.
The steps in the calculation are shown here.

We calculate the angle, alfa.

Here we use formula [ F2.7b ]

F2 = 2 * G * h * Fr1 / c2 * m2 / D2 [ F2.7b ]

A calculation shall consider the following aspects of the photon .

  1. Mass of photon
    The relativistic mass of the photon is
    mrel = h * Fr / c2 = E / c2 [F9]

  2. Energy of photon
    E = m * c2 = h * Fr [F10]

  3. Momentum of photon
    MOM = h * Fr / c [ F11 ]
Then a calculation would look like this :

This gives :
Total angle between path and initial path
alfa= 2 * 360 / Pi * G * mB / Y0 / c2 (degrees) [ F2.8 ]

CONCLUSION
A photon, passing a heavy object, bends off with an angle of

[ F2.8 ]
This is twice as much as we received in 2.2 .

Using this formula a photon passing close to the sun would bend off with an angle of

alfa = 1.75"

This is what Einstein predicted and the result is proved by measurements.
It is the only possible test of the alternative law of gravitation.
The result is positive.


2.9 relativistic density of photons.

Photons have no real mass or rest mass. But they have a "relativistic mass".
mrel = h * Fr / c2 = E / c2 [ F9 ]

For normal materia we talk about the density

Dens = Mass / Volume

For photons we can define a "relativistic density" as

RelDens = RelMass / Volume
Densrel = mrel / Volume
Densrel = h * Fr / c2 / Volume [ F2.9 ]

( If there are photons with different frequencies, Fr is the medium frequency.)


Back to Home page ! ........ Next chapter ! ........ Back to Content List !