curved space

The gravitation

has a finite upper limit, which has consequencies for the concept of the 'black hole'

is not an attracting force but a reduction in a repelling force

'The ether'

is not a constant but a vector dependent on space, defined everywhere by a flow of gravitons

The mathematical model

says that Newtons model needs to be completed with a dependency of dR/dt and describes how the translational field can be calculated

Conclusions

shows that the gravitation and the 'ether' can be described in a way not in conflict with intuition, as the concept of curved space is

Discussions

Recommendation

Verification

The gravitation

The gravitation between two bodies is a pair of forces that has the effect that the bodies seem to attract each other. The forces are acting through what we call vacuum and are probably transmitted by particles that can not be detected. These must have a high penetrating capability and probably high velocity and very small mass. Such a flow of particles (here called gravitons) seems to exist everywhere in the universe

If we concentrate on one of the two forces one body can be called active and the other passive. Therefore we study how a (passive) test mass, m, having its center defined by the position vector R is influensed by an (active) mass, M, positioned in the origin of the coordinate system. M is suposed to have a constant density of q and the form of a spherical shell with the radius R around m and the thicknes d. M is limited by a space angle Omega seen from m. (See figure 1!).

All gravitons inside Omega hitting m have passed a length d through M. The flow of gravitons at m therefore loses its symmetry because M makes the flow weaker inside Omega (fewer or slower particles). The apparent attraction is in fact a decrease in a repelling force from the graviton flow. This means that the gravitation has a finite upper limit.

The loss of symmetry ought to be proportional to the product q*d*Omega (if d<<R and Omega<<2Pi) and can be supposed to cause the acceleration A(R) = F/m on m. By using the relations: d = V/Y; Y = Omega*R*R; q*V = M we see that

A(R) = F/m is proportinal to q*d*Omega = M/(R*R)

which is Newtons law of gravitation. (We can assume that this is true even if M is changed to a spherical form).

'The ether'

We have found that A(R) is proportional to M/(R*R) if m does not have any radial velocity in relation to M. If m is closing M with a velocity, -dR/dt, m will 'see' a different flow. It is reasonable to beleave that there is a special value, V(R), (proportional to M/(R*R)) on this velocity that exactly compensates the loss of symmetry. For this velocity A(R) becomes zero.

We substitute m by a photon and suppose that zero total flow (and A(R) = 0) defines the reference velocity for the light. This means that the velocity of light is C + V(R) (a vector sum) where the ether has been substituted by the translational field V(R).This means that the gravitational field as well as the translational field can be derived from the supposed flow of gravitons.

Mathematical model

For the mass m we have the law of gravitation that says:

A(R) = (-R/R)*G*M/(R*R) if dR/dt = 0

(G is Newtons constant of gravitation)

For the photon we have the law of translation that says:

V(R) = (-R/R)*K*M/(R*R) and the velocity of light is C + V(R)

(K is the constant of translation. New and unknown)

If dR/dt<>0 the value of A(R) can be corrected by multiplication by the factor [1-(-dR/dt)/V(R)]

These laws are approximations

Conclusions

We have found a theory based on a flow of particles (gravitons). This flow can not be seen or detected otherwise (just as the curvature of space). The theory about the gravitons is not in contradiction to our intuition as the theory about curved space is.

Newtons law of gravitation for material particles and bodies has been completed with a law of translation for electromagnetic waves. In every point in space the photons behave in relation to a privileged coordinate system defined by the translational law (unlike in the theory of relativity).This coordinate system has however not an absolute and constant velocity (as predicted by the theory of the ether). Instead it is a vector field related to the gravitational field (differing from it only with a constant). This simple completion to Newtons theory adapts it to Maxwells theory. We no longer need curved space and elastic concepts of space and time. This is in agreement with Michelsons results, containing data gained in a plane horisontal to the earth (ignoring the vertical component).

This new way of describing light rises new questions as:

Can a flow of gravitons explain

the origin of matter

the redshift

Can the gravitations dependency on dR/dt explain the precession of Mercury?

Can the dependency of space in V(R) explain the bending of light near the sun?

Discussions

If matter is supposed to be created (perhaps from the gravitons) in an even distribution in an unlimited universe absolute density is not relevant for a possible expansion. In stead we get expansion where density is lower than in the vicinity and contraction where it is higher. The universe is therefor both expanding and contracting.

Material particles (as electrons and neutrons) are particles but can show a wavelike behavior if they have a velocity in relation to V(R). Perhaps we can explain this by thinking that the particle (like a ship in the water) has to build up a 'bow wave' to be able to move. The energy needed to do this can perhaps explain the concept of inertia. The velocity of a particle in relation to V(R) is always less than c.

Electromagnetical waves are waves but can in some unknown way be quantisized to packets called fotons. The foton (having no mass) can not define its own velocity and always moves with the wave velocity c in relation to V(R). This means that there is a limitation to the complementarity between the concepts of particle and wave.

Eruptions on the sun do not affect the center of gravity for the sun plus the eruption. This means that these waves are attenuated very fast with distance and are not possible to detect on earth.

Recommendation

In the book Beyond the Big Bang by P A LaViolette (1995) the author describes a method developed by E Silvertooth to study the one way velocity of light. (See also "A New Michelson-Morley Experiment", Physics Essays ,vol 5 nr 1!) It should be interesting to use this method (or perhaps modified according to figure 2) to study how the velocity of light depends on elevation angle. Perhaps this could confirm the translational law (and refute the theory of relativity).

Verification

At the surface of the earth (radius = r) we get approximately:

the velocity of light is c + u*cos(z)

where u is approximately K*M/(r*r) and z is the angle between C and -R. Light travels down faster than up . Michelson studied only light travelling horisontally.