Physical Consequences of Decreasing Gravity

Second part of a tretise by Louis Nielsen with new theory for the evolution of the universe with decreasing gravity.
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14. Physical Consequences of Decreasing Gravity

Regarding planetary physics, a decreasing gravity will cause that the moon moves away from the earth and that all distances in our solar system increase.
From the formulas it can be calculated that radius of the Earth increases by about 0.02 cm per year, corresponding to an increase of radius of about 100 km during the last 500 million years. This 'inflation' of the earth can explain the forces, which have been cracking the Earth's crust and split the continents. As an effect of the decreasing gravity, the distance between the Earth and the Moon increases by about 1.2 cm per year. By the increase of the diameter of the Earth, its mass is removed more and more from the rotation axis, which causes the rotation speed to decrease (compare with a skater, stretching out his arms to lower his rotation speed). The slower rotation of the Earth means that the day is longer. During the last 500 million years the day has increased by about 1 hour. Another effect, which has given a further increase in the length of the day, is the tide effect, the phenomenon giving high and low tide. This is due to the gravitational pull from both the Moon and the Sun. These effects cause a slow brake of the Earth.

15. Everything Expands due to Decreasing Gravity

(15.1)

where v is the velocity of m₁ and r is the instantaneous distance between m₁ and m₂. m_1i gives the inertial mass of the orbiting particle. We shall consider velocities relatively small to the velocity of light and shall therefore consider that the inertial mass is equal to the gravitational mass, m_1i = m₁.
Let a dot over a letter mean differentiation regarding time (Newton's notation), and we get from (15.1):

(15.2)

This we can reduce to:

(15.3)

We are handling a central force and there is preservation of angular moment, thus:

(15.4)

From equation (15.4) we get:

(15.5)

Inserting in (15.3) we get for the relative increase of r:

(15.6)

The Expansion Formula

(15.7)

Equation (15.6) shows the radial velocity, whereby two gravitating masses, spaced by the distance r, will move away from each other. The relation is a theoretical deduction of the cosmological Hubble relation!
We shall use (15.6) to calculate the timely increase of the radius of the Earth and the increase in distance to the Moon, presuming that:

(15.8)

and that this value is nearly constant in our epoch.

For the increase of the radius of the Earth we get (r = 6400 km):

(15.9)

If we use equation (15.6) on the Earth - Moon system, we calculate a timely increase in distance (r = 384.4 · 10³ km):

(15.10)

Laser measurements have shown that the distance to the Moon has increased by about 5 cm/year. The result in (15.10) only gives the amount due to decreasing gravity. The rest is due to other gravitational effects, a.o. the tide forces.

Paleomagnetic analyses *) have estimated an upper limit of 0.13 mm/year for the increase in the Earth's radius, in good agreement with the figure in equation (15.9). The value in (15.9) is dependent on the precision of the measurement of
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*) Ref.: McElhinny et al. Nature, 271, 316-321 (1978).

16. The Expansion of the Earth and the Increase of the Day
Continental Drift

The angular momentum L_j of the Earth can be expressed by its inertial moment in relation to the rotation axis and the angle velocity, thus:

(16.1)

where I is the inertial moment and the angle velocity.
Presuming that the angular momentum is constant during 'inflation', we have:

(16.2)

The inertial moment of a ball is:

(16.3)

where m_j is the mass of the Earth and R the present radius. If we differenciate I in relation to time, we get:

(16.4)

As we have:

(16.5)

we get from (16.4) and (16.5):

(16.6)

This equation is integrated and if t₁ and t₂ are two times, where t₂ > t₁, we get:

(16.7)

The relation between and the rotation time is given by:

(16.8)

and we get:

(16.9)

The actual value of the gravity 'constant' depends on the actual age of the universe:

(16.10)

where G₀ is the initial gravity 'constant' and t₀ elementary time.
Using this in (16.9) we get:

(16.11)

This formula we could also have deducted directly from the condition of preservation of angular momentum. We shall calculate some examples. Firstly, we shall calculate the rotation time for the Earth in the Devon period, about 400 million years ago. Using the values T₂ = 10.5 · 10⁹ years; T₁ = 10.1 · 10⁹ years, = 24 h, we get:

(16.12)

Some scientists have analyzed the relative timely decrease of the angle velocity of the Earth. The observed value has been given to:

(16.13)

A relatively great amount is due to the gravitational tidal effects, mainly from the Sun and the Moon. This value amounts to:

(16.14)

and thus not enough to explain the observed value!
To this, however, comes a contribution from the decreasing gravity. From equation (16.11) we get:

(16.15)

Combining (16.14) and (16.15) we get:

(16.16)

which is in good conformity with the observed value.

17. Decreasing Gravity and Mass-Luminosity of Stars

(17.1)

k₁ is a system dependent proportionality constant. The relation is independent of specific energy producing processes.
Let us calculate the relation between energy radiation at two different times, with two different values of the gravitational 'constant', i.e. two different times T₁ and T₂ in the age of the universe. We can write:

(17.2)

If the mass is presumed to be the same at the two times we have m(T₂) = m(T₁) and:

(17.3)

Inserting the expression for the decrease of G relative to the age of the universe, we get:

(17.4)

From this equation we see that the radiation of energy from an object far away from us, for instance a quasar, will be much stronger, as the light from this object was sent off at a time when the gravitational 'constant' was greater, corresponding to a younger age of the universe.
As an example we can use: T₁ = 0.5 · 10⁹ years and T₂ = 10.5 · 10⁹ years, which gives:

(17.5)

It also follows that the extension of the distribution of mass is dependent on G, with higher concentration within a smaller space area in earlier epochs.
The following relation is valid:

(17.6)

For the two ages we get:

(17.7)

With the ages as above we get:

(17.8)

If we in the equations (17.4) and (17.7) use the values T₁ = 10⁶ years and T₂ = 10.5 · 10⁹ years, we get for respectively radiation of energy and the extension of the object (T₁ is age of the universe):

(17.9)

(17.10)

We see from the expressions (17.9) and (17.10) that the farther away and thus the younger objects we observe, the stronger radiation and the smaller extension these objects have. This is exactly what has been observed for the so-called quasars, namely that they have extremely strong radiations from relatively small regions. The quasars are known to be situated in the outermost regions of our universe, i.e. we observe objects in the young universe. The above given explanation thus may be the answer to the quasar enigma. Newer photographs with long exposure times have shown that the quasar proper apparently is only the central region - the core - of a very distant galaxy, similar to the so-called N-galaxies (N for nucleus), situated nearer to us, and the so-called Seyfert-galaxies, which are still nearer. The three types of galaxies, S, N and Q-galaxies, may be proof of a cosmic decreasing gravity.

By the expressions in (17.1) and (17.6) we can calculate the relative variation in time of P and R. We get:

(17.11)

and

(17.12)

As and are functions decreasing in time it will be seen that decreases with time and increases with time.

Post scriptum:
The present theory gives a solution to the 'mystery of large numbers', as N plays the role as a cosmic evolution parameter, the value of which was 1 at the birth of the universe. The theory is compatible with Mach's principle, uniting macro- and microcosmos.
The theory also answers to 'the arrow of time', as time can only increase. This is fulfilled by the cosmic space quantum number and the cosmic time quantum number being integers, moving from 1 to higher and higher values.

18. Centrifugal and Coriolis Forces are identical to the N¯ Field

Since the childhood of mechanics a great interest has been shown the so called 'fictive forces' appearing in accelerated systems. Examples are centrifugal and Coriolis forces. The question is: are these forces really fictive, or are they real physical forces, caused by other physical phenomena? This question was especially taken up by Isaac Newton (1642-1727), George Berkeley (1685-1753), Ernst Mach (1838-1916) and Albert Einstein (1879-1955).
The problem can be illustrated as follows.
Consider a ball rotating relatively to all other masses of the universe. Experience shows that the ball bulges at the equatorial regions. Why is that? Newton said: the ball bulges because it rotates in relation to absolute space. If the ball were at rest it would not bulge. On the contrary, Mach said that it is a relative effect which would also occur if the whole universe rotated and the ball were at rest. Newton and Mach thus did not agree. Einstein adopted Mach's viewpoint - everything is relative - and tried to incorporate Mach's principle in his theories of relativity. Mach's principle can be formulated:
The local physical effects are relatively dependent on the condition of the rest of the universe.

I agree with Mach in his opinion, formulating generally: Everything is dependent on everything. Omnia determinant omnia.
In the following we shall examine the identity of the N Vector field () and the centrifugal and Coriolis forces.

Consider a particle with the gravitational mass m_g in an inertial system. Let it rotate in a circular orbit with radius vector and angular velocity . The centrifugal force will then be:

(18.1)

The mathematical form is exactly identical to the expression for the gravitational field in equation (9.6):

(18.2)

is the velocity of the gravitational mass in the field. The size and direction of this field is thus identical to .

Relatively seen, the total masses of the universe are rotating in opposite direction of the rotating particle. This will induce an field in the area where the particle rotates. The exact formula for calculation of the size of depends on the geometric distribution of masses around the rotating particle. If we consider an field induced by a mass M_g, distributed evenly in a ring with radius R, we get:

(18.3)

   (from equation 9.4)

where K is the dynamic coupling constant to the field.
Setting N = , we get:

(18.4)

A finer analysis, taking into account the final velocity of distribution of the field, the variation of K and an exact geometry, will confirm the above.

19. Inertia. A Measure for Effects of Gravitational Forces

A particle will 'show' inertia (slowness, resistance) against changes to its velocity in relation to an inertial system, i.e. against acceleration. This property was introduced in Newton's 2nd law as inertial mass, m_i.   m_i is the proportionality factor between the acceleration and the resulting force on the particle. Thus Newton's 2nd law:

(19.1)

where is the acceleration and the resulting force. The question is: what causes this inertia, working as a force opposite to the force by which the particle is influenced? A tempting answer is that we have a gravitational self-inductance, caused by the relative movement in comparison with the other masses of the universe. If the above is true, Newton's 2nd law must be changed to a tensor law. The inertial mass is then not a scalar, but a tensor, which we can call the inertial mass tensor. The generalised 2nd law will then be:

(19.2)

where take on all space coordinates and summation is done over . As the universal distribution of mass around a particle orbit most likely will be assymmetric, the inertial mass will be anisotropic. Confirmation of the above must be done by measuring the inertial mass of a particle as it moves in different directions. Please note that the gravitational mass of a particle must be considered invariant.

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Louis Nielsen
Mejerivej 25 A
DK-4700 Næstved
Denmark
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