36.Emergence of Gravity

Introduction

Consider two identical charged spherical bodies of mass m separated by a distance R in a vacuum under the influence of an electric field E and in presence of an external constant and uniform magnetic field B. Let one of the bodies be stationary or rigid and the other free to move. Due to the presence of an external magnetic field the charged body will experience circular motion where the surface area of the sphere created by this motion is, . After a lengthy but straightforward calculation it can be shown that the electric force Ee per unit area A on the system of bodies with charge e is given by

(1)

––––––––

Where is the magnetic force experienced by a charged body, α is the fine structure constant ,ћ is the reduced Planck constant  and c is the constant speed of light.

The magnetic force in this case is perpendicular to the velocity v of the body as

On substitution into (1) we obtain the square of the velocity as

(2)

Keeping the radius of orbit constant, it can be observed from (2) that the weaker the strength of the external magnetic field the greater the velocity and vice versa. Therefore the velocity of a body will depend on a great deal to the coupling constant or fine structure constant.

We notice that the expression is the Casmir force  due to the Casmir effect. Multiplying both sides of the equation by we get an expression for the centripetal force which acts to keep the body in orbit as,

According to Maxwell electromagnetic theory, the electric field is related to the magnetic field by a relation E=Bc and since we obtain the Casmir force under the influence of an external magnetic field between the two bodies as,

––––––––

(3)

From the uncertainty principle the following relation holds,

Where R is the position of the mass m, which means that the circumference takes on discrete values of the wavelength as 2πR=λ.  Then on putting in (3) we obtain the force as

On arranging we obtain the following expression,

(4)

Where   is the internal magnetic field between the bodies and is given as

(5)

Equation 4 reduces to the gravitational force when the external magnetic field is a constant with a value given by,

(6)

Finally on substitution of (6) into (4) we obtain the universal law of gravitation as

Similarly the electrostatic force or the Coulomb force law between two electrons can be deduced in a similar manner. In this case the external magnetic field has the value of the Schwinger magnetic induction limit of

(7)

Also the internal magnetic field (5) between two electrons is

(8)

Finally on substitution of (7) and (8) into (4) we get the Coulomb force law of electro statistics as

While this hypothesis awaits experimental observation, it remains evident that gravitation is a Casmir effect under the influence of a constant and uniform external magnetic field of   .