Abstract

This article is an analysis of current theory of the gravitational time dilatation in different stationary reference frames.This new approach leads us to a new vision of relativity because we find the time dependence relativeto the universal density of potential energy at placeand that density this varies from one reference frame to another reference frame. The time in each location varies in the inverse proportion of the square root of the respectiveuniversal density of potential energy. With the universal expansion the universal density of potential energy decreases and will cause the contraction of the time in the Earth reference.

1. Introduction

In this analysis we will use the same principles and methods used for the deduction of current theory of the Gravitational time dilation caused by the universal density of potential energy at different stationary reference frames.

The time in each location varies in the inverse proportion of the square root of the respectiveuniversal density of potential energy.

With universal expansion the universal density of potential energy decreases and will cause the contraction of the time in the Earth reference.

2. The Gravitational Time Dilation in Different Stationary Reference Frames

Let use the same theoretical principle of relativity between, the time at areference framewithin the gravitational field of mass Mon its surface and another outside of the gravity field of mass M.

Consider a reference frame A within the gravitational field of mass M, on its surface, at a distance R, radiusof mass M and a reference frame C out of this gravitational field.

Where,

G- Universal gravitational constant.

R- Distance between the reference frame A and the center of the mass M, its radius.

M - Massof M.

C²- Potential energy of light inreference frame A.

t_A- Time inreference frame A.

t_C- Time inreference frame C.

Through analysis of Einstein's relativity, derived from the Schwarzschild metric, it is propose the change of time between a reference frame A within the gravitational field of mass M, and another C out of this gravitational field, given by “Ref. ⁵”:

(2.1)

The expression we will now indicate is the same as the previous one

(2.2)

Multiplying thenumerator anddenominator inEq. (2.2) by we have:

(2.3)

Where:

(2.4)

- Universal density of potential energy at reference frame A,

(2.5)

Given that:

- Density of potential energy generated by the mass M, in the reference frame A.

(2.6)

- Universal density of potential energy at reference frame C, outside the reach of the mass gravitational field M.

The variation of the universal density of potential energy from a reference frame to another reference frame is now evident.

If we were able to subtract the density of potential energy generated by an mass, from the universal density of potential energy, is because the first participates in the second.

Substituting the values obtained in Eq.(2.6), at Eq.(2.5), we have:

(2.7)

(2.8)

The time at different reference framesis inversely proportional to the square root of the respective universal density of potential energy at place.

Now, we have a clear view of the time dependence with theuniversal density of potential energy at place.

We are convinced that this new finding will allow a new development of the theory of relativity.

3. Gravitational Time Dilation, in Different Stationary Reference Frames, Located at the Same Gravitational Field

Consider a new reference frame B, located at the same gravitational field generated by a mass M, at a distance b from the same center of mass M.

For the reference frame A and B, we have:

From Eq.(2.7)

(3.1)

As respective universal density of potential energy at the surface level of massMthen at a distance b we will have a lower value in the influence of the mass itself on the universal density of potential energy, with a variation given by:

(3.2)

Considering our planet Earth, we will have:

(3.3)

(3.4)

This is the new expression of the relativity of time in reference framesin relative rest, under the action of a gravitational field.

4. Conclusion

The universal density of potential energy varies from one location to another location.

The time in each location varies in the inverse proportion of the square root of the respectiveuniversal density of potential energy.

With universal expansion the universal density of potential energy decreases and will cause the contraction of the time in the Earth reference

References