# Finite Theory

## Proposal for Wavelength Meter in Motion to Test the Invariance of Light Speed

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### Foundation of the Finite Theory

#### Postulates of the Finite Theory

F inite Theory defines a new representation of the formulas derived from General Relativity based on the superposed potentials of the predicted massless spin-2 gravitons that mediate gravitational fields.Additionally in contrast to General Relativity where the space-time is represented using the non euclidean geometry in order to keep the speed of light constant, Finite Theory considers time to be a positive variable within a space that is characterized by the euclidean geometry. No previous self-consistent results deriving from General Relativity are in violation. ### Definition 1: A 'local reference frame' moves coherently with the source of the local gravitational field where the latter is in turn defined to be the strongest gravitational acceleration. For example, if the observer and the observed object are nearby a planet then the local reference frame is set on the planet's surface, rotating with the same angular speed. Note that this can be a non-inertial frame.Definition 2: The kinetic energy is defined as (classical definition), with being the speed of the object with respect to the observer.Definition 3: A gravitational time dilation is directly proportional to the difference in the superposed gravitational potentials of the observer and the observed object. Hypothesis 1: The speed of light in free space has value c for any observer at rest relative to the local reference frame. However, observers in relative motion with respect to this frame will not measure the same value for c.Hypothesis 2: The time dilation experienced by an object moving with respect to an observer at rest relative to the local reference frame is directly proportional to the ratio between the kinetic energy and the maximum kinetic energy of the object, where the latter is the case when its speed equals c.

#### Introduction

In Einsteins 1905 paper on Special Relativity, two postulates form the basis of the theory:

Postulate 1 (principle of relativity).: The laws of physics are the same in all inertial frames of reference.
Postulate 2 (invariance of c).: The speed of light in free space has the same value c in all inertial frames of reference.

It was assumed that the latter was already tested because of the Michelson-Morley experiment and other replications favored the null hypothesis.
The aim of the experiment we propose here is to search for evidence of a variable speed of light. According to a recent study, it might be possible to predict all phenomena of the Universe based on the fact that gravity is a particle. In contrast with the previously assumed static aether from which the bodies are moving through, the graviton field will have the same spin of the emitting source. Therefore the failure to detect any movement by the Michelson-Morley experiment can be explained by the fact the reference frame simply had the same spin of the Earth. The reference frame simply follows the source of the strongest gravitational acceleration. This reference frame is the Earth for all low orbit experiments that tested Special Relativity, the Sun for solar system wide probes, and so on.
By sending the laser emitter and wavelength meter at a sufficiently large velocity compared to the inertial frame of Earth we hypothesize that a detectable variance in the speed of light will be seen, only now possible with recent advancements in high-precision metrology.
Our proposal is organized in the following way. In Sec. II we consider theoretical foundation of the Finite Theory which considers time to be a positive variable within a space that is characterized by the euclidean geometry. We demonstrate how the dime dilation effects, bending of light and perihelion shift can be explained by only using postulates of Finite Theory and laws of newtonian mechanics. Given we know the result of the measurement of the light bending in the gravitational field, we can “reverse engineer” the entire Universe to find out all its characteristics, as is illustrated in Sec. III. Our experimental proposition described in Sec. IV. Finally, in Sec. V we give some concluding remarks.

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