Introduction

General relativity as a gravitational theory is based on the geometry of space and time called spacetime. An object is moving in spacetime following the shortest geodesic distances. Except for gravity, the other three fundamental forces, the electromagnetic force, the weak force, and the strong force, are explained by quantum theory through the mechanism of exchanging virtual boson particles (photons, W and Z bosons, and gluons). General relativity is fundamentally different from quantum theory which leads to two competing foundations for physics, dividing physics community into two camps. Sometimes, the two even have conflicting results against each other. Nature cannot have two sets of laws, incompatible with each other. Hence, it is desirable to consolidate the two into one by unifying gravity with the other three forces under the same theoretical framework of physics.
It is well known that gravity affects all particles, totally independent of any property of the particle. In contrary to that, for the other three basic forces of nature, each one affects a subset of particles only which have certain properties. That suggests to us that gravity, unlike the other three forces, is related to some fundamental property of nature. Specifically, gravity may not be created through the mechanism of exchanging some virtual boson particle(s).
The speed of light defines a fundamental, very important constant in quantum theory. Since that constant controls the motion of all particles, it is a fundamental property of nature. This paper suggests that gravity is caused by variable speed of light (VSL). It explains why gravity affects all particles, massive and massless, fermions and bosons, unlike the other three forces.
There is no lack of attempts to use VSL to explain gravity in history. Einstein first mentioned a variable speed of light in 1907 and attempted to use VSL to explain gravity. However, his attempt was abandoned later on by himself. Robert Dicke also developed a VSL based gravitational theory in 1957 where both the frequencies and the wavelengths of light change under the influence of gravity. The theory presented in this paper is different from other VSL based gravitational
theories. It is the first to derive the gravitational force based on key equations of motion for particles in quantum theory with VSL. Gravity emerges from those equations naturally when the speed of light is a variable instead of a constant. Thus, this theory presents a way to unify gravity together with the other three forces under the framework of quantum theory.
This paper argues that a gravitational theory should be firmly built on the foundation of quantum theory. This is because quantum theory has been tested in countless times with very accurate apparatus. In contrary to that, there are only a few experiments to validate general relativity, many of them are not conclusive. A noticeable controversy in the theory is related to the prediction of light bending near a massive object. The bending angle predicted by the equivalence principle, the foundation of general relativity, is only half of the value predicted by the Schwarzchild metric derived from Einstein’s field equations. It says that general relativity conflicts with its own foundation directly. Such a conflict implies that there may exist some logic inconsistency in this gravitational theory and the theory itself may have to be re-examined.
The gravitational theory proposed in this paper is fundamentally different from the one proposed by Einstein. The later is based on the equivalence principle, i.e., acceleration is equivalent to gravity. The former is based on changing the speed of light in key quantum equations from a constant to a variable. To find out which one is correct, a simple experiment is proposed in this paper.