A New Interpretation of Mass and Gravitational Field

Author:  Shuai Wu

Department of Modern Physics

University of Science and Technology of China

Hefei Anhui, 230027, P.R.China.


Abstract: A model is proposed to redefine mass as a kind of current in four-dimensional space-time. This kind of current is formed by the directional motion of a virtual particle which is characterized by. Based on this model, the gravitational field in four-dimensional space-time is derived and its features are discussed.

Keywords: gravity, gravitational constant, magnetic force, space-time, virtual particle, space physics, current, energy.


Gravitational force exists between arbitrary two objects just as Coulombian force exists between arbitrary two electrified bodies. The similarity between Gravitation Law of Universal and Coulombís Law indicates that it seems the mass enacts as the same character in the generation course of gravity as the charge in that of Coulombian force. However, in this paper, we propose that the mass is a kind of current formed by the directional motion of a kind of virtual particle. Taken in this sense, the mass is more similar to the electric current than the charge.


As we all know, the material wave frequency n of every object that has the energy of E will satisfy the Material Wave Equation


When the energy of the object varies from E to Eo , its material wave frequency will varies from n to n o, and the relation between Eo and n o will also satisfy the Material Wave Equation


From formulas (1) and (2), the energy difference between the two energy states can be obtained


If considering n and n 0 as the numbers of oscillation in unit time, then the numbers of oscillation in t are




respectively. Here, m and n are integers and by substituting (4) and (5) into (3), one can get


and assuming , then


where, k will also be an integer. Considering the mass energy equivalence, there will be a value M for the mass that will correspond to D E and . By replacing D E with M in formula (7), one can get


If assuming E ³ Eo, we can get m ³ n and therefore k is also an integer which is greater than or equal to1. Comparing (8) to the expression of electric current

where, n is also an integer greater than or equal to 1, one will easily find that mass can be described as a kind of current that is formed by the directional motion of a possible virtual particle which is characterized by .


As we know, electric current can be expressed by current density vector as . Similarly, if we define the four-dimensional mass density vector whose direction is described as the direction of the motion of virtual particle at one point of the four-dimensional space-time, the relation between and M can be written as  where  is a unit volume vector in four-dimensional space-time.


If we introduce four-dimensional column coordinates (r,f ,q , t) which consists of three-dimensional globe coordinates and time axle coordinate t, the four-dimensional vector can be expressed as

where, is a set of normal unit vector, which comply following rules

Here, we discuss a special situation. That is, and are both parallel to the time axle . Under this condition,

where, r is the scalar mass density which is familiar to us.

Based on above, we can redefine the mass as the quantity of virtual particle flowing through a three-dimensional volume (it is vertical to time axle) of four-dimensional space-time in unit time.

Electric current can generate magnetic field, which is expressed as Ampereís Circuital Law . Corresponding to it, mass can also generate a field which is similar to magnetic field. We write this field as . Then where "s" represents a closed curved face of three-dimensional space which mass crosses through.

The unit vector of the normal direction of this close curved face is expressed as () in the four-dimensional space-time.  Because we consider that the direction of motion for virtual particle is parallel to time axis, "s" can be a closed spherical face with arbitrary radius which surrounds mass. Under this condition, one can get


where "g" is the gravitational constant and


If putting an elementary mass (where dt is the unit length of time axis) in the field , this elementary mass will receive a force similar to the Ampere force. This force can be written as


Substituting (9) into (10), one can obtain


Formula (11) tells us that at the moment of measurement, the force which receives in the field is , and the unit vector of the direction of this force is.


Comparing (11) with the expression of the Universal Law of Gravitation  , one can find that these two expressions are completely congruent assuming .  So it would then be proper to call the field , the gravitational field.


From formula (11), one can also get



where, is the Hamilton Operator of four-dimensional space-time. Formulas (12) and (13) indicate that field is more similar to magnetic field than electric field in the condition that one assumes is parallel to time axis.


The directional motion of charge forms electric current and the directional motion of virtual particle forms mass. The moving charge generates magnetic field and the moving virtual particle generates gravitational field. It is so similar between virtual particle and charge that we have to think the stationary virtual particle, if it exists, maybe generates a field just like the Coulombian field. The relations between this field and gravitational field maybe similar to that between electric field and magnetic field. In addition, if considering arbitrary two objects of this world have the same direction of time, that is to say, the directions of their mass density vector are both parallel to the time axle, we can obtain the conclusion that the gravitation force between these two objects is always attraction force, instead of repulsive force.

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