Currently, explanations of effects involving gravitation are based on the General Theory of Relativity because of its sufficient accuracy and simplicity. This theory, however, lacks the consideration of symmetry in its associated parameters. In addition, it fails to be intuitive enough for many people to understand easily although Albert Einstein’s thinking was extraordinary. Therefore, the new theory is introduced that not only takes into account the symmetry but also explains gravity based on that fundamental and appealing requirement.

The explanation of the nature of gravity is based on the symmetry in the concept of energy. The requirement of symmetry, in turn, is based on a rather popular conjecture that the universe started out of absolutely nothing. This conjecture is relevant because the question of why anything exists in the first place is difficult to answer and because the universe can still fulfill its purpose by creating positive and negative parts out of nothing.

Space is the 3 dimensions in which changes in position can occur, and time is the coordinate in which space constantly moves. Space ca n be described as the 3-dimensional surface of a 4-dimensional sphere whose center is the origin of time-coordinate and whose radius is time.

Fig. 1. Space depicted as the surface of a sphere, moving away from the origin of time at a constant rate. Identical depiction is valid for negative time.

Fig. 2. Two sets of space depicted as plain surfaces -- one moving in positive time and the other moving in negative time.

In the "beginning", space is at the origin of time (t=0) and has no volume just as the sphere with zero radius (r=0) has no surface area. At the Big Bang, space begins to move through time away from the origin -- one set of space moves in the positive direction of time (t>0) and another set of space moves in the negative direction of time (t<0).^†

The important concept here is that 2 parallel sets of space exist across the coordinate of time, one in positive time and the other in negative time, and that these sets of space-dimensions are moving through time at a constant rate.

Energy is a quantity that can experience changes in the space-dimensions and that can do work on these quantities. Every physical existence in the universe is energy, including mass: E=mc². Energy can exist only within the 3 dimensions of space which is moving constantly through the coordinate of time. This mean that energy is free to move only in space, not in time; that is what prevents time from being called a dimension. Also, any amount of energy takes up a certain amount of space because that is what the existence of energy in space means. The concentration of energy can vary however. Work is simply a transfer of the energy from one system (body of energy) to another.

The conjecture that no energy was present originally requires that both positive and negative energy be created at the Big Bang to establish the symmetry. Theoretically, the positive energy and the negative energy can cancel out each other completely, leaving absolutely nothing. This annihilation, however, is improbable because the positive energy exists in space that moves in the positive domain of time and the negative energy exists in space that moves in the negative domain of time.

The space in the positive time and the space in the negative time are relatively identical except that different events can take place in each space as long as all parameters are in symmetry overall, or they are conserved in each space.

Because of a tendency of the nature to preserve the initial condition of zero energy, an attractive interaction exists between positive energy and negative energy across the coordinate of time. In space that is in the positive domain of time, positive energy is attracted toward negative energy that exists in the negative domain of time, and vice versa.

This attractive interaction across time causes any amount of the positive energy in space to curve the dimensions of space toward the negative energy, or backward in time. This way, that unit of positive energy exists relatively earlier in time. This warpage of space-dimensions due to the presence of energy extends infinitely across space, decreasing with distance. [As will be shown later, however, the warpage of space is never infinite since any amount of energy has volume: the distribution of the energy within the volume smoothens the slope of space in time so that the slope at the center of the energy-unit is 0.]

Likewise, any amount of negative energy that exists in the negative time is attracted to positive energy in the positive time and therefore warps the dimensions of the space in a similar manner.

This vector has its component vector in the dimension of space which is directed toward a region of space earlier in time and whose magnitude depends on the slope of the space in time. This component vector expresses the force of gravity (). Note that because energy can only move within the dimensions of space, the gravitational force vector is indirect from the original vector expressing the actual attraction of energy across time. Also, even though the force of gravity is a vector directed in both space and time, it produces an acceleration proportional to its magnitude in the space-coordinate [The distance between 2 fixed points in space remain constant even when space is warped in time so that ]. The magnitude of this force vector is proportional to cosine of the angle (q) that the space makes with the time-coordinate:

.

Thus, no force of gravity is experienced where the slope of the space in time is 0 (q=¹/2), and the greater the slope of space in time, the greater the component vector for the force of gravity is.

The slope of space in time in terms of the angle q is:

^*.

Now the universal gravitation law is incorporated to express the slope as a function of distance r:

^*.

As expected, greater mass M results in greater space-time slope at any given distance. The function for time of space-dimensions can now be derived from this slope function:

^* [r >= radius of the mass].

The integration can be eased by using the following approximation of the slope function for sufficiently large distances r:

(r >> radius of the mass).

Fig. 5. Approximation of the slope function is compared to the original. These graphs show how the original function approaches the approximation as distance increases.

Thus, the equation describing the time (t) of space at distance (r) from the mass (M) is:

[r >> radius of the mass],

where T is the time of unwarped space if M is the only mass present in the space. Note that this "constant" is the age of the universe, which is the asymptote of the time of the warped space-dimensions. Or, more accurately, T is the time at the given position in space before the effect of the mass M is considered. The term describes the degree, in seconds, of warpage of space backward in time. The more general form of this equation is in terms of energy:

[r >> radius of the energy-unit].

These functions before approximation are undefined at a certain distance and imaginary within that distance. This is because A / F_g has to be greater than 1, meaning that the space-time slope cannot be infinite. Space cannot be warped infinitely since any amount of energy, however concentrated, exists over a certain volume of space, not at a point.

For derivation of equation for warpage of space within the volume of mass (or energy), a similar process is used. To simplify the calculation, the mass is assumed to be spherical and its density (r) uniform. Then the force of gravity at a distance r from the center of the mass depends on the part of the mass that is within the sphere of radius r because the effect of the mass outside of that radius cancels out as followed from the law of universal gravitation:

As mentioned earlier, the space-time slope at the center (r=0) of mass is 0. Now, the equation for time of warped space as a function of distance r within the volume of mass having a uniform density r is:

To combine them, the density of the mass is set so that the term becomes equal to 1. Also, the radius of the mass is set to 0.5 meter. For the functions regarding the space outside of the mass, mass (M) can be substituted with the product of density (r) and the volume (4¹R³/3) assuming that it is spherical and its density is uniform.

Fig. 10. Slope of space-dimensions in time within (r<0.5m) and around (r>0.5m) the mass [Consider only parts below the intersection point].

Fig. 11. Warpage of space-dimensions backward in time due to the mass [Consider only parts containing the horizontal asymptote and the vertex.].

The slope function shows the relative magnitude of gravitational force experienced at different distances from the center of the mass, although the force is not proportional to the slope. The slope is greatest at the surface of the mass and therefore the force is strongest there as expected. No gravitational force is experienced at the center.

The warpage function shows the relative time at different distances from the center of the mass. The time is earliest at the center of the mass as the space-dimensions are warped to the greatest extent there. The time approaches that of the unwarped space as the distance from the mass increases.

When any separate units of energy exist at different positions in space, the warpage of space due to their presence combine in an additive manner. This means that the slope of space in time is also combined in an additive manner. When 2 energy units, for example 2 masses, are present at a certain distance apart, the warpage of space adds up so that the space-time slope in region between the masses is added destructively while the space-time slope in regions on either side of the masses is added constructively. This is simply because the space-time slopes oppose each other between the masses while they match each other on either side of the masses. The consequence of this is that, for each of the masses, the side facing the other mass lies in a less-sloped region of space than the side away from the other mass does. Therefore, the side away from the other mass would experience a greater force toward the other mass than the side facing the other mass would in the opposite direction. The overall net force on the mass, therefore, is toward the other mass.

In addition, the space-time slope at the center of each mass is no longer 0 because the slope due to the other mass is added to the original slope of 0. Therefore, the mass experiences a force toward the other mass even when it is considered as a point-mass.

This proves that the force of gravitation due to warpage of space-dimensions causes any two units of positive energy (or any two units of negative energy) to attract each other. No actual attraction exists between like energy, but the fictitious force is only a result of the attractive interaction between the opposite energy across time which warps the dimensions of space. The force acts on the energy so that the center of the energy unit accelerates toward the direction in which the space is most negatively sloped in time, that is, toward an immediate region of space earliest in time.

The most remarkable difference between this Symmetric Theory of Gravity and Albert Einstein’s General Theory of Relativity is on the condition of time dilation. While time dilation is thought to be caused by the gravitational field itself in the General Relativity, the Symmetric Theory predicts that an object experiences time dilation only while it is moving toward lower gravitational potential. Time dilation is presented very briefly in the following.

Whenever any object moves toward the region of space relatively earlier in time, the object experiences slower time change compared to time change experienced by something at rest. While the object is still moving forward in time as the space itself is moving forward in time, the object is also moving relatively backward in time along the curved space, making its net movement through time relatively slower. Note that even though the warped region of space is relatively earlier in time than the rest, the rate at which the region is moving through time is the same as the rate at which the other regions are moving through time.

When a mass (or any unit of energy) is attracted to a significantly larger mass that is warping the dimension of space significantly, the small mass will accelerate toward the center of the large mass where the time is the earliest. Since the space in which the small mass is moving is sloped negatively in time, the small mass is moving against the direction of time in which the space is constantly moving -- meaning that the small mass is moving backward in time relative to the space. Normally, the rate at which the mass moves backward in time is insignificant compared to the rate at which the space moves forward through time, so that the net movement of the mass through time is still forward. Still, the mass will move through time at a lower rate than when it is at rest. This slowing of the movement of energy (or mass) through time is time dilation, caused by the energy unit moving backward in time along gravitationally warped space.

To test which of the two theories--Symmetric Theory of Gravity (STG) and General Theory of Relativity (GTR)--makes more accurate predictions regarding time dilation, the experiment must have the following conditions for obtaining different results.

This theory will be developed further for more complete explanation of various gravitational events with less assumptions. In addition to time dilation, this theory is probably capable of explaining such phenomena as gravitational waves and those that occur in and around black holes. Gravitational waves would be movement of space-dimensions relatively backward and forward in time, caused by accelerating body of energy. Also, the velocity limit of "c" might possibly be explained by the limit in warpage of space in time. Quantum mechanical view of this gravitation model as well as its connection to other natural forces should also be explored.

Many questions regarding this theory are still unanswered. An interesting one is whether the attractive interaction between positive and negatvie energy across time is dependent or independent of the time interval between them. Another one is what parameters are affected by a change in the rate at which an object moves through the coordinate of time; the solution to this would allow us to choose experiments to detect time dilation as well as gravitational waves. since these effects are expected to be minute, advancement in space and telescope technologies would hopefully help us obtain conclusive results sometime in the near future.

Thus, the goals concerning this theory are to formulate it more completely, to compare it with existing theories like the relativity, and to test the accuracy of its predictions by experiments. Then this different perspective to gravity may lead to new interpretations of currently mysterious phenomena in the universe.

I sincerely thank Dr. Udo Pernisz for taking his time to meet with me and answer my questions, for trying to come up with an experiment to test my theory, and for advising me on writing this paper. I strongly wished we had met each other earlier. My deep thanks also go to my physics teacher, Mr. Chuck Trzcinski, who was patient with my seemingly slow progress, who was always willing to answer my questions, and who loves to teach physics. I would like to thank Mr. Bill Albe, too, for lending me related books and inroducing me to Dr. Jim Mentele whom I also thank for explaining the relativity theory to me. Finally, I wish to acknowledge my friend, Jake Miller, who originally provoked me to come up with my theory of gravity.