1. Introduction

When the creators of classical science and mathematics defined space and time, they had to predict all experiences related to time and space in their environment. These experiences included measurements with rods (rulers) and clocks, plus the motion of bodies relative to each other. Also, each body was defined within a Galilean reference frame, which postulated that all laws governing these bodies are relative to their reference frames. This principle of the relativeness of laws to a reference frame was reaffirmed in Einstein’s first postulate of the special theory of relativity. [1, 2, 3] However, what made Einstein’s special theory of relativity different from classical theory was his second postulate that states that light had a constant speed relative to any reference frame. In order to satisfy this second postulate, Einstein augmented classical physics, and this resulted in special relativity theory. Although most of the special relativity theory is impeccable, its weak point is that it is an augmentation of the past. Einstein preserved archaic principles of classical space and time in special relativity. These archaic principles include the separation of time from space, the definition of time and space without using particles, the infinite speed of space, a fourth dimension for the time axis, and the concept of a mass defining matter. Also, special relativity gives a particle’s exact location and speed, which contradicts Heisenberg’s uncertainty principle. [4, 5] Furthermore, the probabilistic wave theory for matter cannot be predicted from special relativity. Consequently, special relativity is a classical theory, but not a quantum theory.

In this paper, I create a new theory, one that is a quantum theory of time and space, but not a classical theory of time and space. In doing this, however, I must still predict the results of classical and relativity theories that have been experimentally proven to be accurate. As a result, I must predict rod and clock measurements, the relative motion of bodies, Einstein’s first and second postulates of special relativity, other verified relativistic results, and three dimensions, which is the only number of dimensions verified to exist. (Distance-time theory only uses three dimensions. Generally, new theories of space and time have more dimensions though not less than special relativity, which has four.) However, in these traditional theories of relativity and classical physics, some principles are not experimentally verified; rather, they are assumed. I do not predict some of these principles in my paper. Instead, I derive novel principles in my new theory of time and space. Since I predict experimentally proven results of special relativity in my theory, and derive different principles and results in areas where special relativity is not verified, I am presenting a theory of time and space which is more accurate than special relativity theory.

In section 3 of my paper, I create a new approach to time and distance that contrasts with the traditional approaches of classical and relativity theories. Although, traditionally, distance and time have been treated separately, all measurements of distance and time require that particles move across a distance in a period of time. Therefore, distance and time are not measured independent of each other, but are always measured together in nature. The premise that distance and time are combined in nature is the distance-time premise.

Traditional theories, on the other hand, define time and space independent from particle motion, allowing for their definition of a time separate from a space. Consequently, they do not satisfy the distance-time premise. Yet, in nature, the distance-time premise is always obeyed because space and time cannot be measured without particle motion. Rod measurements obey the distance-time premise. Light particles that move from one end of a rod to the other end must cross a quantity of distance and time. These light particles allow an observer to see the rod extended out, thus, allowing an observer to measure with the rod. As a result, rod measurements obey the distance-time premise. If I were to measure the distance from the earth to the moon, I could use a light beam or possibly a rocket. However, the light beam and rocket are made of particles which travel a distance and a time together; therefore, I would not measure distance separate from time, thus satisfying the distance-time premise.

In order to make a measurement, clocks also require that any particle move across a distance in a period of time. The internal workings of any clock require electron or sprocket motion. Consequently, clocks do not measure time separate from distance and they obey the distance-time premise. Since all measurements of distance and time always obey the distance-time premise, I create, in section 3 of my paper, a three-dimensional manifold in which distance and time are combined and defined with particle measurement by an observer. Furthermore, Einstein’s postulate of the constancy of the speed of light in a vacuum can be predicted in three dimensions, if a distance, D, is equal to a period of time, T, multiplied by the speed of light in a vacuum, c. Therefore, I combine distance to time in this three-dimensional manifold so that D=cT. I call this union of distance and time distance-time. Using this approach, I satisfy the distance-time premise and derive the experimentally proven results of classical and special relativity theories in sections 3 and 5 of my paper. I derive clock and rod measurements, the motion of bodies relative to each other, the observation of a three-dimensional space, and the experimentally verified predictions of Einstein’s special theory of relativity. There are some predictions that result from my new theory of distance-time, and these predictions contrast with those of traditional theories. The following statements contain a brief listing of most of these new predictions; (1) Distance is equivalent to time; (2) Space has a finite speed equal to the speed of light in a vacuum; (3) Space contracts to an infinitesimal point at a single point of time; (4) A structure of time and space which possesses only three dimensions; (5) A structure of time and space that agrees with Heisenberg’s uncertainty principle and the probabilistic position of a matter-wave; (6) Matter possesses a scalar rest momentum instead of a mass; (7) Some predictions about the behavior of light particles; (8) The speed of quantum tunneling. The minimum requirements to be a quantum time and space theory is that it agree with elementary quantum theory. Since Heisenberg’s uncertainty principle and the probabilistic position of a matter-wave agree with distance-time theory, then distance-time theory is essentially a quantum theory of space and time. This is a major reason for creating distance-time theory and it contrasts with special relativity, which is actually a classical theory. The fact that distance-time theory agrees with elementary quantum principles does not mean that distance-time theory is a form of relativistic quantum mechanics. Relativistic quantum mechanics is essentially applying relativity to quantum theory. In contrast, distance-time theory is not about applying relativity to quantum theory. Instead, it is a novel structure of time and space with intrinsic quantum characteristics, and it makes new predictions not found elsewhere.

Next, I will briefly explore the finite speed of space and space that is contracted to an infinitesimal point. In section 3 of my paper, I define a distance-time manifold and delineate unique characteristics of its space. An example of the latter is that space has a finite speed in a distance-time manifold. This is totally different from special relativity theory in which space occurs at an infinite speed, due to the fact that the distance in relativity occurs perpendicular to the time axis at a single point of time. This result contradicts with nature’s behavior. In nature, time and distance can only be observed via a particle and no particle traversing time and distance can exceed speed c. Therefore, distance cannot occur faster than speed c relative to an observer. In distance-time theory, however, distance and time are defined via particles and are combined so that distance occurs over a period of time. Therefore, distance occurs at a finite speed. I often refer to this characteristic as the finite speed of space since space has distance defined throughout it. In the universe, this means that the gap (distance) between an observer and any object occurs at a finite speed. Also since the gap has a finite speed, zero distance occurs at an infinite speed between the observer and any object. Since zero distance occurs at infinite speeds, space is infinitesimal at the single point of time of the present (the now) relative to the observer. This characteristic of space is totally different from any characteristic of space in special relativity, for in special relativity, space occurs infinitely fast and is never infinitesimal relative to the observer.

In section 6 of my paper, I define a reference frame for light traveling in a vacuum and show that light disobeys the principle of causality. This behavior of light is not derived in relativity theory. Also, I predict that photons can interact with each other only under certain circumstances. Although I do not derive a reference frame for light directly out of reference frames for matter, I do define the reference frame for light based on principles of distance-time theory that I define for reference frames of matter.

In section 4 of my paper, I define quantum tunneling as something that happens via an infinitesimal space. Although distance-time theory predicts that faster-than-light travel across a space is impossible, it also predicts that faster-than-light travel via an infinitesimal space is possible. Therefore, I predict faster-than-light speeds for particles tunneling via an infinitesimal space, and I give solutions to different causality paradoxes that maybe caused by these tunneling particles. This is not done in relativity theory nor in classical space and time theory.

In order to understand my theory, one must have an understanding of Einstein’s special theory of relativity, and an understanding of elementary quantum theory.

Overall, the relationship between distance-time theory to the special theory of relativity is best portrayed in figure 1. This figure displays two circles. The smaller is included within the larger one. The larger circle’s area includes special relativistic results plus predictions only found in distance-time theory. Everything enclosed within the larger circle is predictable from distance-time theory. The smaller circle’s area represents only verified predictions made by the special theory of relativity.