2. PREPARATION OF PERSPECTIVE

2.1. The distance-time premise

The distance-time premise is that distance and time are joined together in nature, possessing dual characteristics of distance and time. This premise contrasts with traditional views which do not equate time with a scalar distance. The premise of distance-time may be proven wrong if distance or time can be measured independently. However, if any measurement is accomplished by particle motion, an independent distance or time measurement has not been achieved, as particles travel across distance and time jointly.

The rod (ruler) measurement has been traditionally seen as a measurement of distance separate from time. However, the location of every part of the rod is communicated by photons that traverse distance and time. Therefore, rod measurements are dependent on particle motion. They are not a measurement of distance separate from time. Furthermore, the difference between locations of physical bodies is always communicated by particle motion across distance and time. For instance, if I try to determine the difference of position between the earth's and the moon's surfaces, I may use a light beam or rocket. Yet, both are groups of particles which cross distance and time and move between the earth and the moon. Therefore, I would not achieve measurements of distance independent of time. Consequently, all measurements of distance by an observer in nature are made across a period of time.

Traditionally, the clock measurement has also been seen as a measurement of time separate from distance. However, clocks use particle motion in order to measure. The traditional clock has spindles which sweep across the face of the clock, crossing time and distance together. Also, a digital electronic clock requires electrons to move across time and distance jointly. These clocks do not achieve measurements of time independent of distance.

In the previous examples, measurements of distance or time, which are independent of each other, were not achieved. Therefore, the distance-time premise remains valid. However, traditional theories, such as relativity, do not use particles to define distance and time, and they do not satisfy the distance-time premise; instead, they always separate time from distance.

In chapter 3, I define a structure of time and space so that an observer placed in this manifold would literally measure distance and time the same as would be done in nature. Consequently, an observer in this manifold would literally have the same perspective of time and distance as an observer in nature would have via particles, with distance and time combined.

2.2. Distance-time theory's unique idea of space

Sometimes when scientists come upon a new idea, they try to develop the best terminology to describe their idea. In comparing the difference of how space is defined between special relativity and this new theory, I coined the two phrases: the “finite speed of space” versus the “infinite speed of space”. I make the following scenario, scenario one, the simplest situation. Two people are at rest in the same reference frame, and all forces are negligible. One of them takes out a large ruler to measure the distance between them. How fast does that ruler exist between them? In special relativity, that ruler exists infinitely fast between them. In other words, at any given moment of time, that ruler exists in the gap between them. I would like to see anyone prove the assumption that special relativity has just made. This assumption has never been verified, and I claim in this theory that it can never be verified because it is wrong. There are some special relativity books that do discuss that the ruler does exist infinitely fast between those two people in scenario one. [1] These books are correct in their understanding of special relativity. Nonetheless, it is only an assumption that special relativity makes. (If I am correct about the existence of space in nature, this assumption is wrong.) In special relativity, this gap, or distance that the ruler occupies, is a part of the same reference frame at rest relative to both persons in this scenario, and this gap exists at each given moment of time relative to them. In other words, this gap occurs infinitely fast, or another description is that the gap exists at a single point of time according to special relativity. Hence, with both of them at rest in their shared reference frame, the time axis in special relativity is defined as being perpendicular to the three space axes. Therefore, in special relativity, space is still defined as being separate from the time axis. A person can make a point about relativity claiming that it does bring time and space together in a manner that classical theory never did. Nonetheless, within my own reference frame, I still would measure space separate from time. It is only when there is a difference of velocity between two observers that one's measurement of distance relative to the other is not simultaneous according to special relativity—not when they are both at rest.

Now, in scenario two, a person (Victor) has a constant velocity relative to me. According to special relativity, I should see Victor's measurement of distance contract in the direction he is moving relative to me. In other words, I would indirectly—not directly—measure his distance as existing nonsimultaneously. In special relativity all space that I can directly measure occurs simultaneously relative to me. This includes the space that Victor is moving through relative to me. The idea is that a person's space exists only relative to that person—not relative to me. In scenario two, it is by Victor's direct measurement of space that I can indirectly determine that his space is nonsimultaneous relative to me. The reason for all space being simultaneous relative to me is that in my reference frame all space exists according to my measurements, which is done simultaneously or at a single point of time relative to me. Hence, in special relativity, directly measurable space can only exist simultaneously relative to the observer who is directly measuring it. Furthermore, in scenario two, the nonsimultaneity of space only exists indirectly to me through Victor's measurement but never directly through my measurement. Since all points of space that I can directly measure in my reference frame exist simultaneously, the existence of space is infinitely fast relative to me. This infinite speed of space does not exist in distance-time theory, which is just the reverse.

In contrast, distance-time theory asserts something very different. In a distance-time manifold, distance divided by a quantity of time is equal to the speed c, which is the speed of light in a vacuum. There is a constant scalar relationship between distance and time. To explain its meaning, I use scenario one of two people being at rest in the same inertial reference frame. They again place a ruler between themselves. However, this time the ruler does not exist right now between them; nor does the gap exist between them right now, according to the distance-time equation (D/T = c). Therefore, this gap between them only exists over a period of time, which totally contradicts special relativity's assumption of the infinite speed of space or simultaneity of space. Furthermore, one cannot even imagine a gap (distance) existing right now between two people as special relativity portrays in people's minds. In distance-time theory, all that should be imagined existing at a single point of time is an infinitesimal space, which is a point space. Distance can only be directly measured and perceived as existing nonsimultaneously (over a period of time) in distance-time theory, whereas in special relativity distance could only be directly measured as existing simultaneously. The concept of a finite speed of space is very difficult for the human mind to literally visualize, as the human mind is limited by what it can imagine. It is easier to just interpret the distance-time equation (D/T = c). This equation means that the distance D exists over a period of time, T, at a rate of c, which is the speed of light in a vacuum. In scenario one, the ruler and the space the ruler occupies would literally exist between two persons as fast as they could determine the ruler's existence via particles. And, the speed c is the fastest speed that can be measured.

2.3. The finite speed of space

In our everyday experience, all distance and time can only be observed via particles. In nature, therefore, no distance or time can occur relative to an observer any faster than it can be communicated to that observer. Naturally, I do not discount the possibility that one might think that distance could occur faster than an observer could measure. Nevertheless, the distance would still not exist relative to the observer any faster than the observer could measure it. Also, in our environment, all that is real to an observer is only that which an observer can detect. Thus, in our natural surroundings, neither distance nor time occurs relative to an observer any faster than it can be communicated to that observer. Since no particle moves faster than speed c across space relative to an observer in the universe, no distance can be defined as occurring faster than speed c in the universe. This contradicts the special theory of relativity. In special relativity, distance is perpendicular to the time axis and it occurs at a single point of time. Consequently, all space in special relativity occurs infinitely fast. This result disagrees with nature and the distance-time theory, which I further illustrate in the next paragraph.

I imagine two brothers, Nathan and Steve, tossing a ball between each other. Nathan wishes to determine the speed at which the gap (distance) occurs between him and Steve. Using light beams and subtracting out the time it takes for the light beam to travel between him and Steve, he synchronizes his watch with Steve's. Next, he tosses the ball as fast as he can towards Steve and measures the time it takes the ball to travel from him to Steve. After dividing the distance that the ball travels by the period of time it travels, he derives the velocity of the ball. This proves that there is a distance occurring between him and Steve at least as fast as the velocity of the ball. Nathan realizes that the fastest way he can measure the speed at which the distance occurs between the two of them would be to shine a light between him and Steve. This light is assumed to be traveling in a vacuum. Since all that is real in nature, relative to the Nathan and Steve, is that which is detectable by them, the gap between them cannot occur any faster than speed c relative to them. This result totally disagrees with special relativity theory. In the latter theory, both Steve and Nathan can be placed in space a distance apart at a single point of time relative to each other. Consequently, the distance between each other would occur infinitely fast relative to either one. This allows both brothers to be located a distance apart faster than they could measure each other's location with a particle. In distance-time theory, however, distance is combined with time and is only defined via particles. Consequently, in distance-time theory, distance occurs over the period of time a particle travels. Therefore, the gap between Nathan and Steve can only happen as fast as Nathan or Steve could measure with a particle.

This result agrees with our actual everyday experience. In our natural environment, no object can have a location relative to an observer until that observer detects the object’s location via a particle. Thus, the gap between an observer and any object cannot occur any faster than can be measured with a particle. Therefore, distance cannot be perceived to occur infinitely fast in nature and in distance-time theory. Since distance is defined throughout the three dimensions of space, the speed of space has a finite speed no faster than speed c in distance-time theory and in our everyday environment. Only an infinitesimal space can be perceived to occur at infinite speed in distance-time theory and our everyday environment. In other words, relative to Nathan or Steve, the distance between them at a single point of time of the present (the now) has not yet occurred, and thus, the gap between them is shrunk to zero in distance-time theory and nature.

In sections 3.8 and 3.10, I delineate more about the finite speed of space and about an infinitely quick, infinitesimal space as I delve into the characteristics of the distance-time manifold. Also, since some may assume that the concept of a finite speed of space refers to the concept of an expanding universe, I must emphatically declare that this reasoning is completely without merit. (See section 3.9.)

2.4. Visualizing the finite speed of space within the human mind

To fully appreciate the concept of a finite speed of space, one must first realize that within the model construction of relativity and classical theories space is assumed to be infinitely fast. It may seem to some people that an observer at the origin of a coordinate frame can record the light signals he gets on his retina, apply his assumption about light propagation being at speed c, and infer space-time coordinates for the sources that sent him the signals. In that way, he can come up with space-time coordinates that have a finite difference in space but no difference in time. The underlined part is an assumption that traditional theories make about the speed at which the distance (gap) occurs between coordinates. These theories assume that the distance between coordinates is occurring at an instant ("no difference in time"). Consequently, the distance is assumed to be occurring at an infinite speed. However, it is not necessary to assume that distance occurs infinitely fast, since there is absolutely no physical evidence that supports the concept of an infinite speed of space.

The problem with seeing the assumptions people make is that people often are not aware they are making them. The human mind is limited in what it can visualize. For instance, I cannot literally imagine four dimensions. In my mind, I can only visualize three dimensions. To work in four dimensions, scientists use the mathematics created in three dimensions and then extend this mathematics to both imagine and work with an extra dimension. Therefore, these scientists never directly visualize four dimensions. They only use the mathematics for four dimensions. Summarizing, one cannot literally visualize a space of finite speed. The simple reason for this is that not only does the human mind visualize solely three dimensions, but the human mind also only imagines a space which is infinitely fast. In other words, a whole space that is always there (happening at an instant) is what our minds solely visualize. As a result, it is quite easy to assume that space is infinitely fast without realizing one has made this assumption.

To perceive the concept of a finite speed of space, I need to rely primarily on mathematics. Within distance-time theory, I define distance as being equivalent to time, according to the equation D = cT. Rearranging this equation, I derive D/T = c. I interpret this latter arrangement to mean that the rate of distance occurring per period of time is equal to speed c. In the model construction of distance-time theory, therefore, distance happens over a period of time and at a speed c. Distance does not happen at an instant within distance-time theory.

It is extremely difficult for the human mind to perceive distance not occurring between two coordinates at an infinite speed, since every model construction of space and time I try to conceptualize is embedded within a space of infinite speed as pictured in my mind. As a result, I can be easily fooled. The way to deal with the dilemma of this erroneous picture of space in my mind is to mainly rely on the mathematical interpretation I have postulated.

As I discussed earlier, within the construction model of distance-time theory, distance is defined as not occurring instantaneously between locations in space. At an infinite speed (a single point of time), therefore, I define distance as contracted to an infinitesimal point between all locations in space (an infinitesimal space). Distance is essentially an abstract concept that represents the magnitude of the difference between distinct coordinates in space. Since the distance occurring between coordinates at an infinite speed is contracted to zero, there is no distinction between coordinates at any single point of time. In other words, there is zero distance between different coordinate locations at an instantaneous speed. Space as people normally experience it should not be conceptualized to exist at a single point of time. Only a space that has contracted to an infinitesimal point should be pictured as existing at an infinite speed. The space I live within everyday exists solely at a finite speed, but never does this space that I always see happen at an infinite speed. Space has not occurred yet at speeds faster than speed c, which is the speed of space. Some people may be perplexed about how there could be an infinitesimal space existing at any instant of time. For instance, how could the human body exist within a space that has contracted to a single point? The human body would exist only within a space of finite speed. As a result, all the actions and reactions transpiring within the body could not happen any faster than speed c.

Since a four-dimensional space-time continuum in general relativity theory assumes that space is infinitely fast, an infinitesimal space existing at an infinite speed cannot be derived from the theory of general relativity. Therefore, this infinitesimal space is an independent idea from the concept of a singularity found in general relativity theory. (I answer questions regarding an infinitesimal space in sections 3.10 thru 3.13.)

2.5. A major motivation for the creation of distance-time theory

I claim that distance-time theory is a more accurate theory than the theory of special relativity. This assertion should not be seen as a direct challenge to special relativity theory. In reality, the idea of distance-time is a direct challenge to the four-dimensional space-time continuum, the latter of which is far more similar to the classical space and time theory than it is to the distance-time theory. The four-dimensional space-time continuum and classical theory of space and time always give an exact location and speed of a particle. Thus, they do not agree with Heisenberg's uncertainty principle and do not predict the probabilistic location of a particle. Also, the minimum requirement to be a quantum theory of time and space is that it agree with elementary quantum theory principles. Consequently, the four-dimensional space-time continuum is not a quantum structure but a classical structure. In contrast, the distance-time theory agrees with Heisenberg's uncertainty principle and predicts that particles will have a probabilistic location until their positions are measured by an observer. Then the probabilistic location of the particle collapses to a smaller region where the amplitude of the wave exists relative to the observer, which is also predicted by distance-time theory. It is important to note that the structure of time and space, found within distance-time theory, possesses these quantum properties mostly without relying on quantum theory. The principles of quantum theory are for the most part only discussed as a reference point for predictions made by distance-time theory. These characteristics of distance-time theory are significant, and they lead me to conclude that distance-time theory agrees more with elementary quantum theory than with the classical theory of space and time. Therefore, the theory presented in this article is not a classical theory but a quantum theory. Furthermore, quantum theory by itself is not a structure of time and space, yet it does make inferences about time and space. Both Heisenberg's uncertainty principle and the probabilistic location of a particle are essentially laws stating the relationship of a particle to space and time. These laws about a particle's relationship to space and time are significant! Yet, special relativity does not predict these laws. On the other hand, distance-time theory does predict these laws. This prediction of quantum laws 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 about a novel structure of time and space with intrinsic quantum characteristics, and it makes new predictions not found elsewhere.

In later sections, I define distance and time in distance-time theory as continuous. However, since quantum mechanics does not predict that distance and time necessarily come in quantified amounts, a quantum theory of time and space may define time and space as continuous. In chapters 3 and 4 of this article, I describe further the relationship of distance-time theory and quantum theory. Although distance-time theory is a quantum theory and as such a direct challenge to the four-dimensional space-time continuum, it still predicts the experimentally proven results of special relativity. Furthermore, since it does predict quantum and special relativistic results, it may, in fact, be a more accurate theory of time and space than the theory of special relativity.

Another important item is the search for a quantum theory of gravity. Since modern gravitational theories rely on a warping of space and time, it is important that a quantum theory of space and time be found, if a quantum theory of gravity is ever to be realized.

2.6. New testable predictions only made by distance-time theory

To separate distance-time from special relativity and quantum theory, distance-time theory must make predictions which neither special relativity nor quantum theory can make. One such prediction is the speed of quantum tunneling. The speed of quantum tunneling is given by Eq. 27, which states that quantum tunneling cannot occur slower than speed c. Along with this prediction, I give solutions to causality paradoxes for tunneling faster than light. Furthermore, I define rules of time and space for light that predict that photons only influence each other under certain conditions. These conditions I describe in chapter 5, which deals with a photonic distance-time. Moreover, in that chapter, I predict that the law of cause and effect does not apply to the photon. Since distance-time theory makes predictions not made elsewhere, it is a new theory.