Unifying Quantum Physics and Relativity
The full unification of quantum physics and relativity is brought about in TDVP by applying the tools of CoDD and Dimensional Extrapolation to the mathematical expressions of three well-established features of reality, recognized in the current scientific paradigm: 1.) quantization of mass and energy as two forms of the same essential substance of reality; 2.) introduction of time as a fourth dimension, and 3.) the limitation of the velocity of rotational acceleration to light speed, c. In this process, the need for a more basic unit of quantization is identified, and when it is defined, the reason there is something rather than nothing becomes clear.
Einstein recognized that mass and energy are interchangeable forms of the physical substance of the universe, and discovered that their mathematical equivalence is expressed by the equation E=mc2. In TDVP, accepting the relativistic relationship of mass and energy at the quantum level, we proceed, based on Planck’s discovery, to describe quantized mass and energy as the content of quantized dimensional distinctions of extent. This allows us to apply the CoDD to quantum phenomena as quantum distinctions and describe reality at the quantum level as integer multiples of minimal equivalence units. This replaces the assumption of conventional mathematical physics that mass and energy can exist as dimensionless points analogous to mathematical singularities.
The assumption of dimensionless physical objects works for most calculations in practical applications because our units of measurement are so extremely large, compared to the actual size of elementary quanta, that the quanta appear to be existing as mathematical singularities, i.e. dimensionless points. (The electron mass, e.g., is about 1x10-30 kg, with a radius of about 3x10-15 meter.) Point masses and point charges, etc. are simply convenient fictions for macro-scale calculations. The calculus of Leibniz and Newton works beautifully for this convenient fiction because it incorporates the fiction mathematically by assuming that the numerical value of a function describing the volume of a physical feature of reality, like a photon or an electron, can become a specific discrete finite entity as the value of a real variable, like the measure of distance or time approaches zero asymptotically (i.e. infinitely closely). This is a mathematical description of a non-quantized reality. But we exist in a quantized reality.
Planck discovered that the reality we exist in is actually a quantized reality. This means that there is a “bottom” to physical reality; it is not infinitely divisible, and thus the calculus of Newton and Leibniz does not apply at the quantum level. This is one reason scientists applying Newtonian calculus to quantum mechanics declare that quantum reality is ‘weird’. The appropriate mathematical description of physical reality at the quantum level is provided by the calculus of distinctions with the relationships between the measureable minimum finite distinctions of elementary particles defined by integral solutions of the appropriate Diophantine equations. The mathematics of quanta is the mathematics of integers.
In TDVP we find that, for quantized phenomena, existing in a multi-dimensional domain consisting of space and time, embedded in one or more additional dimensional domains, the fiction of dimensionless objects, a convenient mathematical expedient when we did not know that physical phenomena are quantized, is no longer appropriate. We can proceed with a new form of mathematical analysis, the calculus of dimensional distinctions (CoDD), and treat all phenomena as finite, non-zero distinctions. Replacing the dimensionless points of conventional mathematical physics with distinctions of finite unitary volume, we can equate these unitary volumes of the elementary particles of the physical universe with integers. We can then relate the integers of quantum reality to the integers of number theory and explore the deep relationship between mathematics and reality.
In TDVP, we have also developed the procedure of Dimensional Extrapolation using dimensional invariants to move beyond three dimensions of space and one of time. Within the multi-dimensional domains defined in this way, mass and energy are measures of distinctions of content. If there are other dimensions beyond the three of space and one of time that are available to our physical senses, how are they different, and do they contain additional distinctions of content? If so, how is such content different from mass and energy? We know that mass and energy are two forms of the same thing. If there are other forms, what is the basic “stuff” that makes up the universe? Is it necessarily a combination of mass and energy, - or something else? For the sake of parsimony, let’s begin by assuming that the substance of reality, whatever it is, is multi-dimensional and uniform at the quantum level, and that mass and energy are the most easily measurable forms of it in the 3S-1t domain. This allows us to relate the unitary measure of inertial mass and its energy equivalent to a unitary volume, and provides a multi-dimensional framework to explore the possibility that the “stuff” of reality may exist in more than two forms.
The smallest distinct objects making up the portion of reality apprehended by the physical senses in 3S-1t, i.e. that which we call physical reality, are spinning because of asymmetry and the force of the natural universal expansion that occurs as long as there is no external resistance. If there were no additional dimensions and/or features to restore symmetry, and no limit to the acceleration of rotational velocity, physical particles would contract to nothingness, any finite universe would expand rapidly to maximum entropy as predicted by the second law of thermodynamics for finite systems. But, due to the relativistic limit of light speed on the accelerated rotational velocity of elementary particles in 3S-1t, the quantized content of the most elementary particle must conform to the smallest possible symmetric volume, because contraction to a smaller volume would accelerate the rotational velocity of the localized particle to light speed in 3S-1t, making its mass (inertial resistance) infinite. That minimal volume occupied by the most elementary of particles is the finite quantum distinction replacing the infinitesimal of Newton/Leibniz calculus, and it provides the logical volumetric equivalence unit upon which to base all measurements of the substance of reality.
We can define this minimal volume as the unitary volume of extent, and its content as the unitary quantity of mass and energy. The mass/energy relationship (E=mc2) is linear, since in the 3S-1t context, c2 is a constant, allowing us to define unitary mass and unitary energy as the quantity of each that can occupy the finite rotational unitary volume. This fits nicely with what we know about elementary particles: All elementary particles behave in the same way prior to impacting on a receptor when encountering restricting physical structures like apertures or slits. A particle of unitary mass occupying a unitary volume could be an electron, and a particle of unitary energy occupying a unitary volume before expansion as radiant energy, could be a photon. Einstein explained this equivalence between electrons and photons and Planck’s constant in a paper published in 1905.
This brings us to a very interesting problem: what happens when we combine multiples of the unitary volumes of mass/energy to form more complex particles? How do we obtain protons and neutrons to form the stable elemental structures of the physical universe?
When we view the spinning elementary particles of the 3S-1T physical universe from the perspective of a nine-dimensional reality, we can begin to understand how Planck was quite correct when he said “there is no matter as such”. What we call matter, measured as mass, is not really “material” at the quantum level. What is it then that we are measuring when we weigh a physical object? The real measurement of mass is not weight, which varies with relative velocity and location and can be zero without any loss of substance; it is inertia, the resistance to motion. The illusion of solid matter arises from the fact that elementary particles resist accelerating forces due to the fact that they are spinning like tiny gyroscopes, and they resist any force acting to move them out of their planes of rotation. An elementary particle spinning in all three orthogonal planes of space resists lateral movement equally in any direction, and the measurement of that resistance is interpreted as mass.
Mass and energy, the two known forms of the substance of the physical universe, embedded in a nine-dimensional domain, form stable structures only under very specific mathematical and dimensionometric conditions. Without these conditions, no physical universe could exist because of the second law of thermodynamics23, which dictates that any finite physical system always decays toward maximum entropy, i.e. total disorder, lacking structure of any kind. If our universe were composed of random debris from an explosion originating from a mathematical singularity, because of the continuous operation of the second law of thermodynamics in an expanding debris field, simple particles accidentally formed by random mass/energy encounter, would decay before a new random encounter could occur and form a more complex combination, because the number random encounters would decrease as the debris field expands. If our physical universe is embedded in the nine-dimensional reality described by TDVP, it escapes this fate of dissolution. While it may change and evolve, its form, and even the way it evolves, will always reflect the intrinsic logical order and patterns of the transfinite substrate within which it is embedded. If this is correct, we have the answer to the question Leibniz regarded as the first and most important metaphysical question of all: We can explain why there is something instead of nothing.