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.
