The three fundamental units of measurement in the science of Physics are:

1. Distance [measured in Meters (met.)].
2. Time [measured is Seconds (sec.)].
3. Mass [measured in Kilograms (kg.)].

The British 17^th Century thinker Isaac Newton essentially founded the modern science of Physics by establishing four very simple axioms:

1. The Law of Inertia.
2. Force equals mass times acceleration (F = ma).
3. The Conservation of Linear Momentum (for every action there is an equal and opposite reaction).
4. The Gravitational Constant (Configured in such a manner that the resultant units are in terms of Force, which can describe the elliptical orbits of the planets in the solar system.

The Classical Mechanics initiated by Newton achieved remarkable success up until around the beginning of the 20^th Century.  During the 18^th and 19^th Centuries, certain other physical postulates were asserted, such as the Conservation of Energy [Kinetic Energy plus Potential Energy equals Constant (KE + PE = C)]; as well as the Second Law of Thermodynamics (the state of Entropy of any physical system tends to increase over time).  At the beginning of the 20^th Century, however, the discoveries of the Quantum of Action (h) by Max Planck and the Theory of Relativity by Albert Einstein disparaged the absolute validity of the prior Classical Physics.

During the 1920’s, the branch of Physics known as Quantum Mechanics (QM) was developed by scientists such as Erwin Schrodinger, Werner Heisenberg, and Paul Dirac.  Essentially, the fundamental axiom of Quantum Mechanics is what is called the Schrodinger Wave Function (Psi Function).

The Psi Function is not, strictly speaking, a Kinematic Theory (Kinematics is a branch of Physics which deals with the motions of material bodies) but a Theory of Probability.  The Psi Function can predict, with the utmost accuracy, the likeliness of the outcomes of large numbers of empirical experiments on the microcosmic domain.

To state the case mathematically, the Psi Function predicts the outcome of a particular experiment based on the probability amplitude squared of the resultant vector:
[(PA)² = V].

The tenets of QM are held by contemporary science to be capable of analyzing processes at the atomic and sub-atomic level, even though the Uncertainty Relation of Heisenberg proves that nothing at this diameter (10^-10 met.) can even in principle be an empirical concept.

Since the age of Newton, Physicists and Chemists have searched in vain for the fundamental building block of Nature, the alleged Elementary Corpuscle.  The notion that if we keep building these gigantic particle accelerators, empirical verifications of nebulous hypotheses like the “Graviton” or the “Higg’s Boson” can be accomplished, belies a misunderstanding of the nature of Reality itself.

In the ancient world, Water was held to be one of the four Elements (the other three being Earth, Air, and Fire).  Then in the 18^th Century, Water was shown to be composed of two underlying types of Atoms: Hydrogen and Oxygen.

Yet an Element on the Periodic Table such as Carbon, Hydrogen, or Oxygen was itself later seen to contain even smaller particles: Protons, Neutrons, and Electrons.  Now it seems as though the Nucleons (Protons and Neutrons) themselves are composite structures made up of Quarks, Leptons, etc.  No matter how far science has dug down it has never found these basic, indivisible building blocks of existence.

The Theory of Atomism (that the World is composed of nothing but Atoms in the Void) was merely one of a number of competing metaphysical theories of the ancient world, and can show how Physics has much to learn from Philosophy.  Immanuel Kant demonstrated that, when contrasting different metaphysical constructs, it is not a question of sheer truth or falsity.

Perhaps the world can be thought of as not composed of Elementary Corpuscles but of Infinitesimal Events.  An Event is defined as the appearance of Mass (kg.) at a certain point in Space (met.³) at a certain time (1/sec.).  This paradigm is elaborated on more fully at the website: “http://www.phenomenologybooks.com.”  Also, the reader is referred to the book: HYPERMETROPHIA: A Phenomenological Unified Theory of Fields, where these thought processes are presented in a more organized fashion.

Recently the attempt is being made to synthesize the two major systems of thought within contemporary Physics, namely Quantum Mechanics with the General Theory of Relativity.  This is obviously an unattainable goal, simply because of the fact that these two systems of mathematical thought are axiomatically irreconcilable with each other.  This attempt can result only in a complex, incoherent failure.

The Theory of Relativity is primarily concerned with calibrations of coordinate systems (Invariant Transformations).  There is hardly any empirical data contained in it; notably the equivalence of inertial and gravitational Mass, as well as the Invariance of the Speed of Light in a vacuum.

The vast majority of the General Theory of Relativity (GR) is composed of the Tensor Calculus, a type of Linear Algebra containing 4-Dimensional arrays that are true for all possible observers.  This methodology was successful, for instance, in incorporating the equations of James Clerk Maxwell that describe the electro-magnetic Field.

In the domain of the solar system, GR is essentially equivalent to the Classical Mechanics.  The increase in empirical accuracy of GR is limited to minor fluctuations in the orbit of the planet Mercury.  Yet the entire scientific world-view had been upended by the relativistic theory, going back to the “Relational Space” of Leibniz; and explaining the mysterious “Instantaneous action at a distance” about which Newton famously remarked “Hypothesis non fingo” (I make no hypotheses).

Newton in his axioms defined Mass as a sort of negative resistance to inertia.  Mass was conceived by him to be proportional to the amount of influence necessary to further alter an object’s trajectory.  For example, a bowling ball weighing 1 kg. requires more Force to move it than the Force required to move a billiard ball that weighs 100 grams (0.1 kg).  Likewise, a marble of 10 grams (0.01 kg.) would accelerate even faster given the same Force applied on it upon moment of impact.  To a certain extent, Physics treated Mass as entirely dependent upon these space-time Kinematics to ascertain its quantity.

The Theory of Relativity accounts for the concept of Mass in a rather awkward and incomplete manner within its 4-Dimensional Space-Time Dynamics.  Concepts such as a 4-Force or the Energy-Stress-Momentum Tensor are clearly an area upon which GR can be improved.

Rather than attempting to make progress by clumsily trying to combine QM with GR, we can advance Physics by incorporating the concept of Mass as a primary variable within the Tensor Calculus of GR itself.  I have been working on a set of as yet unfinished equations to accomplish this task.

In these forthcoming equations, Mass is defined as “Substance” and is construed as constituting neither a Particle nor a Wave, but as an expansion and curvature of the Space-Time Continuum.  The “Quantum Jumping” problem can be solved by making the Displacement Vectors discrete rather than continuous.

By incorporating the unit of measurement of Mass (kg.) in a fundamental way into the Tensor Calculus of GR, this series of equations shall seek to unify the Microcosmic Domain (Quantum Mechanics), the Macrocosmic Domain (Classical Physics), the Cosmoscopic Domain (General Relativity), and electromagnetism (Maxwell’s equations).  Here the overall goals will be simplification and explanation, rather than description or predictability.

In an earlier Blog on this post, the distinction between the Empirical Sciences and the Theoretical Sciences was postulated (confer: “Epistemological Difficulties”).  The Principles of the Theoretical Sciences ought to be contrasted with Statements written in vernacular Prose.

For example, “The area of a circle equals its radius squared multiplied by pi” is much easier said by simply stating: “A = π × r².”

The Principles of the Theoretical Sciences seem to exist independently of any conscious observer.  It doesn’t matter who performs the calculation “7 + 5.”  If they get any other solution besides the number “12” it is an incorrect solution.  Likewise with “7 × 5 = 35.”

A certain ambiguity arises when the conventionally held philosophical alternative between what are called “Synthetic a priori Propositions” and “Analytic a priori Propositions” is made.  The word “analytic” means taking things apart and the word “synthetic” means putting things together.

For instance, the Proposition “All bodies are extended” was held to be Analytic; whereas, the Proposition “All bodies are heavy” was held to be Synthetic.  These kinds of arbitrary dichotomies obviously are obsolete.

To allay this confusion, what were formerly called Synthetic a priori Cognitions ought to be replaced by a contrast between the Principles of the Theoretical Sciences and other types of scientific statements expressed in Prose.  These Theoretical Sciences are comprised mainly by Logic, Mathematics, and Geometry.

The most compelling feature of the Theoretical Sciences is their structure.  Simply put, this structure is composed of Axioms, Rules of Inference, and Consequences.  The Consequences of a Theoretical System can be derived in a decidable manner from the Axioms and the Rules of Inference.

The Science of Physics bridges the gap between the Theoretical Sciences and the Empirical Sciences.  This explains the alleged “Pre-established harmony between Mathematics and Physics.”  Yet recently contemporary physics seems to be running up against a glass ceiling of philosophical discourse.  The metaphysics of materialism is clearly no longer a viable hypothesis.  Certain notions such as the multiverse or relativistic space can be analyzed using the methodology of Ontology.  Clearly, physics needs philosophy now more than ever.

The word “Phenomenology” was coined by the 20^th Century German Philosopher Edmund Husserl, which he defined as “Philosophy as a strict science, with an open frame of reference.”  Like most Philosophers from the early 19^th Century onward, Husserl was heavily influenced by the 18^th Century German Philosopher Immanuel Kant.

The book I am working on now, Meta-Scientific Phenomenology, shall pick up Epistemology where Kant left it, informed by the empirical data of Relativity Theory and Quantum Mechanics.  It is important to understand that the ideas of Kant did not come out of a vacuum, but were dependent upon the contemporary thought at that time.

The Classical Physics of Isaac Newton was achieving astounding success both in describing astronomical events as well as helping to foment the Industrial Revolution.  Meanwhile, Philosophy was deducing a null result.

Bishop George Berkeley and David Hume, two British 18^th Century Philosophers, were denying any type of absolute knowledge whatsoever.  Berkeley held that material objects are illusory, and that all reality exists as ideas within the mind of God.  Hume was casting doubt upon the Law of Causality, and asserted that consciousness is merely meaningless thought associations.  A humorous commentator remarked on this series of events by saying “Never mind, no matter.”

That is how Kant discovered the a priori (Latin for “before the fact”).  He marveled at how statements such as “7 + 5 = 12” or “The sum of the interior angles of all Triangles on a flat surface equals 180 degrees.”  These kinds of Propositions Kant called “Synthetic a priori cognitions.”

The principles of Logic, Geometry, and Mathematics are purely Objective, and exist independently of any individual Observer.  In the terminology of the Theory of Relativity these relations are what is called “Invariant.”  They seem to exist independently of human thought.  The Argument Forms presented in Handbook of Logical Validity are examples of this type of concept.  To call them a priori is perhaps obsolete.  It would be better to call them Principles of the Theoretical Sciences.

The Theoretical Sciences are defined as Logic, Geometry, and Mathematics.  In contrast, Physics, Chemistry, and Biology can be called Empirical Sciences.  More details on this scientific compartmentalization can be found within the book HYPERMETROPHIA, which is described on the Website (www.phenomenologybooks.com).

Perhaps Hume was correct, in the sense that the Newtonian Physics of his day did not constitute some kind of inviolable Law of Nature, but was essentially a Principle of Human Understanding.  The extent to which Classical Mechanics corresponds with Reality is an issue which cannot be fully resolved here.

The fact that Quantum Mechanics and Relativity Theory have evolved over and above the older Classical Physics constitutes a kind of Confirmation of Hypothesis for the assertions made by thinkers such as Berkeley, Hume, and Kant.

Relativity had “removed all trace of physical objectivity from time and space.”  The Uncertainty Relation of Quantum Mechanics states that it is in principle impossible to perform an Empirical Experiment without fundamentally altering the Phenomena observed.  The Uncertainty Relation also holds that anything at the Atomic level (around 10^-10 meters) is by definition not an Empirical concept.

Simply put, Physics begins with Inter-subjective Empirical Reality and ends with the Conscious Observer.  Philosophy begins with the Conscious Observer and ends with Inter-subjective Empirical Reality.  Clearly these two branches of knowledge ought to be brought together within the Science of Phenomenology.