last updated: 01/01/2003
CLASSICAL vs. MYSTICAL REALITY
An examination of the ambiguous mathematics and amphigoric logic employed by the special theory of relativity when calculating the kinetic energy and momentum of a photon clearly illustrates the difference between the conceptual framework of a classical and that of a mystical reality.
In accordance with the special theory of relativity the kinetic energy of a material point of mass is given by the expression K. E. = m c²/(sq rt,1-v²/c²). Professor Einstein does not provide an explanation as to how the above expression was logically developed, however it is evident that the equation's denominator (sq rt,1-v²/c²) is identical to the contraction factor employed in the Lorentz equations. See Albert Einstein, Relativity The Special and General Theory (1961), pp. 44 - 48.
However when the above relativistic expression is utilized to determine the kinetic energy of the photon a problem is encountered. When the velocity variable v of the expression is set equal to c in accordance with the law of the propagation velocity of electromagnetic phenomena, the denominator of the equation is reduced to zero, that is (sq rt,1-c²/c²) = 0 so that the resulting relativistic expression for the kinetic energy of the photon becomes K. E. = m c²/ 0.
A review of the classically accepted fundamental arithmetic properties of the number 0 establishes that 0 × a = 0, when a is any number and that 0 / b = 0 when b is any number other than 0. Division by 0 however is not defined and therefore is considered an inadmissible operation.
The Indian mathematician Brahmagupta (A.D. 600) did go as far as to assert that 0/0 = 0, but refused to commit himself on the matter of b/0, when b # 0. See Carl B. Boyer, A History of Mathematics(1968), pp. 242.
Heeding the aforementioned definitive principles of fundamental arithmetic, classical realism endorses the logic that division by 0 is an inadmissible mathematical operation. As a result the relativistic expression K. E. = mc²/0 must be regarded as indecipherable and/or nonfunctional and therewith any and all inferences based on the equation K. E. = m c²/(sq rt,1-v²/c²) as pertaining to the kinetic energy of a photon are invalid and as such incapable of supporting absolute physical law.
The logic of mystical relativism on the other hand concludes differently. Based on unspecified principles of arithmetic, relativism ignores the 0 denominator of the equation and further assumes that the numerator or photon's mass m is equal to 0. As such, the kinetic energy of the photon would then be expressed as K. E. = 0 c², leaving a photon with no energy, an empirically unsound result, a result providing relativism with its next intellectual challenge, a challenge however that is no match for the mystical powers of relativistic logic.
Although the photon's mass m is set equal to 0 and hence the kinetic energy of the photon would appear to be 0, the photon is still deemed to possess energy in the form of rest mass; a concept somewhat difficult to visualize considering the photon's substantial velocity. Nevertheless, armed with this logic and therewith setting velocity v equal to 0, mystical relativism asserts that (rest) E = (rest) mc²/(sq rt,1- 0²/c²) or E = m c² and therefore m = E/c². This allows E/c² to be substituted for the photon's rest mass m wherein the photon acquires energy without the need for mass or velocity, i.e., E = (E/c²) c² or E = E. This puzzling bit of logic produces a photon with mass equal to 0 in terms of kinetic energy while having mass equal to E/c² in terms of rest energy. The terminology of mystical relativism attempts to mask this logical dilemma by defining the photon's rest mass m not as mass but rather as a function of energy, i.e., E/c², supposedly depicting a state of matter without the physical attribute of mass and mystically referred to as "pure energy". This logic then serves as the foundation for the imaginary unification of the mass and energy conservation laws which presumably provides the primary justification for special relativity's acceptance.
This approach however lacks practical appeal. Either the cohesive bundle of radiant matter known as the photon exists as a singularity (particle) or it does not. If, as quantum theory postulates, it does indeed exist as a singularity (particle) then it must by virtue of its singular existence be subject to the forces of nature and respond accordingly. For what is mass if not the measure of a singularities response to force. A response amply attested to by way of reflection, diffusion, refraction, and dispersion of that singularity (particle) called the photon. For inasmuch as the photon's physical mass exists as a function of force, so too must the photon's physical mass exist as a function of kinetic energy, mass in motion and kinetic energy being different sides of the same coin. Understanding the true nature of the photon therefore will more likely come through the realization that the concepts of energy and mass are different measures of the same material phenomenon (matter) then through the elimination of mass from the photon's energy equation.
In fact mass and energy, in the classical sense, are terms that exist merely as part of a conceptual framework of logical mathematical expression and as such provide distinct quantifications of the same material phenomenon (matter). Because mass and energy are attributes only, without substance, they are equated only as interrelated logical constructs (functions) and are not the substance or matter they purport to describe. It is for this reason that matter cannot be converted into "pure energy". The true nature of matter in motion is that it must always be perceived in terms of both mass and kinetic energy. Even the relativistic equation for matter without motion (E = mc²), considered solely in terms of energy, does not convert matter into energy but only redefines energy, solely in terms of energy, i.e., E = (E/c²)c² or E = E. The unification of the laws of conservation therefore can only be achieved through the realization that the words mass and energy provide different quantifications of the same phenomenon (matter).
Another empirical fact testifying to the physical mass of a photon is that of its known momentum. How does mystical relativism impart momentum into its supposedly mass-less photon. Let us objectively contemplate the logic employed in achieving this mystical mathematical feat. Calculating the momentum p of the photon, relativistic theory utilizes the formula p = m v /(sq rt,1-v²/c²). The photon, again judged to be at rest, is considered to have a velocity of 0 and therewith the velocity v in the equation's denominator is set equal to 0, so that p = m v /(sq rt,1- 0²/c²) = m v.
As evident in the resulting expression p = m v, the momentum p of the photon has been reduced to a function of the photon's mass m multiplied by the photon's velocity v. However both the mass and the velocity of the photon must be greater than 0 for the photon to exhibit momentum. Since the only possible mass available in relativistic doctrine exists under the pretense of rest energy, relativistic theory again imputes its alleged non mass energy function E/c² to provide the needed mass for the photon's momentum, so that the new equation becomes p = (E/c²) v. But, as indicated, even the acceptance of this supposed non mass energy as mass is not sufficient to produce momentum, also required is velocity.
Herein comes to play the inevitable mathematical legerdemain of mystical relativism. The intellectual slight hand is accomplished by changing the photon's velocity v from a state of rest to a state of propagation, from the value 0 back to the value c. Of course to be logically consistent as classical arithmetic principles dictate the photon's velocity v in the resultant equation p = (E/c²) v must also be 0, the value originally utilized for velocity v in the denominator of the equation. Doing that however would produce 0 momentum and readily prove the original relativistic expression to be invalid. Instead the value now utilized by relativistic theory for the photon's velocity v mysteriously becomes c, the photon's velocity of propagation, so that p = (E/c²) c or P = E/c. Remarkably the photon's velocity v therewith exhibits a state of mystical duality being equal to 0 km/s and to 300,000 km/s simultaneously, but fret not for all is well in the mathematical fantasyland of special relativity. The peculiar result of this incomprehensible mathematical abstraction is a photon, presumed to be at rest possessing a non-mass mass, with 0 kinetic energy, yet traveling at the speed of light. A duplicitous work of creative logic if ever there was one. Incredibly this alleged mass-less photon concurrently at rest and in motion is capable of wielding all the power of mass times velocity, i.e., momentum, and in so doing purports to validate the mathematical illusion of special relativity.
In an attempt to legitimize the result without deference to the means, relativism's momentum equation p = E/c is ultimately reduced to p = h / l by incorporation of Planck's quantum energy equation E = h f and the light wave equation c = f l. Needless to say, this mathematical illusion is unable to alter reality as the unit of measure for the photon's momentum (kg m/s) still includes the unit of measure for mass (kg). In fact momentum along with force and energy are all products of matter in motion and all contain the unit of measure for mass (kgs). With respect to momentum the matter in motion is assessed in terms of velocity. With respect to force the matter in motion is assessed in terms of acceleration. With respect to the dynamics of energy the matter in motion is assessed in terms of acceleration x distance. Accordingly the mystical concept of a mass-less photon is equally as preposterous as the previously discussed mystical concept of rest energy.
In essence the mathematics and logic employed by mystical relativism are self serving, their primary function being one of validation. Classical realism's mathematics and logic are touted as inadequate with respect to relativity theory. The presupposition of E = mc² as the equivalent of kinetic energy and rest energy i.e., the unification of matter and energy, allegedly confirms the mathematical principles of special relativity. Because relativistic theory is therewith presumed a priori a universally valid theory, the mathematics and logic adopted to validate it remain exempt from the realistic constraints of common sense.
Having thus examined some of the mathematical and logical intricacies of mystical relativism employed by the special theory of relativity, what does reason dictate concerning the merits of this methodology. Can it provide a valid interpretation of temporal reality?
Reason dictates that mathematics is first and foremost an exercise in arithmetic logic. When a mathematical statement is made in accordance with logical arithmetic construct it is said to be mathematically valid. When such a mathematically valid statement can be proven through empirical evidence to define temporal reality, it is deemed an absolute law. Hence to be considered an absolute law of temporal reality a mathematical statement must be both arithmetically logical and empirically evidenced.
Whereas the fundamental design of mathematics aspires to the expression of that which is knowable and empirically provable, the fundamental calling of mysticism aspires to that which is unknowable and inherently not provable, i.e., that which exists outside the bounds of temporal reality. The realm of mysticism free from the laws of temporal reality cannot be reduced to arithmetically logical expression and hence is not testable by empirical methods. In fact because mysticism has no means of achieving logical arithmetical expression or empirical verification, from a scientific perspective it opens up a Pandora's box of of imagined realities all contending for legitimacy as valid interpretations of temporal reality.
Contemporary academicians having embraced the arithmetically flawed mathematics and misguided logic of special relativity, in an albeit adamant attempt to define temporal reality, have inadvertently directed their collective thought process into the realm of the unknowable, a realm outside the bounds of temporal reality, the realm of the mystical. A realm, sad to say, in which they are powerless to conceptualize a mathematically logical system of thought. A realm physical science has spent the better part of the last millennium avoiding. This scientific regression into the realm of mysticism has laid the logical thought process of classical realism bare to the whims of expediency and therewith the conjuring spirit of mystical indoctrination; the symptoms of which are all to evident in today's academic mind set, a mind set unashamedly espousing the mathematical prestidigitation and pseudo logic of special (mystical) relativity.