Essay: Systems of Measurements and Units in Physics
Georgi Stankov, March 11, 2017
“The laws of physics express relationships between physical quantities, such as length, time, force, energy and temperature. Thus, the ability to define such quantities precisely and measure them accurately is a requisite of physics. The measurement of any physical quantity involves comparing it with some precisely defined unit value of the quantity.“ (1)
This is the departing point of any intellectual effort in physics. In this essay I shall explain why the “ability to define“ physical quantities appears to be the “Achilles heel“ of modern physics.
I shall also explain why physicists have failed to grasp that energy = space-time = All-That-Is, which is the very object of their science, has only two dimensions – space and time – and not six fundamental dimensions as they currently claim referring to the SI system. This is the third biggest blunder in physics that is closely linked to their inability to understand epistemologically their own definition of mass as energy relationship which is a dimensionless number. This will be the topic of my next publication. The second one is to confound the basic physical quantity of electromagnetism and quantum mechanics, charge, which is in fact a synonym (pleonasm) of geometric area. This blunder has been thoroughly revealed in my pivotal publication:
which I will present in a simple popular-scientific version later on for the sake of completion of my discussion on all scientists’ blunders in physics and related disciplines.
In many ways, the new Physical and Mathematical Axiomatics and Theory of the Universal Law is a painstaking forensic exploration of the infinite blunders physicists and theoreticians have accumulated in less than four centuries since Galileo Galilei conducted his famous experiment on gravitation and laid the foundation of this natural science. Let us begin our methodological forensics with the epistemological background of the SI system which is in the core of this experimental discipline as not a single experiment can be conducted in physics without employing this system of basic SI units and physical quantities.
Everybody with a modicum of physical knowledge should know that the mathematical (symbolic) expression of any physical quantity consists of a number, which is a relationship between the magnitude of the assessed quantity and the arbitrarily chosen unit for this quantity, and the name of the unit. If a distance, e.g. the length of a soccer field, is 100 times longer than 1 metre (length unit of choice), we write for it “100 metres“. The magnitude of any physical quantity includes both a number and a unit. This presentation is a pure convention.
All physical quantities can be expressed in terms of a small number of fundamental quantities and units. Most of the quantities in physics are composed quantities within mathematical formalism. This is generally acknowledged. For example, speed is expressed as a relationship of a unit of length (metre) and a unit of conventional time (second) v=s/t (m/s).
The most common physical quantities, such as force, momentum, work, energy and power, which are basic to many physical laws, can be expressed with only three fundamental quantities – length, conventional time and mass. The set of all standard units in physics is called “Système Internationale“ or SI system. It consists of a few basic quantities and their corresponding units, from which all other quantities and units can be derived by applying the method of mathematical formalism (method of definition = method of measurement). These are:
- (1) length (metre),
- (2) conventional time (second),
- (3) mass (kilogram),
- (4) temperature (kelvin),
- (5) amount of substance, also called “the mole“ (mol),
- (6) current (ampere) and
- (7) charge (coulomb) (2).
The last two quantities are defined in a circular manner, so that they can be regarded as one quantity.
A major objective of this disquisition is to present theoretical and experimental evidence that these six fundamental quantities are axiomatically derived from the two constituents of space-time – space and time. I will begin with the first two quantities in this essay and will discuss the other four in follow-up publications. As all the other conventional quantities used in physics are known to be derivatives of these few quantities, this is also true for any new physical quantity.
This essay will render the fundamental proof that space-time has only two constituents, quantities, dimensions (synonyms) – space and time. This proof brings about the greatest simplification in modern physics which is now fragmentalized by inadequate definitions the epistemology of which has never been truly worked out in an axiomatic and logical manner. This I define in the new theory of the Universal Law as “applied mathematical formalism” which is another word for the new Integrated Physical and Mathematical Axiomatics of the Universal Law.
By way of introduction, we begin with the definition of the SI units of space and conventional time, metre and second. The definition of these quantities is at the same time the method of measurement of their units, which is applied mathematics and/or geometry. The standard unit of length ([1d-space]-quantity), 1 metre (1 m), was originally indicated by two scratches on a bar made of platinum-iridium alloy kept at the International Bureau of Weights and Measures in Sèvres, France.
This is, however, an indirect system (a surrogate) of standard length. The actual system of comparison is the arbitrarily chosen distance between the equator and the North Pole along the meridian through Paris, which is roughly 10 million metres. Thus the earth is the initial, real reference system of distance – the metre is an anthropocentric surrogate.
As this gravitational system of reference length was found to be inexact, the standard metre is now arbitrarily defined with respect to the speed of light. This quantity is defined in the new Axiomatics of the Universal Law as [1d-space-time] of the photon level: it is the distance travelled by light in empty (?) space during a time of 1/299,792,458 second. This makes the velocity of the photon level c = 299,792,458 m/s. The photon level, of which the visible light is a narrow spectrum (a system), has a constant velocity c.
This has been deduced in the new Axiomatics from the primary term of human consciousness – energy = space-time = All-That-Is – and confirmed by the theory of relativity and physical experience. The universal property of all levels of space-time – their constant specific velocity, also presented as a specific action potential EA being the universal manifestation of energy exchange – is intuitively considered in the conventional definition of the SI unit of length, 1 metre. So far, this fact has not been comprehended by all theoreticians.
Through the standard definition of space and conventional time (see below), the velocity of the photon level is voluntarily selected as the universal reference system of space-time, to which all other physical systems are set in relation (method of measurement).
The standard definition of the length unit reveals a fundamental epistemological fact that has entirely evaded the attention of physicists. The present standard definition of 1 metre by using the speed of light gives the impression of being clear-cut and unambiguous. In fact, this is not the case. The definition of this length unit is based on the principle of circular argument and involves the definition of the time unit, 1 second. If the latter unit could be defined in an a priori manner, all would be well.
When we look at the present definition of the second, which is at the same time the only possible definition of the quantity “conventional time t“, we come to the conclusion that this is not possible. The standard unit of time, being originally defined as 1/60×1/60×1/24 of the mean solar day, is now defined through the frequency of the photons emitted during a certain energy transition within the caesium atom, which is f = 9,192,631,770 per second.
In this case, we have again a concrete photon system with a more or less constant frequency, which has been arbitrarily selected as a reference system of time measurement. From this real reference system of space-time, an anthropocentric surrogate – the clock with the basic unit of 1 second – has been introduced. The conventional time of all events under observation is then compared with the time of the clock. Thus the measurement of time in physics and daily life is in reality:
a comparison of the frequency of events that are observed with the frequency (periodicity) of a standard photon system.
The method of definition and measurement of the quantity “conventional time t“ and its unit, 1 second, is therefore a circular comparison of actual periodicities. Such quantities are pure (dimensionless) numbers that belong to SP(A) (for further information see here). However, any experimental measurement of photon frequency involves the measurement of length – the actual quantity of time cannot be separated from the measurement of the wavelength λ, which is an actual [1d-space]-quantity.
Therefore, the two constituents of space-time cannot be separated in real terms because they are canonically conjugated. The equation of the speed of light c = λ f is intrinsic to any measurement of photon frequency and wavelength. Neither wavelength, nor frequency, can be regarded as a distinct entity – they both behave reciprocally and can only be expressed in terms of space-time:
c = λ f = [1d-space] f = [1d-space-time]p
The wavelength and frequency of photons are the actual quantities of the two constituents, space and time, of this particular level of space-time. The measurement of any particular length [1d-space] or time f = 1/t in the physical world is, in fact, an indirect comparison with the actual quantities of space and time of a photon system of reference. The introduction of the SI system obscures this fact.
The one-dimensional space-time of the photon level [1d-space-time]p is the universal reference system of length s = [1d-space] and conventional time t = 1/f, and their units, 1 metre and 1 second. The SI system is an anthropocentric surrogate of this real reference system and can be easily eliminated. In fact, it should be eliminated in theoretical physics as it only obscures the understanding of energy = space-time = physical world = All-That-Is. This is done in the new Physical and Mathematical Theory of the Universal Law.
This conclusion is of immense importance – I have shown in Volume II that the theory of relativity uses the same intrinsic reference system to assess relativistic space and time of kinetic objects. Lorentz transformations, with which these quantities are presented, are relationships (quotients) of the space-time of the object in motion as assessed by v with the space-time of the photon level as assessed by c. These are formalistic constructions within the system of mathematics. I have proved that these quotients belong to the probability set 0≤P(A)≤1 and can be expressed in terms of statistics as summarized in the new symbol SP(A). This abbreviation means “statistical probability of the event A” and represents the Kolmogoroff’s probability set (0,1), which is equivalent to the continuum of all numbers in Cantor’s set theory.
From this survey, it becomes evident that the physical quantities, length and conventional time, and their basic units, metre and second, are defined in a circular manner by the arbitrary choice of a real reference system of space-time – in this particular case, of photon space-time. The SI system is an epiphenomenon; it is a human convention and can be substituted by any other system through the introduction of conversion factors or better eliminated. This also applies to the other four basic quantities and their units, which will be discussed in separate publications.
Therefore, the definition of any physical quantity cannot be separated from its method of measurement, which is mathematics. The latter is, at the same time, its method of definition. Physical quantities as defined in physics do not have a distinct existence in the real world, but are intrinsically linked to their mathematical definition, which is a product of abstract human consciousness. Mathematics is a hermeneutic discipline without any external object. As any Axiomatics is also a product of human consciousness, the derivation of all known physical quantities from the primary term is essentially a problem of correct organisation of physical and mathematical thinking and not a problem that should be resolved through explorative empiricism.
Thus every method of measurement and every definition of a physical quantity are based on the principle of circular argument. This epistemological result of our methodological analysis of physical concepts is of universal character. The explanation is very simple: as every physical quantity reflects the nature of space-time as a U-subset thereof, its definition has to comply with the principle of last equivalence of the primary term which postulates that all terms that assess the primary term are equivalent independently of the choice of the particular words.
This fundamental axiom of the new Axiomatics is intuitively perceived by the physicist’s mind and is put forward in all subsequent definitions of physical quantities. As these terms are of secondary character – they are parts of the Whole – the actual principle applied in physical definitions nowadays is circulus viciosus. The vicious character of this principle when applied to the parts and the simultaneous negligence of the primary term explains why the existence of the Universal Law has been overlooked in the past.
Physics has produced in a vicious circle a large number of concepts, which are either synonyms or partial perceptions of the primary term. Unfortunately, they have been erroneously regarded as distinct physical entities. This has given rise to the impression that these physical quantities really exist. In fact, they only exist as abstract concepts in the physicist’s mind and are introduced in experimental research through their method of measurement which is mathematics.
Space-time is termless – it is an a priori entity; the human mind, on the other hand, is a local, particular system of recent origin that has the propensity to perceive space-time and describe it in scientific terms. Science originally means „knowledge“, but it also includes the organisation of knowledge – every science is a categorical system based on the primary concept of space-time. Only the establishment of a self-consistent Axiomatics which departs from the primary term of space-time leads to an insight that there is only one Law of Nature and allows a correct organisation of human knowledge on the basis of present and future empiric data.
1. Textbook on Physics, PA Tipler, p. 245 (I have used an earlier edition of this textbook, so that the pages may have changed. Note, George)
2. Some authors believe that candela (cd) is also a basic unit, but this is a mistake.