The Unified Family of all physical quantities will be defined here.
We have to note from the very beginning one important difference between the physical quantities defined in the Unified Family and all traditionally defined physical quantities. In the Unified Physics we consider always quanta of matter. Therefore, also the unified physical quantities, which are physical characteristics of our description of such quanta of matter, have to be considered always as quantum characteristics; for example, quantum length, quantum area (size), quantum time (period), quantum mass, and so on.
The four standard physical quantities of the traditional physics are length r, time t, mass m and the electric current i (or the electric charge q). Now, we are going to define our Unified Family of all physical quantities allowing us to reduce the number of the necessary standard quantities to just two, the quantum length (characteristic size) r and the quantum time (characteristic period) t. Also the quantum mass and the quantum charge will be shown to be uniquely defined by these two quantities.
Firstly, let us shortly recall to the history of the number zero (0). The Hindu-Arabic numerals were probably introduced around 500 AD, and in 825 AD, zero was introduced by a Persian scientist, al-Khwārizmī, in his Book on Arithmetic, synthesizing Greek and Hindu knowledge about fundamental mathematics, including an explanation of the use of zero. However, it was not earlier than in the 12th century, that the Arabic numeral system was introduced to the Western world through Latin translations of his Arithmetic. Zero is extraordinary in arithmetic because it separates two numerical “worlds”, that of the positive numbers from that of the negative ones.
A similar role of a “separator” between two other “worlds” of numbers plays the number 1. It separates the “world” of the large natural numbers (larger than 1) from the “world” of the small numbers (positive but lower than 1, being nothing other than the reciprocals of all natural numbers). A corresponding role of a “separator” plays our new physical quantity, the universal unity. It separates the “world” of the “natural” physical quantities from the other “world” of their reciprocal physical quantities, as shown in the figure below.
The length r is the most popular physical quantity, whereas the wave vector k is its reciprocal quantity, what means that r*k = 1 (remember: always in a quantum sense). Similarly frequency f is a reciprocal quantity to time t, because t*f = 1. (Note that »t« and »f« are bivectors, but we are leaving their dimensions out of our consideration at the moment). Furthermore, also the speed c has its reciprocal vector quantity, the spatial density of mass rho_m. Why it should be so, we are going to explain now.
Let us consider the basic movements across the emerging two-dimensional plane of the physical quantities around the universal unity, as demonstrated in the figure below.
In order to reach the place of the area A (an obviously planar “construction”, thus a bivector too, »A«), we have to repeat twice the same motion as between k and 1, or between 1 and r. We say in that case that we multiply the universal unity 1 twice with the length r. We have therefore the obvious relation: A = r2 (or more exactly, »A« = r1Λr2; compare the previous page in this category). In order to reach the speed we have to multiply the universal unity with the length r and with the reciprocal time, that means with f = 1/t.
These basic movements are always the same, in the whole emerging Unified Family of all physical quantities. This means that in order to make a step within the family to the next quantity on the right is equivalent to multiplication of the given quantity by the length-vector r, whereas a step to the next quantity on the left is equivalent to multiplication by the reciprocal wave vector k, where k = (1/r)1 = (1/r)(ûs + ûv) (compare the previous category point). Of course, every double step to the right means a multiplication of the given quantity by the area »A« = r1 Λ r2, and every double step to the left means a multiplication by Laplacian »∆« = k1 Λ k2, and so forth. Similarly, a change to the adjoining physical quantity immediately below the given quantity just means a multiplication of the given quantity by the bivector of time »t«, and a change to the upper adjoining quantity – a multiplication by the reciprocal bivector of frequency (or rotation) »f«, where »f« = (1/t)»1«.
In the extended figure of the dynamical plane above, we see that for the acceleration a we either have to multiply the speed c with the frequency »f«, or to multiply the frequency »f« with the speed c, or also to multiply the frequency with itself and than the scalar frequency square f2 with the length r. Do you see it? We are just “rediscovering” the simplest relations between the physical quantities. They are the simplest physical equations: c = r*f, a= c*f = f*c = f2 *r.
If you are not a physicist or you need some more details about the Unified-Family planes, click here.
Analyzing the dynamical plane of the Unified Physics we recognize quickly that the only possibility to define the scalar mass °m exclusively by means of some spatial and temporal characteristics of the FL is to choose the bivector of the quantum area »A« and the bivector of the (local) quantum time »t«, and to define the quantum mass as the inner product of these two bivectors: °m = »A« · »t« = »t« · »A«.
What does it mean? If mass °m is the mass of a given quantum of matter, then »A« means the „living“ area of the quantum. This quantum does not need more space to exist, but on the other hand, it cannot exist in the same state on a smaller area. On the other hand, the bivector of the local time »t« can be understood as a period of the internal rotation of the spatially extended quantum of matter. Note that it is not possible to construct a similar model in which both the mass and time are scalars, as in the case of the traditional physics.
Now we can see, why the reciprocal of the quantum speed c is the spatial mass density rho_m, can`t we? Spatial mass density means just to multiply mass three times with the wave vector k.
During the long history of development of our traditional physics some scientists have defined the electrodynamic physical quantities independently of the dynamical ones. Therefore we have to consider these quantities also in our Unified Family as ordered on a separate electrodynamic plane, as shown below.
Fortunately the ancient physicists were consequent enough in their work and thus on this plane are valid the same basic movements as on the dynamical plane. The corresponding positions of these both planes relative to each other are shown with the blue line in the following diagram.
The electrodynamic plane differs from the dynamical plane only by a constant value of the universal magnetic induction B (equivalent to the universal value of the planar current density j); (the universal values will be discussed in one of the following posts in this category). This means that in order to “connect” an electrodynamic quantity (for example, the magnetic field H, or the electric potential U, or the electric charge q) with its dynamical counterpart, we have to multiply the dynamical quantity, lying directly above the chosen electrodynamic quantity, with the scalar quantity B=j. In our examples this gives the following relations (physical equations): H = B*r = j*r; U = B*F = j*F; q = B*m = j*m. Some of them are obvious also for the traditional physics, some should be discussed more extensively (you can do it just here).
As the first task which you can solve with the idea of the Unified Family please try to find out which dynamical quantity should be placed on the right of the mass on the dynamical plane (my secret tip: it is traditionally so-called mr – mass momentum) and what is its electrodynamic “equivalent”. As the result you should define by yourself the electric charge of a quantum of matter by means of its size (A or r) and its period t. (However be aware that the traditional physics maybe would award you with Nobel Prize for this discovery (:-)).
In order to quicker learn the individual positions of all physical quantities in the Unified Family please copy these two small pictures and print them out for your daily exercise.
After only few days you would have all possible physical equations just in your head. You will have never more problems with physical equations.