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 = r^{2} (*or more exactly,* »A« = **r _{1}**Λ

**r**;

_{2}*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)(**û _{s}** +

**û**) (

_{v}*compare the previous category point*). Of course, every double step to the right means a multiplication of the given quantity by the area »A« =

**r**Λ

_{1}**r**, and every double step to the left means a multiplication by Laplacian »∆« =

_{2}**k**Λ

_{1}**k**, 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«.

_{2}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 f

^{2}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 = f

^{2}*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 *m**r*** – 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.

Hello Mr. Jakubowski,

First of all, let me thank you heartedly for you have been the reason for my return to physics … A few years ago, I discovered the Naturics information and it prompted me to try to rebuild a dimensional analysis matrix I made when I was in electronic school. Your work showed me that it was indeed thinkable to unify domains of physics, leading eventually to the definition of physical quantities with respect to space and time only …

However, if you read my paper on this subject (see ref. at the end of this email), you will quickly notice that our results are different regarding the position of quantities on the matrix (not the dynamic plane quantities of course) … Obviously, our results are not compatibles and this is why I open this discussion … Please do not take this as a criticism of your work, which I find excellent, but as an attempt to explore the subject and find a demonstration of our hypothesis …

You will agree, I think, that it is only important to justify the position of 1 physical quantity (say mass for example) because all other can be deducted from the initial quantity … we know that F=ma and that [a]=LT

^{-2}… so, all other quantities can be derived from this … Note: for the electric charge, we must choose between the electrostatic and the electromagnetic version, but once the choice is made, electric domain quantities can also be deducted from mass.While reading your WEB site, I didn’t find the dimensional definition of mass (or the dimensional definition of an “initial” physical quantity) … The presented matrix imply that [M]=L

^{2}T, but how do you explain/demonstrate this?This is really the key to all the rest as a lot of deductions are following from this (new equations, new values, etc.) …

On the other hand, in my study, I decided to use another way of thinking because I couldn’t find anywhere in current knowledge a good demonstration of the space-time dimension of mass (the best mathematical demonstration comes from Xavier Borg’s Blazelabs … but I’m afraid I found a flaw in his reasoning) … Most of the time (e.g.: Maxwell), the dimensional definition of mass comes from an arbitrary initial assumption (i.e.: Maxwell assumes without demonstration that [M]=L

^{3}T^{-2}) … This is why I used the “cartesian product” (which represents all the possibilities of combining two sets: space and time) … In a nutshell:1) If we agree that the dimension of physical quantities can be derived from space-time only

2) Then, by definition, all physical quantities are part of the Cartesian product of the space and time sets

3) If we build a matrix that presents the Cartesian product of Planck space and time sets (Lpx * Tpy, with x and y = 0 to infinity … power exponents)

4) Then all Planck values must appear on this matrix

The point 1 is our initial hypothesis … Maxwell says [M] = L

^{3}T^{-2}… you say [M]=L2TThe point 2 has to be true by definition as the Cartesian product represents all combinations of the two initial sets (Lpx and Tpy).

The point 3 is what I did to represent visually this Cartesian product.

The point 4 is the key to all the reasoning … If point 4 is false, then point 1 must be false also … and mass is really a dimension in itself … But if point 1 is true, then point 4 must also be true.

The last sentence means that the value of the Planck mass should appear at the expected location (L

^{3}T^{-2}for Maxwell or L^{2}T for you) … If the value does not appear, it means that the dimensional proposal is false.Mathematically, we can also say that if [M]=L

^{3}T^{-2}(and so [G]=1, i.e dimensionless), then automatically [F]=L^{4}T^{-4}because F=Ma (the use of F is only an example, we could use any other value instead). Now, in a Planck’s world, we should have then Fp=Lp^{4}Tp^{-4}, the same way we have GMp=Lp^{3}Tp^{-2}. Using a calculator, we accurately find GMp=Lp^{3}Tp^{-2}, but we fail to find Fp=Lp^{4}Tp^{-4}. Finding GMp is mandatory because we know for sure that it corresponds to Lp^{3}Tp^{-2}. On the other hand, finding Fp is related to wether [M]=L^{3}T^{-2}is true or not. Because we do not find Fp=Lp^{4}Tp^{-4}, we can categorically say that [M]=L^{3}T^{-2}is false … The same demonstration can also be done with [M]=L^{2}TThen, what I did was to build the Planck matrix into Excel and search for the Planck quantities (mass, electric charge, force, etc.) without an a-priori assumption about their location/dimension … What I found is quite strange and I will welcome your comments about this …

My original paper:

http://www.worldsci.org/pdf/abstracts/abstracts_5385.pdf

An extended version with more demonstrations:

http://www.losangeinformatique.com/physics/dimension_of_physical_quantities.htm

Regarding unification of physical domains, I went further with this paper:

http://www.worldsci.org/pdf/abstracts/abstracts_5995.pdf

The long version:

http://www.losangeinformatique.com/physics/ospweb.pdf

Again, let me congratulate you for your excellent work that I will continue to read with great pleasure.

Best regards,

Laurent Hollo

Dear Mr. Hollo,

Thank you for your comment and for directing my attention to your interesting work trying to order the physical quantities into some new structural entities. The main problem with your analysis has been introduced already on your Fig.1, where you are defining your Space-Time Matrix. You are using for this construction the two Planck’s „axes“: the Planck space (length) and Planck time. However, as has been discussed in my books („Naturics“, for example), the Planck Scale does not describe any particular physical state. Neither the Newtonian gravity „constant“, nor the „vacuum“ speed of light, nor the universal Planck’s quantum of action belong to the same state of some physical system. Therefore, even independently of the quite surrealistic (non-natural) values of the Planck Scale, your time-axis TP belong to some different physical „space-time“ than your space-axis LP.

The partial success of your analysis has been only possible because of the really unified nature of all physical quantities (as demonstrated with the Unified Family). Nevertheless, the dimension of mass, as you are postulating it ([M]=L

^{7}T^{-7}), would mean that mass should equal for example to the seventh power of some velocity. Nobody has ever found such a relation.On page 2 of your article „Definition of Fundamental Quantities“ , NPA, Vol. 6, No. 2 you write: „In addition, there is nothing in current knowledge that allow us to find the dimension of G and M separately without using a circular reasoning or an initial arbitrary choice. “

It is not longer true today. I have shown that we are able to define the gravity as the effect of a changing acceleration; where the acceleration acting upon a physical body remains constant, there is no gravity acting upon this body. Therefore, the dimension of the gravity factor G (in your sense) is the dimension of the acceleration times T

^{-1}( i.e., [G] = LT^{-3}).In summary, your work is very important as a negative check whether or not the „cosmological“ Planck Scale could be usable in physics. This scale is false as long as the original values of G

_{N},c_{0}, and h have been used in it, and it turns to be a meaningless identity when the unified universal values have been used instead of that. It would be interesting to see your structural investigation in the traditional physics based on my Unified Family of all physical quantities.Thank you once more,

Peter Jakubowski