 ### Unified Theory Foundations

© Engineer Xavier Borg - Blaze Labs Research

A note on h and h-bar

Arguments showing why h-bar (Dirac's constant ) should NOT be used to derive Planck units

Unfortunately, a lot of scientific literature state Planck units expressed in terms of (=h/(2p)) known as Dirac's constant, or the reduced Planck's constant. THIS IS INCORRECT. The 2p factor in fact leads to totally different (and wrong) numeric values for Planck units, than the original values set out by Planck himself. The 2p factor is a gratuitous addition, coming from the failure to address the Hydrogen atom's stable orbits as defined by the orbital path length being an exact multiple of the orbital matter (standing wave) wavelength. The statement that the orbital electron's angular momentum is quantised as in:

m.v.R = n.(h/2p) = n. for integer values of n, is just a mis-statement of

2p.R = n.h/(mv) .... which when substituting for h=E/f, v=f.l, and m=E/(f.l)2... we get:

2p.R = n.l ..... which means that the 2p factor has nothing to do with h as such, and that the orbital path is just an integer number of wavelengths as described by Louis De Broglie! (see diagram above). Dirac's was thus defined due to lack of understanding of the wave structure of matter, and its use should be discouraged. Some physicists still prefer to use h-bar, not for any scientific reason, but mostly for the sake of simplicity in their calculations. Their main point of view about the argument is that preferring h to h-bar amounts to preferring a circle whose circumference is 1 to a circle whose radius is 1, and that setting h equal to 1 instead of hbar = 1 amounts to working with a circle of unit circumference instead of unit radius. Though this may look simple and true when one views the problem in euclidean (plane) geometry, one has to keep in mind that the euclidean geometry is only an approximation to the properties of physical space, and Einstein showed that space gets elliptically curved (non-Euclidian) in the regions where matter is present. The shortest path in a non-euclidean space is a curved path, and though it does not seem logical, the straight line joining two points may be a longer way to go than the curved path between the same two points. The matter wave (De Broglie wave) shown above is not being forced to loop round the circle, it is just following the easiest and shortest path in its non-euclidean space. Planck's work was not about electromagnetic waves travelling in free space, in which euclidean geometry is a good approximation, but on the interaction of such waves with matter. Matter plays an important role in all Planck's work, and thus, a non-Euclidian space has to be preferred for all Planck units, and so, a circumference value must be used in favour of a radius value as the shortest length, whether or not normalised to unity.

For this reason, in all my work, I've chosen to use the original Planck units which are expressed in terms of h, Planck constant. The following derived values in fact are in perfect agreement with Planck's original values. Using the original Planck values for S (Lp) and T (tp), and simply plugging their value in the ST system of units, based on h, one can in fact DERIVE the numeric values for constants such as free space impedance, Von Klitzing constant, Quantum conductance, Josephson constant and more (see next page). If one tries to do the same thing using the numerical values for Planck's length and time based on h-bar, all derived values for the mentioned constants will be wrong! For these reasons, I can say with absolute certainty, that the Planck's values based on Dirac's h-bar are wrong and any scientific literature showing otherwise, would better revert them to the h based units, or at least make sure the readers are aware of the mentioned arguments.

The Spacetime freespace constants & Fine structure constant

In the ST system of units list we can clearly see that ALL physics constants and parameters have spacetime in common. Space and time are inter-related, in that dimension S can be differentiated (observed) by dimension T, and vice versa, depending which dimension is taken as reference by the observer. S and T however can be deduced separately, in conditions where space-time is continuous, that is everywhere, as far as we know. The whole universe can be explained in terms of these two interacting dimensions S and T which have unique values. Note that in this unification theory, unlike what we perceive as human beings, both Space and time have the same number of dimensions, and are both SPATIAL. In such a theory a volume of time T3 with respect to S for an observer in the spatial dimension S, has the same properties of a volume of space S3 with respect to T for an observer in the spatial dimension T. This may sound strange for most of us, because we are used to view the universe with respect to time, and perceive the spatial dimension T only as our temporal dimension. If you cannot grab this concept, do not worry, as you should still be able to understand the main issues. The condition for the universe to exist is that we have TWO such spatial dimensions interacting together. As we say 'It takes two to tango'.

Natural Units (also known as Planck or God's units) So, as we have shown in the conversion table, both Mass & Current can be reduced to space time equivalents with no requirement for any hard particle unit as the kg. However, one cannot expect to put natural values for S and T in the ST equivalent of mass and get a result in kg. The kg unit is not a natural unit, but a fictitious man made unit. It is in fact the last SI base unit to be still based on a prototype. In 1889, the 1st CGPM sanctioned the international prototype of the kilogram, made of platinum-iridium, and declared: This prototype shall henceforth be considered to be the unit of mass. The picture at the right shows the platinum-iridium international prototype, as kept at the International Bureau of Weights and Measures under conditions specified by the 1st CGPM in 1889. This is a worrying fact for NIST, and in fact, we found that resolution 7 of the 21st General Conference on Weight and Measures, had in fact called for a redefinition of the kilogram, and offered to redefine the kg as The mass of a body at rest whose equivalent energy equals the energy of a collection of photons whose frequencies sum to 135639274E42 Hz. Such redefinition has not yet taken place. In fact all physical units such as Candela, Joules, heat capacity, etc... where setup to different standards for historical reasons.

During his lifetime, Planck had derived a set of standard units. As opposed to the SI standard, these units are based on the natural constants : G (gravitational constant), h Planck constant, c Speed of light, k Boltzmann constant and permittivity. They are based on universal constants and thus known as Planck's natural units. The two basic Planck units can be easily derived from my ST conversion table as follows:

h = [k]T2/S
c = S/T
G = [1/k]S6/T5
k = kg conversion factor (read following paragraph)

So, h = [k]T/c and G = Tc6/[k]
Gh = T2c5
T = (Gh/c5)1/2

Substituting S=Tc, we get:
S = (Gh/c3)1/2

 Natural Length (S) (Gh/c3)1/2 = 4.051319933E-35 m Natural time (T) (Gh/c5)1/2 = 1.351374868E-43 s

Knowing the natural values for S and T we can now easily define a conversion ratio between the ST units and the man-made unit we call the kg. This constant works out to be equal to (hc7/G)1/2 or kQ=1.469944166E18 and is dimensionless. So :

 Mass (kg) = 1.469944166E18 (T3/S3) = kQ (T3/S3)

This factor has therefore to be applied to all those units quoting the kg SI unit, for example, for Force (Newtons) we know that its SI units are kg.m/s2 so to convert the ST values into Newtons, we have to apply the same conversion equation that we use for the kg.

The above conversion constant will also be applied to energy. Although the Kelvin unit in ST has the same dimensions as energy, the conversion constant for Kelvin is not the same. We know that 11604.499 Kelvin is equivalent to 1eV, which is equal to 1.602E-19 Joules. One Kelvin is equal to 1.3806E-23 Joules, where 1.3806E-23 is Boltzmann constant k. It follows that the conversion ratio from Space Time parameters to Kelvin units is given by

 Kelvin (K) = [kQ/k](T/S) .... k=Boltzmann constant

This factor has therefore to be applied to all those units quoting the Kelvin SI unit, for example, for Thermal conductivity we know that its SI units are kg.m/s3/K so to convert the ST values into SI units, we have to apply factor kQ for the kg unit and factor [kQ/k]-1 for the Kelvin-1 unit.

The ampere is the next redundant unit introduced in the SI due to lack of knowledge of the EM nature of matter. This unit is defined as that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 Newton per meter of length. In my ST conversion, current simply translates to the much neater definition of velocity of EM energy: S/T.

Now Natural Current= electron charge per unit time = q/(hG/c5)1/2 = j*(S/T)
Dimensionless conversion factor j= 3.954702562E15. So :

 Current (Amps) = 3.954702562E15 (S/T) = j (S/T)

Derived Planck Units

Using the above calculated unit conversion factors, and the ST conversion table, we can derive many other natural units and constants.

For Natural length we have: Length = S = 4.05132E-35m = Planck's length, sometimes also (wrongly) quoted as S/sqrt(2pi) = 1.61624E-35m

For Natural time we have: Time = T = 1.35137E-43 sec = Planck's time, sometimes also (wrongly) quoted as T/sqrt(2pi) = 5.391E-44 sec

For Natural speed we have: Speed = S/T = 4.05132E-35/1.35137E-43 = 299.79E6m/s = speed of light

For Planck constant or Natural Angular Momentum we have: h = kQ (T2/S)

h= 1.469944166E18 * ( 1.351374868E-432/ 4.051319933E-35) = 6.626E-34 kg m2/sec

For Gravitational constant G we have G = (1/kQ)(S6/T5) works out to 6.672E-11 m3/sec2/kg
This time we used 1/kQ since we have kg-1 in the SI units of G.

Now from units of energy kg m2/s2, we know that the same constant kQ has to be applied to energy equations. So for energy we have:

E= kQ (T/S) = 1.469944166E18/ 299.792E6 = 4.9032E9 Joules = Planck energy.

For Natural mass we have: Mass = kQ(T3/S3) works out to = 5.456E-8 kg = Planck mass, sometimes also quoted as M/sqrt(2pi) = 2.17645E-8 kg

For Natural Power we have: Power = kQ(1/S) = 1.469944166E18/4.051319933E-35 = 3.6283E52 Watts = Planck Power

For Natural charge we have: Charge = j (S) = 3.954702562E15 *4.051319933E-35 = 1.602E-19C = electron charge

For Natural current we have: Current = j (S/T) = 3.954702562E15 * c = 1.18559E24 Amps = Planck current

For Natural Temperature we have : Temperature = [kQ/k](T/S) = (1.469944166E18/1.380662E-23)(1/c) = 3.551344E32 Kelvin

A comprehensive list of numeric values for all known physical units has been worked out on the next page.

The FINE STRUCTURE CONSTANT ENIGMA So far so good, all parameters get the exact known natural values by using the derived constants k (for kg unit) and j (for Amp unit). Now for the tricky part: The free space constants. In the SI system of units we note a few units like permittivity, permeability, impedance, conductance, etc... that for some weird reason have the kg as part of their unit. For example permittivity is defined as Amp2.sec4/kg/m3, Impedance = m2kg/sec3/Amp2. Since during the development of the SI system, nobody ever wondered that the kg unit was actually representing a standing wave electromagnetic structure, we see that this unit has been applied also to units which, although represent a volume of 3D energy (T3/S3), are NOT standing waves. The space time dimensions for a 3D outgoing or incoming travelling volume of energy is the same as that of a 3D standing wave, but the conversion constant for the kg in these two cases is different.

Let us take an example to make everything clear:

We know that Freespace Impedance = 376.73 Ohms ... Radio engineers know this very well

Now the ST equivalent for Impedance = T2 S-3 and its SI units are: m2kg/sec3/Amp2

To calculate the natural Impedance, we first put in the natural values for S and T, then multiply by the kg conversion factor kQ, and divide by the square of the Amp conversion factor j.

Natural Impedance = 25812.807 Ohms, also known as Von Klitzing constant Rk.

In 1985, a German physicist Von Klitzing was awarded the Nobel Prize for Physics for his discovery that under appropriate conditions the resistance offered by an electrical conductor is quantized; that is, it varies by discrete steps rather than smoothly and continuously.

And here we have got the interesting discrepancy between Natural & Freespace impedance. This is no mathematical mistake, as we know that both the freespace impedance and the natural impedance have been experimentally confirmed under different conditions. This discrepancy comes from the fact that natural values apply to a standing wave 3D energy structures, whilst freespace impedance applies to travelling waves as we know.

Working out the ratio Z0/ZNAT = 376.7303/25812.807 = 1/68.518 = 2/137.036

I have found out that the ratio of these two impedances is given exactly by:

Free space Z0 = ZNAT * 2a

Where a is the well known Fine structure constant, given by = a= m0.c.e2/(2h)= 1/137.036

From this we deduce that although the SI system does not recognise two types of kg units (having the same dimensions T3 S-3) we have a relation between the kg used in 'matter' equations and the kg used in free space 'wave' equations:

 kgfreespace/kgmatter = 2a ÷ = 2a

This means that for units defining a travelling EM volume of energy, the kg conversion constant kQ, has to be multiplied by 2a. We will call this new product of constants kF denoting it for free space EM waves. Thus, for all free space parameters, we have:

 kgfreespace = 2.145340167E16 (T3/S3)= kF.(T3/S3)...where kF= 2a kQ

This sheds light on the actual significance of the fine structure constant. It is well known that Alpha, the fine structure constant, which is a dimensionless number, is difficult to fit into a rational scheme of physics. Max Born stated "There seems to be little doubt that the existence of this dimensionless number, the only one that can be formed from e, c and h, indicates a deeper relation between electrodynamics and quantum theory than the current theories provide, and the theoretical determination of its numerical value is a challenge to physics." Richard Feynman (4) writes, "It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it".

Now with the aid of the unified ST table, we have a further clue on what alpha might represent. It measures the strength of the electromagnetic interaction between incoming and outgoing spherical waves within the structured standing spherical wave (or matter). It is a ratio of volume of energy between the travelling spherical waves and the standing wave EM structure. It is worth noting that the fine-structure 'constant' maintains its value as long as the entity of matter is at stand still. The effective electric charge of the electron actually varies slightly with energy so the constant changes a bit depending on the energy scale at which you perform your experiment. For example, 1/137.036 is its value when you do an experiment at very low energies (like Millikan's oil drop experiment) but for experiments at large particle-accelerator energies (like 81GeV) its value grows to 1/128. This is not the same as saying that Alpha is not constant. In fact, in April 2004, new and more-detailed observations on quasars made using the UVES spectrograph on Kueyen, one of the 8.2-m telescopes of ESO's Very Large Telescope array at Paranal (Chile), puts limits to any change in Alpha at 0.6 parts per million over the past ten thousand million years. So we might say that Alpha measured at zero Kelvin is a constant of exceptional stability. The reason for its change at high energy levels is that when the standing EM wave starts radiating heat (EM waves), part of the electron's internal EM energy starts travelling outwards, and the travelling wave conversion constant kF changes. If the standing wave is somehow changed all into pure travelling waves, this constant will increase to unity, and thus kF and kQ will be equal, and so kgfreespace will be equal to kgmatter. This is the main reason why forces seem to unify at high energy levels as shown below: Fine structure constant is one of the most wonderful physical constants, a = 1 / 137.036.. The quantity a was introduced into physics by A. Sommerfeld in 1916 and in the past has often been referred to as the Sommerfeld fine-structure constant. It splits some spectral lines in hydrogen atom such that DE = (a/4)2Ei. In order to explain the observed splitting or fine structure of the energy levels of the hydrogen atom, Sommerfeld extended the Bohr theory to include elliptical orbits and the relativistic dependence of mass on velocity. The quantity a, which is equal to the ratio ve/c where ve is the velocity of the electron in the first circular Bohr orbit and c is the speed of light in vacuum, appeared naturally in Sommerfeld's analysis and determined the size of the splitting or fine-structure of the hydrogenic spectral lines. a is simply the ratio of the circumference of the first circular Bohr orbit to the electromagnetic wavelength of the electron's internal energy E=mec2. It is the ratio between the two fundamental velocities c the speed (S/T) of EM energy in free space and ac, the speed (S/T) in the quantum world. Feynman wrote:

There is a most profound and beautiful question associated with the observed coupling constant, e the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to -0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil."

Let's now consider:

Classical radius of an electron re=2.8179403E-15 m

Compton wavelength of an electron, lc=2.42631021E-12 m

Bohr radius of an electron, ao=5.29177208E-11 m

Rydberg constant, Ryd=10973731.5685 m-1.

In order to see the relation between each of the above radii and wavelengths we must express these values in a similar form, for example, as wavelengths or orbit circumferences:

lclass = 2pre = 1.77056410E-14 m
lCompton = 2.42631021E-12 m
lBohr = 2pao= 3.32491846E-10 m
lRydberg/2 = 1 / (2Ryd) = 4.55633525275E-08 m

The numerical values for wavelengths clearly show that:

lclass / lCompton = lCompton / lBohr = lBohr / lRydberg/2 = a.

We can also work out the frequencies from f= c/l

fclass = c/2pre = 1.693203E22Hz
fCompton = c/2.42631021E-12 m = 1.23559E20Hz
fBohr = c/2pao= 3.32491846E-10 m= 9.016536E17Hz
fRydberg/2 = c / (2Ryd) = 4.55633525275E-08 m = 6.57968E15Hz

So we have a similar relation for frequencies:

fRydberg/2/fBohr = fBohr/fCompton = fCompton/fclass = a

Knowing that Energy E=hf, we get the following energy values:

Eclass = hc/2pre = 1.121946E-11 J
ECompton = hc/2.42631021E-12 m = 8.187236E-14 J
EBohr = hc/2pao= 5.974515E-16 J
ERydberg/2 = hc / (2Ryd) = 4.359811E-18 J

ERydberg/2/EBohr = EBohr/ECompton = ECompton/Eclass = a

We usually define one wavelength of motion around a circle as 2pr, and one cycle of travelling wave l as going through 2p radians. However, it is well known that in standing waves, the distance from node to node at its fundamental resonant frequency does not occur at 2p, but rather at p. This explains the factor of 2 attached to a. Thus we can re-write our previous kg units comparison as:

 kgtravellingwave/kgstandingwave = a
..... confirmed above for T3S-3 (3D energy)

 ERydberg/2/EBohr = a
...... 1D Energy form T/S

 EBohr/ECompton = a
..... 2D Energy form T2S-2

 ECompton/EClass = a
..... 3D Energy form T3S-3

From the above we see that the relations for the different energy units of Rydberg, Bohr, Compton and classical orbits obey the same relation as the travelling to standing waves we described previously. Starting from the simplest 1D form of energy T/S denoted by its energy ERydberg, we see that EBohr should represent its standing wave. But we also see that the same standing wave EBohr of this level, becomes the travelling wave of the next level, to create the next higher dimension of standing wave energy ECompton in 2D (on a surface). In turn, ECompton (the photon) becomes the travelling wave of the next level, to create the next dimension standing wave EClassic, the electron! Since photons obey all freespace equations, whilst the electron obeys the natural laws of matter, it means that this dimension level is the same as the 3D energy level T3S-3, and that the previous two, are in fact the 1D and 2D versions of energy. Looking at the ST table, we see that T/S is usually manifested as energy, T2S-2 is manifested as momentum, and T3S-3 as 3D mass, but all three are actually different manifestations of mass or energy. Notice how the standing wave of two plane 2D waves can generate a 3D rotating wave. You have to visualise the blue standing wave as rotating about its axis, in and out of the page. This would become the travelling wave in the next dimension; 3D. It now becomes clear that each energy, for example ECompton can exist as a travelling wave in 3D and also as a standing wave in 2D. This solves the enigma for the wave-particle duality of light. Light will behave as a travelling wave in 3D, but will act as a standing wave (perceived as momentum) when it is projected on a 2D surface, that is, when hitting the surface of a target or sensor.

Tweaking the a fine structure constant using common sense

Since there is no theoretical way to derive the exact value for the a constant, this is usually done experimentally at low energy levels. Current accepted value from NIST reference is 1/137.03599911(46). But we now know something that most scientists do not know. We know that matter is the 3D version of electromagnetic energy T/S, whose structure is made up of elementary energy units connecting the nodes of their structure. We also know that the ratio of the 3D mass to 1D 'unit energy' is EClass/ERydberg/2 = a-3. Hence we know that the number of EM waves joining the structure of an elementary matter unit is equal to a-3 and should therefore be an integer. Taking the present CODATA value we get a-3 = 2573380.53. So at zero Kelvin, the real value should be higher than this. If we stick to our platonic fractal structure, we find out that any structure made up of any combination of platonic shapes will always end up with an even total number of elements, so it makes sense we select 2573382 as our value for a-3, which gives us a value for a= 1/137.0360251 which is also within 1986 CODATA's margin of error, and most important an exact value theoretically derived for a temperature at absolute zero Kelvin. Note that since this tweaking method does not involve other parameters such as gravitational constant, electron charge etc... all of which are known to have limited accuracy, the value obtained does not suffer from inaccuracies of other constants as does the NIST derivation. Also, note that in no experiment is a measured directly, but is always a product of other measured parameters, and always measured above zero Kelvin. Now the biggest challenge left, is to show which 3D structure of 1D EM energy units is composed of exactly 2573382 elements.

 Source Value for a CODATA 1986 1/137.03598(95) Michael Wales 1/137.0359896 (exact) KR/VN-1998 137.0359853(82) LAMPF-1999 137.0359932(83) CODATA 1999 1/137.03599976(50) CODATA 2002 1/137.03599911(46) Dr.M.Geilhaupt 1/137.03603 I. Gorelik & Steven Harris 1/137.036020454 Ing. Xavier Borg 1/137.0360251 (exact)

Derivation of Free space constants

I will now reconfirm the above relation between travelling and standing wave energy factor Alpha by deriving all the free space parameters:

Plugging in these values according to the space-time dimensions given in the table, we get:

Free space speed = S/T = 299.792458E6 m/s = speed of light

Free space impedance = [kF/j2]*T2 S-3 = 376.7303 Ohms

Free space conductance = S3 T-2/[kF/j2] = 2.6544E-3 Siemens

Free space permittivity = [j2/kF]*S2 T-1 = 8.854187E-12 F/m

Free space permeability = [kF/j2]*T3 S-4 = 1.256637E-6 H/m

The above values agree with the known values for these parameters and thus re-confirm the correctness of my ST system of units.

The Universal Limits

Using this unified theory of spacetime units, we find that the calculated units above, coincide exactly to the well accepted constants found in all conventional physics textbooks and define free space (at least all free space that we can account for till now). Since all accepted physics laws conform to the conversion table, we now have the advantage to go further to deduce some more interesting data for free space. So is free space (vacuum) a sea of energy, or can we get a value for the power and frequency we can get from the so called vacuum energy / ether energy / ZPE / radiant energy? Is there a limit to the electromagnetic spectrum? Is there a limit to the maximum density of matter? The answers are positive, and can easily be worked out using the spacetime conversion for power:

Free space power limit Po= kF /S = 5.2968E50 Watts

Free space electromagnetic frequency limit fo = 1/T = 7.39987E42 Hz = Planck frequency

Free space grand unification energy limit Eo = kF T/S = 71.56085E6 Joules or 4.466477E17 GeV ...energy where all forces unify

Maximum permissible mass density = kQ T3 S-6 = 8.208E95 kg/m3

Free space Entropy S = [kQ/(kQ/k)] T0 S0 = +1.380662E-23

Free space power is the maximum rate of transfer of energy that can flow through freespace at any point in space or time. These units clearly show the existence and values for the upper boundaries for power, EM spectrum frequency, grand unification energy and mass density anywhere in the universe. Note that kF relates to the fine structure constant, Planck constant and gravitational constant. These values are thus relating the quantum relativistic physics of electromagnetism to quantum gravity.

So, of particular interest is the derivation of the Energy of Unification from my work, which would also equate to the typical energy of a vibrating string in string theory:

 Eunification (eV) = (2a/e) * sqrt(hc5/G) = 44.66477x1016 GeV