Einstein's Probabilistic Units the Road to Unification

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Einstein’s probabilistic units are a set of units of measurement defined in terms of Einstein A and B Coefficient. Einstein coefficients are mathematical quantities which are a measure of the probability of absorption or emission of light by an atom or molecule. The Einstein A coefficient is related to the rate of spontaneous emission of light and the Einstein B coefficients are related to the absorption and stimulated emission of light.

In Einstein’s paper “On The Quantum Theory of Radiation” (Albert Einstein, Physikalische Zeitschrift, 18 (1917), 121-128-trans”) Einstein remarked that the “states of the internal energy of the molecules is established only by the emission and absorption of radiation.”

Einstein'a Probabilistic Units are developed on the general assumption that all physical states are solely the result of emission or absorption process including those states of space-time.

The ABC of Einstein Probabilistic Units

The Einstein A coefficient is related to the probability of spontaneous emission from an object or system, and the Einstein B coefficient is related to the probability of absorption or stimulated emission from an object or system. C is the speed of light.

These new probabilistic can be expressed using the following base units;

kg = mass
m = distance
s = time

Electromagnet units are defined as;

Q2 = charge squared = N m2
μ0 = permeability = c-2
e0 = permittivity = 1

A - Einstein’s Probabilistic Unit

Spontaneous emission

Schematic diagram of atomic spontaneous emission

Spontaneous emission is the process by which an electron "spontaneously" (i.e. without any outside influence) decays from a higher energy level to a lower one. The process is described by the Einstein coefficient A21 (s−1), which gives the probability per unit time that an electron in state 2 with energy ${\displaystyle E_{2}}$  will decay spontaneously to state 1 with energy ${\displaystyle E_{1}}$ , emitting a photon with an energy E2E1 = . If ${\displaystyle n_{i}}$  is the number density of atoms in state i , then the change in the number density of atoms in state 2 per unit time due to spontaneous emission will be

${\displaystyle \left({\frac {dn_{2}}{dt}}\right)_{\text{spontaneous}}=-A_{21}n_{2}.}$

The same process results in increasing of the population of the state 1:

${\displaystyle \left({\frac {dn_{1}}{dt}}\right)_{\text{spontaneous}}=A_{21}n_{2}.}$

The Einstein A Probabilistic Unit is comparable to a unit frequency measurement.

${\displaystyle A=\left({\frac {1}{s}}\right)_{\ }=v_{A}}$

As a unit of time measurement the Einstein A Probabilistic Unit is solely base on an objects or systems probability of spontaneous emission.

Some general observations;

• All clocks are internal spontaneous emission clocks
• Since Einstein’s A Probabilistic Unit of time is sole base on spontaneous emission this gives time the property of having only a single direction. There is no spontaneous absorption to give time a backward or an opposite direction.
• Because in an isolated system there is no external stimulated absorption or emission time can only measure time by spontaneous emission.
• For a non-isolated system changes in a systems stimulated absorption or emission only speeds up or slows down the rate of change of time not change the direction of time.
• This gives rise to Special Relativity and Heisenberg Uncertainty Principle

For a non-isolated system changes in a systems stimulated absorption or emission must balance one and another. As such due to spontaneous emission and objects entropy must continually decrease and a system’s entropy must continually increase. While the rate of change is dependent in entropy is dependent on stimulated absorption or emission only

B - Einstein’s Probabilistic Unit

Stimulated emission

main article Stimulated emission

Schematic diagram of atomic stimulated emission

Stimulated emission (also known as induced emission) is the process by which an electron is induced to jump from a higher energy level to a lower one by the presence of electromagnetic radiation at (or near) the frequency of the transition. From the thermodynamic viewpoint, this process must be regarded as negative absorption. The process is described by the Einstein coefficient ${\displaystyle B_{21}}$  (J−1 m3 s−2), which gives the probability per unit time per unit spectral energy density of the radiation field that an electron in state 2 with energy ${\displaystyle E_{2}}$  will decay to state 1 with energy ${\displaystyle E_{1}}$ , emitting a photon with an energy E2E1 = . The change in the number density of atoms in state 1 per unit time due to induced emission will be

${\displaystyle \left({\frac {dn_{1}}{dt}}\right)_{\text{neg. absorb.}}=B_{21}n_{2}\rho (\nu ),}$

where ${\displaystyle \rho (\nu )}$  denotes the spectral energy density of the isotropic radiation field at the frequency of the transition (see Planck's law).

Absorption

Schematic diagram of atomic absorption

Absorption is the process by which a photon is absorbed by the atom, causing an electron to jump from a lower energy level to a higher one. The process is described by the Einstein coefficient ${\displaystyle B_{12}}$  (J−1 m3 s−2), which gives the probability per unit time per unit spectral energy density of the radiation field that an electron in state 1 with energy ${\displaystyle E_{1}}$  will absorb a photon with an energy E2E1 = and jump to state 2 with energy ${\displaystyle E_{2}}$ . The change in the number density of atoms in state 1 per unit time due to absorption will be

${\displaystyle \left({\frac {dn_{1}}{dt}}\right)_{\text{pos. absorb.}}=-B_{12}n_{1}\rho (\nu ).}$

Einstein’s B Probabilistic Unit is thus defined as

${\displaystyle B=\left({\frac {m}{kg}}\right)_{\ }}$

The Einstein B Probabilistic Unit bonds space and matter into a single unit of measurement. As a unit of measurement the Einstein B Probabilistic Unit is based on an objects or systems probability of stimulated absorption or emission.

Some general observations for Einstein B Probabilistic Unit ;

• Comparable to the inverse linear density of a string
• It ratio holds from the Planck scale to universe sale
• It's ration is invariant to general and special relativity

C – Speed of Light

In Einstein’s Probabilistic Unit the speed of light, c, is a constant of proportionality.

${\displaystyle c=\left({\frac {m}{s}}\right)_{\ }}$

As we will see this constant of proportionality serves as a transformational and/or scaling utility.

Scaling of Einstein’s B Probabilistic Unit

Einstein’s B Probabilistic Unit from the Planck scale to that of the scale of the universe:

Planck Scale

${\displaystyle B_{Einstein}=\left({\frac {m_{Planck}}{kg_{Planck}}}\right)_{\ }=\left({\frac {1.6163*10^{-35}m}{2.1765*10^{-8}kg}}\right)_{\ }=7.4256*10^{-28}{\frac {m}{kg}}\ }$

Universe Scale

${\displaystyle B_{Universe}=\left({\frac {m_{Universe}}{kg_{Universe}}}\right)_{\ }=\left({\frac {1.6163*10^{-35}m}{4\pi *1*10^{53}kg}}\right)_{\ }=7.0*10^{-28}{\frac {m}{kg}}\ }$

From an order of magnitude perspective these numbers are extremely close due to how the universes critical density is calculated.

Black Hole

A black hole can be defined by the Schwarzschild radius

${\displaystyle r_{s}=r_{bh}={\frac {2GM_{bh}}{c^{2}}}}$

Expressing this using Einstein Probabilistic Units

${\displaystyle r_{bh}={2BM_{bh}}}$

Solving for B give us

${\displaystyle B_{bh}={\frac {r_{bh}}{2M_{bh}}}}$

Force

In Einstein's Probabilistic force is expressed as:

${\displaystyle F=c^{2}/B_{E}}$

Expressed slightly differently it is quite similar to Einstein's energy equation

${\displaystyle F=B^{'}c^{2}}$
${\displaystyle E=M^{'}c^{2}}$

Einstein's Probabilistic force has the potential to be the fifth force.

Newton’s Gravitational Constant

Einstein B Probabilistic Units can be used to derive Newton’s Gravitational constant expressed in terms of Einstein B Probabilistic Units.

${\displaystyle G=B_{E}c^{2}=\mu _{G}c^{2}}$

Einstein Constant

The Einstein Constant expresses how stress energy and deformation space time are related.

${\displaystyle \kappa =G^{\alpha \gamma }/T^{\alpha \gamma }=8\pi B_{E}}$

Gravitational Permeability

At the Planck scale using Planck frequency the Einstein B Probabilistic Units is equivalent to the gravitational permeability of free space and can be expressed as;

${\displaystyle \mu _{G}=B_{E}={\frac {Ns^{2}}{kg^{2}}}={\frac {m}{kg}}}$

Cosmological Constant

The value of the Cosmological is:

${\displaystyle \Lambda =A^{2}=1.927\times 10^{-35}\,{\text{s}}^{-2}}$
${\displaystyle \Lambda _{Univ}=2\pi {\frac {B}{c}}\left({\frac {kg_{mass}}{s_{age}^{3}}}\right)_{Univ}=2\pi {\frac {B}{c}}\left({\frac {1.0\times 10^{35}\,kg_{mass}}{{\bigl (}4.32\times 10^{-17}\,{\bigr )}^{3}s_{age}}}\right)_{Univ}=1.93\times 10^{-35}\,{\text{s}}^{-2}}$

Dark Energy

Viewing space as a system of stimulated absorption or stimulated/spontaneous emission governed by Einstein Probabilistic's Units.

Using Einstein Probabilistic Units dark energy density is defined as;

${\displaystyle u_{D}={\frac {A^{2}}{B}}}$

${\displaystyle u_{D}=\left({\frac {8\pi h}{c^{3}}}\left(\ v_{A}^{2}v_{B}^{2}\right)\right)=\left({\frac {8\pi h}{c^{3}}}\left(\ v_{B}^{4}\right)\right)}$

Assuming the energy density of dark matter is;

${\displaystyle u_{D}=6.20934*10^{-10}{\frac {J}{m^{3}}}}$

Let us calculate the frequency of dark matter;

${\displaystyle v_{D}=1.001*10^{12}s^{-1}}$

Given Rydberg constant is defined as;

${\displaystyle R_{\infty }={\frac {\alpha ^{2}m_{e}c}{2h}}}$

Using Rydberg constant we can define dark energy frequency as;

${\displaystyle v_{D}=R_{\infty }c=1.0008*10^{12}s^{-1}}$

From an order of magnitude perspective dark energy is related to Einstein Probabilistic Units by Rydberg constant

Fine Structure Constant

Given the Fine Structure Constant is related to the probability that an electron will emit or absorb a photon.

Thus the Fine Structure Constant is directly related to Einstein B Probabilistic Unit for spontaneous absorption

Electromagnetism

Several electromagnetic relationships are expressed using Einstein A and B Coefficient

Electric field

${\displaystyle {\boldsymbol {E}}={\frac {A}{B^{0.5}}}}$

Magnetic field

${\displaystyle {\boldsymbol {B}}={\frac {A}{c*B^{0.5}}}}$

Charge

Electric charge squared

${\displaystyle Q^{2}={\frac {c^{4}}{A^{2}*B}}}$

Electric charge

${\displaystyle Q={\frac {c}{A*(\pm B^{0.5})}}}$

Relative strength of electromagnetic and gravitational forces

Using dimensional balancing force is a D2 object and Charge is a D2 object, while Mass is a D3 object.

From this we realize that matter requires an additional dimensional transformation in order to become a force. This additional dimensional transformation results in the reduction of the overall force as a D3 Mass object is transformed into a D2 Force object. Given both A and B Einstein Probabilistic Units are a function of frequency from this we could conclude that relative strength of electromagnet and gravitational force is related frequency.

${\displaystyle {\frac {F_{kg}}{F_{Q}}}=Constant*{\frac {B^{2}}{(B^{0.5})^{2}}}=Constant*B=Constant*{\frac {1}{v^{2}}}}$

From the above the relative strength of an electron’s gravational forces to its electromagnet force is

${\displaystyle {\frac {F_{electron~kg}}{F_{electron~Q}}}=Constant~*~{\frac {1}{v^{2}}}=2.4*10^{-43}}$

For an electron at rest we can use the Compton frequency

${\displaystyle {\frac {F_{electron~kg}}{F_{electron~Q}}}=Constant~*~{\frac {1}{v_{Compton}^{2}}}={\frac {1}{2\pi ~*~(7.76*10^{20})^{2}}}=2.6*10^{-43}}$

Generally speaking this is consistent with prediction that Relative Strength of Electromagnet and Gravitational Force is driven by B Einstein Probabilistic Unit.

Appendix

Black Holes
Convergence Classical and Quantum Gravity
Why is gravity so weak?
Space Time Einstein Probabilistic Units fabric of space