All that is required is some basic starting point from within the numerical system itself a common value appearing to be the energy of the ground state electron. As such, beginning with the the most basic Newtonian equation of Kinetic energy; $$E_e = \frac{m_e {v_e}^2}{2} = 2.179\ 872\ 3611 × 10^{-18}\ \text{J}$$

Where:
\(m_e = \text{Electron mass}\)
\(v_e = \text{Electron velocity} \)

Moving on, somewhat surprisingly it is fould that the energy of the ground state electron can also be calculated using the equation for charge; $$E_e = k\frac{q^2}{2a_0} = 2.179\ 872\ 3611 × 10^{-18}\ \text{J}$$

Where:
\(k = \text{Coulombs constant}\)
\(q = \text{Electron Charge}\)
\(a_0 = \text{Bohr Radius}\)

Furthermore, the following equation can be used to calculate the energy of the electron using the magnetic field. It is of course not unusual to find that the electromagnetic field itself is also inherently related to the properties of the ground state electron; $$E_e = B\frac{v_ea_0e}{2} = 2.179\ 872\ 3611 × 10^{-18}\ \text{J}$$

Where:
\(B = \text{Magnetic field}\)
\(v_e = \text{Electron velocity}\)
\(a_0 = \text{Bohr radius}\)
\(e = \text{Elementary charge}\)

Turning now to the gravitational constant a basic connection with the properties of the electron is discovered; $$E_e = \frac{v_e a_0 c^3}{2G {q_p}^2} = 2.179\ 872\ 3611 × 10^{-18}\ \text{J}$$

Where:
\(v_e = \text{Electron velocity}\)
\(a_0 = \text{Bohr radius}\)
\(c = \text{Speed of light}\)
\(G = \text{Gravitational constant}\)
\(q_p = \text{Planck quanta}\)

Although outdated, the equation for Hartree energy represents the energy of the ground state electron which is seen from the following; $$E_e = \frac{E_H}{2} = 2.179\ 872\ 3611 × 10^{-18}\ \text{J}$$

Where:
\(E_H = \text{Hartree energy}\)

Finally even Einstein himself offers an equation to calculate the energy directly from the frequency or wavelength of the electron; $$E_e = \frac{hf}{2} = 2.179\ 872\ 3611 × 10^{-18}\ \text{J}$$

Where:
\(h = \text{Plancks constant}\)
\(f = \text{Electron frequency}\)

What is extraordianry is not that all of the equations produce an identical value, but rather that the foundations upon which the equations are based undoubtedly appear to have common roots.

A secondary, yet crucial view that can be derived from the above is that gravity must be quantized. This conclusion follows from the preceding equations, further demonstrated by directly calculating the Gravitational Constant using only Planck units. Additionally, this value can be derived from first principles, based upon the exact number of quanta in a hydrogen atom. Beyond establishing a common energy thread, it also becomes possible to calculate he electron's quantum energy levels from a unified base. The ubiquitous equation for calculating the electron energy levels in any atom is as follows:

$$E_n = \frac{-2\pi^2m_e^4Z^2}{n^2h^2}$$

Armed with the knowledge that there are no fundamental constants this equation can be simplified by substituting the values of its component parts, resulting in the following; $$\frac{m_e Z^2}{2 \hbar n^2}$$

By expanding the denominator to include the component parts of the reduced planck constant, the result is the following equation. $$\frac{Z^2}{2 m_e a_o^2 v_e^2 n^2}$$

In this form the energy levels of any atom can be calculated using any of the previously stated equations.

From the results of the previous equations it is not only reasonable to assume but rather an inevitable conclusion can be drawn that the term for energy is a generic term emerging from the underlying numeric system upon which all of physics is based. There can no longer be any doubt that there are no fundamental scalar constants but rather only collections of equations whose values correlate with one another.

Planck units are a set of natural units that are defined using fundamental physical constants. As mentioned they were named after the German physicist Max Planck, who first proposed them. Planck units provide a system of measurement that is based on natural physical scales, making them very useful in theoretical physics, particularly in quantum mechanics and cosmology. Arguably, the most important of these units is the Planck length itself;

$$l_p = 1.616\ 314\ 0683 × 10^{-35}\text{m}$$

The Planck length is an extremely small value that, once again, seems beyond accurate calculation. To determine the Planck length, we must begin from first principles by considering the Bohr radius, which is the assumed distance between the nucleus of a hydrogen atom and its ground state electron, and is known with high precision its value being;

$$a_0 = 5.291\ 7721\ 0903 × 10^{-11}\text{m}$$

The simple question can be asked as to whether the Bohr radius is the smallest value that exists, clearly not, it must consist of many smaller entities or quanta. To find how many of these smaller entities we must turn to Avogadro's number with a little assistance from Euler, it follows that;

$$q_n = \frac{a_0}{2 N_A e} = 3.273\ 975\ 1593 × 10 ^{24}$$

Where:
\(q_n = \text{Planck quanta}\)
\(a_0 = \text{Bohr radius}\)
\(N_A = \text{Avogadro's number}\)
\(e = \text{Eulers number}\)

The number of "quanta" \(q_n\) is the count of individual component parts, entities or quanta which make up the Bohr radius. It is clearly a large number of units, but what does it represent? By dividing the Bohr radius by the Planck length, we indeed obtain the number of elementary units which make up the Bohr radius. Performing this calculation yields the value \(3.273\ 975\ 1593 × 10 ^{24}\).

Having determined the number of quanta in the Bohr radius from first principles, the final step is to actually validate this number by calculating the size of each individual quantum. This is done by dividing the Bohr radius by the number of quanta. The result, is exactly as expected, the value of Planck length \(1.616\ 314\ 0683 × 10^{-35}\). This result clearly illustrates the close relationship between quantum scale Planck units and the atomic scale.

The most important value, the Planck constant, itself represents the angular momentum of the ground state electron in a hydrogen atom. Traditionally, it is considered to express the amount of energy in a quantum, but rather it can be more accurately represented as angular momentum. Max Planck determined its value in response to the "ultraviolet catastrophe," assuming it to be the proportionality between the frequency and energy of electromagnetic radiation. The value of the reduced Planck constant can also be calculated directly from the properties of the electron as follows;

$$\hbar = m_ea_0v_e = 1.054\ 571\ 8176 × 10 ^{-34}\text{Js}$$

Where:
\(\hbar = \text{Plancks reduced constant}\)
\(m_e = \text{Electron mass}\)
\(a_0 = \text{Bohr radius}\)
\(v_e = \text{Electron velocity}\)

As in prior calculations this is based only upon the properties of the ground state electron.

With the principal Planck unit being established, the remaining two important values are the Planck mass and Planck time. The Planck mass can be calculated similarly to the Planck length, using the number of quanta in the Bohr radius as follows;

$$m_p = \frac{q_nm_ev_e}{c} = 2.176\ 354\ 8377 × 10 ^{-8}\text{kg}$$

Where:
\(m_p = \text{Planck mass}\)
\(q_n = \text{Quantum units}\)
\(m_e = \text{Electron mass}\)
\(v_e = \text{Electron velocity}\)
\(c = \text{Speed of light}\)

The final Planck unit of any importance being that of the Planck time, in a similar manner as above this value can be calculated as follows;

$$t_p = \frac {a_0}{q_nc} = 5.391\ 443\ 3973 × 10 ^{-44}\text{s}$$

Where:
\(t_p = \text{Planck time}\)
\(a_0 = \text{Bohr radius}\)
\(q_n = \text{Quantum units}\)
\(c = \text{Speed of light}\)

Newton's discovery of the gravitational constant (𝐺) is perhaps one of his greatest contributions, fundamentally crucial in understanding the gravitational interactions between celestial bodies and significantly impacting astrophysics and cosmology. Despite this, its precise measurement continues to be a challenge in experimental physics. This ongoing difficulty is puzzling, given that Newton's method for determining its value, using Kepler's law, is well understood and the constant's dimensions are well known. The gravitational constant is one of the least accurately measured constants in physics, with an accuracy limited to three decimal places, as determined through basic dimensional analysis.

$$G = [M^{-1}][L^{3}][T^{-2}]$$

Physicists generally agree that the Gravitational constant cannot be derived mathematically and must be obtained through direct measurement. Its small value does not influence the theoretical ability to actually calculate it, given that the dimensions and method for its calculation are well known. The main question becomes which fundamental values should be used to establish its value, the most obvious choice appearing to be the Planck constants. In this context, Kepler's law is evident, as a length cubed divided by a time squared appears in the very dimensions of the Gravitational constant. Utilizing this in the following equation the only additional requirement is the inclusion of a suitable mass.

$$G = \frac{{l_p}^3}{m_p {t_p}^2}=6.674\ 787\ 6501 × 10^{-11}\ \text{m}^3\text{kg}^{-1}\text{s}^{-2}$$

Where:
\(G = \text{Newtons Gravitational constant}\)
\(l_p = \text{Planck length}\)
\(m_p = \text{Planck mass}\)
\(t_p = \text{Planck time}\)

The presented analysis is in direct opposition to the current opinion that the Gravitational constant itself is simply a conversion factor between systems but rather it has been shown that it is an essential fundamental value representative of a much deeper fundamental principle from the quantum scale upto stars and galaxies.

It's astonishing that the straightforward application mentioned has gone unnoticed for centuries. Although the Planck constants were only introduced in the early 20th century, there appears to have been a general disinterest in fundamental physics within the scientific community, with a greater focus being placed upon more abstract and esoteric topics.

The value proposed above, being no less than seven orders of magnitude greater than the currently measured value, will undoubtedly face scrutiny. The primary objection is that Planck units necessitate the use of the measured Gravitational constant. However, it is noteworthy that the values of Planck units correlate when calculated from first principles using unrelated values, as previously discussed.

Additionally, using only the basic properties of the ground state electron in the Hydrogen atom, the result aligns precisely with the calculated value.

$$G = \frac{a_o{c}^3}{v_e m_e {q_n}^3}=6.674\ 787\ 6501 × 10^{-11}\ \text{m}^3\text{kg}^{-1}\text{s}^{-2}$$

Where:
\(G = \text{Newtons Gravitational constant}\)
\(a_o = \text{Bohr radius}\)
\(c = \text{Speed of light}\)
\(v_e = \text{Electron Velocity}\)
\(m_e = \text{Electron mass}\)
\(q_n = \text{Count of Quantum elements (quanta)}\)

The calculation of the Gravitational constant using subatomic quantum scale elements raises one of the most significant questions currently in physics as to whether gravity is quantized. From the previous calculation it would seem to be the case as at the subatomic scale the value of the Gravitational constant is reliant upon Planck units, in particular the Planck length, but this in itself is insufficent to establish the hypothesis.

The Fine Structure Constant (denoted as α) is a dimensionless physical constant that purportedly characterizes the strength of the electromagnetic interaction between elementary charged particles, such as electrons and protons. Its approximate value is 1/137, or about 0.00729735256933. It will be shown that this value can be accurately established to be exactly \(7.297\ 352\ 5693 × 10^{-3}\). This constant plays a crucial role in quantum mechanics and electromagnetism, influencing the fine structure of atomic spectra and the behavior of charged particles. For some reason, the exact origin of its value remains as being one of the fundamental questions in physics.

What is strange however is that the value of the constant is actually known and has already been explained by Arnold Sommerfeld, a simple fact which seems to have been completely forgotten by modern physicists. Arnold Sommerfeld found that the actual value can be determined from the velocity of the ground state electron of hydrogen divided by the speed of light;

$$\alpha = \frac{v_e}{c} = 7.297\ 352\ 5693 × 10^{-3}$$

To understand it's significance requires nothing more than understanding the exact components of the equation. The numerator of the equation is the orbital velocity of the ground state electron of Hydrogen its circumference being calculated from \(2 * pi * a_0\) and represents the distance travelled with respect to time, its velocity. When the denominator is the speed of light, what we have is a simple proportionality between the velocity of the electron and the speed of light.

This particular value becomes important when considering any equations at the quantum scale.

Central to de Broglie's equation is Planck’s constant, denoted as “h.” Planck’s constant is a fundamental constant of nature, representing the smallest discrete unit of energy in quantum physics. Its value is approximately 6.626 x 10-34 Jˑs. Planck’s constant relates the momentum of a particle to its corresponding wavelength, bridging the gap between classical and quantum physics.

$$\lambda = \frac{h}{p}$$

By assuming that h is a fundamental constant, effectively some mysterious scalar value, de Broglie fails to recognize the main components of Planck's constant h and then proceeds to deduce the following equation;

$$\lambda = \frac{h}{mv}$$

Observing the mass in the denominator, deBroglie made a leap of faith in the assumption that all matter objects must therefore have a wavelength. The problem however arises when the Planck constant h is replaced with its component values;

$$\lambda = \frac{a_0 m_e v_e}{m_e c} = \frac{a_0 v_e}{c} = 2.426\ 310\ 2387 × 10 ^{-12}\text{m}$$

The purported "rest mass" of the electron drops out of the equation resulting in the Compton wavelength for the electron. Lacking any reference to mass in the equation, the entire fantasy of matter waves disappears.

The de Broglie hypothesis while apparently accepted by the physics community is not based upon solid foundation lacking any physical evidence to support it. Rather it is based upon on a simple declaration made by de Broglie himself backed by decidedly unconvincing equations.

Should de Broglie's hypothesis be considered correct, why stop at mere photons and electrons, indeed soccer balls could mathematically be considered to have a wavelength. Taking a soccer ball as a simple analogy. A typical soccer ball has a mass of approximately \(4.5 × 10^{-1}\) kg. and the famed Brazilian soccer star Ronny Heberson achieved a world record by kicking a football at the velocity of \(58.57\ \text{m/s}\) in 2006. Substitution into de Broglies equation results in the following wavelength;

$$\lambda = \frac{h}{4.5 × 10^{-1}\ \text{kg}\ × 5.857\ × 10^{1}\ \text{m/s}} = 8.642\ 298\ 0815 × 10 ^{-20}\ \text{m}$$

This record, although certainly impressive is overshadowed by the fact that, if de Broglie is to be believed, Ronny achieved an oscillation frequency of the soccer ball in the gamma ray burst territory of \(3.468\ 897\ 4526 × 10 ^{27}\ \text{Hz}\) presumably alerting NASA in the process.

Indeed it is understood that Erwin Schrödinger in 1926 went on to base his contributions to quantum mechanics being influenced by de Broglies hypothesis.

From the previous description it is clear that the author of the article is not impressed with the hypothesis presented by de Broglie and is of the opinion that it should be dismissed in its entirety.

In The "Electrodynamics of Moving Bodies" published by Albert Einstein in 1905, in section §2 On the Relativity of Lengths and Times, you will find Einstein's first equation. This equation is easily recognized by any high-school student, which links distance time and velocity. Einstein, clearly states light path, rather than simply stating distance in an attempt to confuse the reader.

$$velocity = \frac{light\ path}{time\ interval}$$

Einstein then goes through an explanation of why events are not simultaneous and follows this with the following two equations which form the basis of his entire paper.

$$t_B - t_A = \frac{r_{AB}}{c-v}\ and\ t_A'-t_B = \frac{r_{AB}}{c+v}$$

Where \(r_{AB}\) denotes the length of the moving rod.

It is not neccessary to understand the equation, only what Einstein is actually suggesting. He is saying that the original equation he quoted is actually wrong, and that the correct form is;

$$velocity = \frac{length\ of\ the\ rod}{time\ interval}$$

Obviously the length of a rod is not the same as the distance travelled by the rod and it is clear that the two equations shown are mutually exclusive. Indeed the equation offered by Einstein, which claims that length and time changes with respect to velocity is unsupported by any physical experiment despite the multiple claims offered by his supporters. Quite simply time dilation and length contraction are simply fantasies.

This is the very point in Einsteins paper "The Electrodynmamics of Moving Bodies" of 1905, where Einstein introduces his erroneous concept of length contraction and time dilation. Undoubtedly, this single claim must be one of the greatest errors in modern physics, which has lead the physics community astray and set back the progress of physics for in excess of one hundred years.

The length of a rod and the distance traveled are two distinct physical concepts. the length of a Rod is a measure of the rod's physical size from one end to the other. It is a fixed, static measurement that doesn't change unless the physical dimensions of the rod itself is altered. The distance traveled refers to the total length of the path along which an object moves. It is a dynamic measurement that can vary depending on the path taken. The distance traveled can be more than the displacement (straight-line distance from the starting point to the end point) if the path is not straight. In summary, while the length of a rod is a static measurement of the rod's size, the distance traveled is a dynamic measurement of the path an object moves along. These two measurements are fundamentally different depending on the specific context.

Indeed it can be asked whether this false claim can be proven mathematically and the answer is yes using only high school maths. Beginning with the first of Einsteins equations, we can simply substitute some theoretical values;

$$t_B - t_A = \frac{r_{AB}}{c-v}$$

The exact meaning of the equation as related by einstein is that a bar moves from the origin at a time "\(t_A\)" to a second point in a time "\(t_B\)" at some velocity close to the speed of light. It can be safely assumed that this velocity "\(v\)" can be represented by half the speed of light and in the interests of simplicity the length of the bar at the origin "\(t_{AB}\)" can be taken to be one meter.

The equation can be rearranged to establish the length of the bar following its journey;

$$r_{AB} = (t_B - t_A)(c-v)$$

Using this equation, the example values can be used to establish the length of the rod after its journey for one second at half the speed of light from \(t_A\ \text{to}\ t_B\).

Substitution of these basic values into this equation results in the following;

$$r_{AB} = (1 - 0)(2.997\ 924\ 5800 × 10^{8} - 1.498\ 962\ 2900 × 10^{8}$$

Which when simplified becomes;

$$r_{AB} = 1.498\ 962\ 2900 × 10^{8}\ \text{meters}$$

Effectively, after travelling for one second at half the speed of light the length of the rod did not contract but rather expanded to \(1.498\ 962\ 2900 × 10^{8}\ \text{meters}\) the exact opposite of that claimed by Einstein. To put this into context the rod expanded from one meter to almost half the distance from the Earth to the moon within one second.

the same substitution can be made to the second equation of Einstein. Rearrangement of the second equation to establish the length of the bar following its journey becomes;

$$r_{AB} = (t_A'-t_B)(c+v)$$

Substitution of the sample values results in;

$$r_{AB} = (2 - 1)(2.997\ 924\ 5800 × 10^{8} + 1.498\ 962\ 2900 × 10^{8}$$

The resultant value is even more ludicrous than the first, the rod has again expanded rather than contracting this time to a much larger value;

$$r_{AB} = 4.496\ 886\ 8700 × 10^{8}\ \text{meters}$$

Once more putting this into contaxt the rod has again expanded this time from one meter to a length in excess of the distance from the Earth to the moon in one second. It has been shown that the entire concept of length contraction and time dilation is nothing more than a mathematical fiction and as a result the entire paper should be abandoned.

For some reason, the Hubble tension remains a perplexing issue in cosmology. It involves a discrepancy between two methods of measuring the Hubble constant, which quantifies the rate of the universe's expansion. One method relies on measurements of the cosmic microwave background (CMB) radiation from the early universe, while the other utilizes observations of supernovae and other cosmic objects in the local universe. The Hubble constant values obtained from these two methods do not align, creating tension within the scientific community. Researchers are investigating whether this inconsistency points to "new physics" beyond our current understanding or if it can be resolved with improved measurements and methods, appearing to completely ignore the fact that indeed both methods may be serious flawed, necessitating an alternative explanation.

As with many of the apparent "mysteries" that have arisen in modern physics the Hubble tension is once more easily explained and yet again all that is required is high school physics. the solution to the problem revolves around a simple misinterpretation of velocity. Strangely the solution begins with an apparently unconnected equation, Schwarzschild's equation for escape velocity;

$${v_{escape}} = \sqrt{\frac{2 G m}{r}}$$

the equation itself can be refined as it is understood that mass equals the product of density and volume. Consequently, these values can be substituted into the Schwarzschild equation. Being that the volume of a sphere is \(\frac{4\pi r^3}{3}\) this can also be substituted into the Schwarzschild equation resulting in the following;

The result is an equation that looks exactly like the familiar Friedmann equation which is the very basis of the expanding universe theory.

$${v_e}^2 = \frac{8 \pi G r^2 \rho}{3}$$

The single difference however is subtle, inasmuch as the velocity in the Friedmann equation purportedly represents a "recession velocity" and not actually the mathematical fictional value of the escape velocity as in the Schwarzschild equation.

$${H}^2 = \frac{8 \pi G r^2 \rho}{3}$$

In actual fact the claim made by Friedmann that his equation which is identical in form and function to Schwarzschild's is derived from General Relativity thereby using a velocity claimed to be a velocity of recession rather than escape.

Escape velocity is the minimum speed an object needs to break free from the gravitational pull of a planet, moon, or other celestial body without any further propulsion. However, recession velocity refers to the speed at which galaxies and other celestial objects are moving away from each other due to the expansion of the universe. Mathematically proving the error is particularly simple, by substituting the kinetic energy and calculating the acceleration the resultant value is;

Imagine the following scenario containing a line of trees on each side of the road

The issue with using this calculation becomes evident from the example; it’s a circular argument arising from an initial implicit assumption that the trees are accelerating away. Without this assumption, the calculation provides no meaningful conclusions. To understand this mathematically, see the following:

To calculate velocity using calculus, you need the position function \(x(t)\), which describes the position of an object as a function of time. The velocity \(v(t)\) is the derivative of the position function with respect to time, being expressed as:

$$v(t) = \frac{dx(t)}{dt}$$

Having the position as a function of time \(x(t)\), the velocity can be found by differentiating \(x(t)\) with respect to time \(t\). Once the velocity function \(v(t)\) is known the acceleration can then be found by differentiating the velocity function;

$$a(t) = \frac{dv(t)}{dt}$$

The question arises: is this actually the method being employed to determine the universe's acceleration, and are there any alternative ways to show that this is the case? Fortunately, the response is yes. From published articles the average acceleration is found to be approximately \(\text{70 m/s/Mpc}\). As such it can be asked what energy would be required to produce such an acceleration. After conversion to SI units and basic calculation it is found that the value needed is approxiamtely \(2.179\ × 10^{-18}\ \text{J}\), a value of energy required is so small that it would appear to be at a quantum level. Consequently, if a calculation is made using the escape velocity of the ground state electron in the hydrogen atom the resultant energy is;

$$2.179\ 872\ 3610 × 10^{-18}\ \text{J}$$

This of course is expected considering that the mass and energy of the universe is unknown and manipulation of the equation is so extensive, that nothing remains in the calculation representing actual physical values apart from the most basic units of measure.