The Relativistic Mechanics Of E=mc2 Fails

## 2 Newton's Laws of Motion

Axioms Concerning Laws of Motion
Law 1. Every body remains in a state of rest or of uniform motion in a straight line unless compelled to change that state by forces acting on it.
Law 2. Change of motion is proportional to impressed motive force and is in the same direction as the impressed force.
Law 3. For every action there is an equal and opposite reaction, or, the mutual actions of two bodies on each other are always equal and directed to opposite directions.

### 2.1 The Concepts of Mass and Force

It (mass) can also be known from a body's weight for - by making very accurate experiments with pendulums - I have found it to be proportional to the weight …I have tested this with gold, silver, lead, glass, sand, common salt, wood, water, and wheat.
Force is proportional to change of motion.
Force is proportional to mass $×$ acceleration.
The three laws of motion are axioms of truth.

### 2.2 Newton's Law of Universal Gravitation

$F=GmM/{r}^{2}$
Here we have a truly testable and verifiable law of gravity. For the force $f$ on any body, it is just the quantity $ma$; the second law of motion now being a definition of force. So for the force acting on the smaller mass $m$: $ma=GmM/{r}^{2};$ $\begin{array}{cc}a=GM/{r}^{2}& \left(2.1\right)\end{array}$Theoretically, the law of gravity could be directly tested using different values of mass $M$ and different values of separation $r$ to verify if (2.1) holds by measuring $a$, the acceleration of mass $m$ caused by the other mass $M$. As is well known, Newton's gravitational law is the first quantitative law and the most successful laws of physics to date.

### 2.3 The Interpretation of the Second Law of Motion

The paradigm of Newtonian mechanics has the second law as an axiom of definition of force; force = mass $×$ acceleration.

## 3 Why Relativistic Mechanics Fails

The Conservation Laws are very powerful in classical physics, and we would like to have similar laws in special relativity. To do so we will need to redefine momentum and kinetic energy.
Force is proportional to change of momentum.
Mathematically: $\begin{array}{cc}force=\frac{dp}{dt};\phantom{\rule{20px}{0ex}}force=\frac{d}{dt}\left(\frac{1}{\sqrt{1-{v}^{2}/{c}^{2}}}mv\right)& \left(3.2\right)\end{array}$But the equation (3.2) above is not a valid mathematical expression of the second law as "force is proportional to rate of change of momentum". There are two mistakes inherent in equation (3.2).
1. Firstly, the use of the equality sign in $force=\frac{dp}{dt}$ is only permitted provided the second law is an axiom of truth by definition; but equation (3.2) is now not interpreted as an axiom of truth. It does not define a new unit of force for the new relativistic mechanics.
2. It treats the second law as a law of relation between a force on the one side and a resulting effect on the other side - a strictly cause-effect rule. A simple cause-effect example would be to calculate the motion of a proton when acted on by the electric force that is driving the protons in a particle accelerator. But the force, the cause of motion, has to be defined and known before equation (3.2) may be applied. But the force unit of electromagnetism is still the classical unit, e.g. the newton, which is in conflict with the new relativistic mechanics.
The change to a new relativistic interpretation of Newton's second law represented by equation (3.2) would now require that force be treated as another fundamental dimension on equal footing with L, T and M, say with a new assigned symbol of F. The dimension of force in relativistic mechanics would then be $\left[F\right]$, not $\left[M\right]\left[L\right]/\left[{T}^{2}\right]$ of Newtonian mechanics. The oversight that went unnoticed for a hundred years is :
The force in the new relativistic relation: $force=\frac{d}{dt}\left(\frac{1}{\sqrt{1-{v}^{2}/{c}^{2}}}mv\right)$may not be in a unit of force of Newtonian mechanics, e.g. the newton, the SI unit of force.
The formula $E=m{c}^{2}$ does not evaluate to a value with a real defined unit of energy.

### 3.1 Total Relativistic Energy

The central dynamical identity of relativistic mechanics ${E}^{2}=\left(pc{\right)}^{2}+\left(m{c}^{2}{\right)}^{2}$ is invalid.

## 4 Galilean Relativity and the Laws of Nature

The physical laws of nature are immutable, but the mathematical expressions of the laws are governed by mathematical principles.
No empirical evidence has ever been found that contradicts Galilean relativity.
A law of physics is true only if it obeys Galilean relativity.
Heaviside's field equations had a rocky start in the early 1890's when it was discovered that they were not Galilean invariant for all observers. This meant that one could detect one's velocity by making measurements of the local field quantities which meant that the laws of physics would depend on the motion of the observer which is considered to be unacceptable.

## 5 Special Relativity Has No Physical Reality

• From Marion & Thorton, Classical Dynamics[4, Sec 14.1]: "…it was pointed out that the Newtonian idea of the complete separability of space and time and the concept of the absoluteness of time break down when they are subject to critical analysis. The final overthrow of the Newtonian system as the ultimate description of dynamics was the result of several crucial experiments, culminating with the work of Michelson and Morley in 1881 - 1887...This (a fundamental reorganization of the structure of dynamics) was provide during the period 1904 - 1905 by H. Poincare, H. A. Lorentz and A. Einstein, who formulated the theory of relativity in order to provide a consistent description of the experimental facts".
• Professor Gerard ’t Hooft, Nobel Laureate and current Editor of "Foundations of Physics". The journal has a policy of not accepting any paper that questions the validity of the relativity theory. It would reply to the effect that special relativity is one of the best tested and verified physics theory.
• Gordon Kane, in the introduction to his book "Modern Elementary Particle Physics"[5], wrote: "The theory fully incorporates special relativity"; the "theory" here means the Standard Model of particle physics.
The book by Marion & Thornton is a well recognized text that has served many generations of undergraduate students. Gerard ’t Hooft and Gordon Kane are physicists with the highest standings. From snippets, it is conceivable that many unwary students of physics would form the view that special relativity has incontrovertibly been tested and verified, conclusively replacing Newtonian mechanics - that Newtonian mechanics has finally been "overthrown" as the correct physics describing the "experimental facts" of the natural physical world.
To date, Newtonian mechanics has not been incontrovertibly refuted by experiment.
Special relativity is Lorentzian relativity. Any physics theory based on the Lorentz transformation cannot be physical[15] and, therefore, must be invalid. A theory of physics with no physical reality cannot do any predictions about how real physical phenomena work and develop. The reason why the Lorentz transformation has no place in physics comes down ultimately to the fact that Lorentzian relativity has relative space and relative time. By repudiating absolute space and time of Newtonian mechanics, it in fact rejected the Galilean physical reality of Newtonian physics. If Lorentzian relativity has any physical reality, it has to be independent of the physical reality of Newtonian physics.
The physical reality of Lorentzian relativity and Newtonian physics are independent of each
other.
A physics based on absolute space and time cannot be compared in any way with a physics based on relative space and time.
Quote[14]:
The reality of space time is metaphysical, absolute, unknowable and without attributes. We have set forth a system on how metaphysical space and time may be represented as physical space and time measurable with standard units. Such a system is based on the adoption of set of conventions and rules. In this manner, it may be said that there is physical reality only because of an implied covenant on what physical reality mean.
There is a covenant of physical reality which sets forth in a determinate way what constitutes a physical quantity.
The manner of measure of a standard length has been set forth and agreed upon. What a unit of time in second is also set forth clearly.Only such measures of length and time are physically real - not otherwise.
Physical reality has absolute three dimensional Euclidean space and absolute universal time.
Physical reality is determinate.
In the real Galilean physical world, an observer is free at will to move amongst all inertial frames.
Length contraction and time dilation of special relativity violates the principle of physical determinacy.

## 6 Verification of Special Relativity and Repudiation of Newtonian Mechanics

It is now common to find that, whenever special relativity is discussed, it is accompanied by the assertion that it is one of the best tested and verified physics theory to date. Although the Wikipedia cannot be taken as an authoritative source for citations by the academia, it nevertheless could be the first source of reference in this internet age. It has pages on the experimental verification of special relativity and they do have a significant impact in forming the public's view on the relativity theory. These pages have long lists of experiments purportedly verifying special relativity. The Kaufmann[8], Bucherer[9], Neumann[10] and Rogers et.al(1940)[11] experiments(the KBNR-experiments) from the beginning of the 20th century have always been represented as conclusive experimental verification of relativistic mass, thereby, indirectly also repudiating Newtonian mechanics and verifying special relativity. Such conclusions were the result of a fatal misinterpretation of the experiments.

### 6.1 The Kaufmann Prenatal Repudiation of Special Relativity

In the "Introduction to Special Relativity"[6], the well known author Robert Resnick shows the Bucherer experiment as "proof" that the idea of an invariant mass was contradicted by experiment - mass was verified to vary and even fits the $\gamma$-factor as predicted in special relativity. We will examine the Bucherer experiment as described by Professor A.K.T. Assis[7].

### 6.2 The Bucherer Experiment, 1908

We need not go into the actual details of the 1908 Bucherer apparatus here. It may be considered as a capacitor with a linear dimension $L$ much greater then the separation of of the two oppositely charge plates with charge distribution of $±\sigma$. The $x$-axis is perpendicular to the plates from $-\sigma$ to $+\sigma$. Classical electrodynamics shows that there is a uniform electric field ${\stackrel{\to }{E}}_{x}=-\left(\sigma /{\epsilon }_{0}\right)\stackrel{ˆ}{x}$ between the capacitor plates. The axes origin is a radium $\beta$-particle(electron) source at the center of the capacitor between the plates. The $y$-axis is the path an electron would leave the capacitor after traversing the distance $L$ leaving the capacitor with a velocity ${\stackrel{\to }{v}}_{y}$. A uniform magnetic field ${\stackrel{\to }{B}}_{z}$ in the $z$-axis direction is superimposed on the capacitor. Only those electrons in the $y$-direction could leave the capacitor when the electric deflection and the magnetic deflection in the $x$-direction are in balance and the initial electrons has no velocity component in the $x$-direction else they would collide with the capacitor plates. $\begin{array}{cc}\stackrel{\to }{{F}_{x}}=-e\left({\stackrel{\to }{E}}_{x}+\stackrel{\to }{{v}_{y}}×\stackrel{\to }{{B}_{z}}\right)& \left(6.1\right)\end{array}$Equating force to be zero, we have: $\begin{array}{cc}{v}_{y}=\sigma /{\epsilon }_{0}{B}_{z}& \left(6.2\right)\end{array}$The Bucherer apparatus is also a velocity selector as changing the magnitude of the voltage across of the capacitor and the magnetic field would allow electrons of varying speed to leave the capacitors. Five runs of the experiment were made giving data points for speed from about 0.3c to 0.7c. After the electrons leave the capacitor it would only be under the deflection of the magnetic field and it would travel in a circular path with a constant speed as in (6.2) until it strikes a photographic plate at some known distance away. From the coordinate of the point on the photographic plates and the other dimensions, the radius $r$ of the circular path could be computed. Equating the Lorentz magnetic force with the the centripetal force of circular motion, we have: $\begin{array}{cc}|e\left(\stackrel{\to }{v}×\stackrel{\to }{B}\right)|=ma=m{v}^{2}/r& \left(6.3\right)\end{array}$$a$ being the centripetal acceleration and $v$ is the constant speed equal to the speed in (6.2). Combining equations (6.2)and (6.3): $\begin{array}{cc}e/m=\sigma /r{\epsilon }_{0}{B}^{2}& \left(6.4\right)\end{array}$The RHS of (6.4) could be evaluated as all quantities are from the measured variables of the experiment. The values of $e/m$ changes with velocity and showed that mass is not invariant, but increases with velocity. Equation (6.4) has an excellent agreement if the mass $m$ is substituted with the relativistic mass defined by: $\begin{array}{cc}{m}_{r}=\frac{{m}_{0}}{\sqrt{1-{v}^{2}/{c}^{2}}}& \left(6.5\right)\end{array}$${m}_{0}$ being the invariant rest mass of an electron. The textbook of Professor Robert Resnik [6] gives a table of the data for the experiment.

#### 6.2.1 Interpretation of the Bucherer Experiment

None cast any suspicion on (6.3) which is the basis of experiments such as that of Bucherer. Electrons were deflected in a circular path and the Lorentz magnetic force of $e\left(\stackrel{\to }{v}×\stackrel{\to }{B}\right)$ is equated to the $mass×acceleration$ of Newton's second law. As shown in earlier sections, the application of this definition is based on the concept of mass being an invariant - it is an axiomatic condition that must be adhered to before the definition may be used and applied.
The Newtonian definition of force = mass $×$ acceleration is found on the concept of mass being invariant.
The Kaufmann-Bucherer-Neumann experiments were experimental proof of the failure of electromagnetism and/or the Lorentz force law at relativistic speed conditions.

### 6.3 A Mass Definition Is Not Testable

Experiments in the scientific paradigm is meant only to verify or test predictions of a theory, not any of its defined concepts. As an example, the invariance of mass in Newtonian mechanics is not testable, but the prediction that planets orbits the sun in elliptical orbits is verifiable.
In the scientific paradigm, only predictions of a theory are verifiable or testable by experiment; a definition in a theory is not testable.

### 6.4 Light Speed as a Limiting Speed

This reasoning does not explain how the tiny difference in the proton's speed between the Fermilab Booster and the Tevatron results in the beam's energy increasing by 125 times. So the explanation is wrong, but it is a common one. Be aware of it.
Within the accelerators, the electric force propelling the protons tends towards zero as the proton approaches the light speed. The actual kinetic energy of the proton is classical and is limited to about 470 Mev.

## 7 Newtonian Mechanics or Special Relativity

### 7.1 Calorimetric Test of Special Relativity

Together with his colleagues, Liangzao Fan, Senior Research Fellow of the Chinese Academy of Sciences conducted three experiments with the femto-second Linac accelerators, Shanghai Institute of Applied Physics. The experiments provided data to check the traditional electromagnetic acceleration theory and the formulas of moving mass and kinetic energy. Their conclusion was at odds with that of Bertozzi, clearly refuting the relativistic kinetic energy formula. Their claim was that the purported 7 TeV energy of protons of the LHC of CERN have real kinetic energy of only 663.36 MeV.

### 7.2 A Simple Beta-decay Experiment

To date, despite its simplicity, no one has conducted the experiment.

## 8 There May Not Be Any Relativistic Mechanics

NEWTON'S SIXTH AXIOM
Mass, the quantity of matter, is absolute and invariant.