06 |THE PARADOX OF MASS-ENERGY EQUIVALENCE

E = m x c²

Throughout a number of scientific books, we are frequently told that Mass () and Energy () are related according to the equation
= x ²
The factor ² is the square of the velocity of light. This relationship is based upon Einstein's Theory of Relativity, and has been experimentally confirmed.
This relationship has had a tremendous influence upon the evolution of our industrialised society. Lured by the promise of endless energy resources, modern science has helped to create a mindless, energy-hungry society. Thus, the present insane efforts to harness nuclear energy gradually evolved. Not surprisingly, there are very few scientific textbooks which do not endorse and glorify Einstein's Theory of Relativity. For example, consider the following statement from Lincoln Barnett's "The Universe and Dr. Einstein".
- = x ² provides the answer to many of the long-standing mysteries of Physics. It forecasts how many grammes of Uranium must go into a bomb in order to destroy a city. Einstein showed that matter is energy, and energy is matter. Since July 16, 1945, man has been able to transform one into the other. For on that night at Alamagodro, New Mexico, man for the first time transmuted a substantial quantity of matter into light, heat, sound and motion which we call energy.
What a glorious achievement for science indeed?!
Furthermore, the Physics textbooks provide several experimental data that attempt to confirm the validity of the Theory of Relativity. However, little or no attempt seems to be made to point out the fragility and weaknesses of the "Relativity" equations. The history of science should have taught us that even the most solid scientific theories have had some weaknesses. It would, therefore, appear that the prospect of infinite sources of energy has caused scientists to lose their objectivity. In the next pages, I will endeavour to demonstrate some of the weaknesses of the Theory of Relativity.
If we look back at the history of science, then we can recall that (as early as in the 17th century) Galilei had suggested the possibility of measuring the velocity of light. Later, in 1675, the Danish astronomer Olaf Roemer predicted the finite velocity of light by observing the movement of Jupiter's satellites.
The first successful terrestrial measurements were made with an apparatus constructed by the French scientist Fizeau and later modified by Foucault. Since then, numerous measurements and calculations have been recorded. As a result, we now generally accept the value of the velocity of light to be about 3 x 10⁸ metre/second in the vacuum. When light traverses some transparent media, its velocity diminishes to some degree. Modern scientific textbooks also recognise a duality in the light phenomenon. At times, it has the characteristics of wave motion. At other times, it appears like flying particles which Einstein called "photons". However, in both cases, the velocity is considered to be a vectorial quantity.
By considering as a vector, a very logical supposition can be made. If the light source is animated by a velocity relative to the observer, then the resulting

should be considered. For instance, if a rapid vehicle moved away from us with a velocity of 100 metre/second, and someone aboard this vehicle were to throw an object towards us with a velocity of 120 metre/second, then this object would approach us with a velocity of
120 - 100 = 20 metre/second
Somebody aboard the vehicle can measure the relative velocity (20 metre/second), and he/she knows the starting velocity of the object (120 metre/second). Consequently, he/she can calculate the velocity of the vehicle.
The American physicist Albert A. Michelson suggested that our planet is similar to a vehicle which travels in the "ether" with a certain velocity, which could be calculated by using the known velocity of light. However, the famous Michelson-Morley experiment (1878) ended in a surprising paradox. It was clearly demonstrated that the relative velocity of light does not depend on the velocity of the light source.
This paradox inspired mathematicians like Lorentz and Einstein to formulate the Theory of Relativity. First, they decided to consider the velocity of light as a maximum possible velocity in the universe and as a universal constant. Following that, they deduced the necessary mathematical formulae to explain the remaining paradox.
At this very beginning, they introduced the first contradiction and weakness to their theory. We know today that certain physical phenomena can be transferred over huge distances without any velocity, by what is known as a speed of propagation. Good examples are radio and television transmissions which sometimes use relay stations. Whether a radio broadcasting station is stationary or located in a supersonic jet moving in any direction does not affect our ability to receive those radio signals in the same instant. The media we call "ether" acts like a myriad of individual relay stations, and the signal is transferred from one relay station to another. The speed of the signal propagation depends only on the efficiency and activity of the relay stations.
It is most probable that the light phenomenon behaves in a similar way. With such a "relay" system, the paradox of the Michelson-Morley experiment is explained. What a pity that radio and television technology had not been developed at the end of the 19th century! Einstein would probably never have introduced his Theory of Relativity. Unaware of the notion of "relays", Lorentz and Einstein confused velocity with the speed of propagation. The speed of light is not a vector. It can not be added or subtracted from another vector, as we can not subtract two pears from three apples. The reason for their confusion is understandable, but their conclusions are nevertheless based on a scientific blunder.
In the future, science should introduce the subatomic units acting as relays, diffusion stations and receivers in the light phenomenon. Some contemporary physicists believe that atoms and subatomic units may behave like intelligent entities able to intercommunicate. For example, the American physicist Richard P. Feynman demonstrated that subatomic particles are capable of detecting and adopting the most favourable and effortless trajectory. Indeed, it would seem presumptuous to suppose that humans were the only ones capable of creating long-distance "wireless" communication systems. It would be appropriate to assume that Nature already possesses similar but far superior systems of its own.
Interestingly, this "relay" theory explains not only the paradox of the Michelson-Morley experiment but also all well-known phenomena related to light. The duality of the light phenomenon becomes unnecessary. For example,
1. The receiving stations (the "eyes" of this system) record only those signals which are transferred in shortest time by the most efficiently working relay stations. This phenomenon is known as the Fermat principle.
2. Sometimes, the last relay station, which transfers the light signal to our eyes, is not located on the straight line between the receiver and the light source. Then, it appears to us that the light is somehow "bent", or more precisely diffracted.
3. The light signal influences the relay and receiver stations, and those "intelligent" subatomic units react. Sometimes, we perceive those actions as a form of energy (such as photoelectric effect or the pressure of light). Thus, we no longer need to think of "energy hurtling" through the space.
To continue with our analysis of the Theory of Relativity, let us imagine a coordinate system (^',^',^'), moving relatively to another resting coordinate system (,,), animated by a velocity in the direction or ^', as shown in Figure 06-01. If we want to describe a movement which occurs in the moving system and observe it from a resting system, then we should use the classical "Galilean" transformation equations
= ^' + x
and
= ^'
where is the time.
By introducing the constant velocity of light in both systems (according to the Michelson-Morley experiment),
= (Displacement) / (Time) = ^' / ^' = /
we arrive at the famous Lorentz's transformation equations.
In the kinematic branch of Physics, the Lorentz transformation is a brilliant mathematical exhibition. We can only question the validity of its starting point! The resulting equations
_v = ₀ x (1 - ²)^(1/2)
and
_v = ₀ x (1 - ²)^(-1/2)
where
= /
suggest that the dimension (_v) of an object animated by a high velocity () decreases (dimension in the direction of ), and that this dimension becomes 0 (zero) if the velocity reaches the velocity of light .
In addition, the time factor (_v) of a moving system increases with the velocity. In other words, the "clock" of such a system would appear to slow down.
One should point out, that those changes in size (_v) and time (_v) are observed only by a stationary observer in the resting coordinate (,,). This means that the changes that the Lorentz transformation equations predict are not real but only apparent!!
Einstein extended the Lorentz equations into the dynamic branch of Physics which deals with masses and forces. He postulated that no acceleration would be possible in the vicinity of the velocity of light. Newton's famous equation
(Force) = (Mass) x (Acceleration)
suggests that acceleration must become 0 (zero) if the value of mass reaches an infinitely large value. It became perfectly logical to use an equation similar to the Lorentz transformation. So, the equation
= ₀ x (1 - ²)^(-1/2)
where
= /
was introduced. ₀ is the resting mass value of the body in motion.
Unfortunately, this equation carries with it an element of ambiguity. Why? Because it is very difficult to perceive how a purely scalar value like mass () can apparently change. Einstein's equation is a precarious scientific tight rope act, trying to link the apparent with the real. To add to this confusion, Einstein introduced the concept of energy in those "relativity" based equations. The notion of apparent energy becomes even more ludicrous. However, the mathematical operation is definitely brilliant.
When one calculates the work done by a body of mass increasing its velocity from ₀ to , we obtain the well-known formula of kinetic energy.
_k = (1/2) x x ² - (1/2) x x ₀²
Taking into account the constant velocity of light and the changes of mass due to varying velocities, the formula of kinetic energy should be written in the form
_k = x ² - ₀ x ²
Why? Because if we substitute the value of the transformation equation, then we have
_k = ₀ x ² x (1 - ²)^(-1/2) - ₀ x ²
The
(1 - ²)^(-1/2)
can be expanded by the binomial theorem to
1 + (1/2) x ² + (terms in ⁴, ⁶, etc.)
Remembering that
= /
and if the velocity is low, then the higher power terms can be neglected, and _k can be reduced to that familiar form
_k = ₀ x ² x (1 + (1/2) x ²) - ₀ x ² = (1/2) x ₀ x ²
Consequently, the general classical form of kinetic energy
_k = (1/2) x x ²
should be written
_k = x ²
in the "relativity" form.

Einstein's Strange Idea

This "Mass-Energy Equivalence" equation was an excellent tool for Einstein to predict the immense power of the atom. Nevertheless, this huge "kinetic" energy assumes that within the atomic structure, there are some units which are animated by a real velocity of light . Then, according to the transformation equation, even the smallest mass value becomes infinite. The energy of a single atom could then be infinite?!
If we calculate the energy of 0.001 kilogramme of matter, then we arrive at the awesome figure of 9 x 10¹³ joule. We can similarly estimate how many grammes of Uranium are required to destroy a city! But in each of these calculations, we must use the "resting" mass value ₀, but no one seems to understand why! There is obvious confusion at any rate.
Modern Physics accepts the principle that energy is manifested in a number of forms, and that one form can be transformed into another. All physicists know that heat energy can easily and instantaneously change into motion or kinetic energy. However, the reverse is not the case. Transforming kinetic energy into heat energy can not be done instantaneously. Yet, this is precisely what seems to happen in a fission reaction and in a nuclear explosion. Until the mechanism of this instantaneous transformation has been explained, the
= x ²
formula remains a dark mystery!
With regard to the experimental data which would confirm Einstein's Theory of Relativity, we should point out that in our living space, we can not create sufficient velocities to prove anything. As soon as an object travels with a velocity greater than 12 kilometre/second, it leaves the gravitational field of the earth. And this is still too slow to affect the mass value!!
One possibility is offered by a scientific hypothesis which suggests that inside a cathode ray tube, there are electrons moving at approximately 10% of the velocity of light. Furthermore, there are scientists who report that within some powerful particle accelerators, some "protons" will travel at velocities of up to 0.99 x (i.e., 99% of the velocity of light). Let us note that the flying subatomic particle notion is generally accepted by the scientific community, although no experiment has yet absolutely proved it.
In the famous Thomson experiment (first performed in 1897), it is believed that subatomic particles called electrons are generated by the cathode and accelerated through the hole of the anode which has a high electric potential value of volt. The resting mass value ₀ of the electron is believed to be 9.1 x 10^-31 kilogramme, and it has an elementary negative charge of 1.6 x 10^-19 coulomb. The accelerated electron travels with a velocity , and is deviated by an electrostatic field or by a magnetic field (perpendicular to Figure 06-02). The electron beam then strikes the fluorescent screen at point . The trajectory of the beam can be made visible, and it is possible to measure the radius of curvature in the magnetic field. Naturally, the flying electrons are also influenced by gravity, but one can easily demonstrate that this effect is negligible.
The acceleration of the electron results from the electrostatic energy x . To calculate this, we have the equation
x = (1/2) x ₀ x ²
or
² = 2 x ( / ₀) x
where x is measured in electron-volt which equals to 1.6 x 10^-19 joule.
By measuring the radius and knowing the strength of the magnetic field , we have another equation
/ ₀ = / ( x )
where is measured in (newton) / (coulomb x metre/second) which equals to 1 weber/metre².
Using these two equations, the mass of the flying particle as well as its velocity could be calculated. It is believed that in Thomson's cathode ray tube, the velocity of the electron is in the order of 10⁷ metre/second, which is about 10% of the velocity of light. The mass increase would be very slight (about 1%). However, by making several measurements and by increasing the velocities (with increasing anode voltages ), some increased values of mass were observed. These findings were world-wide proclaimed as absolute proof of Einstein's Theory of Relativity.
In modern particle accelerators and cyclotrons, electrons and other atomic particles are supposedly accelerated by using very high values. Certain accelerators are reported to use values in the range of 500 G (1 G = 10⁹ ). Ignoring for a moment the Theory of Relativity, if we calculate the velocity of an electron accelerated by only 1 G of energy, then we find that the velocity obtained would be about 50 times as much as the velocity of light ! Of course, Einstein's equation
= ₀ x (1 - ²)^(-1/2)
precludes any velocities higher than , and requires instead the electron to increase greatly its value of mass. This time, however, the mass increase can not just be apparent, lest the electrons will beat the unbeatable speed of light record!! In other words, we have a reality explained with a "relative transformation" method. This is indeed a case of real confusion!!
We can find velocity values in the range of 0.999 x for electrons, protons, etc., and for other yet-to-be-discovered subatomic particles. The deflection method used in Thomson's experiment works even with such high velocity values. The particle passes through a cloud chamber in order to be visible, and it is deflected by a strong magnetic field. By measuring the curvature of the deflection, we can calculate the mass value and the velocity of the particle. We can even predict if it is positively or negatively charged.
However, because of such high velocity , there is a huge value of acceleration
² / _e
where _e is the radius of the earth, acting upward (vertical direction). On the long trajectory of the accelerator, the particle is slightly deviated, which diminishes the accuracy of the measurement.
Thus, when we are measuring or calculating the behaviour of subatomic particles such as electrons, protons, neutrons, mesons, etc., we could be just chasing ghosts that do not even exist.
In the cathode ray tube experiment, I would suggest we replace the electron beam theory with that of a special type of magnetic pattern. This could be represented by circular lines of forces forming magnetic "pipes", as shown in Figure 06-03.
The diameter of these pipes would be in the order of atomic dimension (~10^-10 metre). These magnetic patterns are deviated by electrostatic and magnetic fields. They create electromagnetic inductions and visible photoelectric phenomena on a fluorescent screen. They would also explain the reaction force of the deviating force that tends to push the cathode ray tube in the opposite direction (following Newton's third axiom). With the flying electron theory, this reaction force would be hard to explain.

Conclusion

To conclude, a number of present modern scientific theories need to be reexamined and revised using as a starting point the Michelson-Morley experiment.
As a result of this, if Einstein's
= x ²
is shelved, then we will have to explain nuclear power in a different way. It is very easy by adopting the theory of individually acting, intelligent or "living" atoms. This, of course, would have a tremendous impact on our modern over-industrialised society. The most delicate task would be to persuade present-day science to abandon its hopeless dream of achieving fusion energy. This notion came about as a result of Einstein's suggestion of mass-energy equivalence. Once
= x ²
vanishes, so will the fusion idea.
At present, we note an ever-increasing concern for the safety of fission nuclear reactors, and almost everyone is hoping that such unsafe nuclear power will soon cease to be used. At the same time, energy-hungry scientists and technocrats are warning us that, without fusion, our society is doomed to return to the Dark Ages. These are absurd lies and exaggerations.
Although our civilisation is living its declining "old age" period of its history, we can certainly extend its life by thousands of years, using some moderation and by curbing our voracious industrial lifestyle. This would ensure some hope for the future of the next generation.
On the other hand, if we continue to rape our planet, then we are gradually achieving the suicide of our civilisation. This will be a suicide due to ignorance!! A great deal of this is due to Einstein's theories having been totally accepted by modern science.
In Christian Andersen's well-known story of the "Emperor's Invisible Clothes", the people finally discover the truth, and the silly emperor is left only covered with ridicule. Similarly, modern science may have been duped by a clever but erroneous notion.