
E=MC^{2} Fallacies and the NonConversion of Mass to EnergyThe formula E=MC^{2} has long been interpreted to mean that the rest mass of matter could be converted into the energy of massless photons and that the kinetic energy inherent in the motion of bodies of mass increases the mass of those bodies. The validity of this idea rests on the arbitrary assumption that the photon has no mass. However, a classical interpretation of photon experiments would identify the photon as a particle of mass. Experiments show that photons have both energy and momentum and each of these is associated with the motion of mass. A careful examination of these experiments will show that energy and mass are separate and distinct parameters and that one is never converted to the other. 

E=MC^{2}What does E=MC^{2} really mean? This deceptively simple equation is known by nearly everyone to be one of the ultimate secrets of the universe, yet almost no one has the slightest idea of what it says or how it really works. Five widelybelieved fallacies about this formula can be found throughout the most general to the most technical scientific literature. 

Fallacy # 1:E=MC^{2} means that matter can be converted into energy.It is believed that when an atomic bomb explodes, matter is transformed into enormous amounts of energy. This is not true. After the explosion, all of the original matter still exists. All of the protons, electrons, and neutrons making up the uranium, plutonium, or tritium are still within the mushroom cloud. Elements were transformed, neutrons were split into protons and electrons, and protons and electrons combined into neutrons, but in no case was a single particle of matter converted into energy. All of the original components needed to reconstruct the transformed atoms to their initial nuclear states are speeding away in all directions and could, in principle, be reassembled back into the original nuclei. The same exact number of protons and electrons exists after the explosion as existed before. To reassemble these components would require the same amount of kinetic energy that was released in the explosion. The energy of the explosion comes not from converting matter to energy, but from the kinetic energy released when the light elements combine and when very heavy elements break apart. This energy did not just appear from a miraculous transformation of matter into energy, but was always contained within the internal motions of the electrons and protons making up the structure of the fissioning or fusing atoms. The only transformation that occurred was the conversion of rotational kinetic energy into linear kinetic energy. 

Fallacy # 2:E=MC^{2} means that mass can be converted into energy and energy can be converted to mass.This also is not true. For example, much of the energy of an atomic explosion comes from the decay of neutrons that have a mass .0078 times greater than the combined rest masses of the proton, electron and neutrino decay products. However, this .78 MeV of mass does not disappear or convert to energy when the neutron decays. Most of the energy of the decay is contained within the high velocity of the electron as it is thrown from the much heavier proton. The Lorentz transformation mass increase produced by this velocity and to a much lesser extent the velocity of the proton and the neutrino accounts for all of the extra mass contained within the original neutron. The combined masses of the products of a neutron decay are exactly the same as the mass of the original neutron. The surplus mass of the neutron is kinetic mass produced by the rapid spinning of it components. When the neutron breaks apart this same exact quantity of kinetic mass is still contained within the rapidly moving decay products. There is no conversion of mass to energy because mass always remains constant both before and after the decay. Of course as the electron and proton are slowed by collisions with other matter they will loose much of this excess kinetic mass, but only by transferring it to the atoms with which they collide. For example, the electron might interact with many atoms and transfer a little of its kinetic mass to each one by increasing their velocity as well as the rotational kinetic energy of their components. When it comes to rest, all of the electron’s kinetic mass is gone, but it still exists in the atoms that slowed the electron to a stop and thus gained velocity in the process. It is also possible that the electron will hit an atom in just right place and with just the right velocity so that it combines with a proton to form a neutron. Still there is no mass change in either case. Either the electron gives up small amounts of its kinetic mass to many different particles before it comes to rest or it combines with a single proton and keeps all of its kinetic mass as it forms a neutorn. It has the same amount of rotational motion inside the neutron as it had linear motion before it struck the proton and the kinetic mass inherent in these motions remains unchanged throughout the reaction. Mass does not change into energy and energy does not change into mass. The only transformation occurring here is the conversion of rotational kinetic energy to linear kinetic energy and vice versa. For a real world example of this, consider a large flywheel constructed from some strong but brittle material and powered by a very highspeed electric motor. As the moving electrons within the windings of the motor are slowed and loose energy the velocity and energy of the flywheel are increased. As it spins faster and faster the wheel’s kinetic mass increases in direct proportion to its increasing rotational kinetic energy. Eventually, the speed of the wheel becomes so great that the centrifugal force exceeds the tensile strength of the wheel and it shatters into numerous pieces that all fly off in different directions along the plane of rotation. The kinetic mass of the spinning wheel is now divided among the kinetic masses of the individual pieces. The kinetic mass (KM) of the spinning wheel is equal to its rotational kinetic energy (E) times its rest mass (M0) divided by the speed of light squared (C^{2}). The kinetic masses (KM) of the individual pieces of the wheel is equal to their rest mass (M_{0}) divided by the square root of 1 minus their velocity squared (V^{2}) divided by the speed of light squared (C^{2}) minus their rest mass (M_{0}). The total mass in this experiment is constant. Mass is transferred from the electrons in the wire to the wheel and the pieces of the wheel retain that mass after it explodes. Mass moves from one interacting body to another but its total quantity is never altered in the slightest. 

Fallacy # 3:E=MC^{2} means matter and antimatter can be annihilated into pure energy.It is true that electrons and positrons or protons and antiprotons can combine and then split into photons, but a photon in no way fits into the metaphysical concept of “pure energy.” What is pure about the energy of an object that has a precise wavelength, momentum, angular momentum, spin polarity, frequency, and velocity yet will be measured to have different values from these by moving observers? The fact that a photon’s energy as well as some, but not all, of its other parameters have different values for different observers implies that the photon has a definite physical structure. The motion of this structure has energy but it is no more pure than the energy inherent in the flywheel’s motion or that of a bullet. 

Fallacy # 4:Perhaps the most widely believed fallacyis: E=MC^{2} means that all forms of energy have mass except for photons which are massless.The idea that the photon is a massless particle goes all the way back to before the beginnings of relativity theory. This idea that energy could be separated from mass and have an existence independent of mass was one of the primary assumptions of the ether wave theory of light that dominated the nineteenth century. The idea that light consists of particles goes all the way back to the Greeks, but it wasn’t until the beginning of the twentieth century that all experimental measurements began to show that light as well as all of the electromagnetic spectrum was both emitted and absorbed in discrete particles that came to be called photons. When relativity theory came along, the ether was not really abandoned but merely had its name changed to spacetime so it could be split into numerous miniethers called fields and dimensions. There are primarily two reasons why a massless photon seemed to fit the other conclusions of relativity theory. The first is that since a body’s kinetic mass increases toward infinity as its velocity approaches the speed of light, a photon couldn’t have mass because it always travels at the speed of light and therefore its mass would have to be infinite. The second reason deals with the classical determination of a photon’s mass. Suppose the momentum of a particular photon was measured and found to have a value of one unit according to the formula (P = MC = M = 1). Now suppose that the kinetic energy of an identical photon is measured and then its mass is determined using the formula (E=MC^{2}/2 M= 2). In the first measurement, the photon has a mass of one unit and in the second measurement it has a mass of two units. This problem must not be solved metaphysically, as Einstein did, by simply pulling the formula E=MC^{2} out of thin air and then declaring the photon to be massless. The answer to this problem lies in a better understanding of the shape and the dynamic motion of the photon’s physical structure. When a photon goes from rest to the speed of light it does not accelerate. The particles from which it originated were spinning with several types of circular motion in opposite directions at the speed of light. When the circular structure within the particle breaks, the motion of the photon’s mass changes from all circular motion to halfcircular motion and halflinear motion, but its velocity remains unchanged. The wave nature of the photon exists within the complex motions of its physical structure and not within some allpervasive ether, field, dimension or spacetime. 

Fallacy # 5:E=MC^{2} means that the rest mass of ordinary matter contains within it an extraordinary amount of energy, and that, at least in principle, it may someday be possible to release at least some of this energy for a useful purpose.When hydrogen3 nuclei fuse or when uranium235 nuclei fission, the energy inherent in the velocities of the decay products comes from the kinetic mass of the nuclei and not their rest mass. Less than 1/1000th of the nuclei’s total mass is decreased in these reactions. The only way that the rest mass of matter can be converted to photons is when a matter/antimatter pair fuse with one another and then split into photons. This process can never be considered as a source of energy because the universe contains none of the antimatter needed to create these photons. A photon is composed of a body of matter and a body of antimatter spinning in opposite directions. The rest mass of the matter of the universe contains only one of the two necessary components needed to create an annihilation photon. Even if the efficient manufacture and storage of antimatter was not a difficult process, the energy needed to create it would always be much greater than the energy produced by its annihilation. This could only be a way to store energy and never a source of energy. There are virtually no positrons and antiprotons available anywhere to annihilate the electrons and protons contained within the matter of the universe. The energy of matter’s rest mass is in a twolock box and we only have one key. Rest massRest mass is the quantitative value of a body of matter’s resistance to change in motion Kinetic massKinetic mass is the quantitative value of a body of matter’s increased resistance to change in motion that occurs when it is accelerated in any direction relative to its natural position of rest. Kinetic mass is directly proportional to the energy associated with the body’s motion relative to its position of rest according to the formula (E=MC^{2}). Kinetic mass and kinetic energy are complimentary components of a body of matter’s motion that do not exist separately. They are the opposite sides of a coin rather than two different coins. Photonic massA photon with an energy of one has a rest mass of one. When a photon is absorbed by an atom, half of its energy stays with the photon as spin and the other half is transferred to the atom’s structure. Its kinetic energy (_{K}E=MC^{2}/2=1/2) remains with the photon as it becomes imbedded within matter. Its rotational kinetic energy (_{R}E=IW^{2}/2) leaves the photon and is transferred to the atomic structure of the absorbing matter. This energy can either remain within a single atom to be used in the emission of a photon at a later time, or in some substances it can be passed from atom to atom in a coherent wave. When the wave reaches the surface, its energy can be used in the emission of a photon. A photon remains intact with its rest mass after it is absorbed by an atom. When it absorbs the necessary energy from the internal motions of the atom it is emitted. The spin shock waves from photons temporarily increase the kinetic mass of the atoms that they move through. Both rest mass and kinetic mass can be converted to photons but this process does not involve any change in mass because photons have exactly the same mass as the rest mass or the kinetic mass from which they were created. Since a body’s kinetic mass increases toward infinity as its velocity approaches the speed of light, the argument has been made that a photon couldn’t have mass because it always travels at the speed of light and therefore its mass would have to be infinite. The answer to this problem lies in a better understanding of the photon’s physical structure. When a photon goes from rest to the speed of light, it does not accelerate. The stationary photon from which it originated was spinning with several types of circular motion at the speed of light. When the photon’s circular structure within the particle breaks, the motion of the photon’s mass changes from all circular motion to one half circular motion and one half linear motion but its velocity C remains unchanged. EnergyTo make the assumption that matter can be converted to into energy completely changes the idea of energy and gives it an almost supernatural character. Before this great leap of faith, energy had many different forms. Each of these represented a particular way that the motion of mass could be quantified. All of these types of energy could he broken down into the basic kinetic energy formula (E=MV^{2}/2). However, once the equivalence of mass and energy is assumed, energy becomes a pure substance that can exist without the presence of mass rather than just a parameter of mass. Constant MassFor an example of how rest mass can be converted into kinetic mass let’s consider the following thought experiment. We will forget the technical problems involved and just assume that we have developed a miniature matter/antimatter powered spacecraft. The empty weight of this vehicle is one kilogram and one of its two fuel tanks holds one half kilogram of matter and the other holds one half kilogram of antimatter for a total mass of the craft and fuel of two kilograms. The craft’s engine combines the matter and antimatter and uses the annihilation photons to power a gamma ray laser that accelerates the craft with 100 percent efficiency. This laser produces photons of identical wavelength, energy, momentum and direction. In this experiment the engine is turned on and allowed to run at a constant rate until all of the fuel is exhausted. How fast will the craft moving when all of its fuel is exhausted? We know that both the craft and the total of the photons emitted from the laser have equal quantities of momentum (Newton’s third law). We also know the total amount of energy expended by the engine (E=MC^{2}). To simplify the calculations we can use the following units: Speed of light C = 1 Mass M = 1 kg Energy E = MC^{2} = 1 energy unit Momentum P = MC = 1 momentum unit To an observer on Earth, the photons coming from the craft’s laser engine would, at first, all have a wavelength, energy, and momentum of one unit. However, as the craft gains velocity away from Earth, the wavelengths of these photons would increase and their momentum and energy would decrease. At the point where all of the craft’s matter/antimatter fuel was exhausted the craft would be moving away from Earth at 60 percent of the speed of light. The last of the photons to be observed on Earth would have wavelengths of two and an energy and momentum of one half. Using the Lorentz Transformation formulas:
We can determine that the one kilogram craft moving at .6 C would have a momentum of .75 and a total mass (_{T}M) of 1.25 kg (1 kg rest mass and .25 kg kinetic mass). This means that the total momentum of the photons emitted from the engine would also have to be .75 (Newton’s third law). From this we must conclude that the total energy of these photons is .75 and if we permit photons to have mass, their total mass would be .75 kilogram. The total kinetic energy of the craft is represented by its kinetic mass and can be determined to be .25 using the formula E=MC^{2}. As we can easily see from these numbers the total combined mass of craft and photons is still 2 kilograms and their combined energy is equal to one. One kilogram of mass has been “converted” to energy but the mass of the system remains constant. If we try to make the assumption that photons are massless particles then the numbers no longer add up. In this case we still have 1 kilogram of mass being transformed into one unit of energy but the total mass of the system is now 1.25 and not 1.00. We could say that the craft’s .25 kg of kinetic mass represents both mass and energy and that this mass would be converted into photons if the craft were to hit an object at rest such as an asteroid or planet. This leaves us with the task of explaining why kinetic mass is both mass and energy and why rest mass has no energy.


In conclusion, we must realize that there are no experiments that can be interpreted as evidence that photons are massless particles. The idea that photons have no mass is an ad hoc, purely metaphysical concept that cannot be verified experimentally. E=MC^{2} gives us the energy of the photons produced from matter/antimatter annihilation and the energy needed to produce kinetic mass. M=E/C^{2} gives us the rest mass of a photon and the kinetic mass of a moving body. In no way do these equations imply that mass is converted into energy or that energy is converted into mass. Both remain constant in all interactions. Nowhere is there any evidence to support the widelyheld, but erroneous, belief that photons are massless particles.  
Photon Flywheel 

As an example of how the change in a body’s kinetic energy must also change its mass, consider a thought experiment in which a flywheel made of an exceedingly strong imaginary material is spun at the velocity of 1/3 C. The wheel has mirrors attached to its outer surface like the fins of a paddlewheel. Two lasers, A and B, shoot photons at the mirrors on opposite sides of the wheel. These photons, which all have a wavelength, energy and mass of exactly one, relflect from the mirrors at a velocity of exactly C relative to their velocity before striking the mirror. The velocity of the mirrors has no effect on the photons’ velocity but it does changetheir wavelength, energy and mass.
The photons from laser A are blueshifted to a wavelength of .70711 as they reflect from the approaching mirror, and their energy and mass are increased to energy 1.414. In this process, the velocity of the spinning wheel is slowed as mass and energy are transferred to the reflecting photons. The photons from laser B are redshifted as they reflect from the receding mirror to a wavelength of 1.414 and an energy and mass of .70711. In this case, the velocity of the wheel increases as mass and energy are transferred from the photons to the wheel. In both of these examples, momentum is conserved and both mass and energy remain separate and constant. If we attempt to explain this experiment in terms of massless photons then the conservation of mass is lost. The photons from laser A take energy away from the wheel and decrease its mass. Laser B photons transfer energy to the wheel and increase its mass. In both cases, energy remains constant but mass either vanishes into or appears from nowhere. How can mass and energy be equivalent if energy remains constant but mass does not? If energy has mass how can photons not have mass? 


< < Back to Essays 