E=MC2 Fallacies and the NonConversion of Mass to Energy
The formula E=MC2 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=MC2
What does E=MC2 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 widely-believed fallacies about this formula can be found throughout the
most general to the most technical scientific literature.
Fallacy # 1:
E=MC2 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=MC2 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 high-speed 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 (C2).
The kinetic masses (KM) of the individual pieces of the wheel is equal to their
rest mass (M0) divided by the square root of 1 minus their velocity squared (V2)
divided by the speed of light squared (C2) minus their rest mass (M0).
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=MC2 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=MC2 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 space-time so it could be
split into numerous mini-ethers 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=MC2/2 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=MC2 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 half-circular motion and
half-linear 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 all-pervasive ether, field, dimension or space-time.
Fallacy # 5:
E=MC2 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 hydrogen-3 nuclei fuse or when uranium-235 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 mass
Rest mass is the quantitative value of a body of matter’s resistance to change in
motion
Kinetic mass
Kinetic 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=MC2). 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 mass
A 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 (KE=MC2/2=1/2)
remains with the photon as it becomes imbedded within matter. Its rotational
kinetic energy (RE=IW2/2) 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.
Energy
To 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=MV2/2). 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 Mass
For 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=MC2). To simplify
the calculations we can use the following units:
Speed of light C = 1
Mass M = 1 kg
Energy E = MC2 = 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 (TM) 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=MC2. 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.
Mass of photons = .75
Mass of craft = 1.25
Energy of photons = .75
Energy of craft = .25 (E=MC2) .225
(E=mv2/2)
Momentum of photons
= .75
Momentum of craft = .75
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=MC2 gives us the energy of the photons produced from
matter/antimatter annihilation and the energy needed to produce kinetic mass.
M=E/C2 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 widely-held, 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 blue-shifted 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 red-shifted 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?
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