E=MC2 CRITIQUE
James A. Putnam
ã 2003
Einstein’s equation is interpreted by embracing a theoretical disconnection. It is said to establish that mass and energy are essentially alike. They are just different expressions of the same thing. This ‘thing’ is commonly referred to as energy. There is no support for this interpretation contained within the equation. There is no support for it in the fundamentals used to derive the equation. Einstein insisted its support was demonstrated in radioactive processes. He stated that: “The equivalence of mass at rest and energy at rest as expressed by E=mC2 has been confirmed in many cases...”
So
Einstein believed energy could be at rest. Since energy is defined as the measurement
of a force applied across a distance (force times distance), this is analogous
to saying: The measurement of a force applied across a distance can exist at
rest. This is an example of a theoretical disconnection. Instead of energy
being a quantitative measurement, it is arbitrarily assigned the status of
having a material existence. In Einstein’s theory, and even more generally
since then, energy is simply assumed to have physical substance. This is not
empirical knowledge.
Empirical
evidence cannot be used to support this conclusion. We can only apply force and
not energy. We can only observe changes in velocity and not changes of an
energy substance. Energy exists only in today’s theoretical speculations about
the mysterious unknown realm of the universe that we call cause. In many ways, theoretical physics relies upon artificial,
even hidden, explanations of why events occur. It is lack of understanding that
is being hidden.
It
is my position that both the form and interpretation of E=mC2 results from fundamental errors. I demonstrate
a change of form and interpretation in detail in the body of the theory. Here I
present an introductory reinterpretation. It is intended to show that
Einstein’s equation, even in its familiar form, is susceptible to
reinterpretation. Beginning with the definition of energy:
Einstein’s
equation can be written as:
If the force is constant, then:
A
constant force is used to derive Einstein’s energy equation. Therefore:
Looked at in this way, the equation gives recognition to the fact that matter is defined by its property of force. Instead of reading Einstein’s equation as representing the maximum amount of energy, the equation is saying there is a maximum amount of force available from a particle at rest. What is the connection between this maximum amount of force and the term mC2? The answer lays in a demonstration that mC2 actually represents a value of mass times acceleration times distance. Therefore C2 is, in part, representing a maximum acceleration achievable due to the maximum, or total, force available.
It
is known what can be the maximum possible acceleration. An object can only be
accelerated to the approximate speed of light. The question to be answered is:
What is the minimum distance over which this maximum acceleration can be
achieved? That distance is the length of a photon. Photons cause a change of
velocity and can, therefore, be modeled as having length. The definition of
energy requires that the photon cause a force to be exerted over a distance.
Force times a point gives us nothing. The term C2 is the mathematical equivalent of the maximum
possible acceleration times the length dxc of the photon:
The
magnitude of dt is
a specific value for this example. The shortest possible time for the maximum
change of velocity to occur is the period of time it takes for a photon to pass
a given point. Adding this criterion to the equation:
The
maximum possible change of velocity is from zero to the speed of light.
Therefore, the expression on the right side can also be written as:
It
can also be seen that:
Therefore:
So,
the maximum acceleration times the shortest possible distance is:
Therefore:
Writing
an equation that includes all pertinent expressions of the total energy:
This string of equalities demonstrates the physical meaning of mC2.