Chapt15.42 Deriving E=mcc purely from the Maxwell Equations; energy and mass are dualities not equivalencies #1196 New Physics #1316 ATOM TOTALITY 5th ed
Feb 2, 2013 1:49 AM
Chapt15.42 Deriving E=mcc purely from the Maxwell Equations; energy and mass are dualities not equivalencies
Alright, I need a chapter on how the Maxwell Equations derives E = mc^2, which I like better writing as E = mcc
I like that because in the analysis we consider the maximum possible momentum of a mass m as being P = mc since there is no speed greater than c.
So that we ask the relativistic question of the Maxwell Equations that commonplace energy of kinetic energy is
E = 1/2 mvv
and so, what is the maximum possible energy since the speed of light is maximum speed and it is a constant.
Would we have E = 1/2mcc ? The answer is no, for the maximum would be mcc not 1/2mcc.
In the literature there are many logical arguments that derive E = mcc, except they get hung up on not applying relativistic Maxwell Equations to eliminate the constant term of 1/2 or any other constant except that of 1.
One Argument, usually called the Units argument:
E = FD, energy = force x distance
F = MA, force = mass x acceleration
E = MAD
V = D/T, velocity = distance/time
A = V/T, acceleration = velocity/time
A = D/TT
E = M(DD/TT) = Mcc
Now the reason that physicists never accepted that as a full fledged proof, is that they were unsure the constant in front of Mcc is something other than a 1.
But in their haste to object to the argument, they failed to apply Maxwell Equations as relativistic.
Application of Maxwell Equations: 1) c is a constant speed 2) c is a maximum speed
Now, we have E = M(DD/TT) = mc^2
If the constant K in Kmc^2 was something other than 1, suppose it was 1/2mcc as in kinetic energy 1/2mvv, then we have the speed of light less than c. If the constant K were greater than 1 then it violates the c as maximum speed.
Second Argument: We have a second logical units argument using momentum rather than kinetic energy:
P = MV, momentum equal to mass x velocity
P = FT, momentum equal to force x time
E = FD and relativistic D is thus c, for if not we violate c is a maximum
E = Fc
now since F = ma and where light speed cannot accelerate but remain the constant c we have
F = mc
Substituting we have
E = mcc
So the units argument of both kinetic energy and of momentum rely on removing all constants K except for the constant of 1. And those are removed by the two facts of light speed-- a constant and a maximum. Only the constant 1 allows no contradictions to light speed.
But the logical argument above tells us more about the thorny issue of rest mass versus energy. Are we to believe that the two transition from one to the other, as a equivalence or equality? Or better yet, that the two are dualities. For example when a electron and positron annihilate, are we to believe the rest mass no longer exists and converted to a light wave energy, or that the rest masses still exist in the light wave? For a answer to that question we look at electricity and magnetism. Are we to say that electricity equals or equivalent to magnetism? Or better say they are dualities, where depending on the experiment used, displays electricity more than magnetism or displays energy more than mass.
A nice analogy is a slinky toy. The toy is rest mass of a particle when packaged in the box. When let loose and stretched as far as it can stretch it is energy wave. But it is still a particle, only a stretched particle.
So physicists have to be very cautious about equal signs and equivalence statements, because when we get down to the axioms of physics, the Maxwell Equations, electricity, magnetism, particle, wave, rest-mass, charge, energy, time, distance, there is no equality or equivalence but duality and duality transformations.
We do not speak of the equivalence of proton to electron to that of a neutron. We think of the proton and electron as duality of charge and that they reside inside the neutron until the neutron decays. So the formula 0 = -1 +1 is not saying the neutron equivalency of electron and proton, but rather the duality of parameters involved.
We still use the equal sign and the equivalence sign borrowed from mathematics and we use the language of equal or equivalent, but in physics, we should not mistake our borrowing of mathematical symbols with what is physically going on. Energy is not equivalent to mass, nor is electricity equivalent to magnetism, but rather they are dualities of physics.
Duality is a concept that is lower than what equality is a concept in mathematics. In fact, mathematics has no concept lower than equality. But Physics is richer than mathematics and physics subsumes all of mathematics. And so, in physics there is a concept of equality, but a concept even lower in that of duality.
Google's archives are top-heavy in hate-spew from search-engine- bombing. Only Drexel's Math Forum has done a excellent, simple and fair archiving of AP posts for the past 15 years as seen here: