On Feb 2, 12:23 am, Archimedes Plutonium <plutonium.archime...@gmail.com> wrote: > Sorry, I need another chapter. > > 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. >
Maxwell Equations derivation of E = mcc is an axiom system of units.
Now in that derivation of E= mc^2 from purely the Maxwell Equations of units such as force, energy, velocity, acceleration, momentum, etc. that such units can be an alternative axiom system of physics.
Instead of the 4 Maxwell Equations we can set up an alternative axiom system for physics composed of many terms such as
The trouble with this alternative axiom system of physics is that it is not short and concise as 4 Maxwell Equations.
So, even though no physicist of the 20th century ever realized that Physics must have an axiom system, they had one anyway and were totally unaware that they had an axiom system. Their axiom system, was the units such as force, acceleration, momentum, angular momentum etc etc.
I remember a old teacher of mine once remarked to me "so, you do not like force or energy units, well, dream up your own units, and whatever you dream up, will eventually be the same units in physics as what we currently use only yours will have different names."
So we have a nice choice at present. We can claim the axioms of Physics are the 4 Maxwell Equations, or, the axioms of physics is a huge long list of terms such as force, momentum, energy, etc etc.
The beauty of the Maxwell Equations as axioms is that they have all those terms included in the 4 equations and they have a dynamics and interrelationship of those terms, whereas the terms of units by themselves have a dynamics but no apparent interrelationship of those dynamics, for they are missing duality. Units do not tell us that electricity is a dual of magnetism.
So it is very difficult to replace the Maxwell Equations as the axioms of physics. Units come close but fail on many aspects.
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: