The razor of Ockham

In a conductor cable (not superconducting) crossed by electric current, intuitively it would seem that:

– the energy flow that generates the Joule effect has the direction of the cable axis

– the Joule effect is somehow caused by a sort of “friction” between the charges that move along the cable and the atoms of the material of which the cable is made

– the motion of the charges along the cable “thermally agitates” the atoms of the material of which the cable is made

– the potential difference has the purpose of “compensating” the energy loss due to the Joule effect, allowing the charges to move along the cable without “slowing down”.

According to Henry Poynting, the phenomena are completely different:

– the energy flow(1) that generates the Joule effect has a radial, not an axial direction and comes from the electromagnetic field surrounding the cable

– the Joule effect is somehow caused by a sort of “friction” between the electromagnetic energy coming from the field generated by distant charges and the atoms of the material of which the cable is made

– the interaction of the electromagnetic energy flow with the atoms of which the cable is made “thermally agitate” the atoms

– the potential difference has the purpose of “aspirating” the flow of energy coming from the surrounding electromagnetic field making it interact with the material of which the cable is made.

Starting from the general consideration that, for the conservation of energy, the temporal variation of the energy contained in a certain volume (let’s call it “A”) must equal the sum of the flow of energy leaving the surface that encloses the volume considered (let’s call it ” B ”) plus the work done on the matter contained in the volume considered (let’s call it“ C ”), in 1884 Poynting manipulates Maxwell’s equations and, with a series of mathematical passages, finds the three components of the equation A = B + C in function only of the electric field “E” and the magnetic field “B” (except for the constants “c” = speed of light and “ε0” = dielectric constant).

Until the advent of electronic computers, physicists were frightened by the non-linear differential equations. For example, in the case that we are analysing, in addition to the Poynting deductions that lead to two simple equations exclusively containing the first two scalar products(2) and the second a vector product(3) there are theoretically possible infinite other solutions, all more complex than the one found from Poynting(4).

The principle of Ockham’s Razor, by the philosopher William of Ockham, is famous: “The simplest solution is often the right one”. It is true, but not always.

Chaos theory teaches us that nature often enjoys using complex mechanisms that require complex theories to be studied.

Fortunately, with the advent of supercomputers, it has become easy to solve even extremely complex equations numerically. For example, in the case we are analysing, the solution of equations alternative to those of Poynting, could lead to phenomenological descriptions of the propagation of electromagnetic energy different from those deriving from the Poynting theory. It is then obvious that it will be only the experimental verification that objectively determines which of the various mathematical descriptions is the correct one.

Fortunately, with the advent of supercomputers, it has become easy to solve even extremely complex equations numerically. For example, in the case we are analysing, the solution of equations alternative to those of Poynting, could lead to phenomenological descriptions of the propagation of electromagnetic energy different from those deriving from the Poynting theory. It is then obvious that it will be only the experimental verification that objectively determines which of the various mathematical descriptions is the correct one. 

Turin (Italy)

Gianfranco Pellegrini

(1) the Poynting vector represents the energy flow in the unit of time (= energy in the unit of area and time).

(2) u = ε0/2(E · E) + ε0c2/2(B · B)

(3) S = ε0c2(E X B)

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