The Quantum Border
In classical electromagnetic theory, the
one developed in the period from 600 to 800 by scientists such as Coulomb,
Volta, up to Maxwell, a pair of charges of opposite sign forms a dipole, the most basic system of charges in
interaction, the simplest of electromagnetic sources.
The study of the dipole can be addressed at various levels of complexity. Usually a pair of charges placed at a certain distance of interaction is taken into account without the problem of the actual dynamic conditions: energy, momentum and trajectories of interacting particles.
To analyze the electromagnetic emission of a dipole source, we consider as
fundamental variables of the physical model the spatial extension of the
source, determined by the distance of interaction and the distance of an
observer (physical observation
and measurement system) reputed placed in the center of the source.
Moving away from the center of the source and examining the structure of the electromagnetic field surrounding the source with distance, three physical regions can be distinguished:
(A) a neighboring region, spatially
bounded by the inner and outer rays of the source. This encloses the area of
space between the charges of the dipole and the first front of the
electromagnetic wave emitted by the source;
(B) a region of magnetic induction, for distances
from the source of the order of the emission wavelength;
An observer is naturally embedded in the radiation region (C) of any microscopic dipole and is able to perceive and measure, based on the dynamic conditions that determine the movement of the dipole charges, an emission of one or more front waves associated to an electromagnetic signal at a given frequency; However, nothing can be said for the near regions (A) and (B) of the source, which are too small to be measured.
To perceive and measure the
characteristics of the electromagnetic signal emitted in each of the three
regions of the dipole field, the wavelength must be large enough to hold the
observer. Given the microscopic size of a dipole formed by charged elementary
particles, these mean that the emission wavelength must be much larger than the
reciprocal interaction distance and that the relative motion between the
particles is so slow(so little energetic)that it generates an
electromagnetic emission with a wavelength large enough to hold the observer.
In this case, the volume occupied by the source is negligible compared to that
occupied by the emitted spherical wavefront and the source can be considered
point-made.
In fact a dipole is not exactly pointy and the wave emitted is not exactly spherical symmetry, that is, it does
not emit in all directions with the same intensity. More precisely it has
cylindrical symmetry, that is, it emits with varying intensity depending on the
angle between the direction of emission and the axis of the dipole(the axis
that joinsthe two particles) and only if the wavelength of the source is
very large compared to thedistance of interaction between the charges, the gap
between cylindrical and spherical symmetry becomes negligible. Unlike a
cylindrical symmetry electromagnetic field, the dipole is unable to emit all
the energy and momentum produced during interaction [1].
At the time of my physics studies I was intrigued by the fact that
although the hydrogen atom can be considered a dipolar system with a distance
of interaction determined bythe fundamental distance between the nucleus(proton)and
electron, the behavior during the emissive phase is different from that of a
"classic" dipole.
In fact, in atoms excited by an
external electromagnetic field, the electron moves away from the nucleus not
for any energy and momentum absorbed values, but only for certain values. During
the transition phase then, from the excited state to the fundamental one, the
atom re-emits the energy and amount of excess absorbed motion by emitting a
single photon, a kind of neutral body without mass, which mediates the exchange
of energy and momentum between electromagnetic field and matter.
According to the classical dipole, the
atom being a dipole should also behave like a macroscopic source and emit an
electromagnetic wave with energy proportional to the square of the amplitude of
the electric field of the wave that has "It's not the first time we've had
a lot of people get to know what's going on," he said. If, on the other
hand, we imposed on a macroscopic dipole a change in the distance of
interaction between the charges similar to that produced in the hydrogen atom
during the disexcitation phase, the energy and quantity of motions emitted
would be exactly those Maxwell's classical electromagnetic theory. So why does
electromagnetism not allow correct predictions on a microscopic scale and the
behavior of the sources is so different?
The answer may be the usual one, that
electromagnetism is able to perfectly describe only the interaction produced by
the collective motion of a large number of electric charges but not the
microscopic interaction of a pair of charges such as proton and electron, which
instead follows the laws of quantum mechanics, or can be drastically unusual if
we address the problem from a new point of view [2].
To examine the problem as
realistically as possible, consider a dipole that emits wavelengths of the
order of the interaction distance of the charges that form it. In this case the
conditions for treating the source as if it were spherical symmetry are not
verified because the interaction distance and wavelength are comparable:
consequently the difference between the energy produced in the interaction and
that emitted by the source is negligible only accepting to lose much of the
information both on the actual local structure of the electromagnetic field of
the source, and on the amounts of energy and motions not emitted and localized
in the source. So it is precisely the lack of spherical symmetry of the
electromagnetic field of the dipole source that is the cause of a different way
of perceiving by the observer the energy exchanges between radiation and
matter.
The macroscopicity of the observer with respect to the microscopicity of the electromagnetic source is therefore the phenomenological border, the frontier between the observation of the macroscopic world, where the laws of classical mechanics and electromagnetism apply, and the microscopic one where quantum mechanics dominates.
Bibliografia
[1] M.Auci. "Natura fisica del fotone nella teoria
elettromagnetica". Proc. LXXII Cong. SIF
(1986) 209.
[2] M.Auci. "A
Conjecture on the physical meaning of the transversal component of the Poynting
vector". Phys. Lett. A 135 (1989) 86.
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