When a unique concept such as a ‘useful hole’ has been shown to help in understanding the workings of nature in one field, it is natural to consider analogous concepts in trying to understand complex behavior in other fields. Notably in this case, the emission and absorption of light.
The exploitation of semiconductors that became key to the development of modern electronics, involved conceptualizing the symmetry of roles for electrons and the holes they leave behind. A hole is an absence or a ‘nothing’ that is the negation of a ‘something’. But the significance of that ‘nothing’ is the expressed lack of the ‘something’ that is itself considered significant. In electronics the significance of the electrons is that they provide the moving negative charges that are the electric current in the semiconductors. There is a countermovement of the holes the electrons leave behind that provide the positive, oppositely directed current; both contributions are significant to the operation of the semiconductor circuits.
Let me explain where I’m coming from here: The intricacies of photon emission and absorption have not been properly explained in my opinion. Einstein’s two types of emission—‘spontaneous’ and ‘stimulated’ defy reason; nature does not provide multiple mechanisms for doing the same thing. Einstein himself said on other topics, “God would not have done it that way.” My investigation suggests God would not have ordained spontaneous emission. Emission can’t occur without absorption. G. N. Lewis, opined that:
“…we can no longer consider one atom the active agent and the other as an accidental and passive recipient, but both atoms must play coordinate and symmetrical parts in the process of an exchange.”
This was in his paper in 1926, where he coined the term ‘photon’. And thus, a century later I herald the passing of spontaneous emission – not because G .N. Lewis said so, but because the conservation laws demand it. This is illustrated and explained in the figure below where an atom is depicted as in its high energy state but is precluded from emitting a photon unless and until it exhibits an initial relative velocity. Why? A velocity is undefined unless it is specified with respect to aother receptive atom (an ‘observer’ in the parlance of Einstein’s relativity). Thus, a receptive atom (a ‘hole’, if you will) is an essential element in the emission of a photon. Photons are not just cast out into the ether independent of the availability of absorbers, they are working agreements between atoms in the exchange of energy and momentum.
Consider a relatively stationary atom in one of its higher quantum energy states, i.e., a situation in which one of its electrons is in a high energy ‘orbit’ within the atom. When the electron relaxes and ‘falls’ into a lower orbit, a photon of radiation is emitted. The remaining atom will possess less energy, and now will recoil at a velocity to match the energy and momentum of the emitted photon. Conservation of energy and momentum require the transition from an initial to a final state that preserves the total amount of energy and momentum. Let’s consider what this involves for Einstein’s spontaneous and stimulated emission, taking into account the differences in the relationship between energy and momentum for an object such as an atom and a photon of radiation.
Spontaneous Emission Dilemma
However, upon further examination, to solve these simultaneous equations, we are faced with the following dilemma: We must have that,
on the one hand, and
on the other, implying unrealistically that there can be no recoil, because vR = 0.0 is required to satisfy the equations, in which case f =0.0. Both energy and momentum cannot be conserved if spontaneous emission is allowed.
Stimulated Emission Dilemma
Stimulated emission involves an interaction between two atoms in which the wave function originating at one of the atoms causes the other to emit a photon. In the figure above, if the emitting atom is in relative motion with respect to another atom such that v > vR > 0 there will be emission. It is the relative velocity of these two participants that establishes the recoil of the emitting and ultimately the absorbing atom. The minimum value of v is h f / moc or no such transmission can occur.
To obtain an analytic expression for vR as a function of v, we need to rearrange and simplify these sets of conservation of energy and momentum equations.
Admittedly, I have screwed up several times in getting the expression correct (and the manipulations probably require more inspection). It’s complex. but the point is that there are solutions when a relative velocity is addressed that accommodates recoil.
To understand this phenomenon and why there is the necessity of a recipient prior to emission of a photon, consider the classical physics analogy with Maxwell’s well-known wave equation:
Where the leading symbol is a gradient differential operator squared. E is the electric field of the source of the radiation, c is the speed of light in a vacuum, and the second order partial differentiation is with respect to time. A similar equation exists for the magnetic field. These equations accommodates both a ‘retarded’ solution and an ‘advanced’ solution. The former is associated with wave propagation into the future and the other from the past.
Retarded Wave solutions have been interpreted as waves emanating from sources and affecting receivers after a time delay, which is consistent with causality and the common experiences with electromagnetic phenomena (e.g., light from distant stars reaching us after years of travel). Emitted photons are generally associated with the retarded wave.
Advanced Wave solutions have been interpreted to constitute effects preceding their causes, with waves converging from the future absorbers of radiation. These solutions are generally not considered physically meaningful due to their apparent violation of causality, but they are mathematically legitimate within the framework of Maxwell’s equations. The ‘advanced’ wave solutions have been summarily ignored as the non-physical solution.
This nonentity, associated with the ‘advanced’ wave moving in the opposite temporal direction of the more conventionally acceptable ‘retarded’ wave motion, should ring a bell as a useful ‘hole’ pre-arranged to absorb the photon. By analogy a body of water with a sealed cylindrical tube with the capability of raising or lowering the height of the water inside the tube and then suddenly releasing the seal to increase or decrease the level to that of its environment. In either case there will be waves emanating away from the tube. The essential difference in the wave structure in the two cases will only be the phase of the waves upon release.
Back to the situation of atoms, when transitioning to a higher energy or lower energy state of their charge distribution, electromagnetic waves will emanate outward from the atom in classical and quantum theory. The atom whether in a high state or a low state is a charge distribution of narrow positive protonic charges surrounded by negative, more widely distributed negatively charged electron clouds. When a distribution of charge is altered, electromagnetic waves emanate from the altered distribution. Notice the significant point, that it is the change, not the initial or final distribution that causes the waves. So Maxwell’s waves will be generated whether the atom absorbs a packet of energy altering its distribution of charges, or if it emits a packet of energy, which also alters the distribution of charges. So there would seem to be two situations that cause an atom to emit electromagnetic waves, but not two different mechanisms for emission. On closer examination, these two cases are both associated with the very same physical phenomenon – a photon having been emitted. What has been misunderstood is the unity of the instagation and resulting aspects of that phenomena.
The cause-and-effect argument that rejected Maxwell’s advanced waves is erroneous in the sense of being conceptually backwards. It is the perspective that is reversed. Maxwell’s wave theory can be applied most directly to the absorber requesting the photon, not to the emitter offering it. The quantum theory analogy is the wave function being associated with the absorber where the wave reaching the emitter results in collapse of the (advanced) wave function like a pin prick on a bubble. That is what has been considered ‘spontaneous emission’, but it isn’t spontaneous al all. It’s induced. Then, having emitted the photon, the emitter becomes a requesting absorber transmitting its own wave function. That wave function travels outward at the rate of the photon that heads for its destiny, but the wave function goes in all directions ‘in search’ of a replacement packet of energy. If/when this wave passes an atom in its high state, it will trigger that atom to emit its photon, i.e., ‘stimulated emission’, with the stimulation exactly the same as experienced for ‘spontaneous emission’. So the photon ‘hole’, initiating the ignored ‘advanced’ wave is the driving force in all photon emissions.
Leave a Reply