C. F. Bohren, "How can a particle absorb more than the light incident
on it?", Am J Phys, 51 #4, pp323 Apr 1983

H. Paul and R. Fischer "Light Absorption by a dipole", SOV. PHYS. USP.,
26(10) Oct. 1983 pp 923-926

The two papers above provide a solution. If an atom behaves as an electromagnetic resonator similar to a coil/capacitor tank circuit, and if the resonant frequency of the "atom/circuit" is the same as the frequency of the incoming light, then the atom will absorb a tiny portion of an incoming light wave and store it as a region of oscillating local EM fields surrounding the atom. Oddly, these fields strongly interact with the incoming light because they are naturally phase-locked to it.

The "trapped AC fields" around the atom act to cancel out some of the light waves in a volume surrounding the atom. Is this impossible? Energy cannot vanish! When EM energy is "cancelled out", the energy must go somewhere. Correct. This is simply absorption. It's a circuit effect, a localized "electrical transformer phenomenon", where some energy vanishes from the light wave and ends up inside the structure of the atom.

EM energy flow around a small antenna (Poynting vector field)
Figure 1

The authors of the two above papers provide another way to visualize this. If we superpose the EM field of the incoming light waves with the oscillating EM dipole field surrounding the atom/resonator, and if we then observe the superposed field shape and plot the Poynting vector field (energy flow lines) surrounding the atom, we'll see that the addition of the oscillating fields has *BENT* the Poynting vector field (the energy-flow lines) of the incoming light waves throughout a significant volume surrounding the atom. This is depicted in Fig. 1 above. The energy-flow lines are bent towards the atom so that they "impact" on its "surface." As a result, the atom gathers a large "sheaf" of incoming electromagnetic energy flux, where the diameter of this "sheaf" is hundreds of times larger than the known diameter of the atom (see fig 2.) Angstrom-sized atoms can act as thousand-angstrom antennas.

Figure 2

In this way an atom behaves as an "electromagnetic funnel." It actively "sucks" EM field-energy from its surroundings. This cannot happen without the sharp resonance, the locally stored EM energy, and the resulting dipole field surrounding the atom.

Weird, eh? Have you every heard anything like this before?

This phenomenon is well know to antenna designers. In fact, it is the basis of operation of all portable AM radios. The wavelength of AM radio signals is immensely larger than the size of a pocket radio. How can these devices intercept significant energy? A 1/4-wave dipole should be needed, yet at 1.5MHz, a 1/4-wave dipole is about 150 feet long! AM radios rely upon the oscillating fields surrounding a coil/capacitor circuit which is sharply tuned to resonate with the incoming EM waves. The ferrite-core coil in a portable AM radio has a capacitor across it. It is an "electromagnetic funnel" of the same type as I describe above regarding atoms. This kind of tuned-circuit coil/capacitor antenna has been understood at least since the time of Nikola Tesla. He used them as part of his "worldwide wireless power " scheme.

I've never encountered these concepts in all of my physics reading. As far as I know, they are not part of Quantum Mechanics. Yet they reveal details of atom/photon interactions, as well as the stimulated emission and lasers! These "oscillating fields" do not radiate from atoms (they remain limited to the electromagnetic nearfield region surrounding an atom, where "nearfield" is about 1/3-wavelength in diameter), and so they do not really involve either the photons which fly between atoms, nor do they involve the free-space EM waves which fly between atoms. The oscillating fields can either be seen as a cloud of "virtual photons" which builds up just before an atom absorbs a "real" photon... or they can be seen as the familiar EM fields from classical physics, and we can imagine the atom to be a tiny coil joined to a tiny capacitor.

Note that these bound, oscillating atomic fields must arise *BEFORE* an atom intercepts a real photon. I find this sort of astounding. In most of Quantum Mechanics we imagine that EM radiation is either particles or it is waves. However in this case, the EM radiation seems to be waves alone. The resonance-effect must build to a certain level BEFORE a photon-interception even occurs. After all, if the atom had to absorb photons in order to build up its oscillating bound fields, then it couldn't absorb any photons in the first place. It appears that the atom first absorbs energy from the classical EM field, and only later does it experience a photon-capture event. Which is another way of saying that first the atom experiences "virtual photon" interactions similar to those in transparent solids, and only later absorbs a narrowband photon and undergos an electron-state change.

Another issue: when the atom is first illuminated with EM waves, there are no oscillating EM fields present, and so the atom cannot perform its "energy funnel" trick, and it cannot absorb much energy from the propagating EM waves at all. The atom will be transparent to that frequency of radiation. However, if there is a bit of noise in the system, then the atom will have a slight amount of field-oscillation already. As the oscillating fields grow, the atom absorbs incoming wave-energy at a higher rate, which makes the fields stronger, which increases the absorption rate... and this suggests that the growth of the oscillating fields is far faster than linear with time. It doesn't just rise, instead it waits for awhile before suddenly and exponentially going "bang!"

Interesting. A bit interesting.

An analogous situation would be to have a piece of cardboard laying flat on the street during a windstorm. The cardboard sheet is stable as long as a tiny corner is not poked up into the flow. If the tiny corner does poke up, then it lifts the cardboard a tiny bit, which intercepts more wind, which drives the cardboard upwards with greater force, etc., in a runaway "mechanical reaction." The flat cardboard will initially sit unmoving. Then it will suddenly spring upwards into the wind and be flung violently downstream.

Just suppose that a "dead" atom is suddenly illuminated with EM waves. At first it sits there trying to "start up". Then it finally grabs a tiny bit of EM wave-energy. Once it has surrounded itself with weak AC fields, its oscillation suddenly takes off like bandits, and the oscillating EM fields pop up to maximum strength. Almost as if...

the atommmmm...

...had been struck...

...by a physical object. (See where this is leading?!!!)

An object like a TINY BASEBALL. Yet no such object is present. No such object is needed.

Huh.

Maybe wavefunctions don't "collapse" into particle events.

Maybe photons...

...DON'T EXIST?!!!!!!!!!!!!!!!!!!!!!!

(AIEEEEEEEE!!!!! ARRRRRRRRRRRRRG!!!!!)

"All these fifty years of conscious brooding have brought me no nearer to the answer to the question 'what are light quanta?' Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken" - A. Einstein, 1951

Another issue: the diameter of an atom is far, far smaller than that of the wavelength of the light which the atom absorbs. For this reason, in order to become an efficient "electromagnetic funnel", the intensity of the trapped, oscillating fields must be extremely large at the 'surface' of the atom. We want the field strength to be significant at a distance of up to 1/6 wavelength, which is hundreds of times the radius of an atom. We could make an analogy with the AM portable radio above, and we would see that the tiny "capacitor" within the atom would experience a analogously huge AC voltage, while the "coil" within the atom would need to support an absolutely immense AC electric current in order to spread it's bound EM fields out into the entire electromagnetic nearfield region surrounding the atom.

Think of it this way: in theory a portable AM radio could be made thousands of times smaller than a normal-sized radio if the oscillating current within its tuned antenna-circuit was allowed to grow large enough to produce a volume-filling field which reaches out for many tens of feet surrounding the radio. By reducing the size of the antenna-coil while increasing the allowed limit on the oscillating current/voltage, we keep the "electromagnetic funnel size" the same, even though the "physical antenna size" becomes smaller and smaller. In theory the AM radio could be reduced to the size of an atom, yet it could still intercept the 100-meter-wavelength EM waves of the AM radio band. It would simply need to generate a field which was so intense at the surface of the tiny radio, that the field extended for many tens of feet outwards from the radio. Just imagine! An atom-sized radio circuit that creates a radio-frequency field strong enough to bend AM radio signals for many tens of feet around the radio, so that they flow into the circuit.

Obviously the "antenna coil" within the microscopic AM radio (and within an atom!) would have to have a very low resistance, and the capacitor's breakdown voltage would have to be extremely high. The question arises: what is the "Q-factor" of the tuned circuit within a single atom? Is the "coil" inside the atom a perfect conductor? Is the "Q-factor" infinite? And, is the Q even linear with current? (I mean, do strange things happen when the internal "current" within an atom grows to be extremely large?)

Now I'm on a roll. I hadn't thought this through until I started this article. My subconscious is directly pouring information into my typing fingers as needed. Feels very strange.

As a single atom absorbs field-oscillation energy from a light wave (no photons yet!), the current and voltage within the atom grows higher and higher, and the resonant AC EM fields around the atom become very intense and very large in diameter until ...something breaks. In conventional physics we would say that an electron in the atom was forced to leap to a higher energy level. In an AM radio circuit, we would say that the increasing stored current in the tuned circuit finally burned out a wire (or perhaps blew a fuse.)

In both cases the energy contained within the oscillating fields is suddenly dumped into some other energy-storage mechanism, and the resonance of the "circuit" is ruined. It's almost like discharging a capacitor, except the act of discharge ends up altering its capacitance value. Or perhaps it's like opening the loop in the RLC circuit during the short time that the circuit current goes to zero; when the energy is entirely within the "capacitor". (Or it is like shorting out the coil during the brief time that the voltage across the capacitor goes to zero.) Perhaps I can build an electronic model of this using MOS circuitry.

Upon absorbing one quantum of energy, the AC fields around the atom freeze, they stop oscillating. The energy has gone into lifting the electron to a higher orbital, and orbital which has a different resonant frequency. (Note that since the fields were already entirely in the nearfield region, their sudden alteration during the zero-crossing point in time probably WON'T be radiated as an EM pulse which flys outwards from the atom.)

In the AM- radio analogy, the stored-oscillation energy went into the heating of the melting fuse. In the atom-analogy the energy went into the state-change of the electron. The "circuit" has suffered a nonlinear event. It has been "damaged." It might still have other resonant frequencies remaining, but they are at frequencies other than the one which just finished receiving a quantum of energy.

UPDATE 9/13/99
Hey, maybe the circuit in the atom doesn't need to break down. If it does not, then what other limit will be reached? Simple. The fields will stop growing when they become significant at the boundaries of the electromagnetic nearfield region, and so the atom starts to radiate EM energy at the same rate at which is absorbs EM energy. When the non-oscillating atom first wakes up and goes "bang", it absorbs just enough energy to bring its trapped local fields to maximum. Forever after it behaves as if it were transparent to that frequency of EM wave. It "eats" a quantum of EM energy. (So, would the value of this quantum be related... to frequency? One could hope...)

UPDATE 9/16/99
Nah, the above doesn't work. The atomic maximum "quantum" would be related to the amplitude of the incoming light, and would not be a constant photon. Brighter light would cause atoms to swallow bigger photons, not more photons. And Planck's constant could not be calculated from first principles. Rats!

Dan Y. points out that infinite-Q circuits take infinite time to absorb energy. If an atom has a single frequency, then it cannot absorb wave energy at all... yet it still apparently "swallows photons." Or perhaps infinite-Q 3-D circuits can absorb 3-D wave energy, even though infinite-Q 1-D circuits cannot absorb energy through their circuit connections.

UPDATE 10/25/99
If the resonators within atoms have infinite Q, then they would only respond to a PERFECTLY matched frequency. What if atoms cannot respond to light, since light isn't perfectly monochromatic? Instead, what if they can only respond to the monochromatic emissions of distant, individual atoms? In other words, a "receiver" atom would only see the emissions of a "transmitter" atom if there was no doppler shift and the atoms happened to have zero relative motion. Hmmm. Maybe their relative motion would have to be zero only for a brief instant, so that the resonance process could lock the phase of the receiver-atom to the phase of the waves coming from the transmitter atom? Then, if all atoms always transmit waves of a particular amplitude, "photons" might be explained. Atoms might only "see" the emissions of individual distant atoms, and never "see" the broad-spectrum averaged emission of multi-atom physical objects. A spectral line of a glowing gas is after all a collection of infinitely-thin spectral spikes, each spike being radiated by a single atom in the gas. And correspondingly, an absorption line is a collection of infinitely narrow slots, each slot being contributed by one atomic absorber. The atoms can't see the emission or absorption bands, they can only see the infinitely thin spikes!

What does Planck's Constant mean in terms of EM waves? It means that high-frequency waves would trigger fewer "energy suction" events, yet each event would deliver more energy. I don't see that this makes sense in terms of geometry. If we assume that waves of a particular intensity illuminate an atom, then the received energy would be proportional to the atomic currents and voltage, but should be independent of frequency, no? If the atomic radius is much smaller than the wavelength, then a certain resonant AC loop-current within the atom would produce a certain energy flow, but I don't see how lower frequencies and longer wavelengths would lead to less energy flow.

Separate topic: how fast does the stored energy within an RLC circuit change? Suppose an RLC circuit has been excited by an incoming wave, and it has absorbed all the energy it can. If the amplitude of the incoming signal suddenly doubles, will the amplitude of the stored voltage on the RLC resonator change over many cycles? Or will it double itself in far less than one cycle? And, if the incoming amplitude should suddenly fall by half, this will trigger "stimulated emission", and the RLC circuit will spew energy out. Think of an "EM horn" rather than an "EM funnel". How fast will the voltage on the RLC circuit fall? An equivalent question: if we build a tuned-primary, tuned-secondary RF transformer, and we find that the coupling is nearly 100%, how fast can we modulate the input signal and still see that the output signal follows it?

Once the two halves of the circuit are in phase-lock, they are behaving like a pair of atoms. I'm wondering... might they be "entangled" in fact, and not just by analogy? If they are, then there should be photonlike state transitions arising. If the amplitude of the incoming signal is changed instantaneously (by flipping a physical switch), will the output wave change instantaneously as well? If so, then once the two halves of the circuit are in resonance, we can modulate the primary at a rate far higher than the "carrier wave", yet the secondary will follow along! Imagine impressing a 1MHz modulation upon a 60Hz carrier... and yet the receiver reproduces the 1MHz signal! Naaah. That's too weird. If it could happen, someone would have noticed it. (But... the organized blindness taught in school might have KEPT everyone from ever attempting such a whacked out thing as impressing wideband data on a low-frequency carrier!)

All this is sheer speculation. However, it now has me very scared. I've definitely crossed totally into the "crackpot realm", and I'm now saying that perhaps Einstein was wrong, and the founders of Quantum Mechanics are wrong, and modern physics is on a totally wrong and dead-end highway, and space-filling electromagnetic fields have real existence apart from photon-particles. The second step on the stairway to total insanity turns out to be slippery, and the remaining steps take the form of a greased slide which delivers one rapidly all the way to the bottom!

:)

Now if I can just appeal to this resonance/funnel effect and therefore figure out how PHOTON EMISSION works without requiring photons, then I'll be ready for the big time. Any ideas?

BRAINSTORM! 9/10/99 Suppose that an atom/circuit has built up a large resonance signal. Suppose that the cycle has moved to the state where the atom's internal "capacitor" contains a large instantaneous voltage, and the instantaneous current in the "coil" is zero. Suppose we then break the connection between coil and capacitor. We have now stored energy as DC voltage across the capacitor. The oscillation ceases, although an external dipole field may remain behind. The atom's internal "capacitor" is "charged" (or we could say that the electron has been boosted to a higher state.)

Now suppose that we reconnect the capacitor to the coil. The oscillation will commence, and things will be as they were before the connection was broken. But wait a second. If the connection is switched on asynchronously with the illuminating waves, then the phase between the bound oscillating atomic fields and the incoming waves will most probably be incorrect. The "energy sucking" effect will no longer hold. What will occur? Most probably the atom will become a wave emitter. It will begin broadcasting. Depending upon the particular phase, it will create a certain diffraction pattern around itself. If one of the maxima of this diffraction pattern should land upon an adjacent atom, perhaps it will trigger that atom into going into "energy sucking" oscillation. In this way it appears that the first atom has emitted a photon, and the second atom has absorbed it. But in reality, everything involved fields alone, and no photons were needed.

The above thought-experiment implies that once a single photon-like event has occurred, there is a good chance that any energy dumped by the atom during stimulated emission will trigger a second event in a neighboring atom. For this reason it will *appear* that a particle of energy is bouncing from atom to atom like the silver ball in a pinball machine. It will look like a "gamma particle" is caroming around within the lattice, whacking molecules left and right. Yet the whole process will involve waves alone, with no photons needed anywhere. Weeeeeeird!

For my next trick, I will attempt to pull a quantum-entanglement instantaneous communication system out of a hat.

Nothing up my sleeves... Ooops! Naked Singularity! Wrong hat! (I take a size seven and a half.)

Other stuff...

If these AC atomic EM fields are real, what other impacts might they have on Electrodynamics? In solid matter, these fields must interact with those of neighboring atoms. Perhaps chemical bonds are based on these oscillating classical fields, rather than upon electron-sharing. Or perhaps these fields "sculpt" the distribution of electrons in the orbitals. And how do these AC atomic fields affect our understanding of "refractive index", or "conductivity"? Can energy be transferred via these fields rather than via EM waves? How do they affect our very picture of the internal structure of an atom? What if the atom is a linear electromagnetic receiver with a sort of nonlinear "energy counter" which can be bumped up to higher levels when the trapped resonant waves become intense? Can we generate strong EM fields and thereby manipulate the "tuned circuits" inside of atoms at off-resonant frequencies? If so, might we be able to alter the opacity of matter, or alter its refractive index, or affect chemical bonds directly through externally-applied EM fields? What odd things might occur if the externally-applied EM fields cause the bound AC oscillations of atoms to ROTATE with X-Y quadrature oscillation, rather than just oscillating in a line?

That's enough for now. My brain is smoking. Just *what* my brain has been smoking is the real question. ;)