About a year or so ago, I had an interesting email exchange with Dave Walton about photon size and how photon can be seen as a form of energy current extracted from an atom, much like a pulse or pulse train is generated when we discharge a capacitor …

Herein I am reproducing our exchange:

**Alex Yakovlev:**

An example of the demonstration that quantum physics is NOT the way to explain physics. Here is a story about lasers from Electronics Weekly:

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“Markus Pollnau, Professor in Photonics at the University of Surrey, said: “Since the laser was invented in 1960, the laser spectral linewidth has been treated as the stepchild in the descriptions of lasers in textbooks and university teaching worldwide, because its quantum-physical explanation has placed extraordinary challenges even for the lecturers.

“As we have explained in this study, there is a simple, easy-to-understand derivation of the laser spectral linewidth, and the underlying classical physics proves the quantum-physics attempt of explaining the laser spectral linewidth hopelessly incorrect. This result has fundamental consequences for quantum physics.””

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**Dave Walton:**

I have puzzled for some time over two simple questions:

1. How long is a photon?

2. Why is the wavelength of light so much longer than the physical size of an atom.

As far as question 1 is concerned, the authors of this paper seem to be seeing the photon as a truncated sine wave which leads to its finite spectral width when expressed as a Fourier transform. This can lead directly to a calculation of photon length.

Question 2 is a puzzle to me. As engineers we are familiar that the size of an effective antenna must be of the order of the radiated wavelength. (1/4 wave or 5/8 wave etc). But the atom is much smaller than the wavelength of emitted light. The type size of an atom is 5×10^-10 m, but the wavelength of light is of the order of 5 x 10^-7 m, which is a factor of 1000 times larger. So how does it succeed in being such an efficient radiator?

Of course, Quantum Theory does not address these questions at all. It simply states that the ‘Quantum Jump’ happens, and we cannot dissect it any further.

**Alex Yakovlev:**

I like both of your questions a lot.

Questions about real physical size dimensions are most pertinent if we think about energy current propagating in space (but how else to think?!).

Quantum Theory does not seem to address the dynamics of energy in real space, succumbing to abstract transitions between states in phase (state) space.

Reading your points regarding these questions is fascinating. Re: Q2, in particular, it begs for something like the sine wave period (i.e., wavelength) can only be 1000 longer than the atom IFF this sine wave is constructed of many (order of 1000 or so) steps, each the size of the atom, and each such step is the time of flight of the ExH current travelling between the ‘walls of the atom’. Pretty much like we have the time constant of the capacitor charge (discharge) exponential via resistor R, where the cap is a TL.

Isn’t it?

So, generally all these different wavelengths, can they be the result of the epsilon/mu (i.e. characteristic impedance of the medium) plus sizes of the unit of space that generates the light producing the sine wave in a manner similar to an L&C TL?

And photon is indeed a section of that sine wave.

I reproduced in my RS paper [cf. Energy current and computing | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (royalsocietypublishing.org)] your derivation of the time constant for the exponential charge/discharge of the stepwise processes, i.e., tau= eps*l*R/f, where l is the TL length, f is a geometric parameter linking the unit cap f=eps/c.

Perhaps, we can derive the period of the sine wave for the case of the L&C pair of TL? and this way determine the length of photon?

**Dave Walton:**

Very Interesting Alex.

It is amazing how the obvious can escape one for so long, but I had honestly never considered a transmission line model for the atom (!!).

Given the factor of 1,000 between the atomic diameter and the wavelength of the photon, this would suggest about 1000 transitions before all of the energy current escapes. This suggests a reflection coefficient of the same order, i.e., 1/1000.

The next questions would seem to be,

1. What is the energy current arrangement in the atom?

2. How exactly do these arrangements change during the process of emission?

I would be very interested to hear your thoughts on these and other issues which arise.

**Alex Yakovlev:**

Just to clarify, if we have 1000 steps for one swing of the wave (or exponential) between High and Low, should not the reflection be a complement, i.e., 999/1000.

That is basically to say that the characteristic impedance of the internals of the atom is 1000 times smaller than the ohmic impedance of the interface, right?

For comparison, Fig. 10 of Forrest’s paper

http://www.naturalphilosophy.org//pdf//abstracts/abstracts_6554.pdf

Shows quite an opposite effect where the TL is so long that the time of flight in TL is twice that of the time constant of the equivalent RC circuit. Here, despite the fact that the reflection coefficient is even negative, the step is commensurate with the time constant. So, this is probably the effect of the capacitance of the TL being relatively small.

So, we somehow, need to take into account not only the Z0 vs R ratios, but also C as a function of the length and epsilon, which in the atomic case needs to be relatively large compared to ordinary coax like TLs. For the atom, we probably talk about much higher C per size unit, i.e., very high epsilon, right?

Incidentally, can we also calculate the frequency/clock period of the TL-based LC circuit? Was it your or Mike Gibson’s derivation of the sinewave for the TL-based LC oscillator? In Ivor’s Electromagnetics 1 book, I cannot find the frequency-period parameters of the sine wave, so we could work out some likely L and C values for the atom.

Your Qs:

1. What is the energy current arrangement in the atom?

That is a good question. If we think about 3D this might be some kind of cube with the Poynting vector rotating around the nucleus, with E directed radially and H azimuthally?

2. How exactly do these arrangements change during the process of emission?

What would trigger emission? some sort of window opening so that the sine wave will be radiate out?

**Alex Yakovlev, continued:**

Just played a bit with numbers.

Suppose we play with a cap model of the atom, and we’d like to find the length unit C, bearing in mind that the exponential’s time constant tau should be 1000 that of the step.

The key equation is

RC*l = 1000*l/c

R is the resistance of discharge

C is unit length cap

l is length

c is speed of light in the medium, let’s say 2*10^8 m/s

eliminating l, we have

RC=1000/c,

suppose R=1000Ohm.

We have C=1/c=5nF/m

Does it sound reasonable?

Suppose we use the parallel plate cap model:

C=eps*(w/a), where w is width and a is distance between the plates.

What should they be?

Suppose the ratio between w and a, w/a is 5000.

This means that our eps then must be 10^(-12), does it sound realistic?

In vacuo, I think eps0 is about that order, 8.85*10^(-12).

**Dave Walton:**

Yes, the numbers do seem reasonable, but would you agree that the real challenge is to understand (or at least model) how the energy current distribution changes when a photon is emitted. This should ultimately lead to the undemanding of the probability distribution in the orbitals.

This is tough.

**Alex Yakovlev:**

Dave,

This is puzzling.

Assuming that the atom is an LC loop with distributed parameters and a normally closed door, then it emits a photon in the form of an exponential/sine wave section. What then happens? My knowledge of atomic physics is rusty and weak. But presumably the aperture and interval of door opening depends on some external factors, right?

It’s a bit like we control the switch (externally) for a TL when the energy current comes out during the discharge process. Can we extract energy from Capacitive or LC-ive by portions – sections of exponential or chunks of sine wave?

I am pretty sure there should be a deterministic model – or at least one based on some sort of histograms of frequencies of spending time in different states – rather than purely stochastic probability model.

On a slightly different yet related side:

It seems that with energy current trapped in units like atoms or TLs, we have to deal with the two levels of dynamics:

1) higher frequency one – which is concerned with the vacillating TEM inside the atom or TL – basically where the step or period is determined by the eps and mu parameters and the geometry of the atom/TL

2) lower frequency one – which is concerned with some macro-elements – like resistors and switches that are controlled outside – these are parameters like time constants of charge/discharge exponentials or periods of sine waves.

Interestingly, that (1) is about the level of 100s of THz – that close to infrared and higher frequency light – people seem to know how to sense it at the level of photonic materials

(2) is the modern analogue electronics – with lumped LC loop antennas – somewhere up to 100 GHz.

What’s between is some sort of dead zone – a gap (between materials level and circuits level), where not much can be done.

This is my own perception, maybe I am wrong. I wonder what you think about it.