Geoff Harries’s Web site


The Phoney Photon

The reader of this site

This site is intended for readers with a good general physics background. It shows how the three effects (PE, CE and PP), can be explained in terms of waves, using “classical’ wave physics. I use concepts (radio antenna theory, information/noise theory, feedback theory), well-known to electronic engineers but perhaps not so well-known to some physicists. I include a short Tutorial.

1. Introductory notes

I use Microsoft Word. Parts of this site should appear in green or red.

Green is used to indicate a reference or some generally accepted data.

Red is an original and possibly controversial conclusion.

Black is normal linking text.

As usual, links are blue and underlined.

2. General information

Name of author - Geoffrey William Harries

Size of this file – approx. 300KB.

E-mail -

Work phone - (089) 691-22-88


Date written – May 3 2007

3. Abbreviations used in this site

CE - the Compton effect

Emr - electro-magnetic radiation

PE - the photoelectric effect

PP - pair production

PMT - the photomultiplier tube

QM - quantum mechanics

4. Site contents


The wave particle duality of light

Motivation for this site

Summary science _today

My solution to wave particle duality>

Results of displaying this site

The message behind this site

Logical track of this site

What I did

Miscellaneous experiments and concepts

The photoelectric effect

the Compton effect

Pair production

The blackbody spectrum

Interference experiments

Redefinition of Plancks constant

Abbreviated tutorial

The Bremsstrahlung effect


End of the site


A strange Effect was discovered about 100 years ago. Light, formerly thought to be a wave, was apparently behaving like a particle in what became known as the Photoelectric Effect (PE). Science tried to explain it in terms of contemporary knowledge (“classical physics”) but without success.

Einstein, using a previously discovered relation between the energy of light and its frequency, (Planck’s Constant), invented a particle whose properties corresponded to those needed. He called it the “Photon” and was awarded a Nobel prize.

The wave-particle duality of light

Since then two more effects have been discovered which science can only explain by light considered as a stream of particles (“photons”). These are the Compton effect (CE) and “pair production” (PP).

In spite of the wildly different properties of waves and particles, science has been obliged to consider that light can manifest itself as a wave or a stream of particles. This is called the “wave-particle duality” of light and has caused untold damage to science and the scientific method.

The purpose of this Site is to resolve the wave-particle duality paradox of light.

Light cannot be a wave AND a stream of particles. I must either explain all the wave properties with it as a particle OR explain all the particle properties with it as a wave.

Motivation for this site

My CV shows I am an electronic engineer. I have always felt that our brains had evolved to enable us to cope with anything we might meet in the Universe. My view is that of Rutherford who said “No physics can be good unless it can be explained to a barmaid.”

But Quantum Physics, with its complex maths and strange philosophical concepts (coherence, decoherence, Copenhagen Interpretation, delayed choice, Schrödinger’s cat, guiding waves, collapsing wave functions, Bell’s Inequality, EPR, etc. ) seemed to be an exception - a subject obviously way out of my intellectual range. Confirmed by Prof. Feynman’s notorious quotation:“The theory of quantum electrodynamics describes Nature as absurd from the point of view of common sense. And it agrees fully with experiments. So I hope you can accept Nature as she is - absurd.” Ref_6

Then I bought a book “Quantum Mechanics, Illusion or Reality?” by Alistair Rae, published by Cambridge University Press in 1998, which after the usual descriptions of mysterious phenomena ends: “One thing that should be clear is that there is wide scope for us all to have opinions and there is a disappointing lack of practicable experimental tests to confirm or disprove our ideas,” Ah! Alistair Rae is a Professor of Physics at Birmingham University and if he has doubts … So I decided to do some experiments.

Summary - science today

In 1905 Einstein invented a particle – the “photon”- to partly explain the recently discovered photoelectric effect and was awarded the Nobel Prize for it. The accepting of this invention created a discontinuity in the smoothly advancing progress of science, which even today cannot be bridged without the use of yet more mystical concepts such as “wave-particle duality”. It also gave a bad example to following scientists, who instead of grinding through what Schrödinger called the “intricacies of classical physics” when a new phenomenon is encountered, are routinely tempted to invent new concepts.

Many big brains who should be occupied in removing the need for the “photon” are instead trying to exploit its supposedly magic properties. The present condition of science can be graphically illustrated in the following picture:



On the left is the solid interlocking, often tested and checked Classical science, firmly bedded in the work of the many pioneers. Shakily leaning against it is a rococo faery castle with elaborate turrets and battlements. At its base is marked the names of its constructors and on its ornate façade is inscribed the names of some of the magic concepts they have invented. 

Note that this castle is supported on only three matchsticks! Three experiments! One is called the Photoelectric Effect (PE): the other the Compton Effect (CE) and the last Pair Production. If it were possible to explain these three experiments in terms of Classical Physics, the whole baroque structure would crumble. It is the purpose of this site to cut through these three matchsticks.

My solution to the wave-particle duality paradox

I have found a solution. It is essentially an up-to-date “classical” explanation of that first proposed by Bohr, Kramers and Slater in their paper (around 1925). They said, “Light of all wavelengths behaves as a wave process (interference) with pure propagation, but behaves as particles (light quanta, photo-effect, Compton effect) on conversion into other types of energy”… “Light interacts with matter on a probability basis (my italics).”

In other words, light behaves like an expanding unquantized wave when it travels through space. But it reacts statistically with matter, which is quantized. The greater the light’s intensity the more probably it will react. To detect light (or emr generally) we can only use atoms which are digital measuring instruments with quantum resolution, and so we mistakenly think the emr is arriving in quantum sized steps. (This is like measuring a DC voltage with a digital voltmeter having millivolt resolution and thinking the DC voltage is quantized into millivolt steps.)


Against this solution

Walther Bothe performed a Nobel prize-winning experiment (based on the Compton Effect) purporting to show this “ingenious way out of the wave-particle problem was a blind-alley.” Ref_11 Later in this site I show that Bothes conclusion was wrong. Bohr, Kramers and Slater  were right.

Results of displaying this site

I have shown my results to many scientists but there has been almost no response. Most physicists are committed to wave-particle duality, they have had to swallow it as a sort of Rite of Passage when they were undergraduates. Some resist my solution because they have written books or papers on the subject, others because they think they can use the magic properties of “photons” to produce fast parallel computers or transmit data at faster than the speed of light. Others are less concerned about the classical purity of science and say merely “the concept works”. Still others disbelieve that so many famous scientists from Einstein on could be proved wrong by a simple electronic engineer.

The message behind this Site

The message of this Site is that the behaviour of light can everywhere be explained as a wave and so if you ever see an article or paper in which the word “photon” appears, put that paper aside.

Logical track of this site

1. First presented is The_photoelectric_effect the interaction of emr (light) with electrons. It is conceptually easy to understand and immediately reveals Planck’s constant. I give Einstein’s explanation, using his invented particle, the “photon”, then follow it with a wave explanation.

2. Next is the_Compton_effect - also an interaction between emr (X-rays) and electrons. Very surprisingly, the wave solution of the photoelectric effect leads immediately to a simple, satisfying and obvious wave explanation of the Compton effect, leaving it otherwise untouched as a proof of Relativity. Again I first give Compton’s explanation using “photons”, and follow it with a wave explanation.


3. Third is “Pair_production” – an extension of the Compton Effect, where very short wavelength X-rays, gamma rays, interact with matter to produce electrons and a new particle of antimatter called the “Positron”.


4. Last covered is The_blackbody_spectrum, which is an example of the more general interaction of emr and matter. It was the first effect to be studied and introduced the concept of “quantum” and Planck’s Constant. It is the most difficult to understand and so will be studied last.


For an overall picture of how emr reacts with matter, see the Absorption_coefficient_of_lead

What I did

The keystone of the whole baroque structure seemed to be the “photon” and so I focused all my efforts down to removing its necessity. [After all, the purpose of science is surely to reduce the number of axioms, not increase them.]


1. I did many ingenious experiments (interference, refraction, non-linearity) with laser light of all intensities using photographic films then a photomultiplier tube as detector, and they all “supported the hypothesis” that light was a wave. See Interference_experiments.


2. I made a calculation showing “photons”, if they existed, were far too far apart even in a strong laser beam to ever interact. See Calculation_of_photon_density I also show that there is normally no “photon bunching”. So there are no “photons”.


3. If I assumed that the free electrons in a sodium crystal behaved like the free electrons in the carbon load of an RF dipole in the presence of emr, I could explain the photoelectric effect using conventional RF antenna theory. And more completely than Einstein. See The_photoelectric_effect


4. The Compton Effect, using X-rays and first seen as a much more difficult target, fell surprisingly easily. See the_Compton_effect.


5. “pair production” is a strange phenomenon showing how very high energy emr reacts with matter. Its conventional explanation requires the emr to be quantized into “photons” and also requires the invention of a new particle, the Positron. My classical explanation removes at least the need for “photons”. 


6. Once the keystone of the “photon” was dislodged, the whole  structure of Quantum Mechanics came tumbling down and an enormous number of scientific papers and  books are revealed as pseudo.

The photoelectric effect


In studying the photoelectric effect, one way is to shine light of varying frequencies and intensities onto a thin metallic sodium “photocathode” film in a vacuum. Nearby is a metal plate - the “anode”. The anode is connected to the photocathode via a current measuring instrument and its voltage, with respect to the photocathode, can be varied. In this way the number of electrons (the anode current) can be measured. By putting different negative voltages (the “stopping voltage”) on it, the energy of the electrons can be conveniently measured. The higher the voltage needed to stop an electron the higher its energy. Energy here is measured in Electron_volts or eV.

Electron volts (eV)

            An electron volt is the energy gained by a particle of charge e when it falls through a potential difference of one volt, where e is the charge on an electron.

Energy in joules can be converted to eV by dividing by 1.6 x 10 –19  (and vice versa). [Energy = capacity to do work.]

Background to the photoelectric effect – the sodium target

The sodium crystal photocathode acts as an “emr energy to kinetic electron energy” converter. 

The first reason for using a sodium crystal photocathode is that it is a way of concentrating many electrons into a small volume. Their mutual repulsion is nullified by the positively charged nuclei. 

The second is because the distant “free” looping electrons can be easily influenced and detached by incident emr (light). The sodium crystal behaves like an “opened out” sodium atom.

Thirdly, the sodium crystal photocathode is “flat-tuned” and so can respond to emr of any frequency within its range (unlike the sodium atom which only has definite resonant frequencies.) See Initial_conditions_in_the_photocathode

All  these characteristics facilitate the demonstration of the  photoelectric effect.



Fig. 2 shows how the energy of the photoelectrons (in eV) varies with the frequency of the incident emr (light) in Hz for sodium.

Note that the amplitude of the incident light does not appear in this graph.


Work function

Even at room temperature some electrons spring from the surface of the crystal. They do not go far because they leave the crystal positively charged and this pulls them back. There is therefore a negatively charged cloud of electrons surrounding the crystal.

  “There must be a minimum energy required by an electron in order to escape from a metal surface, or else electrons would pour out even in the absence of light. The energy characteristic of a particular surface is called its work function.” Ref_1 Pg.45.

Fig. 2 has been extrapolated backwards to show how it intercepts the y-axis at the work function.

Continuation of the description of the photoelectric effect

It can be seen that if the photocathode is sodium, no electrons are emitted until the light frequency is around 5.6 x 1014 Hz, which is yellow light. This corresponds to a work function of  -2.3 eV which must be overcome before any electrons at all can leave the photocathode.

Then the energy of the emitted electron increases linearly with frequency and the slope, the constant of proportionality, is h or  6.62 x 10-34 joules per sec per Hz  or 4.13 x 10-15 eV per Hz if the energy is measured in eV.

This Constant of Nature, h, was discovered previously by Max Planck in his study of  The_blackbody_spectrum and is called Planck’s Constant. 

The graph in Fig. 2 shows overall how emr reacts with electrons. The constant of proportionality is h/ce, ie. :


Planck’s constant h         =     6.62 x 10 -34  =   4.13 x 10 –15 eV/Hz  

Charge on an electron              1.6 x 10 -19


Two other curves are required to describe the photoelectric effect. Fig. 4 shows that photoelectric current is proportional to light intensity for all retarding voltages. The cut-off or “extinction voltage” V0 is the same for all intensities of light of a given frequency


             One of the features that particularly puzzled its discoverers is that the energy distribution in the emitted electrons (called photoelectrons) is independent of the intensity of the light. A strong light beam yields more photoelectrons than a weak one of the same frequency, but the average electron energy is the same. These observations cannot be understood from the electromagnetic theory of  light. Equally odd from the point of view of the wave theory is the fact that the photo-electronic energy depends on the frequency of the light employed. At frequencies below a certain critical frequency, characteristic of each particular metal, no electrons whatever are emitted. Above this threshold frequency the photoelectrons have a range of energies from 0 to a certain maximum value, and this maximum energy increases linearly with increasing frequency. Thus a faint blue light produces electrons with more energy than those produced by a bright red light, although the latter yields a greater number of them”. Ref_1 pg.42.


Fig .3 shows that the “extinction voltage” V0 depends upon the frequency of the light employed.



Einstein’s explanation of the photoelectric effect

Einstein writes  - “It is clear that the relationship between Kmax (maximum photoelectron energy) and the frequency f involves a proportionality which we can express in an empirical formula:

            Kmax = h(f - fo) = hf - hfo

            where fo is the threshold frequency below which no photoemission occurs and h is a constant. Significantly, the value of h, 6.626 x 10-34 J.sec is always the same, although fo varies with the particular metal being illuminated.

            Einstein proposed that light not only is emitted a quantum at a time, but it also propagates as individual quanta, (my italics) a more drastic break with classical physics. In terms of this hypothesis the photoelectric effect can be readily explained. The empirical formula may be rewritten:

     hf = Kmax + hfo

    Where hf = energy content of each quantum of the incident light

 Kmax = maximum photoelectron energy

    hfo = minimum energy needed to dislodge an electron from the metal surface being illuminated. “Ref_1Pg. 44.

Summary of Einstein’s explanation

In words, the incoming light must be considered as particles, as “photons” of energy hf. A “photon” strikes a free electron in the photocathode and  transfers all its energy to it. The “photon” then “drops out of existence”.

The kinetically energized free electron now has to fight its way out of the photocathode, losing a random amount of energy as it bounces off the unenergized free electrons and then by the braking effect of the Work Function barrier at the photocathode surface. It exits the photocathode and is renamed a “photoelectron”. The energy of these photoelectrons can be easily measured  by the voltage required to stop them and is found to be linearly proportional to the frequency of the light producing them. Einstein received the Nobel Prize for this interpretation.

The photoelectric effect explained with wave light

My explanation is much more complicated than Einstein’s   but explains the effect more completely, and of course needs no “photons.” And as Occam says ‘you should always look for a natural explanation, however complicated, before you start inventing new phenomena.’ 

If you are not familiar with the transmission and reception of low frequency (radio frequency) emr, I suggest you click here for a short  Abbreviated_tutorial on concepts leading up to  Antenna_theory.

Initial conditions in the photocathode

The standard textbook description of the metallic sodium crystal as positive ions floating in an “electron gas” is simplistic. Sodium vapour has sharp resonant peaks over the visible light range, but if it is slowly compressed in a glass tube these peaks gradually coalesce until they disappear and the metallic sodium film, now found to be formed on the inside of the tube, is aperiodic. The two far-out electrons in each sodium atom are now shared between all the atoms, linking the atoms into a sodium crystal.

These “free electrons” in the sodium film crystal must have exceedingly complicated looping orbits, winding in and out of the positive ions in three dimensions at widely varying speeds, as the radii of curvature of their orbits change and they generate and react to complex internal emr and magnetic fields. But as there are no emr or magnetic fields detectable outside the crystal, these internal “restraining fields” must cancel. Superimposed on these free electron orbits is a small thermal noise jitter. This noise jitter, being random, sometimes unbalances the restraining field and must be the reason for the occasional ejection of “thermal” electrons.

Ei = Er + En

Where Ei = internal field

           Er = self canceling restraining field

           En = thermal noise field

Widely varying electron speeds correspond to a wide frequency range, which must be why the sodium crystal has no tuned peaks of absorption or emission.

Note that the thermal noise level En in the photocathode (like in a resistor) will increase with temperature, kB, where k = absolute temperature and B = Boltzmann’s constant.

I analyze the photoelectric effect under four Conditions:

Condition 1

See Fig. 1. No illumination. Anode at the same voltage as the photocathode. Room temperature. There is a very small current flowing between photocathode and anode. This is due to electrons which have gained enough energy through thermal noise orbit jitter, (>2.3eV = 5.6 x 1014Hz = threshold frequency for sodium = yellow light) to have escaped the photocathode through the 2.3V “work function” barrier surrounding the sodium crystal. They are called “thermal electrons.”

Condition 2

Very faint illumination by 7 x 1014Hz emr, wavelength 428nm (green, and so over the threshold frequency for sodium.)

Operation. Fig. 2  above, showing the relation between the frequency of the incoming emr (green light) and the energy of the photoelectrons emitted, makes no mention of the amplitude of that emr. But it cannot be zero. Incoming wave emr must have a minimum amplitude in order to “significantly” influence the moving electrons. In telecommunications parlance, we would say the signal to noise ratio (SNR) must be >1. The “noise” here is the internal field Ei, already existing in the photocathode, which is the vector sum of the “restraining field” and random thermal noise.

Consider a small circle on the photocathode with a radius of 107nm (lambda/4 of green light). In the middle of this circle an electron, which by chance has a temporary component of motion parallel to the voltage vector of the incident green emr, behaves like a loaded dipole. Like an RF dipole, it snaps into series  resonance with the incident emr and absorbs energy from it over the whole area of the circle, (containing  approx. 360 000 atoms if the sodium photocathode is 1 atom thick), thereby halving its field strength, as described under Antenna_theory, and thereby inhibiting (or more strictly, “reducing the probability of”) any other electrons in the circle from resonating, as the incoming emr voltage vector amplitude applied to them is now smaller than Ei. (Remember the incident emr amplitude has been adjusted to be just over Ei,  the internal field.)

Under the most favorable conditions, this electron exits the photocathode with a velocity which requires 0.59V to stop it. See Fig. 2 above. Its exiting energy is therefore 0.59eV. As it lost 2.3eV on passing the work-function barrier, it must have abstracted 0.59 + 2.3 eV = 2.89eV from the incident emr. This amount of kinetic energy, which we call a “quantum”, has been absorbed from the emr and resonance is destroyed. 

But from Antenna Theory  a further quantum of energy has been reradiated or scattered from the resonating electron, before resonance was destroyed. [This ties up with the fact that the photocathode has been measured as reflecting 50% of the incident light.]  

In sum, a one quantum “bite” of energy of  2.89eV has been taken out of the emr wavefront leaving a localized “hole” or “shadow” of radius 107nm. No further electrons can be detached in the + lambda/4 circle for the moment, as the green emr field there is now too weak  (SNR < 1).

            The “hole” in the field will now be “filled” by the oncoming green emr diffusing into it. The time for it to  “refill” will be inversely proportional to the amplitude of the oncoming emr. As the hole “fills up”, the emr will again reach the minimum amplitude necessary to overcome the internal field, Ei, (SNR > 1) couple again with an electron somewhere in the photocathode and produce another photoelectron. (This is analogous to a bucketful of water suddenly scooped out of a small stream, which leaves a hole in the stream and temporarily reduces water flow. The time taken for the hole to fill up and the water flow to resume its former rate depends on the rate of flow, the “amplitude”, of the stream.)

Call the following sequence an Event  -

 “Incoming emr finds a resonating electron dipole somewhere in the photocathode and transfers two quanta of energy to it. One quantum of energy is immediately scattered from the dipole as emr. The other quantum of energy kinetically accelerates the dipole load, the electron, destroying the dipole and so destroying resonance. This leaves a one-quantum energy hole in the wavefront. The accelerated electron leaves the photocathode, its actual energy on exiting depending on its random passage through the photocathode crystal, minus the Work Function. Pause as the oncoming emr refills the hole. Hole filled. End of Event.” 

One Event = a one quantum “bite” taken from the wavefront. In the presence of emr, Events are occurring continuously all over the photocathode.

Condition 3

As for Condition 2 but with greatly increased emr amplitude.

Operation. As for Condition 2, but now slowly increase the amplitude of the incoming emr. “Events” will occur as before, ejecting photoelectrons and producing energy holes in the wavefront, but the greater amplitude oncoming emr will fill these holes quicker. There will therefore be a shorter pause before the emr strength at the photocathode rises to the minimum value (SNR=1) necessary to (probably) eject another electron. The pause between Events is inversely proportional to emr amplitude. There will be more Events per second,  and so anode current is also proportional to emr amplitude, as required.


Automatic gain control

It can be seen that the average amplitude of the emr applied to the temporary electron dipoles at any one frequency is kept constant at just over Ei, the internal field strength, independently of the incoming emr amplitude, by a sort of pulse-width modulated feedback loop. Standard one-quantum energy “bites” reduce and maintain the emr amplitude at a SNR of just over 1, just over the internal field level, Ei. The greater the incoming emr amplitude, the greater the number of “bites” per second. The higher the incoming emr frequency the larger the “bites.” The energy of  ejected photoelectrons therefore only varies with the incoming emr frequency and is independent of the emr amplitude, as required.


Following the classical theory of free electron gas, the electrons in a metal are free particles influenced by the incident emr:

                        F = -ce E = -ce E cos t

  where  F  = force on the electron

       * =  2f where f is emr frequency

            -ce = charge on an electron    

             E  = electrical field strength in volts per meter   


The feedback loop standardizes the effective incoming emr field strength in the photocathode by width modulation to just over its internal field, Ei,  adjusting it to have a signal to noise ratio of 1.

     F = -ce E  cos t  where  E  = 1    

                 Ei                           Ei     

And so the force on the electron is only proportional to f.

The energy given to the electron in eV, as shown in Fig. 2,  is  hf


          where f = emr frequency                           

                    h = Planck’s (empirical) Constant, 6.626  x 10-34 J  per sec.  

                     ce = charge on the electron

Condition 4

Incoming emr at any amplitude and at any frequency below threshold.

Operation. As in Condition 3, 1 quantum “bites” are abstracted from the incident emr as   electrons are ejected out of their complex orbits. But the peak kinetic energy of these electrons is too small (<2.3eV) for them to penetrate the work function barrier so they stay in the photocathode. The ejection  of   these electrons nevertheless “loads” (takes bites out of) the emr wavefront, limiting its amplitude in the photocathode to just above Ei, using the feedback mechanism described for conditions 2 and 3 above. All the ejected electrons can do now is to heat the photocathode. At very high amplitude incident emr their energies finally start to cumulate as the “holes” begin to overlap, producing thermal electrons at >2.3eV.

Comparison of the alternative wave explanation with the Einsteinian

The Einsteinian explanation of the photoelectric effect requires the invention of a “photon” which deterministically knocks out one photoelectron from the sodium photocathode with energy proportional to its frequency. An Einsteinian Event is where a  “photon” gives up all its energy to a photoelectron and then “drops out of existence”. The energized photoelectron may or may not pass the work function barrier. Increased emr amplitude means increasing the number of “photons” per second and so the number of Events per second.

The alternative wave explanation needs no “photon”. It uses classical radio frequency antenna concepts throughout. By intercepting two  quanta of energy   2(h/ce x 7 x 1014 )eV over an area equivalent (with green light and a sodium photocathode one atom thick) to 360 000 atoms, I say the incoming emr  “increases the probability” a photoelectron will be ejected from this relatively large area with an energy equal to one quantum or h/ce x 7 x 1014  eV. The other quantum of energy is reradiated or scattered as 7 x 1014 Hz green emr. As with the Einsteinian particle explanation, the electron in the wave alternative may or may not penetrate the photocathode and the work function barrier. Increasing emr amplitude increases the number of Events by reducing the recovery time of the photocathode.

Experimental support for the wave explanation

1 - Reflection coefficient of the photocathode

If the free electrons in the photocathode behave like the free electrons in the load of a radio frequency dipole, 50% of the incident energy will be scattered. See Abbreviated_tutorial and click on Antenna_theory  So half the incident light on a PMT cathode should be wastefully scattered. Indeed the published Quantum Efficiency of Hammamatsu photocathodes is never greater than about 30%. Further proof is given by the fact that the sensitivity of a reflection mode photomultiplier tube can be almost doubled if the photocathode is covered with an anti-reflective coating. I quote from Andor Technology (“Europhotonics” June 2005, pg. 42) where they describe one of their digital cameras …“The sensors respond to a broad range of wavelengths from the UV to the near-IR, and the customer selects the proper antireflective coating (my italics) to maximize the quantum efficiency (QE) in the appropriate waveband. The BV model’s coating produces peak QE of 95% at about 550nm and the BU2’s at about 250nm”

In other words, the 50% of the incident emr normally scattered away is reflected back onto the photocathode. Anti-reflective coatings support the concept of  light as a wave.

For an analogy in the world of radio frequency, think of the “director” rod mounted a quarter wavelength in front of the receiving dipole in a Yagi antenna.


But some PMTs are the transmission type, having a semi-transparent photocathode. Such a one is the Hammamatsu R464, which I use. This type of photocathode should also behave like a radio antenna, scattering 50% of the incident light. But because of its construction, 25% should be scattered backwards (reflected) and 25% forewords. I can only measure the part scattered or reflected backwards and I find it to be indeed 25%, as expected. See The_reflection_coefft_of_a_PMT  The other 25% presumably passes through the semi-transparent photocathode without reacting with any free electrons. (I can visibly confirm that light does pass through the photocathode, but I have not been able to confirm its relative intensity as 25%.)


The Einsteinian explanation gives no reason why  only 50% of the  incoming “photons” react with the free electrons. In the Einsteinian explanation all the incident “photons” “drop out of existence” so the photocathode should appear black.

2 - Temperature dependence of the photoelectric effect

“The validity of the Einstein relationship was examined by many investigators and found to be correct but not complete. In particular, it failed to account for the fact that the emitted electron's energy is influenced by the temperature of the solid.” Ref_9

            The alternative wave explanation relates this to the temperature dependence of the Automatic Gain Control feedback loop. As described above, this stabilizes the amplitude of the emr actually applied to the temporary electron dipoles, keeping it constant at just over the internal field, Ei, (SNR = 1). But a component of Ei is thermal noise En, and as in a resistor the effective thermal noise (En)2 increases with the ambient absolute temperature. (En)2 = 4kTR(f2 – f1) where k = Boltzmann’s constant, T = absolute temperature, R = resistance component of impedance and  f = frequency.

3 – The Einsteinian invention of a “designer” particle, whose properties complement the photoelectric effect, leads to circular argument: -

The photoelectric effect is explained by assuming light is  in "photon" particles.

The only way to detect a "photon" particle is by the photoelectric effect.


An alternative wave explanation for the photoelectric effect based on RF antenna theory has shown that the standard Einsteinian explanation, invoking the invention of  “photons”, is an unnecessary construct, which furthermore fails to fully explain this phenomenon.

The Compton Effect

Now that the Photoelectric Effect has been explained in terms of classical physics, thereby removing its need for the concept of  “photon”, I turn to what is known as the Compton Effect (CE), after the name of the American physicist who studied it in 1926. I will describe this very important experiment under:


History of the CE

The tools Compton used to explain it

Compton’s Nobel Prize winning explanation of the CE.

The argument between Bohr, Kramers, Slater and Bothe

The tools I must find if I wish a classical explanation

A_classical_explanation_of_the_CE (really a restatement of  that by Bohr, Kramers and Slater)


In 1926 it had been known for some time that if a beam of X-rays (the Primary Beam or PB) were directed at a carbon target, it was scattered in a shell in all directions with no change in wavelength, as expected. But there was also another concentric shell of scattered radiation of a longer wavelength than the PB, its wavelength depending on the angle with which is exited the target. See the “Scattering of em radiation” diagram below.



            It was Compton’s genius in finding a mathematical relationship showing that  the wavelength change or shift equals h/me c (1 – cos ), where h is Planck’s constant, me the mass of an electron and c the velocity of light.

The shift at 900 (where 1-cos  = 1) is called the Compton Shift for an electron and is 0.002426nm. Being derived from constants it is therefore a constant itself, independent of the PB wavelength (and amplitude.)

Compton explained this strange phenomenon using the concept of  “photon” invented by Einstein for the PE, 20 years previously. It became known as the Compton Effect and he received the Nobel Prize for it. Because no one over the last 85 years has found a satisfactory “wave” explanation for this effect, it is now regarded as the strongest proof for the existence of the “photon” and its denial is very important to my thesis.

Frequency changing (an aside)

The Compton Effect is remarkable even from a “concept” point of view. Emr (the PB) enters the crystal and comes out at a lower frequency, the actual frequency depending on the angle of emission and the PB frequency.

Its explanation is not a trivial problem and the solution is quite subtle, requiring the PB energy to be quantized into pulses of emr before it passes through the target. This means there are “spaces” between the pulses for them to be “stretched into”. (Continuous emr waves cannot be stretched [reduced in frequency or increased in wavelength]  except by Doppler shifting or using a different medium having a lower propagation speed, neither of which is applicable here.) The reduced frequency (“stretched”) emr pulses are produced randomly and combine statistically to produce an output with a lower average frequency than the PB. This also explains the observed wide bandwidth of the scattered radiation.

The mathematical relation connecting the PB frequency, the Compton down-shifted frequency and its angle of emission is quite complex and by an interesting but unimportant mathematical artifact is much simpler if the frequencies are expressed in wavelengths and the angle of emission is at 90o. Hence the term “Compton Shift”.         [Note that the frequency f of emr is its fundamental parameter but as it is at the moment impossible to measure it directly at such high frequencies, wavelength, lambda, is substituted. Wavelength can be measured with a grating and frequency is derived using f = c/lambda, where c = velocity of light].

The Tools used by Compton

Before I  reveal Compton’s explanation of the CE, I review for you the “tools”, the concepts, he used. The most controversial is that of the “photon”.

If the PB of frequency f is considered to be a shower of particles called “photons”:


- this fulfils the quantization requirement allowing “stretching”. See Frequency_changing above.


- the energy associated with each “photon” is hf joules, where h is Planck’s

   Constant and f is its frequency.


- As the moving “photon” has energy, Relativity says it behaves like a small mass and can bounce off other particles, such as the free electrons. As with billiards, momentum and angle are conserved.


- If the momentum of a “photon” is for any reason reduced, eg. by bouncing off and thereby sharing its momentum with another particle, its energy and so its implied frequency is also reduced.


- “Photons” of frequency f bounce off a Bragg grating just as if they were wave light of frequency f.

Compton’s Nobel Prize-winning explanation of the CE

The Primary Beam, PB,  “can be considered” as a series of particles, “photons”, which strike and bounce off the carbon target free-electrons at random angles. As an example, see below how the electron shoots off top-right and is renamed the “recoil electron”. The “photon”, having given up some of its energy, exits bottom right. Because it has given up energy it now “can be considered” as having a lower frequency.

And here is Compton’s maths:

I quote - “Quantum theory tells us that the energy of a photon is hf and the theory of Relativity requires that we associate an energy mc2 with a mass m. Linking these two concepts, Compton suggested that we may put hf = mc2, which implies that the photon has momentum mc=hf/c. The interaction between the photon and  the electron may now be treated as a simple collision problem in mechanics. The initial momentum vector hf/c (Fig. 6.15) of the X-rays is equal to the two vectors mf and hf’/c where hf ‘/c is the momentum associated with the scattered X-rays  and mf is the momentum of recoil of the electron. The vector triangle gives the equation:


            m2f2c2 = (hf ’)2 + (hf)2 – 2h2ff’cos  -------------------(6.1)


The conservation of energy requires that:

            hf + moc2 = hf’+ mc2  --------------------------------------(6.2)

where mo is the rest mass of the electron.


Relativity gives the relation:

            m2(1- f2/c2) = mo2 -------------------------------------------(6.3)


From equations (6.1) and (6.3) we get:

            m2c4 – mo2c4 = (hf)2 + (hf’)2 – 2h2ff’cos                       

Substituting for m2c4 from equation (6.2) yields                           

[h(f – f’) + moc2]2 – mo2c4 = (hf)2 + (hf’)2 – 2h2ff’cos


On simplification this gives

            moc2(f-f’) = hff’(1-cos ) which becomes

      *’ –  = (1 – cos ) h/moc

and inserting the numerical values we get

            *’ –  =  2.4pm when   = 90o


which is independent of wavelength and becomes increasingly important at shorter wavelengths.” Ref_3 Pg. 88.


            Alternatively, the frequency version of Compton’s equation is:

               1/f’ – 1/f = (1-cos ) h/mo2


The CE remains the strongest  empirical proof for the existence of a “photon” and Relativity. 

Complaints from the scientific community

            One of the first came in a paper written by Bohr, Kramers and Slater in 1925. They proposed  that “light of all wavelengths behaves as a wave process (interference) with pure propagation, but behaves as particles (light quanta, photo-effect, Compton effect) on conversion into other types of energy”. They go on to propose that “light interacts with matter on a probability basis.” In other words, light normally behaves like a wave when it goes through space but like quantized particles when it interacts with quantized matter. [This is partly my thesis for the PE – the stronger the light the greater the probability that photoelectrons are ejected from the photocathode.]

            Walter Bothe thought that this could be checked experimentally and decided to do it using the CE. His “Question to Nature” was - “Is it exactly a scatter-quantum and a recoil electron that are simultaneously emitted in the elementary process, or is there merely a statistical relationship between the two?” He used two parallel detectors, one to detect the frequency down-shifted X-ray pulses and another to detect the recoil electrons, and measured the coincidence of the pulse outputs of these two detectors. Bothe’s conclusion was that “systematic coincidences do indeed occur – a scatter quantum (he meant “photon”) and a recoil electron are generated simultaneously. The strict validity of the law of conservation of energy even in the elementary process had been demonstrated and so the ingenious way out of the wave-particle problem (my italics) discussed by Bohr, Kramers and Slater was shown to be a blind-alley.” Ref_11 He received a Nobel prize for this experiment.

This important experiment has since been repeated by MIT using more modern equipment, and gives the same result.         Ref_12.

And so the “photon” concept is apparently required to explain the Compton Effect.

A classical explanation of the Compton Effect

The clever part of my wave explanation of the Compton Effect is that I very slightly modify Compton’s method and maths but use a classical particle substituted for the imaginary “photon”. If I want to use Compton’s maths, this classical substitute particle must obviously have almost the same properties as the “photon” in that… 


It must first be a particle.


Like a “photon”, it is produced from the incoming PB emr and its energy depends on the frequency of this emr. (energy = hf.)


Like “photons”, the number of these particles arriving per second depends on the intensity of the incoming emr.


Like  “photons”, it must be possible to somehow convert these particles back into wave emr of the same frequency as that used to produce them.


Like a “photon”, its associated frequency must decrease if it loses energy/mass for any reason, (frequency = energy/h).


Like a “photon”, it must have momentum and so be able to bounce off a free electron in the carbon crystal and lose energy (and thereby drop in frequency when/if it is converted back to wave emr.)


And last but not least, it must be available in the carbon target.


I propose the photoelectron as the “classical” substitute for the “photon” in the Compton effect.


In confirmation, let us look at the properties of a photoelectron compared to the properties of the imaginary “photon”:  


            We know the energy of a photoelectron if we know the frequency of the light producing it in the photoelectric effect. Forgetting space charge, it is hf joules per Hz per sec. The photoelectron’s energy can be checked in two ways:


By measuring the voltage needed to stop it. If this is V volts, its energy is eV Electron_volts.


Alternatively the photoelectron can be suddenly decelerated. If it is completely stopped it will produce a burst of emr, a quantum of  frequency f, by The_Bremsstrahlung_effect. If it is only partially

decelerated, the frequency of the burst will be < f.


And so all the qualities of a “photon” are combined in a photoelectron.


  I repeat, the photoelectron is a particle and has energy (one quantum) corresponding to the frequency used to produce it in the PE. Relativity says it therefore has mass and  momentum which it can kinetically exchange with another particle. Any reduction in energy corresponds to a reduction of its velocity which causes it to emit emr (by the Bremsstrahlung effect) at a lower frequency than that used to produce it.

Briefly, I classically explain the CE by first dividing up (quantizing) the incoming PB by bouncing it off the free electrons in the outer layer of the carbon target, giving one quantum to each, using the PE.

Using Compton’s methodology, these now high-velocity, high kinetic energy photoelectrons kinetically strike the slow-moving free-electrons deeper in the carbon target and are deflected, sharing their energy with them, the ratio depending on their random angle of impact. On impact they release their reduced energy as wave emr by means of the Bremsstrahlung effect.

Essentially I take over Compton’s calculation, replacing the fictive “photon” which carries one quantum of energy, with a photoelectron also carrying one quantum of energy. These high energy photoelectrons are produced inside the target.

Here is my modified vector diagram, showing  an extra stage where I first use the PE to quantize the PB into photoelectrons: -


The overall principle is diagrammed below.

[Note that Bremsstrahlung is often termed the “reverse PE.” And as the Bremsstrahlung effect can be explained without the concept of “photon”,  the PE can too.]

My explanation of the Compton effect using Compton’s maths with photoelectrons

            As there is so little difference between mine and Compton’s explanations, I quote them together. In order to show where I have altered Compton’s explanation, I will use my usual colour scheme. I repeat his original words in green, mine are in red.


“Quantum theory (alt. The photoelectric effect)  tells us that the energy of a photon (alt. photoelectron) is hf and the theory of Relativity requires that we associate an energy mc2 with a mass m. Linking these two concepts, I suggest that we may put hf = mc2, which implies that the photon (alt. photoelectron) has momentum mc=hf/c. The interaction between the photon (alt. photoelectron) and  the free electron may now be treated as a simple collision problem in mechanics. The initial momentum vector hf/c (Fig. 6.15, alt. Fig. 6.16) of the X-rays is equal to the two vectors mf and hf’/c where hf ‘/c is the momentum associated with the scattered X-rays  and mf is the momentum of recoil of the electron. The vector triangle gives the equation:


            m2f2c2 = (hf ’)2 + (hf)2 – 2h2ff’cos  ----------------------(6.1)


The conservation of energy requires that:

            hf + moc2 = hf’+ mc2  --------------------------------------(6.2)

where mo is the rest mass of the free electron.


Relativity gives the relation:

            m2(1- f2/c2) = mo2 -------------------------------------------(6.3)


From equations (6.1) and (6.3) we get:

            m2c4 – mo2c4 = (hf)2 + (hf’)2 – 2h2ff’cos                       

Substituting for m2c4 from equation (6.2) yields                           

[h(f – f’) + moc2]2 – mo2c4 = (hf)2 + (hf’)2 – 2h2ff’cos


On simplification this gives

            moc2(f-f’) = hff’(1-cos ) which becomes

      *’ –  = (1 – cos ) h/moc


            and inserting the numerical values we get

            *’ –  =  2.4pm when   = 90o


which is independent of wavelength and becomes increasingly important at shorter wavelengths.” Ref_3 Pg. 88.


           Alternatively, the frequency version of Compton’s equation is:

               1/f’ – 1/f = (1-cos ) h/mo2


      And so the result is the same whether we use the concept of “photon” or photoelectron.


The CE is now seen as just The_Bremsstrahlung_effect, where the  electrons being decelerated are fast photoelectrons produced inside the carbon target, rather than separately accelerated electrons produced outside the target.

Being produced inside the carbon target must account for the greater proportion of solid hits with the relatively stationary free-electrons.

Comparison of the two explanations

The biggest difference is that my explanation requires an extra stage but uses only classical concepts.

In my explanation, 50% of the incident radiation PB is reradiated, as in the PE. This should hold for the Compton effect too but I have not yet found anything in the literature. In any case, reradiation is at the same frequency as the PB and it will only slightly increase the amplitude of the normal scattered PB.

Here is my interpretation of Bothe’s experiment:

            In my description of the PE, (see The_photoelectric_effect explanation with wave light), I say “the incoming light increases the probability that electrons are emitted from the photocathode”.

In exactly the same way, the incoming PB wave in the CE is statistically quantized by the free-electrons it first encounters in the outer layer of the carbon target. As in the PE, the energy of the photoelectrons produced is proportional to the frequency of the PB and their number per second is proportional to the intensity of the PB. But from here on in, the PB incoming energy has been quantized, and the quantum pulse of  Bremsstrahlung energy produced at each impact with a free electron must obviously be coincidental with the recoil electron. This fulfils the requirement allowing “stretching” and simultaneously explains Bothe’s result.   

So I have arrived independently at what Bothe called the “ingenious way out of the wave-particle problem” by Bohr, Kramers and Slater, but I can refute Bothe’s objection to it. And therefore their way out is not a “blind-alley”. I repeat their solution to the wave/particle duality paradox - Emr behaves like a wave when it traverses space, but like a particle when it interacts with quantized matter.

And so there is no need for the “photon” particle.


            Supporting my two-stage detection of high frequency emr is Ref_14 Pg. 307 which states “An X-ray or gamma-ray photon is uncharged and creates no direct ionization of the material through which it passes. The detection of gamma rays is therefore critically dependent on causing the gamma-ray photon to undergo an interaction that transfers all or part of the photon energy to an electron in the absorbing material. …Energy loss is therefore through ionization and excitation of atoms within the absorber material and through Bremsstrahlung emission.”


Pair production (PP)

This is the third way emr reacts with matter. The observed data is that if  gamma rays of   minimum 1.022MeV enter the target, a reaction occurs in the target and streams of two sorts of particles exit in pairs. One is an electron, the other is a new particle, identical in every way to the electron except it carries a positive charge. It is called the ”positron”. These particles can be identified in a cloud-chamber and each have 0.51 MeV which is the equivalent energy of the rest mass of an electron. Increasing the energy of the gamma rays above 1.022MeV increases the energy of the exiting pairs by the difference. Ref_5 Pg. 140.

PP occurs in parallel with the PE and CE. See the Absorption_coefficient_of_lead picture below.


The conventional explanation of PP is that the incoming Primary Beam must be considered as a stream of “photons” and each “photon” produces a “pair” in the high voltage field surrounding a proton. There is no explanation, classical or otherwise, as to how positrons are actually formed. 

I need to explain pair production with classical physics and my first objection is the use of the concept “photon”, which I hope I have shown you does not exist. I replace the fictive “photon” by short radar-like pulses of emr generated inside the atoms using the high speed photoelectrons already existing in the target, produced by the PE at the target’s surface. The photoelectrons strike the target atoms and being abruptly stopped produce the needed short radar-like pulses of emr gamma ray pulses by Bremsstrahlung. Like science, I offer no explanation of the conversion of these pulses into pairs.

The blackbody spectrum

It is a strange fact that if lots of different atoms exchange emr energy with each other, some acting as transmitters, the others as receivers, the spectrum of their communication frequencies is the same. This “blackbody” spectrum is obviously based on a Constant of Nature and Planck virtually by pure thought found two things –


1. that the atoms were communicating in short bursts of emr, now called quanta, all of different frequencies depending on the individual atoms and how their levels of excitation were changing.(“…coherent wave trains of 3 or 4ft. in length, as can be observed in an interferometer”) See



2. that the energy in each quantum was hf where f is the frequency of the burst and h is a constant of Nature, now called Planck’s constant.

As h = 6.625 x 10-34 joules s-1 the size of the quantized “bits” or “quanta”, are exceedingly small, as is to be expected with atomic energy levels.


The black body spectrum is the result of “digital communication” between atoms. Digital communication is used by Nature for the same reasons we do – to increase the signal to noise ratio and to ensure stability.  Witness how atoms take part in the most complex electron-swapping chemical reactions and yet emerge as atoms identical to those that entered.

            Being emr and usually emitted from nearby atoms, quanta can join up and so we normally see them as apparently continuous emr. But like the familiar radar pulses, quanta spread out (follow the inverse square law), getting weaker and weaker until they slide into the noise level and can no longer be detected by any receiving atom. (If light were in  particles, “photons”, they would  presumably go on for ever.) It is important to realize that a quantum is a unit of energy and not a particle (“photon”). Einstein and Compton made this mistake and sent Science off on a wild-goose chase which has still not ended.

            For my purely speculative idea of how atoms are constructed, see Inside_the_atom


Redefinition of Planck’s constant

The importance of Planck’s Constant, h = 6.625 x 10-34 J s-1,  (called the “Quantum of action” by scientists,)  is now seen as what an engineer would call the Coupling Factor between emr energy and matter. If the energy is coupled to an electron, for instance, as in the photoelectric effect, the energy coupled can be measured in Electron_volts.

The energy coupled to an electron is h/ce where ce is the charge on the electron. For this reason the slope of the line in the photoelectric effect is:

     Planck’s constant h         =     6.62 x 10 -34           =   4.13 x 10 –15 eV/Hz  

 Charge on an electron ce             1.6 x 10 –19


The alternative wave explanation of the PE, CE and PP implies that Planck’s constant now needs slightly redefining:


 “h = 6.625 x 10-34 J s for a signal to noise ratio > 1.”


            This confirms Maxwell and shows that the power in emr is independent of its frequency and depends only on its rms amplitude. But its Effective Power, how much of it actually couples to matter, depends on its frequency and which matter it is coupling to. Evidence of this is seen in the increased losses in RF components, antennas and feeders at high frequencies. Also the way the radiated power density from an antenna increases with frequency for the same transmitter output. For a given antenna size the radiated beam becomes narrower. Hence the use of high frequencies for radar and long distance communications.

As defined by Maxwell, emr is an “analog” quantity - it is not quantized. It is only quantized by the way it reacts with  matter which is quantized.

This solves the 85 year-old enigma of how emr can behave as a wave and a particle. It does indeed “behave like a wave when it travels from A to B but like a particle when it reacts with matter.”


Abbreviated Tutorial


This section may serve to remind some physicists of the simple concepts leading up to the transmission and reception of electromagnetic radiation. Excuse me starting from fundamentals.


Moving electrons.

Electrons are charged particles and so can be moved by putting them in an electric field. If electrons are moving at a constant velocity they constitute a constant electric current and generate a constant magnetic field. This is a “Fact of Nature”

A piece of wire can be considered as containing  a number of “free” electrons. Under the influence of a small voltage which provides an electric field through the wire, the electrons move and generate the circular lines of magnetic field. The magnetic field lines push each other apart if they are going in opposite directions.

Accelerating electrons

If electrons  accelerate they produce electromagnetic radiation (emr). This is most easily explained by thinking of a piece of wire with a sinusoidal voltage generator in the middle. The sinusoidal alternating voltage produces electric field lines which spread out into space at the speed of light as the voltage increases then momentarily freeze when maximum is reached. As the voltage drops the field lines return, finally disappearing when the voltage is zero. The voltage now starts to increase in the opposite direction and the field lines spread out again, this time of the opposite polarity.

Now think of the electrons in the wire. The electrons are pumped up then down in synchronism with the alternating voltage. Moving electrons upwards  produces a clockwise circular magnetic field which increases as the voltage increases, expands into space, holds when the maximum is reached, collapses to zero as the voltage drops, then expands out anticlockwise as the electrons accelerate downwards. (Not shown in the above diagram.)

OK at low frequency. But now increase the frequency. As before, the field lines expand out into space but when the polarity between the ends of the wire change, all the magnetic and electric fields (which are limited to the speed of light) cannot “get back” before the alternating voltage has changed over and  new magnetic and electric field lines are produced in the opposite directions. These newly generated emerging fields “push away” or repel the inward falling field lines that have not returned “in time”. These fields, finding themselves alone in space and being pushed away, “join up” to form emr. These loops of electric and magnetic field, isolated in space and propagating away from the source, are called electromagnetic radiation (emr).

The critical factor in their formation is the rate of change of the electric and magnetic fields. A minimum is necessary in order to “launch” significant emr energy. Either a low current and high frequency or low frequency and high current can achieve this measurable minimum. In practical transmitters the antenna current is limited so it is more profitable to operate at high frequencies.  In practice this limits the lowest transmitter frequencies to around 10kHz.

Definition of electromagnetic radiation, emr

Emr is a changing electric field which produces a changing magnetic field which produces a changing electric field …Accelerating electrons are needed to “launch” emr but once launched it is a strange self-supporting construction of electrostatic and magnetic “field lines” which flies through space at the velocity of light. One field “bootstraps” the other. No electrons needed!

Generating emr

Generating emr therefore means accelerating charged particles (usually electrons) and there are several ways of doing this.

The way that mostly interests us is that already discussed above. A sine wave voltage source causes the electrons in the antenna wire to move up and down. The emr produced is at a single frequency and its amplitude, (defined in volts per meter), depends on the amplitude of the accelerating voltage.

It will be seen later that the power in emr depends only on its amplitude but its equivalent power depends on its frequency as its Coupling Factor to matter ( Planck’s constant) depends on its frequency.

Detecting emr

Emr is detected by the way it interacts with charged particles, usually electrons because they are light and plentiful. In order to get lots of electrons together (being negatively charged they repel each other) we use those found in a conductor (such as a piece of copper wire) where they are loosely attached to copper atoms and their negative charges cancelled by the positive nucleus of the copper atoms. These more-or-less “free electrons” are forced to follow the voltage part of the incoming emr and moving electrons constitute an electric current, which can be amplified. The effect can be magnified by making the piece of wire resonate at the emr frequency. The wire is now called an “antenna”.  If it is a half wavelength long, it is called a half-wave “dipole”.

Detector noise level

Not usually discussed in physics books on QM but very important in engineering, is the amplitude of emr. Emr cannot be reliably detected unless it can move an electron significantly more than that electron’s  random or thermal movement. Engineers say the emr amplitude must be above the “noise level” or signal to noise ratio (SNR >1)

Quantization of emr

As seen above, emr can be generated in many different ways and its method of generation determines its character. Emr generated by a continuous process, as by the sinusoidal vibration of an electron in a radio antenna,  or a laser, is a continuous or “analog” signal.  Attenuated by dispersion it can take all amplitudes down to zero.

Such emr is not quantized – it is not in pulses or particles. However in practice it usually appears quantized because of the way it interacts with matter, which is quantized. For example, if an atom is used as a detector, the electron can only take certain definite orbits or energy states. A similar error would be made in the laboratory if an analog voltage (which can have any value) were measured with a digital voltmeter.

But emr which is generated by a discontinuous process, as for instance when an atom drops down from a high energy state to lower energy state, appears as a burst of emr – whose frequency corresponds to the energy change (f = energy change/h, where h is Planck’s constant.) But such emr is still an analog pulse, like a radar pulse. And like a radar pulse it will disperse with distance and its amplitude follow the inverse square law. Emr, however it is generated, is a continuous wave or “analog” signal. A further important comparison between an atom used as a quantizer for emr and an Analog Digital Converter instrument used to measure an analog voltage, is that the amplitude of the signal being quantized in either case must be greater than the quantization interval. For example, a digital voltmeter which digitizes to 1mV resolution will not notice an analog voltage whose amplitude is <1mV.

We will see later that the size of the quantized “bits” or “quanta”, are exceedingly small, as is to be expected when they are determined by atomic energy levels.

In brief, non-quantized emr is quantized by quantized matter.

Absorption of emr

If electrons are in some way hindered in their movement (by being in soot, for instance), energy is absorbed. The energy, which heats up the soot, is absorbed from the emr, which is therefore weakened. In a radio antenna, where we want to extract the maximum energy from the emr, we must connect it somehow to a load and  “match” this load to the source.

Alternatively, the emr can be absorbed in a molecule and cause it to “rearrange” itself. Subsequent chemical treatment reveals which atoms have received emr over threshold and been rearranged. This it the principle of photography and farming.

Attenuation of emr

I use this to mean some system which inputs emr at one power level and outputs it at a lower power level. There are several ways to construct an attenuator.

Attenuators use combinations of absorbers and dispersers. Pure dispersion could be with a lossless convex mirror or a concave lens. Pure absorption would be a lossy plane mirror or an absorbing medium. A convenient example is a piece of black overexposed photographic film.

Absorption is easy to explain if emr is considered as a wave. Electrons in the absorbing material behave as loaded dipole antennas. They vibrate in sympathy but because they cannot move freely they reradiate less energy than they receive. The surplus energy heats up the absorber.

Reflection vs. scattering of emr

If light is shone on a clean polished surface it reflects geometrically. On a greasy or rough surface it scatters randomly. Fundamentally this is because both surfaces contain electrons which vibrate up and down sinusoidally, following the voltage vector of the incident emr and reradiate it. The polished surface has many nearby (within lambda/2) electrons which also vibrate and reradiate. Their reradiated outputs are in phase and so recreate and merely deflect the incident wavefront.

If all these electrons were in some way  slightly inhibited in their movements (like being tied to an atom) so they reradiated less than they received, the reflection would still be geometrically clean but weaker.

            If the other electrons were at random distances, there would be no combination of their outputs, each would be a point source and the incident wavefront would be scattered.

The key difference between reflecting and scattering is the distance between the electrons. At a low frequency a surface often reflects – at a higher frequency it usually scatters.

Antenna theory

One of the important sections of this paper is to convince you that the PE can be explained with the classical concepts of emr as a wave.

There is a large body of information on long-wave emr or radio waves.

 I argue that anything that is valid for radio waves must be valid for light waves and ultimately X-rays. Studying the large structures (antennas) used to launch and receive radio waves must surely give us an insight into the behaviour of small structures (single moving electrons) used to launch and receive light waves.

Transmitting or launching emr

The first and simplest way is where a sine wave voltage source causes the electrons in the antenna wire to move up and down. The emr produced is at a single frequency and its amplitude, in volts per meter, depends on the amplitude of the accelerating voltage. See accelerating_electrons

Receiving emr

Receiving emr is much more complicated. By “receiving” is meant converting the (say 100MHz)  emr wave signal which is flying through space into a 100MHz sine-wave current in the antenna load resistor and examining  it to see if it is carrying any signal. Like being switched off and on in the Morse code.

Now there are many types of receiving antennas and they all have different characteristics. The only one I am interested in here is the simplest one, the “half-wave dipole”, as I think this one can be compared to how free electrons behave in the photocathode of the photoelectric effect. I will therefore describe it in detail.

The half-wave dipole

The half-wave dipole is a piece of wire, one half-wavelength (lambda/2) long, cut in the middle and the two halves joined by a load resistor, RL.  RL = 72 ohms. Placed in an emr field of frequency f and amplitude E volts per lambda and lined up with the electric field lines, it behaves like a signal generator of voltage E with an output impedance of RR, the antenna’s “radiation resistance”. In order to extract the maximum power from the receiving antenna it must therefore be loaded (matched) with a resistance equal to RR.


From classical antenna theory: 

1.“Total power in watts abstracted from a radio wave by an antenna: 


            =       (Eh)2

    RL + RR + Rl



            E = field strength (rms value) of the radio wave in volts per meter

           h = effective height of the antenna in meters

         RR = radiation resistance

          Rl = antenna loss resistance

          RL= antenna load resistance


The fraction RL /(RL + Rr + Rl ) of this total energy represents the portion of the abstracted energy which is usefully employed. Of  the remainder, part is accounted for by the antenna losses, such as wire and ground resistance, while the rest is reradiated or reflected. Ref_10 Pg. 654


2.“The maximum amount of energy that it is theoretically possible for a given antenna to abstract from a passing radio wave occurs when the antenna loss resistance is negligibly small and its load resistance RL is equal to the radiation resistance. Under these conditions the rate at which energy is abstracted from the wave is:


             E2 watts        where E = rms field strength in volts/meter.

            2RR                                   RR = radiation resistance


3. “The reradiation of energy results from the fact that, when current flows in an antenna, radiation takes place irrespective of whether the voltage producing the current is derived from a passing radio wave or from a transmitter tube.”

Ref_10  Pg. 654


So only E2   watts is available as useful power to the antenna load

           2 RL


           4. Furthermore, “Calculations show that a section of wavefront extending for only about one-quarter of a wavelength on each side of the receiving antenna will be capable of supplying the received energy.

Analysis shows that the effect of the receiver antenna on the passing wave is, first, abstraction of energy which weakens the main wave, and second, reflection or reradiation of energy, which redistributes the energy of the passing wave in a manner depending upon the antenna tuning.” Ref_10 Pg. 655


In words, the half-wave dipole behaves like a tuned concentrating lens, focussing and matching half the incident energy over an aperture of + ¼ lambda onto the load resistance RL. The other half is reradiated/scattered. There is therefore a + ¼ lambda, –3db “shadow” directly behind a loaded half-wave dipole. Pictorially the position is as shown below:


And so the field strength far behind a row of receiving antennas is uniform but weaker than that in front of them. Uniform because the small discrete shadows behind each antenna have disappeared (been smoothed out) as the oncoming emr has diffused around them.

The Bremsstrahlung effect

Electrons can be given a high velocity by putting them in an electrostatic field. If the electrons are now decelerated suddenly by firing them at a piece of metal, they  produce a cone of wide bandwidth emr called “Bremsstrahlung.” This is how X-rays are produced. The highest frequency produced, due to a solid hit with a metal ion, is eV/h. Lower frequencies are due to glancing hits.

The Bremsstrahlung effect is the exact opposite of the PE. Instead of emr accelerating (photo)electrons, decelerating electrons produces emr. To quote “when an electron loses a large amount of energy by being decelerated, an energetic pulse of emr is produced.” Ref_5  Pg. 138

For this reason the Bremsstrahlung effect is often termed the “reverse PE.” And as the Bremsstrahlung effect can be explained without the concept of “photon”,  the PE can too.



Absorption coefficient of lead

The three ways in which emr reacts with matter overlap at different frequencies, at different energies, as shown below: Ref_5  Pg. 177.

Interference experiments

Having shown that the photoelectric effect can be explained with classical physics, see The_photoelectric_effect, I now describe a series of experiments which constitute the second half of my argument. The results of these experiments can best be interpreted by considering light to be a wave. And I postulate that if light behaves like a wave it cannot be a particle - the properties are too different.

Concept of “Gradualism

The following test was designed using the concept of “gradualism”.

Many experiments are described in popular books on QM where first strong light is used and visibly behaves like waves. Then this light is attenuated and the experiment repeated using a sensitive light detector such as photographic film. Now the results are described in terms of light as particles. Strong light is supposed to display the characteristics of waves whereas  weak light the characteristics of particles. The idea behind my version of these experiments was that it should be possible to slide slowly from strong light to weak light and see one characteristic slowly blend into another. A key factor is the way the strong light is converted into weak light – the attenuation method.


At the time I was testing an ingenious theory that wave light was constructed of individual hooked-together “photons”, in the same way a piece of metal is constructed from hooked-together individual atoms. Attenuation was imagined as pulling the “photons” apart but leaving random “bunches” of still connected “photons”. These bunches of “photons” would exhibit  the wave properties seen for example in Youngs_two_slit_experiment with weak light. The problem was to design experiments which should differentiate between wave and particle light and then perform them with strong and weak light, using different types of attenuators, and see if there was any difference.

The first experiment  will make the idea clear.

Experiment 1

Shine an unattenuated laser onto a 0.5mm single slit and observe the sinx/x  pattern on a distant screen. Now put a lens in front of the screen to collect the entire pattern into a single bright dot.

Shine the dot into a PMT desensitized with an attenuator in front of it to protect it and also so it has a reasonable (say) 100kHz count rate.

Now place a mask in front of the lens so only light from the side lobes of the sinx/x pattern enters the PMT. The main lobe is screened out. The count rate drops to C1. Note C1. 

Place a different mask in front of the lens, this time screening out all the side lobes. Only the main lobe passes. Note the count rate, C2.

Compute C1/C2 which represents the ratio of light in the side lobes to the light in the main lobe for strong light.

Remove the attenuator in front of the PMT so it now has its normal full gain.

Repeat the experiment with some sort of attenuator directly in front of the laser to produce “weak light” (average 1000 clicks per sec.)  and compute C1/C2 again.


The rationale behind this experiment was the idea that more  “weak light”, which was supposedly “photons”, would go straight through the slit into the main lobe, (like golf-balls, as the popular-science books say)  and not be diffracted into the side lobes. This would be confirmed if the C1/C2 ratio decreased as the light was made weaker.

            I used different types of attenuators as I was looking for evidence to support my wave/particle duality “clump” theory (now abandoned). These attenuators  were usually 10mm disks punched out of overexposed photographic film but also crossed-polarizers and band-pass filters operated far outside their band.


There was no change in the C1/C2 ratio.  


Conclusion  1– This result is consistent with the concept of weak light

as a wave. Therefore there are no “photons”.

Conclusion 2 – This result also helps the understanding of an “emr attenuator”. It shows that the attenuators I used behaved as they should if emr could be considered as a wave. They reduced the size of the E and B vectors, presumably heating up in the process, in the same way they work in wave guides. The greatly attenuated light was still coherent. But if emr is “photons” they would act as “dividers” ie. 1000 photons per second “in” and 1 “photon” per second “out” means an attenuation factor of 1000.  And if emr is considered as “photons” each attenuation method requires a different exotic explanation. All the attenuators I used could be simply explained by considering emr to be a wave and Occam says we should take the simplest explanation and “not multiply our  entities”.

Other experiments I have done

The logic behind most of the following experiments is that “weak light”, which gives a small number of “clicks” per second when measured with my PMT, may be “photons”. But if this weak “photonic” light behaves exactly like regular “strong” wave light, the concept of particle light is wrong. I.e. there is no need for “photons”, there is just weak wave light.

Experiment 2 (This is similar to Experiment 1)

           I wanted to measure numerically the beam profile of my laser and so fitted my PMT with a 0.5mm wide vertical slit mask. I covered the slit with an “over-exposed film” attenuator, otherwise the laser would have damaged the PMT.


A. I mechanically scanned the PMT across the laser beam in 0.5 mm steps, noting the PMT count rate at each step. Distance between laser and PMT  2m. The count rate in the beam was 1kHz. I then drew the beam profile, which was about 5mm wide. This diagram confirmed what my eyes saw.

B. Now I wanted to repeat this experiment using attenuated (“weak”) light (possibly “photons”.) To do this I would have to attenuate the laser and return the PMT to its normal sensitivity by removing the attenuator from in front of it. What more natural than to remove the attenuator from in front of the PMT and place it in front of the laser? Working in complete darkness I now repeated step A.


The count rate per step was approximately the same and the beam profile unaltered at a sharp 5mm. (Intuitively there should be no difference. All we have done is changed the position of the attenuator in the beam – from directly in front of the PMT to directly in front of the laser. Out of curiosity I placed the attenuator in the beam half-way between the laser and the PMT and as you might expect, it made no difference.)


Again the problem with attenuators if light is considered as particles.

The input to the attenuator is the output of the laser and is surely wave light as it produces interference patterns. How does the attenuator work? Two possible methods:

1. The film attenuator “somehow” converts or quantizes its high-power wave input into 1 000 “photons” per second which individually knock  1 000 photoelectrons per sec from the PMT photocathode.

2.  The film attenuator weakens its input by resistive absorption, reducing the size of the E and B vectors and so heating up. The output is low amplitude wave light whose amplitude “increases the probability of electron ejection” in the PMT photocathode to the point that 1 000 electrons per sec. are ejected.


Explanation 1 requires an attenuator capable of “somehow” converting or quantizing wavelight into particle light. Explanation 2 uses a standard component. The wave light explanation is more convincing. And so there are no “photons”

Experiment 3

I shone attenuated white light (10 000 clicks per second) through a 80nm wide green pass-filter into my PMT and noted the average count rate. (Incidentally, this filter works by interference, by internal reflection between several carefully spaced half-silvered surfaces.) I then replaced the green filter with one of exactly the same pass frequency except that it is 8nm wide. The average count rate was 10 times smaller. These counts correspond to the areas under the filter response curves, as would be expected if the light were a wave. I cannot reconcile this result with the particle picture of light. The energy in a “photon” is supposed to be that of a “quantum”, hf joules, where f is the frequency. Surely there is an infinite number of “photons” in wide-band light as there is an infinite number of  frequencies?


The simplest explanation is that weak light is a wave and so there are no “photons”.

Experiment 4

The beam-width of a radio frequency dish antenna is given by the well-known rule-of-thumb formula:


                                      b = 70 lambda         



           Where      b = degrees between half- power points  

                                        d = reflector diameter in wavelengths

                               lambda = wavelength of the emr


And so for lambda = 600 x 10-9 m and d = 0.4mm, (my red pointer laser shone through a 0.4mm slit) the beamwidth should be 0.120.


The width of the main lobe was actually measured at 0.0950



With only a small error the laser beam is behaving as it should for wave light. So there is no need for the concept of a “photon” to explain this result.

Experiment 5

a. Shine strong light from a laser onto a screen. Note the impact point. Now put a prism in the beam to refract the beam through some angle theta. Note the new impact point. Scan the screen with a movable PMT (with attenuated input to prevent damage). The count rates confirm what the eyes see – all the laser output has been refracted through an angle theta.

b. Darken the workplace, remove the attenuator from in front of the PMT and attenuate the laser beam until it makes 100 clicks per second when shone into the unattenuated PMT. Now scan the screen again with the now unattenuated input PMT.


– all the light was refracted through angle theta even though the PMT is registering only 100 clicks per sec. [Refraction of light can be compared to a line of soldiers marching in step, arms linked, across a field. The soldiers on the left encounter a muddy patch and slow down, causing the whole line to pivot anti-clockwise to the left. If the soldiers were not linked, the line would just break up, all the soldiers marching straight on forwards individually at different speeds. And so unconnected “photons”, if they exist, would merely slow down but not change direction.]


– This result is adequately explained by the concept of light as a wave. Weak light refracts just like strong wave light and so there are no “photons’.

Experiment 6

I have a green laser, which works by doubling the frequency of a  IR laser in a non-linear crystal. I am quite familiar with waves being deformed and producing harmonics by a non-linear device. But what does non-linearity mean in terms of photons?


Light is surely behaving like a wave here. And if light is a wave there are no “photons”

Further experimental data supporting the wave theory of light

            In the Bremsstrahlung effect, constant velocity electrons  are suddenly slowed down or decelerated in a block of metal. Emr over a wide bandwidth is produced. The highest frequency produced depends linearly on the voltage accelerating the electrons (their velocity) and the constant of proportionality is h/ec where h is Planck’s constant and ec is the charge on an electron.

Make a film of this and play it back in reverse. Wide bandwidth emr is focused onto a block of metal and electrons are emitted. This is the same as the PE and for this reason the Bremsstrahlung effect is often called the “reverse PE”. 

            Note that the concept of “photon” is not  required to explain Bremsstrahlung. And therefore not for its reverse, the PE .

Youngs two slit experiment

Almost every book on quantum mechanics contains this picture:


“Strong light” is shone through slit O and then spreads out to cover slits A and B. The light from A and B spreads out even more and overlaps. The waves beat, producing a wave pattern on the screen C. The following diagrams show more exactly what is happening: 

If you believe that light is a shower of  particles (“photons”), it is possible to attenuate the light so much that it consists of (say) 1 particle or “photon” per second. You think you have done this because your light detector gives 1 click per second if it is a PMT. Or before the invention of the PMT, say 50 dots on a sensitive photographic film in 50 seconds.

Now darken the workplace and replace the screen C with your light detector – for example a piece of photographic film. After say 50 seconds exposure remove the film and develop it. It looks like “50” below. Repeat the experiment with another piece of film but make the exposure times 200 and 2000 seconds. The developed films look like “200” and “2000” below.



This experiment was designed to illustrate how very weak light, which is supposedly just particles, produces a dot interference pattern on the film – one particle, one dot. So there are 50 dots in 50 seconds, 200 in 200 seconds and 2000 in 2000 seconds. BUT – even though the “photons” are supposedly single entities flying through space one at a time, kilometers apart, it is amazing to see them form an interference pattern – as though they were waves! Even more amazing is how  physicists have misunderstood this experiment. The core of the misunderstanding is that the available light detectors (the molecules in the film, in this case) are digital detectors – they quantize the analog light falling on them.          

And so when I do Young’s experiment with weak light (say 100 clicks per second as measured with a PMT) it is not being done with 100  “photons” per second, but  with weak wave-light which has “increased the probability” that the photocathode will produce an average of  100  photoelectrons per second.

            Covering one slit to try to find which “photon” went through which slit will of course destroy the complex double-slit interference pattern and leave the simpler single-slit sinx/x interference pattern due to the other slit. (This is sometimes incorrectly reported in popular books as a vertical bar behind the uncovered slit.) Nature is not trying to stop mankind from finding through which slit the “photons” are passing - there are no “photons”, only weak wave-light which divides itself evenly between each slit. The same applies to any experiment where you think you are working with “photons”. [Incidentally, Young’s two-slit experiment is overly complicated if you are testing to see if light is a wave. A single slit is adequate – the incident light reflects off the edges of the slit and spreads out, overlapping on the screen.]


A point I am making here is that building comparators to correlate “clicks” between the outputs of PMTs behind each slit in “weak light” experiments is meaningless. You are just finding accidental correlations between random pulses. An amazing number of experiments are done with PMTs assuming a “click” is a “photon”, and they are all wrong.

            Of course there is nothing wrong in correlating “clicks” if the signal to noise level is  over 1 (SNR>1), as in the Cerenkov flashes from underground neutrino detector pools.




            Geoffrey William Harries, Welsh father, English mother. Born in Liverpool, England. As a little boy fascinated with radio, bought and renovated old “crystal sets”, then built 1,2,3 valve “wireless sets”. Went to a Grammar school until 18 or so and was usually at the top in science subjects. Six years Military Service in the Royal Air Force in “Ground Radar”, becoming an instructor. Through correspondence courses he obtained a City and Guilds of London Technological Certificate. Leaving the RAF he was offered a job in the R&D department of Marconi’s in Baddow, Chelmsford. After 5 years, married a local girl and emigrated to Canada and worked in the R&D department of Canadian Marconi in Montreal. Emigrated to the US after 3 years and worked in a small company (Applied Science Corp.) in Princeton NJ which made telemetry equipment for the US space program. Awarded two patents. Then helped form a start-up, Applied Electronics Inc. ( See below an extract from this company’s brochure.) After three years, divorced and with the custody of his now 6-year old eldest daughter he returned with her to Europe and worked for 2 years at Schlumberger in Paris in International Sales. Then he went back to Engineering in a small French company and when this company folded became an independent importer and consultant, finally moving to Munich, Germany, where he now lives, retired. His life has mostly been driven by a desire to do unusual things, to solve problems “his way”. And on the health front “no pain, no gain”. He describes himself as a Hardware Aerospace Electronic Engineer. He would like to think he is not a crank, but admits that after a few beers he does get philosophical.

To his surprise he has discovered in himself an almost spiritual streak, where clean corruption-free  Science is the only thing really worth doing. This project is mostly motivated by the desire to uproot what he considers a heresy.



Miscellaneous experiments performed and concepts explored in the preparation of this site

Collecting information for this Site required performing unusual experiments and thinking about concepts which seem to have been too hastily accepted by Science. Coming from a different background, my views may have some interest for you.

1. Calculation of photon density in the beam of a red “pointer” laser.

2. Inside the atom

3. The Heisenberg uncertainty principle

4.The wave particle duality of electrons

5. The reflection coefft of a PMT

Calculation of photon density in the beam of a red laser pointer

I look up the definition of a “photon” in the McGraw-Hill Technical Dictionary I read: -


“Pho’ton - A single mode or polarization of the electromagnetic field. There are also two other definitions of photon in use, not entirely consistent with the first definition or each other: an elementary light particle or “fuzzy ball,'' and an informal unit of light energy. The fuzzy-ball definition emphasizes the particle character of light suggested, for example, by momentum exhibited in the Compton effect and light levitation phenomena. However, the fuzzy-ball picture lacks a rigorous foundation and is not required for the explanation of any fundamental phenomenon. (My italics)  As an informal unit of energy, the photon equals hv, where h is Planck's constant (= 6.626 x 10 -34 joule-second or watts), and v is the frequency of the light in hertz.” Hardly a very sharp-edged  definition.


Now Young’s two slit experiment demonstrates interference, and therefore the wave nature of light, by beating together widely separated parts of a coherent wavefront. The Calculation below shows that light considered as "photons", even in strong light (the output of a 1mW red “pointer” laser which is stronger than sunlight) are on the average 160 wavelengths apart! It is difficult to see how these “photons” could ever interfere, as they must hardly every meet – the figures are even more outrageous as the beam is attenuated into “weak light”  (and still forms an interference pattern!) Of course it is difficult to say how a speculative particle like the “photon” behaves, but for the dipoles in an antenna array to usefully combine their radiation, they are in general never more than half a wavelength apart.

The calculation

A green 500nm “photon” corresponds to: (frequency x Planck’s constant) joules.

                                      = 0.6 x 1015 Hz x 6.62 x 10-34

                          =  4 x 10-19 joules

So 1mW of green light    = 10-3 / 4 x 10-19                                               

                                         = 0.25 x 1016 “photons” per sec.            

Assume the laser aperture is 4mm x 1mm and it is switched on for 1 second. The output is a thin beam 1 light-second long whose volume:

=  (4 x 10-3 x 10-3 ) x (3 x 108 ) m3

=  12 x 102 m3 (or 1200 cubic meters)

So the average volume occupied by each “photon”:

                                    = volume of 1 sec. laser beam/number of  “photons” in it

                                    = 12 x 102 / 0.25 x 1016

                                    = 48 x 10-14 m3

Assume for a moment the “photons” are points and each “photon” is sitting in the middle of this “average” volume. For ease of calculation imagine this volume is a cube of side D. Then:  

                             D3  =  48 x 10-14m

                                  =  480 x 10-15 m          

                             D   =  7.8 x 10-5 m

                                  =  7.8 x 10-5 x 109 nm

                                  =  78 000 nm. 

So the “photons”, considered as points, are 78 000nm apart. But “photons” are described in the McGraw-Hill Technical Dictionary – see above - as “A single mode or polarization of the electromagnetic field” and so must have a dimension of lambda (in all dimensions). And as the wavelength of green light is 500nm these “photons” are:

                                   =  78 000/500 wavelengths apart

                                   = 156 wavelengths


The concept of “photon” must be wrong. So there are no “photons”.


Reflection coefft. of a PMT

The following experiments show two independent methods of measuring how much of the incident light is reflected from the photocathode of a transmission type PMT (with the PMT “dead” – not connected to any counting circuitry.).

Method 1


The PMT used is as illustrated. It is a transmission type – Hammamatsu type R464. It has a glass envelope and I use the fact that most of the end of the PMT is like a mirror, with a 10mm diameter circular section which is the semi-transparent photocathode. I want to measure the reflection coefficient of the photocathode which I define as the ratio:

R = Reflected light

        Incident light


The reflection coefficient of the mirrored section = 1/1 = 1.


To measure R, diffused light of some undefined intensity A is shone on the end of the PMT and a photodiode is used to measure the relative intensity of the light reflected from the two sections, photocathode and mirror-like screening.


           1. The photodiode is first pointed at the photocathode to detect light reflected from the photocathode. The amplifier gain is adjusted to give full scale.

2.The photodiode is now pointed at the mirrored section and the amplifier

output, as expected, goes off scale. Put an adjustable cache in front of the lamp to reduce its intensity and adjust it until the amplifier output comes back to full scale. It is found that the intensity must be reduced to a quarter or A/4.


We can now write R x A = A/4 x 1 and so R = ¼ or 25%.


This result supports the antenna analogy of the PE, where 50% of the incident light is reflected and 50% used to produce photoelectrons. Here we can only measure the 50% of the reflected light that is reflected backwards ie, 50% of 50% or 25%.  See Antenna_theory

Method 2


In this method a distant light source is reflected into the eye via two parallel paths: 

reflected from a unconnected PMT photocathode and

reflected from the silvered surrounding of the photocathode via a

piece of attenuating film.


The attenuation of the piece of film is selected until the two images appear the same brightness.

            Under these conditions: –

A x R = A x (film attenuation)2                                                 

          (Remembering light passes through the attenuator film twice.)


So R, the coefft of reflection of the PMT photocathode = (film attenuation)2


R can now be determined by measuring the attenuation of the attenuator film. This is done in Fig. B using the PMT as a light intensity measurer and of course connected to its normal counting circuitry.


Place the measuring PMT in a light-tight box with a lamp and put a piece of the type of attenuator film as used above in front of the PMT. Adjust the lamp drive so the PMT is counting say 100 000 pulses per second. This is equivalent to the output of the lamp, bandwidth limited to the bandwidth of the attenuating film. Now put the exact piece of film used in the test between the PMT and the bandwidth filter. Without changing the lamp drive, note the PMT count. Call this C.

            The attenuation of this piece of film, A is C/100 000

            In practice = 50 000 so A = 0.5. The coefft of reflection of the PMT photocathode is therefore A2 or 0.25.

            In other words, 25% of the incident light on the PMT semi-transparent photocathode is reflected: the rest passes through. This result agrees the result obtained by Method 1.



Inside the atom

The hydrogen atom

The hydrogen atom contains one negatively charged electron and one positively charged proton. These both have the same size of electrical charge and so the hydrogen atom is electrically neutral.

One model (by Rutherford) of a way to keep the electron and photon apart is to have the electron spin around the proton like a planet around the sun. If the masses of the proton and electron and the attractive force between them are plugged into the calculation, the dimension of the resulting structure is not far from the measured dimension of a hydrogen atom. So this is a possible solution.


1.The first flaw in the planetary argument is that if an electron accelerates, as it does if it is in a circular orbit (centripetal acceleration), it radiates emr as synchrotron  radiation, loses energy, slows down, decreases orbit radius and should finally crash into the proton. 

But there is no emr radiation from hydrogen - it is a stable gas.


2.A second flaw is that if white light (containing all frequencies) is passed through hydrogen gas, a number of absorption lines, corresponding to many resonant frequencies are seen. The problem is that these lines correspond to wavelengths much greater than any possible electron orbital and so resonance frequencies of the hydrogen atom. In particular, the lowest (red light) has a wavelength 1 500 times greater than the hydrogen atom’s diameter!


Science has “solved” this flaw by  accepting de Broglie’s concept of “matter waves”. The electron is considered to be a wave wrapped around the proton.


            Forced myself to invent a classical explanation of these “flaws”, I would use the following comparison with a radio frequency transmission line and a resonator:



Step A. A transmitter is connected to an antenna via a conventional transmission line. Radiation from the two wires is self-canceling. All the emr power that is traveling along the line is confined  between the two wires.


Step B. Here a high frequency oscillator drives a load through a looped transmission line. Again there is no radiation as all the emr is confined between the two conductors.


Step C. Here the loop has been cut and quickly reconnected. As the output impedance of both sides of the momentary break match (Zo), any trapped energy will circulate indefinitely without loss.


Step D. This is the same as C except that the distance between the conductors has been increased by reducing the diameter of the inner connector.


Step E. Expand this to three dimensions with the central conductor being a reflecting point, a proton, and we are looking at the hydrogen atom. The proton can be considered as a ground-plane reflector. With phase reversal it reflects the emr generated by the rotating electron. And so all the emr field generated by the orbiting electron is confined inside its orbit. The atom behaves as a multi-mode cavity resonator with many resonant frequencies, (Schrödinger’s equation), as familiar in microwave technology.


Classical  emr replaces de Broglie’s “matter waves”. I invite any competent reader to tidy this up mathematically. 


The Heisenberg Uncertainty Principle

“One of the consequences of wave-particle duality is that it sets limits on the amount of information that can ever be obtained about a quantum system at any one time. We can choose either to measure the wave properties of light by allowing it to pass through a double slit without detecting through which slit the photon passes, or to observe the photons as they pass through the slits, so long as we sacrifice the possibility of performing an interference experiment, but we can never do both these things at the same time.” Or generally..  it is impossible to make simultaneous position and momentum measurements on a quantum object such as a photon.” Ref. 7 Quantum_physics_illusion_or_reality Pg. 9-10

            I think the Heisenberg Uncertainty Principle is correct but not for the reason quoted. If there are no “photons” there is no wave-particle duality and the above statement is clearly meaningless.  But the concept is familiar to anyone making measurements.

An example – if you want to measure a spectrum, one way is to construct a group of contiguous filters which cover the band of interest (a “comb filter”). The output of each filter is rectified and smoothed (integrated) to produce a DC voltage proportional to the power in that filter. Now if the spectrum is not completely stable (not a completely stationary series, in the jargon), you cannot  integrate for an infinitely long time, and so the DC output of each filter will have some noise-like jitter on it which limits the accuracy of the measurement. If you make the filters narrower, in an effort to measure the frequencies with greater resolution, you will find even more jitter on the filter outputs. And vice-versa, if you make the filters wider you will find less jitter on their integrated outputs, but you have obviously sacrificed frequency resolution. You can trade off frequency resolution against amplitude precision.

            Analytically, Shannon says the same thing. Information is measured in “bits” and you can only collect a certain number of bits in a given time.

Information vs. data

       "The receipt of information in the form of a message implies uncertainty in the mind of the recipient before the message arrives. A measure of the information content of a message can thus be based on the amount of uncertainty it has removed".


    Shannon defines the Channel Information Capacity

C = W log2 (1+S/N) bits per sec.

where W = bandwidth and S/N = signal to noise ratio of the     channel.


In other words, you only have a limited number of bits (bits over the noise level) available in any given time interval and so any measurement has a limited overall precision.

If you want to measure something that has two parameters (like frequency and amplitude in the example above), you can “spend” these bits anyway you want – for any ratio of frequency to amplitude resolution.  But the individual precision per parameter is limited to the number of bits you decide to spend on that parameter.

More generally, the more parameters the measurement, the more the limited number of available bits have to be shared out, and as the precision per parameter is proportional to the number of bits you spend on it, the more limited the precision per parameter. 

Wave-particle duality of electrons

This is an often quoted experiment. A beam of electrons is shone on a piece of very thin conducting wire at right angles to the beam (the experimenter made the wires by coating fibers from spiders' webs with gold). The electrons that pass are allowed to strike a screen which can detect and then record the arrival of the electrons (a fluorescent screen backed up with photographic film, for instance). A sin x/x interference pattern builds up on the film! Even though the electrons are only shot once per second! [This is exactly the same pattern you see if laser light is shone through a narrow slit onto a distant screen. Here light has reflected from the edges of the slit and is interfering  with itself on the screen.] This electron experiment is generally taken as proof that electrons, which we know (from Millikon’s oil drop experiment) are particles, can also behave as waves. The fine wire is supposed to be behaving like an electron biprism, splitting each incident electron into two wave components, which then interfere with each other.


The importance of this notorious experiment is that it is supposed to demonstrate the general principle  that matter (in this case electrons), can exhibit particle or wave properties. If we accept this particular proof, where undoubted particles produce a visible interference pattern, it can be used to support the argument that light, which has an undisputed existence as a wave (in the 2-slit experiment), can also show the properties of a particle. By a rather circuitous reverse-logic route we then have a proof that light can show the properties of a wave or a particle - ie. a proof of the existence of “photons”.

How can electrons classically behave like waves?

A little thought shows that the electrons have random positions in the approaching beam. Some will hit the wire head-on and won’t reach the screen. Some will bypass the wire completely and hit the screen unaffected.  But others will graze the wire at random distances. A single moving electron, (which we know behaves like an electric current and has a magnetic field around it),  passing the more-or-less stationary free electrons in the wire, is not going to be unaffected. It will induce a current in the wire which will produce an opposing magnetic field, transformer-like, and deflect the electron. And the faster the electron or the closer the grazing, the more the deflection. And this phenomenon can occur on a single electron-by-electron basis.

Note that the experimenter did not use uncoated fibers. We can safely assume the experiment would not work without a supply of free electrons in the biprism “lens”. 

To complete my denial  of this phenomena as a demonstration of wave/particle duality, I should now make a calculation to show the expected screen pattern. (And maybe I will in a later version of this site.) But here I am concentrating on the wave/particle paradox of light. So I am satisfied if I can find a rough non-mystical explanation for a phenomenon which doesn’t directly concern me. (I invite any competent reader to tidy this up mathematically and I will give him full credit.) 


A somewhat similar experiment was performed by Davisson and Germer in 1927. An electron beam strikes a crystalline nickel target and bounces back at  50o if the accelerating voltage is 54V.  Ref_1 Pg. 86. The reason is surely that  the magnetic fields surrounding the moving electrons react with the regularly spaced “free” electrons in the metallic crystal in a regular fashion. No need to invoke “electron waves”.


I would like to expand this argument to explain the apparent self -interference phenomena of other particles. They also surely cannot graze the atoms in their target without being affected by them in some way. Remember we know very little about how an atom “works”. See Inside_the_atom.


1. “Concepts of Modern Physics”. Beiser. Mc.Graw-Hill. ISBN 0-07 004382-5

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