Einstein: Genius by Definition of Law of Photoelectricity

Einstein opened to the new brave world of modern physics in two articles in his 1905 annus mirabilis, one giving humanity a breath-taking entirely new view on space and time through the special theory of relativity, and the other on photoelectricity introducing light quanta carried by light particles later named photons preparing the development of quantum mechanics.

Einstein's science is difficult to understand because it is never clear if the basic postulates of his theories are definitions without physics content, that is tautologies which are true by semantic construction, or if they are statements about physics which may be true or not true depending on realities.

The special theory of relativity is based on a postulate that the speed of light (in vacuum) is the same for all observers independent of motion with constant velocity. With the new definition of length scale of a lightsecond to be used by all observers, the speed of light for all observers is equal to one lightsecond per second and thus simply a definition or agreement between different observers.

Yet physicists by training firmly believe that the speed light is constant as physical fact behind the definition. For Einstein and all modern physicists following in his footsteps, definition and statement about physics come together into one postulate of relativity which can flip back and forth between definition and statement about physics and thereby ruin any attempt to bring clarity in a scientific discussion. Einstein played this game masterfully by formulating special relativity as a prescription or definition or dictate that different observers are to coordinate observations by Lorentz transformation. A dictate cannot be false. It can only be disastrous.

Let us now check if Einstein's law of photoelectricity, which gave him the 1921 Nobel Prize in Physics is also a definition and thus empty of physics content. The law takes the form

• $h(\nu -\nu_0) =eV$,  

which expresses an energy balance for one electron of charge $e$ being ejected from a certain metallic surface by incoming light of frequency $\nu$ with $\nu_0$ the smallest frequency for which any electrons are ejected and $V$ is the potential required to stop a current of electrons for $\nu > \nu_0$. The relation can be written 

• $h\nu = h\nu_0 + eV$

expressing a balance of incoming energy $h\nu$ as release energy $h\nu_0$ and electron (kinetic) energy after ejection $eV$ measured by the stopping potential $V$.  

There is one more parameter in the energy balance and that is $h$, which is Planck's constant.

Measuring the stopping potential $V$ for light of different frequencies $\nu$ including determining $\nu_0$ and finding a linear relationship between $\nu -\nu_0$ and $V$, would then allow the determination of a value of $h$ making the law true. This shows to work and is in fact a standard way of experimentally determining the value of Planck's constant $h$. 

In this perspective Einstein's law of photoelectricty comes out as a definition through which the value of $h$ is determined, which effectively corresponds to a conversion standard from the dimension of Joule of $h\nu$ as light energy to the dimension of electronvolt of $eV$ as electron energy, which says nothing about the existence of discrete packets of energy or light quanta.  

The physics enters only in the assumed linear relation between $\nu$ and $V$. From the derivation of Planck's law on Computational Blackbody Radiation it is clear that $h\nu$ in the  high-frequency cut-off factor $\frac{\alpha}{\exp(\alpha )-1}$ with $\alpha=\frac{h\nu}{kT}$ in Planck's law, acts as a threshold value, that is as a certain quantity $h\nu$ of energy per atomic energy $kT$ required for emission of radiation. This strongly suggests a linear relationship between $\nu$ and $V$ since $V$ also serves as a threshold.

We thus conclude that the general form of Einstein's law of photoelectricity as a linear relationship in an energy balance for each electron between the frequency of incoming light $\nu$ and the stopping potential $V$, naturally comes out from the role of $h\nu$ as threshold value modulo $kT$. 

Once the linear relationship is postulated as physics, the value of $h$ to make the law fit with observation is a matter of definition as effectively determining energy conversion between light energy as $h\nu$ in Joule and electron energy as $eV$ in electronvolt. The quantity $h\nu$ is then a threshold value and not a discrete packet of energy and $\frac{h}{e}$ sets an exchange rate between two different currencies of frequency and stopping potential.

In other words, Einstein received the Nobel Prize for formulating a definition almost empty of physics content. It shows that the concept of a photon as a light particle carrying the discrete packet of energy $h\nu$ is also a definition empty of physics content. 

Another aspect emerging from the above analysis is an expected (and observed) temperature dependence of photoelectricity, which is not expressed in Einstein's law. The release energy is expected to depend on temperature and there is no reason to expect that the stopping potential should compensate so as to make determination of $h$ by photoelectricity independent of temperature.  What is needed is then an extension of Einstein's law to include dependence on temperature.

It remains to sort out the appearance of the parameter $h$ (determined by photoelectricity) in Planck's radiation law and in Schrödinger's equation, which has already been touched in a previous post, but will be addressed in more detail in an upcoming post.

The advantage of using definitions as postulates about physics is that you can be absolutely sure that your physics is correct (but empty). This aspect came out when Einstein confronted with an observation claimed to contradict special relativity, with absolute confidence could say that the observation was wrong:

• If the facts don't fit the theory, change the facts.
• Whether you can observe a thing or not depends on the theory which you use.
• It is the theory which decides what we can observe.
• What I'm really interested in is whether God could have made the world in a different way; that is, whether the necessity of logical simplicity leaves any freedom at all.

In this form of physics what you see depends on the glasses you put on and not on what you are looking at. In this form of physics the observer decides if Schödinger's cat is dead or alive by the mere act of looking at the cat, and not the cat itself even if it has nine lives.

PS1 To view $h\nu$ as a packet of energy carried by a photon is non-physical and confusing for several reasons, one being that radiation intensity as energy per unit of time scales as $\nu^2$ and thus the scaling as $\nu$ of photon energy is compensated by a flow of photons per unit time scaling as $\nu$, with each photon occupying a half wave length. 

PS2 If now Einstein is a genius by definition, there is as little reason to question that as questioning that there are 100 centimeters on a meter.