Photon Issues

We might start this discussion with another basic question: what is a photon? However, in this case, the answers can be even more ambiguous than those provided for a particle, as the concept of rest-mass is not an option. Therefore, we might return to the idea of an energy-density confined within some volume of space. However, this description is not helped by Planck’s energy equation [E=hf] as it gives no hint of any containment volume or causal mechanism of propagation. Therefore, we might initially make reference to two very different descriptions provided by Maxwell’s electromagnetic theory and Quantum Electro-Dynamics (QED), where the former is essentially a wave model and the latter a particle model. However, while the quantum model supports the description of QED, it still appears to accept the validity of Maxwell’s equations, at least, in part. However, before discussing some of the potential issues associated with QED, some reference might be made to the Photoelectric Effect, which quantum theory would cite as evidence that cannot be explained by classical electromagnetism, i.e. a wave model. While this discussion will not attempt to explain all the issues, it might initially try to summarise those issues pertinent to the photoelectric effect.

  • Increasing the intensity of the light increases the number of ejected electrons.
  • The kinetic energy of the electron is not a function of light intensity.
  • Light below a given frequency ejects no electrons.
  • Light above a given frequency ejects electrons, irrespective of intensity.
  • The ejection speed of electrons is a function of frequency.

We will first define intensity as energy per time per area, e.g. [W/m2]. So, within the standard model, a single photon within some minimal collective intensity can eject an electron provided it individually has enough energy [E=hf].

Note: A question might simply be tabled in order to consider whether an EM wave produced by an oscillating charge is fundamentally different from a photon produced within a quantized atomic transition. The former is a continuous wave, while the latter might be described as a time-limited pulse of energy. If so, it might explain why the concept of an EM wave might be problematic, in respect to the photoelectric effect, and why a photon as a pulse of energy is not subject to intensity. 

While it can be argued that a photon is particle-like, there is no description of its structure or how it propagates. While this discussion will not replicate the details outlined in the ‘Historic Framework’, some brief reference might be made to Einstein’s 1904 paper that established the basic ideas of the photoelectric effect. Only later, in 1926, did G. N. Lewis coined the word ‘photon’, although his description conflicted with Einstein’s earlier work. While Lewis was a physical chemist, not a physicist like Bohr, he knew that Bohr’s model of the atom could not explain the idea of ‘valency’ as understood in chemistry.

Note: The idea of a ‘complementarity principle’ was part of Bohr’s 1927 Copenhagen Interpretation. However, with the hindsight of history, many now recognise that many of the original assumptions were primarily theoretical and, in some instances, essentially philosophical in scope. However, in 1932, Fermi published a paper entitled ‘The Quantum Theory of Radiation’ that was the fore-runner of what is now called Quantum Electrodynamics, although both concepts are based on the 1927 work of Dirac.

Today, despite some of the reservations implied in the outline of historic developments, most references invariably assume that you can either model light as an electromagnetic wave or as a stream of photons, but not both at the same time. So, let us start by making some reference to Maxwell’s electromagnetic wave equations, which suggested that light had to be a wave. In the 1962 version of the 700-page book by Lorrain and Corson entitled ‘Electromagnetic Field and Waves’ only two brief references are made to the idea of a photon, p.224 and p.546. Of course, it might rightly be pointed out that this is primarily a classical treatment of EM waves, although published 58 years after Einstein’s paper and 30 years after Fermi’s paper, such that we might have thought some of the details of a photon might have been outlined. Naturally, we might expect a more detailed explanation of a photon in a 2010 book entitled Quantum Field Theory by Mandl and Shaw. However, while there are more references to the word ‘photon’ in the index, most only describe the photon in terms of Feynman diagrams or abstract mathematics with little attempt to discuss any causal mechanism. In many cases, any review of the development of quantum theory tends to focus on replicating earlier assumptions or mathematics, as in the case of Fermi’s paper in respect to Dirac’s original work.

Note: It is possibly important to highlight that Feynman diagrams should not be interpreted literally, as they do not represent the kinematics of events in space-time. As such, they imply nothing about how a particle, or photon, gets from one point to another in space or time. They do not imply that the particles are moving with fixed speeds. They do not imply that the particles, or photons, move in straight or curved lines. The representation of a photon as a wavy-line does not imply that it is more wave-like than an electron within the QED model.

So, what is a photon?

Let us anchor what we believe we know about a photon to Planck’s energy equation [E=hf] and the assumption that a photon always has velocity [c] in vacuum, as shown in [1].

[1]     

However, as to be covered later in the ‘Time and Energy Issues’ discussion, it is possible that Planck’s constant [h] is obscuring some wave-like attributes, as simply illustrated in [2] below.

[2]     

In [2], we relate the energy back to an amplitude [A] and frequency [f], where [ρ] represents the energy-density that exists within some volume [V] defined by the photon structure. In 1922, Compton published his findings of scattering experiments involving ‘photon’ collisions with electrons, although his work also predated Lewis coining the term photon in 1926. The Compton Effect led to the definition of the Compton wavelength and while often associated with a particle, like the electron, it always defines the wavelength of a photon, not the particle, which can be directly derived from Planck’s energy equation, as shown in [3].

[3]     

Without going into the details, the idea of a kinetic mass [mK] in [3], we possibly need to reiterate the assumption that photons have no rest mass [m0]. This assumption needs to be explained in terms of the energy–momentum relationship of relativity, such that we might justify the idea of kinetic mass [mK] as shown in [4].

[4]     

In the case of a photon, the energy equation reduces to [E=pc], where [p=mKc], which might be seen as confirmation of [3]. While this review has questioned the idea of mass [kg] as a fundamental unit of energy [E], we might use these units of energy [E] and momentum [p] to simply illustrate that they are both related to the kinematics of velocity [v=c].

[5]     

However, it needs to be highlighted that [c] is not necessarily a function of [E/p], but rather the constraint that a propagation media would put on [c]. Of course, anybody trying to determine the nature of a photon will not necessarily believe that equations [1] through [5] is all that can be said about photons from a causal perspective and, in some respects, they are right, because much has been written about photons. For those wishing to pursue the details, the easiest way to become more familiar with the arguments of Quantum Electrodynamics is possibly to read Richard Feynman’s book ‘The Strange Theory of Light and Matter’. However, while this is an excellent starting point and one followed in an earlier discussion entitled ‘Feynman’s Model of QED’, it is a model that does not necessarily explain causal reality, which Feynman possibly recognised in the following quote.

You will have to brace yourselves for this, not because it is difficult to understand, but because it is absolutely ridiculous: All we do is draw little arrows on a piece of paper, that’s all!

As it is beyond the scope of this discussion to pursue the details of QED, we will now focus on the issue of the emission spectrum associated with an electron transition and the energy difference between two atomic orbitals, which can be equated to a photon of a specific frequency [f].

Note: For the purposes of this discussion, we will revert to the simplified Bohr model of a hydrogen atom consisting of a positive nucleus around which an electron might exist in a number of different energy-level orbitals. Each orbital has a specific energy level, which corresponds to the electrostatic potential.

Within this simplified model, a hydrogen atom has a composite structure in which an electron can make a transition between different energy levels by emitting or absorbing a photon. However, the photon energy must be equal to the quantised potential energy difference between the two levels before and after the electron transition.

On the left, we see a transition from [E2] to a lower level [E1] that results in the emission of a photon with energy [E=hf], while on the right, we see a transition from [E1] to a higher level [E2] that requires the absorption of a photon with energy [E=hf]. Again, we might generalise this energy relationship, as in [6].

[6]     

However, referencing the diagrams above, we might attempt to quantify the energy associated with a transition between orbitals in electron-volts, as shown in [7], where 13.6eV is the energy of ground state [n=1] orbital of the hydrogen atom.

[7]     

Based on the previous outline, along with the diagrams above, is the suggestion that a photon is a quantum of energy, often described as more particle-like than wave-like. However, previous discussions have also outlined that a particle, like the electron, may be better described as wave-like, which exists with some circumference of the orbital. Within this model, an electron has an integer wavelength [λ], such that it might explain the quantised energy associated with any atomic transition. Therefore, at this point, we might try to consider a causal mechanism by which a photon is both absorbed and emitted within an electron transition, which starts with a question.

How might an electron physically transition between atomic levels?

Before indulging in any further speculation, it might be outlined that the emission spectrum of atomic hydrogen is divided into a number of spectral series, with wavelengths that can be derived from [7], as characterised in the diagram below. Based on this diagram and the original assumptions of the simplified Bohr model, the electron was often described in terms of a particle, even though the quantisation of energy in each orbital was explained in terms of an integer wavelength. Therefore, we might table another question.

What, if anything passes between the space between orbitals?

As a particle, we might reasonably assume that the electron would have to physically transit the space between the orbitals. However, if we proceed on the assumption that the electron has a wave structure without introducing the ambiguity of the wave-particle duality issue, we might pursue the details of just one of the transitions within the Lyman series, e.g. [n=6] to [n=1].

[8]     

In [8], we see confirmation of the wavelength of the energy released when an electron transitions between the [n=6] and [n=1] orbitals. However, we might also establish the energy-wave characteristics of the electron orbitals, as per [9].

[9]     

If we now attempt to consider the transition process in causal terms, it might be suggested that the electron wave structure must undergo a positional shift associated with [n6] to [n1], but without necessarily transitioning the space between the orbitals. For example, we might assume that a standing wave structure associated with an electron in one energy level becomes unstable and simply reforms in another orbital with a revised wavelength.

Note: In this speculative model, the entire atom is an energy-wave construct, where the idea of a particle like the electron might be described as a component quasi-stable resonance within the overall atomic energy wave-field structure. As such, an electron transition involving the absorption or emission of a photon is a reconfiguration of the energy within the atom as a whole in order to restore a more stable configuration.

However, there is another issue that appears to be rarely discussed, for we might recognise that any causal mechanism associated with this orbital transition must take some finite amount of time. So, as originally shown in [1], the energy [E] of a photon is defined by its frequency [f], which in-turn allows its wavelength [λ] to be calculated as a function of the velocity [λ=c/f]. However, if a photon has the attribute of a wavelength [λ], then it also defines some spatial distance in which any electric and magnetic field vectors would oscillate through a full cycle. As such, it defines a linear distance [x] between two points, where the [E] and [B] vectors would return to the same value. Again, based on the propagation velocity [c], we can define the cycle time [t] associated with the frequency [f] of oscillation. 

[10]   

However, we might assume that this process involves an internal transition starting with a wavelength [λ=32,800nm] within the [n6] orbital to the wavelength [λ=91.2nm] in the [n1] orbital and the associated change in energy [ΔE=13.22ev]. As outlined, this change in energy requires the emission of a ‘photon’ to maintain the energy conservation within the atom, although it might be suggested that the energy associated with the photon might not be an actual wave, but possibly more like an energy pulse with a spatial length and time duration. Based on [10], we might consider the minimal requirements of a photon, as a pulse of energy, having a spatial length of just one half-wavelength.

[11]   

Clearly, the inference in [11] is speculative and might only represent some ‘minimal value’, which depends on the electron transition in question and potentially many other details that this discussion is simply ignoring. However, if we pursue this speculation, it might lead to the idea that a photon and an EM wave are not an example of a wave-particle duality, but rather two entirely different physical processes. However, historically, it was assumed that the energy emitted from atoms had to have the attributes of an EM wave, i.e. electric [E] and magnetic [B] fields. As such, these fields were assumed to conform to Maxwell’s equations, where the wave also had the attributes of frequency [f] and velocity [c]. However, if a photon is described as a quantised unit of energy emitted during an electron orbital transition within an atom, its length [x=c.Δt] must be defined as a function of the speed of light [c] and therefore this transition must take some finite time [Δt]. This said, this outline has not really addressed the next question.

What is the shape and form of a photon?

We might consider 3 possibilities based on the assumption of finite length and time, as simply illustrated right. In the first form, left, we might assume that the Planck equation [E=hf] could infer a sequence of oscillations of unknow duration, although any estimate of time [Δt] would help determine the number of oscillations possible at a given frequency. While not supported by the assumptions underpinning [1], a photon might be considered as a sequence of EM field oscillations, again shown left, although we might question how many. Of course, this sequence would still have to be localised by time [Δt], where its total energy would also be proportional to both the frequency [f] and some pulse amplitude [A2], although it is unclear how this structure could be explained in terms of the simplicity of [E=hf]. While, the complexity associated with the waveform, shown centre, will not be pursued, some reference might be made to the idea of a Fourier series of superposition waves of multiple frequencies, which might then localise the structure of a wave packet. However, while such an approach might make sense from a mathematical perspective, we might question it as a physical solution for an orbital transition associated with a single frequency associated with quantised wavelength. Finally, we might consider whether the uncertainty principle, as it relates to the energy [ΔE] shown in [12], could provide support for the assumption in [11].

[12]   

Based on [12], it might be argued that this relationship could define the shortest time [Δt] associated with the photon energy and support the half wavelength assumption. If so, then we might have to consider the idea that a photon is actually a wave-pulse, which would appear to be different from an EM wave and might not even contain the [E] and [B] field components. However, this wave-pulse model of a photon is not without its own problems.

What determines the direction of the wave-pulse and why does it not disperse?

First, we might simply assume that the direction a photon leaves the atom is essentially random, although the issue as to why this pulse would not disperse in all directions appears more problematic. Normally, the Schrodinger equation assumes the wave function will spatially disperse as a function of time, whether this is actually the case might be questioned – see Schrodinger Issues for details.

Note: While this discussion will not pursue the idea, the OST model addresses the problem of dispersion by assuming that electrons and photons are structures with quantized angular momentum that are confined within spacetime, similar in fashion to vortices in a superfluid. However, more generally, wave models often proceed on the assumption that 1) space is a media for wave propagation, 2) waves transport energy, 3) energy is the substance of all particles and 4) energy differentials cause action – see Wave Model Considerations for more details. However, it is unclear that such a model would explain why a photon energy does not disperse in 3D space, while the MMW model forwards a more radical proposal to explain ‘The Light’.

While there are undoubtedly many unresolved issues within all the wave models, some possibly fatal, they have an attraction because of the principle of Occum’s Razor, i.e. all things being equal, the simplest explanation is the most likely. While this is not a law of the universe, it is one the universe may, at least, consider. Whether the universe really needs all the quantum fields outlined has been questioned, see Field Issues for details. Therefore, in terms of Occum’s Razor, the idea that the energy only exists in the form potential and kinetic energy, which propagates as waves has appeal. However, the following note might provide a more mainstream description, although not one that can be easily understood.

Note: For anybody wishing to understand the current state of play in describing a photon within quantum field theory (QFT), then reference might be made to a 75-page paper entitled ‘Solutions of the Maxwell equations and photon wave functions’ but summarised as follows: ‘A single photon is described quantum mechanically by the Maxwell equations, where the solutions are taken to be complex. The Maxwell equations can be written in the form of the matrix Dirac equation, where the Pauli two-component matrices, corresponding to half-spin electrons, are replaced by analogous three-component matrices, corresponding to 1-spin photons. Since the Dirac equation and corresponding Maxwell equation are fully relativistic, there is no problem with the mass of the photon being zero, as there would be for a Schrodinger-like equation’.