The Idea of Photons

The idea of a photon was first introduced by Einstein, in 1904, in a paper outlining the photoelectric effect. However, the idea of a photon was not generally accepted until Compton published a much later paper detailing the results of his famous scattering experiments in 1922.

1

So, up until this time, everybody had come to accept the idea that light, and the rest of the electromagnetic spectrum, conformed to Maxwell’s equations based on a wave paradigm. However, the following two basic equations might be seen as representative of the fundamental difference  between the wave and photon models:

[1]      1

The first equation defines a wave propagation velocity, which when associated with an EM wave in vacuum equals the speed of light [c], as supported by Maxwell’s equations. In contrast, the photon appears to be primarily defined in terms of Planck’s energy equation, i.e. a photon is simply a ‘bundle of energy’ ; although we might need to question the structure of this ‘object’ in a little more detail. However, let us start by defining the general range of the EM spectrum so that we can assign some values to the variables in [1]:

Spectrum Frequency Wavelength Energy
Gamma 1.00*1022 3.00*10-14 6.63*10-12
X-rays 1.00*1019 3.00*10-11 6.63*10-15
Ultra-violet 1.00*1016 3.00*10-08 6.63*10-18
Visible 1.00*1014 3.00*10-06 6.63*10-20
Infrared 1.00*1013 3.00*10-05 6.63*10-21
Microwaves 1.00*1012 3.00*10-04 6.63*10-22
FM Radio 1.00*1008 3.00*1000 6.63*10-26
AM Radio 1.00*1006 3.00*1002 6.63*10-28
LW Radio 1.00*1003 3.00*1005 6.63*10-31

Note: The table above has used some very generalised approximations for visual simplicity for each example within the various spectrum categories shown. Based on frequency, the wavelength is calculated from λ=c/f, where c=3*108 and energy is calculated from E=hf, where  h=6.63*10-34.

Now, in the context of the table above, it would seem that the idea of frequency is central to the description of both an EM wave and a photon, as this variable is used to calculate the energy of the photon and the wavelength of the EM wave. However, at this point, it would seem reasonable to ask a few  questions of the photon description:

How does a photon propagate energy through space?

As a particle, we might simply assume that kinetic energy is imparted to the photon at source, which inertial momentum preserves on route to some destination where it interacts with a matter-particle. However, it is unclear that there is any empirical evidence in support of this assumption. Therefore, let us turn to another question.

If a photon has a frequency, surely it has some sort of associated wavelength?

However, attempting to answer this question only appears to lead to a series of other questions about the possible, but unverified structure of a photon. Now, from a possibly naïve perspective, it might be assumed that any structure of a  photon would have to occupy, at least, one wavelength of space, such that a photon of visible light would occupy 400-750 nanometres, while a long-wave radio photon could be over 60km. Equally, if the photon is described as a bundle of energy, i.e. an energy-density, it seems reasonable to assume that this structure might have an associated volume in 3-dimensional space; hence the next question:

What shape is a photon?

Of course, even if we were to assume a simplistic spherical volume, we might also have to take into consideration the effects of special relativity, as anything travelling at light-speed would presumably be subject to infinite space contraction in the direction of motion from the perspective of an inertial observer. As such, we might ask:

Would any photon be flatten to a disk of zero thickness?

However, before getting too carried away with tabling questions that may have no obvious answer at this time, it might be more productive to outlined what is known and what can be reconciled with the EM wave description based on Maxwell’s equations. First, it might be asserted, based on Compton’s experiments, that the scattering of EM radiation by a free electron can also be described as a collision between a ‘particle’ of zero rest mass and the free electron. In this case, the energy [E] and momentum [p] of this zero rest mass particle, i.e. the photon, can be quantified as follows:

[2]      2

Based on [2], we do not necessarily have to jump to the immediate conclusion that that EM radiation is a stream of photon particles, only that any interaction with a ‘charged particle’ , e.g. electron, can result in a transfer of energy [E] and momentum [p]. In this context, it is the ‘quantum’ transfer of energy and momentum that is interpreted as a photon. Of course, from the wider perspective of this section, we have also questioned the ‘substance’ of any particle, e.g. the electron,  at the quantum level and, by inference, the description of charge being quantified as the property of a particle. While such issues are still just speculation, it might be interesting to provide some sort of comparative table showing the overlap of parameters used to describe radiation and particles, e.g.

Form Type m0 mk Frequency Wavelength Energy
Wave Radio 0 2.21*10-44 3.00*10+06 9.99*1001 1.99 *10 -27
Wave Light 0 4.42*10-36 6.00*10+14 5.00*10-07 3.98 *10 -19
Wave Gamma 0 2.21*10-28 3.00*10+22 9.99*10-15 1.99 *10 -11
Particle Electron 9.11*10-31 0 1.24*10+20 2.42*10-12 (8.20*10-14 )

Note: The last 2 entries are highlighted because the frequency-energy of gamma radiation actually exceeds the mass-energy of an electron. Of course, an electron at rest [v=0] would have an infinite deBroglie wavelength or zero frequency. However, we might still consider the conversion of the electron rest mass into a frequency using [f=mc2/h] as shown in the table, such that we might also assume that some wavelength must still be associated with this frequency, although it cannot be the deBroglie wavelength. This said, we might reasonably assume that any wave structure associated with a matter-particle restricted to propagate below the speed of light [c] must be different to an EM wave.

At this point, it might be highlighted that the frequency used for the electron would equate to the Compton wavelength, while a particle with a velocity [v] would also have a deBroglie wavelength. Therefore, the energy shown for the electron in the table above equates to the rest mass energy of the electron only, i.e. [v=0, mK=0], where this energy is normally much greater than the kinetic energy unless relativistic velocities are involved. However, the main purpose of this section of the discussion is to simply table questions that have arisen throughout the  previous review of scientific theory. In this context, the most fundamental question appears to be:

Is physical reality predicated on particles or waves?

While quantum mechanics might say both, it might also be argued that the duality position appears to be little more than an interim holding position in the absence of any acceptable alternative. However, on the other hand, the particle model in isolation always seems to run into the same basic question:

What are fundamental particles made of?

If the retort is just energy, then this scalar quantity seems to require a mechanism for the propagation of energy in space and time. However, any model based on only waves would, according to the table above, have to described two distinct mechanisms of energy propagation, i.e.

  • The waveform for radiation, propagating at light speed [c], with a single frequency determined by its Compton wavelength and the speed of light [c].

  • A possible composite waveform for particles requiring two frequencies determined by the Compton and deBroglie wavelength, which is also capable of explaining all the emergent properties of a particle and the ability to maintain a stationary position in space.

At this stage, this discussion is not proposing any solution to any of the issues outlined above, as the goal is only to table issues that may not necessarily be raised in most standard references. However, within the scope of this opening section, it has been suggested that there may only be 3 fundamental units, i.e.

  • Space: metres
  • Time: seconds
  • Energy: joules

In this context, ‘the idea of charge’ becomes a specific manifestation of energy, although such a suggestion would need to be supported by some tangible mechanism that has not been described. However, it has been suggested that energy, as a scalar quantity, would also require some mechanism to explain its movement in space and time. So far, the only option that seems to be supported by any known science is the physics of a wave, which returns us to the fundamental question:

Is physical reality predicated on particles or waves?

In many respects, we might realise that this discussion regarding photons and EM waves is also a reflection of the question above. However, if we were to remove the concept of mass, as a fundamental unit, on the grounds that it is simply a convenient description of an energy-density, then we are forced to consider the possibility that energy may have to be described in the form of some sort of a wave structure. Equally, based on [2] above, the idea of a photon as a ‘bundle of energy’ might only be verified in terms of its interaction with a charged particle, i.e. the ability to transfer energy and momentum. If so, there might be a need to further consider exactly how EM waves are said to propagate energy in the vacuum of space. In part, some earlier discussions, as listed below, have already gone some way into outlining the concepts and issues associated with this model, which this  discussion is now only adding some commentary rather than attempting to replicate:

While there may also be  some value in reviewing the derivation of Maxwell’s equations  the discussions above are more relevant to the issue of EM energy propagation. For example, the discussion of ‘EM Wave Propagation’ focuses on how Maxwell’s 3rd and 4th equations form the basis of a wave equation, which in principle may not appear so different to that previously derived for a ‘mechanical wave’, e.g.

[3]      3

In the specific description of Maxwell’s EM wave equation, the implied amplitude [A] is replaced by either the electric [E] or magnetic [B] field, while the propagation velocity is changed to [c]. However, while the description of a mechanical wave, conforming to [3], is supported by the physics of a propagation media, this doesn't seem to be the case for EM waves. Therefore, we might still wish to table the question:

Do Maxwell’s equation really explain how  EM waves or photons propagate in vacuum?

In this context, the discussion of 'EM Energy' attempted to review the implications of the interaction of the electric [E] and magnetic [B] fields, when described in terms of an energy-density. This point was also outlined in ‘the idea of charge’ based on the following SI equations, where the square of the amplitude of the electric [E] and magnetic [B] fields are equivalent to an energy-density:

[4]      4

The discussion of EM Energy also touches on the idea of a ‘Poynting vectorin connection with the electric and magnetic fields, which is said to define the energy flux of an electromagnetic field in watts/m2,

[5]      5

In the context of [5], the Poynting vector [S] is said to represent the flow of energy through a surface, where its direction is that of the propagation and its magnitude corresponds to the intensity [I]. However, while the form of [5] describes the mathematical vector product of the electric [E] and magnetic [B] fields, which points in the direction of the propagation of an EM wave, it is not clear that it actually provides a description of any physical mechanism. In the subsequent discussion of EM radiation, the applied physics of a dipole antenna are considered, where the source of EM radiation is an oscillating charge under going acceleration. Of course, in the wider description of a photon or EM radiation, the source may no longer exist, so that we again return to the issue of the self-propagation through space, i.e. a vacuum. Clearly, there appears to be an inference that some form of interaction between the electric [E] and magnetic [B] fields explains the self-propagation, which we might try to examine in terms of the following energy-density relationship:

[6]      6

While the derivation of [6] is outlined in the EM Energy discussion, we might combine the results in [6] such that it might implied an associated velocity [c]:

[7]      7

However, the inference of [7] as an explanation of the propagation velocity [c] is not directly supported when the definition of [E] and [B] are switched to Gaussian units, i.e. the result is just a number. It might also be pointed out that Maxwell’s equations proceed on the basis that the electric [E] and magnetic [B] fields are two orthogonal in-phase transverse waves, which we might characterise in terms of the following sine wave functions:

[8]      8

So, on the basis of [3], [6] and [8], the energy as a function of the [EY] and [BZ] wave amplitudes will be in-phase and therefore have a combined value that falls to zero at some point in space. At face value, this appears problematic in terms of any implied self-propagation mechanism, which cannot be aggregated over some larger section of the wavelength.

So is there a propagation mechanism in terms of either an EM waves or photons?

Clearly, some key aspects of Maxwell’s equations may not have been fully understood, when it comes to actually describing how an EM wave propagates in space. For example, if we step back from all the equations for just a minute, we might still question the fundamental nature of an electric field, which is normally described as existing between two charged particles. The existence of the magnetic field might also be questioned further in the sense that it only exists in a frame of reference where the ‘charged particles’ are in motion, i.e. constant velocity. Finally, only in the case of a charged particle undergoing acceleration, does the idea of EM wave propagation emerge, although we might still need to question why an electron does not radiate in an atomic orbital or when observed in a gravitational field. Of course, such questions might then be compounded, if we pursue the idea that particles, charged or otherwise, do not exist at the lowest level of reality. Therefore, when we consider the results of combining Maxwell’s 3rd and 4th equations in either the SI or Gaussian system, it is not clear that we really have a description of a physical mechanism or just a logically deduced mathematical representation:

[9]      9

So while the EM wave description seems to share the same basic mathematical logic as a mechanical waves, as per [3], the actual exchange mechanism between potential and kinetic energy in the absence of any propagation media is not so obvious. So, in a sense, it might be argued that we have returned to the epistemological versus ontological argument. If you accept the epistemological position, such that physical reality is not a requirement to do calculations, then maybe the equations are all that are required. However, in the case of the ontological position, it might be argued that some physical mechanism is still required to explain the cause of any effect. In this latter respect, there seems to be scope for further speculation.