# 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.

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]

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*10^{22} |
3.00*10^{-14} |
6.63*10^{-12} |

X-rays | 1.00*10^{19} |
3.00*10^{-11} |
6.63*10^{-15} |

Ultra-violet | 1.00*10^{16} |
3.00*10^{-08} |
6.63*10^{-18} |

Visible | 1.00*10^{14} |
3.00*10^{-06} |
6.63*10^{-20} |

Infrared | 1.00*10^{13} |
3.00*10^{-05} |
6.63*10^{-21} |

Microwaves | 1.00*10^{12} |
3.00*10^{-04} |
6.63*10^{-22} |

FM Radio | 1.00*10^{08} |
3.00*10^{00} |
6.63*10^{-26} |

AM Radio | 1.00*10^{06} |
3.00*10^{02} |
6.63*10^{-28} |

LW Radio | 1.00*10^{03} |
3.00*10^{05} |
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*10^{8 }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]

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 |
m_{0} |
m_{k} |
Frequency |
Wavelength |
Energy |

Wave | Radio | 0 | 2.21*10^{-44} |
3.00*10^{+06} |
9.99*10^{01} |
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=mc^{2}/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, m_{K}=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 3^{rd} and 4^{th}
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]

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]

The discussion of EM Energy also touches on the idea of a ‘*Poynting
vector’ *in connection with the electric and magnetic fields, which
is said to define the energy flux of an electromagnetic field in watts/m^{2},

[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]

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]

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]

So, on the basis of [3], [6] and [8], the energy as a function of
the [E_{Y}] and [B_{Z}] 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 3^{rd} and 4^{th}
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]

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.