Chapter 1 Space and Photons
Empty space has properties that enable it to transmit electro-magnetic radiation. This presentation describes how those properties support photons and gives them their properties.
That the universe exists is obvious. We are part of it. We look around and we experience our little corner of it in so many ways. Why it exists is another story. One of the original explanations was “In the beginning God created the heavens and earth” (Gen 1, 1). The book of Genesis went on to explain how it was completed by seventh day. The first serious variation to that theory came from Muhammad. He pointed out that al-ilah (“the god” in Arabic) completed the task in seven periods of time. He did not define the length of those periods. Early humans saw the universe as the Earth, the moon, the Milky Way and other fixed stars, a few wandering stars and a couple of fuzzy patches (nebulae) that could be seen in the night sky with unaided eyes.
The emergence of modern science saw other explanations for the universe’s existence. Telescopes showed that the nebulae were other galaxies like our Milky Way. More powerful telescopes showed more distant galaxies. The universe was much larger than previously imagined. By the early 20th century CE the generally held view was that the universe was infinite and static. Further studies suggested an infinite universe would collapse under its mass. Observations showed that the light from distant galaxies was redshifted. The further away were the galaxies, the greater was the redshift. Hubble (1929).
That led many scientists to believe the universe was expanding and that it started from a Big Bang (Lemaitre 1936). By the 1970’s CE the Big Bang theory for the formation of the universe was widely accepted. It goes something like: “In the beginning there was nothing (or something – we don’t know yet). 13.82 billion years ago it explode in a Big Bang, which created space and time. The whole universe expanded, space, time and light. What astronomer can see represents only 4% of what is required to explain its existence. The remainder is dark energy and dark matter. Scientists have been searching for signs of either and haven’t found anything after many decades of searching”. And so it goes on!
All rather confusing! If you really want to find out what is going on, the best way is to build a universe step by step from scratch. To do that, it is best to start out with what we all know exists. Everybody knows about the three space dimensions, x, y and z. Nobody has detected any other dimensions, so we won’t use them. People are familiar with time. It ticks by at the rate of 60 seconds per minute, 60 minutes per hour, 24 hours per earth day, etc. It ages us all. We won’t worry about hypothetical particles like quarks and gluons that haven’t been independently isolated and detected. We will use measured physical constants known, physical principles and the most common component in the universe.
1.2 Empty Space
It doesn’t take too much to realize that the universe is mostly empty space. That doesn’t mean there is nothing there. Empty space is occupied by fields, electric, magnetic and gravitational. In turn those fields are generated by charged and neutral particles. No particles, no fields! So to build a universe we must first build us some particles. The only thing we have to do that out of is empty space – nothing!
Empty space may be nothing. But that nothing has some interesting properties. It is able to support and transmit electric, magnetic and gravitational fields. The electric fields are facilitated by a property of space called its electric permittivity, denoted εo. Magnetic fields are facilitated by the magnetic permeability, denoted μo, of free space. Their importance was well presented by Maxwell (1865). Gravity is facilitated by the fabric of space-time (Einstein, 1915, 1916, 1952 b). We need first to consider the electromagnetic properties of free space to derive matter with mass. Then we can consider the effect of mass on the structure of space and time and its facilitation of gravity.
There are four important features of electric permittivity εo and magnetic permeability μo. εo can transmit and resist the passage of an electric field through free space. It can store electric energy in free space. Similarly, μo can transmit and resist the passage of magnetic fields through free space and store magnetic energy. The other important feature is that the two are totally interconnected. Whenever there is a change in the electric field in one direction, there will be a change in the magnetic field in a direction perpendicular to it. And vice versa, a changing magnetic field will produce a changing electric field perpendicular to it.
Maxwell went on to point out that the combination of a changing electric field in one direction in free space, say x, would generate an associated magnetic field in a second perpendicular direction, say y, and the assembly would travel in the third dimension, say z, at the speed of light determined from
εo.μo = 1/c^2. (1.1
The measured value for ε0 is 8.85418.. x 10^-12 Farad per metre (F/m). The value for μ0 is 4π.10^-7 Henry per metre (H/m).
The speed of light, c, has been measured experimentally as 2.9979.. x 10^8 m/sec. Many experiments established that there were experimentally verified by diffraction measurements, the generation of radio waves and others observations. They had a frequency ν and wavelength λ, related through
νλ = c= 1/√(ε0.μ0) (1.2
Together the work of Planck (1900 a, b) and Einstein (1905 a, b, 1952 a) established that those electromagnetic waves were discrete packets of electromagnetic energy. Each packet, now called a photon, has energy E given by
E = hν (1.3
where h is Planck’s constant, 6.62607.. x 10^−34 m^2kg/sec. They were experimentally verified by predictions of the shape of black body radiation and the photoelectric effect. They still retained their properties of wavelength and frequency.
Having established some of their properties, it is necessary to describe a structure of photons that can give them those and other properties. The starting point is εo and μo. This presentation rejects the Born model and its associated Copenhagen convention that the photon is a point particle that has its various properties mathematically attached in a Hamiltonian (Chandrasekar, 2012). That enables the correct answer to be obtained mathematically. It does not give any insight into its structure.
The universe does not operate on mathematical principles. It operates on physical principles. Mathematics is required to check the magnitude of the physical principle. If the mathematics associated with the physical principle match observation, the physical theory has some validity. Mathematics by itself does not provide a physical reason for an event to occur. This representation starts with the Einstein (1905 a, b, 1952 a) – de Broglie (1957) model (Vigier, 1992; Evans and Vigier, 1994) that a photon can be described as a wave function Ψ by giving a mathematical and physical description to Ψ using classical concepts.
1.3 The Role of εo and μo
One of the properties of mass is its inertia, its ability to resist change. A moving mass has momentum, mass multiplied by speed. Momentum has the ability to impart inertia to another body. The Einstein-de Broglie model implies that photons have momentum, given by
p = E/c = hv√(εo.μo) (1.4
Momentum is a property of mass multiplied by velocity. From known properties of free space and observation, equation 1.4 gives photons a mass
mp = hν.εoμo (1.5
That photons have mass was one of Einstein’s conclusions (Einstein, 1905b, 1952b). It has been verified experimentally (Pound and Rebka 1959; Pound and Snider; Pound 2000). It was well expressed by van der Mark and ‘t Hooft (2000). This model agrees with their work.
Equations 1.1 to 1.5 establish some fundamental properties of photons.
i Photons are transmitted through space by its properties of electric permittivity and magnetic permeability.
ii A photon consists of an electric field E oscillating in one direction with an inseparable magnetic field B oscillating in unison perpendicular to it and the combination moving at c through space in the third direction perpendicular to both E and B. The oscillation is characterised by its frequency v and wavelength λ, through equation 1.2.
iii εo and μo can both transmit and resist the passage of electromagnetic energy, as well as store it. This energy comes in discrete electromagnetic packets now called photons. Each photon has energy given by equation 1.3.
iv Their energy gives them momentum, indicated in equation 1.4.
v In turn their momentum gives them mass, given in equation 1.5.
One of the properties of mass is its ability to resist the application of a force and hence energy. Energy is applied to εo and μo. Combined they resist the passage of that energy.(If they didn’t, the energy would travel with c = infinity.
Although c is very rapid, it is not infinite.) That ability of εo and μo to resist the application of energy gives the property of mass to the disturbance. This gives the disturbance inertial mass with a velocity, giving it momentum. That momentum can be imparted to an object upon which the photon impinges, increasing its mass.
This presentation shows the structure of a photon’s wave function Ψ and how that structure gives photons many of their properties. Those properties of photons originate from the properties of free space, the properties of nothing.
Before that can be done, we need to answer the question: How do εo and μo, which are properties of nothing, support electromagnetic radiation? In the physical world, nothing is nothing and you can’t take something away from nothing. That precludes any suggestion of any possibility that electromagnetic radiation causes oscillations about median values of εo and μo. However you can add something to nothing. The answer appears to be that the presence of the electric and magnetic fields increases their values. Electromagnetic waves become oscillations in εo and μo about their increased values.
Some support for that idea comes from the refractive index of optically transparent media, such as glass. The presence of the matter with the appropriate values increases the refractive index of that material, taking it from 1 in free space to n > 1. The speed of light in a material with refractive index n is given by c/n. From equation 1.1 this means that n = √(εn.μn/εo.μo), where εn and μn are the respective electric permittivity and magnetic permeability of the substance that has a refractive index of n.
Referring back to the properties of εo and μo, the addition of electromagnetic energy is stored in them by increasing the product of their values. The rate at which their values can change determines the resistance offered by them to the passage of photons.
1.4 Physical and Mathematical Models of Ψ
Having established those fundamental properties of photons, it is necessary to establish the form of their wave function Ψ. In its simplest form, a photon is generated when energy E is imparted to ε0 and μ0, generating an oscillation of frequency v and wavelength λ. The oscillation starts out from zero, building E to a maximum E0 and B to a maximum B0, each of one polarity, before decaying back to zero. The oscillation then repeats in the opposite polarity before again going back to zero. In its simplest form, that describes a single wavelength plane polarised photon, as illustrated in figure 1A. An oblique presentation is used to give a three dimensional effect. The fields rise to a maximum in one direction, reverse to zero before repeating their fields in the opposite direction and again reverting to zero. The whole oscillation travels on the central axis perpendicular to both fields at the speed of light c. Those fields are strongest close to the axis diminish with the distance from it. In the absence of other information it is suggested the electric and magnetic field intensities Ed and Bd at distance d from the central travel axis are given by exp-d/λ giving
Ed = E0exp-d/λ and Bd = B0exp-d/λ (1.6
That gives the wave function Ψ for a single wavelength plane polarised photon as
where k is the wave number and ω is the phase frequency. Other expressions can be used. It should be noted that a positive field in one direction means a negative field in the opposite direction, giving the representation in figure 1.1 B. This also indicates that there is energy stored in ε0 and μ0. Energy is imparted to start the oscillation. As it travels, it rises to a maximum, goes back to zero and restarts in the opposite direction. That cannot happen unless that energy was stored in ε0 and μ0. As mentioned in equations 1.4 and 1.5 above, this gives photons their properties of momentum and mass. When the oscillation is absorbed, its momentum is imparted to the absorbing particle, also altering its mass. Integrating over one cycle gives Ex = Ey = Bx = By =0.
Another interpretation of a single wavelength plane polarised photon is shown in figure 1.2. For the field to extend beyond the photon’s travel axis, it must impart some of its energy into that surrounding space. The energy permeating that space is illustrated in figure 1.2. The arrows away from the travel axis represent “photons”. They also provide a new direction for the photon if its original passage is partially blocked. In that manner, figure 1.2 illustrates the instantaneous strengths of the electric and magnetic fields. For that reason those “photons: are hereinafter referred to as field photons. They are the electric and magnetic fields associated with the photon. The length of each field arrow represents the energy contained within its segment, not its wavelength. The total of all of these arrows equals the energy hν of the photon.
Figure 1.1 Oblique schematic illustrations of oscillations in the electric, E, and magnetic, B, fields associated with a single wavelength plane polarised photon.
Figure 1.2 An illustration of a single wavelength plane polarised photon in which the electric and magnetic fields are as field photons. A illustrates an oblique side view. B illustrates the end view as seen from its direction of travel.
An electric charge placed near the photon’s axis and in the electric field plane would experience an attraction towards and repulsion from the photon as it passes. Similarly, a magnetised object, monopole or otherwise, would experience the photon’s magnetic field if it were similarly positioned near the photon’s magnetic field plane. Using the quantum electrodynamics concept of force being due to photon exchange, as the first half of a photon passes a charged (or magnetised) particle, one of the field photons is exchanged with the particle, causing the attraction (or repulsion). As the second half of the photon passes, another field photon. That simplistic representation requires two significant modifications. One is that photons are not necessarily single wavelengths. That is determined from time taken from when an atom starts to emit a photon until it is finished being n/v, where n is an integer greater than or equal to 1. At this stage the value of n appears to vary with different situations. It is often represented as being less than 10, somewhat as illustrated in figure 1.3.
That gives the wave function Ψn,p for a plane-polarised photon of n oscillations as
where n is the number of oscillations in the photon and E*x and B*y are the maximum field strength of the central oscillation. Figure 1.3 illustrates the situation where n = 7. Equations 1.8 and figure 1.3 illustrate that the oscillation starts out small, building up to a maximum E*x and B*y before decaying back to zero. While it is decaying back to zero again as the photon passes each space point. Equations 1.8 are one equation set that fulfills those requirements. Other equation sets are possible.
Figure 1.3 Schematic illustrations of oscillations in the electric, E, and magnetic, B, fields associated with a plane polarised photon consisting of seven wavelengths.
The second modification required is that most photons are circularly polarised, not plane polarised. Circular polarization means their electric and magnetic fields rotate as the photon moves, as illustrated in figures 1.4. It uses the arrow representation in figure 1.2. Figure 1.4 A illustrates the positive field making three complete 360˚ revolutions over three wavelengths. The field starts from zero, rising to a maximum at λ/4 before going to zero again at λ/2 while rotating through 180˚. This process is repeated once more to complete one wavelength. Because the polarity reverses after one wavelength, the same situation is repeated for the second half of the wavelength. This is repeated as the photon travels.
This gives the wave function Ψ1,c for a single wavelength circularly polarised photon as :-
Figure 1.4 Oblique schematic illustrations of circularly polarised photon oscillations in the electric, E, and magnetic, B, fields, with those fields rotating 360˚ in one wavelength. A shows an isometric view of the electric field making six revolutions in three wavelengths. B shows the four fields in a horizontal isometric view of one wavelength. C shows the distribution of the fields when looking at the approaching photon.
where ω is the rotational velocity. Integrating equations 1.9 over one complete cycle gives Ex = ½ E0, Ey = 0, Bx = 0, By = ½ B0. That is reflected in figure 1.4 C. The vertical (Y) values of E and the horizontal (X) values of B cancel each other out.
Figure 1.4 B illustrates the situation involving a single wavelength circularly polarised photon. Just as plane polarised photons have multiple wavelengths per photon, so too do circularly polarised photons.
Figure 1.5 illustrates the situation of a circularly polarised photon consisting of seven wavelengths. The photon rotates once every wavelength. Note that to show the rotation, the electric field is displayed in an oblique manner. The oblique presentation gives the appearance of the electric field below the axis, as mentioned earlier in relation to figure 1.4.
Drawing the remaining three fields, − ve, S and N would create further confusion and is not attempted. A circularly polarised photon of n wavelengths would start out with a small amplitude its fields rotated while going through their respective maxima and minima every half wavelength, build up to a maximum and decay back to zero. Each half wavelength would increase in magnitude, reaching the maximum intensity by the middle oscillations, decaying back to zero as the photon passes through that region of space.
Figure 1.5 Oblique schematic illustrations of oscillations in the positive electric fields associated with a circularly polarised photon consisting of seven wavelengths.
The above gives a physical and mathematical representation of different forms of photons. The electric and magnetic oscillations in εo and μo. The remainder of the chapter deals with other properties of photons. Oscillations in E and B give it wave properties. Its limited extent gives it particle properties. Unlike the standard model they both exist in photons at the same time. Other properties are also described.