The words used to describe the fundamental world are notoriously difficult and the source of many confusions. As best we can, we define here how specialist terms are used on this website.

Term used in this book for the technical definition of what is often called acceleration. Unlike the everyday term ‘acceleration’ below, it is about the separation of two things and excludes increases in speed due to gravity – see acceleration, below.

Two meanings: the everyday increase of speed of, say, a car and the technical meaning of two things being separated by a force. To avoid confusion, we use the term ‘Acceltion’ for the technical use. This is explored in detail at the start of the Fifth Heresy: Gravity is not a force but the effect of the slower speed of the Field in the presence of mass and increases in speed (kinetic energy and momentum) caused by gravity are not acceltions.

The maximum distance of separation is determined by the total amount of force used and two masses involved.

The rate of separation is determined by the speed that the force is applied and the size of the two masses involved.

A three-dimensional, reciprocating wave, normally spherical in shape. Some variable stars act as ball-waves, expanding and contracting regularly. Fundamental ball-waves are started by area of divergent field density, low or high. If we start with an area of high field density, it will naturally expand, gaining momentum such that it leaves behind an area of low field density. The visual analogy is with a stone dropped in water that force the water higher, this then expands out in a circle and behind it comes an area of lower water-level, forming a circular wave. The central area, which now has the opposite divergent field value, attracts the wave back (You can see this with the water wave example as well, where the return wave will repeat the process, sending out another ripple, but most of the wave energy continues outwards.) Fundamental waves must retain a fixed harmonic size, so are unable to split like a water-wave. Instead, they reciprocate without energy loss.

The wave moves, and so reciprocates, at the speed of the Field, so, to other ball-waves, it provides an apparently solid surface at the edge of the ball. Because they prevent other things from occupying the same space and time, ball-waves are categorised as ‘things’ (Fermions) and can be described as ‘particles’ – but they are not the same as the QM mathematical use of the term ‘particle’ to designate an object of zero size.

Ball-waves can absorb the kinetic energy of an F-wave that has the right wavelength for them to harmonise with. They can also emit energy as spherical F-waves at specific wavelengths. Momentum (vectored energy) is not involved in harmonic absorption and emission.

When a ball-wave is hit by either another ball-wave or an energetic F-wave, it shares their kinetic energy and momentum. This requires the ball-wave that has been hit to shorten its wavelength in the direction away from the side it was hit, accelling it in that direction. The shortening of the wavelength absorbs kinetic energy, a characteristic we call inertia. This, combined with solidity, is known as mass. Electrons, protons, neutrons and positrons are the best-known ball-waves, mostly formed at high energies from longitudinal waves in the early universe. However, there is a zoo of other but unstable ball waves, both mesons (related to protons and neutrons) and higher energy forms of the electron and positron. These are formed in high energy events in stars and accelerators.

From the Greek ‘to measure’. Each additional dimension allows relationships between locations an additional degree of freedom. In one dimension, a change in the relationship (distance) between points A and B must change the distance between A and all the other points. In two dimensions, a change in distance between A and B can leave the distance between A and point C unaltered. In three dimensions, when the distance to B changes the distance between A, C and D can be unaltered and so on for four and more dimensions. The issue is not the unaltered relationships but that they are independently variable, unaffected by any variation in the relationship to the other points. The more independent variables, the more dimensions.

While time is sometimes called a dimension, we will exclude it from our definition – it is not fundamental but a product of distance and the speed of the Field.

Longitudinal waves in a three-dimensional environment form a spherical surface with a two-dimensional wavefront at right angles to the direction of the wave. Sound waves and shockwaves are familiar longitudinal waves in a 3-D environment.

Lateral waves, such as water-waves, in a three-dimensional environment, have a longitudinal, one-dimensional, wavefront at right angles to both the direction of travel and the direction of oscillation. Lateral waves can only exist in a three-dimensional environment if they are constrained to one or two dimensions, such rope waves or water waves. Unconstrained, they become longitudinal waves.

Ball-waves move in three directions, where the movement is into and out of a (mostly) spherical centre of attraction. An electron surrounding a proton in a hydrogen atom is an example of a ball-wave.

In four dimensions waves can move in four directions. In 4-D, ball-waves can only exist at a small scale because an inverse cube law applies. The same rules apply to higher dimensions, 5-D, 6-D and so on, with the scale of possible things getting orders of magnitude smaller with each additional dimension.

A fundamental wave, the most famous of which is light. The Heretics refer to EM waves as fundamental waves or F-Waves. They can have a great variety of wavelengths from radio waves, kilometres in length, through microwaves in the centimetre range, to infra-red waves, light waves, ultraviolet waves, X-rays, gamma rays and the extremely energetic waves found in ‘cosmic rays’. The shorter the wavelength, the higher the energy content of the wave. They consist of alternating areas of high and low field values expanding out from their point of origin and are normally emitted with a spherical wavefront.

All fundamental waves travel in a vacuum at the speed of the Field, commonly known as ‘The Speed of Light’, 300 million metres per second.

A ‘negative’ ball-wave centred on an area of ‘high’ Field values, as opposed to a ‘positive’ positron, which is centred on ‘low’ field values. Here ‘high’ and ‘low’ simply denote opposite values, we have no idea what they are opposite in.

The electron’s radius is about 2.8 x 10-15 metres. It has spin in units of one half and, in the presence of positive charges, forms semi-stable pairs (Cooper pairs) with electrons of the opposite spin, possibly by forming a standing ball-wave together.

To other electrons, it has a surface that resists them, so has rest mass, specifically 9.11 x 10-28 g. But protons and neutrons, being much smaller and ‘harder’, go through the surface of the electron ball wave and can sit inside one or many electron ball-waves, forming an atom. In atoms the number of electrons matches the number of protons to achieve overall EM neutrality. That is that, the balance of higher and lower Field values in the atom overall is the same as the average Field value.

Electrons cannot ‘react’ with protons, due to the size difference, despite the opposite Field values at their centres.

In Hydrogen and Helium, electrons simply form a ball round the nucleus but, in larger atoms, electrons adopt more complex wave patterns around the nucleus. Electrons in atoms can resonate with F-waves to absorb energy from them but frequently re-emit an F-wave returning to their base-level energy value.

Electrons can form semi-stable pairs with protons under the influence of the Strong Nuclear Force or fourth dimension to form neutrons. The conditions for this to happen are unknown, apart from under conditions of extreme gravity forming a neutron star. Neutrons are unstable without associated protons and decay into a proton and electron in about 15 minutes.

At the fundamental level there are only two, closely related forms of energy from which all other forms of energy we see are derived.

  • F-wave energy lies in the difference between the high and low values of the wave and so has no specific location within the wavelength. The shorter the wavelength the higher the `F-wave energy.
  • Ball-waves have energy in two forms: the first is same as F-wave energy, the wavelength energy of its reciprocating ball-wave. Smaller ball waves, like protons, with shorter wavelengths than electrons, have more energy. The second form of energy ball-waves can have is kinetic energy. This is vectored – it is only in one direction – and is known as momentum. It is caused by the shortening of the ball-wave in the direction of movement – which is relative to the observer.

Heat is the kinetic energy of a collection of small particles. Nuclear energy is the kinetic/heat energy released by reforming atomic nuclei into arrangements closer to equilibrium.

Gravitational potential is treated as negative energy: it increases the speed of objects towards each other – and hence, their relative kinetic energy.  The effect of gravity is to turn gravitational potential into kinetic energy.

The ‘No Special Place’ rule means that things and waves that have differing qualities and that are able to interact, will do so in a way that, on average, makes them more similar. ‘Entropy’ is generally taken to be the measure of the degree to which this happens, the amount a system has moved closer to equilibrium. However, the history of the word ‘Entropy’ has left it with at least five different meanings – as well links with ideas, such as ‘order’ and ‘probability’, that have historically caused much confusion. Because of this confusion, the Heretics avoid using the term ‘Entropy’ and instead we use appropriate equivalent phrases. See the Heresy on Entropy for a full discussion.

Derived from the Greek words for “equal balance”. If things are ‘in equilibrium’ that have the same characteristics. Most commonly ‘equilibrium’ is used to refer to temperature, where it means that groups of two or more objects have the same average kinetic energy. The ‘No special place rule’ means that objects able to influence each other do so in a way that makes them more alike, so bringing them closer to equilibrium.

These are patterns that have properties different to those attributable to the individual elements that make it up. For example, a tiger is an emergent phenomenon of living cells. Waves are emergent phenomena – a sound wave, for example, is made up of patterns in air molecules.

A field is any volume or area that can have a different value at each point. We refer to the fundamental Field as ‘the Field’ with a capital F, see below.

Something that has different values at every location throughout space. Field values can be both lower and higher than the average value, rather as air pressure can be lower or higher than average air pressure. Neighbouring areas of the field affect each other: if their Field values differ they move to become more similar. This can form waves of alternating higher and lower field values that travel through the field. The speed that each area affects its neighbour, determines the speed of waves’ movement through the Field. The example of sound in air forms a close analogy. Normally references to the Field and the speed of the Field refer to the field in a vacuum. The speed of the field in the presence of matter is slower than it is in a vacuum and this effect also moves outwards as neighbouring areas with different Field speeds affect each other.

The Field has constant small-scale turbulence. It can be compared to ‘white sound’ or a choppy water surface, where the pull to flatten out is constantly disturbed by small, irregular wavelets, consequences of innumerable disturbances and no frictional damping.

We do not know the nature of the Field at all or what its varying values mean, other than that divergent values  between neighbours  affect each other towards their average value (a consequence of the “No Special Place’ rule. While many comparisons are drawn between waves in the Field and sound in air, air is a medium with defined physical characteristics, including being made up of physical particles and the Field is not.

The fundamental Field fills all space. It can vary in value. Variations in the Filed value of one part (called a ‘unit’ of the Field) affect their neighbouring units, so that they move towards a value average between all their starting values. The time it takes for this change to happen determines how fast waves move through the Field.

Regular longitudinal oscillations moving through the fundamental Field, moving energy across space at the speed of the Field. ‘Electromagnetic’ waves such as light are F-waves. Because there is nothing smaller than the fundamental wave for them to break into, when an F-wave is absorbed by harmonising with something, it is absorbed completely – however large its wavefront has become.

  • Fundamental waves are longitudinal waves of alternating high and low field value, similar in form to sound waves.
  • When a fundamental wave is emitted from a spherical source, such as an electron, it has a spherical wavefront. This wavefront can be distorted or focussed by reflection, lensing and other effects, just as with a sound wave.
  • Fundamental waves vary in energy content. The shorter the wavelength, the more energetic.
  • Like all waves, fundamental waves move at the speed determined by the medium they are moving through. In a vacuum, they move at the ‘Speed of the Field’, 300 million meters a second, they move more slowly in the presence of mass and more slowly when travelling through matter.
  • F-waves interact with things in different ways, depending on their energy:
    • At low energy, ball-waves block fundamental waves. Depending on the relationship of the wavelength to the size of the objects hit, F-waves reflect off them or they allow the transit of the waves but slow their speed. F-waves go slower through materials than in the empty Field.
    • If something, typically an electron in an atom, harmonises with the wavelength of a fundamental wave, it will absorb the energy of the F-wave at one point and one time, ending the whole F-wave immediately, however large its wavefront has become. This does not transfer momentum.
    • At medium energy, F-waves can transfer some or all their momentum to things they hit. This can be an electron, the photoelectric effect; or an atom, the Compton effect. The F-wave gets a longer wavelength in the process and accelerates the things hit. This can only be done if the wavefront of the F-wave hits two things at close to the opposite point on its wavefront or if the thing emitting the F-wave is able to recoil to conserve momentum.
    • Above a high energy, around 1.02MeV, an F-wave will turn into two ball-waves, an electron and a positron, much like a thin stream of water turning into drips. (This requires an atom or similar nearby to absorb the excess momentum.)
    • Fundamental waves are not subject to the constraints of space and time that things must follow. Although their wavefront propagates at the speed of the Field, the different parts of the wave can affect each other ‘non-locally’, that is, regardless of distance and time.

The effect that makes objects move relatively closer in proportion to their joint masses. In common parlance, the force of gravity increases the speed that objects approach each other. This effect is a consequence of the slower speed of the field in the presence of mass (and seen from a frame of reference further away from mass).

Mass is the combination of two characteristics of ball waves:

Solidity: the resistance of a ball-wave to another ball-wave being in the same time and same space.

Inertia: when hit by something, part of the energy accelerates the whole ball wave and part is absorbed in shortening the wavelength of the ball-wave in the direction of motion – keeping the internal ball-wave speed plus the overall movement to the speed of the field. Hence: resistance to acceleration/acceltion in the direction of motion. The same applies if it is hit by a ball-wave.

The presence of mass reduces the speed of the field (when seen from a frame of reference further away from mass). This has the effect of attracting both ball-waves and F-waves.

Substance through which waves move. The medium determines the speed of the wave. Sound waves in (sea-level, etc.) air moves at 456msec-1

Neutrons are similar to a proton in size but slightly heavier and with no charge, no net central field value variance. It seems that Neutrons are a combination of proton and electron, held inside the range of the strong force effect, a combination that is unstable on its own, breaking into a proton and electron in about 15 minutes. The proton part seems to be at the centre of the neutron, which has a distinctly positive element, surrounded by a much shrunk electron, giving the neutron a slightly negative exterior which enables it to act as a glue for protons in the nucleus. This also supports the ‘donut’ picture of electrons coming from their hFv expansion origin. We do not know how the neutron, which is essentially just a compressed hydrogen atom, comes to be so compressed, although once compressed we can see how the (4-D) Strong Force effect would keep it there in the presence of external positive charges.

Neutrons are essential to the structure of all atomic nuclei apart from Hydrogen and are also critical to the way atoms fuse to provide steady energy and create elements heavier than hydrogen.

Behaviour does not differ between locations. If things are different, they will become more similar in any aspect where they can affect each other. If there is no reason for things to differ, then they are the same. The No Special Place Principle is a logical requirement of consistency.

The term ‘particle’ is used in QM for a bundle of values in one location, for example, an electron. If the values are spread over space, they are properties of ‘virtual particles’. Like the number 3, this is an extremely useful mathematical concept that has no physical expression separated from a physical example.

The word ‘particle’ can be used for ball-waves, because they are in a definite location and resist other ball-waves from occupying the same space. However, as the wave inside the ball-wave moves at the speed of the Field, they can be ‘seen’ by F-waves as being waves – hence the absorption and emission of F-waves by electrons. In the past, the term ‘particle’ has also been applied to F-waves, on the grounds of their point absorption but this seems confusing.

Ball-wave very similar to the electron but with a centre that has low field values (rather than the electrons hFv. It merges with an electron to turn into an F-wave. Because of the preponderance of electrons, positrons are, in practice, very short-lived. The longest it has been seen to exist (at non-relativistic speeds) is 150 nanoseconds.

Ball-wave much smaller than the electron or positron, with a radius of around 8.7 x 10-16m and a weight 1,836 times the weight of an electron. It cannot ‘react’ with the electron because of the difference in size but there may be something else preventing it reacting as, even when an electron is compressed with a proton inside into a neutron, which is only marginally bigger than the electron, they do not react together (spin?). In some scattering experiments the proton ‘interior’ has shown a distinctly tripolar patterns. In the standard model both the proton and neutron are composed of three ‘quarks’ linked by gluons.

The rate of change of the separation distance between a thing and another thing. The speed of a thing is best given as the rate of change of the distance of the thing to yourself as it is very easy to get things wrong about speeds measured anywhere other than in relation to your own frame of reference. The Sermon on Relativity adds detail to this.

In common parlance, speed relates to the rate of change of distance coordinates relative to the surface of the earth, but we will specifically not be using the term in this way.

The stage on which things move and is measured by the time it takes for waves to travel between points. In this book, we will treat space as a 3-D chess board, pieces have a location that can be defined by three numbers relative to us and that can change in a limited number of ways.

Space shares the stage with time, the basic rule starting from the fact that things can be at the same time but not in the same space and in the same space but not at the same time.

All longitudinal waves travel at a speed determined by the medium they are travelling in. In the case of F-waves, we have called the medium the ‘Field’ – this is what we also call a vacuum.

The presence of matter reduces the speed of the Field, generating the effect we call gravity, although this can only be seen from outside the gravity pool as the lower speed of the Field inside the pool also reduces the rate at which clocks ‘tick’.

F-waves also travel at different speeds in other mediums, such as water, which is one reason why the term ‘speed of light is misleading.

The speed of the Field is 300,000,000m.s.-1, metres per second.

Something that prevents another thing from being at the same place and time as the first thing. All ‘Things’ that we know of are ball-waves or collections of ball-waves. Typical simple things are electrons, protons and neutrons, although there is a ‘zoo’ of other short-lived, simple things such as mesons and tau. Bigger things are made up of collections of simple things. In contrast to things, waves can happily have the same coordinates, pass through each other, etc. and are not ‘things’. Because they require energy to make their ball-wave shorter to match the overall speed of the ball wave, things have inertia and mass.

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