by Darryl Penney

 

Abstract: mathematics has neglected the most basic and important construction in the series: point, line, orthogonality, the plane, circle etc. because orthogonality generates the fractal that is a mathematical probability space that is similar to our space in construction, but not in operation and allows us, as evolved parasites, to visualise that construction through four search axioms. Physics has been based, bottom-up on the dimensions of a probability space: x, y and z, time passing and energy is equivalent to (a +/and b)=1, for measurement/recorders a and b that lead to the derivation of a constant speed of light, space creates energy, energy is conserved, a and b are orthogonal and the orthogonality of ‘+/and’ allows us to build a mind-space, a mathematics of concepts and a general mathematics. Orthogonality and the creation of energy necessarily create gravity and the universe as a Big Whoosh in a natural progression. The orthogonality of energy/gravity produces the organization of the universe as well as the logical/organizational basis of quark-antiquark confinement. This is the same logical confinement that creates the binding energy of the nucleus between the proton and neutron and thus, gluons are not needed. The three Fundamental operators that produce what is available are determined and show the basis of fractals and why there are three elementary particles (electron, protons and neutrons) that are orthogonalised by charge (doublets) and the suggestion is that photons and neutrinos are strangeness doublets. The orthogonality of the quarks/antiquark bond greatly simplifies Quantum ChromoDynamics.

 

The previous chapter concluded with the thought that the basis of the Grand Unified Theory (GUT) of elementary particles was the relation/similarity between quarks/anti-quarks (the quark confinement) and what I called the energy/organization orthogonality. This chapter is a bottom-up look at the elementary particles to try to simplify the situation. ‘This classification into baryons and leptons seems rather elaborate to describe these four particles. Its usefulness only becomes apparent when we appreciate that, over the past 50 years or so, hundreds more such ‘elementary’ particles have been discovered.’ (The New Quantum Universe, Tony Hey and Patrick Walters, p 251) The reason for such a number of particles is the production of orthogonalities as the input energy to the accelerator rises.

 

Our universe, is indescribable because the total energy, I believe, at every point in it, is zero, but can be described as a probability of existence space based on the dimensions of a mathematical probability space, lengths x, y, and z, time passing and the fifth dimension (a+b)=1 for measurement/recorders a and b, with the proviso that the mathematical computation of energy is zero, universe-wide, not zero at every point as appears to be the case. This situation is to ease our minds because we are parasites that have evolved/infiltrated the universe and tend to use units (Newtonian physics) to describe the universe that are based on the predator/prey situation with which we evolved. Our universe is simple, and we, as parasites have redefined and made use of concepts and contexts that we have evolved out of the physical relationship (a +/and b) =1 and these are the mind space ‘+/and’, the mathematics of concepts and general mathematics that link us into the physical universe.

 

Our universe is built on orthogonality/independence that, like the Cartesian coordinates, separates two independent factors, x and y that we usually use to make a plane, but are used in the universe in a more fundamental role, as independent entities. Fundamental mathematics contains the geometric series: point, line, orthogonality, the plane, circle etc. in rising complexity, but orthogonality has never had an important role apart from defining a plane surface. The reason for looking at a probability space is that it contains questing and relevance, as mentioned before, but I now realize that I did not give enough ‘weight’ to orthogonality that is apparent in the fifth dimension. I thought of it mainly as being crucial in the mathematics of concepts, but I now realize that orthogonality is as important as questing and relevance throughout the universe.

 

It is not surprising that questing corresponds to quantum mechanics and relevance to relativity, but orthogonality is not so obvious. We need to look at Newtonian physics in a new light, and it is obvious that the mathematical computation of the total sum of all points in a mathematical probability space is produced by questing and relevance in a physical sense, but in a logical sense, orthogonality is needed. A moment’s thought will show that, in our universe, not only is the energy zero at every point, the mechanism to understand it, that is, relevance, questing and orthogonality disappear also, and the creation of energy/energy and energy/gravity at the same time does not mean that the use of the minimum energy is logically necessary as required by the law of least action in a probability space because there is always equality between the two.

 

The basic problem with mathematics and physics is that they have developed top-down and would benefit from a bottom-up approach because huge areas, such as the social sciences and social networks have been neglected to the extent that our civilization and even our planet are in jeopardy. Hence, I will ignore top-down historical research into the effects of the Grand Unified Theory, Quantum ElectroDynamics (QED) and Quantum ChromoDynamics (QCD) and concentrate on the basic principles behind the elementary particles. The starting point is the Unified Field Theory from chapter 74.

‘According to the current understanding of physics, forces are not transmitted directly between interacting objects, but instead are described by intermediary entities called fields. All four of the known fundamental forces are mediated by fields, which in the Standard Model of particle physics result from exchange of gauge bosons. Specifically the four fundamental interactions to be unified are:

• Strong interaction: the interaction responsible for holding quarks together to form hadrons, and holding neutrons and also protons together to form atomic nuclei. The exchange particle that mediates this force is the gluon.
• Electromagnetic interaction: the familiar interaction that acts on electrically charged particles. The photon is the exchange particle for this force.
• Weak interaction: a short-range interaction responsible for some forms of radioactivity, that acts on electrons, neutrinos, and quarks. It is mediated by the W and Z bosons.
• Gravitational interaction: a long-range attractive interaction that acts on all particles. The postulated exchange particle has been named the graviton.

Modern unified field theory attempts to bring these four interactions together into a single framework.’ (Wikipedia, Unified field theory) It will be shown below, that,I believe that changes are needed.

The Ancient Greeks thought that atoms had tiny hooks on them to enable atoms to combine together and the modern concept of ‘all four of the known fundamental forces are mediated by fields, which in the Standard Model of particle physics result from exchange of gauge bosons’ is not much better, as will become apparent. Traditionally in physics, stable states arise where the energy needed is lowest, but this is a Newtonian mechanistic idea because, how does the space or atoms know that the energy is lowest? In other words, what carries the concept of energy? This logic is recognised in quantum mechanics as ‘tunnelling’ and is allowed. The ether theory was ‘debunked’ by the Michelson-Morley experiment and that left the wave theory of light unexplained because, without the ether, what ‘carried’ the light wave? To explain this, I need firstly, the concept of general mathematics and secondly, the unfolding of (a +/and b)=1 to reveal the orthogonality of ‘+’ and ‘and’.

 

Firstly, from chapter 87, ‘a definition of general mathematics/organization consists of:

 

(1)    the mathematics of concepts, and in particular, the orthogonality of concept and context and the necessity of numericalization of context,

(2)    the four search axioms (forward-planning, questing, relevance and elegance) that are derived from Life, the probability space and the fifth dimension, or from common sense,

(3)    recognising physical-space, logical-space and mind-space as consisting of both world O and P.’

 

Secondly, I think that orthogonality is the keystone of relevance and questing and this linking of independence is the ‘glue’ that holds everything together. This will become apparent with the questing of (a +/and b)=1.

 

From chapter 86, ‘let us unfold (a+b)=1, where unfolding is following the questing [of quantum mechanics, evolution, business etc.]. The fifth dimension (a+b)=1, in this simple form produces five operators (ignoring, for the moment, the fact that the speed of light is an absolute and must be constant, that the energy per unit of space is constant and the law of conservation of minimum energy):

 

(a) measurement/entanglement that are local physical and independent/orthogonal (a+b)=1 [classical local action and reaction of matter that provides expansion of the universe, reflection, diffraction of light and water waves],

(b) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b)=1 [conservation of (zero) energy across the universe, gravity, creation of space/mass/energy/time through the Lorentz contraction],

(c) measurement/entanglement that are local physical and independent/orthogonal, (a+b) [local/personal appreciation], and

(d) measurement/entanglement that are universe-wide logical and independent/orthogonal (a and b) [universal/reality-wide appreciation]

(e) measurement/entanglement that links the operators ‘+’ and ‘and’ together in the fundamental relationship that links the physical/logical/organizational [mind-space, conservation of minimum energy]’

 

To reinforce the concept of orthogonality, which is the cornerstone of the organization of our universe, I would like to restate from (a +/and b)=1, a and b are measurement/recorders in the physical world (P), whereas they are concept/context in world (our) O, ‘+’ and ‘and’ are the physical and organization in world P, and the gradation forms the mind-space in world O. The Big Whoosh (in my opinion a more correct description of the Big Bang) results from the splitting of no/zero energy into positive/energy and negative/gravity, the photon into physical-energy/gravity (see chapter 88) as well as other examples, such as the Cartesian coordinates, male/female, positive/negative etc. are more examples.

 

The core idea is ‘the splitting of no/zero energy into positive/energy and negative/gravity’ and this produces the formation of the universe, including accounting for inflation, but orthogonality only arises if positive/energy and negative/gravity are different to our normal concept of ‘energy wells’ where there are different levels of the same energy. The orthogonality of energy comes from (a+b)=1 and (a and b)=1 as quests of (a +/and b)=1, where (a+b)=1 is the physical/energy summation across the space and (a and b)=1 is the logical/energy summation in a probability space. The summation over the space can be relaxed if every point in the space has equal amounts of the two different energies that are orthogonal, as appears to be the case in our universe.

 

This is shown in the following quotation from chapter 72: ‘One requirement any law of nature must satisfy is that it dictates that the energy of an isolated body surrounded by empty space is positive, which means that one has to do work to assemble the body. That’s because if the energy of an isolated body were negative, it could be created in a state of motion so that its negative energy was exactly balanced by the positive energy due to its motion…. Empty space would therefore be unstable.’ (The Grand Design, Stephen Hawking and Leonard Mlodinow, p 179). If we quest [measure] the energy of the particle in the quotation, what is the potential [negative] energy, according the law of conservation of energy, to balance the energy of creation? Effectively, there is no energy locally, but there is a particle to show that something happened and the energy is within the particle and any interaction.

 

The following quotation is from the close of chapter 88, ‘since the early days of nuclear physics, physicists had hoped that the theory of the strong force would be simple and elegant. With the discovery of the pion and the menagerie of all the other hadrons, together with their excited states, it rapidly became apparent that the force between neutrons and protons was very complicated…. Perhaps the so-called strong interactions are merely a feeble shadow of enormously powerful inter-quark forces that can be described by a simple and elegant law.’ (The New Quantum Universe, Tony Hey and Patrick Walters, p 266) [such a simple law will be derived below, for electrons, between a quark and its antiquark, or, equivalently, for a neutron and proton that contain the equivalent quarks] This paragraph sums up and points the way because the ‘enormously powerful inter-quark forces’ are, possibly, logical/organizationally and independent of any energy thrown at them. If the universe can be built from five dimensions, the universe is simple and the problem is in our view of it.

 

From above, the idea has been put forward, based on the dimensions, that every physical energy is accompanied by a logic/organizational gravity energy and from chapter 81: ‘The Math Book, (by Clifford A. Pickover, p 284) gives the five Peano Axioms as a basis of arithmetic, and certain things appeared to be missing, such as the mind/brain to determine elegance of content, forward planning (dimension 6), the measurement of each numeral (questing) and the relationship between numerals (relevance)’.

 

Further, ‘If we unfold (a+b)=1 in a probability space, as above, including Life, we get:

concept/forward-planning/quest/relevance/beauty/context.

 

If we unfold (a+b)=1 in a probability space, as above, excluding Life, we get:

measurement/quest/relevance/orthogonality/entanglement.’

 

‘Notice that forward-planning is a dimension specific to Life and necessary for the predator/prey basis of iteration and the four axioms are immediately obvious in the above.’ I have also added orthogonality.

 

Another example of orthogonality, and a necessary digression is the quotation  ‘physicists believe most matter and antimatter did meet and implode shortly after the Big Bang. But they cannot explain why some matter survived to create everything that exists in the visible Universe.’ (Nature magazine) The answer is, possibly, two Big Bangs/ Big Whooshes with only one type of particle in each universe that come from orthogonal particle pairs that are being created and destroyed. ‘According to quantum mechanics, the vacuum state is not truly empty but instead contains fleeting electromagnetic waves and particles that pop into and out of existence.’ (Wikipedia, Vacuum state) Further, ‘our empty box should be regarded as a bubbling soup of virtual particle-antiparticle pairs! (The New Quantum Universe, Tony Hey and Patrick Walters, p 237) These quotations state that these particles are antiparticles that are created within the constraints of the Heisenberg Uncertainty principle and this leads to the problem, often cited, of huge energy being created in empty space.

 

‘It is sometimes attempted to provide an intuitive picture of virtual particles based upon the Heisenberg energy-time uncertainty principle: Δ E Δ t ≥ ℏ   , {\displaystyle \Delta E\Delta t\geq \hbar \ ,} (with ΔE and Δt being the energy and time variations respectively; ΔE is the accuracy in the measurement of energy and Δt is the time taken in the measurement, and ħ is the Reduced Planck constant) arguing along the lines that the short lifetime of virtual particles allows the “borrowing” of large energies from the vacuum and thus permits particle generation for short times.Although the phenomenon of virtual particles is accepted, this interpretation of the energy-time uncertainty relation is not universal. (Wikipedia,Virtual particles)

 

A point of interest is that textbooks tend to picture a vacuum as being composed of a constantly seething/‘boiling’ of particles that are created momentarily, and that is justified by the above quotation, but it does not give a reason why those particles are formed, nor where the prodigeous energy that antiparticles contain comes from. The Heisenberg uncertainty principle might suggest a way, but is not a convincing reason for ‘why?’ it should happen. May I suggest that this ‘constantly seething/”boiling” of particles’ is the questing of possibilities to present them to see if they are used. A physical measuring space cannot decide when something is needed, only to constantly present the opportunity to use that possibility. Also, orthogonal pairs contain no net energy and can be presented for use at all times without disturbing the conservation of energy in any way, and further, and extremely importantly, orthogonality presents both physical and logical opportunities at every point, all of the time.

 

All these problems disappear if the particles are orthogonal because there are no energy nor time constraints. This concerns the matter that we call ‘antimatter’ and it is not the same as ‘orthogonal-matter’, ‘In 1927, Dirac published a paper in which he presented a wave equation for the electron … the equation of the electron. Curiously, though, the equation had two solutions, rather like the way in which the simple equation x2=4 has two solutions… By 1931, he realized (along with other people) that the equation was actually predicting the existence of a previously unknown particle, with the same mass as an electron but positive charge…. Antimatter, as it came to be known, was a real feature of the physical world, and every type of particle is now known to have an antimatter equivalent with opposite quantum numbers.’ (Science: a history 1543 – 2001, John Gribbin, p 521)

 

This quotation presents two enigmas, firstly, the one stated that ‘every type of particle is now known to have an antimatter equivalent with opposite quantum numbers’ is an enigma until it is realized that the physical world has no way of deciding which particle to choose, and then it is more complicated to decide on one particular particle. Further, this is the basis of a fractal that every possibility is there if quested. Secondly, matter that we call ‘antimatter’ is not the same as ‘orthogonal-matter’, because positive and negative orthogonal matter combine to zero, whereas, a ‘pair of particles’ will produce a pair of gamma rays through the intermediary of two quarks, ‘even in a reaction in which we believe an electron is annihilated by a positron to produce a quark and an antiquark going off in opposite directions, we still do not see any quarks … two jets of normal hadrons.’ (The New Quantum Universe, Tony Hey and Patrick Walters, p 269) A quark and antiquark encounter quark confinement, below, so they have to change into gamma rays, and secondly, orthogonal matter has a sum of zero, not two gamma rays.

 

The fractal generating nature of the universe implies:

questing à orthogonality à relevance

is a natural process and orthogonal pairs might be generated without the energy and time constraints of the above. Further, the quark/antiquark is possibly negative/orthogonal and positive/orthogonal energy/organization because ‘no-one has ever been able to observe a quark all by itself.’ (p 268) This parallels the internal construction that I proposed in chapter 88 for the physical and logical parts of the photon.

 

It might help if we construct an atom to show the constituent parts more clearly. The first orthogonality, above, is energy/energy and gravity/energy for everything all of the time [zero/zero can be ignored], and the second is the condensation of energy into a particle called the neutron, then thirdly, what we call charge is orthogonalized, electron (negative), proton (positive) and neutron (zero) and the neutron eventually decays to a proton and electron outside of the nucleus.

 

The ‘key’ to the construction of the atom is the ‘strong force, unlike electric, magnetic and gravitational forces, does not obey an inverse square law. It is very strong indeed over a limited range of about 10 to the minus13 centimetres, and essentially cannot be felt at all beyond that range. This is why nuclei have the size they do’. (Science: a history 1543 – 2001, John Gribbin, p 522) This Newtonian explanation for the formation of the atom hinges on the concept of ‘force’ and glosses over, I believe, a more complete explanation of why protons should congregate together in spite of them having the same charge. There are several reasons that the protons and neutrons could be at the centre of the atom and that is firstly, a ‘construct’ to discover a strong force that holds them together, secondly, perhaps there is a ‘shielding’ of the strong force by the neutrons, or thirdly, an organizational ‘construct’ that is orthogonal and independent of the charge on the protons. In terms of Newtonian physics, this bringing a number of like charges together is an enigma.

 

‘If we try to pull a quark out of a baryon, we have to put in so much energy that we create a quark-antiquark pair. Instead of breaking up the baryon, we end up with a baryon and a meson. According to this quark picture, Yukawa’s meson exchange model of strong interactions is clearly not at all fundamental.’ (The New Quantum Universe, Tony Hey and Patrick Walters, p 270) The quark-antiquark pair is predominantly logical/organizational and answers, in an extraordinarily simple manner the nature of the strong ‘force’ between the protons. Both protons and neutrons are composed of quarks, and can be thought of as quarks themselves and the strong-‘force’/shielding is the logical/organizational relationship between the proton and the neutron.

 

I would like to repeat that, the quark/antiquark joint/double particle is necessary to overcome the huge forces of bringing the protons into close contact. The electrons are far enough away and spread over a surface (quantum mechanically) so that they can balance the attraction/repulsion/standing-wavelengths of the atom and electron. However, the nucleus is a cyclotron/accelerator in reverse and instead of smashing particles together, we can lean a lot of why they are together, and that force, of holding them together, is so great that, I believe that it uses the orthogonality/independence of energy and logic/organization to do the job. Repeating, orthogonality cannot be physically broken under any circumstance and physics has taken the quark/antiquark that is (effectively) one particle and called it two particles. The use of energy has no effect on logic/organization because it is orthogonal/independent and is the simple explanation of why a quark and antiquark cannot be separated

 

The question is a simple mathematical/organizational one of, if there is an orthogonality of quark, zero and antiquark, what combination must the proton and neutron have to produce a neutron with no charge and a proton with a positive charge? Clearly, the answer is that the proton is 2 up quarks (+2/3 charge) and 1 down quark (-1/3 charge), and the neutron is 1 up quark and 2 down quarks and that is the strong binding energy fixed.  A quick check shows that the charges are correct and the reaction of a:

 

proton + electron à neutron    +4/3 + -1/3 + -3/3 à +2/3 + -2/3  balances!

 

The simple strong law referred to above is orthogonality because it is simple, exists and is unbreakable and does away with the concept and problem of quark confinement because they are confined logically and physically, by orthogonality, also, it does away with the (theoretical) binding particle, the gluon. I am emphasising the simplicity of this explanation because the textbooks devote pages to the subject of quark confinement and gluons. So, continuing this simplification, from above, about the hope that ‘the theory of the strong force would be simple and elegant’, ‘it is the electroweak force that distinguishes between these different flavours of quarks: the strong force is the same whether it acts on a strange or a charmed quark’ (p 266) In the light of these quotations and that the universe is based on five dimensions, I would like to suggest that the strong force is, in reality, simple in action and the flavours, used in the ‘electroweak  force’ are higher orthogonalities of the up and down quarks.

 

It seems strange that no one seriously asked why there are an equal number, more or less, of protons and neutrons in the nucleus, nor considered that the binding energy comes from the ‘togetherness’ of the neutrons and protons. Thus the atom is a cosy use of simple orthogonality of electron, proton and neutron so that all are used with very good reason. Many textbooks contain the ‘compilation of all observed nuclei plotted in terms of protons in the nucleus versus the number of neutrons. Stable nuclei are shown in black, and unstable nuclei lie within the marked boundary. More massive nuclei contain more neutrons than protons. (p 95) What could be simpler! No need for gluons! The proof is in the exception, where the hydrogen atom contains only one proton and so does not need a neutron for binding energy! Further, deuterium and tritium show that there is an attraction to the proton, if it is needed/quested.

 

I could be accused of the above being speculative, and the way to ‘prove’ a theory is to predict/extrapolate into unknown territory, and the best way to do that is to seek out the enigmas. ‘Although the model can accommodate both the muon and the tau leptons along with their neutrinos, in addition to the electron-neutrino doublet, there is no compelling reason for their existence nor any predictions of their masses. Nor do we have a real understanding of why there are three doublets of quarks – (up, down), (strange, charm) and (top, bottom) – to accompany these lepton doublets or any real understanding of the large range of masses of the different quarks’ (p274) Clearly, the doublets and triplets are a result of orthogonality and the masses are those that are relevant to the organization from the organization of the questing because they work. From above, if all quests are presented, clearly the one that will be used is the ‘best fit’ with the principle of least action and (eventually/usually) requires the least energy.

 

A more definitive example of the role of quarks can be given to solve an enigma, to me, of long standing and that is the types of radioactivity: alpha particle, beta particle and gamma ray or high energy photon that can be used by the nucleus. ‘We show a plot of the ‘average binding energy per nucleon’ for all the different elements. We see that the binding energy rises from about 2 MeV, the value we have just calculated for the deuteron, up to a maximum of around 8.8 MeV per nucleon for iron (Fe) and then falls generally to about 7.5 MeV for heavy nuclei out to uranium and beyond. Notice that alpha particles (helium nuclei) are especially stable compared with the elements nearby. This is why they are sometimes formed inside heavy nuclei and can tunnel out causing radioactive decay of the nucleus.’ (p 93) This quotation is possibly ‘glossing over’, perhaps under-stating, I believe, a better explanation, as follows.

 

Undoubtedly the bonding energy is high because the packing density is high due to the tetrahedral shape of the bonding allowing for close bonding and this reflects on the role of quarks and maximizes the alpha particle’s self containment and minimizes its relation to the rest of the nucleus. This answers the question, to my mind, that I have had for a long time, of why an alpha particle is preferentially ejected, and that is reinforced by the role of quarks, that the proton and neutron form a quark/anti-quark pair with orthogonal bonding and that two pairs shield each pair more effectively, to the extent that an alpha particle is preferred for ejection. I would add that the quark/orthogonal-quark bond cannot be broken by energy, but the alpha particle is able to be broken apart, so the effect is presumably similar, without the independence of true orthogonality.

 

In chapter 87, I made the point that the Pauli exclusion principle was developed for the simple picture of the atom to give a set of quantum numbers for the orbits and, in particular used the logic/organization of the indeterminacy of the standing wave that allowed two electrons to share an orbit. Further, the point was made that electron spin was a logical, not a physical quantity and is, basically, a product of orthogonality because orthogonality is negative, zero and positive and this explains why many elementary particles have three ‘guises’. Up to this point I have been thinking that orthogonality quested the universe and the null case was not considered for obvious reasons, but now we should consider that an addition to orthogonality of a particle would necessarily produce negative, zero and positive forms of particles, where relevant.

 

The answer to all of these questions is, that they are there because they need to be there and the real answer is that questing produces ALL possibilities and orthogonality is the fractal way of expansion, and relevance decides whether they are measured. In other words, to put it into perspective, using a probability space, the dimensions allowed us to derive the three Fundamental operators quoted above:

questing à orthogonality à relevance, and a probability space is a measurement space and will give the answer required [particle or wave] depending on the question/experiment devised. These three operators were derived from the dimensions of a probability space and I have yet to find an enigma that cannot be answered and that is the power of this bottom-up approach. Whether the answers/suggestions are correct is another matter.

 

Perhaps the easiest way to present the simplicity of this approach is to quote the current explanation. Using the Pauli exclusion principle and building on it contains dangers, as can be seen, ‘the quarks are fermions and must obey the Pauli principle. As things stand, all of the quarks in the omega(-) have the same quantum numbers and Pauli does not allow this. The introduction of a colour quantum number for the quarks allows us to solve this problem.’ (p 267) Further, using ‘the so-called “special unitary group SU(3)”. The threeness of this group means that there are three different possible states for the quark …. So each quark in the omega(-) must have a different colour – red, green and blue, say – to satisfy the exclusion principle.’ (p 268) Again, it is apparent that using orthogonality instead of colour simplifies matters.

 

‘Quantum ChromoDynamics, QCD – the long sought theory of the strong force. QCD is a gauge theory based on the local phase invariance of the colour properties of the quantum amplitudes of the quarks. Although this may sound intimidating, it is difficult to imagine that any theory of the strong interactions could be simpler.’ (p 268). I have to say that I believe that orthogonality is very much simpler, especially in view of the following. ‘Just as the electromagnetic forces are mediated by zero mass gauge particles – the photons that we have met so often – so we expect that the quark-quark interactions are described in terms of the exchange of similar “strong photons”. Physicists have given these particles the name gluons, because, in a very real sense, they are the glue that holds everything together.’ (p 268)

 

‘Photons couple to the ordinary electric charge of the quarks: gluons couple to the colour charge of the quarks. Moreover, the gluons themselves carry a colour charge and the gauge principle dictates that, unlike our photon example, gluons must interact with themselves. Physicists believe that it is this key feature that makes quantum chromodynamics (QCD) – chromo is for colour – so different from quantum electrodynamics (QED). Why do we say that QCD is so different from QED? This is because it is easy for us to observe electrons in the laboratory. No-one has ever been able to observe a quark all by itself.’ (p 268)

 

Conclusion: this is still a work in progress, but a few comments can be made, and will be continued in the next chapter, that the universe came into existence by orthogonality, and the fractal nature is shown in the expansion of the universe and in the other direction, in the increase in elementary particles. Questing à orthogonality à relevance is basically the whole simple theory.

 

The above does shows that particle accelerator projects may not be worth further investment because the more energy used, the more disintegration products, but of a type that are orthogonal creations of a fractal and thus necessarily somewhat predictable.

 

The Unified Field Theory appears to be both, in tatters and strengthened, as above, gravitons and gluons appear to be superfluous, the strong force has been found, so that the nucleus is stable and everything in the atom is used to good advantage and has a role, in particular, the neutrons’ role.

 

Also, the photon and the neutrino have been temporarily/hopefully linked, at the moment, through orthogonality, and this will be shown in the next chapter.

The example, above, has shown the strength of my approach, especially the realization of the fundamental operators (questing à orthogonality à relevance) that have been derived previously from the dimensions of a probability space, and are paramount to any discussion of the physical world.

 

‘There is one final challenge for quantum mechanics. This is the unification of quantum mechanics with gravity to produce a consistent theory of quantum gravity…. Some theoretical physicists are looking at a new way of constructing a theory that could encompass both the Standard Model and gravity in a consistent and calculable way’ (The New Quantum Universe, Tony Hey and Patrick Walters, p 282) Orthogonality also provides a means of including gravity and a way of constructing a conservation of energy that is workable by taking into account the ways that energy can and cannot be created.

 

Again, the above shows that Newtonian physics must be updated and mathematics must be expanded through the mathematics-of-concepts/orthogonality so as to tackle the social problems facing us within our environment.

 

As mentioned above, this is a work in progress and it is unfair to present something unfinished, so, the following is from the next chapter and foreshadows the simplicity of our universe.

 

So, What are quarks and how do they build a universe? They are like the plumbing or wiring in a building, essential, but not seen and are the solution to an organizational situation/problem that creates a unique solution that always works and avoids logical/physical singularities that cause chaos and form a fractal universe of matter from a null space where each and every point is zero/nothing. They are created as orthogonals with half energy/energy and half energy/organization/gravity with fractional electric charges and form the fundamental particles of neutron, proton and electron with a basic electric charge of unity. As the basis of fundamental particles, they have the organizational property/solution of only forming orthogonal doublets and triplets with unity electric charge and never exist alone, and where the binding organization between two quarks is orthogonal/organizational and independent of the application of energy.

 

The preferred form, or binding force within the nucleus of an atom is roughly equal numbers of neutrons and protons because they form a stable organizational bond of three up/down quark bonds, with one up/down bond in/forming the neutron and proton and one up/down bond between the neutron and proton. Outside of the nucleus, the alpha particle is similarly built and its bonding strength is crucial to nuclear reactions and element building in stars [by tunnelling] because it is unusually stable, probably because of the close tetrahedral packing of the fundamental particles and the quark organizational bonds.

 

Antiparticles are always formed because logically/organizationally it is simpler to create the mirror-image as well, than to decide on one form and the electron is anti-up/down quarks and the positron is up/anti-down quarks with the appropriate unit electric charges. This solution is the third orthogonality [after positive/negative energy and the neutron] giving neutron, proton and electron and these are carried on to form the universe by the fractalization and energy creation orthogonalities [of the fifth dimension, energy is equivalent to (a+b)=1, where a and b are measurement/records, of the probability/fractal view of the null space].

 

It should be noted that the story of the quarks is the story of the beginning (and growth) of the universe that I call the Big Whoosh because it contains the necessary inflation as a constant ratio of space to time, being what they may be, that bedevils the Big Bang concept as an ‘add-on’. Further, the elegance and simplicity of the construction of the elementary particles is enhanced by the simplicity that orthogonality allows for an unlimited/adequate number of particles of higher energy, when needed, with every particle contributing to and affected by gravity.

 

References: all quotations are fully referenced in the body and earlier chapters can be found on    darrylpenney.com    if required.

 

Chapter 74: Extending the Unified Field Theory

 

Chapter 87: The Problems with Science and Mathematics, Local Entanglement, the Pauli Exclusion Principle, General Mathematics/organization, a Call to Expand Mathematics and a Proof of Completeness of General Mathematics/organization.

 

Chapter 86: How the Mind Works, Evolution in Mind-space, the Placebo/nocebo Effect Has Two Parts, Combating Chronic Pain, Why Eastern and Western Medicine are Similar, Unfolding Mind-space from the Fifth Dimension and the Law of Conservation of Minimum Energy

 

Chapter 72: The Why and the How of the Big Bang, Why the Universe is ‘Flat’, Inflation and Quanta are Explained, Why Feynman was Correct, Why Matter Predominates over Antimatter, Why the Speed of Light is Constant and an Absolute, Relativisation is the Work-horse of the Universe, the Fifth Dimension, Dark Energy Might be Necessary for Survival, the Super-world of the Mind, Gravity and the Law of Conservation of Energy Unfolded

Chapter 88: Inside the Photon, the Law of Conservation of Energy, the Big Whoosh, Our Universe Viewed as a Probability Space, Unifying the Photon with Gravity, the Quark Confinement and the Grand Unified Theory (GUT)

 

Chapter 81: Parasites in Probability Space, General Mathematics, Logic, Measurement, Organization, the Four Axioms of Measurement that Link the Mind/brain to Mathematics and the Dimensions of a Probability Space, Life as a Possible Sixth Dimension, the Why of Godel’s Incompleteness Theorems and the Goal of Explaining Everything by a Single, Elegant, Unified Equation is Attained.