The goal of this discussion is simply an attempt to understand some of the basic concepts as many of the reference papers have not been read at this stage. However, most learning processes have to start somewhere, usually in ignorance, and then attempt to assimilate more details, while in the process highlighting any issues that appear questionable. Overall, the Cordus Conjecture describes itself as a non-local hidden-variable (NLHV) model. As such, it assumes that the structures of its particule model physically exist at the sub-particle level of the standard model although the scale at which these structures are assumed to exist is not necessarily specified. However, the Cordus model states that it wants to anchor its description of causality to physical mechanisms and variables that exist objectively, although they may not be measured directly, even if they exist.
Note: We might compare the Cordus model with Bell's theorem of quantum mechanics, which assumes each measurable quantity of a system is described by potentially random variables. The value of these variables might depend in some way on other values, which are not known or measurable, i.e. they are also hidden variables. In order to match the predictions of quantum mechanics, the variables of spatially separated systems are assumed to influence one another in a non-local way, i.e. without any known means of causality. Bell’s theorem also implies that any other theory that reproduces the predictions of quantum mechanics either works by some means other than hidden variables or it is non-local. A non-local hidden variable theory implies that there are hidden variables, but they are non-local, such that the most fundamental laws of physics must also be non-local. In this respect, the main difference between the Cordus and quantum models is that the latter is essentially limited to a mathematical solution that possibly does not attempt to provide a description of physical causality.
The Cordus model introduces the idea of a ‘generic particule’ that is assumed to have a physical sub-structure, while recognising that its variables are both ‘hidden’ and surrounded by ‘conjecture’. At this early stage many aspects of the particule model are not really understood, such that its description appears somewhat abstract for a model with the stated goal for physical realism. However, some attempt will be made to introduce the basic idea of a particule, which can be generally applied to both ‘electrons’ and ‘photons’, although the photon is subject to some caveats. So, as a general description, the sub-particle structure of the particule is said to comprise of two ‘reactive ends’ that are physically separated, but connected by a ‘fibril’, which is described as a ‘ persistent and dynamic structure’ that does not interact with ‘normal’ matter. The fibril is assumed to supports some form of superluminal communication between the reactive ends of the particule, which is then used to explain quantum entanglement. The ‘reactive ends’ are also described as being ‘energised’ at a given frequency that defines a specific particle and emit discrete forces along the [r,a,t] axes, although the exact number and direction of these forces also depends on the type of particule being described, e.g. electron, photon, neutrino etc. It is suggested that these forces propagate along ‘flux lines’ out into the space between particules, where the nature of these flux lines can be used to explain electrostatic, magnetic, and gravitational fields. As a consequence, the vacuum of space is filled with a ‘tangle of flux force lines’ that defines the functional nature of the fabric of space.
Note: Even at this initial stage, it is not unreasonable to question the physical nature of the ‘reactive ends’, if they are assumed to be physical entities. For example, we might ask whether they represent some form of energy-density and, if so, how do they exist and move in space-time?
However, despite the degree of ambiguity surrounding the internal structure of the particule model, the Cordus model assumes that it can replace the point-particle of quantum theory. As such, this model claims to be different to other NLHV models in that it can physically explain phenomena that quantum mechanics cannot. The model then claims to explain multiple phenomena encompassing particle, wave and cosmological effects, which are briefly summarised in the following list. As such, the Cordus Conjecture seeks to provide:
- An alternative explanation of the
wave-particle duality concept often associated with double-slit experiments, but now anchored in physical realism.
- The necessary internal structure and functionality of the most
fundamental components of the
particle model, i.e. electrons, positrons, neutrinos, quarks and
- An alternative derivation of
laws from a particle perspective.
- A more qualitative explanation of
- An explanation of mass-energy equivalence by proposing
a mechanism for pair production, e.g. the creation of an electron
and positron from a photon and a complementary annihilation process.
- A description of the physical process of
photon emission , i.e. where a photon is emitted from
- A description of entropy and the arrow of time, where
time becomes an emergent property of matter.
- An explanation of the finite speed of light [c], but with the
prediction that this speed is not constant.
- A mechanism explaining
asymmetrical baryogenesis in the
- A formulation for the
transforms, time-dilation and
effects based on a particle model.
- An explanation of the
nuclear force that predicts the structure of atomic nuclei.
- An explanation of decay processes and the instability of free
- An explanation of the quantum spin characteristics of neutrinos.
However, this review has yet to examine the substance of any of these claims as it is still in the process of trying to understand some of the many ideas and concepts being forwarded, such that the focus will return to some of the more basic details. For while bullet-1 above claims that the Cordus model can provide an alternative explanation of the wave-particle duality concept forwarded by quantum mechanics, it seems that this model is orientated to the semantics of particles, which differentiates it from earlier wave models.
Note: Wave models as described in terms of the WSE, WSM and WWM discussions formulate a fundamental model based on wave structures that confined energy propagating through the media of space as a function of time. As such, there are no particles, or particules, only forms of energy-density contained within spherical standing wave structures, which are then used to explain both the nature of matter waves and the phenomena of light waves. This leads to a fundamental difference in the concept of photons, which in the view of both the WSM and WMM models do not exist. See LaFreniere’s webpage discussing light for more details.
Therefore, in comparison to earlier wave models, the Cordus model appears to be more orientated towards a particle model, especially in terms of its description of a photon. The first 3 papers in the Cordus Conjecture series, as cited in Cordus References, are a description of the photon particule model, which this discussion will only attempt to briefly summarise. The behaviour of a photon is described in terms of its two ‘reactive ends’ interacting with other matter particules as in reflection, refraction and absorption. However, it is assumed that the reactive ends of a single photon may take different paths, as per the double-slit experiment, where this positional duality may also provide an explanation of quantum entanglement. The first paper in the series details 6 variant developments of the photon particule model, although C.1.6 is now preferred.
Broadly, all variants encompass the idea of having two reactive ends connected by a fibril. In the final C.1.6 variant, energy is shown flowing in and out of the two respective reactive ends before reversing. Within this model, the two reactive ends of a single photon can pass through both slits of the double-slit experiment, although an extension of this experiment involving three slits seems more problematic. However, it is assumed that the photon particule model can provide a physical explanation of various quantum behaviours. For when one reactive end touches a material object, presumably a matter particule, its reactive end is described as being ‘grounded’ such that the entire photon particule structure collapses. However, in the C.1.6 variant, only an ‘energised’ reactive end can be ground and the other reactive end ceases to exist.
Note: The photon model outlined above might be compared with the mainstream perception of wave-particle duality, which while able to predict outcomes appears to fall short in terms of its description of any physical mechanisms at work. Again, Bell's theorem suggests that there can be no internal model for the photon, such that the problems associated with the wave-particle duality approach may be unsolvable. Of course, this is one of the many issues that the Cordus conjecture now seeks to address.
Within the obvious limitations of this initial outline, we might begin to understand how the Cordus model differs from the quantum model, which assumes that the most fundamental sub-atomic particles, e.g. electrons and quarks, have no sub-structure and can therefore be modelled as a conceptual point-particle. In contrast, the Cordus model introduces the concept of two ‘reactive ends’ separated by a very small, but finite spatial distance, which in the case of a matter particle can emit ‘discrete forces’ in up to three orthogonal directions, as defined by the [r,a,t] axes. However, we possibly need to table a more fundamental question at this point.
What is a force?
Normally, we might initially consider Newton’s second law [F=ma], where [m] is mass and [a] acceleration, but we immediately run into another ambiguity, i.e. what is mass? Alternatively, a force [F=dE/dx] might be expressed in terms of a change in energy [dE] with distance [dx]. In terms of previously discussed wave models, see Matter of Energy, it was argued that the concept of mass [kg], which classical physics assumes to be one of four basic units of measure, has to eventually give way to the idea of energy at the most fundamental level of existence. Likewise, it has also been argued that the source of all motion is caused by a differential of potential energy between two spatial positions, which then creates an energy gradient to which a force [F=dE/dx] might then be associated. While this issue will not be pursued at this stage, the following note might be seen to question the use of the word ‘force’ to explain one of the most fundamental causal mechanisms at work between particules within the Cordus model.
Note: Is it possible that energy has to be the most fundamental causal mechanism, not only of mass, but all kinematics, such that force is simply a convenient description of energy transfer. It is also highlighted that energy is a scalar quantity subject to conservation laws, while a force as a vector quantity is not.
At this stage, many of the concepts are only being introduced, although it is not unreasonable to highlight issues relating to the physical causal mechanisms being assumed by the Cordus model. However, this outline will now try to introduce both the similarities and differences between the electron and photon particule models.
As a broad generalisation, the Cordus model replaces the idea of a point-particle in quantum mechanics with the idea of a particule that can have variations of sub-structure, as outlined above, which can presumably be extended to explain all the other fundamental particles of the standard model. However, issues have been raised about this model in terms of the physical nature of the reactive ends, i.e. how were they created, what are they made of, what causes them to oscillate with a given frequency and how does the fibril physical connect them.
Note: This model clearly identifies itself as being conjecture, where its primary components cannot be observed and possibly lack the necessary mathematical rigor when compared against modern quantum field theory. However, the stated objective of the Cordus model appears to want to anchor its description of causality to physical mechanisms, such that cause and effect must presumably be associated with every element of the particule model.
From the perspective of any form of physical description, the idea
of zero-dimensional point-particles has to be seen as a questionable
mathematical abstraction to which the properties of mass, charge and
spin are assigned without necessarily explaining the actual physical
mechanisms at work. In this context, it is still unclear as to how the
substructure of the Cordus particule model, i.e. reactive ends, fibrils
and force flux lines, really provide a more substantive description
of cause and effect at the most fundamental level. At this initial stage,
the idea that a particule has two conceptual reactive ends interconnected
by a somewhat ethereal description of a fibril supporting the questionable
concept of superluminal signalling appears to add little to the
idea of physical realism. However, some attempt will now be made to
expand the description of the photon and electron particule models in
the following discussions.