10. Reinterpreting Spinors
An alternative approach to interpreting the “otherliness” at the foundation of the usefulness of Spinors.
Introduction
Spinors, as mathematical objects in the geometrical plane, are unique in their ability to represent themselves in their original and identical mathematical orientation, not after 1, but only after 2 full rotations (720°) as demonstrated in Dirac's belt-rotation trick.
This paper is a set-theoretical definition change-proposal to be applied to Spinors for use and extrapolation to computational logics. Consequences of this definition change are discussed in the associated writings.
The classic scheme of the motions of the mathematical functions and its various manifolds in this 720° rotation (made synchronously across two separate, yet statically entwined fields), is defined not by the Spinors but the functions they seem to make tangible: entanglement. Spinors entangle two data layers of the same object to create a semi-stable, albeit “fuzzy”, data-mesh we call “observed reality” and can represent computationally for analysis.
That Spinors accurately represent reality is widely accepted in the success of QFT but what they represent as reality, is what these papers question with good cause.
In the past, meaning was attributed to Spinors as being the various geometric movements representative of real-world physics, in mathematical terms. Geometric functions like square root or functions with pi or log representing 3-Dimensional movements we attribute to physical behaviours, like “spin”. As such, Spinors are thought of as the equations that describe the fabric of reality.
The totality of these functions executed in sequence by Spinors can be seen as describing (in calculus-terms) the geometry of entanglement. Spinors are also considered both not really understood by anyone, psychologically counterintuitive, and suffering from a vagueness we experience as the wave collapse.
A way to view Spinors
By means of elucidation, we suggest their real-world meaning is that they, in the form of mathematical formulation (the yellow band connecting the two matrices in the diagram below) and like all formulas, take data that mean something in one field and reliably translate it into accurately representative data that mean something “real” in another field without losing their internal “sameness”: f(x)=y.
As such we classically represent them as two separate matrices (red and green) joining to describe the spin-object (yellow) or Spinor in the following picture:
The two data fields are mathematical matrix-based descriptions of the same dataset as two different matrices known to emerge in a spinor. These Spinors, however, have the peculiar trait that both these fields are as diametrically opposed as the ability to observe reality can tolerate (maximum difference whilst still being of the same). This distance between the matrices (the “void”) is described by the same computational perspective from which the Spinor is yielding an observable result (point-particle location).
They are also functionally defined by the “equal” (=) sign between two functions: F1=F2, where if one value x in F1 changes, the value y in F2 must change for the equation to successfully represent an existing spinor.
With the above visualisation in mind, the suggestion we make in this paper is that rather than computing two distinct fields, they can in fact be seen as two interwoven fields with small vertical discrepancies (measurement error/wave collapse) between the X and Y vertices where the data is considered “less-present” (where we don’t have enough data –enough similarity/aka it is “too strange” to make a connection across the Spinor) topologically speaking):
This suggestion can make us view Spinors a “search engine” for the numerical value of ‘y‘ from ‘x’, where making a change in the ‘x value’ in F1, will automatically produce the ‘y value’ for the same object, as it forces its way into either of the matrices by virtue of the equality of the two matrices. Once this ‘y’ value is derived from one static function (the Spinor’s sequential orientation of the various geometric functions), its values can be directly and instantly introduced relative to the x value in another matrix and the two layers can be superimposed to understand and calculate the relationships of the object better.
Understanding the ‘y value’ for an object, from its ‘x’ value, effectively makes the product of the function knowable and enables the object to travel across the Cartesian schemes. It also instantly makes two, one-dimensional computational schemes, three-dimensional.
Our proposal:
A change in the understanding of the angular motion – angular position relationship of the spinor and realisation that it does not only rotate in the horizontal plain, but simultaneously in the vertical plain.
Visually, here belongs the depictions of the cube with strings and the wires untangling on 360-degree, rotation and a matching video with not one but two axes’ rotation in both the Y and X axes, equally demonstrating a wave-motion that enables complete disentangling by a single bi-axial 360-degree rotation, contrary to the traditionally accepted definition of teh Spinor:
This new, bi-axial motion-pathway, just as in the classic Spinor representation in the mono-axial rotation, does not entangle the ribbons, even after a full, single 360˚ rotation. This, courtesy of the emergent wave-function that holds separate the “fabric of reality”. This model however, with its bi-axial rotation, consequentially does not require a “half-integer” counterpart, but rather the acceptance that it is just our perception that is limited.
This means in no uncertain terms, that angular position and momentum may be the ultimate physical reality, but they are perhaps not the only conjugate variables to be considered in computational mathematics. They certainly offer a useful approximation and computational understanding of a version of reality made real by means of the wave-collapse, but not of that reality which is not directly observed. Sadly, consequentially causing our understanding of reality to suffer from this wave-like lack of definition too. As if looking at the Spinor for information, but having the observer focus on where the membrane is, causing fuzziness and lensing of the surrounding area.
In this model we can represent the conjugated values of the Quantae as angular motion to angular inversion and not angular position, as previously stated in the defining use of the mathematical concept of the Spinor. The meaning of “inversion” as the (“most-conjugated (distant), yet still real (observed), -variable" (maximum strangeness)) conjugate value to angular motion could then be thought of as the absolute absence of it ever even having been there and the possibility of anything being there. Existence and potentiality.
They (the SO3 and SU2 matrices of F1 and F2) are considered two different expressions of the same thing, and their ‘sameness’ is the suggested location of entanglement, yet the functions that describe them produce a description of the same object from two different computational perspectives. As the same object’s data are processed through the different matrices, their initially “identical” values are calculated/perceived differently and create the two membranes, which are then interlaced at the nexus point of the Spinor. This creates relative computational loss through the different types of multiplications of irrational numbers by the different schemes. This relative “loss” becomes the data that defines the exclusion principle that arises from them, and in a sense, quantises the quale.
This latter sentiment reverberates the sentiment of a “maximum-strangeness the definition of the relationship can tolerate before it (the relationship) becomes irrational”. Enabling this notion of a quantisable “maximum-strangeness” or “otherliness”, as described by Pauli giving that trait the quality of either being a) of such a “Strangeness” (or of being strange in that specific way) or b) not. Offering all the Cartesian options that emerge from that binary position.
Holding this ability to quantise quale is of course interesting and Spinors can do this by holding that trait within them as a mathematical object that is either there, or not there (i.e. the two matrices are connected and form a point-particle, or they are not). We propose here that this makes them highly interesting mathematical objects that can be manipulated for specific types of “Strangenesses”.
What is simpler to explain however, is to show they successfully juxtapose the movement of SO2 and SU3 matrices and allow for reliable evaluation of the data within these pairs of matrices. Their juxtaposition has been proven efficient in all fields of calculation and is undeniably effective.
This utilitarian perspective on mathematics allows us to re-imagine the meaning of the limitations necessarily introduced on Spinors by Pauli et al. Even if those limitations have previously demonstrated value in their usage and development and will continue to do so in their current applications.
Pauli and colleagues did put the Spinors’ meaning as having the ability to contain/perform a certain type of “Otherliness”. One, they said, that most diametrically opposed the objects described by “Angular Momentum”, and they consciously selected to pair it with “Angular Position”. This was a choice. One that resulted in the creation of the set of “most distant-yet-related" sentiments within that computational dimension as being location bound. This has computational connotations that might make this choice challengeable. Our proposal is to make it perception- or observer bound instead by adding a rotation around the Y axis.
Time for a change?
The suggested change in this paper is for a “one-case use”-ful change in meaning of that “Otherliness” as described by the companion variable of “Angular Momentum”, and for it to be something other than “Angular Position”. We suggest “Angular Inversion” instead.
Angular position describes the orientation of the particle, which we feel might not get to the core of, or be the only type of, “maximum strangeness” that can be sought for and analysed when evaluating an object’s “existence” or its behaviours.
The position, after all, is not the strangest thing about it. Its “being” however, is. Yet they describe the same thing as data-layers, just from different perspectives. This shift in computational perspective emerges from the suggested change in Spinors' meaning and in real-world terms translates to:
An object’s data-load, sought to be understood by another, is added to by the other in a way that is optimised to achieve the computational goals of the agent receiving the data.
Or otherwise put: the observer changes their understanding/relationship to the object by observing it. Or: human, experiential (observed) reality changes by observing it. A wholly comfortable notion in the world of Quantum physics and demonstrated repeatedly by experiment.
And all we’re saying in this paper, is that adding this one rotational axis affords mathematical and real world (by means of the data-technical clinical experiment) proof of it being a correct description of our experienced reality.
Our suggestion is that the total and utter strangeness Pauli aimed for is perhaps only partially but not wholly contained within the juxtaposition of “Angular Momentum” to “Angular Position” and instead wholly contained within “Angular Inversion”
It presents a partial differentiation where the two conjugates are positioned as each other’s vectoral opposites. That is, perhaps, not quite as “Strangely” opposite as possible. Maybe only vectorially. “Strange” would potentially be something like “total inversion in meaning of its being (its existence)”. The companion variable of angular momentum, i.e. “existence of something” could therefore be “the potentiality of existence of anything” in the location of that point-particle at that time.
We suggest here this “inversion” could be a more diametrically opposed, and closer to the “maximum-strangeness” type of Strange that Pauli was looking for. One still with valid opposed companion variable meaning to Angular Momentum: that of Omni-potentiality of the orientation of the particle, but now with added mystery.
The reason given from a set-theoretical point of view would be that “that which is” is inherently linked to “everything which is that which isn’t what this is”. Because they are and otherwise couldn’t be. Very confusing sentences to say: they (what is, and what can be) are attached to each other i.e.: Entangled.
From a physics point of view this is useful as we accept one thing about reality: two absolutely the same things cannot be in the absolute same place at the same time.
Note: they can neither physically be the same “thing” nor be at the same “time”, encapsulating both temporality and locality.
That of being in a state of “being able to become something that is anything but that which it already is, from what it currently is”. The emergent property of possibly being anything even the thing it just was, but just that thing at a different point in time and therefore not the “same”.
The proposal:
To achieve this and as stated earlier:
We appeal to the meaning of the Spinor’s surface rotation around the Y-axis to validate a computing logic that would enable the development of a revolutionary healthcare solution by means of logic and pure math. Support to this proposal would change little for new discoveries in certain branches of physics but will help lots of people receive better healthcare.
To do so, we suggest that it is permissible (or at least there are no known theoretical objections) to, rather than go through only one single geometric rotation around the Y-axis, go through both the X and the Y axis rotations.
The inclusion of a rotation over the X axis would provide:
an inversion in the meaning from Quantum to Quale as suggested adaptation to Pauli’s notion of Strangeness
a mirror to the famous “Mexican hat” that is continuous to our current one
and would reframe Pauli’s exclusion principle to an “inclusion principle”, if, and when the perspective is taken to calculate the emerging fabric of nexus points instead of that of the membrane.
Meaning:
In a sense, this process suggested in the dot theory antropomorphises the meaning of Spinors from being “representative of the interactions that produce reality”, to being representative of “individually observed reality” (i.e. the observation of the disruption of trends, rather than the observation of trends). In this sense too, “time” as we understand it observationally, only exists because we are seeing its observed effect, whether it be the moving of the clock hands, or the change of seasons. In “reality” however, time only exists as an individually observed byproduct of the record of those changes.
This has significant implications to the framing of the meaning of data processed through the General Theory of Relativity, but in effect is merely a shift in one order of function of the whole theory and offers impeccable continuous computational perspective.
In that sense “time” is the record of the nature, pace and rate of change of data cross-referenced to our individual human notion of time as meaningfully experienced and partitioned into segments of the period between solar positions. As such it doesn’t, in and of itself, “exist” without observer to perceive the rate of change of the data that define the lived experience of the observer.
It is important at this stage to highlight the entwined, yet separate, nature of the fields of matrices as suggested in this discussion on change in meaning. Visualisation would be suggested as two topological meshes that have consistently emerging relationships keeping them in contact. This can be visualised as two elastic parallel membranes with hoops connecting them randomly across the space in between them:
The Spinor as such, can then be thought of as the nexus point “floating” within a matrix (yellow) described by the voids between Spinors and between the two membranes and as describing points within its own membrane. It is essentially the mathematical construct that connects the two membranes and interlaces their vectors in such a way as to give rise to a 3rd membrane made of rationally organised voids and functionally interconnected Spinor point-particles.
These nexus points then form the topological landscape of changes and rate of changes, which when observed from the individual lived experience’s point of view can gain meaning, one emerging meaning of which is our notion of “time”.
This is the change in computational perspective suggested. I think we just tended to think of ourselves as describing reality by describing the membranes when, alternatively, we can take the calculational perspective of being “in the space in between”.
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