Why Quantum Mechanics is a Coordinate System – (1362 words)

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nobody understands me… well, almost nobody…

Definitions

Ψ: The uppercase Psy is the General form of a Quantum Mechanical Waveform

The Measurement Limit: There are 3 dimensions of Space and 1 of Time.

For a refresher, please see the Periodic Table as the microcanonical Measurement Limit, and Quantum Geometry I. In short: there are 3 spatial and 1 temporal dimension on all levels of magnification. The level of magnification determines to what degree these dimensions are entangled, with the minimally entangled limit observed on the macroscale (Special Relativity) and the maximally entangled limit observed on the microscale (no elements past 118).

Introduction

A coordinate system is a means of ordering a space so that measurements can be made. This may seem silly at first: can’t we take measurements anywhere? Let’s examine the simplest metric: distance. Since our experience feels continuous (we cannot detect intermolecular spacing with our eyes, for example), it seems natural that we could make a continuous measurement between two points. However, given the discrete (indivisible) nature of atoms, it follows that that macroscopic measurements will only be approximately correct: QM Uncertainty precludes the absolute certainty of any measurements. Although we won’t often run into this limit in real life, it is helpful in understanding that all geometric coordinate systems (CS) are only approximations (by the discrete nature of the atom).

Of course this does not mean it is realistic (or desirable) to model space as discrete. Mathematics usually prefers an idealized CS (= continuous, that is: for any two different measurements, there exists a third measurement (different from the first two) which is larger than the smaller and smaller than the larger one (i.e. the average)). This seems reasonable … until we reach distances on the order of a single atom. At this point, attempts to measure the system will greatly perturb it: distance is not continuous on the fine scale.

Although the atomic nature of reality precludes true continuity, we still use geometric CS’s (because what else are we going to use?).

Geometric Coordinate Systems

Some popular 3D geometric coordinate systems are: R3 (Cartesian Coordinates), cylindrical and spherical coordinates.

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Cartesian Coordinate System

Although these coordinate systems are (pretty much) equivalent in the sense that they hold the same amount of information (a sphere is a sphere regardless of the coordinate system in which it exists), one CS will be optimal for modelling a particular shape. If we take a sphere centred on the origin for example, such is complex to define explicitly in R3: {x, y, z, | x2 + y2 + z2 = a2}, where a = radius of sphere. It is comparatively simpler in the spherical coordinate system which defines the sphere as: {a,0,0}. This is not because of any fundamental change or loss of information, but rather because R3 regards points in space as 3 orthogonal (perpendicular) linear measurements (x, y & z) and spherical coordinates regards points as an absolute distance from the origin, and two perpendicular angular displacements (see diagram below). The surface of a sphere is all points equidistant from a centre (“Origin”) and thus is much easier to model in spherical coordinates, where we have only to define the radius to fully describe the sphere.

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Spherical Coordinate System

Regardless of the situation we are modelling, the choice of the proper coordinate system is crucial. In geometric problems, measurements can be greatly simplified by changing coordinate systems. A popular transformation used by Physics and [the limitations of which were] elaborated in my previous post involves changing the centre of mass of the object to the geometric centre of the coordinate system. This operation is beneficial as it has the potential to reduce the number of variables (unknown quantities), simplifying calculations. That is: from the perspective of the CoM, the total linear momentum of the system is zero (because the CoM does not feel its momentum relative to itself). This is easy to understand by way of example. If we were watching Earth from a spaceship, we would see it moving. When we are on Earth, we do not. Thus we can [largely] ignore this motion in terrestrial calculations with no loss of accuracy and great gains in simplicity.

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The Cylindrical (Polar) Coordinate System

Fundamentally, a coordinate system is a lens through which a phenomenon is examined. It does not [usually although there are some exceptions by way of numerical limits] change the phenomenon under observation, but rather can be changed to better suit the experimental circumstances.

Quantum Mechanics

I have long argued that Quantum Mechanics (specifically the Copenhagen Interpretation) is a coordinate system. While the language of the Copenhagen Interpretation is more general than geometric coordinate systems (the QMCS can be applied to all geometric coordinate systems), we still note that its postulates are intimately linked to measurement vis-à-vis the event of [QM] observation. If the imposition of coordinate system serves to make measurements possible and QM measurements are restricted by the postulates Copenhagen Interpretation, it seems plausible that QM must be a coordinate system.

Below are the 8 postulates of the Copenhagen Interpretation.

  1. A wave function Ψ represents the state of the system. It encapsulates everything that can be known about that system before an observation; there are no additional “hidden parameters”. The wavefunction evolves smoothly in time while isolated from other systems.
  2. The properties of the system are subject to a principle of incompatibility. Certain properties cannot be jointly defined for the same system at the same time. The incompatibility is expressed quantitatively by Heisenberg’s uncertainty principle. For example, if a particle at a particular instant has a definite location, it is meaningless to speak of its momentum at that instant.
  3. During an observation, the system must interact with a laboratory device. When that device makes a measurement, the wave function of the systems is said to collapse, or irreversibly reduce to an eigenstate of the observable that is registered.
  4. The results provided by measuring devices are essentially classical, and should be described in ordinary language. This was particularly emphasized by Bohr, and was accepted by Heisenberg.
  5. The description given by the wave function is probabilistic. This principle is called the Born rule, after Max Born.
  6. The wave function expresses a necessary and fundamental wave–particle duality. This should be reflected in ordinary language accounts of experiments. An experiment can show particle-like properties, or wave-like properties, according to the complementarity principle of Niels Bohr.
  7. The inner workings of atomic and subatomic processes are necessarily and essentially inaccessible to direct observation, because the act of observing them would greatly affect them.
  8. When quantum numbers are large, they refer to properties which closely match those of the classical description. This is the correspondence principle of Bohr and Heisenberg.
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Subjective Consciousness is Wavelike

Geometric coordinate systems tell us how measurements are made (i.e. with lines or spheres). The QMCS tells us the same, but not from a geometric standpoint. We postulate that the parameters of the QMCS derive solely from the Measurement Limit of the universe.

The major difference with the QMCS is that we are not describing an ideal object (i.e. the Sphere in R3), but the fabric of SpaceTime itself (and associated measurement limits). Since reality is quantum mechanical, it is subject to the exclusions imposed by the Heisenberg Uncertainty Principle and measurements will thus be limited.

We must take great care to understand the action of imposing metrics on SpaceTime in the QMCS, lest we accidentally violate the Measurement Limit leading to 15 false particles in the Standard Model.

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It’s too many particles.

Additional Applications of the QMCS

Although above is likely difficult to understand, it must be viewed as prerequisite knowledge for understanding the QM nature of the mind. The individual subjective conscious (Ψ) is multi-dimensional, localized (of specific origin), entangled (particular measurements can affect Ψ in its entirety) and coherent (coherent enough to take meaningful measurements from). All of these attributes must be understood before we can draw meaningful predictions from the Quantum Mind Hypothesis.

We additionally note that although the Measurement Limit, there is no reason that Ψ (defined as the individual subjective conscious) should be bounded by 4 dimensions (basis vectors). This is because Ψ exists on multiple orders of magnitude (and such are approximately independent), both spatially and energetically.

Thank you 🙂

 

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