Quantum
Dynamics of Morphing Psy ~ Trance ~ Formations |

The Quantum Century December 2001 |

Introduction
Psy~trance~formations The Quantum Seeds of Revolution and Resonance Lets start from the beginning. The era of quantum theory kicked
off in 1900 with a discovery made by Max Plank. Plank was studying
the so-called black body radiation problem. Classical physics predicted
that black bodies should glow bright blue, a stark contradiction to the
experience of steelworkers everywhere. In order to simplify the
mathematical calculations, Plank restricted the vibration of the matter
particles according to the following rule: In 1905, Einstein produced three major publications that revolutionized
the world of physics. The first of these papers proposed a theory
in which a beam of light behaves like a shower of tiny particles. Picking
up where Plank left off, Einstein showed that energy is not only absorbed
and emitted in quantas, but energy itself comes in discrete quantum packets. Einstein
demonstrated his theory by explaining the photoelectric effect, light’s
ability to knock electrons out of metal. The fact that individual
electrons could be detected as they were knocked off a metal surface
seemed to imply that light was behaving like a particle. Moreover,
reducing the intensity of the light beam did not effect the energy of
the ejected electron. On the other hand, the energy of the ejected
electron could be effected by changing the frequency of the light. Einstein
proposed that these light particles, called photons, come in packets,
each with energy given by Plank’s expression: Einstein’s discovery was completely contradictory to the previously held scientific theories of electromagnetic radiation. In 1864, Clark Maxwell formalized the basic equations that govern electricity and magnetism, which are both now known to be aspects of a single entity we call the electromagnetic field. According to Maxwell’s theory, light is a wave. In other words, light is an electromagnetic vibration at a particular frequency. The electromagnetic field is actually the spectrum of all possible frequencies of light. In fact, the visible light we perceive with our eyes is a tiny fraction of this spectrum. Maxwell’s theory predicted the existence of light waves at lower and higher frequency than visible light. Shortly thereafter, radio waves were discovered, as were X-rays, infrared waves, ultraviolet waves, microwaves, and gamma rays. These different types of waves are just different names for light at various wavelengths. On the other hand however, Einstein’s theory demonstrated that light behaves like a particle. Further evidence supporting Einstein’s quantum theory of light
came in 1923 when Arthur Compton made an important discovery. The plot thickened even more in 1924 when Louis de Broglie proposed
that every particle of matter was associated with a wave. De Broglie
reached this conclusion by using Einstein’s two equations for energy: In the classical view of physical reality, there was no way to reconcile the differences between waves and particles. A wave can spread out over a large area, be split up in an infinite number of waves, and two waves can interpenetrate and emerge unchanged. On the other hand, a particle is located in a tiny region, travels in one direction, and crashes into other particles. Although waves and particles appear to be contradictory aspects of reality, we have discovered that all waves are also particles, and all particles are also waves. In order to further illustrate this peculiar wave/particle coexistence, let’s briefly consider a simple type of quantum experiment. Imagine we have an electron gun, a device that produces a beam of electrons. Also, our experiment will include a phosphor screen. If an individual phosphor in the screen is struck by an electron, the phosphor gains a little energy and immediately returns to its ground state by emitting a photon of light. Firing the electron gun at the phosphor screen produces a point of light on the screen. In this way, we can easily observe the particle nature of the electron. Next, in between the gun and the screen, let’s place a card that has a small hole in the center. If our hole is sufficiently small enough, we will observe very different pattern than before. The image on the screen is no longer a point of light, but a series of bright and dark concentric rings resembling a bull’s eye target. This pattern is caused by wave diffraction, and the light and dark rings are caused by wave interference. Interference is an inherent property of all wavelike interactions. If two waves come together that are completely in phase, the resulting wave has an amplitude which is the sum of the two original wave amplitudes. If the two waves are completely out of phase, the original waves simply cancel each other out. In general when waves meet, their amplitudes add. This rule is known as the wave superposition principle, and it applies to all types of waves. The bull’s eye pattern on the phosphor screen clearly demonstrates the wavelike nature of the electron. This pattern is created by a large number of electrons, which individually look like little points of light on the screen. That is, each electron is observed only as a tiny flash of light, but after a large number of electrons have hit the screen, the pattern of the bull’s eye emerges. This can be demonstrated in the following way. If we lower the intensity of the beam, such that only one electron can pass through the hole at a time, we would be able to observe each electron hit the phosphor screen. The exact location of each impact is completely unpredictable. However, if we use a photographic plate to record each impact, and allow the system to continue firing one electron at an interval of say one every ten minutes, then, when we observe the plate later on, we will see the same bull’s eye pattern as before. This experiment seems to imply that although it appears on the screen as a particle, each electron by itself travels from the gun to the screen as though it were a wave. It should be noted that this type of experiment could have been done using any type of charged particle, or any frequency of light such as infrared or X-rays. Entities, Attributes, Waveforms, and other Finite Fields of Possibility
Quantum theory is the method that has been developed to analyze experiments such as the one outlined above. This theory was created to deal with tiny creatures such as atoms, electrons, and photons. However, quantum theory has also proved successful in dealing with the atomic nucleus as well as subatomic particles such as quarks, gluons, and leptons. In principal, quantum theory also applies to the macroscopic world which we inhabit, as well as large scale astronomical entities such as galaxies and black holes. To date, quantum theory has successfully predicted the results of every experiment the human mind can devise. However, the predictive strategy of quantum theory is quite different than classical mechanics in one fundamental way: quantum theory cannot predict what will happen in a measurement situation, it can only predict the statistical probabilities of how likely an event is to occur. For any quantum entity, quantum theory predicts the probability of each possible value of a specific physical attribute. Depending on the nature of the measurement situation, a quantum entity may demonstrate many different types of attributes. Quantum theory does not say anything about what happens when the quantum entity is not being measured. First of all, let’s discuss what we mean by quantum entity, and how
the theory addresses these entities. A quantum entity is any thing, regardless
of its size, which exhibits both wave and particle characteristics. Usually,
a quantum entity will demonstrate either particle nature or wave nature depending
on the type of measurement it is subjected to. A typical quantum entity
could be a photon, an atom, or an electron; but a human, a planet, or the entire
universe could be considered a quantum entity as well. In this project,
we will refer to a quantum entity as a In most ways, the wave function, Ψ, is just like any other wave we are familiar with. Before discussing quantum waves, let’s take a look at waves in general. A wave is typically characterized by qualities known as amplitude, wavelength, frequency, and phase. The amplitude of a wave is a measure of the deviation from its rest state. In general, the amplitude is the maximum height of a wave. If the wave is cyclic, then the wavelength is the space spanned by one cycle. The length in time of one cycle is called the period. The number of complete cycles in a certain interval of time is called the temporal frequency. The number of complete cycles in a certain interval of space is called the spatial frequency. The phase of a point in a cyclic wave is a measure of how far into a cycle that point is located. As mentioned earlier, all waves obey the superposition principle, which states: when two waves meet, their amplitudes add. After the two waves move through each other, each wave retains its respective amplitude, and is thus unchanged by the temporary superposition. As we shall see later, any two waves can interact and depart each other’s company with their respective amplitudes intact, but the phases of the these two waves become entangled, and are thus phase correlated for the rest of eternity. When any two waves meet, the superposition of amplitudes depends on the phases of the each wave. This is characterized by constructive and destructive interference. For example, if two waves, each with amplitude of one, meet each other completely in phase, the resulting amplitude is two. If two waves, each with amplitude of one, meet each other completely out of phase, the resulting amplitude is zero. If two waves, each with amplitude of one, meet each other at arbitrary phases, the resulting amplitude will be between zero and two. Quantum waves have all the characteristics of ordinary waves that have been outlined above. In general, the energy of a wave is a measure of intensity, and is given by the square of the amplitude. For example, if you double a wave’s amplitude you quadruple the wave’s energy. Quantum waves are different from ordinary waves in one important way. Quantum waves do not have energy. Instead, the square of the amplitude is a measure of probability. This idea lies at the heart of how quantum theory works. To predict the results of an experiment, we must find the amplitudes of each possible value of the attribute we are measuring, and then we square the amplitudes to get a probability distribution which indicates how likely each possibility is to occur. Before we can make any type of measurement, we must first decide what attribute we want to measure. In general, quantum entities have two kinds of attributes: static and dynamic. The static attributes of an elementary quantum entity always have the same value. The major static attributes are mass (M), charge (Q), and spin magnitude (S). The values for the dynamic attributes of a quantum entity change over time. The major dynamic attributes are position (X), momentum (P), energy (E), and spin orientation (S z ). Before we can understand how quantum theory represents the dynamic attributes of a quantum entity, we must first discuss some more basic properties of waves in general. Early in the 1800’s, a man named Joseph Fourier developed a new language
which could be used to express any type of wave. Fourier showed that
any wave could be decomposed into a unique recipe of sine waves. Each
sine wave has a particular value of frequency Sine waves represent one type of waveform family. Another type of waveform family is the impulse family. An impulse wave is an infinitely narrow spike located at a specific location. Just as Fourier showed that any wave could be broken up into sine waves, the same wave could be broken up into impulse waves. The basis of digital electronic music is that any wave can be constructed by putting together a bunch of these impulse waves. The sine waveform family and the impulse waveform family are just two examples of waveform families; in fact, there are an infinite number of waveform families. Any imaginable wave can be decomposed into a unique recipe of particular members of any type of waveform family. This idea is sometimes called the synthesizer theorem. Any wave can be expressed as a unique sum of members from any particular waveform family. This means that any wave can be taken apart in an infinite number of ways, depending on which waveform family we choose to use. Conversely, if we choose a particular waveform family, we can create any wave imaginable. Quantum theory makes use of this so-called synthesizer theorem in a peculiar way. Quantum theory represents each dynamic attribute with a particular waveform family. In other words, every possible waveform family corresponds to some dynamic attribute of the quantum entity. The individual members of each waveform family represent different physical values of the dynamic attribute. To illustrate, let’s give a few well-known examples. First of all, the position attribute is associated with the impulse waveform
family. Each individual impulse wave is a narrow spike, characterized
by a value x which describes the position of that particular impulse wave. Each
possible position attribute value, Quantum theory works by associating each dynamic attribute with a particular waveform family. The relationship between the values of an attribute and the individual members of a particular waveform family is given by a rule, which can be quite simple in some cases, or very complicated in others. For the most part, physicists are concerned with the major dynamic attributes, which have been described above; however, there are an infinite number of different dynamic attributes since there are infinitely many waveform families. A specific waveform family has special types of relationships with other waveform
families. To understand these relationships, we must first introduce
some terminology. By the synthesizer theorem, we know that any arbitrary
wave can be broken up into different sets of component waves, depending on
which waveform family we choose. Breaking up an arbitrary wave into component
waves is analogous to putting the original wave through a prism. For
example, If we analyze an arbitrary wave with different waveform prisms, we will discover that some prisms break the wave into a small number of components while some prisms break the wave into a large number of components. The number of waveform components which a prism spits a wave is known as wave’s spectral width, or bandwidth. If a particular waveform prism breaks an arbitrary wave into a small bandwidth of components, we could say that the waveform family is similar to the original wave. If a waveform prism produces a large bandwidth of components, we could say that the waveform family is not similar to the original wave. If we take an arbitrary wave and put it through its own family prism, the resulting bandwidth will consist of only one wave component, which is the minimum spectral width. For example, if we put any sine wave through a sine waveform prism, the result will yield only one wave, which is exactly the original sine wave.We will refer to this prism, which does not split the original wave at all, as the kin prism. For any arbitrary wave, there exists such a kin prism, which does not decompose the wave into any components expect for itself. Conversely, for any arbitrary wave, there exists a particular waveform prism, which breaks the original wave into the largest possible bandwidth. This is to say that for any wave, there exists a waveform family which resembles the original wave the least. We will refer to this prism, which yields the maximum spectral width, as the conjugate prism. Thus, every wave belongs to a unique waveform family, and every waveform family bears a special relationship to a unique conjugate waveform family. An example of such a conjugate relationship is found between the sine waveform family and the impulse waveform family. Because of their mutual relationship to an arbitrary wave, we could say that these two waveform families are conjugate to each other. To illustrate this relationship between a prism and its conjugate prism, let‘s consider the following experiment. Imagine we have identified two conjugate waveform families, called A and Z. Fist, take any arbitrary wave X, and analyze this wave by using the A prism. The result will be a particular bandwidth ΔA of output waveforms. If we analyze X by using the Z prism, we will get a bandwidth ΔZ of output waveforms. Because A and Z are conjugate waveform families, if X is very similar to A, then X will not be very similar to Z. Conversely, if X is very similar to Z, then X will not be very similar to A. Consequently, there exists a limit on how small both bandwidths of A and Z can get for the same input wave. This limit is usually expressed by the following relation: ΔA ● ΔZ ³ C, where A and Z are conjugate waveform families, and C is some positive constant. We will refer to this relationship as the spectral area code. The spectral area code is a fundamental feature of all waves, including quantum waves. In the above example A and Z are as dissimilar as two waveform families can be. Now suppose we have chosen another waveform family K. Let’s assume that K is not very similar to A, but K is more similar to A than Z is. If we analyze the original wave X using the A and K prisms, there will still be a limit on how small both bandwidths of A and K can get for the same input. This can be expressed in the same way as above such that ΔA ● ΔK ³ C’, where C’ is another constant. However, since A and K are more similar than A and Z, the constant C’ will be less than C. If we were to use two waveform prisms that are very similar such as A and B, the spectral area code may yield a resolving limit that is close to zero. In other words, if two waveform families are very similar, there is no limit on how small both bandwidths can be for the same input wave. On the other hand, if two waveform families are strikingly different in character, the spectral area code limits the product of the two spectral widths. In this case, a small resulting bandwidth from one prism means that the resulting bandwidth of the other prism is huge. In quantum theory, every dynamic attribute is represented by a particular waveform family and a specific rule, which translates how individual members of the family correspond to particular values of the physical attribute. As a direct consequence of the spectral area code, every conceivable dynamic attribute bears special relationships to other particular types of dynamic attributes. Each dynamic attribute has a conjugate attribute in the same sense that each waveform family has a conjugate family. In general, if two dynamic attributes are related in this way, such that the spectral area code applies, we could say that each attribute is conjugate to the other. We noted earlier that the sine family and the impulse family are conjugates. We
also know that the sine family can be associated with the momentum attribute
of a Heisenberg’s uncertainty principle directly implies that the assumptions of classical physics were incredibly naïve. Before Quantum theory, physics was based on the formulation of deterministic physical laws, which could be used to predict the exact outcome of any system. In general, classical systems were represented by relationships in phase space. Every particle, or object, in phase space is characterized by a definite position and momentum. Assuming that one knows all the laws which govern a system, as well as the position and momentum values of a particle in such a system, one should be able to predict exactly how the system will change with time. This ideal formed the basis of classical physics and inspired the conception of a universe that operates like a giant deterministic machine. However, according the scientific discoveries of quantum theory in the early twentieth century, it is impossible to know the exact value of an object’s position and momentum at the same time. Thus, Heisenberg’s uncertainty principle delivered a fatal blow to the antiquated conception of long term predictive determinism in physical systems. In general, quantum theory does not predict the result of a measurement on a physical system at all; however, quantum theory predicts the probability of each possibility in the quantum system. Classical physics also assumed that all objects have inherent definite attributes which exist independently of the observation of those attributes. As we will see, the structure of quantum theory implies that the attributes of any aspect of reality are inseparable from the observation of those attributes. In fact, it is impossible to say for sure that something possesses any type of attribute whatsoever outside the context of some measurement situation. Quantum Theoretical Foundations of Morphing Psy-waves in the N + 1 Dimension
Before we delve any deeper into this mysterious theory, let’s review the basics so far. Quantum theory represents all quantum systems with a wave function, which we call Ψ. This wave function is not only determined by the quantum entity in question, but by the type of attribute we wish to observe as well as the measurement situation we have designed to detect such attribute values. For simplicity, we could say that Ψ is determined by the entire measurement situation. Granted, this description is vague, but it sufficiently expresses the fact that there can be no separation between the observer and the observed. The Ψ-wave represents all possibilities of the quantum system. Choosing a specific attribute to measure is analogous to choosing a waveform family prism which analyzes the Ψ-wave into component waves. Each component wave represents a possible value of the attribute we are measuring. Moreover, each component wave has a particular amplitude and phase. In other words, each possibility is assigned a specific coordinate value that represents the amplitude and phase of that possibility. The square of the amplitude at each possibility gives the probability that a particular attribute value will be observed if we were to actually make a measurement. The first mathematical version of quantum theory was developed by Werner Heisenberg in 1925. In Heisenberg’s model, a quantum system is represented by a set of matrices. Each matrix represents a specific dynamic attribute such as position, momentum, or energy. The probability that a system has a particular attribute value is determined by the diagonal entries of the matrix. An important property of matrices is that many types of matrices do not commute when they are multiplied together. If two attribute matrices don’t commute, then the measurement of these attributes is limited by the uncertainty principle. The progression of the quantum state in time is represented mathematically by certain laws of motion expressed using matrices. This first version of quantum theory is usually known as Heisenberg’s matrix mechanics. A few months after Heisenberg’s theory was created, another physicist,
named Erwin Schrödinger, introduced a different version of quantum theory. Schrödinger
created a wave equation, which represents the evolution of a quantum system
over time. The quantum state of a system at any instant is represented
by a certain field of possibilities, Ψ, such that each possibility has
a certain probability of occurring. As the quantum system evolves, the
amplitudes of the Ψ-wave change continuously according to Schrödinger’s
wave equation. The time dependent Schrödinger equation is usually
written in the following way: x is vector
whose component values represent all possible values of any attribute X, and Ĥ is
the Hamiltonian. The Hamiltonian is a linear operator that represents
the total energy of the system. An operator is a mathematical device
that transforms a given function into some other function according to a certain
rule. In the case of Schrödinger equation, the time dependent Hamiltonian
operator Ĥis equal to - (h / 2π i) d/dt. Without being
too technically specific, the important thing is that Schrödinger’s
wave equation defines a rule Ĥ, which describes how the Ψ-wave
changes over time. At about the same time as Schrödinger proposed his theory of wave mechanics, a third quantum theory was developed by Paul Dirac. This theory was rigorously formalized a few years later by the world famous mathematician John von Neumann. Dirac showed that the fundamental ideas of quantum theory can be represented in abstract mathematical terms by placing the theory in what is called Hilbert space. Dirac also showed that both Heisenberg’s and Schrödinger’s theories are special cases of his own Hilbert space version of quantum theory. Dirac’s theory is a mathematical formulation that resembles our previous description of quantum theory, which we described solely in terms of waveform families and spectrums. Hilbert space is not geometrical, but is an abstract way of organizing functions. Although
it is of little relevance to the goals of this project, we will present the
conditions which define Hilbert space. Hilbert space is a vector space
on which an inner product is defined, and which is complete, i.e., which is
such that any Cauchy sequence of vectors in the space converge to a vector
in the space. This abstract function space provides a natural reference
frame for analyzing the wave function Ψ. To illustrate the idea of Hilbert space and how it applies to quantum theory,
let’s take a general example. Imagine we have a quantum system,
which is composed of a The wave function, Ψ, is represented by a vector in Hilbert space. This
vector, which we will call the quantum ray, is simply a direction, which passes
through the origin of our given coordinate frame of reference in Hilbert space. The
quantum ray, Ψ, represents one quantum state of the system which is being
analyzed. Given our particular reference frame, the wave function assigns
a specific coordinate value, or point, to each basic ray. This coordinate
point of each dimension is just the projection of the quantum ray onto each
single basic ray. However, the coordinate value is not a point on a real
line, but is a point on the complex plane. Each coordinate value is represented
by a 2-dimensional complex vector which, if defined in exponential form, can
be written in the following way: Each dimension,
or basic ray, of Hilbert space, is associated with its own complex plane. The
projection of the Ψ-wave onto each basic ray
is given by a specific complex vector. If we let c
c
i
Φ
i
(x), for all i. The Ψ-wave, or quantum ray, is just
the sum of all these coordinate values, or complex vectors. Thus, Ψcan
either be represented as a single entity such as a vector in Hilbert space,
or by a collection of vectors in the complex plane such that each vector represents
a specific possibility. The quantum wave is a field of possibilities. Each possibility
is characterized by an amplitude and a phase. To find
the probability that a particular possibility will occur, we simply take the
square of the amplitude. If c
As noted above, the quantum wave function is a vector, in Hilbert space, which represents one quantum state. Without actually observing the measurement situation, we can ask how the Ψ-wave might change over time. For simplicity, lets assume there is only one dimension of time and that it always travels in the same direction. If the original Ψ-wave is calculated at time t o , then the Ψ-wave at time t 1 will be represented by a vector in Hilbert space which is different than the original vector. If we assume that time is a continuum, we can show that the quantum vector changes its orientation continuously. Thus, our spinning quantum vector, in Hilbert space, represents the continuously morphing Ψ-wave. Therefore, Schrödinger’s equation, which describes our spinning vector, is actually a mathematical representation of a morphing field of possibilities. As the quantum wave moves and changes direction, the magnitudes and the relative phases of all the coordinate values also change. Note, if the quantum vector travels continuously in Hilbert space, then each projection, which determines the possibility amplitude, also changes continuously. The probability distribution for each quantum vector also changes continuously because the probabilities are the squares of the continuously changing amplitudes. It is important to remember that although this theory can be used effectively to determine the probability distribution for the attribute values we are concerned with, these potential tendencies to exist are not inherent in the representation of the quantum entity. Unless we first assume a frame of reference, such as a measurement situation designed to observe the value of a specific dynamic attribute, the quantum entity is simply a wave of infinite possibilities. The frame of reference in Hilbert space is created based on which attribute we choose to measure. Only after we have chosen an attribute, can we analyze, or decompose, the quantum wave into complex projections along the orthonormal basic rays. In order to calculate the probability distribution for the possible values
of a quantum entity, we must first Without a reference frame of observation, it is meaningless to say that the
quantum entity possess any attribute whatsoever, let alone values for that
attribute. Perhaps this claim is too far out to except right off; however,
it at least appears safe to say that the internal structure of quantum theory
implies that the attributes of any aspect of reality are inseparable from the
observation of those attributes. For example, a In 1948, Richard Feynman developed a method for calculating a In the context of our phosphor screen experiment, quantum theory implies that
just before a flash is made on the screen we should not imagine that a tiny
The early interpretations of quantum theory reconciled this peculiar
phenomenon by assuming that the world is divided into two separate parts. The
unmeasured world, it was assumed, consists only of quantum potentials. On
the other hand, the measured world consists only of classical type actualities. This
interpretation of quantum theory was primarily advanced by Niels Bohr and Werner
Heisenberg and is known generally as the These two assertions are based on the idea that the dynamic attributes of
a In classical mechanics, the unpredictability of an event was attributed to
the ignorance of the observer. The observer’s ignorance, in the
classical sense, arose because the observer did not have a complete knowledge
of all the variables in a system, or the measuring device used in the observation
was technologically unable to yield perfectly accurate readings. It was
assumed that this ignorance could be overcome by making further technological
improvements to the measuring devices. However, in the Quantum ignorance is closely tied to the idea of quantum randomness. In
order to understand this idea better, let’s consider the The
Copenhagenists explain this phenomenon by appealing to what they call quantum
randomness. The basic principle of quantum randomness is that identical
physical situations give rise to different outcomes. If it is true that
the Ψ -wave gives us all the information we can know, then it is impossible
to predict exactly where the It should be noted that the In 1932, John von Neumann published a book called the Von Neumann showed that it is indeed possible to represent everything in the
world with Ψ-waves; however, the all-quantum theory only works if we make
one crucial assumption. Before dealing with this assumption directly,
let’s consider again the structure and dynamics of the wave function
in Hilbert space. We know that a particular quantum state is represented by
a normalized vector in Hilbert space. The dimensionality of our frame
of reference in Hilbert space is determined by the attribute operator we choose. It
is often the case that this frame of reference consists of an uncountably infinite
number of dimensions. Each dimension represents an orthonormal eigenfunction
of the quantum operator that we are using. Each of these orthonormal
eigenfunctions represents a specific attribute value of the The amplitudes and phases of each possibility are determined by decomposing the wave function into complex vector components, which are just the projections of the wave function along each dimension. However, a quantum system has a definite value for an observable attribute if and only if the quantum vector, Ψ, is an eigenstate of the attribute operator. This means that the system only has a definite state if the quantum vector is parallel to a particular eigenfunction. Since each eigenfunction of the operator is independent, or orthonormal, to all other eigenfunctions, any vector which lies along one single eigenfunction has no components along any of the other eigenfunctions. In other words, if the quantum vector lies along one specific eigenfunction, the amplitude at that possibility is one, and the amplitudes at all other possibilities are zero. However, in most cases, the wave function can only be expressed as a linear combination consisting of coordinates from many eigenfunctions. According to Feynmann’s version of quantum theory, the unmeasured In von Neumann’s analysis of the quantum measurement problem, he proposed
that the measurement act could be broken up into a series of small steps. In
this way the entire measurement act is visualized as a chain of events stretching
from the This idea of consciousness-created reality is a step beyond the claims made by those who subscribe to the observer-created reality interpretation. Observer-created reality enthusiasts simply claim that the observer is free to choose which attribute will be measured. However, they do not claim that the observer determines what the actual result of the measurement will be. Consciousness-created reality enthusiasts, on the other hand, claim that consciousness selects which one of the many possibilities actually becomes realized. Granted, these claims have not been experimentally proven, yet we might still consider some general consequences of this interpretation of quantum theory. If we assume that the basic principles of quantum theory are correct, we can easily derive two such interesting general conclusions. Firstly, as far as the final results are concerned, there is no natural boundary line between the observer and the observed system. Secondly, it is apparently the case that no such interpretation of quantum theory would be complete unless it successfully incorporates the function of consciousness, which seems to be inseparable from the manifestation of particular outcomes in the quantum measurement. There is, however, another interpretation of quantum theory, which is similar
to von Neumann’s ideas, but is not dependent on the idea of a wave function
collapse. This theory, called the many-worlds interpretation, was developed
by Hugh Everett in 1957. Up until now we have only considered the orthodox The most famous of these physicists, who opposed the quantum orthodox interpretation,
is Albert Einstein. Einstein strongly believed that quantum theory was
incomplete because it only gave a statistical account of elementary phenomenon. He
believed that it was possible to construct an ordinary object model of reality
in which the quantum entities had definite attributes whether or not anybody
was observing them. Einstein and the other physicists who believe that
an ordinary object model of reality is possible are sometimes referred to as
neorealists. The neorealist position is basically that there exists a
deeper, more fundamental, level of reality, which is not described by the quantum
wave function. As we have already seen, if we assume that the Ψ-wave
tells us everything there is to know about the As noted above, von Neumann’s proof asserts that no such theory of ordinary
objects can explain the quantum facts. However, David Bohm, a protégée
of Albert Einstein, was able to develop a hidden-variable theory which is seemingly
consistent with the observed quantum facts. Bohm’s hidden-variable
model of reality, which was developed in 1952, assumes that quantum entities
are ordinary objects, such as real particles, which have at all times a definite
position and momentum. Whereas the The Copenhagenists assert that the Ψ-wave is not real, but merely a fictitious mathematical device which happens to be effectively useful in calculating quantum probabilities. Bohm, on the other hand, asserts that both the quantum entity and the pilot wave are real things which actually exist. Although the pilot wave is supposedly a real entity, in order for Bohm’s theory to be consistent with the facts, this pilot wave must have certain remarkable characteristics which defy our conventional definitions of what is possible in reality. For instance, this pilot wave must connect with every particle in the universe, it must be entirely invisible, and it must transfer information at superluminal speeds, i.e. faster than light. Of these three, the first two properties of Bohm’s pilot wave are familiar within physics in that they are both aspects of the gravitational and electromagnetic fields. Superluminal connections, on the other hand, seem to be the one thing most physics hate most. This is primarily because the existence of superluminal connections would violate many fundamental assumptions of the orthodox theory on physical reality. For example, real superluminal transfers would contradict the orthodox themata which asserts that influences can only be mediated by direct interactions. This assumption, that object A can only effect object B via direct subluminal interactions, is called the locality assumption. Also, faster than light connections directly imply that the past can be influenced by the future. Most physicists, however, would like to believe that time travels in only one direction, and that what happens within each moment is solely influenced by what has already happened. In Bohm’s model, each particle in the universe, it is assumed, is associated with a pilot wave. This pilot wave is sensitive to the entire environment of the quantum entity, and the wave changes its form instantly whenever there is a change anywhere in the environment. Conversely, this instantaneously morphing field informs the quantum entity of such changes in the environment, at which point the quantum entity alters its values of position and momentum accordingly. However, this theory predicts that all pilot waves of all particles are instantaneously connected across the entire universe. This implies that the relevant environment, or measurement situation, which determines the form of the pilot wave, includes all events in the universe across all dimensions of space-time. Understandably, most physicists abhor the idea of faster than light, let along instantaneous, connections, and consequently, many physicists consider Bohm’s theory to be absurd. However, although it seems absurd to the quaint common sense intuitions of most physicists, it was soon proven that these superluminal connections are no accident, but a necessary condition of any theory of reality. Big news!
This proof we mentioned above was devised by John Stewart Bell in 1964,
and is known as As described earlier, Albert Einstein believed that quantum theory was not
a complete theory of reality. Thus, Einstein designed a specific thought
experiment, which supposedly demonstrates that there are aspects of reality
that are not accounted for in the quantum theory. In brief, the EPR source
emits a pair of phase entangled photons in opposite directions at the speed
of light toward two spatially separated detectors. Let’s label
these detectors A and B. In a generic form of the EPR experiment, these
detectors are designed to measure the polarization attribute of the photons. A
simple form of a polarization detector can be realized by using a calcite crystal
whose optic axis is pointing in a certain direction. The crystal divides
light into two beams. The If we assume that each calcite detector is positioned at any arbitrary angle,
then each detector will measure a fifty-fifty percent mixture of Quantum theory predicts that except at certain angles, such as zero and ninety degrees, the result of B’s measurement is determined by quantum randomness. In other words, at angles between zero and ninety degrees, the measurement at B is determined by blind chance. However, Einstein argues that since the photons are in what can be called a twin state, if detector A is measured first at any particular angle, then the photon at the other detector must possess a definite polarization attribute value prior to its interaction with the detector, which could be set at any angle. Einstein also argues that quantum theory only gives a statistical interpretation of attribute values which truly have a definite existence before the act of measurement. Therefore, Einstein concludes that quantum theory is not a complete theory of reality. The basic assumption which Einstein makes is that, after the photons have left the source, the situation at detector B is not affected by how detector A chooses to hold its crystal. This premise is known generally as the locality assumption. Einstein’s argument can only be refuted in two ways: either the locality assumption is violated, or there is no such thing as two spatially separated events. This perplexing thought experiment is known as the EPR paradox. While studying this thought experiment, The value of PC(θ), for angles between zero and ninety degrees, can be
measured by firing many pairs of phase entangled photons and then comparing
the series of measurement values recorded at each detector. The
polarization correlation attribute is a measure of the fraction of matches
between two detectors over a long series of photon pair emissions. Imagine
that each list of measurements is a type of binary message. If A and
B receive exactly the same messages, then the PC(θ) value is one, and
the angle between each crystal must be zero degrees. If A and B receive
exactly opposite messages, then the PC(θ) value is zero, and the relative
angle must be ninety degrees. In between these two extremes, the two
messages will contain a fraction of errors. For example, let’s
assume that if the crystals are orientated at a relative angle α, then
the two binary messages differ by one out of every four bits. In other
words, the error rate between the two messages is To understand However, the equation for the polarization correlation attribute can be derived
mathematically such that PC(θ) = cos
2
θ. For this equation, PC(30) = Although John Bell only proved that non-locality is a necessary factor in
describing a particular twin-state photon experiment, we can extend this idea
to include everything that exists in reality. We can make this type of
assertion because quantum theory predicts a phenomenon known as phase entanglement. Whenever
two quantum entities interact, their phases get mixed up. As these entities
interact and then depart their separate ways, the amplitudes of each Ψ-wave
come apart, but the phases of the two The basic idea of phase entanglement and non-locality rests on the idea that
once two entities have interacted, they are eternally connected by the correlation
between their mutual phases. An important consequence of all this is
the fact that the so-called entire measurement situation, which determines
the attribute values of a
Thus far, we have embarked on quite a lengthy discussion of quantum theory and it’s various interpretations. Although many concepts have been addressed in this project, the majority of the details have been left out. In addition, our exploration through this quantum realm has merely scratched the surface, and much of the most interesting terrain has yet to be explored. Although there are more advanced forms of exploration which lie beyond the scope of this project, it is my hope that this preliminary exploration will form a stable foundation such that further developments and interpretations may be explored at a latter time. For now, let’s conclude this journey with an overall survey of some ideas which might form the basis of future, more detailed, endeavors into quantum theory. It should be obvious to the reader that the implicate seeds contained within some of the ideas to follow will certainly contradict, and bring into question, many of our presently held notions concerning the nature of reality and consciousness. First of all, quantum theory, in the broadest sense, is a theory of whole entities. Any representation of a quantum entity must include a joint description of the entity itself as well as its observational context. It must be remembered at all times that there is no real distinction between the attributes of any aspect of reality and the experience of those attributes relative to a specific observer. Furthermore, if multiple observers are measuring the same quantum system but in different ways, the experience of these observers will also differ. That is, the experience of reality is relative to one’s frame of reference. In addition, regardless of whether we subscribe to an ordinary-object based interpretation, or to a statistical interpretation, the idea that the manifestations of physical reality are self-organized by abstract fields of possibility is unavoidable. Another unavoidable conclusion is that these fields must be interconnected in such a way that it makes absolutely no sense to speak of them as separate fields. For example, let’s consider two seemingly separate quantum entities, each resented by its own quantum vector in its own frame of reference in Hilbert space. If these two entities become entangled, then the composition of two Hilbert spaces, H a and H b , can be represented by the tensor product H a Ä H b , which itself forms an entirely new vector in a new Hilbert space. In other words, entangled entities are not represented by separate quantum fields, but are represented by only one Ψ-wave. However, it my contention that every aspect of reality is already phase entangled. This would certainly be the case if the cosmological Big Bang theory were correct. If it is true that everything that exists is indeed part of one phase entangled quantum system, then it might prove useful to consider the likely existence of a universal wave function. Although this field would be incomprehensibly complex, the nature of non-locality assures us that whatever it is, it is within every thing. Another interesting aspect of quantum theory is the manner in which quantum
waves morph over time. To consider a particular example, let’s
measure the position attribute of a However, it appears that we could modify our example to give the full picture
at one glance, as opposed to watching our quantum vector spin around. Firstly,
we will expand our domain of possibilities from all points in 3D configuration
space to the domain of all points in 3D configurations space for all time. Thus,
each possible value of position is now a point (x, y, z, t). The corresponding
Hilbert space is exactly what we would get if we assumed each possibility is
a point in a 4D continuum. Thus, we still have an uncountably infinite
number of dimensions, albeit a much larger uncountable infinity. Regardless,
we can still represent the wave function as a vector in this new Hilbert space
which decomposes into projections along each dimension. The square of
the possibility amplitude in this example will give the probability of measuring
the We have also seen that one quantum vector in Hilbert space looks exactly like
every other, namely a unit vector which has a absolute magnitude of one. Indeed,
it is merely our choice of which attribute we want to measure that determines
the probability distribution of all unrealized possibilities. The quantum
vector can only be analyzed by choosing a specific frame of reference. In
this way a For example, each possible reference frame could be represented by an independent dimension in some new type of space for which we have no name. Obviously, there are an infinite number of possible reference frames, and thus this symbol truly represents an infinite-dimensional field, which includes all possibilities. Whereas the coordinate values of Ψ are represented by complex vectors, the coordinate values of could be represented by vectors in Hilbert space; that is, each dimension in our new space represents a possible Hilbert space. If each specific frame of reference is a sense, i.e. context, then the field of all possible reference frames is truly the broadest sense. In general, we could say that by itself, is completely undefined, and at the same time, assumes all possibilities at once. Any particular Ψ-wave is generated simply by slicing this infinite-dimensional field with a lower-dimensional reference frame. This idea of slicing is a metaphor used for the creation of level-sets, which are lower- dimensional projections of a higher-dimensional object. In other words, all morphing quantum fields of possibility are created by reflecting at different angles. Each angle of perception constitutes it’s own frame of reference. In reality, all possible reference frames, or dimensions, are realized simultaneously. However, as a result of our ordinary mode of human consciousness, we specific ego-centered entities only perceive reality along one dimension at a time. If one is able to broaden his perception to include multiple reference frames, it is possible to experience reality along more than one dimension at a time. This is by no means a rigorous treatment of the concept in question; however, it is purposed simply because it is interesting to consider such claims given our current exploration into the unknown. In addition, it will also be said that this idea, outlined above, will not
work unless we assume that the ultimate source of all creation is right Another claim, which I feel is justified, is that the existing formulation of quantum theory applies to all entities regardless of their size. Quantum theory was discovered in the realm of atomic and sub-atomic particles because at these scales of reality, the effects of quantum waves become dramatically obvious. It is generally assumed that at a certain limit, the quantum laws converge to the normal everyday laws of ordinary experience. This may be the case for many types of attributes which physicists are preoccupied with, but in no way does it rule out the possibility that there may exist presently undiscovered quantum relationships between macroscopic entities such as humans, plants, star systems, or ant colonies. Logically, quantum theory applies to all things primarily because everything is made from the same stuff. It is all woven from the same fabric. It should be obvious that there is no natural division between the realm of a super-cluster of galaxies and the realm of a bunch of quarks. However, macroscopic entities such as humans and stars are not made of atoms, nor are they made of quarks. In general, it seems that everything consists of frequencies of energy-mass; however, on an even deeper level, these frequencies don’t exist unless we first define a reference frame. Therefore, it appears that the ultimate stuff of reality is simply pure infinite possibility As noted earlier, quantum entities are necessarily whole beings. Obviously, physical scientists have been able to detect atomic and sub-atomic phenomenon; however, I would argue that as opposed to being made of such building-block like parts, each quantum whole is a hyperdimensional complex within which reside lower-dimensional wholes. At the same time, each whole is embedded in a broader context of an even higher dimension. In other words, the fields which organize individual quarks are contained within broader sense fields which organize individual atoms. Atom fields, in turn, can be represented within molecular fields, which can be represented within cellular fields. In this way, we can easily conceptualize human fields, collective species fields, planetary fields, star system fields, and galactic fields.
It is also extremely likely that similar fields exist
which organize other types of dynamic systems as well. The following
list represents just a few examples: the weather, the stock market, a flock
of birds, the rise and fall of human civilizations, and the development of
an embryo. I would even go one step further and propose that quantum Ψ-waves
could also be utilized to represent entities such as thoughts, ideas, dreams,
and memories. These exotic entities, such as ideas, should qualify
as Physicists have been able to derive formulas for elementary quantum processes because they are simple in comparison to the more complex entities such as galaxies and ideas. It is extremely difficult to derive the wave function for a molecule, let alone a human being. In fact, I would say that it is impossible to calculate the dynamic field properties of a simple multi-cellular organism even with the most advanced supercomputers of the next 100 years. You might as well forget about using a pencil and paper. The main reason is that there are simply too many variables to keep track of. The only available mechanism, which is capable of computing such astronomically complex forms of relationships, is the electromagnetic neuro-chemical circuitry of the organismic bio-computer that we call the human body. In other words, we already possess a natural mechanism which can navigate through these fields intuitively, as opposed to analytically. Moreover, advanced forms of bio-technology, such as human beings and stars, can easily tap into even more powerful systems of organic bio-technology. For example, humans can open a direct connection to the planet, our larger whole, which in itself, is an incomprehensibly more evolveded expression of the one quantum entity. This idea is analogous to a network of computers which are all connected by a main frame or a hub. The sun, in turn, can open a direct connection to the center of the galaxy, an even larger whole. Implicit in this view is the necessary assumption that all forms of quantum whole entities are expressions of consciousness. This does not mean that galaxies are conscious in the same way that humans are, but it does imply that all forms of creation, no matter how alien, are truly conscious in their own way. In fact, it seems that humans today are operating in
Hyperdimensional human in trance
Hyperdimensional human beyond 2012
Morphology Bohm, David. Herbert, Nick. Von Neumann, John. University
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