Particle Manifestation of Quantum States Part 2

©Fernando Caracena 2014

Manifestations of Reality

What is Physical Reality?

Physics has grown organically from man's experience with nature and the development of his rational mind as he explored the internal mental world that is mathematics. The interaction of experience, through controlled dialogue with nature (experiments), with mathematical reasoning resulted in the growth of theory that is constantly being tested. In the process, properties of nature that were once judged to be fundamental, are no longer seen as such. At the present, physicists wrestle with the question of what is fundamental. Some have given up the quest for the true nature of reality and tell their inquisitive students to just shut up and calculate. This may be somewhat sound practical advice for graduate students, who do not want to spend most of their life working for an advanced degree, but after graduate studies, the nagging question of what is real remains.

In a previous set of blog entries, we have covered associated topics that touch on what is reality in physics. See for example, "Nature's Ultimate Joke" and "Emergent Properties and Physics" .

Particles as events

On the subatomic level, quantum mechanics governs the motion of “particles”, which are no really objects that can be followed along trajectories the way we follow ordinary projectiles. The word “particle”, on the quantum level, suggest a very small object. In quantum physics it really is a name for field quanta, which are discrete bundles of energy, momentum, angular momentum and other properties such as charge that characterize those quanta. However, as these “particles” move from some point A to another, their motion is not described as along a trajectory, but rather as along a wave train, and perhaps within a wave packet (such as a patch of ripples sometime seen on a lake's surface). When it is detected, this usually happens as a flash or equivalent, at some point B, i. e., as a point-like event. Because of its discrete properties that are delivered to the small area of impact, and its point-like source, our mind jumps at an image of a very small particle travelling along a well defined trajectory from source to point of delivery, not as an extended wave. This is the origin of the idea of a wave-particle duality. But, discreteness of of the properties of each quantum is all that quantum physics specifies. Between the source of the quantum and its point of impact, quantum physics does not assign a position to the particle. The quantum is spread out over the entire landscape [or universe]. Where it will likely be detected is described as an expanding wave train that progresses at a speed consistent with causality: the quantum cannot be detected as progressing much faster or slower than its initial speed, which is also not absolutely defined, but with a precision limited by Heisenberg's Uncertainty principle.

Although we can think of field qaunta as being spread out over an expanding volume of space that is described by a propagating wave train, the moment it is detected, its position collapses to a point. This is known as the collapse of the wave function, which is a paradox because it brings in motion that is faster than the speed of light. Quantum mechanics itself contains strangle nonlocal effects, what Einstein called spooky action at a distance.

The Matter Matrix and Localizaton

“What produces localization?” is an interesting philosophical question in connection with quantum physics. It is obvious that empty space cannot localize a field quantum because the space does not contain anything that the quantum can interact with, except the zero point fluctuations that form the basic fabric of space and alter the properties of the quantum, but are not localizable except as modifying the properties of field quanta. This is an important clue. It is the material medium that can receive a field quantum as a localized event. In the universe we have a matrix of matter that is made up of quanta trapped in stationary states, which constitute the atoms and molecules that make up the matter matrix. Quanta are emitted by processes on an atomic and subatomic scales by well defined transitions from excited states in matter, and they are absorbed by the reverse of the same processes in matter. A fundamental principle of quantum physics is that energy must be emitted or absorbed by matter as whole units, or quanta. If there is no way that a field quantum can be absorbed by a large area of a medium, because there is no resonant process there to absorb it, then the quantum cannot be absorbed. So it turns out that the most likely way that the quantum is absorbed is by the reverse of the process that created it, that is, in an atom, which is held somewhat fixed within a material matrix. Thus a quantum comes into http://existence in some very localized volume of a material medium and subsequently delivers its full load of properties at another localized volume of a material medium. The conclusion is that the large scale structure of the material medium forms the basis for localizing both the emission and absorption of field quanta. In transit between the point of emission and detection, the quantum travels like a wave that interacts as a wave with larger scale distributions of matter without losing any energy.

There are many subtleties surrounding the above question, the complete discussion of which, would expand to become the dominant theme here that would dwarf that of our main theme, but I will not raise these technical points here, reserving any such discussion for future blog entries.


The Fabric of Space and Time


Looking for a Correspondence

How do pure quantum states, which are not localized in physical space, become attached to that space? The answer to this question is partially related to ideas discussed in the blog entry, Substance and Form–Philosophy and Physics Part III.

Size of Atoms and Atomic Nuclei

To gain some physical intuition about what is going on in the generation of particle tracks in various types of chambers and their relation to quantum states, we need to look at the relative sizes of objects where interactions occur.

Atoms are very small fuzzy, ghostlike balls of activity consisting of negatively charged electrons bound to much smaller, but much heavier, positively charged nuclei. (See the blog entry on the electron.) Atoms do not have sharp boundaries, but are described by distributions of the orbital electrons that are shaped in space by the various bound states of electrons, well described by the Schrödinger equation. The bound states of orbital electrons are represented by standing waves, which can be demonstrated using sound. The electron wave patterns range in size from  0.3 to 3 Angstroms (Å), where 1 Å =10-10m. An example of the application of of the Schrödinger equation to the hydrogen was presented in the previous blog entry, The Hydrogen Atom Analyzed Using Commutator Algebra I.

"The diameter of the [atomic] nucleus is in the range of 1.75 fm (1.75×1015 m) for hydrogen (the diameter of a single proton) to about 15 fm for the heaviest atoms, such as uranium." --Wikipedia

Particle Trajectories

The question of localization of quantum events is touched on, but in an unsatisfying abstract way, in a Wikipedia article on the observer effect in physics, from which we take the following quote (from the section on Quantum mechanics):

"The theoretical foundation of the concept of measurement in quantum mechanics is a contentious issue deeply connected to the many interpretations of quantum mechanics. A key topic is that of wave function collapse, for which some interpretations assert that measurement causes a discontinuous change into an eigenstate of the operator associated with the quantity that was measured. More explicitly, the superposition principle (ψ = Σanψn) of quantum physics says that for a wave function ψ, a measurement will give a state of the quantum system of one of the m possible eigenvalues fn, n=1,2...m, of the operator \hat{F} which is part of the eigenfunctions ψn, n=1,2,...n. Once we have measured the system, we know its current state and this stops it from being in one of its other states.[3] This means that the type of measurement that we do on the system affects the end state of the system."

OK, I will try to translate some of the above mathematically abstruse statements into English after a small mathematical side comment.

Pure quantum states are represented by eigenfunctions that give precise values for measurements of key characteristics, called eigenvalues. The process of measurement is represented by the application of a mathematical operator to an eigenfunction, which simply gives back the original eigenfunction multiplied by the corresponding eigenvalue. The mathematics is part of advanced mathematics and the theory is well known. For example, see the Wikipedia article on eigenfunctions. Also, I wrote a previous blog entitled Further Mathematical treatment of Quantum States, which touched on these issues.

The pure states of momentum for a free "particle" in the physical vacuum (space) are represented in quantum mechanics by harmonic functions (sine and cosine functions), which go on forever along a particular direction. Such a particle in a pure quantum state has no position, rather it is everywhere, which is consistent with Heisenberg 's Uncertainty Principle as stated in a previous blog entry called, The old Quantum Theory.

Δp Δx ≥ h.                                                                              (9b)

Mathematically, the reason goes as follows: if the momentum is known for certain, then  Δp =0 and so the error in location, Δx, must go to infinity.

A previous blog entry entitled,  Holistic Physics--Some proposed solutions for some qauntum qandaries, argues that a lot of the wave effects of quantum mechanics result from the changes in possible states of motion that result in space as a result of the distributions of matter.

Looking for a Correspondence

So there is some kind of coupling between possible quantum states and the distribution of visible matter in the universe. Yet, matter emerges from the interaction of quanta according to a strict set of laws that result in spatial wave patterns, which may be confined to extremely small spacial dimensions. This process is somewhat like a solid 's (say ice) crystallizing out of freezing cold water. The process is dynamic, having both states exchanging water molecules. The limitation in this analogy is that the difference between the seething energy that constitutes space and forms of matter is vastly different, but is more like what Swedenborg describes as a discrete degree.


Quantized levels and continuous gradations

As in the case of the semi-autonomous functioning of organs, Swedenborg proposed that there are semi-autonomous levels of creation [called discrete degrees] that endow ..[these semi-autonomous levels] with the proper isolation and interactive properties to serve as articulating parts of the whole, which cooperate to fulfill the purposes of creation. In describing the organization of these quantized levels of creation, Swedenborg followed the general classification of ancient Greek philosophy of end, cause and effect, which correspond to beginning, middle and end.--Substance and Form–Philosophy and Physics Part III

In the emergence of matter from deeper levels of energy, we see a model of how the correspondence between the operation of levels comes about. First, a proto-space emerges as a sea of energetic activity, in which there is really no time and space, then by various internal processes, particle-like states (quanta) emerge, which are really still not confined in space. The various quanta next interact with each other to form various components of matter, which eventually condense into matter that is comparatively at rest and has shape. Space is then created out of of the feed back between the proto-space and the matter generated by it as a cause. Time results through the motion of matter. In this way, time and space are not really fundamental properties of anything, but really they are emergent properties of a holistic universe.


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