Primer On Quantum Mechanics

"It's about the balance between exclusion and inclusion"

    Introduction. It is said the best way to enter QM is through the double slit (two slits, dual slit, twin slits) experiment performed with photons of light or with electrons. Indeed, as there are several different ways of interpreting this experiment, it makes an excellent gateway. For completeness, QM behavior of both an electron and a photon are described side by side, because their interaction mechanisms with double slit geometries are a bit different. For example, an electron has an inherent ("natural") propensity to spread while a photon does not. The {pod} insertion signifies the point-of-departure from college text QM.

    Background. The basic parameter is an electron's moving energy, which is no other than the electron's momentum. There exists de Broglie's relation between a momentum and a wavelength, each of which represents a particular electron as a 'moving particle' and (or?) as a 'wave,' and each of which is the measure of the electron's energy. When an electron is localized, it is (or becomes) a particle with mass and, therefore, the electron's moving energy is its momentum. As a wave the electron is nonlocal (disappears, spreads, unbecomes definite) and has a virtual mass {pod}, while the electron's energy is (proportional to) its frequency. In Pythagorean-speak, an electron becomes the 'undefined dyad.' "Dyad" means even or twofold or double-ended, while "undefined" means nonlocal. The electron's frequency is the reciprocal of its wavelength. Yes, the first question you always ask is, "Where is the energy?"

    Although the double slit experiment is a gateway to quantum mechanics, Clinton Davisson and Lester Germer 1927 experiment shows an electron behaving as a wave: A single electron (spreads and) interacts as a wave with plurality of atoms in a crystal. Refraction, a wave property, begins to manifest because the angle of departure is no longer the same as the angle of incidence.

    What's been corrected. The term 'particle-wave duality' is incorrect because it is clearly 'momentum-wave duality.' The wave relates -- via de Broglie -- to momentum and, since we can give any particle any momentum we want, we can get any wavelength we want. A particle such as an electron must be moving to have momentum and only then it could manifest its wavelength. This is big because it is about the absolute rest {pod}. Being a follower and talking about the particle-wave duality instead of momentum-wave duality is not bad, it just isn't the best [it takes you on a detour but many end up in a never-never land of an intractable context, which is fine by me]. If you need some background on de Broglie momentum-wave relation, you'll find it as one of our DSSP topics. The thing here is that the reductionists don't want you to understand quantum mechanics. Once you understand QM you will never go back to the reductionists' fold.

    What's new. The state of a (moving) particle electron and the state of a (vibrating) wave electron are mutually exclusive {pod} and, therefore, there is an act of transformation between the two states. I like to call the wave state of an electron the virtual electron or the virtual wave. This is because there are real waves (ocean waves) and there are virtual waves -- also called wavefunctions. The real-virtual electron transformation is reversible. An electron disappears {pod} when it becomes virtual but continues to exist (it is not "gone") and can localize again (reappear). A virtual electron is in the virtual domain and is not in some "other reality," for each the real and virtual domains, though unique, share the same and everyday 0D-3D space. The way you bypass the befuddled scientist is by appreciating that any wave, including the virtual electron wave, is one contiguous entity. The virtual electron is at several places at one instance of a time but only as a wave. This is not unlike the wave of a photon and this is also the reason the electron wavefront arrives at multiple slits (or multiple atoms) simultaneously. A scientist is vexed by thinking that a virtual electron could be in different places as a whole electron -- or in different places as several fractional electron(s) -- but the scientist then quietly ignores the fact that the virtual electron has wave properties.

    What's not new. NASA's clueless but they are getting better at picking up the falling debris.

    What is in the book. An accelerated electron has moving energy yet such energy is one-dimensional. Can we modulate a single (free) electron with any form of 0D, 1D, 2D and/or 3D energy? Yes, the how-to is in there.

    What's not in the book. Quotes by the so-called famous people (because I could write several contradicting books each backed up by such quotes). Fundamentally, science gets politicized and thus corrupted, particularly if new laws or power moves are to be rammed through. This is particularly prevalent in countries without direct elections although the "global warming" is a good if unsuccessful US example.

    We are now ready for the dual slit experiment.. ..

Take this page out of frames

 Double slit experiment - position measurement happens at screen. Top view

A free electron, when moving toward two or more narrow slits, spreads out and becomes a wave. A single electron wave then goes through the slits simultaneously and -- landing on a screen on the other side -- makes (reduces into) a single dot on the screen. The second and other electrons that follow, however, do not always land on the same spot and after a while a pattern is discerned called interference (I prefer superposition). The electron superposition pattern emerges while each and every electron-as-wave moves individually through the slits, and it is then also appropriate to call it the electron self-superposition.

When the experimenter allows but one electron (or one photon) through the slits at any one time, the superposition pattern continues to form without a change in shape. Electrons (or photons) could then be released at will and produce an identical pattern: each electron (photon) acts on its own as it is passing through the slits -- that is, electrons (photons) do not interact with each other as they move and pass through slits. At this point we are not mixing electrons and photons, so it is either electrons or photons. Electrons alone do not interact with each other as they pass through the slits. Ditto for photons. Self test:-) If the last two sentences are correct, how can we get the superposition pattern? After all, something must be interacting if the pattern is to form. You will want to get the book to get at the mechanics. Think superposition vs. self-superposition.

The book you will thoroughly enjoy
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How can an electron go through both slits but make a single appearance (dot) on a screen? Quantum Pythagoreans book illustrates and describes quantum mechanics at all scales. More ..

As a follow-on, you may want to visit the exact division of a circle, for the electron in the atomic orbital is able to close upon itself only if its wavelength can fit into a circle in exact integer multiples. Not all integers divide a circle exactly. It is beginning to look like the numbers rule..

Interference vs. Superposition. The word 'interference' implies mutual displacement while 'superposition' implies inclusiveness. Mass particles are displacing each other and no two mass particles can be in one place together -- whenever, for time always follows. Because virtual electrons are mutually inclusive, and because photons of light are also mutually inclusive, superposition is a more descriptive word when dealing with the two-slit experiment in general. Real electrons have exclusive qualities of a mass particle, virtual electrons do not {pod} -- part of the transformation. Here is where the reductionists hold their ground. If they were to use the word 'superposition,' you might get attached to the truth.

Waves can add to zero during superposition. Waves are nonlocal and If you have energy questions arising from zero superposition then click on through to this DSSP topic.

As you become more familiar with this site, multiple electrons under radial symmetry must also deal with harmony (more in the book, too).

An electron acquires a wavelength that is commensurate with its speed. (Photons, on the other hand, move at a constant speed and their wavelength is fixed after leaving their source.) Treated theoretically by de Broglie, the duo of Davisson and Germer showed how electron's lab behavior matches up with math's wave mechanics. The electron speed, which is also the electron's momentum (through a mass multiplier), transforms into a wave and, consequently, an electron becomes nonlocal {pod}. The electron wavefunction now has a position uncertainty -- really a position spread -- as well as a velocity spread. An electron's position spread is easy to visualize, for the electron is not localized and becomes a "cloud" along with its charge. One could also call it a mass spread or a "parallel" mass. A velocity spread calls for a visualization where the wavefunction can move and expand -- independently or simultaneously -- in one, two, or three degrees of freedom, depending on the (computable) geometry of the external environment. An electron, then, can travel in up to three different dimensions simultaneously {pod}, for the virtual electron is but a wavefunction.

Wavelength uniformity. You want to use light consisting of identical wavelengths such as those of a laser -- or electrons accelerated to identical speed. Since each photon acts independently of all other photons, you can mix different light waves or apply white light, but then the superposition pattern will not be sharply delineated. You don't want to mix photons and electrons because they interact (see text), but you may want to see the result of the interactions to help you with the understanding of the inherent mechanics of the double slit experiment.

Scientists eagerly label anything that moves. Light has a wide frequency spectrum and it is then appropriate to talk about heat, radio, visible, or hard (X, gamma) radiation. Virtual electrons, however, do not lend themselves to easy labeling because in addition to frequencies they also have spatial existence in up to three dimensions. But of course, ether is the perfect and proper word for the virtual electrons but I would reserve that word for those occasions when you feel like keeping your science friends quiet. They are clueless about ether and you can even enjoy watching them rolling their eyes.

Some textbooks go to great lengths stating that the electron acquires the wavelength "computationally" but not in actuality. On this site, an electron becomes a wave -- that is, a wavefunction. This is our early and fundamental point-of-departure. The electron's wavefunction is inherently nonlocal. Can you follow how the energy conservation holds during electron transformation? -- Very important that the conservation of energy holds at all times because the conservation of energy has priority. The concept of priority is of the Pythagorean origin. (Why energy has priority is in the Quantum Pythagoreans book.) A virtual electron is in (hyper)space undergoing hyperflight. In the illustration (compound image) of the undulating pattern above, the electron's probability distribution is the electron. Ditto for the photon. Different geometries, then, shape the electron or photon in space without reducing it.

 momentum-wave duality

A transformation between a particle (real, hard electron) and a wave is really a transformation between the momentum of an electron (or another particle) and its corresponding wave. The electron must be moving to acquire mo and a wave property. We are thus dealing with a momentum-wave duality rather than a particle-wave duality. When an electron is not accelerated, it could be bound as a particle with mass but it has no mo and no wave properties.

Self test:-) If you have some background on de Broglie's work and realize that de Broglie has worked with the linear but not the angular momentum, you are doing well. Angular momentum is a rich subject and (before you put a flywheel in your car's trunk) you may take a looksee on a page dealing with the spin of an atomic electron as well as the macro spin of a planet.

A quick treatment of a moving particle -- wave duality is in this January 2006 DSSP topic, which makes a case for an electron's mass disappearing. If the electron's mass remains in one spot instead of becoming a nonlocal wavefunction, the dual slit experiment explanation becomes intractable. That is the reason Feynman does not even get close, for he offers but intractable "solutions" such as sum-over-histories. Summing up all possible paths is an intractable process for the lonely electron. Intractable methods -- exemplified by the 'traveling salesman' problem -- are not found in nature. Any scientist offering intractable methods simply does not know. For example, [our favorite dumb math guy] Dedekind uses an intractable proof which concludes at infinity [guess he is still at it]. Schrödinger was the first to apply de Broglie wave postulate to mathematically model and solve the actual wave-based behavior of an atomic electron.

The superposition pattern an electron makes is the same as the one caused by light. For a single photon of light, the pattern forms when a branched photon exits as two waves, one from each slit, and the branches are added for lighter shade or subtracted from each other for darker shade as their relative position (phase) shifts. Light's relative position shifts because light comes out of the two slits simultaneously (coherently, in phase) and arrives at different parts of the screen along different paths. Simultaneity is a crucial property because if light were not coming through the slits coherently, the superposition pattern could not form. If photons were to pass through either one of the slits as individual photons the superposition pattern cannot form. Each and every photon must "split" -- really branch -- because coherence at the exit from the slits is a necessary condition for the creation of superposition.

Every individual photon and every individual electron behaves the the same way. Each photon (and each electron) behaves independently of all other photons (electrons). The wave representation of a moving electron or photon forms superposition ("interference") pattern that is computable in accord with its own, and therefore individual, de Broglie wavelength.

Does a photon physically split or is "split" photon a parted photon? You need to know the answer if you want to continue at fast pace. Take a side order with a "split" photon DSSP topic from February 2007. If you struggle with that, you will need to review the entire section about light. You will then have fun with another topic in February '05, where a split photon is split again and its wavefunction added (superposed) for a preferential path. You will also understand why light propagates at different speeds through different media even though no energy exchange takes place.

For electrons, the superposition pattern is visible to us as stripes of various gray levels. A single electron strikes a particular position on the screen, another electron strikes another position and, over time, the superposition pattern becomes apparent even though only one electron at a time passes through the slits. A particular stripe on the screen is a lighter shade of gray because electrons strike there in greater numbers (stripe is more luminous). Since the electrons strike a particular region on a screen with certain probability, many electrons need to go through the slits before the pattern emerges. The same phenomenon is observed with any particle -- that is, the attribute of the electric charge is not necessary.

Earlier we made a fundamental assertion that a free electron spreads and becomes nonlocal. But now I claim that the electron makes a zero dimensional dot on the screen as it becomes (again) the hard electron with the parameter of mass. There is no problem here if you figured out that the realization of an electron is the same as an electron's near instant reduction. (Also think about differences between the electron and the photon at reduction -- each behave differently.)

One of the most significant misunderstandings concerns the shape of the wavefunction of either a photon or an electron. Almost all scientists think that the undulation of the wavefunction is about the energy the virtual entity carries. Not so. The wavefunction is strictly the probability distribution (or "density") of an entity. In and of itself, the shape of a wavefunction is not indicative of the particle's energy. The experimenter must know the interacting geometry before he or she can make energy assessment.

A photon or an electron wavefunction can be changed dramatically from one geometry to another while the energy remains the same. The wavefunction, in and of itself, does not reveal the energy component even if subjected to Fourier analysis. The wavefunction is about the spatial reach of a photon or an electron. An electron can be spatial in up to 3D while a photon takes but 2D -- although a photon's 2D wavefunction can rotate (circular polarization). The energy content is another component of matter {pod}, which is also wave based. As you may well imagine these components are interconnected but the difficult part is in figuring out the interconnection geometry and the computing mechanism (Quantum Pythagoreans book treats this in some detail because energy is the only parameter that can form a continuum).

If you like to supplement your work with esoteric dimensions, think Sphinx. Yes, Shu makes an appearance and when Tefnut runs away to Nubia all hell breaks loose.

.. and then Thoth sends an eye to look for her ..

Oh, the ancient Egyptians strongly associate with sound and you also want to think of Shu as the sound of the "expanding air," for example. (Chinese don't use sound but associate visually, and so you want to see what the associated patterns might be.)


The electron has never been split and so the parameter of charge appears to escape the quantization. This is but a rudimentary viewpoint that presumes that partitioning is the same as quantization. Quantization, however, refers to particular and non-continuous values the atomic electron's properties (electron's variables) can acquire such as the angular momentum.

Since the mass of the atomic particle becomes nonlocal, its charge -- if any -- becomes nonlocal as well (spreads in space as one entity). The electron thus acquires a new variable -- that of position spread. Electron's nonlocality, at times called the electron charge cloud, may give the impression that the electron, as well as its charge, may partition or split. For example, quantum mechanical solutions for some orbitals indicate that a single electron is above and below the nucleus. [Nothing metaphysical here -- it could just as well be left and right.] That is indeed the case but the wavefunction is contiguous in volume and is never zero going through the nucleus. The apparent partitioning of the electron and its charge is then the result of the geometric solution (and a standing wave at that). The claim that there exist sub-sub atomic particles with fractional charge such as quarks is trying to treat the electron's distribution peak(s) as separate entities, which is incorrect [stupid, really] because the electron will reduce before it could be partitioned. Only silly scientists think that a wave can be split because they apply left brain methods to virtual entities and without being cognizant of the variables' priorities (independence-dependence character). Scientists also cannot differentiate between partitioning (left brain method of division) and parting (right brain method of disconnecting), which happen during the operation of cutting, for the cutting operation has different results depending on the (real or virtual) entity being subject to the cutting operation. Algebra is inadequate.

[Well, at least we all understand the operations of partaking and partying.]

The reduction of a virtual entity (a wavefunction) is at times called decoherence. Coherence happens when the virtual entity is subject to symmetrical environment (slits, crystal, beam splitter). The symmetry, in and of itself, introduces coherence to the wavefunction's distribution. A photon can be split four ways and one of its branches could later be reduced but that does not mean that the wavefunction decohered. Scientists fancy terms such as 'collapse' or 'decoherence' but the wavefunction can be modified in an infinity of ways. In fact, a wavefunction can partially reduce and do so instantly.

Quantum Pythagoreans book introduces a relationship between a wavefunction measurement and the probability of a full wavefunction reduction.

 To our store. This design is called Mars Again. We have a collection of nature inspired designs in general and the five point star designs in particular. We are inviting you to see select designs -- or visit our store at Zazzle (.com/Mike_Geo) to see how you could look in a tee, a hoodie, or a long sleeve shirt. You'll be cool in the best Pythagorean dress up tradition. The design shown here is called Mars Again. The design at the top of the page is called The Great Pumpkin but at times I also call it The Twins.

We can also line up electron detectors instead of a screen and keep a cumulative electron count for each detector. Using detectors with counters, the superposition pattern will look similar to the following illustration:

 Electron or photon superposition (interference) and subsequent reduction after passing through two slits, Mathematical simulation with statistical methods.
Electron or photon (self)superposition after passing through a dual slit.
Graph produced by the author's adaptive sort algorithm

The two-slit experiment with the resulting undulating envelope pattern may not seem a particularly difficult phenomenon to pursue. There are instruments that can detect an electron as it is passing by, and an experiment was set up to do just that — by placing detectors just in front of the slits. When we do determine which slot the electron passes through, though, the superposition pattern disappears and the electron behaves like a straight-moving particle. When we remove the electron detector the superposition pattern comes back. The dual slit experiment shows nicely that an electron can be a virtual entity or a real entity but not both. The electron detector facilitates the operation of positional measurement.

The real-virtual behavior of an electron goes at the heart of the present scientific method. The classical definition of the scientific method is to objectively describe a phenomenon by determining its repeatable and quantifiable characteristics. The objectivity is gained by measurement that enables verification of a hypothesis and confirmation of theoretically obtained equations. There is great comfort in the ability to describe, by equations, any phenomenon. In the case of a single electron simultaneously passing through two or more slits, the measurement does not work. Not only does the measurement spoil the experiment, but also one can never hope to understand the first phenomenon with direct measurement. When an attempt is made to verify the hypothesis by measurement, one phenomenon is replaced with another. The measurement shifts us into a qualitatively different context which has very little to do with the initial observation. The premise of "under controlled conditions" forces one kind of behavior to exist in one domain while excluding the experience of another behavior in another domain {pod}. While a single electron indeed passes through the slits simultaneously, we can reach this conclusion only indirectly and through the preponderance of evidence.


The validation of the 'momentum-wave' duality is through the conservation of energy. An electron is given energy through acceleration and the wavelength computed. The wavelength's value is verified using known geometry and wave mechanics.

Because a particle must be moving before its wave properties are able to manifest, a better way of seeing this mechanism is as the momentum-wave duality and not as particle-wave duality. If an electron is not accelerated, it still could be a particle but it has no wave property and then such an electron has no mo and no wave. (The actual electron with all of its properties is described -- along with applications considerations -- in the Quantum Pythagoreans book.)

Correcting 'particle' to 'momentum' seems innocuous but the visualization of a 'particle' results in an error that could take you on a detour courtesy of your inept and politically saddled teachers.


The Book
 To Publisher...
Smart questions come from those who know the truth. Yes, you can sculpt light and virtual electrons in 1D, 2D, even 3D -- but not in 0D. More .. ..

Should you pursue optics in more depth, you will be able to confirm that the interferometer instrument can operate the way it does if and only if each and every photon coherently splits (parts) as it passes through the beam-splitting mirror. The interferometer cannot work the way it does if some photons reflect and some pass through. Half-reflecting mirror (also called half-silvered mirror), then, presents the photon with qualitatively identical construct as the dual slit. If the photonic components are recombined coming from each branch of the interferometer, a self-interference also happens but the pattern does not resemble the two-slit interference pattern [think degrees of freedom]. Visit Here, have some light with ether on top! that talks about the Michelson-Morley experiment. Also relevant is our DSSP topic for September'00.

Every book and textbook on quantum mechanics treats the dual slit experiment. If the author takes the position that photons or electrons do not spread, he or she then has no choice but to ignore the requirement of coherence (at slit exit) to get the superposition pattern. Some authors argue that an electron cannot spread and define the electron as "irreducible," even thought an electron does not have a well-defined position within the atom and while irreducibility, in and of itself, does not preclude an electron to spread while remaining whole. If the author maintains that an electron passes through one slit or the other slit as one piece, the classical interpretations of the dual slit experiment are at their most charlatan — some claiming the existence of phantom electrons with field-perturbing characteristic. Feynman interpretation is wacky. He introduces an intractable any-path-is-possible method so that he can claim that the point electron could travel "everywhere," which then allows the electron to go through both slits -- all this at finite point-electron speed. You should get a refund for a reductionist nonsense such as this. This ain't even entertaining.

The present mainstream science consensus is that a photon can split and go through both slits simultaneously but an electron cannot. Scientists ignore the fact that the superposition patterns of a photon and electron are qualitatively and mathematically identical.

But of course the electron enters the two slits simultaneously. Here is an illustration of it in our Jan. 2012 DSSP topics.

Claus Jönsson was the first in 1961 to show the electron dual-slit superposition experimentally and with the precision of slit dimensions that today would be in the category of 'microstructure.' Tonomura at. al. performed the electron interference experiment in 1989. Tonomura shows electrons parting around the bar and reducing at the screen behind the bar. [There is a great Japanese myth of the ancient Japanese gods "parting around heavenly bar" and having good time while doing it -- as long as she is not very noisy about it. For brainwork you want to figure out why their spear created the largest island.]

Binding a particle. Electron-photon interaction

Once we reach the conclusion that an electron actually spreads as it must if it is to pass through both slits coherently, one can extend the quantum mechanical foundation to the macroscopic scale {pod}. If we want to see this electron again and determine its position in space, we can use short wavelengths of light because a longer wavelength would go around the spread out electron. The light (or a laser beam) we use for observation goes around or "hugs" the electron, but nevertheless interacts with it such that the electron does not spread out beyond the light's wavelength {pod}. The particle's spreading is bounded {pod} by light's wavelength. Electron spreading can thus be modulated with different light frequencies. For a particle that is spread out, and once the wavelength we use for the binding experiment is "short enough," we will obtain high positional accuracy of the particle when we make the position measurement later on because the particle is now tightly bounded. Once we bind the particle with shorter and shorter wavelength, the uncertainty in the particle's position will be near zero and, therefore, the particle is no longer spread out. The result of bounding should, with a particular light's wavelength, prevent an electron from passing through both slits concurrently. This is indeed the case. When certain wavelengths of light illuminate the dual slit region, the superposition pattern disappears. Observing or illuminating an electron with light reduces (bounds, collapses) an electron. The 'instantaneous collapse' is the mainstream term but the instantaneous reduction invokes the reversible nature of the transformation from the virtual and into a real electron (or particle). 'Instant manifestation' or 'instant actualization' terminology is also appropriate when the spread out particle encounters a screen and becomes real (manifests, actualizes) in one spot.

A photon, then, does not collide with an electron and the photon-electron interaction does not result in momentum exchange between the two {pod}. This is equivalent to directing a laser beam onto a free electron path: an electron becomes bounded but will not be deflected from its path. Treating photons and electrons classically (as real particles with mass) is perhaps the most egregious corruption of quantum mechanics, Heisenberg taking a major portion. (Yet once an experiment establishes that a photon cannot impart momentum to a mirror at reflection, it will also become apparent that both a photon and an electron cannot be treated classically.) Classical (collision) treatment is a pretty easy error to make in the 1920s, particularly since lasers were not available until the 1960s. This error continues to be perpetuated, for physicists cannot let go of billiard balls and rubber sheets when explaining QM [-- and perhaps they should give it up and let chemists take it from there].


If you need an equation, do Internet search for 'de Broglie.' We think equations are inferior to logical reasoning that keeps in mind the available degrees of freedom (of Pythagoreans) and transformations. For example, de Broglie never addressed the transformation of the angular momentum to the (you guessed it) angular frequency of an electron. Transformations alert you to what is real and what is virtual. Algebra is weak to the point of being detrimental, and you may want to take a peek at Circle and Pi to see its limited applicability. Schrödinger figured out electron spreading but he did not work on the reduction. Both Schrödinger and Bohr missed the virtual aspects of the instantaneous response of the virtual electron -- von Neumann closed that part [but not fully]. Dirac came pretty close to the systemic electron because he spoke of the electron's transformation, but he did not go as far as to claim the electron becomes the virtual electron after transformation. Dirac was also very close to figuring out antimatter but his explanation of the antimatter coming in from a "pool" of "negative" matter misses the mark.

All physicists think that a photon collides with the whole (reduced to a point) electron and so they apply classical mo conservation equations because they think they are dealing with a collision. This is utter nonsense that caters to their childish and possibly degenerate view of physics. They do this in spite of the fact that a higher energy photon refracts at a greater angle than a lower energy photon -- that is, lower energy photon produces a straighter path when interacting with matter. When it comes to explaining the workings of a prism, physicists are suddenly quiet because their billiard balls don't work. Yes, the tools scientists use for the "uneducated people" just might reveal the clueless scientist.

If you stay with geometry (rather than jumping on equations) you will figure out that the quantization of the electron spin is not intrinsic to quantum mechanics but, instead, it is a result of the mathematical solutions using electron, proton, and neutron parameters along with geometry. In general, a free electron can have any spin but the atomic electron's spin is limited to certain values because the atom is a mathematical construction and the electron subscribes to particular values that are the solutions (available in circular geometry).

An electron must be allowed to spread if the superposition pattern is to be observed. Spreading, incidentally, is an innate propensity of a free electron [Aristotle would be happy about that, for he made quite a case for the existence of potentia], which for an electron was mathematically described by Schrödinger but conceptually first introduced by JJ Thomson through his (pudding) model of the spread-core-charge atom. Because just before the measurement a particle is spread out, there exists "uncertainty" about this particle's velocity and position. There is no way of attaching the parameter of velocity and position to a particle that is actually spreading out {pod}. Because the particle's velocity is uncertain just before we measure the particle's position, we do not know how fast or in what direction the "particle" may have been traveling. In other words, once a particle spreads, the classical (and local) parameters of position, velocity, and mass no longer make sense. Heisenberg should get a big credit for the uncertainty component but he would not go all the way and claim particle spreading.

The relativistic presumption fails, there is absolute rest
The second part to an electron becoming a wave deals with the electron's energy. This seems easy but here is where the relativistic presumption does not hold. The superposition pattern reflects the energy electron has. You understand that if the electron were not accelerated but, instead, the dual slit apparatus were accelerated, the pattern will be different. This is easy enough to figure out but you may have hard time understanding why teachers are not quick to pick up on this. Of course, the relativistic postulate would have to go, but so what! At this point, then, take a pause for a self test: If the energy given to the particle stays with the particle then that means there is such a thing as the absolute rest. With absolute rest Newton is in and Einstein is but a pretender he always was.

QM math describes reality with wave mechanics. You need to be cognizant where to put the frame of reference because the "relativistic postulate" does not work. Energy (momentum) takes precedence (priority) because the energy given to the particle stays with the particle while manifesting with wave properties that are commensurate with the imparted energy and that are needed for calculations and for agreement with reality. If your teacher tries to wiggle out of this one -- you may want to think what is best for you. All scientists ignore the fact that the relativistic presumption cannot be applied in the dual-slit experiment.

This is a sore spot and you will need to figure out that here is the basic juncture where the theory of relativity falls apart. It gets worse. This theory cannot be reconciled with quantum mechanics or the QM of gravitation because it is flawed to begin with and it is flawed to the core. Quantum mechanics is energy based -- that is, the parameter of energy is always conserved and cannot be snitched at the whim of the reference. Einstein logic is grossly political [yes, on the pink side].


An electron is at absolute rest when such unbounded object (free electron) has (manifests) no wavelength at the dual slit {pod, Oct 21, 2005}.

Every moving object has a corresponding (de Broglie) wavelength. Under the relativistic presumption the frame of reference can be moved onto the moving object but then the experimental results will no longer be in agreement with math. The relativistic presumption actually corrupts reality. The speed of any particle is absolute and the absolute rest can be established by measurement.


The art on the left shows the atomic electron having four orbital levels available to it. The orbital changes are via the hyperstars, three of which are shown: blue, red, and turquoise.

The art on the right shows three atomic orbitals being serviced by one hyperstar. Distances a and b are the golden numbers (a/b being the golden ratio and so is a'/b').

Hyperstar is a non-regular ten pointed star that has all of its triangles golden. There are two kinds of the golden triangles in the hyperstar. Hyperstar is original [as far as I know and since late 2009] and issues out of a unique and quick construction of a pentagon I dubbed the Boston pentagon construction.

Write to Mike Ivsin and request the paper number 2202-723-455-2012.

Other properties of the hyperstar are also included in the new book (out in Fall 2012 mid 2013).


Heisenberg uncertainty principle continues to make sense

When a small particle starts to spread out, there are some things we can do. We can materialize, that is measure, the particle at some point, but by so doing we will never know the particle's velocity and position prior to the measurement because there is no particular or unique path the particle has taken. The product of velocity and position uncertainty now must be treated together (as a "fuzzy combo" of velocity and position) and this was first proposed by Heisenberg — and became known as the uncertainty principle. The uncertainty in velocity and position relate to each other above a hyperbole, which represents the bounds of such uncertainty. The reason the hyperbole is a bound is because the product of velocity and position is greater-than-or-equal to a numerical constant h. The uncertainty in velocity-position is the area inside the hyperbole. h is the Planck constant that is proportional to the distance from the origin to the hyperbole's intersect with its own axis of symmetry.

 electron nonlocality


Velocity-position meld

Because the uncertainty in velocity and in position merge together (represented as area above the curve) and we cannot separate one from the other, we can also speak of velocity-position meld. The velocity-position meld, VPMeld, makes discontinuous jumps not only possible, not only doable, but executable in a logical — that is computational, manner (see below) {pod}.

In literature and in physics classes, the uncertainty principle is treated as just another funny thing that happens on the way to the atomic scale. One easy mistake to make is that, looking at the hyperbole, the classical interpreter goes from one extreme to another while trading the uncertainty in position with that of velocity. This is superficially true but it ignores we are dealing with a two-dimensional area rather than with one-dimensional curve, and the velocity-position meld is the area itself. As we continue here, we will stay with the VPMeld and, keeping in mind the mechanism of particle spreading, we will develop the rest of the introduction to QM.



On the square-the-circle page, Thoth (the chief magician of the ancient Egyptians) wears a funny skirt with a hyperbolic cut and a bunch of diagonals.

Matter can instantly appear

Once we measure the position of a particle and continue to interact or continue to measure, the particle becomes well behaved — classically speaking — and we will be able to predict where the particle is going. The interaction associated with the measurement and consequential reappearance of a particle is called the collapse of the wavefunction, by now generally accepted term coined by von Neumann. Presently the term collapse is being replaced by the term 'reduction.'

The uncertainty principle explains the electron's behavior quite nicely. When we do not measure the electron's position in space, the electron's position is uncertain and the electron can and does spread out and is at different places simultaneously. We can also say that the electron is in the velocity-position meld. Once the electron encounters the physical screen, it then has no choice but to appear as one real entity, since the act of encountering the impenetrable screen facilitates its position measurement {pod}. The electron's wavefunction collapses (reduces), and the electron materializes instantly because, just prior to encountering the screen, the electron was spread out in space. The electron materializes in a particular spot on the screen along a probabilistic distribution that eventually adds up to the superposition pattern.


Free vs. bounded electron

When the electron is being focused by electrodes, or moves inside a wire [careful here, think dimensions], or is irradiated by light, then the electron's spreading is bounded. Only when the electron becomes free will it acquire the wavelength that is proportional to its velocity. For example, a plurality of electrons striking the CRT screen will never form a perfect point because each electron starts to spread (acquires a wavelength) as soon as it leaves the deflecting plates, and materializes on the screen in a single-slit (or pinhole) distribution.

A better way of looking at the just-prior-to-measurement position-velocity uncertainty is through relevancy. Once the electron spreads out, its velocity component and its positional (path) components become irrelevant and so will our use of classical equations. We can also say that the velocity and position cease to exist as separate physical parameters because they meld. When particle's velocity becomes irrelevant or uncertain, the particle loses the most poignant characteristic of matter: its velocity or its punch. The particle dissolves and "disappears."


The measurement "problem"

The measurement problem is a problem only for classical scientists who tend to see the QM environment as a collection of things so funky there are problems everywhere. The measurement problem stems from the fact that the scientist cannot envision the world without at-will measurement. In QM, the principle of superposition lends itself nicely to comparing and relating, yet the scientist still wants to measure things repeatedly and predictably because determinism is what the classical science is about. In the real environment the measurement happens without a problem because subsequent measurements yield results that are the same or that are predicted through some movement equation. In QM, the measurement results in the reduction of the particular wavefunction, but all other wavefunctions remain superposed because wavefunctions are unbounded and they exist in superposition. An electron reduces when measured but if it remains free it then spreads out again and begins to relate (compute) as soon as the measurement ends. The measurement in general is applicable to entities that do not spread (remain localized) or to entities that can be reduced into the real domain (some wavefunctions are difficult to reduce). Predictable measurement is applicable only to entities that are components of a formally organized (non-chaotic) system. Unlike an electron, a photon measurement results in a conversion to other forms of energy.

As an example, take the measurement of parts in an inventory. We run a query that gives us the quantities of parts available to the manufacturing floor at the time the query is executed. We now have a measurement (snapshot) of parts. Yet, as soon as the query completes and the database unlocks, parts quantities fluctuate as normal business takes place and we can say that the part count returns to the superposition of receipts, returns, repair, drawdowns, spares, obsolescence, reserves, and human errors. Somehow, the classical scientist has a problem with that. Conceivably the scientist can substitute functions and averages for various parameters in an attempt to describe "parts reality" at any given point in time, but, in the QM universe the superposition is unbounded and such descriptions quickly become intractable. In our example, the execution of the query is quick and it then does not interfere with the manufacturing floor. But we understand that if the database is locked for extended periods then the measurement itself (the query) becomes a problem -- rather than the "problem" of the inability to describe reality without a measurement.

There is a similar environment applicable to the options trading. Each option is tied to a particular underlying stock but we can only guess what the stock is really doing as far as its fundamentals are concerned. Between the ends of the reporting periods the price of stock acquires a price uncertainty and because its option is highly leveraged by the underlying stock, the option price can acquire a considerable spread -- just like the particle's position uncertainty spread. The trader's skill, then, is in the prediction of the price spread movement -- without the actual stock measurement -- but before the reality sets in at the option's expiration (or at the reporting point).


Qualitative point of departure

Presently, mathematical modeling of the atom uses a central point charge around which electrons exist (orbit) in a real Coulomb field. The model generalizes variables into complex variables — that is, variables have real and virtual components. The resulting Schrödinger wavefunction equations also have real and virtual components and produce an excellent agreement with the observed reality although, of course, we can only infer the virtual once the reality is manifested. For example, we can measure the momentum (velocity) of free atoms but the value of such momentum is uncertain during the unobserved existence of the atom — even if the later-measured momentum is zero. The qualitative point of departure is to understand that physical parameters become computational parameters in the virtual domain where quantum mechanics applies and, therefore, one must model an electron as computing its way around rather than moving in space or propagating under the influence of a field.

A free electron in the two-slit experiment can be computed and modeled. The added benefit is that each electron has a known computational sequence — that is, the computed electron materializing in the detector (or on the screen) has a known history. When many paths overlap — and they must if a solution is to exist — as they do in the dual slit experiment, a certain convergence or overlay results. The overlay is the result of symmetries (geometry in general) inherent in the slits.

Let's Take It From Here

New Scientific Method is about tractability

The nice part of quantum mechanics is that it comes out of logic that converges towards a new reality, albeit after trying a large number of constructs and after many trials. In the classical context, billiard balls move the way the cue stick wants them to. When a ball strikes and excludes another ball, there are exact laws that describe their behavior such that all events become predictable and repeatable [and possibly boring]. In another context, when particles acquire nonlocal momentum, there is also a logical, relational and at times probabilistic framework for their behavior. Particles start to develop linkages and relationships with each other. The wave-like linkage component allows particles to relate to each other more inclusively, while the physical component of the particle continues to have the exclusion properties from the classical context. The very nice part is that the atomic particles can reversibly transform between their wave-and-inclusive state, and their real-and-exclusive state.

Quantum mechanics is about the balance between exclusion and inclusion

You want to make a correction here to the mainstream QM texts, which in connection with particle's wave properties routinely state "when the particle becomes small." The wave property of the particle depends on its momentum and not on its size or its mass. If your teacher does not get it, you want your money back.

The tunneling effect describes the ability of an electron to jump over, or through, some energy barrier. The classical way of visualizing this is in terms of balancing where the electron borrows energy from the neighborhood and then returns the energy back as it instantaneously reappears on the other side of the barrier. Energy's bookkeeping account is in balance, and the energy is conserved. The inclusive nature of the virtual electron, however, enables the electron to actually go through the energy barrier. Because the energy is conserved at all times and the electron transitions to another domain where it is virtual, does this mean that the electron's energy changed to virtual energy? Yes indeed. Then, just as we continue to rely on energy conservation, we know that the electron's virtual energy can become real energy.

Electron tunneling or electron balancing defies the force of gravity. Once the particle spreads out, its point-like gravitational component disappears. At this juncture, however, it is best to point out that the gravitational force has nothing to do with the electron, spread out or not. Quantum mechanics of the disappearing electron, though, has everything to do with the understanding of the quantum mechanical foundation of gravity.

Bridging the gap, tunneling through..

When a small particle spreads out, we never doubted that the spread out particle eventually reduces by measurement. It seems all we need to do is use light of sufficiently high energy to reduce the wavefunction at will. Alternately, the spread out particle collides with a screen, a wall, or some kind of a structure that reduces or captures the spread out particle. Small particle's materialization, however, is not all that simple because a shot of high energy beam of light into space does not produce a wholesale reduction of spread out particles, be it in the path of the beam or otherwise. Experimentally, on the other hand, if we shine light on the entire setup of the two-slit electron experiment, electrons reduce and the interference effect diminishes and disappears altogether once light reaches sufficient intensity. Light is bounding the spreading of the electron all right, but there are additional parameters associated with this capability.

Particle can escape altogether


There are phenomenal opportunities in quantum mechanics, for QM works at any scale. The scientific percept is, unfortunately, largely afraid of dealing with the virtual aspects of QM. A stage magician may smash your watch and add insult to the injury by making the watch disappear, but you know it's only a trick and you will get your watch back.

The place to start is with the irreversible and reversible transformations. If you put your money into irreversible transformations such as E=mc2, you will never get your watch back. De Broglie and Heisenberg transformations between momentum (moving energy) and wavelength are reversible and your watch (or the electron) will reappear, as if by magic.


 Book by Mike Ivsin
 To Publisher...

Does the electron have the spatial and the energy component? Each component would have its own behavior but both components are joined through a zero-dimensional point. What happens to these components when energy is applied? What happens when the components are subject to geometric constructs? Does antimatter arise when these two components are separated?

Quantum Pythagoreans explains the creation of matter, antimatter and the condition under which antimatter can be healed.

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