Reference: INERTIA: A Summary
You cannot locate the whole snake at a point, but you can locate it with total certainty in a patch of space. If you assume that the snake must be located at a point then you will come up with something like the Heisenberg’s Uncertainty Principle.
This is the case with an electron. An electron is much smaller than an atom, but it cannot be located at a point because it hardly has any mass. An electron is spread out in space like a snake.
There is no uncertainty if the location of an electron is recognized as a “patch of space” rather than a point. Then there would be no “probability function,” which makes Quantum Mechanics math very complicated.
The physical location can be approximated as a point only to the degree there is mass. To the degree there is less mass and more wavelength, the location cannot be approximated as a point.
Maybe the Heisenberg’s Uncertainty Principle gives the minimum size of a “point” location.
The current view of Electron as a “point particle” seems to be inconsistent.
Electron has a wavelength and it is definitely spread over a patch of space. The location of electron cannot be approximated as a point because it hardly has any mass.
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The mathematical inconsistency is saying that continuous space (that has dimensions) is made up of discrete points (that have no dimensions).
This inconsistency is then carried forward into physics into thinking that physical locations in space must always be defined in terms of points.
This leads to physicists computing the probability of electron appearing at a “point location.”
So the inconsistency is between the mathematical assumption above (which underlies Quantum Mechanics) and the reality.
The reality is that infinite “no dimensions” cannot generate a dimension.
The reality is that a physical location for mass-less waves cannot be defined in terms of point locations.
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A response that I wrote on http://www.Quora.com:
Contradiction has to do with two statements or assertions that oppose each other. You had framed your earlier request that way. What I am looking at is an assumption that does not match the reality. There is a disharmony or incoherence there. So, I am calling it an inconsistency.
Let’s just look at any dimension. By definition a dimension is an extension like a scale. A line may be used to represent a dimension. A line may be filled with discrete points, but a point being discrete can only represent rational values on the line. It cannot represent irrational values. And there are plenty of irrational values on a line. So, I don’t think that discrete points, by themselves, are capable of completely filling a line.
There will always be that gap represented by epsilon in calculus. It may be ignored in most cases, but not in this case. The very existence of epsilon breaks the continuity.
So we have to say that a line is a continuous entity on its own right independent of discrete points.
Physicists have been using the word “point particle” indisctriminately. An entity with mass may be approximated by a point, because mass has the property of being centered at a “center of mass.” But this approximation cannot be extended to an entity with no mass. I don’t think that a photon can be looked upon as a “point particle,” Do a thought experiment with wave motion. You will find that it cannot be pinpointed at a point location even mathematically, as it is the case with a mass particle.
A wave “particle” is very different from a mass “particle.” The two compare like the irrational number compares to the rational number. Quantum Mechanics tries to find the location of a wave “particle” in terms of probability over discrete locations. It completely misses its location over non-discrete locations.
We are not talking about spatial extension here. A mass particle has spatial extention but it can be approximated mathematically as a point particle. The crux of the matter is that a wave particle, by its very nature, cannot be approximated mathematically as a point particle. A pseudo approximation in terms of probability over point locations falls short even mathematically.
The “mass” of an electron could very well be inertia that is formed by highly converging frequencies. It may not be the the mass present in atomic nucleus.
Application of Quantum Mechanics may provide certain predictions quite accurately, but a better theory could be waiting in the wings. The situation is pretty much like the Geocentric versus the Heliocentric theory of the Solar system. People are swearing by the Geocentric theory, while the Heliocentric theory is waiting in the wings.
In case of an electron, both wavelength and mass characteristics seem to be present. Wavelength is spreadout, whereas, “supposed mass” is concentrated, but not to the level of a point. The key to understanding this situation, seems to be inertia. The inertia model that is emerging is described at the following link.
INERTIA: A Summary
You may need to look up also the links referenced in the document.
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V: ” A line may be filled with discrete points, but a point being discrete can only represent rational values on the line. It cannot represent irrational values. And there are plenty of irrational values on a line.”
You could also divide any rational number by two any number of times and still be able to divide the result by two any number more of times. Discreteness of points is likely less important than the continuity of the function describing the points.
V:”A line may be filled with discrete points, but a point being discrete can only represent rational values on the line. It cannot represent irrational values.”
Rationality of numbers is only a factor of the base of the numbering system.
In our base ten number system pi looks irrational. But, if the number system was base “circle”, then pi would be a rational 1/2.
It appears that “circle” has a circumference equal to the Planck length.
Thus it would be practical to have a numerical system of base “h”, and in that system, “h” would have the unit value, i.e. cardinal one.
It also appears that all increments of energy are integer multiples of h (as E = h*nu and all nu must be in whole wavelengths).
It would seem, then, that a number system of base h could describe all other phenomena and physical constants as integer values, getting rid of the problems of irrationality (a speculation, otherwise not yet inspected).
Would this imply that our seemingly irrational pi would actually repeat at about the 10^34th term?
V: “A mass particle has spatial extension but it can be approximated mathematically as a point particle.”
The minimum dimensional length in this physical universe will likely be the Planck length which, while small, is far larger than an infinitely small “point”.
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From Going Beyond Counting:
It seemed at that point in time that rational numbers represented all possible numbers that could ever exist. A unit could be broken into smaller and smaller units making it possible to represent any quantity as a ratio of its mutiples. Therefore, it came as a big surprise when numbers, such as √2, were discovered that could not be written down as a ratio based on some indivisible common unit. It meant that no small enough common unit could be found for such numbers. The idea of an ultimate indivisible unit came under intense doubt.
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Well said Vin.
It seems to me that some of the properties of sub atomic physics fall under the heading of concept, rather than data. The gathering of accurate data may lead one to the realization of the concept, instead of the other way around.
Just a thought.
Mark.
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Well, there is experimental data and that is what it is. The issue becomes how does one interpret the experimental data. And that requires a conceptual model.
A mathematical model, which Quantum Mechanics uses, is also a conceptual model. It says, “If we get predictable results by computing with the experimental results this way then that’s it. This is enough. We do not have to search for any more significance.” And then we find out that Quantum Mechanics does not answer many questions.
This makes the Quantum Mechanics model inconsistent, because it thinks it is complete but it is not. It does not have the answer for, “Why do certain mathematical relationships work and other do not?”
The mathematical model may be consistent within itself, but it is not consistent with classical experience. Classically, the solutions to algebraic equations are “quantized,” and so is the interference of waves, or standing waves. The mathematical model does not take these classical concepts into account. It is inconsistent with classical mechanics.
This inconsistency was bothersome to Einstein. It is also bothersome to me. My current effort is to resolve this inconsistency. The breakthrough I seem to have made in this direction is,
The physical location can be approximated as a point only to the degree there is mass. To the degree there is less mass and more wavelength, the location cannot be approximated as a point.
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Quantum Mechanics is trying to find probability of electron at a point, assuming it to be a point particle.
But electron is more like a snake than a “point particle” because it has wavelength instead of mass that can be concentrated at a point.
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The reason is that mass can be assumed to be concentrated at a point. The “center of mass” is a well established classical concept. So we can use a point location where mass is concerned.
But, when it comes to an electric or magnetic field, it cannot be treated as being concentrated at a point. It has more to do with spread of inertia versus concentration of inertia. It is more basic than space.
We don’t see “space” as a special condition of inertia; but that is what it is. Space is not the ultimate basic concept.
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For Electromagnetic radiation, inertia is manifested as frequency (Disturbance Level). For a particle, inertia is manifested as mass.
The frequency-mass may be determined by the energy relationship, E = hf = mc^2
c = 2.998 x 10^8 m/s
h = 6.626 x 10^-34 J.s
We get, f = (c^2/h) m; or f = (1.356 x 10^50) m, where m is in kilograms
The mass of electron is 9.1094 x 10^-31 kg
The frequency which is equivalent to the mass of electron is 1.235 e^20 Hz. The disturbance level for this frequency is 66.7.
The mass of a proton is 1.6726 x 10^-27 kg
The frequency which is equivalent to the mass of proton is 2.268 x 10^23 Hz. The disturbance level for this frequency is 77.6.
Gamma radiation has a frequency > 10^19, or a disturbance level > 63.1
A hydrogen atom has a proton in the nucleus and the one electron surrounding it. The electron provides the frequency at the surface of the hydrogen atom. This is the threshold frequency, or disturbance level, at which the electromagnetic radiation starts to converge toward the nucleus of hydrogen atom.
The proton provides the frequency at the surface of the hydrogen nucleus. This is the threshold frequency, or disturbance level, at which the electromagnetic frequency starts to transition into mass. See Propagation of Light
We may say that the disturbance level at the surface of the hydrogen atom is about 66.7. And the disturbance level at the surface of the hydrogen nucleus is about 77.6.
The radius of hydrogen atom is 5.3 x 10^-11 m. The disturbance level of EM radiation increases from 66.7 to 77.6 in this short distance. This is equivalent to the wavelength of EM radiation decreasing from 2.43 x 10^-12 m to 1.32 x 10^-15 m within this short distance of 5.3 x 10^-11 m.
This starts to give us an interesting picture of the condensation going on inside the atom.
* The values in bold are from Wikipedia.
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Highest energy gamma rays from gamma ray decay are around 10 Mev. The equivalent disturbance level (DL) is 71.
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The DL equivalent to the mass of the nucleus of Uranium atom is 85.5.
frequency = 5.4 x 10^25, and wavelength = 5.55 x 10^-18 m.
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10-31m. That’s really small. 10 to the 19th hz. That’s really fast.
In my metallurgical research, I am unable to produce frequencies anywhere near that. Nor am I able to produce pressures at temperatures great enough to produce a plasma state while enclosing the material I’m working with.
What I am able to do is produce lower harmonics of higher frequencies by generating multiple frequencies and combining them. I have found that a proper chord cannot be produced by one frequency generator alone. Frequencies must be produced separately and combined in the material itself. One frequency generator will not produce a true waveform as frequencies combine. Peaks are clipped and near instant changes as the frequencies interact are subdued.
I have also had trouble removing the material from the press mold after an experiment. I have a .75 sq, In. crucible in a 50 ton press. The frequency generators are located under the mold. I can generate frequencies of 10 Hz. to 50 GHz. at 20,000 watts with peaks to 50,000 W. I have a capacitance discharge system that allows me to produce pulses of up to about 1 second. I would like to be able to produce continuous frequencies as the metals cooled so that I can find that sweet spot of temperature and frequency and pressure. There have been several times that I had to cut the material out of the mold after it cooled. The tungsten-carbide molds are getting expensive.
I have also had a little trouble with liquid metal squirting from the edges between the crucible mold and the press plunger. Tolerances have to be tight and the edge of the mold must be chamfered just right. The plunger cannot be chamfered or the liquid metal will always seep around the edges.
I have had some success getting copper and aluminum to chemically combine, rather than alloy. The density was greater than 15 specific gravity, almost as great as lead. I’m testing its properties. I’m working with some friends to get a hold of some X-ray diffraction time on a machine at Redstone.
When I hit that perfect combination of frequencies, the near liquid metal mixture shrank down to a forth its size. Since my press was not fast enough to follow the fast reduction rate, the metal was not homogeneously combined. Maybe next year I can get a hammer forge. My hydraulic press is just too slow.
Mark
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I am adding a small accumulator to the hydraulic supply line. This, I hope, will allow my press plunger to travel perhaps one half inch in less than one tenth of a second. At the moment the metal alloy reduces to a chemically combined material, it cools 2 or 300 degrees F. That may not be fast enough to maintain pressure as the metal is combining, but I’ll give it a try.
Mark
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!0^-31 is in kg and not in m as you wrote.
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Sorry, I was scanning through your numbers and grabbed the wrong one. When I try to be clever and witty, I lose accuracy. Hope I don’t strike a funny chord while the press is running.
Mark
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Correction.
Almost as heavy, dense, as uranium, not lead. Nearly 50% more dense than lead.
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