Vinaire's Blog

The idea of space comes from dimensions of solids or matter. But matter is not the most basic physical substance. Underlying matter we have the field. How does this change the concept of space?

It is interesting to study the interface between matter and field. That is the area Quantum Mechanics is looking at. Quantum Mechanics have had lots of successes, so Quantum Mechanics is mostly right. But its math is very complicated. Can that math be simplified without rendering QM wrong, because QM is not wrong! If we can simplify the math of QM then I am sure we can get further mileage out of it.

Where is the limitation on QM coming from? I think it is the uncertainty in our concept of space. Our feel for space is based on matter. We do not have a feel for field. Our concept of space is tied to physical substance. Our understanding of the basic physical substance has moved from matter to field, but not the understanding of space.

What is field compared to matter? When particles collide in atomic and nuclear reactions, we see emission of radiation. It seems that matter cannot be divided indefinitely as matter. Somewhere along the way matter seems to divide into field.

What is wave function? A wave function is trying to define the field. What does probability in a wave function mean? I don’t think it provides the chance of locating a particle in space because the concept of particle and space is in question here. A particle seems to be a “peak in probability”, and the background is not space but the adjacent valley. These “peaks and valleys” are relative, which are mimicking “particles and space”.

The atom exists as a “particle” in the relative “space” of outside low-frequency field. The nucleus of an atom exists as a “particle” in the relative “space” of the electronic region. This idea is not very different from the idea of a “quantum” in QM.

Different particles are different “peaks” in the space provided by the “valleys” of the field. The “peak” is a sudden jump in frequency (energy) from the frequency that is characteristic of the field. The characteristic frequency of a field gives a character to “space”.

There seems to be a spike in frequency at the surface of the atom, and another huge spike at the surface of the nucleus. “Particles”, such as, electrons, atoms, and nuclei are stable configurations. The “particles” of Standard Model are also relatively stable configurations. This explains how there are particles within particles.

What does the zero mass of a photon means? Mass seems to come about when there is sharp spike in frequency. That means there is no sharp spike in frequency within a photon. The photon is the “space” part of a field. The photon then stands out as a “particle” in a “space” of lowest frequency possible. That would be a field approaching zero frequency. That would be “pure space”.

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Please see The Uncertainty Principle.

Here is an excellent explanation of uncertainty principle by Richard Muller, Professor of Physics, U. Calif. Berkeley, coFounder of Berkeley Earth.

“Fourier analysis has a very important theorem: If a wave consists only of a short pulse, such that most of it is located in a small region Δx (read that as “delta x”), then to describe it in terms of sines and cosines will take many different wavelengths. The wavelengths, in math, are commonly described by a number k. This number is such that k/2π is the number of full waves (full cycles) that fit into 1 meter. Physicists call k the spatial frequency or wave number. A wave confined to a region  Δx  in size must contain a range of different spatial frequencies,  Δk . Then the Fourier math theorem says that these two ranges have the following relationship: ΔxΔk≥1/2
 
“This equation has nothing to do with quantum behavior; it is a result of calculus. This theorem predated Heisenberg; Jean-Baptiste Joseph Fourier died in 1830. It’s just math—the math of waves, water waves, sound waves, light waves, earthquake waves, waves along ropes and piano wires, waves in plasmas and crystals. It is true for all of them.

“In quantum physics, the momentum of a wave is Planck’s constant h divided by the wavelength. The wavelength is 2π/k. That means we can write the momentum (traditionally designated by the letter p) as p=(h/2π)k=ℏk. Taking differences for two values of p, this equation becomes Δp=ℏΔk.

“If we multiply the Fourier analysis equation ΔxΔk≥½ by ℏ, we get ℏΔxΔk≥ℏ/2. Then we substitute Δp=ℏΔk to get ΔxΔp≥ℏ/2

“This is Heisenberg’s famous uncertainty principle. Once we accept that all particles move like waves, the uncertainty principle is a mathematical consequence.

“In math, the theorem wasn’t an uncertainty principle; rather it described the range of wave frequencies in a short pulse. But in quantum physics, the range of frequencies translates into an uncertainty of momentum; the width of the pulse becomes an uncertainty of where the particle will be detected. That’s because of the Copenhagen probability interpretation of the wave function. If different momenta (velocities) and different positions are available in the wave function, then making a measurement (such as observing it being deflected in a magnetic field) means picking one out, choosing one value out of many.”

The key point is that the Heisenberg’s uncertainty principle is the result of math applied to wave-like property.

The mathematical analysis assumes that we can always approximate a location in space as a Euclidean point. Is this assumption correct?

I believe that this uncertainty comes from using Euclidean point for location in space. The dimensionless Euclidean point seems to adequately define locations occupied in space by mass. But this doesn’t seem to be so for locations in space occupied by energy field.

When we look closely we find that location in space has an innate dimension equal to the wavelength of disturbance at that location. The de Broglie wavelength for matter is very, very small and it is possible to approximate it by the “dimensionless” Euclidean point. But the wavelengths of disturbance in energy field are not small enough to be so approximated.

The uncertainty seems to come from the use of this assumption for locations in energy field. We cannot “pinpoint” a location that has a significant dimension.

If this is properly understood and we can correct the mathematics being applied at quantum levels, then probably it will lead to much simpler understanding of the quantum phenomenon.

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