## Calculus and Quantum Mechanics

##### Reference: Mathematics of Space and Location

The usefulness of calculus is limited to Classical Mechanics.  Classical mechanics deals with mass that is “centered” and with waves that are “spread out.” In both cases, physical locations may be assumed to be uniform in their characteristics and to be distributed uniformly as points in space.

This assumption no longer holds in the subatomic region, which is the concern of quantum mechanics. In this region, the inertia (state of motion) starts to transition from “mass of particles” to “frequency of waves.” With this transition the nature of locations starts to change from “centered” to being “spread out.”

Thus the locations in the atomic region cannot be considered to be uniform, and they cannot be treated by the infinitesimals of calculus with any certainty.

Calculus cannot be applied with any certainty to the problems of Quantum Mechanics in the subatomic region.

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• 2ndxmr  On January 20, 2015 at 5:43 PM

V:” In this region, the inertia (state of motion) starts to transition from “mass of particles” to “frequency of waves.” ”

This is an unfounded assertion based on your earlier incorrect assumption that you could directly equate frequency to mass with your assumption of
E = hf and E = mc^2 implying hf = mc^2. Nope. You’ve got to get the idea of angular momentum as it relates to the energy of the wave. Its effect is directly observed in Compton scattering. It can’t be ignored. It’s very much like the difference between a bowling ball simply rolled down the lane and a ball that has spin put into it as well. At the impact point very different energy distribution patterns occur making it possible for an observer to distinguish between a rolled ball and a spun ball.

Also, I see no reason why calculus would not be able to describe quantum states. Calculus is a mathematics of change. That is all. As long as the changes at the quantum level are continuous within a domain, then calculus can describe the changes within that domain.

I believe it would greatly help your understanding of quantum phenomena if you were able to properly grasp the concept of “root of -1”.

To not do so leaves you in a condition of being “physical-centric” i.e. having to have a matter, energy, 3-space and time explanation of things.

The math of quantum mechanics – as we saw back in the Schrodinger discussion – requires the inclusion of the “imaginary” operator. It can’t be ignored, either.

• vinaire  On January 21, 2015 at 6:56 AM

E=hf applies to photons only. E=mc^2 applies to particles only. The common characteristic between photon and particle is inertia.

I asked myself the question, if mass represents inertia in particles, then what would represent inertia in photons. The obvious answer is frequency. I am implying no equivalency other than that.

• vinaire  On January 21, 2015 at 7:36 AM

I am approaching from the level of consistency among broad physical concepts. Then I shall find the math that is consistent with physical concepts.

• vinaire  On January 21, 2015 at 7:54 AM

The forward and oscillatory motion of a photon may be visualized as a corkscrew motion. As frequency increases the translation decreases, and the threads of this motion seems to come closer together. Ultimately, that corkscrew motion of frequency transforms into spinning motion of mass.

• Chris Thompson  On January 28, 2015 at 1:50 PM

How is the QM class going?

• vinaire  On January 28, 2015 at 2:26 PM

It is going good. Of course, I am creating my own concepts, which are different from the concepts being taught.

In fact, nothing much exists in Quantum Mechanics in terms of concepts. It is just mathematics. The mathematical concept that it is based on is that space is a set of points and a point determines a location. So, it is calculating the probability of a point location even when there is no such thing in reality actuality.

• vinaire  On January 28, 2015 at 2:30 PM

It is like determining the location of a snake at a point, like how much of a snake is at this point… funny.

• vinaire  On October 17, 2020 at 4:37 AM

The following is an approximation of universal substance:

Matter = “Solid” Mass
Quantum particles = “Liquid” Mass
EM Waves = “Gaseous” Mass