Difference between revisions of "Quantum Mechanics"

Revision as of 16:54, 16 April 2023

Full Title or Meme

This page focuses on the first development of the Quantum Mechanics of the Eventful Universe as developed by Werner Heisenberg.

Context

Werner Heisenberg was not happy with the state of Quantum Mechanics as articulated by the Copenhagen school of Niels Bohr and so went off to an isolated island in the North Sea (for his Hay Feaver) to think through a better solution focused on the observed events. Shortly after this Edwin Schrodinger developed another model based on the flow of a quantum from one event to another known as the wave equation. It was later shown that these two models were consistent with each other in spite of the differences between the models, the wave equation dealt with the flow of the particle and Quantum Mechanics dealt with the event that was observed when the electron was measured.

Fourier transforms

Fourier created these long before their wide applicability was known.

Spectroscopy

It was discovered that each element was likely to generate "spectral" lines only in very specific patterns when it was headed to luminescence.

Problems

The Bohr Model

In 1920 there was a model of a quantum atom that has electrons spinning around a nucleus, that fad just been discovered by Rutherford, a New Zealander working in Canada and England. Some success was obtained in determining the differences between electron "orbits" as a light photon of a specific energy was emitted and measured whenever an electron "fell" from one orbit to another at a lower energy. Unfortunately, that Bohr model of electron orbits is unable to predict the fine details of the simplest atom, Hydrogen, and Bohr, in the 1920's, was adamantly opposed to the concept of light quanta.

The Particle Model

Ever since Newton developed his theory of gravitation a fully mechanistic view of moving bodies had led physics to believe that physical laws were deterministic, that is, that if all of the positions and velocities of the physical objets in the unirverse could be know that the entire past and future could also be known. But if we consider a photon to be a particle, then when it is sent through the two slit experiment, we cannot know with certainty where it will land on the detection screen. Many physicists, including Enstein and Bohr rebelled against any such interpretation. Einstein by insisting on certainty and Bohr insisting that light could not be composted of quanta.

This model is focus on actual observations of discontinuous events (an action plus a transformation) when particle interact. The distinction between the particle and wave models is like a Fourier transform: it can describe a wave in tine, or in an analysis which has no time component to it.

Probabilities

It was a know fact that a probability must be in the range of 0 (will not happen) to 1 (must happen). This definition did not work with quantum mechanics. We will see below that Heisenberg allowed negative numbers that in effect corresponded to the adjustments needed to make the particles behave like waves with constructive and destructive interference.

The Wave Model

The Wave Model was very good at predicting the distribution of light photons (and electrons) impacts on a fixed screen when they were diffracted, as is clear in the "two slit" experiments from the beginning of Quantum Mechanics. In the wave model and is many of its predecessors, the interesting part of physics was in the descriptions of the states of the reality. In the Quantum Mechanics of Schrodinger its was the state of the wave as it propagated through space. Every formula was a linear equations of differential equations. Space was continuous and the core of physics follows the calculus invented by the same Issac Newton that established the laws of gravity.

The Wave Model is not testable by directed observations. It exists only in theory and does not describe what happens when an observation occurs.

Is it Logical?

Law of excluded middle can be violated by some quantum operations. So in that sense we can say the Aristotle's rules of logic (aka Boolean logic) was not up the the challenge of describing how Quantum Mechanics worked.

Heisenberg's Solution

While his original solution created a new mathematics for multiplication, it was realized by Born that this type of multiplication was already known as matrix multiplication and so Heisenberg's solutions was recast as matrix mechanics, later to be renamed as Quantum Mechanics. The following will be presented in the matrix formalism that has come to be standard as it was described by Dirac. When Heisenberg left for^[1]

Consequences

Entanglement

When two particles are entangled, they share a quantum state that is described by a wave function. When one of the particles is measured, it collapses the wave function of both particles, which means that the other particle’s wave function is also collapsed. This means that the other particle’s state is determined by the measurement of the first particle. The order of measurements does not matter because both measurements will collapse the wave function of both particles and determine their states.^[2]

Specific Uses

In keeping with the purposes of this wiki the application of Quantum Mechanics to computer and communications applications. Click on the names below for more information.

• The Quantum Computing Threat describes how existing private keys can be exposed.
• The Quantum Information Theory describes how quantum effects can be used create provably secure communication channels.

References

1. ↑ David Lindley, Uncertainty Doubleday ISBN 9780385515061
2. ↑ https://physics.stackexchange.com/questions/561382/what-exactly-is-the-difference-between-entanglement-and-correlations