The fundamental concepts of classical physics, space, time, mass, and derived concepts, velocity, momentum, force, angular momentum, energy … all rest on the principle that material points have trajectories. They are defined as lines in space-time. Even the dynamics of continuous, solid or fluid media describes the trajectories of the material points which constitute the bodies in motion. But the indeterminacy relation of Heisenberg prevents quantum particles from having such classical trajectories, since their position and velocity can not be exactly defined at the same time. How then can it explain all the appearances which legitimize the fundamental concepts of classical physics?

Installation

Systems, in one sense, are devices that take input and produce an output. A system can be thought to operate on the input to produce the output. The output is related to the input by a certain relationship known as the system response. The system response usually can be modeled with a mathematical relationship between the system input and the system output.

$ git clone https://github.com/gingerbread-lang/gingerbread
$ cargo install --path .

The principle of relativity states that all inertial systems are “created equal”: the laws of physics are the same as long as they are formulated with respect to an inertial frame — no matter which. The first three items tell us that one inertial frame is as good as any other frame as long as the other frame differs by a shift of the coordinate origin in space and/or time and/or by a rotation of the spatial coordinate axes. What matters in physics are relative positions, relative times, and relative orientations (the orientations of objects relative to each other), inasmuch as these are unaffected by translations in space and/or time and by rotations of the spatial axes. In the physical world, there are no absolute positions, absolute times, or absolute orientations.

fun main -> {
    add 2, 2;
};

fun add(x: s32, y: s32): s32 -> x + y;

Physical systems can be divided up into a number of different categories, depending on particular properties that the system exhibits. Some of these system classifications are very easy to work with and have a large theory base for analysis. Some system classifications are very complex and have still not been investigated with any degree of success. By properly identifying the properties of a system, certain analysis and design tools can be selected for use with the system.

Electronic modes (their polarization features are described by Spin 1/2) are calculated by the Dirac equation, or, to a very good approximation in cases where the theory of relativity is irrelevant, by the Schrödinger equation and the Pauli equation. Modes of Spin 0 would be calculated by the Klein-Gordon equation. In order to calculate the modes exposed to potentials that attract or repulse the waves or, equivalently, exposed to a change in refractive index and wave impedance, or exposed to magnetic fields, there are several equations depending on the polarization features of the modes.