# Quantum physics terms

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This page is intended to give very short explanations of various quantum physics terms encountered elsewhere on the site.

## Contents

### Forces

There are four classes of force in the Universe, from weakest to strongest. In quantum mechanics and the Standard Model of particle physics, each force is carried by a corresponding particle:

• Gravitational; theories of "quantum gravity" hypothesize the force to be carried by gravitons of spin 2 and mass 0. These have never been observed in experiment.
• Electromagnetic; carried by photons of spin 1 and mass 0.
• Weak nuclear; carried by W+, W- and Z0 of spin 1 and mass circa 100 GeV (100,000,000,000 electron volts).
• Strong nuclear; carried by gluons of spin 1 and mass 0.

### Hamiltonian

The operator (often marked by the letter H, sometimes Ĥ and sometimes in a fancy font e.g. $\hat \mathcal H$), which, when operating upon a wave function, gives its energy. Another way to look at it is that this is the time-translation operator of the system. The Hamiltonian is what is usually used in quantum mechanics to describe the system — if you give the system's Hamiltonian, you have described it.

Notice that the Hamiltonian serves a double-role in quantum mechanics. On the one hand, it is the operator that determines how the system evolves in time (the time-translation, moving the system to its future or past) between measurements. On the other hand, it is also an "observable", a quantity that can be measured (or, more accurately, the energies associated with it can be observed).

### Quark

Quarks are the building blocks of subatomic particles that interact via the strong nuclear force. There are six "flavours" of quark: up, down, strange, charm, bottom & top. Each of these has an additional property "colour": red or green or blue. (These "flavours" and "colours" have no relation to any macroscopic properties of the same name.) A proton is made of three quarks, 2 up and 1 down, and a neutron has 2 down and one up. All of this is laid down in the Standard Model of particle physics.

### Spin

Spin is a quantized property of all particles, both matter and force, in the Universe. Matter particles have half-integer spin (1/2, 3/2,…) and force particles integer spin (0, 1, 2,…). Spin is intrinsic angular momentum possessed by the particles. The spin of a particle is sort of analogous to that of a spinning top, except that the particle can only spin at one speed, can't stop or even slow down, and is infinitesimally small (the particles are "pointlike" and have no size). It is important to note that in no way are the particles actually spinning. The phenomenon of spin was predicted initially in 1924 and the explanation/interpretation that this was due to the particle "spinning" was put forward later. This property is exploited in NMR and MRI.

### Wave function

A wave function is a mathematical description of the probability wave of a physical system (usually sinusoidal or exponential in form, for simple physical systems), which describes much of the information that can be obtained by measurements on it. The treatment of quantum systems in terms of their wave function is something of an idealization, so you can always know when someone isn't showing a full understanding of the theory if he remains constricted to this term. In real physical systems some uncertainty always exists regarding the system's physical state, so that the theoretical treatment is done by a combined treatment of several wavefunctions, in what is called a density operator (or simply state). So if you're being fed tales about how wave function behaves — know that you're being told a simplistic tale, rather than the full story.

### Uncertainty relations

#### Heisenberg's inequality

The uncertainty principle (put forward by Werner Heisenberg) states that there will always be an intrinsic uncertainty in determining both a particle's position and momentum (i.e., you cannot know both exactly at the same time). This has nothing to do with science's ability to detect the properties of momentum and position as some anti-science and pseudoscience proponents suggest, it is merely an intrinsic property of any wave-like system. It is also put forward by some to be the origin of "free will" as the uncertainty principle leads to a degree of unpredictability in some experiments; however, the scale of the uncertainty principle is far too small for it to apply to everyday life.

It is formally stated as: $\Delta x \Delta p \ge {\hbar \over 2}$

where $\hbar$ is the reduced Planck's constant.

More generally, this applies not only to position and momentum, but to any two observables whose self-adjoint operators do not commute with one another; for example, it is impossible to know all of the components of a particle's spin at any given time, and it is also impossible to know both the energy of a particle and the time at which the particle had this energy with arbitrary accuracy.