Quantum theory and relativity revolutionized physics in the 20th century with laws that go beyond human intuiton.

## Quantum Theory

Energy is not transferred continuously but in small discrete packets called quanta.

### Wave Mechanics

The wave-like particle properties of light also apply to electrons. De Broglie discovered that particle and wave properties of these objects are correlated.

$\lambda = \frac {h}{mv}$

Electron microscopes make use of this feature, as the wavelength of electrons is much smaller than that of photons. This allows for more detail.

Electrons trapped in particles are represented by standing waves – oscillations without movement.

### Energy Levels and Line Spectra

Electrons residing in atoms may only possess certain energy values that depend on their positions in the atoms' shells. It follows that the momentum and wavelength of electrons may only have certain values, depending on the charge in the nucleus and the amount of total present electrons.

The line spectrum of emitted by an atom depends on its energy levels. An atom emits light when one of its electrons moves from a shell to another of a lower energy level. The electron loses a certain amount of its energy to a photon. Each atom has its own unique and well-defined line spectrum signature.

### The Uncertainty Principle

Quantum effects are observed when the act of making an observation influences the outcome of an interaction. The uncertainty principle postulates that the speed and position of a particle can never both be determined with certainty. If a particle's speed is measured with certainty its position will be uncertain. If its position is measured with certainty its speed will be uncertain.

## Relativity

According to Newton's laws of motion an object $O$ thrown on a moving vehicle $V$ moves at a combined speed realtive to the ground: $O$v + Vv. An observer in motion at the speed of $V$v would observe the speed of $O$v to be just that – $O$v, while a stationary observer on the ground would observe it to be of speed $O$v + V_v. However the speed of light is equal to all observers regardless of their frame of reference. Therefore:

• time runs slower for fast moving objects
• the mass of a moving object increases with its speed (infinite at the speed of light)

This implies $E = mc^2$. High energy photons are capable of turning into matter in the form of particle and anti-particle pairs (that annihilate each other) muche like matter can be converted into energy.