**Modern Physics**

November 02 2018

**Relativity**
- Galilean relativity states the laws mechanics are valid in all inertial reference frames
- but the laws of electromagnetism seemed valid only in a reference frame where the speed of light is c
- the study of the rest medium for the speed of light led to contradictions
- showing both that the earth must be still in the rest medium but also moving through it
- the contradictions are resolved if the speed of light is deemed to be the same in all inertial reference frames
- the invariance of c leads to time dilation and length contraction
- implying the commonsense notions of space and time are dependent on one's reference frame
- in order to maintain the consistency of the natural laws of physics in all frames of reference
- underlying the changeable Euclidean reference frames of space and time
- is the invariant four-dimensional structure of the universe called spacetime
- in which exist 4-vectors whose magnitude is independent of reference frame
- the magnitude of spacetime intervals are independent of reference frame
- whose dimensions in ordinary three-dimensional space shake out depending on the observer's frame of reference
- similarly, the energy-momentum 4-vector is reference-frame invariant
- the total energy of a system breaks out into energy and momentum depending on the observer's frame of reference
- at rest, the energy is of a system is mc2
- showing that mass, of the rest energy of a system, is a relativistic invariant
**Particles and Waves**
- reality at the atomic scale is radically different
- quantization: some physical quantities, such as energy, appear only in discrete values
- wave-particle duality: light and matter exhibit both wave-like and particle-like aspects
- uncertainty principle: it is impossible to measure simultaneously and with arbitrary precision a particle's position and momentum
**Quantum Mechanics**
- matter, as well as light, exhibit both wave and particle properties
- matter waves can be described in terms of wave functions
- which relate to the probability of finding a particle at a certain location
- wave functions are the most thorough description of matter physics can provide
- yet its link to the behaviour of an individual particle is only statistical
- as analogous to standing waves, wave functions lead to the quantization of energy for confined particles
**Atomic Physics**
- atomic electrons are quantum particles trapped in the three-dimensional potential well associated with the electric force
- solving the wave function leads to quantized energy levels, defined by 4 quantum numbers
- the exclusion principle permits only one atomic electron per quantum state, leading to the shell structure of atoms and the periodic table of elements
- quantum effects are important in molecules and solids
- molecules have a structure of quantized energy and resulting spectra
- in solids, individual atomic energy levels separate to form bands, informing electric conductivity
**Nuclear Physics**
- the tiny but massive atomic nucleus is a repository of vast energy
- the protons and neutrons that make up the nucleus can take many configurations
- with the atomic number of protons determining the element and the mass number determining the isotope
- protons and neutrons are held together by the nuclear force
- while protons repel each other by electrical repulsion
- models of nuclear structure are yet incomplete
- stable isotopes require a delicate balance between protons and neutrons
- with equal numbers for lighter stable nuclei and more neutrons for heavier nuclei
- unstable isotopes are radioactive and decay by shedding particles
- alpha decays emit helium nuclei, beta decay emit electrons, and gamma decay emit photons
- isotope decay is characterized by half-lives, which range from instant to universe-aged
- the curve of binding energy shows that nuclei around atomic number 60 have the greatest binding energy
- energy can be released either by fission of heavier nuclei or fusion of lighter nuclei
**From Quarks to the Cosmos**
- the structure of ordinary matter and its interactions can be explained in terms of a handful of particles
- the quantum mechanical view of electromagnetism includes gauge bosons
- such as the photon, that act as force carriers that mediate the fundamental forces
- the three fundamental forces
- strong, electroweak, and gravity
- are believed to be manifestations of the same fundamental interactions that appear unified at high energies
- the standard model describes the elementary particles and their interactions
- it sheds light on the structure of matter today as well as in the early universe
- only 5% of the universe consists of familiar matter, the rest is dark energy and dark matter, about which we know very little