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