Problem Set #10

Blackbod

Structure of matter, 3

The particle zoo Prior to the 1930s the fundamental structure of matter was believed to be extremely simple: there were electrons (each with mass about 0.5 MeV), e− , photons (no mass), γ , and protons (mass about 938 MeV), p+ . Starting in 1932 the world began to get a lot more complicated. First came Dirac’s positron ( e+ , with same mass as the electron), postulated in 1928 but mostly ignored until Anderson’s accidental discovery (see SM 1). Soon after, the neutron ( n ) was identified (mass about 940 MeV). In beta decay, the neutron transforms into a proton and an electron. The energy of the electron in beta decay has a maximum cutoff and is otherwise “never” observed to be the same–as it would be if there were only two products. It is almost as if energy is not conserved in beta decay. In 1930, Wolfgang Pauli proposed that a third, unseen, particle was also emitted and that the three products conserved energy and momentum by sharing them in a variety of unpredictable ways. The new particle would have to have spin-1/2 (because the neutron, proton, and electron all have spin-1/2 and not even the crazy rules of addition in quantum mechanics allow 1/2 +1/2 = 1/2 ) and be electrically neutral (because the neutron is neutral and the proton plus electron is also neutral). Eventually, Pauli’s particle–the neutrino, ν –was directly detected in the 1950s. This set of particles was all that was needed to make sense of nuclei and their properties

Special relativity, 3

A few kinematic consequences of the Lorentz transformations How big is gamma

Special relativity, 4

More kinematic consequences of the Lorentz transformations Light cones: A “light cone” is a set of world lines corresponding to light rays emanating from and/or entering into an event

Physics 3710: Intermediate Modern Physics

Physics 3710 is about the principles and applications of special and general relativity and of the nuclear and sub-nuclear structures of matter. Though some of the topics of 3710 are more than 100 years old, others continue to rapidly evolve—and their interplay provides a fascinating, living example of science at work. Moreover, the course is predicated on, and aspires to convey, two thoroughly modern, coherent, and interconnected themes: (1) the largest (e.g., stars, galaxies, and galactic clusters) and smallest (e.g., quarks, leptons, and force-carrying bosons) observed forms of matter are intimately related to one another; and (2) dynamics, conservation laws, and symmetry are all essentially equivalent

Structure of matter, 4

Antiscreening: The triumph of lattice QCD QED is a phenomenally accurate theory of the interactions of electrically charged particles with photons. The way interactions are described in QED—by adding electromagnetic potential fields to the energy and momentum operators in the charged particle field equations— is essentially exactly correct given that the detailed calculations that can be made in QED agree so well with observation. These calculations are possible because simple processes (involving small numbers of interaction vertices) are significantly more important than complicated processes. That is, QED is a “perturbative” theory. Higher order QED effects, therefore, invariably consist of small corrections. QCD is different. The strength of the color interaction is greater than that of the electromagnetic interaction and, because gluons carry color, the processes that contribute importantly are more complex. In general, QCD is not a perturbative theory. Higher order QCD interactions are essential. While QED calculations typically involve only a few Feynman diagrams, QCD calculations of similar accuracy might involve hundreds of thousands

Structure of matter, 1

In the hot early universe, prior to the epoch of nucleosynthesis, even the most primitive nuclear material—i.e., protons and neutrons—could not have existed. Earlier than 10–5 s or so after t = 0 , the universe would have been a hot soup consisting of the most elementary of particles—photons, electrons, positrons, neutrinos, quarks, and gluons. We now turn to the,” “Standard Model of Particle Physics,” our current understanding of these elementary building blocks and their interactions. The Standard Model of Particle Physics (SMPP), developed in fits and starts over the past 50 years, is a quantitatively predictive theory of subatomic matter. It accurately describes the structure of matter at the smallest length scales yet probed, just as the Standard Model of Cosmology (SMC)—the FLWR spacetime (including cold, dark matter and vacuum energy)—accurately describes the structure of matter at the largest observed length scales. The SMPP and SMC are not only complementary in scale, they are also complementary in “force”: the SMC is only about gravity, while the SMPP says nothing about gravity at all

Physics 3710 – Problem Set #12

Problem Set #12 Quarks and gluons In the following solid lines represent quarks or antiquarks and dotted lines represent gluons. Time increases upward