Physical Sciences and Mathematics Commons^™

General Relativity, 8, David Peak

General Relativity

The Cosmic Microwave Background (CMB)

As previously noted, the universe is filled with microwave radiation. The frequency spectrum of this ubiquitous radiation follows a blackbody curve, as shown to the right. (http://map.gsfc.nasa.gov/media/ContentMedia/990015b.jpg) Note that photon energy (proportional to 1/wavelength) increases to the right. You might think the curve shown is the plot of a theoretical equation, but what is shown is actual measured data taken during the flight of the COBE (Cosmic Microwave Explorer) satellite/microwave observatory in 1990. The uncertainties in the measurements are about the thickness of the curve plotted. When compared with a theoretical blackbody curve the disagreement …

General Relativity, 7, David Peak

General Relativity

The expanding universe

The fact that the vast majority of galaxies have a spectral redshift can be interpreted as implying that the universe is expanding. This interpretation stems from the Doppler effect in which the relative motion of an emitter and a detector produces a frequency shift of the detected light with respect to the emitted light.

Rudiments Of Quantum Mechanics (Qm), David Peak

Structure of Matter

Rudiments of Quantum Mechanics (QM)

Structure Of Matter, 2, David Peak

Structure of Matter

Quantum electrodynamics

Quantum electrodynamics (QED) is the quantitatively best physical theory yet developed. Where it has been tested, it agrees with experiment to at least a few parts in 10¹¹! It is a theory of how charged particles and photons interact. It starts with electrons, for example, described by the Dirac Equation, interacting with photons described by a suitable electromagnetic potential energy.

Structure Of Matter, 6, David Peak

Structure of Matter

Quantum Flavor Dynamics (QFD), I

That each generation of the quark and lepton periodic tables (i.e., electron, muon, and tauon–see SM 1, p.1) has two members (a neutrino and a charged particle) that can be flipped into one another by emission or absorption of W bosons is reminiscent of how the angular momentum spin-1/2 component of a charged particle can be flipped between “up” and “down” orientations along some direction ( z ) in space by emission or absorption of photons. This analogy is made more graphic by labeling flavor rows by a new kind of “spin” (completely unrelated to …

Structure Of Matter, 1, David Peak

Structure of Matter

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 …

Structure Of Matter, 4, David Peak

Structure of Matter

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 …

Structure Of Matter, 3, David Peak

Structure of Matter

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 …

Structure Of Matter, 8, David Peak

Structure of Matter

Neutrino mass and family mixing

Neutrinos are products of radioactive decay in many stellar fusion processes, primarily starting with the reaction p + p → ²He*→ ²H + e⁺ +ν_e . The nucleus ²He* is a highly unstable (that’s what the * represents) isotope of helium consisting of four primary u quarks and two primary d quarks. For years (since 1962 or so), various groups have been measuring the solar electron-neutrino flux, invariably observing it to be lower than theoretical predictions. Moreover, neutrinos are generated in the upper atmosphere, via collisions of cosmic ray particles …

Structure Of Matter, 9, David Peak

Structure of Matter

Beyond the Standard Models

As noted in SM 8 there are problems with the standard model of particle physics that beg for resolution. Indeed, there are significant unknowns concerning the standard model of cosmology as well—for example, what really is “inflation” and what preceded it? The latter suggests the need for the unification of gravity and quantum mechanics. In addition, both models involve bizarre empirical parameters. Why are the elementary particle masses so wildly different? Why are the strengths of the interactions so different? What is dark matter? What is dark energy and why is its density so small? Why …

Structure Of Matter, 7, David Peak

Structure of Matter

More about the matter with mass

To repeat, the basic premise of QED is that the physical world doesn’t care about the phase of the electron wavefunction; calculations and observations strongly support that idea. The basic premise of QCD is that the physical world doesn’t care about the color of the quark wavefunction; calculations and observations strongly support that idea. The basic premise of QFD is that the physical world doesn’t care about the flavor (isospin) of the quark or lepton wavefunctions. But that’s not true! For example, a “free” d quark can certainly emit a (virtual) W particle and …

Structure Of Matter, 5, David Peak

Structure of Matter

The quark-gluon plasma

At the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory on Long Island in New York (the only major research accelerator functioning in the US) and the Large Hadron Collider (LHC) at CERN in Switzerland, heavy atoms, stripped of most or all of their electrons, are collided with energies approaching 100-1000 GeV per nucleon. Traveling at nearly the speed of light, these heavy ions are Lorentz contracted into pancake shapes in the laboratory frame of reference and, consequently, have very large quark and gluon densities within the constituent protons and neutrons. The energy density in the …

Physics 3710 – Problem Set #2, David Peak

Problems

Physics 3710 – Problem Set #2 Newtonian relativity

Problems 1-4 refer to: Sound travels at about 330 m/s in still air. Observer O is at rest with respect to still air, observer O′ travels with constant velocity +50 m/s in the common x, x′ direction. Event A is the emission of a sound pulse from a stationary source at the origin of O; it occurs at x_A = 0 at t_A = 0. Event B is the reflection of the pulse at x_B = +100 m. Event C is the detection of the reflected pulse at x …

Physics 3710 – Problem Set #3, David Peak

Problems

Physics 3710 – Problem Set #3 Relativistic kinematics, I

Physics 3710 – Problem Set #10, David Peak

Problems

Physics 3710 – Problem Set #10 Relativistic gravity, III

Problems 1-3 refer to: The maximum measured z value for a galaxy is 11.1. As on page 1, GR7, z = λ_d − λ_e / λ_e.

Physics 3710 – Problem Set #5, David Peak

Problems

Physics 3710 – Problem Set #5 Relativistic dynamics, I

Problems 1-5 refer to: One mass, m₁ = 1 (in some units), collides head-on with a second mass, m₂ = 2 , and sticks to it, forming a composite body of mass M . There are no external forces. Observer O records m₁ as initially moving with dimensionless velocity, u1 = +0.9 in the x - direction, while m₂ is recorded to be at rest. Do not make unwarranted assumptions about M , please; that’s the point of this set of problems.

Physics 3710 – Problem Set #9, David Peak

Problems

Physics 3710 – Problem Set #9 Relativistic gravity, II

Physics 3710 – Problem Set #6, David Peak

Problems

Physics 3710 – Problem Set #6 Relativistic dynamics, II

Problems 1-5 refer to: The mass of the neutron is 1.008664 u and that of the proton is 1.007276 u, where 1 u = 931.5 MeV.

Physics 3710 – Problem Set #11, David Peak

Problems

Physics 3710 – Problem Set #11 QED Feynman diagrams

The solid arrows are electrons or positrons, the wavy lines are photons. Describe the “in” and “out” states shown below and describe what happens at each vertex. What is an overall name for each of the diagrams shown? (e.g., “electron-photon scattering”)

Physics 3710 – Problem Set #4, David Peak

Problems

Physics 3710 – Problem Set #4 Relativistic kinematics, II

Physics 3710 – Problem Set #13, David Peak

Problems

Physics 3710 – Problem Set #13 Some weak interaction stuff

Questions 1-4 refer to the diagram at the right. In it, a particle p₁ absorbs a particle X and transforms into a particle p₂. Time increases vertically.

Physics 3710 – Problem Set #12, David Peak

Problems

Problem Set #12 Quarks and gluons

In the following solid lines represent quarks or antiquarks and dotted lines represent gluons. Time increases upward.

Physics 3710 – Problem Set #7, David Peak

Problems

Physics 3710 – Problem Set #7 Newtonian gravity

Physics 3710 – Problem Set #8, David Peak

Problems

Physics 3710 – Problem Set #8 Relativistic gravity, I

Special Relativity, 4, David Peak

Special Relativity

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.

Special Relativity, 7, David Peak

Special Relativity

Relativistic electromagnetism

Let’s return to the problem posed at the end of BK2.

Special Relativity, 2, David Peak

Special Relativity

Events not connected by light propagation

Previously, we considered two events (A, with s-t coordinates (x_A, y_A,z_A ,T_A ) = (x^′_A, y_^′A,z^′_A,T ^′_A ) = (0,0,0,0) according to both O and Oʹ [moving relative to O with constant velocity β along the mutual x, x^′ -axes], and B, with coordinates (x_B,0,0,T_B) and (x^′_B,0,0,T^′_B)) connected by a light pulse.

Special Relativity, 6, David Peak

Special Relativity

Energy-momentum vector

Special Relativity, 1, David Peak

Special Relativity

Newton and Maxwell

We have seen that simple magnetic forces are incompatible with Newtonian mechanics. There are far more profound incompatibilities between electromagnetism and Newton. In particular, Maxwell’s equations predict that an accelerating charge produces a time changing magnetic field, which, in turn, produces a time changing electric field, which, in turn, produces a time changing magnetic field, which, in turn, produces … . This self-sustaining production of magnetic and electric fields propagates away from the source charge at a finite speed given by 1 µ0ε 0 (in empty space), the numerical value of which is approximately 3x108 m/s. But, …

Special Relativity, 5, David Peak

Special Relativity

No abstract provided.