[toc][latexpage] What you need to know from each major topic.
Let’s define our terms. I’ll use 3 levels of “importance,” and that should help you to gauge your efforts.
- “Important” means that an idea, technique, theory, term will reappear later and that later understanding will rely on understanding of the idea, etc.
- “Useful” means that the idea, etc. is a natural part of the current discussion–that things wouldn’t make sense without its introduction, but that its use will be limited to the particular section or module in which it was introduced. For example, an Important idea might require the Useful idea in its definition, but it’s only the Important idea that will crop up later.
- “Cultural” means that it’s sort of something that you ought to know as an intelligent person, but not necessarily necessary for what we’re doing in the main thrust of ISP220.
Basic Physics – Mechanics
Important
- speed and acceleration definitions and simple calculations like $x = vt$ and $v=at$.
- the fact that displacement, velocity, acceleration, force, and momentum are vectors
- vector addition and subtraction, in pictures and in components.
- vector combinations will almost always be in graphics form, component combinations will be rare.
- momentum as $\overrightarrow{p} = m\overrightarrow{v}$
- momentum conservation
- in words: the sum of the momenta of all objects before an event is equal to the sum of all of the momenta after the event
- in symbols (assuming 2 objects before and after the event): $p(1)_0 + p(2)_0 = p(1) + p(2)$
- remember that the sum is along the same directions. If the event takes place all in one dimension, then it’s easy. If the event takes place in, say two dimensions then the sums must be done separately for each of two directions – usually along the $x$ and $y$ axes.
- Newton’s Gravitational Model $F=G\frac{Mm}{R^2}$
- Newton’s Cosmological ideas about Absolute Space and Time
- our current confusion about galactic motions and motions within galaxies that suggest a significant Dark Matter composition in the cosmos
- kinetic energy is $K=1/2 mv^2$
- potential energy can be in the form of elasticity, or springs
Useful
- Newton’s second law in the $F=\frac{\Delta p}{\Delta t}$ way
- gravitational potential energy for an object suspended a distance $h$ above a surface is $U(g) = mgh$
Cultural
- Newton’s second law in the $F=ma$ sort of way is important
- energy is conserved when all forms of energy are taken into account
Basic Physics – Electromagnetism
Important
- Electric charges exert forces on one another according to Coulomb’s Law. (see Glossary)
- Electric charges create Electric Fields (see Glossary)
- Currents create Magnetic Fields concentrically around the current (see Glossary)
- Accelerated electric charges radiate electromagnetic energy
- Electromagnetic fields carry energy
- Electric Potential Energy (see Glossary)
- The various field shapes from charges and currents that were demonstrated
- The magnet-coil demonstration of Faraday’s Law
Useful
- Currents exert forces on one another
Cultural
- Motors and radio transmission and reception
Tools of the Trade
Important
Particle Accelerators
- The active principles of particle accelerators come from the use of electric and magnetic fields. The electric fields are used to accelerate the particles and give them increased Kinetic Energy. Magnetic fields are used to bend the beams.
- The unit of energy of “electron Volts” is necessary in physics. One eV is equal to $1.6 \times 10^{-19}$ Joules.
- Accelerators come in basically three kinds:
- Linear accelerators
- Synchrotrons, in which the radius of the beam pipe is fixed and in which the magnetic field must increase as particles are accelerated in order to keep them in the same circular path.
- Cyclotrons, in which the radius changes as the particles are accelerated.
- There are two arrangements of accelerators used in Particle Physics:
- Beams can be accelerated to high energies and then taken out of the synchrotron and used directly, or directed to fixed targets where secondary, or even tertiary beams are produced for special purposes. These are called Fixed Target experiments.
- Beams can be created which counterrotate in synchrotrons and collide inside of the accelerator. These are called Colliding Beam experiments.
- The numbers of collisions depend on the number of particles in the colliding beams. The amount of beam is quantified by the “Luminosity,” which is the number of particles per unit area, per unit time. The symbol is $\mathcal{L}$ and the units in particle physics are per second per cm$^{-2}$.
- The likelihood that a collision might take place and that it would result in a particular reaction is quantified by the “cross section,” which is can be thought of as an area, which is a mate to the use of Luminosity, since the areas cancel when they are multiplied together. The symbol for cross section is $\sigma$ and the units in particle physics are either cm$^2$ or “barns.” 1 barn is equal to $10^{-24}$cm$^{-2}$.
- The Large Hadron Collider (LHC) is the largest synchrotron ever constructed and is just outside of Geneva, Switzerland, straddling the French-Swiss border.
Detectors
- Ionization detectors are commonly used in various guises to detect the passage of charged particles. These are used primarily to indicate points in space where a particle passed.
- Telescopes
- Many telescopes are in use which observe energy from space using many different wavelengths of electromagnetic energy as well as individual kinds of particles.
- Optical, infrared, microwave, and X-ray observatories are useful for modern cosmology and are typically satellite based.
Useful
Accelerators
- Acceleration of particles in synchrotrons is done by passing the beams through Radio Frequency cavities, or RF Cavities. In a synchrotron, the particles go through the same RF cavity every time they go around and so that’s a particularly efficient arrangement.
- RF acceleration actually causes the beams to clump into bunches. In the LHC there are 2808 bunches with 25 nanoseconds between each bunch.
Detectors
- Ionization detectors can be categorized into two different sorts:
- There are visual ionization detectors in which images are created and often analyzed by humans. Emulsions, cloud chambers, bubble chambers, and spark chambers are examples.
- There are electronic detectors in which current pulses are recorded for computer analysis, off-line. Wire chambers, proportional chambers, and Silicon detectors are examples.
Telescopes
- Ultraviolet telescopes have been used in astronomy.
- Radio telescopes are very prevalent.
Cultural
- The LHC startup was a complete disaster, but while recovery took more than a year and the replacement of a lot of magnets, the accelerator is running flawlessly now.
- The LHC is running at half-energy until 2014 in order to give time for implementing the permanent repair to the design problem that was the cause of the 2008 accident.
Special Relativity
Important
- An inertial frame is one which is not accelerating.
- I refer to a frame from which observations are being made as the “home frame” and any frame that’s in non-accelerated motion relative to it as the “away frame.”
- The Principles of Relativity:
- That no experiment – mechanical or electromagnetic – can be done in any inertial rest frame that would indicate that it is moving.
- The speed of light is constant as observed in all inertial rest frames.
- Clocks as observed in a colinear, co-moving inertial frame of reference – Away – appear to run slowly as observed from Home. Time Dilation.
- Lengths as observed in a colinear, co-moving inertial frame of reference – Away – appear to be shorter as observed from Home. Length Contraction.
- It is impossible for the concept of Simultaneity to exist outside of one’s own rest frame. Any other frame will observe two events which are simultaneous in one frame to be not simultaneous in another.
- The relativistic gamma function is $\gamma = \frac{1}{\sqrt{1-u^2/c^2}}$ where $u$ is the speed of the Away frame relative to Home.
- mass in an Away frame appears to a Home observer to increase.
- The Rest mass of an object is the actual mass of it in its own rest frame.
- Relativistic mass is the term used to refer to the mass in an Away frame.
- Relativistic momentum is: $p = m\gamma$
- Rest Energy is $E_m=mc^2$, the energy due to rest mass.
- Total Energy is: $E_T = m\gamma c^2$ and $E_T^2 = m^2c^4 + p^2c^2$
- Relativistic Kinetic Energy is: $K=mc^2(\gamma -1)$
- The “interval” in flat space is an invariant: $\Delta s^2 = c^2 \Delta T^2 – \Delta x^2$
Useful
The Length contraction can be calculated easily using the Relativistic Gamma function (see Glossary): $L_H = L_A/\gamma$, where $L_H$ means a length as observed by Home and $L_A$ means the length in the Away frame.
The Time Dilation can be calculated easily using the Relativistic Gamma function (see Glossary): $T_H = L_A \gamma$
Velocities transform as: $v_H = \frac{v_A+u}{ 1 +\frac{u}{c^2}v_A}$
Cultural
It is not correct to say that “moving clocks run slowly” since “moving with respect to what” matters!
Everything is not relative. Relativity theory is more about constancy, than relative notions.
The rise of German Nationalism along with the Nazi Party led to an extreme distrust of Special Relativity, denying Einstein the Nobel Prize for his achievement and putting his life in danger causing him to eventually emigrate to Princeton, NJ. “Jewish Science” was the slur that was used to stir up distrust and animosity against him personally and was led by rival colleagues within the German physics community. Not all, by any means, but a few with influence.
General Relativity and Early Cosmology (in progress)
Important
The Equivalence Principle
Masses warp space, time, and spacetime
Black holes are a real phenomenon which is are the result of an extreme warping of space and time.
Einstein’s 10 Field Equations of General Relativity are schematically $G=T$ where $G$ refers to all of the pieces of the 10 equations that refer to space and time while $T$ refers to all of the terms involving energy, mass, pressure, and density.
There were classic tests of the predictions of General Relativity, in particular the bending of light by the sun confirmed by Eddington were historically a major intellectual event of the 20th century.
Useful
Free-fall is a true intertial frame.
GPS units require both special and general relativity in order to work properly.
Cultural
General Relativity was a unique intellectual event in this history of thought.
Quantum Mechanics
Important
Useful
Cultural
Forces of Nature
Important
Useful
Cultural
Quarks
Important
Useful
Cultural
Standard Model of Particle Physics
Important
Useful
Cultural
Standard Model of Cosmology
Important
Useful
Cultural
Beyond the Standard Models
Important
Useful
Cultural