Physics Stuff
Odds and Ends for the Classroom and Beyond
Some answers, useful resources and more questions.
Retain the child-like inquisitive nature that so aggravated your parents.
Use the "Why" question selectivley, making do with a "How" is enough.
After all even the best must submit to Quantum physics in the end.
Got you thinking?
A Stack of Concept Maps
Electromagnetic
Inducton
Imagine a cornfield with the combine harvester cutting the corn stalks. The cutting is more effective when the cutting edge is at right angles to the corn stalks: the cutting of magnetic flux by a wire is similarly more effective generating a greater potential when wire is moving at right angles to the field direction.
In The News
The Conservation of energy (1st law of thermodynamics) relates potential, kinetic energy to heat transfer. Implications of second law is that heat will not flow spontaneously from a cold to hotter body, rather it moves down temperature gradients. Energy always diffuses into a less useful and disorganised pattern and every isolated system grows more disordered with time. This is captured in the system's Entropy. Energy thus has both a Quantity and a Quality.
Maxwells equations rewritten by Heavyside as 4 sets of vector calculus equations describe the divergence and circulation properties of electric and magnetic fields.
Magnetic fields lack divergence (no monopoles) and electrical circulation. The two fields are relative and complimentary in the sense that they can induce the other: circulating currents are induced by moving magnetic fields and need not be formed of actual moving charges in a closed wire circuit: called a (fictitious) "Displacement" current.
Maxwell's equations are Charge, Parity and Time invariant in representing the same physics if t=-t, a positive is swapped with a negative charge and the orientation of the axis of obersvertion is altered to its mirro image. This is not so for the Weak and Strong forces. The loss of CPT invariance with these forces points to an overarching theory from which these symmetries are broken. Useful Concept Maps on next page collate the symmetries of gauge bosons and fermions. Presentation on Particles.
In an expanding Universe, light from stars at its furthest reaches effectively travel faster than the speed of light as the space-time between us and the star stretches in the time interval it takes light to reach us, making the Stars apparently older than 13.8 billion years of the age of the Universe.
New Cosmic Background Microwave Radiation (CMBR) data is still inconclusive about whether there is the tell-tale signs of polarised gravtiational waves inside the map.
Being the most penetrative of radiation, Gravitational waves will pass through the surface of Last Scattering (of electromagnetic radiation-light) that is the CMBR.
Kinetic theory of Gases
Cosmology
Maxwells Equations,
Faraday's Field & Charge Parity Time Invariance
Conspiracy exploits Science's scepticism
As Scientists we must counter the scammers, the Charlatans and the amateur politicans in their selected world-views: while Occam's razor says the simplest interpretation is always preferable politicans deploy Occam's broom that sweeps inconvenient facts under rugs, while conspiracy theorists leave out a few choice facts (an extreme form of inverse cherry picking) to make an erroneous assertion..
Feb 2015
Published Papers by Lee McC-J
Einstein's field Equations and Linear systems. The relationship between Einstein’s Field equations and the "Lax Pair" of classical higher spin field equations is investigated using two-component spinor valued differential forms. Linear systems of equations associated to both the vacuum and coupled gravitational matter field equations are constructed. The latter equations are shown to be the integrability conditions of the linear systems.
GL(2,C) extension of the Tung-Jacobson chiral quadratic spinor Lagrangian. The local symmetry group in the chiral quadratic spinor Lagrangian of Tung and Jacobson is extended from SL(2,C) to GL(2,C). The resulting field theory includes both spin-1 and spin-2 fields. The field equations admit solutions which are also solutions of the Einstein-Maxwell equations, including some with anti-self-dual Weyl tensor and anti-self-dual Maxwell field.
Classroom Physics & Maths in Context
While Dimensional analyssi is not required for A level an appreciation of the units of the variables of a theory adds to a good physicist's arsenal of Quality Control of their calculations and theories. In the presentation we use dimensional analysis, and some theory from the AS and a bit of A2 to come up with an order of magnitude figure for the of the inertaila mass density of the universe. Sciama who was Stephen Hawking's superviser, in his book "Unity of the Universe" develops a theory of the originof inertia from the receding stars. We develop his physical arguments, from the resolution to Olber's paradox to drawing parallels between magnetic and Coriolis forces to derive a formaul that is used n OCR syllabus as the critical density of the Universe
Dimensional
Analysis
Aphorisms from those of note
It is mere rubbish, thinking at present of the origin of life; one might as well think of the origin of matter
Charles Darwin
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..I find myself attached to one corner of this vast expanse [universe] without knowing why I have been put in this place rather than that, or why the brief span of life alloted to me should be assigned to one moment rather than another of all eternity which went on before me and that which will come after me
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Blaise Pascal
Another thing I must point out is that you cannot prove a vague theory wrong.
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Richard Feynmann
Maxwell's theory is Maxwell's system of equations
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Heinrich Hertz (1886)