SOME KEY PHYSICS CONCEPTS

JACK SARFATTI

WHO IS PROMINENTLY

FEATURED IN MIT PROFESSOR DAVID KAISER’S

AWARD-WINNING BOOK

HOW THE HIPPIES SAVED PHYSICS

QUANTUM FIELD THEORY Quantum fields create and destroy particles. Special relativity without the spacetime curvature of real gravity is assumed here. Artificial gravity fields correspond to using non-inertial local frames of reference with proper acceleration relative to the local timelike geodesics. This works whether or not there is any local curvature.

SYMMETRY Noether’s Theorem Continuous global symmetries of the physical action have conserved global charges and local current densities. 1)  Space translation symmetry conserved total linear

momentum in a closed system. Example, if A is isolated and emits B with momentum P then A will recoil with momentum – P in the initial inertial rest frame of A.

2)  Rotational symmetry conserves total angular momentum = orbital angular momentum + spin.

3)  Time translation symmetry conserves total energy. 4)  Internal gauge symmetries conserve electric, weak and

strong charges.

GAUGE FIELDS Gauge fields are induced when global continuous symmetries of the physical action of a system are enlarged to local symmetries. Global symmetries require faster than light signals to enforce them. Local symmetries agree better with Einstein’s special theory of relativity which keeps the speed of light in classical vacuum invariant for all inertial frame observers moving on different timelike real-force free geodesics. The electromagnetic, weak and strong sub-nuclear forces are internal symmetry gauge fields from the groups U1, SU2 & SU3 respectively. Einstein’s 1916 gravity is the gauge field of the Poincare group of special relativity when the torsion is constrained to be zero and only curvature is permitted from the back-reaction of stress-energy currents on the spacetime continuum itself.

THE PHYSICAL MEANING OF U1 EM GAUGE TRANSFORMATIONS The gauge transformations are usually introduced as purely mathematical sleight of hand without any direct physical meaning. In fact they have direct physical meaning as the four-momenta of virtual photons emitted and absorbed by a charge in a simple Feynman vertex diagram. They express the local action-reaction principle between the kinetic momentum and the EM field momentum of the charge. The gauge function is the local quantum phase S of the charge in the Bohm Q-particle picture. The global U1 → local U1(x) induced gauge potentials and quantum waves transform as

!(!) !→ e!" ! !(!)!!!

!!! ! = e!" ! [!! + !!!! ! ]!(!)!!!

!!! = (ℎ/!)!!! +!! !!!!

!

(ℎ/!)!!! → (ℎ/!)e!" ! [!! + !!!! ! ]!(!)!!!

!! → !! − (ℎ!! )!!! !

!

!

!!! → !!!!!!= e!" ! ℎ

! !! +ℎ! !!!! ! ! + !

! !!e!" ! ! − ℎ!!! ! e!" ! ! !!= !!!!!

!

!! = !!! !!!

!

ELECTROMAGNETIC ACTION-REACTION The virtual photon 4-momentum that cancels out in the local U1(x) gauge transformation is

h∂µSx The canonical 4-momentum of charge plus its near field of virtual longitudinal photons is conserved in the local gauge transformation in accord with Newton’s third law of motion. Indeed, the real contact forces between objects are due to this purely local gauge transformation, which is more than a formal symmetry of the mathematics. Einstein’s equivalence principle yields a subtler somewhat similar picture for gravity using the proper acceleration of a test particle away from a timelike geodesic rather than its canonical momentum, which I will discuss in detail elsewhere.

SUPERCONDUCTING LIGHT Photons inside a BCS superconductor acquire rest mass from the macro-quantum coherent Glauber state of electron Cooper pairs bound by phonons of the crystal. This is analogous to the superconducting coherent vacuum Higgs field that gives rest mass to the W-bosons and the leptons and quarks. The internal symmetry U1 SU2 SU3 gauge bosons all have spin 1 with three independent polarization states. When the rest mass is zero only the two transverse polarizations are in the far-radiation field as “real photons.” The longitudinal polarization is still very important for electrical technology in the near field made from coherent states of virtual photons. For example, the electrostatic Coulomb field in the rest frame of a charge is entirely made from virtual longitudinal photons.