Relativity and Quantum Mechanics

Transcription

1 lativity and Quantum Mechanics Flamenco Chuck Keyser The following is a discussion of some of the salient points in Theoretical Physics in which I am interested. It will be expanded shortly to include Newton/Maxwell and General lativity relationships. Special lativity and Quantum Mechanics The following diagram shows the relation between the parameters in the time dilation equation of Special lativity: ct ct vt (ivt ) Fig 1 There are two interpretations.

2 For Quantum Field Theory, c and v are mass creation rates (e.g. m cmm t ), t and t are mass creation times, and c and v are scaled in terms of t and t in the relation: For Einstein s inertial frames, c is a ruler creation rate, and time is the time it takes to generate the ruler ( xv ct where c is a global c constant for all observers (actually only those on the surface of the earth at sea level) ( ct ') ( vt ') ( ct) ( m') ( m ) ( m ) v The first equation can be solved for t to give the time dilation equation: 1 v t' t,, 1 c

3 Multiplying this equation by c gives the mass transform relation ct ' ( ct) m' m Scaling the above diagram (dividing each leg of the right triangle by ct ) show the relation to the unit circle: 1 Fig Note that 1 sin cos for any whatever., and that the circumference c This idea can be extended to a general concept where the initial condition (ct) is subject to an (increasing) perturbation (vt ) to give a final result (ct ) where v and c are general parameters to be specified. (e.g., for a coordinate system, Einstein interprets x ct, xv vt, and v x ct, where v ( x, t ) signify proper (space, time) as an initial condition (inertial frame) for a specific (ruler, clock) (length, period). m

4 In Quantum Mechanics, these concepts are grouped together in the equation: hc h E mc h h h h P mc c c The equation for momentum suggests the following relation in terms of Planck s constant: m h Fig 1 If we back-solve the time dilation equation for v and c, we have: v c c ' 1 ( ), So that the relation between ponderable matter and a single photo-electron (electron mass-equivalent photon) is given by: m' h m m h m' m m' 1 m'

5 m' m And finally, 1 1 h m', which shows its relation to the unit circle. This is the fundamental equation for the interaction between any ponderable matter and a single photo electron in Quantum Mechanics. For the Wave equation in radial coordinates ( a circular path) we have: m exp( rm) h m 1 1 rm' rm' 1 r m', m' m' m' m 1 m' Note that is inversely proportional to previously calculated 's (in terms of space and time ), m and so is contravariant to that coordinate representation. This shows the relation for v < c in relativistic quantum mechanics. For v = c (i.e., h =, m = m, r = ), exp() 1 ; that is there is no change. Finally, note that the initial condition and perturbation are positive definite, m ct m v ( vt ') which implies that the interaction absorbs the energy of the perturbation to give an increased final result. To decrease the initial condition, one can substitute an imaginary perturbation (ivt ) so that m v ( ivt ') 1 vt '. The final result then is a model of radiation from the initial condition. Since QM is concerned with absorption from an initial condition for conserved particles (whose number can never be < 1), the radiation component is eliminated by the prescription of d reducing the rest mass (i.e., the initial condition) * m. In this case a negative mass dr indicates the interaction with anti-matter ; for a complete system of two particles (in a lab on the surface of the earth), the total matter can never be negative existing matter can only be radiated away until there is nothing. (This restriction is removed by Dirac through his prescription of positrons as well as electrons, but requires an immersive sea of electrons in relation to Fermi Levels, relative to a zero point energy the sea of electrons is eliminated by multiplying the derivative of the wave equation

6 by the complex conjugate of the original wave form to give only absorbed components that increase from the rest mass. Therefore, for m' m the interaction of light is irrelevant; neither relativity (Poincare transforms) or quantum mechanics apply (i.e. Newton s laws (Galilean transforms) and Maxwell s equations apply, but describe separate phenomena, since for radiation, the mass of light is. This latter case describes ordinary perception, for which the mass of light is zero (except for sunburns) and the speed of light is (subjectively) instantaneous. (If distance is measured by the speed of light (e.g. by radar), one has to ultimately consider resistance in the antennas as functions of Fermi levels in conductors).