Quantized conic sections; quantum gravity
Starting from free relativistic particles whose position and velocity can only be measured to a precision < [Delta]r[Delta]v > [equivalent to] [plus minus] k/2 meter[sup 2]sec[sup [minus]1] , we use the relativistic conservation laws to define the relative motion of the coordinate r = r[sub 1] [minus] r[sub 2] of two particles of mass m[sub 1], m[sub 2] and relative velocity v = [beta]c = [sub (k[sub 1] + k[sub 2]])/ [sup (k[sub 1] [minus] k[sub 2]]) in terms of conic section equation v[sup 2] = [Gamma] [2/r [plus minus] 1/a] where +'' corresponds to hyperbolic and [minus]'' to elliptical trajectories. Equation is quantized by expressing Kepler's Second Law as conservation of angular niomentum per unit mass in units of k. Principal quantum number is n [equivalent to] j + [1/2] with square'' [sub T[sup 2]]/[sup A[sup 2]] = (n [minus]1)nk[sup 2] [equivalent to] [ell][sub [circle dot]]([ell][sub [circle dot]] + 1)k[sup 2]. Here [ell][sub [circle dot]] = n [minus] 1 is the angular momentumquantum number for circular orbits. In a sense, we obtain spin'' from this quantization. Since [Gamma]/a cannot reach c[sup 2] without predicting either circular or asymptotic velocities equal to the limiting velocity for particulate motion, we can also quantize velocities in terms of the principle quantum number by defining [beta][sub n]/[sup 2] = [sub c[sup 2]]/[sup v[sub n[sup 2]] = [sub n[sup 2]]/1([sub c[sup 2]]a/[Gamma]) = ([sub nN[Gamma]]/1)[sup 2]. For the Z[sub 1]e,Z[sub 2]e of the same sign and [alpha] [triple bond] e[sup 2]/m[sub e][kappa]c, we find that [Gamma]/c[sup 2]a = Z[sub 1]Z[sub 2][alpha]. The characteristic Coulomb parameter [eta](n) [triple bond] Z[sub 1]Z[sub 2][alpha]/[beta][sub n] = Z[sub 1]Z[sub 2]nN[sub [Gamma]] then specifies the penetration factor C[sup 2]([eta]) = 2[pi][eta]/(e[sup 2[pi][eta]] [minus] 1]). For unlike charges, with [eta] still taken as positive, C[sup 2]([minus][eta]) = 2[pi][eta]/(1 [minus] e[sup [minus]2[pi][eta]]).
- Research Organization:
- Stanford Linear Accelerator Center, Menlo Park, CA (United States)
- Sponsoring Organization:
- USDOE; USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC03-76SF00515
- OSTI ID:
- 6499314
- Report Number(s):
- SLAC-PUB-6057; CONF-9302102-1; ON: DE93010950
- Resource Relation:
- Conference: ANPA WEST 9 conference, Stanford, CA (United States), 13-15 Feb 1993
- Country of Publication:
- United States
- Language:
- English
Similar Records
Insertion and alkyne coupling reactions on early-transition-metal centers. Structures of CpTa(ME)(. eta. sup 2 -ArCCAr)(. eta. sup 2 -MeCN sup t Bu), CpMeTaC(Ph)C(Ph)C(Me)N sup t Bu, and CpClMo(CPh) sub 4 (Ar = p-tolyl)
Cyclobutyne ligands. 2. Reactions of the cyclobutyne triosmium complex Os[sub 3](CO)[sub 9]([mu][sub 3]-[eta][sup 2]-C[sub 2]CH[sub 2]CH[sub 2])([mu]-SPh)([mu]-H) with diphenylacetylene
Related Subjects
GENERAL PHYSICS
QUANTUM GRAVITY
QUANTUM ELECTRODYNAMICS
RELATIVISTIC RANGE
SCATTERING
SPIN
ANGULAR MOMENTUM
ELECTRODYNAMICS
ENERGY RANGE
FIELD THEORIES
PARTICLE PROPERTIES
QUANTUM FIELD THEORY
661310* - Relativity & Gravitation- (1992-)
661100 - Classical & Quantum Mechanics- (1992-)