The noise in gravitational-wave detectors and other classical-force measurements is not influenced by test-mass quantization

It is shown that photon shot noise and radiation-pressure back-action noise are the sole forms of quantum noise in interferometric gravitational wave detectors that operate near or below the standard quantum limit, if one filters the interferometer output appropriately. No additional noise arises from the test masses' initial quantum state or from reduction of the test-mass state due to measurement of the interferometer output or from the uncertainty principle associated with the test-mass state. Two features of interferometers are central to these conclusions: (i) The interferometer output (the photon number flux N(t) entering the final photodetector) commutes with itself at different times in the Heisenberg Picture, [N(t), N(t')] = 0, and thus can be regarded as classical. (ii) This number flux is linear in the test-mass initial position and momentum operators x_o and p_o, and those operators influence the measured photon flux N(t) in manners that can easily be removed by filtering -- e.g., in most interferometers, by discarding data near the test masses' 1 Hz swinging freqency. The test-mass operators x_o and p_o contained in the unfiltered output N(t) make a nonzero contribution to the commutator [N(t), N(t')]. That contribution is cancelled by a nonzero commutation of the photon shot noise and radiation-pressure noise, which also are contained in N(t). This cancellation of commutators is responsible for the fact that it is possible to derive an interferometer's standard quantum limit from test-mass considerations, and independently from photon-noise considerations. These conclusions are true for a far wider class of measurements than just gravitational-wave interferometers. To elucidate them, this paper presents a series of idealized thought experiments that are free from the complexities of real measuring systems.Comment: Submitted to Physical Review D; Revtex, no figures, prints to 14 pages. Second Revision 1 December 2002: minor rewording for clarity, especially in Sec. II.B.3; new footnote 3 and passages before Eq. (2.35) and at end of Sec. III.B.

Unusual Effect of α-olefins as Chain Transfer Agents in Ethylene Polymerization over the Catalyst with Nonsymmetrical Bis(imino)pyridine Complex of Fe(II) and Modified Methylalumoxane (MMAO) Cocatalyst

Ethylene polymerization with bis(imino)pyridlyiron precatalysts generally produces linear polyethylene (PE) even with the presence of α-olefins because α-olefins are not incorporated into polymeric products. Interestingly, α-olefins, such as hexene-1 or butene-1, have been found to act as effective chain transfer agents in the ethylene polymerization promoted by nonsymmetrical bis(imino)pyridyliron complexes with modified methylalumoxane (MMAO), resulting in higher catalytic activities with higher amounts of polymers with lower molecular weights, and, more importantly, narrower molecular weight distributions of the resultant polyethylenes (PE). This phenomenon confirms the assistance of α-olefins in the chain-termination reaction of iron-initiated polymerization and regeneration of the active species for further polymerization. Besides higher activities of the catalytic system, the formation of linear PE with trans-vinylene terminal groups and lower molecular weights are explained. The observation will provide a new pathway for enhancing catalytic activity and improving the quality of polyethylenes obtained by regulation of molecular weights and molecular weight distribution

Effect of Mono- and Multichlorinated Organic Compounds—Chlorocyclohexane and Hexachloro-<i>p</i>-xylene—On the Catalytic Properties of Titanium–Magnesium Catalysts in the Homo- and Copolymerization of Ethylene with 1-Hexene

Ethylene polymerization and ethylene/1-hexene copolymerization over the titanium–magnesium catalytic system in the presence of chlorocyclohexane (CHC) and hexachloro-p-xylene (HCPX) has been studied. Modification of TMC with chlorocyclohexane and hexachloro-p-xylene increased catalyst activity severalfold for both ethylene polymerization and ethylene/1-hexene copolymerization. The key kinetic regularities of ethylene homopolymerization and ethylene/1-hexene copolymerization in the presence of CHC and HCPX were determined, and the copolymerization constants were measured. Molecular characteristics and the copolymer composition were determined for the synthesized samples of ethylene homopolymers and ethylene/hexene copolymers. Modification of the titanium–magnesium catalyst with chlorinated organic compounds reduced 1-hexene content in the copolymer; polymerization was sensitive to 1-hexene as a regulator of polymer molecular weight. The potential mode of action of chlorinated organic modifiers on catalytic properties of titanium–magnesium catalyst is discussed