The Path Integral, Perturbation Theory and Complex Actions

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• If we spin the sphere (or cylinder) about an axis perpendicular to the separation to the detector we get φ = − GM |⃗x − ⃗ R| + Gm 1 ((r 1 + δ 1 sin ωt) 2 + δ 2 1 cos2 ωt) 1/2 − Gm 2 ((r 2 + δ 2 sin ω(t +∆t)) 2 + δ 2 2 cos2 ω(t +∆t)) 1/2 = − GM |⃗x − ⃗ R| + Gm 1 (r 2 1 +2r 1δ 1 sin ωt + δ 2 1 )1/2 Gm 2 − (r2 2 +2r 2δ 2 sin ω(t +∆t)+δ2 2)1/2 Tuesday, 2 April, 13
• Thus the potential is to lowest order is given by φ = − GM |⃗x − ⃗ R| − GM R ɛ(sin ωt − sin ω(t +∆t)) = − GM |⃗x − ⃗ R| − GM R 2ɛ sin(ω∆t/2) cos ω(t +(∆t/2)) • thus the oscillating masses should drive the detector if the frequency is at resonance <strong>and</strong> the Q value is sufficiently large Tuesday, 2 April, 13
Page 1 and 2: A proposal to measure the speed of
Page 3 and 4: Motivation • Tests of Newton’s
Page 5 and 6: • The cylinder is about 60 cm lon
Page 7 and 8: • Here the lower disc is rotated
Page 9 and 10: Tuesday, 2 April, 13
Page 11 and 12: • The masses generate equal and o
Page 13 and 14: Tuesday, 2 April, 13 In a greatly e
Page 15 and 16: • Which can be written as: F = Gm
Page 17 and 18: • The denominators should be: F =
Page 19 and 20: • For a path difference of the or
Page 21 and 22: ulated from the gravitational analo
Page 23 and 24: • Then the solution is given by t
Page 25 and 26: • expanding then to lowest order
Page 27 and 28: • Hence we get e assumption that
Page 29 and 30: Perspectives for measurement • Th
Page 31 and 32: Negative mass and the gravitational
Page 33: • A sphere with a spherical cavit
Page 37 and 38: Q Bounce • This experiment places
Page 39 and 40: Interferometric gravitational wave
Page 41: Conclusions • We have proposed a

The Path Integral, Perturbation Theory and Complex Actions

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