Quantum Theory in Accelerated Frames of Reference
Bahram Mashhoon
Abstract and summary · read the original at the source
In one page
Bahram Mashhoon, at the University of Missouri, asks a question that sounds simple and turns out to be deep: what does an observer who is accelerating actually measure? Standard relativity answers with the hypothesis of locality — at every instant the accelerating observer is treated as an ordinary, unaccelerated observer moving alongside. Mashhoon shows where that assumption runs out. A wave has a length, an acceleration has a length scale of its own, and when the two are comparable, what the observer measures depends on the whole recent history of the motion rather than on the present instant alone. He builds that memory into the theory as an integral over the observer’s past path, then walks through the consequences laboratories already see: the Sagnac effect measured for Cooper pairs, neutrons, atoms and electrons; the coupling of a particle’s spin to the rotation of the frame, which shifts a photon’s frequency as it crosses a spinning half-wave plate and shows up in the Global Positioning System as phase wrap-up; and the inertial potential measured with an accelerated neutron interferometer.
Why it matters hereChapter 3 holds that inertia is the vacuum’s reaction to acceleration, and this chapter is the careful quantum accounting of what acceleration does to a measurement in the first place — including the exact interferometry experiments that test it. Chapter 13 needs it because spin-rotation coupling is one of the few places where rotation, intrinsic spin and the geometry of spacetime already meet in measured, published physics.
What it claims
01The hypothesis of locality — that an accelerated observer is at every instant equivalent to a momentarily comoving inertial observer — is an approximation whose accuracy is set by the ratio of the wavelength being observed to the acceleration length, c squared divided by a for linear acceleration and c divided by Omega for rotation. It is excellent for laboratory devices, which must be much smaller than that length, and it is not exact.Section 2, Hypothesis of locality; Section 3, Acceleration tensor, Eq. (9) and the definition of the acceleration lengths
Settled physics02The field an accelerated observer measures is related to the inertial field by a Volterra integral over the observer’s past worldline, with a kernel directly proportional to the acceleration; Volterra’s uniqueness theorem, extended to square-integrable functions by Tricomi, makes that relation invertible, so the nonlocal theory carries no ambiguity of principle. When the acceleration is switched off the kernel vanishes and what remains is a constant memory of the past acceleration that is in principle measurable.Section 4, Nonlocality, Eq. (11) and the unique kernel of Eq. (14)
Published and peer-reviewed03A basic scalar or pseudoscalar radiation field cannot exist. Under the locality hypothesis a scalar wave of frequency equal to M times the rotation rate would stand completely still for every observer rotating uniformly about that axis, which the nonlocal theory forbids; scalar fields can therefore only be composites of other basic fields. The author notes this matches the observational record, which shows no trace of a fundamental scalar field.Section 4, the paragraph following Eq. (14)
Published and peer-reviewed04Rotation of the frame couples to the orbital angular momentum of a particle and produces the Sagnac phase shift, twice the mass over h-bar times the integral of the rotation rate over the interferometer area — a result already measured for Cooper pairs in a rotating Josephson-junction interferometer, for slow neutrons using the rotation of the Earth itself, for neutral atoms, and for electrons.Section 7, Sagnac effect, Eq. (25) and Eq. (26)
Settled physics05Intrinsic spin couples to rotation independently of the orbital term, adding an energy of minus gamma times the rotation rate dotted into the spin. For light this is helicity-rotation coupling: a uniformly rotating half-wave plate becomes a frequency shifter of twice the rotation rate, first seen in microwave experiments and since used optically, and the same relation appears at about one gigahertz and an eight hertz rotation rate as phase wrap-up in the Global Positioning System.Section 8, Spin-rotation coupling, Eq. (29), Eq. (31) and Eq. (32)
Settled physics06What to watch: in a laboratory fixed on the Earth every Hamiltonian should carry a spin-rotation-gravity term. Earth’s rotation splits spin-up from spin-down by about 10 to the minus 19 electronvolts, and the gravitomagnetic field of the rotating Earth by about 10 to the minus 29, against a present experimental reach near 10 to the minus 24. The named route to a direct measurement is a neutron interferometer with a rotating spin flipper in one arm, whose interference beat frequency equals the rotation rate.Section 8, Eq. (35) and Eq. (36), and the rotating-spin-flipper proposal that follows
What to watch
Read it · abstract
Abstract
The observational basis of quantum theory in accelerated systems is studied. The extension of Lorentz invariance to accelerated systems via the hypothesis of locality is discussed and the limitations of this hypothesis are pointed out. The nonlocal theory of accelerated observers is briefly described. Moreover, the main observational aspects of Dirac’s equation in noninertial frames of reference are presented. The Galilean invariance of nonrelativistic quantum mechanics and the mass superselection rule are examined in the light of the invariance of physical laws under inhomogeneous Lorentz transformations.
Bahram Mashhoon, Department of Physics and Astronomy, University of Missouri-Columbia. Quantum Theory in Accelerated Frames of Reference, Lecture Notes in Physics 702, Springer Berlin Heidelberg, 2006. Author version arXiv:hep-th/0507157, 15 July 2005.
(Abstract only. The author version is free to read on arXiv — see the rights note for why no further text is reproduced here.)
On this site: Unruh’s 1981 proposal that a horizon can be built on a bench is at /library/stm-dcc76e413a, the switched Unruh-DeWitt detector realised by electro-optic sampling at /library/stm-4144311706, and the theory of acceleration-induced thermality at /library/stm-405e905447. For inertia read as the vacuum’s reaction to acceleration, see Haisch, Rueda and Puthoff at /library/stm-0f2b09effd and the passive-gravitational-mass argument at /library/stm-dfc45c66c7. The Aharonov-Bohm paper whose matter-wave analogue is the Sagnac effect is at /library/stm-6ec95a6893.
The way in
https://doi.org/10.1007/3-540-34523-x_5The published chapter is closed at the publisher. The author version is on arXiv as arXiv:hep-th/0507157 version 1, dated 15 July 2005, and that is the copy the summary and every locator below were written from — the arXiv abstract page carries the assumed-1991-2003 arXiv licence, which is not a Creative Commons licence, so only the author’s own abstract is reproduced here and no other text of the chapter. REGISTRY NOTES: the batch instruction named arXiv hep-th/0507079 as the preprint; the copy actually fetched, and the one whose section and equation numbers the locators use, is hep-th/0507157, whose title page reads Quantum Theory in Accelerated Frames of Reference, Bahram Mashhoon, Department of Physics and Astronomy, University of Missouri-Columbia. The registry record carried no year and no creators at the top level; the chapter appears in Lecture Notes in Physics volume 702, Springer, 2006.
How to cite it
Bahram Mashhoon (2006) Quantum Theory in Accelerated Frames of Reference. doi:10.1007/3-540-34523-x_5
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