Historical research guide · 0931 · 2006
Quantum Theory in Accelerated Frames of Reference
Bahram Mashhoon
In one minute
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.
Connection
Chapter 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.
From the source
The 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
The 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)
A 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)
Rotation 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)
Intrinsic 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)
What 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
The way in
https://doi.org/10.1007/3-540-34523-x_5How to cite it
Bahram Mashhoon (2006) Quantum Theory in Accelerated Frames of Reference doi:10.1007/3-540-34523-x_5