Macroscopic Test of the Aharonov-Bohm Effect
Adam Caprez · Brett Barwick · Herman Batelaan
Abstract and summary · read the original at the source · APS default licence
In one page
The Aharonov-Bohm effect is the cleanest evidence that the electromagnetic potential is physically real: an electron passing a shielded magnetic flux shifts its interference fringes even though no field, and so no classical push, ever reaches it. Adam Caprez, Brett Barwick and Herman Batelaan at the University of Nebraska-Lincoln test the second half of that sentence head-on. If a hidden force were secretly doing the work, it would have to shove the electron sideways by just the right amount — and a shove that large would also make the electron arrive late. So they measured the arrival time. A femtosecond laser pulse strips electrons from a sharp tip, the pulse flies between two solenoids joined by iron bars into a square magnetic toroid, and a channelplate records each landing to about a tenth of a nanosecond. As the solenoid current is turned up, the arrival time does not move. The whole class of force explanations is ruled out, and the potential is left holding the result on its own.
Why it matters hereChapter 10 rests on the vector potential being a real and usable handle on phase rather than a bookkeeping device, and this is the measurement that closes the obvious escape route — there is no hidden force of the right size doing the work. For chapter 1 it is a model rung on the evidence ladder: name the alternative explanation, derive the signature it would leave, then go and look for that signature. Read it with the transverse-deflection experiment at /library/stm-81bc78c3b1, the gauge-invariance proof at /library/stm-9369e78ff5 and the spacetime-topology schemes at /library/stm-1897890324.
What it claims
01The original Type-I Aharonov-Bohm phase shift exists under experimental conditions where the electromagnetic fields, and therefore the forces, are zero; it is that absence of forces which makes the effect entirely quantum mechanical, and although the phase shift itself has been demonstrated unambiguously, the absence of forces had never been shown.Abstract
Settled physics02Excellent agreement has been found between the measured phase shift and the theoretical prediction that the shift equals the electron charge divided by h-bar, multiplied by the line integral of the vector potential around a contour enclosing the magnetic flux of a solenoid — from Chambers onward, including Tonomura’s toroid experiments.Introduction, Eq. (1)
Settled physics03A semiclassical force can be constructed that reproduces the Aharonov-Bohm phase shift exactly: modelling the solenoid as a stack of current loops, or as a line of magnetic dipoles as Boyer did, the Lorentz forces between the passing electron and the carriers in the coil give a path-length difference whose semiclassical phase equals the flux times the charge divided by h-bar. That coincidence is what makes an experimental test worth doing.Eqs. (5) to (8); Boyer, Found. Phys. 32, 41 (2002)
Published and peer-reviewed04A displacement large enough to account for the phase shift would also produce a time delay equal to the flux times the charge divided by the electron mass times the square of its velocity, so a time-of-flight measurement can rule out the entire class of semiclassical force theories at once, whatever their internal details.Eq. (4) and the paragraph following it
Settled physics05In the experiment a femtosecond laser pulse extracts electrons from a field-emission tip, the pulse passes between two identical solenoids joined by high-permeability magnet-iron bars into a square magnetic toroid to suppress flux leakage, and arrival is timed with a channelplate; the scatter of the arrival times is about a tenth of a nanosecond, and the same apparatus does register nanosecond-scale electromagnetic effects when the acceleration voltage is changed.Experiment description with Fig. 2; Fig. 4
Settled physics06No time delay is observed as a function of the current through the solenoids, with or without the magnetic shield in place, so there is no force acting on an electron passing a macroscopic solenoid of a magnitude that could explain the Aharonov-Bohm effect, and all force explanations leading to such a delay are ruled out.Results, Fig. 3; Conclusion
Settled physics
Read it · abstract
Abstract
The Aharonov-Bohm (AB) effect is a purely quantum mechanical effect. The original (classified as Type-I) AB-phase shift exists in experimental conditions where the electromagnetic fields and forces are zero. It is the absence of forces that makes the AB-effect entirely quantum mechanical. Although the AB-phase shift has been demonstrated unambiguously, the absence of forces in Type-I AB-effects has never been shown. Here, we report the observation of the absence of time delays associated with forces of the magnitude needed to explain the AB-phase shift for a macroscopic system.
Adam Caprez, Brett Barwick and Herman Batelaan, Department of Physics and Astronomy, University of Nebraska-Lincoln. Physical Review Letters 99, 210401 (2007). Preprint: arXiv:0708.2428 [quant-ph].
(Abstract only. The force derivation of Eqs. 5 to 8, the toroid apparatus of Figure 2 and the time-of-flight data of Figures 3 and 4 are at the source — see the rights note above. The preprint is free to read at arXiv.)
The way in
https://doi.org/10.1103/PhysRevLett.99.210401Licence checked on the source itself: the arXiv posting 0708.2428 [quant-ph] carries an arXiv distribution licence and no Creative Commons statement, and the published version, Physical Review Letters 99, 210401 (2007), is under the APS default licence. This sheet therefore carries the summary, the claims and the authors’ own abstract, and sends the reader to the source. The preprint is free to read at arXiv. Claim locators cite the preprint, whose equation and figure numbering matches the published Letter.
How to cite it
Adam Caprez, Brett Barwick, Herman Batelaan (2007) Macroscopic Test of the Aharonov-Bohm Effect. doi:10.1103/PhysRevLett.99.210401
Where it sits in the curriculum
Scalar waves and the field behind the fieldsThe evidence ladder