Historical research guide · 0627 · 2016
Solar wind test of the de Broglie-Proca massive photon with Cluster multi-spacecraft data
Alessandro Retinò · Alessandro D.A.M. Spallicci · Andris Vaivads
In one minute
Alessandro Retinò, Alessandro Spallicci and Andris Vaivads use the four Cluster spacecraft, flying in formation in the solar wind at the Earth’s distance from the Sun, to test whether light’s particle carries a mass. If the photon has even a tiny mass, Ampère’s law picks up an extra term set by the vector potential — which in that theory stops being bookkeeping and becomes a physical quantity whose value changes the fields. So the team measures one electric current two ways: from the curl of the magnetic field, using the four spacecraft as the corners of a tetrahedron, and from the ion and electron velocities read by the particle detectors. Any mismatch bounds the mass. For the cleanest event, 7 March 2006, the upper limit lands somewhere between ten to the minus forty-ninth and ten to the minus fifty-first kilograms — roughly twenty orders of magnitude below the mass of an electron — depending on which estimate of the ambient vector potential is used. It is a deliberately cautious bound, measured in place rather than modelled.
Connection
Chapter ten turns on the vector potential being a real, physical quantity rather than a gauge convention, and this is a spacecraft experiment whose entire result depends on assigning the interplanetary potential a value. It also shows chapter one’s discipline in action: a bound is only as good as the assumptions under it, and these authors deliberately trade a tighter number for fewer of them.
From the source
In de Broglie-Proca electromagnetism the curl of the magnetic field gains a term equal to minus the photon mass parameter squared times the vector potential, so a massive photon shows up as a discrepancy in Ampère’s law rather than as anything exotic.Section 1, equations (1) to (4)
Because the theory is not Lorenz gauge invariant, the vector potential is perceived as a measurable quantity whose value implies a change in the fields — the paper has to estimate the interplanetary potential three separate ways before it can quote a mass limit at all.Section 2.1
The test measures one current twice: from the curl of the magnetic field, computed by the curlometer technique across four spacecraft separated by about six million metres, and from the ion and electron velocities measured by the particle detectors, with the difference between them setting the bound.Section 2, equation (7); Figure 2
For the 7 March 2006 solar-wind event the three estimates of the ambient vector potential — 0.4, 29 and 637 tesla metres — give photon-mass upper limits of 1.4 times ten to the minus forty-ninth, 1.6 times ten to the minus fiftieth and 3.4 times ten to the minus fifty-first kilograms.Section 2.2, Table 1
These bounds are deliberately weaker than the ten to the minus fifty-second and minus fifty-fourth kilogram figures usually quoted for the solar wind, because those rest on a steady-state Parker model and an argument about integrated magnetic stresses, while this test uses the field measured in situ and propagates the experimental errors.Section 3; Section 4
The limit is instrumental, not fundamental: reaching ten to the minus fifty-second kilograms would mean resolving an ion-electron velocity difference of a few centimetres to a few tens of metres per second against the 6.8 times ten to the fourth metres per second now resolvable, so better particle detectors and further multi-spacecraft missions, MMS among them, are what would sharpen the answer.Section 3, equation (16) and Figure 3; Section 5
The way in
https://doi.org/10.1016/j.astropartphys.2016.05.006How to cite it
Alessandro Retinò, Alessandro D.A.M. Spallicci, Andris Vaivads (2016) Solar wind test of the de Broglie-Proca massive photon with Cluster multi-spacecraft data doi:10.1016/j.astropartphys.2016.05.006