If I had a million $USD to do physics, I'd do some experiments.
Berry Phase/Electromagnetic 4 Potential experiments
First purchase/rental - a SQUID - Superconducting QUantum Interference Device.
My first hypothesis to check is regarding the A field, also known as the electromagnetic vector potential. I hypothesize that if you were to take a bifilar wound coil of quite a few turns, the flux when the windings were connected to oppose each other would correctly generate no B field (detectable with a compass, magnetometer, etc), but I believe there WOULD be an A field generated, perhaps much weaker, than that of the field when the windings aided each other, but non-zero.
I'd then investigate the polarity and form of this field in 3d around the coils, etc.
I'd also perform the same experiment with a set of toroidally wound coils, a pair, and see what type of A fields they generate, and see if everything matches simulations.
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A refinement of this experiment would be to use a pair of atomic clocks, one outside a "null set of coils", and the other inside them (with actual B magnetic fields canceled), to see if there was any drift with power applied.
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Gravimetric / Inertial measurements
Purchase - Vacuum Pump
Next, a torsion bridge, in the manner of Cavendish... a long (as long as I could get in the garage) rod inside a copper/aluminum tube, pumped to as good a vacuum as I could reasonably get. Using electromagnetic forces on the ends, test out various materials to see measure their gravimetric effects on the bridge.
I'm particularly interested to see if some materials have a different G than others
Also, it would be interesting to see if a large capacitor had a different gravimetric effect if it were charged/not charged (whilst inside a faraday cage, of course)
