What’s the cheapest scientific instrument that can get an average amateur to the bleeding edge of discovery work? So not just scutwork that the pros with billion dollars instruments like CERN or Hubble indulgently farm out.
RF bias here but an inexpensive software defined radio + home made antennas + GNU Radio/derivatives.
For real fun: a microwave oven + wooden partitions covered w aluminium foil + anything you dare put in there.
No sharp metallic objects! Outdoors/fume hoods if plastics.
For SDRs, there are plenty of online tutorials. I haven't published any of my work yet.
For microwaves, I will pool together some fun experiments in a blog. Very top level highlights here - https://tejpochiraju.in/portfolio/ (search for microwave).
All of those started in a domestic oven!