Is there a theory for what "effect" would be produced by a theoretical object going faster than light? The relevance is that, I thought a "sonic boom" was defined as what happens to an object and its surroundings after going faster than sound. A "sonic boom" of light seems nonsensical, even after reading the article. Isn't this just a cone shaped wave?
Cherenkov radiation[0] is when a photon is travelling faster than the speed of light through water. To overly simplify, the speed of light in a vacuum is different than the speed of light through a medium.
It doesn't happen with photons. Photons themselves always travel exactly at the (vacuum) speed of light, even in water, and they aren't charged particles. Cherenkov radiation happens with charged particles like electrons.
I guess that's relative, depending on which photon is referenced. The corollary is that from the photon POV, not its speed changes, but spacetime is warped, so it sees time in its own frame of reference going faster and/or distances shorter than we.
No, in water, the spacetime is not significantly warped, certainly not warped enough to slow down light. The different speed of light in a medium compared to vacuum comes from the interaction between the photons and the medium. The photon then, effectively, becomes a hybrid "photon-medium excitation" which is an effective particle with an effective speed lower than the vacuum speed of light.
Maybe not from our point of view, but from the POV of the photon the water is moving with c_0 through the photon, so certainly relativistic effects apply.
Is there a theory for what "effect" would be
produced by a theoretical object going faster than
light?
There really isn't an effect. The speed of light (in a vacuum) is just the speed of causality. The fabric of space-time will bend around you to ensure you can never get there. Objects without mass move at the speed of light, and no other speed.
Now if you don't mean in a vacuum but in a medium like water, or air, or ice, etc.
No, there's no (experimentally supported) theory that would work at all with an object going faster than light. It just isn't in the geometry - asking for a hyperbolic rotation that stretches your motion's vector past c is like trying to turn an apple around in your hand in a way that makes it twice as big.
What they're doing here is based on the fact that you can make light move at under c if you force it to travel through a dielectric material. The c in E=mc^2 is the speed of light in a vacuum: not necessarily through a carefully designed atomic obstacle course.
The speed that light propagates is not always C. Light travels at C in a vacuum, but at a slower speed in any medium, e.g. water. Objects, and light itself, can travel faster than "the speed of light in water" in water.
https://en.wikipedia.org/wiki/Cherenkov_radiation
The experiment specifically used mediums, where the speeds are not the speed through through the vacuum, the report from which smithsonianmag took the info and provides the link is somewhat more precise:
"study lead author Jinyang Liang, an optical engineer at Washington University in St. Louis, and his colleagues designed a narrow tunnel filled with dry ice fog. This tunnel was sandwiched between plates made of a mixture of silicone rubber and aluminum oxide powder."
"Then, the researchers fired pulses of green laser light — each lasting only 7 picoseconds (trillionths of a second) — down the tunnel. These pulses could scatter off the specks of dry ice within the tunnel, generating light waves that could enter the surrounding plates."
"The green light that the scientists used traveled faster inside the tunnel than it did in the plates. As such, as a laser pulse moved down the tunnel, it left a cone of slower-moving overlapping light waves behind it within the plates."
