On the physics of Chuck’s Gun
It’s rare for Supernatural to give me something that is distinctly in my wheelhouse, about which I might be able to contribute a viewpoint that is fairly unique, but Chuck’s description of how the “Equalizer” gun works lands squarely in the realm of physics.
Much to my surprise, the description isn’t complete gibberish.
“So, this doesn't so much fire bullets as it sends a wave of multi-dimensional energy across a perfectly balanced quantum link between whoever's shooting it and whoever they're shooting at.”
This description has two major points:
1) Wave of multi-dimensional energy
2) A perfectly balanced quantum link
Let’s start with the first point: The use of the term energy technically makes this somewhat pseudo-scientific as energy does not have dimensions. At least, not in the strictest sense. Energy can be transmitted by waves, either through a physical medium (water, the earth during an earthquake, a slinky) or through radiation (photons, electrons, or other similar particles). Especially when dealing with photons, physicists end up using equations describing the “wave function” of the particle, from which various aspects of the particle can be derived (such as momentum, position, or energy).
The important part is that Chuck seems to be describing that the gun fires destructive, presumably high-energy radiation. A bit like a military laser. Of course, he could also be trying to indicate that whatever form of radiation that gun emits, that type of wave-particle can also interact with dimensions beyond the usual three spatial dimensions (often suggested to exist within the SPN universe, as well as hypothesized in string theory), permitting it to damage the extra-dimensional aspects of entities like Chuck and Jack.
The second point is easier to determine what Chuck is talking about. “A perfectly balanced quantum link” is a poetic way to describe quantum entanglement.
Quantum entanglement generally only occurs between two particles, as it requires those two particles to interact in a way that causes their wave functions to become dependent on one another. For so long as their wave functions are correlated in this manner, any interaction with one particle will cause an equal but opposite reaction in the other, regardless of the distance between the two particles.
Disregarding the difficulty of quantum linking on the macroscopic scale (as any interaction with particles outside of the entangled system can cause the entangled particles to decohere and therefore no longer by entangled, so the more particles involved the more difficult it is to keep the entangled system... well, entangled), if one were capable of scaling entanglement up to the human scale and quantum entangled two humans, it’s entirely within the realm of possibility that an injury sustained by one would be transmitted to the other. Precisely as Chuck’s “Equalizer” gun does.
TL;DR: Chuck’s description of the gun is reasonably scientifically sound. It fires weaponized high energy radiation of some kind, and also utilizes quantum entanglement to transmit the injury of the shot party to the shooter.
Also, it occurs to me that creating a weapon capable of shooting whatever kind of energy / particle almost certainly DOES NOT require the use of quantum entanglement to make the damage stick. The damage can only be transmitted, after all, if the initial damage is done. [Thus whatever energy was being fired at Chuck was capable of harming Chuck irregardless of his state of quantum entanglement with Sam.]
Unless, of course, the reason Chuck tries to name it “Equalizer” is because in order to harness the weapon, the user must be entangled with the target in such a way as to briefly gain power on par with the entity that is the target. Which would necessitate the use of quantum entanglement. [And yes, if this thought is true, that does mean for a moment, when Sam shot Chuck, Sam was wielding power that would have put him on par with Chuck.]