> The problem with dark matter is that there does not exist any second relationship from which to verify its existence.
This is exactly it! Dark matter is strictly defined by its effects. The only 'theory' part is a belief that it's caused by yet to be found particle that's distributed to fit observations. Take all the gravitational anomalies that we can't explain with ordinary matter, then arbitrarily distribute an imaginary 'particle' that solves them: that's DM.
The problem is that the language used to talk about DM is wrong. It's not that DM doesn't interact with EM, or the presence of DM is causing the galaxies to rotate faster than by observed mass. These are all putting the cart before the horse. What we have is unexplained gravitational effects being attributed to a hypothetical particle. If we discovered a new unexplained gravitational property, we would merely add that to the list of DM's attributes rather than say "oh then it can't be DM".
All physical entities are defined by their effects! Suppose we found axions and they had the right mass to be dark matter. Would that mean we now "really knew" what dark matter was, in your sense? No, it would just push the defining effects further back - because all an axion is is a quantum of the (strong CP-violation term promoted to a field).
Just like the electromagnetic field is the one that acts on charged particles in such and such a way, and a particle is charged if the electromagnetic field acts on it in that way. There's no deeper essence, no intuitive "substance" with some sort of intrinsic nature. All physical properties are relational.
This is exactly it! Dark matter is strictly defined by its effects. The only 'theory' part is a belief that it's caused by yet to be found particle that's distributed to fit observations. Take all the gravitational anomalies that we can't explain with ordinary matter, then arbitrarily distribute an imaginary 'particle' that solves them: that's DM.
The problem is that the language used to talk about DM is wrong. It's not that DM doesn't interact with EM, or the presence of DM is causing the galaxies to rotate faster than by observed mass. These are all putting the cart before the horse. What we have is unexplained gravitational effects being attributed to a hypothetical particle. If we discovered a new unexplained gravitational property, we would merely add that to the list of DM's attributes rather than say "oh then it can't be DM".