If these mental properties affected the behavior of particles in the same way that physical properties like mass and electric charge do, then they would simply be another kind of physical property. You are free to postulate new properties that affect the behavior of electrons and photons, but you’re not simply adding new ideas to the Core Theory (the enormously successful model of the particles and forces that make up you, me, the sun, the moon, the stars, and everything you have ever seen, touched, or tasted in all your life). Instead, you are saying that it is wrong. If mental properties affect the evolution of quantum fields, there will be ways to measure that effect experimentally, at least in principle, not to mention all of the theoretical difficulties with regard to conservation of energy and so on that such a modification would entail. It’s reasonable to assign very low credence to such a complete overhaul of the very successful structure of known physics.
There are 2 points to be made here.
First of all, science as currently conceived cannot in principle explain consciousness (see my essay Neither Modern Materialism nor Science as currently conceived can explain Consciousness ). The "Core Theory", as he labels it, therefore we know is false. Or, as I would prefer to say, at least it cannot be a complete description of reality. Hence, to say that any modification has little credence simply fails to understand this point. Necessarily the "core theory", is incorrect, or at least it is not wholly correct.
Secondly, there's this persistent misunderstanding, and one that Carroll seems to share, that scientific theories describe reality in their totality. But that's not what we learn from the history of science. The history of science teaches us that our theories give approximations only, even if those approximations might be very close approximations. Generally, our old scientific theories are often perfectly adequate to describe a given domain, but break down when attempting to describe that which resides outside that domain. Thus, the science prior to relativity and quantum mechanics is "wrong", however, that does nothing to prevent the Newtonian mechanical description of reality being able to be used to get us to the moon and back. In addition, the classical mechanics espoused before the advent of Quantum Mechanics is perfectly adequate to describe the macroscopic realm, even though it might be "wrong". Quantum Mechanics is only needed when we describe the microscopic realm.
Now, consciousness has only existed for a vanishingly medium part of the history of the Universe and is confined to planets which presumably will be very few and far between. I suggest the "core theory" describes non-conscious reality -- that is to say the overwhelming majority of the physical realm -- to a very close approximation, just as classical mechanics describes the macroscopic realm to a very close approximation. But that it breaks downs when it comes to consciousness, just as classical mechanics breaks down with the physics of the very medium.