Other able physicists, Evan Harris Walker and Roger Penrose among them, would not agree, if this is argument from authority.
The speed of light in classical physics is constant relative to what? To the observer. Or am I mistaken?
Physicist, the mind cannot be this easily discounted or dismissed.
I don't know about Walker, but Penrose most emphatically does believe that it is electrochemical. In fact, he believes to have pinpointed the crucial trick mechanism as a quantum electrodynamical effect owing to a particular molecular arrangement in microtubules. In any case, his ideas are simply hypotheses, and don't count as evidence for or against anything. But make no mistake: Penrose is a frank and unabashed materialist when it comes to consciousness.
Personally, I think Penrose is wrong. First, I didn't accept the arguments he laid out in The Emperor's New Mind that consciousness cannot be algorithmic. (I confess to having only skimmed his arguments in Shadows of the Mind, despite owning a beautiful signed first edition of same.)
Second, trick mechanisms such as the one he describes don't make evolutionary sense. (I know, that doesn't count as a strike against it in your book, but he doesn't present his ideas as being in anything but perfect consonance with evolution.) You see, according to Penrose, microtubules possess exactly the physical properties necessary for the apparently non-algorithmic aspects of human thought. But microtubules aren't peculiar to humans, or even to organisms that could remotely be construed as conscious, and yet they have always had that structure. How likely is it that this crucial mechanism has lain fallow for a billion years against the day when a creature could make proper use of it? It has teleology written all over it (I know, I know) but Penrose doesn't see it.
[Aside: Penrose would say that lesser minds do make use of the mechanism for what consciousness they possess. But since their consciousness isn't anything that couldn't be functionally (if not specifically) modelled algorithmically, no quantum hocus pocus was necessary. But since human consciousness does (according to Penrose) require such trickery, the accusation of teleology stands.]
(Although I didn't agree with the conclusions of The Emperor's New Mind, it really is an excellent book on many levels. It lays out the basics of both quantum mechanics and computer science as well as I've seen anywhere.)
The speed of light in classical physics is constant relative to what? To the observer. Or am I mistaken?
Relative to everything in the universe.
You're mistaken. The speed of light is constant, regardless of the frame of reference.