This feels similar to a gauge transformation in physics, where there seems to be an extra degree of freedom that cannot be eliminated.  But even within the same mind there is still a problem with qualia: Take the visual field for example.  Imagine reflecting your visual field as in a mirror. Would anything change in the external world? I would argue this would also be a perfectly viable mapping of the external world to phenomenal states, and yet, it would seem to imply that the reflected visual field is isomorphic to the original field.  It would seem that this experiment can be done in reality, and although I haven't tried it myself, it is reported that people quickly adjust to this reflected field, and somehow the brain "realizes" the correct orientation of the visual field. 

But what does this say about the qualia of spatial orientation? It would seem that I myself would not be able to distinguish whether or not I am seeing a reflected field or the original field. This isomorphism problem seems to lie within the same mind, and not between minds. Both fields seem to map onto a "canonical" representation of spatial orientation that represents all isomorphisms of the same field.

This is missing a key feature of substrate dependence, namely the role of time in the universe.  What is implicit in the substrate, is that it exists in the universe. By existing in the universe, it must "flow" through time. And it is this connection to time that is key to its role in consciousness. 

Take the standard thought experiment of a simulated digital mind. Is this mind conscious? Well here is the thing about "digital existence": it lies outside of time. You can run the simulation at 1x speed or 1000x speed, but it makes no difference to the simulated mind, as long as it is isolated from the external world. Even if it was connected to the external world, the fact that it is digital in nature means that save states are possible and there is no longer a linear world line that the digital mind can follow.

And this is why substrate dependence is crucial: everything in the physical world must flow in time, and there is no "going back". That is, you cannot copy the state of the conscious being, which would be akin to time travel. Digital minds lie outside of time.

So how do we address the fading qualia argument? Well the entire argument falls apart at step one: namely they would be functionally equivalent. Nonsense, they are not equivalent for the most important feature: for something to be digital means perfect knowledge of the state. Perfect knowledge of the state is not a feature of base reality, but is an abstraction layer that lies in a Platonic realm. Having digital neurons is equivalent to the statement that time travel is possible from a subjective point of view.

Of course, this has no bearing on whether or not these minds can act on the world, just that they would not experience time or have subjective experience.

This brings up an interesting consideration: Imagine two observers existing in the same universe, one being the time reverse of the other. From their internal perspectives, each views its own observations as defining an arrow of time, yet their arrows point in opposite directions. It would seem then, that the arrow of time resides in conscious experience itself, and is not a property of the universe. And yet it would seem to define a "canonical" direction to time, even if the external time parameter were reversed.

So would it even make sense to have an observer that can experience time from the opposite direction? Why can't I experience my death and then age backwards until my birth?  It would seem like the key here is memory itself: that is, memory requires observation, which is inherently a time asymmetric process. But what is experience itself but a brain state, ie. an impression, or memory of the world at large? But then are we saying that qualia themselves have an arrow of time impressed upon them? That a universe that is running backwards nonetheless cannot have conscious beings in the sense that they can experience the same "flow" of time?

Imagine that this time reversed observer were only run partially to completion. That is, their internal states were only run until say the middle of their life instead of to their birth. In what sense do they experience their life? Would it not be the case that their life from birth to the middle of their life was undetermined? But what would it be like to have an internal experience that corresponded to this scenario?  It would seem like the way out of this confusion would be the fact that experience only relies on the current state and not on any future or past state. That is, all the information necessary to render a conscious experience is contained in the present moment. This would be similar to a Boltzmann brain scenario where the impressed past is not the "actual" past.

And yet there is still something confusing about this picture, namely which of these moments should be the one being experienced as "now"? Do they all exist in some platonic realm? But then what prevents us from thinking that we are living in a perpetual groundhog day? No, it seems like something is missing from this picture. It definitely seems like time is flowing, that I have not yet experienced this exact moment before, yet it would seem like everything in our physical theories cannot rule out the fact that this could be deja vu, because physical theories are memory-less theories. That is, they can be fully determined from one time slice only and not on any future or past state.

But this cannot fully be the case, because the dynamical equations of motion involve first and second derivatives, which would involve at least two more snapshots of time, at least to get the ball rolling to a calculation of the evolution of the state. But to a first approximation, all the information necessary to determine the state of the universe is contained in only one time slice, and this is the key to the question of the problem of time reversal symmetry. For it would be trivial to break this symmetry if the universe depended not just on the present state, but on future or past states as well, giving them further "existence".

But then what would the laws look like if they depended not just on the present moment, but on other moments as well? Well for one, there would be no way to just "run the universe backwards" since this would assume you can just use the current state of the world to run the universe backwards, plus two time slices, to get the ball rolling. 

But what does this entail? Well, if the physical laws depended on more than one slice of the past, then the time reversed implication would imply that the reversing the universe would require knowing future states that have not yet occurred.

And therefore if we are to believe that we are "extended objects" in time and not just one slice and are forced to trust our senses that we are not living in groundhog day, it would seem as if the future has yet to be "determined".

I didn't want to derail this conversation into another free will debate, it wasn't my main focus, so I will try to be "brief" on responding to your view on free will:  

It seems that you subscribe to the "standard model" against free will, that is, either things are determined by external causes, and you have no free will, or they are random, in which that would also constitute the nullification of free will. I am not sure your 3 arguments are actually distinct; they basically point to the same source, namely that "randomness" is not free will, and neither is determinism.

However, this seems like a too simplistic picture, which assumes that people are "point particles" with no internal state.  That is, in a deterministic world, the assumption of no free will basically posits that the internal state, however deterministic, cannot be a source of free will. However, I would argue that this is indeed the source of free will, that is the internal state that constitutes "you".  You also state that you do not "choose" which thought occurs to you, it simply arrives. However, I would argue that this is not correct; that is, you are your thoughts, there is nothing else that is "choosing" your thoughts.

Perhaps what you mean is that "your" brain does not choose which thoughts come into view. However, I would argue that "you" are not your brain, but rather the thoughts that constitute your brain, ie. the software layer.

Perhaps a more concrete argument would help here: I claim that learning is impossible without free will. That is, if you cannot choose among a set of actions freely, there is nothing to learn, and thus nothing of value that humanity has ever created would be possible. This is the sense of free will that I am talking about. But perhaps you would argue that everything that humanity has created in a sense was already "determined". But this determination was the result of a set of agents that collectively exercised their "free will" to generate the fruits of their labor.

In other words, free will is a subjective phenomenon, and only arises from an internal perspective. It is then clear that the "objective" world contains no free will, since by definition, the "objective" world ignores any subjectivity.

Going back to your "standard model" arguments against free will, it seems like the core problem here is the definition of "randomness".  But I would argue that it is in the "randomness" where the free will comes in: that is, when you have a possibility of many different outcomes, and a probability of choosing between any of an "equipotential" of outcomes, this constitutes the source of free will. 

Again the word "randomness" is doing most of the work here, which leads to the second point of your comment, namely the connection to time itself and the question of why am I me and not you? You could extend this question to any "random" process, that is, why was this particular outcome "chosen" among a set of outcomes from a probability distribution? Note that this does not have to include the existence of other minds as you have commented previously. Even with a single mind that can make "choices" there is still the question of the non-algorithmic nature of randomness that is elusive, but seems to be a necessary component of the nature of time.

I would also argue that Einstein's revelation that there is no global "now" actually has been understated substantially. That is, if there is no global "now" then what determines which "now" is in view? With a unified time picture, there is no question here: all persons experience the same now and thus everyone in a sense "exists" at the same "time".  This perhaps more than anything else that Einstein worked on highlights the essence of time itself and its non-algorithmic nature.

Yes, once you think about consciousness for some time, you could conclude that there might be some sort of Platonic existence for subjective experience. However, this seems to nullify free will and makes things kind of pointless in the sense that if all moments have already happened, it doesn't really matter what you do, you are just navigating a space that already exists and will always exist. Intuitively, this doesn't sound right, and perhaps there is something missing in this picture.

This brings up the vertiginous question. That is, why is THIS moment currently in view, and not another? The trivial answer is that all perspectives somehow "exist" in some Platonic realm. But the reality is that from a subjective point of view, only one particular experience can be in view. So why THIS experience and not another?  

Assuming that there is a space of subjective experience, how is it possible to navigate this space such that the present moment is the one that should be in view? In other words, can you establish a metric on the space of subjective experience? What makes one experience different from another? Is it possible to state that one experience is closer or farther from another within this space?  

What I can say is that the current moment seems to be "interesting". From the principle of indifference we should conclude that THIS moment is just a mundane experience from the space of all possible moments, but I am not sure this is correct.  

As you allude to I believe this problem is tied to the nature of time itself. After all, without time, all moments are on equal footing. Time seems to lie outside of any mathematical formalism including Tegmark's MUH in the sense that any formal system is independent of time. The "mechanism" which selects THIS moment must be non-mathematical, or non-algorithmic in nature.

We seem to be living in interesting times indeed.

I reject the first step. 

Most posts on this site just seem to posit that there is some "stuff" called information which just exists "somewhere" that is independent of any reference frames. That you can reference a "state" whatever that means.

Consider the set of all possible states in which an observer is reading a page out of a book from the library of babel. Now take one of these states that corresponds to a mind within the library of babel. From its subjective point of view, it has information about its environment corresponding to the page that it is reading, yet the total information contained in the system is actually less than that of the single observer, which can be specified as the set of all possible observers reading a page from the library of babel. 

So where is the information coming from? It is the self location of the observer that contains the information. All the information is contained in the reference frame, and this is the primary concern of all condundrums about consciousness. Fundamentally consciousness is about reference frames and the semantics of language.

I could continue making objections at every step, but to keep things brief I will make only an objection which may bear some useful fruit, which occurs at step 5, that is the possibility of digital consciousness.  I object to this step in the sense that a digital consciousness means an ability to copy or clone a system "perfectly" with digital accuracy.  Again, the problem here is the relationship between reference frames and the ability to copy information. I posit that copying information is forbidden in the sense that you cannot copy reference frames. You run into the usual paradoxes around teleportation and sleeping beauty problems. 

In physical reality the only way for an object to be copied is to be destroyed and instantiated somewhere else, and I posit this is how objects actually move through space. Motion is possible because it is impossible to make a digital copy of that object. If you allow for a digital copy of reference frames, suddenly you could perceive all sorts of physical law violations from a subjective point of view, and you may argue this is possible because this happens all the time in dreams. But we enter a slippery slope here, as now we must question our very foundations of physical reality and how to make sense of it.

I think this is related to the idea that intelligence is compression. But when we think of compression we immediately run into a conundrum: If something is compressible, it means the language used to express the piece of information is not optimal. An optimal description of a thing must be expressed in the most economical way possible. This can only be done if the right frame is used to express the thing in mind. In the right frame you can just "see" the answer, because any translation between your frame and the optimal frame represents a suboptimal routine that can be compressed away. Therefore there is no upper limit on intelligence in the sense that there is no computable way to get the shortest description of a thing. There is always the possibility of compressing an idea further and reaching greater levels of understanding. 

In this sense, understanding a physical theory such as classical or quantum mechanics is something akin to being able to just "see" the answer without having to grind through the physical equations used to represent a phenomenon. In some sense this would be akin to developing an intuition behind the equations.  But wait one moment. How is it that one can develop an intuition for such physical models? Why is it that it may be hard for some to just "see" the outcome of the equations that are used to express physical phenomena? My hunch is that the physical equations themselves are suboptimal ways for expressing the underlying physical reality in the way that our minds can quickly comprehend. What is really going on inside my mind is that I am building up a world model that tracks the phenomenon of reality and placing "checkpoints" that represent known points corresponding to the outputs of the physical equations. But the physical equations themselves are not a complete description of reality, but only represent these "checkpoints" that correspond to the physical quantities that we can measure at well defined locations. What is really going on I suspect then is just building up of a neural network that is able to predict such phenomena in detail and works surprisingly well for almost all domains of interest.