QM does away with any notion of conservation of information. Time reversibility (T symmetry) is usually talked about at macro scales where QMs effects are vanishingly small. IANAP
Regarding free will -- rigorously define it for us, without evoking the supernatural, and as distinct from pure randomness and absolute determinism, and it should be easy to tell whether the law of conservation of information allows for it. Before spending too much time in e it, though, note that such a definition is widely considered impossible. IANAP
Time reversibility exists in quantum mechanics because observables are self adjoint operators. Closed systems evolve unitarily. In simpler terms, you can think of it as the requirement that maps preserve distances and are easily invertible. We need this so that the information describing a system (which we can still talk about in terms of traces), remains invariant with time. In the classical sense, the corresponding violation leads to probabilities not summing to 1! We clearly can't have information shrink and for pure systems, dropping distance preserving maps leads to a really awesome universe (I believe this also ends up highly recommending L2). We literally go from a universe that is almost certainly near the bottom end of the Slow Zone of Thought to the Upper Beyond (https://en.wikipedia.org/wiki/A_Fire_Upon_the_Deep#Setting). We gain non-locality, causality violations and powerful computational ability.
In practice, our confusion about a system does increase with time as classical systems become ever more correlated, losing distinguishability, aka decoherence.
To me, a lack of free will would mean that a mind's future state is entirely determined by its current state. "Free will" would mean that its future state can be altered by some nonphysical entity (whether you call that a soul, consciousness, or whatever).
Free will is an obvious idea for a self aware consciousness to adhere to. The purpose of consciousness is to keep its organism viable. It does that by collecting an essence of past and from that predict an essence of the future. This expectation of the immediate future is then corrected according to actual perceptions and transformed into appropriate actions.
The full past is abstracted into an essence state, lots of information is lost to elsewhere, so there is no way to determine what details of the past went into forming the precise state from which the brain makes its actions. Of course it has to feel like at least some of our choices emerges from nowhere. But the only way to know if a brains thoughts are really free is to replay its entire brain state building past in every minute detail and look for alternative actions. An impossible experiment.
I said without evoking the supernatural. The concept of a soul is supernatural. There's no reason to think consciousness is anything other than physical in nature -- but to the extent that you mean it in some kind of supernatural, extra-physical way, it's not part of this conversation.
By all means go on thinking there might be some supernatural thing called a "free will" if you want. But if it's supernatural, then the utterly natural laws of QM wouldn't have much to say about it.
> There's no reason to think consciousness is anything other than physical in nature
Consciousness is not the same thing as agency. It is possible that we are conscious but do not actually have free will / agency.
> By all means go on thinking there might be some supernatural thing called a "free will" if you want. But if it's supernatural, then the utterly natural laws of QM wouldn't have much to say about it.
I am not sure I agree. If QM implies a strict determinism, to me that rules out free will. For free will to be plausible, there has to be a place for non-determinism to "hide." If QM can rule that out, to me that rules out free will.
When you formulate it so, the problem is the question itself, as, except if we are religious believers, we don't have any reason to consider a "soul" (or a "consciousness") to be a "nonphysical entity." Look at the etymology of the "psyche:" it's "the breath." At the time people explained their environment unscientifically they considered that the existence of "breath" makes the difference between the dead and the living person but also between the conscious and the unconscious bodies. Animals do breathe too. But humans saw themselves as "special" in their religious setup. As a kid would ask "does my dog go to heaven too when he dies?" See, we go deeper and deeper in religious explanations which just postulate something non-existing (once you accept nonphysical soul, it's easier to believe in heaven or reincarnation or whatever). Now go back and ask, if you believe that the only thing we can "see" around us that doesn't have the "physical entity" is the "soul" of humans why do you do so? Are humans by any way "the chosen ones" in the animal world, looking at their physical bodies and the processes in them? The scientific view doesn't see them so. The human "consciousness" is, so observed, more complex than the "consciousness" of the crow on the lawn due to the more complex brain, but both of these can be explained as the function of their physical "hardware" (the body and the brain) and the interaction with the environment. The "consciousness" as a "neurological process by which the animal or the human sees it as special, the center of its attention in order to protect itself" can be seen as a product of evolution. (And now I have a weird feeling of explaining a grown up person that Santa doesn't exist). So it looks that we humans, if we don't destroy ourselves first, will be able to eventually produce a "conscious" computer. (Hal, open the door, please).
> Now go back and ask, if you believe that the only thing we can "see" around us that doesn't have the "physical entity" is the "soul" of humans why do you do so?
I don't think this. I don't think that anything about the consciousness or agency of humans is exceptional to humans.
> The "consciousness" as a "neurological process by which the animal or the human sees it as special, the center of its attention in order to protect itself" can be seen as a product of evolution.
This is an interesting perspective that definitely made me think, but I think it ultimately begs the question. If you're talking about "seeing" or "attention," you're already speaking in concepts that presume the existence of consciousness. I'm not sure this gives us a useful framework to know when any computational process we have created does indeed have "consciousness," or where the line is between animals advanced enough to have it and animals (or even plants) that don't.
> If you're talking about "seeing" or "attention," you're already speaking in concepts that presume the existence of consciousness.
Maybe I wasn't clear enough. The world around us (and animals) is projected in our (and animal's) neurological system as some kind of the model. The question is just if the model is such that favors the representation of the uniqueness of the organism or not. I claim that there's evolutionary advantage in producing a system (hardware and software) where organism cares for itself and where the model is so formed that "me" is in the center, to the level that "me" is "conscious" in the sense, processing the stimuli as much that the dog understands that the paw is "his paw" and that it's dangerous to put the paw in the fire and up to the level of you and me considering "us" "us" and being able to talk about it. Therefore we're not so much different from the rest of the animals.
> I'm not sure this gives us a useful framework to know when any computational process we have created does indeed have "consciousness,"
I'd still like to know how you can define consciousness in a way that it doesn't sound religious. If you can't, then of course we can't progress in our discussion.
Let me give you very "primitive" and "simplified" view of the "free will" subject. I see it as a purely religious construct, based on the following history: initially, gods weren't "almighty and omnipresent." If you've read ancient Greek literature, there are such gems like "Zeus was at that moment in Egypt so he wasn't there when the soldiers he supported lost." If you've read Bible, the oldest myths (I mean, stories in the Bible) are actually based on such concept of god(s). Then the theology "theory" grew more demanding, postulating the "almighty omnipresent" but also the "loving" god. Which made the myths (stories) much absurder than they were as they were written. How can almighty loving god produce the world and then see that it's bad, so that it has to send the flood to destroy it? It's either not almighty or not loving etc. As a rescue, the priests invented the concept of "free will" as in "once god creates humans, they have their own free will (which god can't control!?) and they do what they do so then they get to deserve to suffer, go to hell and all that nice stuff." Most of the "modern" theological concepts are constructed as an attempt to make less absurd the whole "body of work." A kind of "justification by obscurity" which obviously works for believers, giving them easy covertly nonsensical sentences to answer the "hard questions" others would give them.
In reality, we just have what user jonsen formulates here as "the purpose of consciousness is to keep its organism viable. It does that by collecting an essence of past and from that predict an essence of the future."
Now you ask about the "framework to know when any computational process we have created does indeed have "consciousness."" It depends on the definition of he consciousness, but that definition can't involve gods and "nonphysical entities." As soon as that is clear we can measure the "consciousness as what we observe in a dog" or the "consciousness as what we observe in a six months kid," the "consciousness as what we observe in a twenty years old healthy human" and the "consciousness as what we observe in 80 years old human with Alzheimer's disease which progressed this much."
Note that neurologists as the part of their daily routine have to evaluate the level of consciousness in their patients. It's very instructive to read just some examples of he cases they work with.
When we're there, do you think that a human with Alzheimer's disease which progressed so much that he can't remember anybody from his life or what he did just 15 seconds ago has a "soul?" (a lot of healthy animals remember for months different things, or if you talk with the owners of pets, you'll hear that there are animals which have traumas and a lot of the psychological symptoms you'd just associate with humans). So back to the patient, do you consider him "conscious?" If not, at which point did he lost his consciousness which you equate with soul? If yes, where is he different from some good Perl script? There is no "single unique unchangeable" consciousness, there are just different levels of functioning of the model I mention at the start. Of course, when you die, the model completely stops functioning as it needs both the hardware and the software, the brain and the body as the hardware and all these nice electrical impulses and chemical reactions in the living organisms as the software. There's no such thing as the "agency of the nonphysical entity" there.
I think it depends on your perspective. From the perspective of my keyboard, my input is random/unpredictable (it doesn't have perfect entropy, but it doesn't follow rules that make it completely predictable). From the perspective of my body, I have complete control over what I am typing, and there is nothing random about it.
No it doesn't depend on your perspective. If it did the conversation would make no sense. The only perspective worth considering is the global objective perspective. Quantum events are globally, objectively random. Nothing else seems to be, which means, by definition, that everything else is deterministic.
The question I'm trying to get at is: from the perspective of the physical realm (which may be, even likely is, all that exists) is there any possible mechanism by which something nonphysical could influence events in the physical realm?
For example, is there any physical property that is not "locked into place" by the laws we know and the observations we can make? Is there any fundamental impossibity (not practical impossibility) of snapshotting the state of the universe and using that snapshot to determine every past and future state of the universe?
Regarding free will -- rigorously define it for us, without evoking the supernatural, and as distinct from pure randomness and absolute determinism, and it should be easy to tell whether the law of conservation of information allows for it. Before spending too much time in e it, though, note that such a definition is widely considered impossible. IANAP