Thermodynamic entropy isnt information in the relevant sense.
There's a wide class of computational mysticism born of people going around and equivocating between "information" as it means radically different things where it is used.
thermodynamic entropy (a real number) != information theory entropy (bits) != information in csi != information in stat mech' != information in QM != information in a turing machien !=. ...
This is basically pseudoscience at this point. If you hear people talking about "information" as if its defined in a general sense (ie., equivocating across physics, computer science, etc.), they have no clue what they're talking about.
Eg., the "entropy" of real-valued quantum states as measured by integer-valued notions of entropy is 1 bit (the measured state is UP,DOWN) -- but QM requires the state be real-valued (having infinite information in the computability sense).
These kinds of information are not measuring the same thing, and largely irrelevant to each other.
I enjoyed the thread the other day, just want to point out there are some basic misunderstandings here - informational entropy and thermodynamic entropy in fact _do_ have a deep connection (Edwin Jaynes famously wrote about this). The key idea is that both are measures of the uncertainty of a system with respect to some distribution over it.
Saying that a real-valued state has infinite information in the computability sense is nonsense - information is a property of a _distribution_, not a _state_. You could talk about the Kolmogorov complexity of a real-valued state, but even this is generally not infinite, as anyone who's written a program to generate the digits of pi can attest.
> but QM requires the state be real-valued (having infinite information in the computability sense).
The unobservable state, which is merely a physical model that may have little resemblance to reality. All observable states necessarily have finite precision and beyond 60-70 digits are effectively undefined due to the uncertainty principle, which is yet another reason why people suggest physics is effectively computable.
While the types of information you mention are not strictly equivalent in some 1:1 sense that I don't think anyone has really suggested, there are formal correspondences, so your explanation ultimately just seems like a lot of special pleading, eg. you can derive a Bekenstein Bound for bits, thermodynamic entropy, information in QM, and so on.
No one here disagrees that measurement produces finite information; that is obvious and a necessary --- if it wasnt, we would never be able to know anything. Knowing requires an "early termination".
The issue is that there's no evidence this property of measurement is a property of reality, and all the methods, premises, etc. of physics attribute the opposite to reality.
Here, it is absolutely necessary for QM to work that the unmeasured state is real-valued,.
I'd also say that since measurement is finite in this manner, it then follows large swathes of reality are unknowable.. and this makes it clear why we cannot obtain the latent state of a QM system.
> Here, it is absolutely necessary for QM to work that the unmeasured state is real-valued
You're just doubling down on the premise that a theory founded on a formalism based on unbounded numbers requires unbounded numbers to work. Sure, but why is that necessarily reflective of reality? Why does that entail that no other formalism that doesn't embed infinities / continuity is also not possible? I simply see no reason to accept your conclusion. The infinities you see as essential could very well simply be artifacts of our formalisms.
In fact, I'd conjecture that our continuous formalisms are at the very heart of some core problems in physics [1], and that at least some of those problems can be resolved by exploring more discrete formalisms. I suppose we'll see.
There's a wide class of computational mysticism born of people going around and equivocating between "information" as it means radically different things where it is used.
thermodynamic entropy (a real number) != information theory entropy (bits) != information in csi != information in stat mech' != information in QM != information in a turing machien !=. ...
This is basically pseudoscience at this point. If you hear people talking about "information" as if its defined in a general sense (ie., equivocating across physics, computer science, etc.), they have no clue what they're talking about.
Eg., the "entropy" of real-valued quantum states as measured by integer-valued notions of entropy is 1 bit (the measured state is UP,DOWN) -- but QM requires the state be real-valued (having infinite information in the computability sense).
These kinds of information are not measuring the same thing, and largely irrelevant to each other.