No entropy/environment = no time flow?

[dmtr]

Is that right, that it is only makes sense to talk about the time evolution (or particle paths) in the presence of the environment? That without the environment any closed system would simply stay in the superposition of states and there wouldn't be any time flow?

-- Dmtr

 

[xepma]

Time evolution of the wavefunction is dictated by the Schroedinger equation. You don't need an environment from that.

Besides, you cannot really talk about a static state of a closed system anyway. There is always some internal stuff going on.

 

[dmtr]

The Schroedinger equation doesn't say that the wave function have to evolve. True, it describes unitary transformation with the time flow, but it doesn't specify that the time has to flow! And to which direction the arrow of time should point.

-- Dmtr

 

[dmtr]

Not even wrong?

-- Dmtr

 

[Haelfix]

Their will be time flow (you are free to stick in your own time coordinates if you want, even with a vanishing hamiltonian -- the hamiltonian constraint will hold the dynamics), but without the 2nd law of thermodynamics each subsystem could in principle have their own arrow of time so macroscopic comparison would be difficult and bizarre.

 

[Atakor]

I don't see how there wouldn't be any flow of time if there's a certain dynamics going on there..

The Schroedinger equation doesn't say that the wave function have to evolve.

Of course it does !
if we believe in the hypotheses that lead to its formulation, like the existence of time.

 

[dmtr]

Their will be time flow (you are free to stick in your own time coordinates if you want, even with a vanishing hamiltonian -- the hamiltonian constraint will hold the dynamics), but without the 2nd law of thermodynamics each subsystem could in principle have their own arrow of time so macroscopic comparison would be difficult and bizarre.

That would be the time flow from the point of view of some subsystem of that closed system (subjective time flow). And as you said (without the 2nd law) their own time arrows would not have a preferred direction.

Now, I'm not really interested in that subjective perspective from the inside of a closed system. I'm interested in the (normal in physics) objective perspective of an outside observer! And what I'm saying is that from that perspective it doesn't make sense to talk about the time flow/direction in the closed system. It could be anything (without the 2nd law).

-- Dmtr

 

[Fra]

Now, I'm not really interested in that subjective perspective from the inside of a closed system. I'm interested in the (normal in physics) objective perspective of an outside observer! And what I'm saying is that from that perspective it doesn't make sense to talk about the time flow/direction in the closed system. It could be anything (without the 2nd law).

-- Dmtr

In physics a real observer, as opposed to some mathematical gedanken observsers, is always in contact/interacting with the system, or it isn't making any real observations.

Ie. if the system is really closed, then it also means no observations can be made on it, because the system is by definition isolated from the observer.

In such a case then it's IMHO not even a scientific question. It's a complete realist construct of what is going on inside a completely isolated closed system that no one can look into. And then sure, it could be anything. Because the system is closed and nonone could every verify anything.

OTOH, taken one step further, a properly isolated system would even be indistinguishable and invisible. Noone would see it.

The usual notions of closed and open systems in "normal physics" are idealisations, so that the systems are sort of isolated by a boundary of limited transmission for a short period of time etc. Or where the measurements performed are neglectable.

But from a fundamental point of view, the closed system idea with an outside observer is hard to make sense out from an operational perspective.

/Fredrik

 

[Fra]

I figure it's motivated to clarifiy how I interpret the normal "time evolution" of closed systems, given my view above.

One of the standard views is that the schrödinger equation describes the time evolution of an isolated system, or the time evolution of the system _in between_ measurements. So then, in what sense does that make sense in a more radical view?

IMO, I see the schrödinger equation, as the expected self-evolution of a system (ie. given information; hamiltonian, inital condistions etc), but in the more radical view this expectation is observer-dependent. Ie. to have such an expectation, the system can not have been isolated in the past, the observer must have some kind of interaction history with the system (part of the preparation of experiment). Thus the hamiltonian itself, beeing an expectation, must IMHO be encoded in the observers internal state too.

So then what is the point of an expected evolution of a system (when I called evolution of an isolated system a realist construct)? IMO, the point that makes a different is when you consider the action of the observer itself. The observers action will follow from it's expectations on it's environment.

I like to think of it so that the observers almost "simulates" his own environment, in between, or parallell to, if you think in continuous terms, his interactions with the environment. So in a holographic sort of way, the observers evolution is in consistency with the expected evolution of the rest of the universe.

But the probability of expectations beeing in tune, should intutively decrease if the interaction is isolated for a long time.

Do you perhaps share C.Rovelli' and J.Barbours views on time in that it has no place in the fundamental laws of physics? (I don't, btw)

"The nature of time" but Julian Barbour
http://www.platonia.com/nature_of_time_essay.pdf

"Forget time" by Carlo Rovelli
http://www.fqxi.org/community/forum/topic/237

as a good CONTRAST to these ideas, check out smolins

"On the reality of time and the evolution of laws" but Lee Smolin
http://pirsa.org/08100049/

/Fredrik

 

[Atakor]

IMO, I see the schrödinger equation, as the expected self-evolution of a system (ie. given information; hamiltonian, inital condistions etc), but in the more radical view this expectation is observer-dependent. Ie. to have such an expectation, the system can not have been isolated in the past, the observer must have some kind of interaction history with the system (part of the preparation of experiment). Thus the hamiltonian itself, beeing an expectation, must IMHO be encoded in the observers internal state too.

the same could be said about the observer himself I think. In fact, in my opinion this leads to a global view where the observer becomes part of the system ie. not really an observer.
Or I didn't get your point.

I think that the quantum zeno effect is a good illustration of what you're saying.

 

[Fra]

IMO, I see the schrödinger equation, as the expected self-evolution of a system (ie. given information; hamiltonian, inital condistions etc), but in the more radical view this expectation is observer-dependent. Ie. to have such an expectation, the system can not have been isolated in the past, the observer must have some kind of interaction history with the system (part of the preparation of experiment). Thus the hamiltonian itself, beeing an expectation, must IMHO be encoded in the observers internal state too.

the same could be said about the observer himself I think. In fact, in my opinion this leads to a global view where the observer becomes part of the system ie. not really an observer.
Or I didn't get your point.

I'm not sure,It doesn't sound like I was able to convey the point clearly. I reject a global view where the observers are internal subsystems, that are described globally.

It seems you suggest that the problem of the observers is to be solved by removing the observer (dismissing it to a subsystem) and instead replace the operational view with a global or birds view. This is _exactly_ what I reject. The operational perspective is fundamental IMO.

For sure the observer is a player, not just an inert observer. So in that respect you are right. However this does not in my reasoning at least imply that there is a global perspective.

The point is that all we have are subjective perspective, and these are interacting, and each observers witnesses an evolving world. But there is no global or external description of this evolution in my thinking. If there was one, it would certainly be nice, but unfortunately it's a realist picture that IMO lacks justification.

I instead suggests that there is always some residual undecidability at every physical scale. It's the lack of a global perspective to hang onto, that causes me to adpot the idea of evolving law.

/Fredrik

 

[dmtr]

It seems you suggest that the problem of the observers is to be solved by removing the observer (dismissing it to a subsystem) and instead replace the operational view with a global or birds view. This is _exactly_ what I reject. The operational perspective is fundamental IMO.

An example of a completely closed system would be a system going away from an observer with the speed of light. Interestingly this effectively stops the observed time evolution of such a system.

-- Dmtr

 

[Atakor]

The point is that all we have are subjective perspective, and these are interacting, and each observers witnesses an evolving world. But there is no global or external description of this evolution in my thinking. If there was one, it would certainly be nice, but unfortunately it's a realist picture that IMO lacks justification.

I instead suggests that there is always some residual undecidability at every physical scale. It's the lack of a global perspective to hang onto, that causes me to adpot the idea of evolving law.

Quantum mechanics itself (as a theory) plays the role of the external description.. or does it ?
Special Relativity doesn't tell us the momenta and energies of all the particles, but gives invariant descriptions that we can use for each observer-dependent -subjective- case.

Finally I think your views are very statistical by nature, it seems you consider statistical (interacting) systems as more fundamental than individuals (whatever that means).
But as far as I see this, both are metaphisical prejudices.. at least for me.

 

[Fra]

Quantum mechanics itself (as a theory) plays the role of the external description.. or does it ?

This sounds pretty much like Carlo Rovelli's view (Relational QM).

I guess QM is "supposed to be this". But my view is that ts doesn't make sense. I think it's an approximation, and I've elaborate on before why I think it's a good approximation in many cases. But why it's not satisfactor in a fundamental sense.

But I reject Rovelli's otherwise nice reasoning because of this. He is simplifying things IMO, and he happens to simplify the most important things.

Special Relativity doesn't tell us the momenta and energies of all the particles, but gives invariant descriptions that we can use for each observer-dependent -subjective- case.

But Special realtivity only covers a very special set of observers, namely those related by poincare transformations.

Two such "sets" have invariant descriptions only for a constrained set of subjective observers, so when they suddently experience an strongly accelerating observer or strong gravitational fields, their invariants break down.

If you consider a more general set of observers, related by differmorphisms, you get a more complicated relation between observers.

But the question I ask, is how can a in inside observer infere these symmetries from interactions only? it's tempting to consider massive statistics, but there is a limit to how much statistics an observer can related to, and there are also choices on howto store and represent data.

Also, things are worse since GR and SR are classical realist models that isn't formulated operationally. I think the union of them and QM will require that we answers some of these questions.

/Fredrik

 

[Atakor]

SR was just an example of course, I meant a theory that relates observables by certain invariant links or relations.

But the question I ask, is how can a in inside observer infere these symmetries from interactions only?

by essence those relations must involve more than one observer to be discovered (to get rid of subjectivity and extract the invariance) which leads us back to the conventional view of first principles (ie. outside observer) !

But one can argue that we ARE already insiders in a certain sens: we're inside the universe we're describing not outside of it.
For me the most fundamental question is not about the emergence/imposition or direction of description (top-down or bottom-up) but about the nature of the observer himself : consciousness.

 

[Fra]

which leads us back to the conventional view of first principles (ie. outside observer) !

But one can argue that we ARE already insiders in a certain sens: we're inside the universe we're describing not outside of it.

Indeed! This is IMO a major key insight, it's not just a curiosity of no interest. IT's actually a difference between fundamental principle and effective principle.

What we call and most think of as "objective science" IS in fact highly conditional on a specific perspective, namely the earth/human based perspective.

If we are talking about atomic physics, our perspective is objective scientists in between, no doubt - and this is the important point in science. That there is a scientific consensus within the community.

But there is more to this than just this, it's when it comes to the foundational issues, then what is FAPP objective, must be seen for what it really is.

From a human perspective, no doubt the knowledge of laws of physics has evolved - and this knowledge determines how we humans act. But similarly (this subtle point is apparently hard to convey) the distinguishable laws of physics from the point of view of the subatomic observers, might actually be determine it's action as well.

For me the most fundamental question is not about the emergence/imposition or direction of description (top-down or bottom-up) but about the nature of the observer himself : consciousness.

I am not very into the discussion of conscioussness, since it often leads to absurd discussions. However, with some stretch of the associations here I find it possible to picture what conscioussness might mean for a subatomic system - it's the awareness of it's own actions, in the sense that the physical action of the system takes into account that it's not a passive observer, but that it's own actions actually make a difference to the future. This "basal" level is I think in all systems, and it's IMO nothing divine or religious about this, I just see it as a condition for constructivity.

Then the fact that there are different LEVELS of complexity and awareness, like animals with brains, and ultimately humans, is a somewhat different discussion. But I think some of the principles of self-organisation is similar.

/Fredrik

 

[Atakor]

From a human perspective, no doubt the knowledge of laws of physics has evolved - and this knowledge determines how we humans act. But similarly (this subtle point is apparently hard to convey) the distinguishable laws of physics from the point of view of the subatomic observers, might actually be determine it's action as well.

I'm not sure that the physical knowledge has really changed the way humans act..but I got now your point about evolving laws.
However, I immediately see a problem in this view. Indeed, those evolving laws will change according to a certain 'order' right ? at least if you're not considering chaotic evolutions (which I guess is ruled out but simple observation of order around us).
So in this case..there should be meta-laws that tell the laws how to evolve.
You just add a new layer of complexity. Actually that's how I conceive the scaling of physical laws (in particular the far from obvious passage -if any- from CM to QM ).
So in this view the meta-laws should be seen as the real fundamental and ontological laws.

I am not very into the discussion of conscioussness, since it often leads to absurd discussions. However, with some stretch of the associations here I find it possible to picture what conscioussness might mean for a subatomic system - it's the awareness of it's own actions, in the sense that the physical action of the system takes into account that it's not a passive observer, but that it's own actions actually make a difference to the future. This "basal" level is I think in all systems, and it's IMO nothing divine or religious about this, I just see it as a condition for constructivity.

I don't want to discuss this either especially when I don't know what you mean by awareness (an ill defined concept)..and I don't understand your last comment. I mean people could argue that everything IS divine and religious and you objectively cannot refute that.. others would say nothing is divine and you cannot argue either !

 

[Fra]

I'm not sure that the physical knowledge has really changed the way humans act..but I got now your point about evolving laws.
However, I immediately see a problem in this view. Indeed, those evolving laws will change according to a certain 'order' right ? at least if you're not considering chaotic evolutions (which I guess is ruled out but simple observation of order around us).
So in this case..there should be meta-laws that tell the laws how to evolve.
You just add a new layer of complexity. Actually that's how I conceive the scaling of physical laws (in particular the far from obvious passage -if any- from CM to QM ).
So in this view the meta-laws should be seen as the real fundamental and ontological laws.

This is somehow a somewhat expected response. I suspect it's the one Rovelli could be expected to come up with to.

But to give a short response, I do not rule out chaotic evolutions and the result is not a meta-law. Part of evolution is predictable, part isn't. This is what gives stability to the chaotic evolution. A decent analogy is learning - human learning. Clearly human brains learn, and even learn howto learn, and this process is somewhat chaotic but still for the majority of cases produces a good/stable learning curve. Evolution needs both diversity, selection and stability to prevent total chaos.

This is apparently difficult to explain. I think it's very intuitive but I've understood from the response of others that I have tried in several threads to present various philosophical arguments for the beauty and sense of evolving law as well as the potential of this.

Unfortunately I have not (yet) written down in any publictly available form this reasoning, that's what I've referred to others, that are related.

One nice talk, that I think really does not convey the most important points, but still contains an idea, is this talk of Smolin. (Smolin has a specific idea of evolving law - CNS).
"On the reality of time and the evolution of laws" by Lee Smolin I posted in post 8 is http://pirsa.org/08100049/.

It's available as mp3 and video+sound. It you have the time, check it out and see if it triggers any thoughts.

In the talk, one guy in the audince in the end of the file, raises the question you do - then anre't there metalaws? Smolin responds that he doesn't know. Well, my opinion is that there is no metalaw.

/Fredrk

 

[dmtr]

I'm not sure that the physical knowledge has really changed the way humans act..but I got now your point about evolving laws.
However, I immediately see a problem in this view. Indeed, those evolving laws will change according to a certain 'order' right ? at least if you're not considering chaotic evolutions (which I guess is ruled out but simple observation of order around us).
So in this case..there should be meta-laws that tell the laws how to evolve.
You just add a new layer of complexity.

Yeah. Please. Four no's:
* No tower of turtles,
* No laws,
* No continuum,
* No space, no time.

Anyway, it's all nice, but doesn't answer the original question. Would a closed system evolve with time or there is a need for a (shared with the observer?) environment? I can think of only a few examples of a really closed systems, namely:
* a system from which an observer moves away with the speed of light;
* a system beyond the event horizon of a black hole;

In both cases (assuming GR/SR classical approximation) the observed time evolution of such a system seems to be stopped. Stopped in the classical approximation, on the microscale level the time evolution still proceeds, but at both (forward and reverse) directions at once. And without any leakage of information to the observed environment the symmetry is not breaking.

-- Dmitry

 

[Atakor]

Thanks for the link Fra, I'll try to check that out.

Yeah. Please. Four no's:
* No tower of turtles,
* No laws,
* No continuum,
* No space, no time.

Anyway, it's all nice, but doesn't answer the original question. Would a closed system evolve with time or there is a need for a (shared with the observer?) environment? I can think of only a few examples of a really closed systems, namely:
* a system from which an observer moves away with the speed of light;
* a system beyond the event horizon of a black hole;

I don't understand what you mean with your "four no's".
anyway.. the flow of time seem to stop also for some systems that are in constant interaction with the environment, I mentioned earlier the quantum zeno effect for example.

 

[dmtr]

I don't understand what you mean with your "four no's".
anyway.. the flow of time seem to stop also for some systems that are in constant interaction with the environment, I mentioned earlier the quantum zeno effect for example.

These were J. A. Wheeler's four no's, not mine. They are relevant to the topic under the discussion in general and the 'tower of turtles/meta law' part in specific.

Yes. I think you are right. Quantum zeno effect pretty much freezes the observed unitary time evolution. Different method, same result. Again the amount of information that the observer have about the system doesn't change with time and that stops the observed time evolution.

From these examples it seems to be, that in order to observe the time flow in some system, there is a need for an environment and information loss to the environment (decoherence, increase of entropy). Does that sounds right?

-- Dmtr

 

[stealth666]

Time comes from expansion, right?

From these examples it seems to be, that in order to observe the time flow in some system, there is a need for an environment and information loss to the environment (decoherence, increase of entropy). Does that sounds right?

-- Dmtr

In a perfectly reflective islolated closed box in which particles move, time does not exist. All paths are deterministic. All particle motion can be described as basic trig functions.

But if you let the box expand, all paths lose their determined trajectory. Am I right?

So you have created the illusion of time, by expanding the box.

Thus does the expanding universe create time and entropy, but not vice versa.

 

[dmtr]

In a perfectly reflective isolated closed box in which particles move, time does not exist. All paths are deterministic. All particle motion can be described as basic trig functions.

I'd say there is no preferred time direction. Forward and reverse time evolution interfere with each other and cancel out.

But if you let the box expand, all paths lose their determined trajectory. Am I right?

So you have created the illusion of time, by expanding the box.

Thus does the expanding universe create time and entropy, but not vice versa.

I guess there are probably two effects in play. The universe expansion and the unitary time evolution. The universe expansion (extension of the state space dimension?) breaks the symmetry of the forward/reverse time evolution, so it is not unitary any more. And that shows up as the subjective time flow to the observer. But it is cosmology and a way outside of the topic scope.

-- Dmtr

 

[Haelfix]

Its pretty well accepted that the universe's scale factor isn't the reason behind the asymmetry between past, present and future. Point being, its quite easy to imagine scenarios where the scale factor changes sign where you wouldn't expect time to start flowing in the opposite direction (and people who believe that are crazy).

The 2nd law + the asymetric boundary conditions (eg a low entropy past) is the reason, period.

The quantum arrow of time points in arbitrary directions, its only when you introduce the environment, decoherence and macroscopic system where we have a notion of entropy increasing and where a unique arrow is singled out for all macroscopic observers.

 

[dmtr]

Its pretty well accepted that the universe's scale factor isn't the reason behind the asymmetry between past, present and future. Point being, its quite easy to imagine scenarios where the scale factor changes sign where you wouldn't expect time to start flowing in the opposite direction (and people who believe that are crazy).

The 2nd law + the asymetric boundary conditions (eg a low entropy past) is the reason, period.

How about the Hilbert space state dimensions expansion? That would break the symmetry. The 2nd law is supposed to be a limit in the classical approximation.

-- Dmtr

 

[stealth666]

Its pretty well accepted that the universe's scale factor isn't the reason behind the asymmetry between past, present and future. Point being, its quite easy to imagine scenarios where the scale factor changes sign where you wouldn't expect time to start flowing in the opposite direction (and people who believe that are crazy).

Agreed. If it started to shrink, time would still move forward in the box, because time is simply the determinate variable of the function that describes the boundary condition of the universe, where as entropy describes the condition of every particle inside the universe.

I guess, really, that the contents of the universe are just expressions of it's boundary condition. Taken to an extreme, this line of thinking leads you to the idea that the inside of the universe is just an expression of what is happening on its boundary.

The 2nd law + the asymetric boundary conditions (eg a low entropy past) is the reason, period.

The quantum arrow of time points in arbitrary directions, its only when you introduce the environment, decoherence and macroscopic system where we have a notion of entropy increasing and where a unique arrow is singled out for all macroscopic observers.

Yes. The Universe is a macroscopic system, so that makes sense.

 

[dmtr]

The 2nd law + the asymetric boundary conditions (eg a low entropy past) is the reason, period.

The quantum arrow of time points in arbitrary directions, its only when you introduce the environment, decoherence and macroscopic system where we have a notion of entropy increasing and where a unique arrow is singled out for all macroscopic observers.

What you are saying, is that there is no time asymmetry on the quantum level, yet the macroscopic arrow of time and the observed increasing entropy magically appears on the macroscopic level. Well, if this is indeed the case it could be nice to get some understanding of that magic, maybe we can invent some incantations that violate causality or something.

The alternative is that there is some asymmetry on the quantum level and it shows up as the thermodynamic arrow of time on the macro scale. E.g.:
* entanglements are irreversible with the time;
* the Hilbert state space [dimensions] are expanding;
* the wave function 'collapse' is biased toward the more entropic outcome;
* ?

-- Dmtr

 

[Haelfix]

Forget about quantum mechanics, its already evident at the classical level. Reread the Feynman lecture section on entropy.

Classical EM eoms are time symmetric, there is no hint of an asymmetry. But the classical picture of a tank full of a red liquid and a tank with clear liquid mixing is clearly a violation of this symmetry. The liquids always mix, they never unmix. You can wait >> the age of the universe until you see a tank spontaneously rearrange itself into its original configuration.

Yet, if you zoom in on the molecules at work, you see a perfectly time symmetric action taken place (molecules bounce willy nilly, with no obvious preferred direction of time), yet macroscopically (magically in your words), there is a clear direction that is evident, even to children.

That is the 2nd law in action, and its no different for quantum mechanics (if anything its more pronounced, b/c of decoherence time scales). No amount of mysticism about the scale factor (with clocks and rods that are vanishingly small on solar system scales) can change this basic physical fact.

 

[dmtr]

"That is the [STRIKE]2nd law[/STRIKE] magic in action..."

-- Dmtr

 

[xepma]

Magic? Have you ever seen a proper derivation of the 2nd law? It's just probability theory. Probability theory of really, really large numbers.

The 2nd law is perfectly fine. Just look around you -- you see it in action every day.

 

[dmtr]

Magic? Have you ever seen a proper derivation of the 2nd law? It's just probability theory. Probability theory of really, really large numbers.

The 2nd law is perfectly fine. Just look around you -- you see it in action every day.

What I've seen is a few circular definitions. Namely probability defined in terms of probability. Time defined in terms of time. Somewhat murky entropy definitions. The arrow of time referring to the direction of the entropy increase. And of course the 2nd law using all these terms.

-- Dmtr

 

[dmtr]

The alternative is that there is some asymmetry on the better defined quantum level and it shows up as the thermodynamic arrow of time on the macro scale.

-- Dmtr

 

[Fra]

What I've seen is a few circular definitions. Namely probability defined in terms of probability. Time defined in terms of time. Somewhat murky entropy definitions. The arrow of time referring to the direction of the entropy increase. And of course the 2nd law using all these terms.

-- Dmtr

I'm not sure if I make the right associations to your thinking here, and at what level you picture this, but if you have objections about the use of probability theory and the notion of entropy then I can just add that I have such objections as well.

It is completely true however, that there is no different in principle between QM and classical physics. That however doesn't mean it's more sound, it just means the same unsatisfactory reasoning is used in both places :) This is why the context of which I would want to raise this objection is in the "beyond the standard model" context.

I don't know if this is what Dmtr also means, or not?? but by objection is that from the point of view of (what I personally seek) an intrinsic measurement theory, entropy measures are not uniqe. There are as we know several different definitions of entropy measures. They can be "derived" in severals ways, from cox axioms, or from other considerations. My opinion is that it makes no sense to consider a universally objective information measure. This has been briefly discussed in several threads mainly in the BTSM I think.

There are also some threads here discussing the relatvivity of entropy.

I've question continuum probability theory itself, on the basis thta the continuum notion implies (IMHO at least) an infinitely massive observer - which I think, makes no sense except as an APPROXIMATION (where instead of actually using large numbers, you describe it as a "continuum" - this is fine in the limit, but care must then be taken when you "scale it back" to the small number limit).

/Fredrik

 

[dmtr]

I'm not sure if I make the right associations to your thinking here, and at what level you picture this, but if you have objections about the use of probability theory and the notion of entropy then I can just add that I have such objections as well.

It is completely true however, that there is no different in principle between QM and classical physics. That however doesn't mean it's more sound, it just means the same unsatisfactory reasoning is used in both places :) This is why the context of which I would want to raise this objection is in the "beyond the standard model" context.

I don't know if this is what Dmtr also means, or not?? but by objection is that from the point of view of (what I personally seek) an intrinsic measurement theory, entropy measures are not uniqe. There are as we know several different definitions of entropy measures. They can be "derived" in severals ways, from cox axioms, or from other considerations. My opinion is that it makes no sense to consider a universally objective information measure. This has been briefly discussed in several threads mainly in the BTSM I think.

I have no objections to the use of the probability theory, entropy, or the 2nd law. These are very good instruments. For instance in the QM we can calculate probabilities which very often agree with the experiments very well. And we would be very much surprised if suddenly they wouldn't.

What I don't like however is when these instruments are used to give the ultimate definition of the arrow of time. Use of the 2nd law to define the time arrow makes sense only in the classical approximation, where the 2nd law is defined. It hardly makes sense even there, because time/causality is an axiom in the classical approximation.

An alternative to that is to think of some properties of the quantum state space that would ultimately result in the 2nd law and the familiar time arrow in the classical approximation.

-- Dmtr