I think you may have misunderstood the OP's point - the entropy you calculate for a system depends on how you factor the system into micro and macro states. This doesn't really have anything to do with changes of reference frame - in practice it's more about limitations on the kinds of measurements you can make of the system.
(you can't measure the individual states of all the particles in a body of gas, for instance, so you factor it into macrostate variables like pressure/temperature/volume and such)
Can we take the anthropic out of this? I reckon it'll make things easier.
Instead of me knowing, do other physical objects get affected. I might get anemsia and forget what the dots on a dice mean and say they are all the same: all dotty!
Imagine each hydrogen atom has a hidden guid but this is undetectable and has no effect on anything else. This is a secret from the rest of physics!
I guess!!! (Armchair pondering!) that that guid cannot be taken into account for entropy changes. At least from any practical standpoint.
You could imagine each atom having a guid and come up with a scheme to hash the atom based on where it came from ... but is that info really there and if so does it affect anything physically beyond that atoms current state (as defined by stuff that affects other stuff).
What anthropic do you mean? I'm describing properties of models, not people. Physics (probably) doesn't care what you "know".
On the guid idea - fundamental particles are indistinguishable from one another in quantum mechanics, so they don't have anything like a guid even in principle. There is no experiment you could perform on an electron to determine whether it had been swapped out for a "different" one, for instance.
Sorry ... I am replying mostly to the dice idea which wasn't you.
Yes correct about the guid idea. My point is the discussion is easier to follow if grounded in reality (as best modelled since that is all we have plus some evidence stored in the same "SSD"!)
Oh I see. But on your guid thing, people often describe entropy in terms of the set of micro states of your system (the actually physical states in your model) and the macro states (sets of microstates that are described by a collection of high-level state variables like pressure/temperature).
Physically indistinguishable stuff would have the same micro state, so yeah, they wouldn't affect entropy calculations at all, no matter what macro states you picked.
But I disagree a bit about grounding things in reality - some concepts are quite abstract and having clean examples can be helpful, before you start applying them to the mess that is our universe!
From a thermodynamics point of view only the differential of the entropy matters, so if there is only a fixed difference between the two computations they do not influence the physics.
If the way one does the coarse graining of states results in different differentials, one way should be the correct one.
There is only one physics.
If I remember one of Plancks relevations was that he could explain why a certain corrections factor was needed in entropy calculations, since phase space had finished cell size.
That's true - for instance I believe many of the results of statistical mechanics rely on further assumptions about your choice of macrostates, like the fact that they are ergodic (i.e. the system visits each microstate within a macrostate with equal probability on average). Obviously exotic choices of macrostates will violate these assumptions, and so I would expect the predictions such a model makes to be incorrect.
But ultimately that's an empirical question. Entropy is a more general concept that's definable regardless of whether the model is accurate or not.
(you can't measure the individual states of all the particles in a body of gas, for instance, so you factor it into macrostate variables like pressure/temperature/volume and such)