I don't get the example under "What is entropy?". This works only under the assumption that reality (phase space in particular) is somehow "pixelated". If reality is continuous, 9 particles that are clumped together can already be in uncountalbly many states.
What is entropy? A measure of just how little we know
121–130 of 169 posts
Re: What is entropy? A measure of just how little we know
#122Interesting to read this, 27 years after my PhD* (theoretical physics), in which I did compare the view WITH and the view WITHOUT ‘unknowns’ causing entropy as a driver. * My PhD was about how to treat a (quantum mechanical) system inside a cavity: a cavity with one perfect mirror and one 99.999999% perfect mirror. The (one dimensional) universe was made whole by another perfect mirror at the other side of the non-pe…
Interesting. Could you share a link to your thesis?
Sure.
Had to do some searching;-)
Info on thesis: https://dare.uva.nl/search?identifier=0ae63403-264b-4bf0-91c...
The document itself (self hosted) https://gofile.me/7uDSJ/sGJCFD3W7
Probably most important article: (sorry, only abstract): https://journals.aps.org/pra/abstract/10.1103/PhysRevA.54.24...
Re: What is entropy? A measure of just how little we know
#123Earlier quoted context omitted.
I read you're comment with interest, but ultimately I can't understand the point being made because I don't know what kind of mirror you're referring to (optical?), I don't know what 'l' or 'L' represent (lateral spacing of mirrors?, vacuum energy desnities?), and the last sentence I think maybe the word 'how' should be deleted?
Answers to your questions: 1): all the way to the left, a mirror with a reflectivity|r| of 1 (or a 100%). In the middle an |r| of slightly below 1. Yes, optical, system with photons (a and a^dagger with [a,a^dagger]=1). 2) distance between mirrors 1 and 2: l. Distance mirror 2 and 3:L. (Later taking the limit L/l ==>> infinity) 3) the how is actually correct, I guess the word behaves is missing twice: .... how .... b…
This is madness.
Re: What is entropy? A measure of just how little we know
#124Earlier quoted context omitted.
> Maybe I have the benefit of giant shoulders, but this seems like a fairly mundane observation. It is not mundane, and it is also not right, at least for entropy in Physics and Thermodynamics. > High-entropy states are those macrostates which have many corresponding microstates. That is how you deduce entropy form a given model. But entropy is also something that we can get from experimental measurements. In this ca…
> Fundamentally, entropy depends on the probability distribution, not the observer. Right but a probability distribution represents the uncertainty in an observer so there is no inconsistency here (else you're falling for the Mind Projection Fallacy http://www-biba.inrialpes.fr/Jaynes/cc10k.pdf ).
This is only true if one assumes that (a) physical processes are fundamentally completely deterministic, and that (b) it is possible to measure the initial state of a system to at least the same level of precision as the factors that influence the outcome.
Assumption (a) is currently believed to be false in the case of measuring a quantum system: to the best of our current knowledge, the result of measuring a quantum system is a perfectly random sampling of a probability distribution determined by its wave function.
Assumption (b) is also believed to be false, and is certainly known to be false in many practical experiments. Especially given that measurement is a time-consuming process, events that happen at a high frequency may be fundamentally unpredictable on computational grounds (that is, measuring the initial state to enough precision and then computing a probability may be physically impossible in the time that it takes for the event to happen - similar to the concept of computational irreducibility).
So, even in theory, the outcomes of certain kinds of experiments are probabilistic in a way that is entirely observer-independent; this is especially true in quantum mechanics, but it is also true in many types of classical experiments.
Re: What is entropy? A measure of just how little we know
#125Earlier quoted context omitted.
Some people have coined the term explorable explanation/explorables https://explorabl.es/ https://en.wikipedia.org/wiki/Explorable_explanation
aah, this is nailing it. It helps to differentiate from game-like experiences and special purpose apps. Another interesting term from the wiki link is "active essays": > The related term "active essays" was used by Alan Kay to refer to text-based explorable explanations But I don't know if by text-based he meant strictly no visuals. Like just ASCII art? :-)
It looks like this might be the original paper by Kay, can anyone provide a link that isn’t behind a paywall?
Search results seem to indicate he was referring to text based plus interactive components something something Java(script?). I’m not a programmer and know less about the history..
Re: What is entropy? A measure of just how little we know
#126Earlier quoted context omitted.
> can you give/link a specific physical example? About the lack of subjectivity of the states? If we consider any bit of matter (for example a crystal or an ideal gas), the macrostate is completely independent of the observer: it’s just the state in which the law of physics say that bit of matter should be. In an ideal gas it is entirely determined by the pressure and volume, which are anything but subjective. For a…
Agreed, sure. Of course it's not subjective. Is there a concrete physical example where the information-theory definition of entropy conflicts with experiment?
Others in this thread do believe that entropy is a subjective measure, or more precisely a measurement of the information that an observer has about a system instead of a measurement about the state of the system itself. Information theory easily leads to this interpretation, since for example the informational content of a stream of bytes can very much be observer-dependent. For example, a perfectly encrypted stream of all 1s will appear to have very high entropy for anyone who doesn't know the decryption process and key, while in some sense it will be interpreted as a stream with entropy 0 by someone who knows the decryption process and key.
Of course, the example I gave is arguable, since the two observers are not actually observing the same process. One is looking at enc(x), the other is looking at x. They would both agree that enc(x) has high entropy, and x has low entropy. But this same kind of phenomenon doesn't work with physical entropy. A gas is going to burn my hand or not regardless of how well I know its microstates.
Re: What is entropy? A measure of just how little we know
#127Earlier quoted context omitted.
Thank you for articulating what was bothering me about this. I couldn't quite put my finger on it, but you're right. They are confusing defining the system with defining the entropy of a system and then saying it's the entropy that is subjective. That isn't the case at all. Entropy is just a measurement.
That can't be right, because the arrow of time depends on the universe being in a high entropy state when the Big Bang happened. There were no observers then. Also, the 2nd law of thermodynamics doesn't depend on observers. The universe overall will continue to evolve into a higher entropy state without any intelligent observers making measurements. As in stars will burn out and blackholes will evaporate, and the tem…
> the 2nd law of thermodynamics doesn't depend on observers
Thermodynamics entropy is not just a property of a system - it depends on how we choose to describe the system. Of course, we can define the thermodynamic entropy for a system without observers. (In fact, we can only define the classic equilibrium thermodynamic entropy for a system without observers!)
Re: What is entropy? A measure of just how little we know
#128Earlier quoted context omitted.
I would say an even more limiting measure of entropy shows that entropy isn't subjective. That is entropy is the ability to extract useful work from a system by moving the system from a state of lower entropy to a state of higher entropy (in a closed system) No subjective measure of entropy can allow you to create a perpetual motion machine. The measurements of any two separate closed systems could be arbitrary, but…
> entropy is the ability to extract useful work from a system https://www.damtp.cam.ac.uk/user/tong/statphys/jaynes.pdf The amount of useful work that we can extract from any system depends - obviously and necessarily - on how much “subjective” information we have about its microstate, because that tells us which interactions will extract energy and which will not; this is not a paradox, but a platitude. If the entro…
I think this is a very weird thought experiment, and one that is either missing a lot of context or mostly just wrong. In particular, if two people had access to the same gas tank, and one knew that there were two types of argon and the other didn't, so they would compute different entropies, one of them would still be wrong about how much work could be extracted out of the system.
If whifnium did exist, but it was completely unobtainable, then both physicists would still not be able to extract any work out of the system. If the one that didn't know about whifnium was given some amount of it without being told what it was, and instructed in how to use it, they would still see the same amount of work being done with it as the one who did know. They would just find out that they were wrong in their calculation of the entropy of the system, even if they still didn't know how or why.
And of course, this also proves that the system had the same entropy even before humanity existed, and so the knowledge of the existence of whifnium is irrelevant to the entropy of the system. It of course affects our measurement of that entropy, and it affects the amount of work we can get that system to perform, but it changes nothing about the system itself and its entropy (unless of course you tautologically define entropy as the amount of work the experimenter/humanity can extract from the system).
Re: What is entropy? A measure of just how little we know
#129Entropy got a lot more exciting to me after hearing Sean Carroll talk about it. He has a foundational/philosophical bent and likes to point out that there are competing definitions of entropy set on different philosophical foundations, one of them seemingly observer dependent: - https://youtu.be/x9COqqqsFtc?si=cQkfV5IpLC039Cl5 - https://youtu.be/XJ14ZO-e9NY?si=xi8idD5JmQbT5zxN Leonard Susskind has lots of great talks…
why is it exciting at all? it is the most depressing concept i have ever heard.
Re: What is entropy? A measure of just how little we know
#130Earlier quoted context omitted.
Agreed, sure. Of course it's not subjective. Is there a concrete physical example where the information-theory definition of entropy conflicts with experiment?
Others in this thread do believe that entropy is a subjective measure, or more precisely a measurement of the information that an observer has about a system instead of a measurement about the state of the system itself. Information theory easily leads to this interpretation, since for example the informational content of a stream of bytes can very much be observer-dependent. For example, a perfectly encrypted stream…
>A gas is going to burn my hand or not regardless of how well I know its microstates.
Or perhaps that's the secret of the Shaolin monks!