[HN Gopher] What Is Entropy? A Measure of Just How Little We Know
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What Is Entropy? A Measure of Just How Little We Know
Author : nsoonhui
Score : 210 points
Date : 2024-12-14 07:49 UTC (15 hours ago)
(HTM) web link (www.quantamagazine.org)
(TXT) w3m dump (www.quantamagazine.org)
| kqr wrote:
| > As physicists have worked to unite seemingly disparate fields
| over the past century, they have cast entropy in a new light --
| turning the microscope back on the seer and shifting the notion
| of disorder to one of ignorance. Entropy is seen not as a
| property intrinsic to a system but as one that's relative to an
| observer who interacts with that system.
|
| Maybe I have the benefit of giant shoulders, but this seems like
| a fairly mundane observation. High-entropy states are those
| macrostates which have many corresponding microstates. The
| classification of several microstates into the same macrostate,
| is this not a distinctly observer-centred function?
|
| I.e. if I consider 5 or 6 to be essentially the same outcome of
| the die, then that will be a more probable (higher-entropy)
| outcome. But that's just due to my classification, not inherent
| to the system!
| niemandhier wrote:
| In physics the requirement for a valid changing the frame of
| reference is, that the laws of physics transform according to
| the transformation.
|
| Every observer should discover the same fundamental laws when
| performing experiments and using the scientific method.
|
| To stay in your analogy, saying 5 and 6 are the same would only
| work if the rules of the game you play could transform in such
| a way that an observer making a distinction between the two
| would arrive at the correctly transformed rules in his frame of
| reference.
|
| Given that we have things like neutron stars, black holes and
| other objects that are at the same time objects of quantum
| physics and general relativity, the statement feels pretty
| fundamental to me, to a degree even that I wonder if it might
| be phrased to strongly.
| bubblyworld wrote:
| 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)
| lizzas wrote:
| 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).
| bubblyworld wrote:
| 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.
|
| Maybe I'm missing your point though?
| lizzas wrote:
| 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"!)
| bubblyworld wrote:
| 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!
| niemandhier wrote:
| 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.
| bubblyworld wrote:
| 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.
| guerrilla wrote:
| > mundane observation
|
| What makes an observation mundane? I think what you said is
| insightful and demonstrates intelligence. I don't think it's at
| all obvious to the masses of students that have poured over
| introductory physics textbooks. In fact, it seems to me that
| often entropy is taught poorly and that very few people
| understood it well but that we are beginning to correct that. I
| point to the heaps of popsci magazines, documentaries and
| YouTube videos failing to do anything but confuse the public as
| additional evidence.
| LudwigNagasena wrote:
| Maybe if you opened only introductory physics textbooks then
| it's not mundane; but If you opened introductory information
| theory textbooks, statistical textbooks, introductions to
| Bayesian probability theory, articles about MaxEnt
| thermodynamics including articles by E.T. Jaynes, then it's a
| quite mundane observation.
| guerrilla wrote:
| So, what you're saying is, not very mundane at all and, in
| fact, that it's specialized knowledge requiring advanced
| education. ;)
| mitthrowaway2 wrote:
| Jaynes definitely made the case for this a long time ago,
| and in my opinion he's correct, but I think that view is
| still not mainstream; or even if mainstream, certainly not
| dominant. So I think we should welcome other people who
| reach it on their own journey, even if they aren't the
| first to arrive there.
| kergonath wrote:
| > 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 case, the experimental setup does not
| care about microstates and macrostates, it just has properties
| like enthalpy, heat capacity and temperature.
|
| We can build models after the fact and say that e.g. the
| entropy of a given gas matches that predicted by our model for
| ideal gases, or that the entropy of a given solid matches what
| we know about vibrational entropy.
|
| That's how we say that e.g. hydrogen atoms are
| indistinguishable. It's not that they become indistinguishable
| because we decide so. It's because we can calculate entropy in
| both cases and reality does not match the model with
| distinguishable atoms.
|
| > The classification of several microstates into the same
| macrostate, is this not a distinctly observer-centred function?
|
| It seems that way if we consider only our neat models, but it
| fails to explain why experimental measurements of the entropy
| of a given materials are consistent and independent of whatever
| model the people doing the experiment were operating on.
| Fundamentally, entropy depends on the probability distribution,
| not the observer.
| LudwigNagasena wrote:
| > It is not mundane, and it is also not right, at least for
| entropy in Physics and Thermodynamics.
|
| Articles about MaxEnt thermodynamics by E.T. Jaynes where he
| talks about the "anthropomorphic" nature of entropy date back
| to 1960s. How is that not right in physics?
| kergonath wrote:
| By the look of it, it is another misguided attempt to apply
| information theory concepts to thermodynamics. Entropy as
| information is seductive because that way we think we can
| understand it better, and it looks like it works. But we
| need to be careful because even though we can get useful
| insights from it (like Hawking radiation) it's easy to
| reach unphysical conclusions.
|
| > How is that not right in physics?
|
| Why would it be right? Was it used to make predictions that
| were subsequently verified?
| kgwgk wrote:
| That misguided attempt has resulted in full graduate
| courses and textbooks. Maybe one look is not all that it
| takes to fully assess its worthiness.
|
| https://www.amazon.com/Microphysics-Macrophysics-
| Application...
|
| https://arxiv.org/pdf/cond-mat/0501322
| kergonath wrote:
| Plenty of bad stuff made its way into textbooks, I saw
| some really dodgy stuff at uni. And for every
| uncontroversial statement we can find a textbook that
| argues that it is wrong. Sorting the good from the bad is
| the main point of studying science and it is not easy.
| What is also important is that approaches that can work
| in some field or context might be misleading or lead to
| wrong outcomes in others. Information theory is obviously
| successful and there is nothing fundamentally wrong with
| it.
|
| Where we should be careful is when we want to apply some
| reasoning verbatim to a different problem. Sometimes it
| works, and sometimes it does not. Entropy is a
| particularly good example. It is abstract enough to be
| mysterious for a vast majority of the population, hence
| why these terribly misleading vulgarisation articles pop
| up so often. Thinking of it in terms of information is
| sometimes useful, but going from information to knowledge
| is a leap, and then circling back to Physics is a bit
| adventurous.
| kgwgk wrote:
| Plenty of bad stuff makes its way into hackernews
| comments as well. Saying that "it could be wrong" doesn't
| really support the "it's wrong" claim, does it?
| kergonath wrote:
| I did not make that point, though. I rejected an appeal
| to authority because something was in a textbook. I made
| no comment about the validity of that person's work in
| his field, I just pointed out that this transferability
| was limited.
| kgwgk wrote:
| My bad, I thought you considered Balian's work another
| misguided attempt to apply information theory concepts to
| thermodynamics.
|
| For the record, this is the abstract of the "Information
| in statistical physics" article: "We review with a
| tutorial scope the information theory foundations of
| quantum statistical physics. Only a small proportion of
| the variables that characterize a system at the
| microscopic scale can be controlled, for both practical
| and theoretical reasons, and a probabilistic description
| involving the observers is required. The criterion of
| maximum von Neumann entropy is then used for making
| reasonable inferences. It means that no spurious
| information is introduced besides the known data. Its
| outcomes can be given a direct justification based on the
| principle of indifference of Laplace. We introduce the
| concept of relevant entropy associated with some set of
| relevant variables; it characterizes the information that
| is missing at the microscopic level when only these
| variables are known. For equilibrium problems, the
| relevant variables are the conserved ones, and the Second
| Law is recovered as a second step of the inference
| process. For non-equilibrium problems, the increase of
| the relevant entropy expresses an irretrievable loss of
| information from the relevant variables towards the
| irrelevant ones. Two examples illustrate the flexibility
| of the choice of relevant variables and the multiplicity
| of the associated entropies: the thermodynamic entropy
| (satisfying the Clausius-Duhem inequality) and the
| Boltzmann entropy (satisfying the H-theorem). The
| identification of entropy with missing information is
| also supported by the paradox of Maxwell's demon. Spin-
| echo experiments show that irreversibility itself is not
| an absolute concept: use of hidden information may
| overcome the arrow of time."
| oh_my_goodness wrote:
| "We need to be careful", agreed. "It's not mundane",
| agreed. (It's mundane in information theory because
| that's how they define entropy.)
|
| "It's [...] not right" (from your first comment), can you
| give/link a specific physical example? It would be very
| cool to have a clear counterexample.
| kergonath wrote:
| > 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 crystal it is
| more complex because we have to account for things like
| its shape but the reasoning is the same.
|
| Then, the microstates are just accessible states, and
| this is also dictated by Physics. For example, it is
| quite easy to see that a crystal has fewer accessible
| states than a gas (the atoms' positions are constrained
| and the velocities are limited to the crystal's vibration
| modes). We can calculate the entropy in the experimental
| conditions within that framework, or in the case of
| correlated liquids, or amorphous solids, or whatever. But
| the fact that we can come up with different entropies if
| we make different hypotheses does not mean that any of
| these hypotheses is actually valid. If we measure the
| entropy directly we might have a value that is consistent
| with several models, or none. The actual entropy is what
| we observe, not the theoretical scaffolding we use to try
| to make sense of it. And again, this is not subjective.
| oh_my_goodness wrote:
| Agreed, sure. Of course it's not subjective.
|
| Is there a concrete physical example where the
| information-theory definition of entropy disagrees with
| experiment?
| markisus wrote:
| Maybe the experimental apparatus is not objective. The
| quantities we choose to measure are dictated by our
| psychological and physiological limitations. The volume of a
| container is not objectively defined. An organism which lives
| at a faster time scale will see the walls of the container
| vibrating and oscillating. You must convince the organism to
| average these measurements over a certain time scale. This
| averaging throws away information. This is the same with
| other thermodynamic quantities.
| kergonath wrote:
| > The quantities we choose to measure are dictated by our
| psychological and physiological limitations.
|
| No. The enthalpy changes measured by a calorimeter are not
| dependent on our psychological limitations.
|
| > The volume of a container is not objectively defined.
|
| Yes, it is, for any reasonable definition of "objective".
| We know how to measure lengths, we know how they change
| when we use different frames of reference so there is no
| situation in which a volume is subjective.
|
| > An organism which lives at a faster time scale will see
| the walls of the container vibrating and oscillating.
|
| This does not matter. We defined a time scale from periodic
| physical phenomena, and then we know how time changes
| depending on the frame of reference. There is no
| subjectivity in this, whatever is doing the measurement has
| no role in it. Time does not depend on how you feel. It's
| Physics, not Psychology.
|
| > This is the same with other thermodynamic quantities.
|
| No, it's really not. You seem to know just enough
| vocabulary to be dangerous and I encourage you to read an
| introductory Physics textbook.
| notfed wrote:
| Sometimes I wish HN had merit badges. Or if you like, a
| device to measure the amount of information contained
| within a post.
| kergonath wrote:
| I am not sure it would help, I think it would just
| enhance groupthink. I like how you need to write
| something obviously stupid or offensive for the downvotes
| to have a visible effect and that upvotes have no visible
| effect at all. (Yes, it changes ranking, but there are
| other factors). People are less prejudiced when they read
| the comment than if they see that it is already at -3 or
| +5.
|
| Yes, it means that some posts should be more (or less)
| visible than they are but overall I think it's a good
| balance.
|
| Besides, I am not that interested in the absolute amount
| of information in a post. I want information that is
| relevant to me, and _that_ is very subjective :)
| whatshisface wrote:
| The enthalpy changes measured by a calorimeter are
| dependent on the design of the calorimeter, which could
| have been a different piece of equipment. In a sense,
| that makes it dependent on the definition of enthalpy.
|
| If you introduced a new bit of macro information to the
| definition of an ensemble, you'd divide the number of
| microstates by some factor. That's the micro level
| equivalent of macroscopic entropy being undefined up to
| an additive constant.
|
| The measurables don't tell you S, they only tell you dS.
| kergonath wrote:
| > The enthalpy changes measured by a calorimeter are
| dependent on the design of the calorimeter, which could
| have been a different piece of equipment.
|
| Right, but that is true of anything. Measuring devices
| need to be calibrated and maintained properly. It does
| not make something like a distance subjective, just
| because someone is measuring it in cm and someone else in
| km.
|
| > If you introduced a new bit of macro information to the
| definition of an ensemble, you'd divide the number of
| microstates by some factor. That's the micro level
| equivalent of macroscopic entropy being undefined up to
| an additive constant.
|
| It would change the entropy _of your model_. An ensemble
| in statistical Physics is not a physical object. It is a
| mental construct and a tool to calculate properties. An
| actual material would have whatever entropy it wants to
| have regardless of any assumptions we make. You would
| just find that the entropy of the material would match
| the entropy of one of the models better than the other
| one. If you change your mind and re-run the experiment,
| you'd still find the same entropy. This happens e.g. if
| we assume that the experiment is at a constant volume
| while it is actually under constant pressure, or the
| other way around.
|
| > In a sense, that makes it dependent on the definition
| of enthalpy.
|
| Not really. A joule is a joule, a kelvin is a kelvin, and
| the basic laws of thermodynamics are some of the most
| well tested in all of science. The entropy of a bunch of
| atoms is not more dependent on arbitrary definitions than
| the energy levels of the atoms.
|
| > The measurables don't tell you S, they only tell you
| dS.
|
| That's true in itself, the laws of Thermodynamics are
| invariant if we add a constant term to the entropy. But
| it does not mean that entropy is subjective: two
| observers agreeing that the thing they are observing has
| an entropy of 0 at 0 K will always measure the same
| entropy in the same conditions. And it does not mean that
| actual entropy is dependent on specific assumptions about
| the state of the thing.
|
| This is also true of energy, and electromagnetic
| potentials (and potentials in general). This is unrelated
| to entropy being something special or subjective.
| kgwgk wrote:
| > But entropy is also something that we can get from
| experimental measurements. In this case, the experimental
| setup does not care about microstates and macrostates, it
| just has properties like enthalpy, heat capacity and
| temperature. [...] experimental measurements of the entropy
| of a given materials are consistent and independent of
| whatever model the people doing the experiment were operating
| on. Fundamentally, entropy depends on the probability
| distribution, not the observer.
|
| https://bayes.wustl.edu/etj/articles/gibbs.vs.boltzmann.pdf
|
| Thermodynamics does have the concept of the entropy of a
| thermodynamic system; but a given physical system corresponds
| to many different thermodynamic systems. [...] It is clearly
| meaningless to ask, "What is the entropy of the crystal?"
| unless we first specify the set of parameters which define
| its thermodynamic state. [...] There is no end to this search
| for the ultimate "true" entropy until we have reached the
| point where we control the location of each atom
| independently. But just at that point the notion of entropy
| collapses, and we are no longer talking thermodynamics! [...]
| From this we see that entropy is an anthropomorphic concept,
| not only in the well-known statistical sense that it measures
| the extent of human ignorance as to the microstate. Even at
| the purely phenomenological level, entropy is an
| anthropomorphic concept. For it is a property, not of the
| physical system, but of the particular experiments you or I
| choose to perform on it.
| pndy wrote:
| http://www.thelastquestion.net/ - in case someone missed it
| somehow
| niemandhier wrote:
| Wow.
|
| When did we take the turn from sci-fi like that to the ever
| dystopian laments we read today.
| rcxdude wrote:
| It's pretty cyclical, there's older sci-fi that's more
| dystopian and still older sci-fi then that which is
| optimistic. (and of course, the trends are only trends)
| pixl97 wrote:
| I mean they had dystopian sci-fi back then too...
|
| Technology changes, yet people remain ever the assholes.
| guerrilla wrote:
| This is my favorite Isaac Asimov story and the reason I started
| reading him.
| srean wrote:
| For all who haven't, please read the other two as well.
|
| Last Answer
|
| Nightfall
| pndy wrote:
| Gotta mention that _Nightfall_ exists as both Asimov 's
| short story and a novel he co-wrote with Robert Silverberg
| nearly 50 years later
| pessimizer wrote:
| And that the short story is the important one.
| lizzas wrote:
| This will be my favorite Issac Asimov story and the reason I
| will start reading him
| WillAdams wrote:
| Anyone know how to contact the person responsible for that
| site?
|
| Typo:
|
| >Planetarv
|
| should be "Planetary".
| widea wrote:
| Entropy, a measure of freedom in a contained environment.
| rapjr9 wrote:
| Life, a short term attempt to reverse some entropy by creating
| more entropy.
| perihelions wrote:
| A related thread from earlier this year,
|
| https://news.ycombinator.com/item?id=41037981 ( _" What Is
| Entropy? (johncarlosbaez.wordpress.com)"_, 209 comments)
| ChaitanyaSai wrote:
| Lovely article. The subjective nature of entropy and information
| immediately makes me think of the IIT theory (integrated
| information theory) of consciousness and its foundational
| futility. Information cannot be discussed without perspective.
| Someone has to define the states. A die have 6 states only to us
| humans. What about an ant that's likely to have the die land on
| it? Bringing the observer back into discussions of information is
| fascinating because it then begs the question: How is the
| observer put together? And how does a perspective, an I, emerge
| in a multi-trillion-cell entity? For those interested in this
| detour, you might like reading this and our book (mentioned in
| there)
|
| https://saigaddam.medium.com/consciousness-is-a-consensus-me...
| 3abiton wrote:
| For me CS with Physics BSc, it's always fascinating to still
| see how entropy is still sich a wild measure.
| tsoukase wrote:
| My perspective:
|
| 1) entropy is a mathematical concept. Physics apply it, like any
| other mathematical one
|
| 2) math entropy does not change, everything is reversible, as it
| is based on known quantities
|
| 3) entropy measures how far we are from perfectly knowing a
| system
|
| 4) logarithm is chosen to measure entropy because of its
| convenient properties, not because of any deeper law. It could be
| a sum, a product etc
|
| 5) the Second thermodynamic law is a tautology: "every system
| tends to higher entropy state because it is more common" becomes
| "the more common is the more common"
| currymj wrote:
| i think those convenient properties are the sign of some deeper
| law. you do want to work with the exponential and logarithm,
| same as in so many other places. you don't necessarily want
| some other generalized "entropy".
| openrisk wrote:
| Is there a specific name for the art and craft of presenting a
| topic online (as a web page) using a flow of text interspersed
| with interactive activities?
|
| Whatever the name of this approach, quantamagazine is definitely
| good at it!
| gyomu wrote:
| Some people have coined the term explorable
| explanation/explorables
|
| https://explorabl.es/
|
| https://en.wikipedia.org/wiki/Explorable_explanation
| openrisk wrote:
| 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? :-)
| TheSpiceIsLife wrote:
| Multimedia?
|
| https://en.m.wikipedia.org/wiki/Multimedia
|
| _Multimedia refers to the integration of multiple forms of
| content such as text, audio, images, video, and interactive
| elements into a single digital platform or application._
| openrisk wrote:
| Multimedia is fairly general, so it includes this but also
| much more.
|
| Including video in particular tends to highjack the
| experience (you switch mode), whereas interactive elements
| that you explore as you keep reading feel more integrated.
| johnea wrote:
| I'm pretty sure this is called "writing"
| inshard wrote:
| Fails to mention Heisenberg uncertainty, which in my opinion is a
| theoretical ceiling to this approach. Also it needs to account
| for cost of compute relative potential useful work from these
| quantum engines. If the energy cost of compute exceeds potential
| useful work, then it's still net negative (or useless work).
| Finally there's the question of hidden patterns and the spectrum
| of randomness. Some systems are more random than others. The
| potential for useful work within a reasonable energy cost of
| compute will decline when we travel down the spectrum of
| randomness. Systems which are at maximal Heisenberg uncertainty,
| I.e. particles are not entangled, and have no correlation with a
| superstructure of other entangled particles, will not hold any
| further improvement to knowledge and thus zero potential work.
| This is the ultimate entropy of the local and macro system.
| Probably also the cause of certain violation of conservation of
| energy principles, such as dark energy.
| daoboy wrote:
| The interactive graphic that tries to show entropy is subjective
| doesn't sit right for me.
|
| They fail to properly define the macrostate of the system under
| consideration, then show two different observed entropies for two
| different macrostates (Colors for Alice and Shapes for Bob).
|
| That doesn't show entropy is subjective, it shows that defining
| the system is subjective. The same two macrostates would still
| have the same entropy
| Serenade wrote:
| 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.
| markisus wrote:
| Maybe if you take Alice and Bob to be two separate alien
| species it could make more sense. Alice's species has no
| measurement devices capable of detecting Bob's version of
| entropy, and therefore Alice is not able to extract any useful
| work from Bob's system and vice versa. Therefore any objective
| definition of entropy needs to include the capabilities of the
| measurer. Which is just the same as what you were saying about
| macrostates.
| plank wrote:
| Interesting 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-perfect mirror (in ASCII art:
|
| [100%] --l-- [100-epsilon] ----L------ [100%]
|
| With L >> l. The 'whole universe' solution was simple (using
| standard quantum mechanics techniques), the 'lossy' 'small
| universe' was not. But they needed to be the same (physically).
| Thus using the exact solution for the 'complete' (l+L) universe
| and comparing it to possible 'small' (l) universe models in which
| some non-linear term accounted for loss. The connection between
| how a lossy system (in which entropy exists/is a driving 'force')
| and a losless system (in which everything is conserved) is thus
| not a new insight;-0
| mojomark wrote:
| 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?
| plank wrote:
| 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 ....
| behaves and a .... behaves.
| IIAOPSW wrote:
| The imperfect mirror means that epsilon% of the time the
| light goes through to a much larger "back room" whereas
| (1-epsilon)% of the time the light just reflects like normal.
| The point being made is that this is an extension of an
| ordinary ideal cavity to include unavoidable (but weak)
| interaction with the much larger system outside of it (aka
| the whole universe). It just so happens the much larger
| external system is also being modeled as a simple 1d cavity.
|
| In other words, entropy is equivalent to bits of information
| needed to specify the complete state of the system leaking
| outside of the confines of where those bits are being
| observed by an experiment (eg tunneling through an imperfect
| mirror).
|
| Entropy is an accounting tool to keep track of how many bits
| are missing, and how far this ignorance has percolated into
| what you can safely predict about the system.
| revskill wrote:
| So i am curiouys to know how did u invent new knowledge without
| computer science
| mike_ivanov wrote:
| Interesting. Could you share a link to your thesis?
| amelius wrote:
| Makes sense. If we knew the theory of everything and the initial
| conditions of the universe, then we could just compute the next
| episode of a series instead of streaming it.
| api wrote:
| Not necessarily. A theory of everything does not imply either
| the computability of a future state or determinism.
|
| Even if our ToE is deterministic the universe may be
| computationally irreducible, meaning it cannot be computed
| accurately at lower resolution in all cases. Note that such a
| universe could contain within it regions that are
| computationally reducible, just not the whole and not all
| regions.
|
| I would expect a ToE to give us knowable bounds to either
| determinism or computability. It should tell us what is
| precisely knowable or predictable and what isn't.
|
| Edit: to understand how a ToE could leave some things
| unknowable (but tell us what they are) consider the Hubble
| horizon. Light beyond it will never reach us making
| sufficiently distant things unknowable.
|
| Limits may be great. It means we can at least subjectively
| consider ourselves as having free will -- even with a
| deterministic theory it may be unknowable determinism. It's
| just like how the speed of light might be why we got to evolve
| before being bum rushed by aliens.
| FrustratedMonky wrote:
| "cannot be computed accurately at lower resolution"
|
| The Map is not the Territory.
|
| Our universe is the lowest resolution. So to compute the next
| instant in our Universe, would need another entire Universe.
|
| We could be the computation occurring.
| api wrote:
| That's what I meant, but perhaps did not describe well.
| FrustratedMonky wrote:
| Sorry, I was really just re-stating it, to see if I was
| grasping the point.
| j7ake wrote:
| Try it with a chaotic system like a double pendulum you'll see
| the dynamics are not predictive in the long term.
| adrianN wrote:
| Is that true? It was my understanding that chaotic systems
| (with a known initial state) could be predicted to arbitrary
| precision by throwing enough compute at the problem. Of
| course knowing the initial state is impossible in the real
| world, ,,enough" compute might not fit in the observable
| universe, and quantum mechanics contains true randomness...
| philipov wrote:
| Yes, chaotic systems can be simulated, and that's the
| _only_ way to find out what happens with them. The thing
| one can 't do is reduce them to a closed-form function of
| _x_ and compute their value for any point along their
| domain. The only thing we can do is inductively figure out
| the next _x_ from the current _x_.
| mitthrowaway2 wrote:
| The issue is more that simulations diverge exponentially
| with time from any nonzero error in the initial state.
| With perfect knowledge of the initial conditions and
| parameters you could simulate the system perfectly, but
| you'd also need to accumulate zero numerical error along
| the way.
|
| If you don't demand perfection, then in practice you can
| do pretty well for short times.
| wtcactus wrote:
| I remember that somewhere during my physics degree this idea of
| the article clicked with me.
|
| Entropy is just a simpler way of manifesting properties of a
| system that we didn't measure because it is too difficult (when I
| was still at classical physics level) or it's not possible to
| measure (when quantum mechanics became present in everything we
| learned).
|
| We use it because we can't measure the position and momentum of
| every particle (same goes for temperature) so we created theories
| on how a system with a particular entropy behaves, but it's just
| a clever way to work with aproximations.
|
| I find this idea fascinating.
| noiv wrote:
| What about the efficiency to remove entropy? Is there a threshold
| our combined efforts called science cannot surpass?
|
| Do we need Frank Herbert's spice to progress?
| Trasmatta wrote:
| A localized reduction of entropy will always result in an
| increase of entropy in the larger system.
|
| It doesn't matter how efficient your process is, the entropy of
| the surrounding system will ALWAYS increase as the result of
| the work needed to effect a localized reduction.
| ganzuul wrote:
| Unless the surrounding system is already at infinite entropy.
| ziofill wrote:
| Very nice article. There's an alternative way of thinking of the
| Gibbs paradox, which is to attach labels to the particles. This
| naturally makes them distinguishable and increases the total
| number of possible configurations, and with it the maximum value
| of the entropy.
| bee_rider wrote:
| Attaching labels to the particles would make them fundamentally
| different types of particles, right? So it doesn't seem that
| surprising that a system with different types of particles
| would be different.
| zV62drdTw6CM wrote:
| Happy to see the article being discussed here! I was responsible
| for the technical implementation of the interactives. If you are
| interested in the source code, you can find it here:
| https://github.com/jnsprnw/mip-entropy It's built in Svelte 5
| with Tailwind.
| azemetre wrote:
| May I ask why you chose svelte 5 rather than something else?
| I've noticed that a lot of "one off" interactions are being
| built with svelte nowadays. What are the benefits of using it?
| zV62drdTw6CM wrote:
| First, when I joined the project, it wasn't clear how it
| would be published. Svelte, which outputs compiled
| JavaScript, can fit into many CMS workflows that
| newspapers/publishers use.
|
| I believe Svelte was developed by Rich Harris at the NY Times
| for this very reason.
|
| We ended up using iFrames, so other frameworks like React
| could have been used.
|
| Second, Svelte is very well suited for these small
| interactives because it has built-in state, transitions, and
| reactivity with low overhead.
|
| Third, it was a personal choice, as I now do most of my work
| in Svelte.
| kqr wrote:
| > We ended up using iFrames, so other frameworks like React
| could have been used.
|
| Wait, wasn't one of the original selling points of React
| that it could be embedded piecewise to enhance
| interactivity of the parts of pages that needed it? It
| should certainly not need a separate page!
| gligorot wrote:
| It's a PITA to extract a stateful react component to a
| standalone piece of code that can be inserted in a random
| place (in another page, served via API etc.). Not sure
| about Svelte, but achieving this in React was
| unexpectedly hard/impossible in our use case.
| codethief wrote:
| It doesn't.
| johnea wrote:
| But consider the "monkeycide paradox". If we start a nuclear war,
| and kill every single primate on the planet, does the universe
| cease to exist? Does time start running in reverse? Maybe time
| would go back to before we nuked everyone out of existence, and
| life would be like one of those endless time loop anime? Will
| matter start spewing out of black holes instead of going in
| because there was no monkey there to watch it? Would it be enough
| if a dog observed the universe? (they're "like our family" after
| all) or a squid? What about a yeast cell?
|
| Obviously this is hyperbole 8-) but I think the point is clear.
| If anyone really believes that the existence of primate life on
| our little planet "observing the universe" is what makes all
| physical processes advance, they have some serious issues of
| overcharged ego.
|
| Of course a theory doesn't have to be completely correct to be
| useful. Old ideas of heat as a fluid have been supplanted, but
| they still helped design working systems in their time. Modern
| ideas of quantum mechanics, as incomplete as they are, still
| model a concept of "tunneling" that's sufficiently accurate to
| make semiconductors work.
|
| Or, you can just run with the Rovelli quote from the article:
| "What they're telling me is bullshit" 8-)
| shorefire wrote:
| For the longest time I had no real intuition of what entropy
| actually represented. This veritasium video explained it in a way
| that finally clicked for me:
| https://www.youtube.com/watch?v=DxL2HoqLbyA
| TexanFeller wrote:
| Entropy 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 and books about quantum
| information and calculating the entropy of black holes which led
| to a lot of wild new hypotheses.
|
| Stephen Wolfram gave a long talk about the history of the concept
| of entropy which was pretty good:
| https://www.youtube.com/live/ocOHxPs1LQ0?si=zvQNsj_FEGbTX2R3
| Jerrrry wrote:
| Computers are finite ergo the largest number any computer can
| compute is all ones in binary.
|
| That's it's Busy Beaver number, but think how easy all ones in
| binary is to compress from an information theory standpoint.
|
| So the most entrophic state would be the one state requiring the
| most compression.
| kayo_20211030 wrote:
| Why has Quanta degenerated into a mad combination of ineffective
| science communication and breathless, and slightly envious
| references to yoga retreats in the North of England. It's become
| a lifestyle magazine for the self-important, science-adjacent
| middlebrows. Most obviously, it's nerd-sniping for HN.
|
| And before you _instinctively_ (it will be instinctive) downvote
| me to oblivion, please read the piece and assure yourself that
| it's not truly a piece of rote trash.
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