Great article, I had hoped it would also cover locally anti-entropic processes. We do see liquids turn into regular solids after all: https://www.youtube.com/watch?v=caGX6PoVneU
Profound and enlightening, thanks!
Entropy explained, with sheep (2016)
31–40 of 107 posts
Re: Entropy explained, with sheep (2016)
#32As a physicist, this is such a great explanation that's actually correct for a change. Entropy must be one of the if not the most misunderstood physical concept out there (along with Planck metrics like Planck energy or Planck length). Entropy is commonly used and written about by so many people that clearly lack the understanding of it that this blog post is a refreshing change.
The author is a physicist as well. https://mobile.twitter.com/aatishb
Yeah, it showed in the way he explained things.
Re: Entropy explained, with sheep (2016)
#33So one thing I've never understood is how you can "count" microstates, or bits required to describe them, when the relevant physical parameters all seem to be real numbers. For instance, a gas of N atoms is described by 6N real numbers (3d position and velocity) regardless of how hot it is. The article talks about quanta of energy, but that seems like a simplification at best: a given interaction might be quantized,…
This is an excellent, and puzzling, question! Let me try to provide some insight into how physicists think about such paradoxes, by addressing the specific example you mention, of the presumed uncountable infinity of different possible photon energies in a finite range of frequencies. In the case of blackbody radiation, when physicists analyze the set of possible photon energies more carefully, they find that there is really only an infinite number of different possible photon energies (for a finite range of frequencies) if the volume of space containing the photons is infinite. In any finite volume of space, if we allow ourselves to place boundary conditions on the electromagnetic fields at the edges of that volume (for example, suppose we think of our volume as a cube with mirrored walls), we find that there are only a finite number of oscillating modes of the electromagnetic field in any finite range of frequency. In the case of a cube, there is a very lowest frequency of radiation whose wavelength will allow it to form a standing wave in the box, and all the other allowed modes are multiples of that lowest frequency. So the density of possible photon states per unit of frequency is actually proportional to the volume of space we allow to hold the photons. (By the way, this is also precisely related to the quantum complementarity of uncertainty between momentum and position. To confine a photon to a volume of space, the uncertainty in its momentum must be the same order as that carried by the lowest frequency standing waves which would be compatible with the container.)
Re: Entropy explained, with sheep (2016)
#34Earlier quoted context omitted.
No. In a forever-existing universe, as you go back in time, entropy could asymtotically approach zero (or some other limit) without ever actually reaching it. It doesn't have to be zero at some point in the past. In fact, if it is zero at some point in the past, then what happened before that? Did it not increase before that point, or was it less than zero before that point?
I get your point about the asymptote, but I should have clarified: I was synthesizing two rules, "entropy always increases" and "matter cannot be created or destroyed" Beyond that, metaphysically, how does something increase without having an origin? "Everything just always was" seems to conveniently handwave away a very important line of inquiry. This line of inquiry might be uncomfortably close to religious thought…
>"Everything just always was"
Or it wasn't and came into existence with a 'big bang'. So how did it come into existence? There's no scientific or religious answer for it. You'll still be skirting the question with the old 'who made the gods' problem. I know what you're getting at and trying to conflate science with religion. Spoilers here: Scientists don't know these answers and just because we don't know doesn't mean the thousands of denominations of thousands of gods of thousands of religions of thousands of years has a true answer either.
>we are supposed to be satisfied
No one said you should be satisfied by it. That's what's good about science, you're expected to not be satisfied and to survey and question, it's not infallible nor claim omniscience.
>God manipulates the minds of top scientists so that they do not definitively prove his existence, which would ruin the point of his simulation. Each time they get close, he finds an idiosyncratic way to make them forget about it or dismiss the idea.
And of course it's the gods, or all created thereof, who are behind helping or hurting belief in gods. Ask a god believer and it's always god's plan.
Re: Entropy explained, with sheep (2016)
#35Earlier quoted context omitted.
This is true! I oversimplified a bit, because it's much easier to concretely discuss that scenario and its consequences, and it's more important from a philosophical perspective. Just like it's much easier to catch ice cubes forming on film by rewinding a tape than to run the camera waiting for spontaneous entropy decrease. Nonetheless, if the entropy of the whole universe were to consistently decrease for a sufficie…
I think you're priviledging microstates. There are plenty of entropy decreases that are possible without the ice cube reforming. They're (extremely) unlikely of course, but somewhat less unlikely than the new, singular microstate you're asserting is somehow "less of a coincidence". It's vastly more likely (for example) that 1% of the particle velocities reverse than all of them doing so, and that could (depending ...…
Ah, I think we're just miscommunicating. I'm not saying that local time-reversal is more likely to happen than other kinds of entropy decrease; I'm not saying that a system is more likely to retrace its past than to enter a different state of low-entropy. Spontaneous local entropy decreases happen all the time, of course (but are overpowered by entropy increases), and the majority of those won't be exact reversals.
And I'm not saying that locking yourself in a refrigerator will allow you to predict the future!
I'm mainly picking on time reversal because it's easier to concretely communicate and reason about as an example of how a system behaves under entropy decrease, and is philosophically important because depending on one's definition of the sign of 't', you could actually view our universe as undergoing entropy decrease right now. But redefining the arrow of time won't let you form memories of the future -- you'll have memories of the lower entropy universe, regardless of which way you call "the future".
The deeper point is, that's not a coincidence and doesn't depend on entropy decreases specifically being tied to time reversal. If we lived in a universe where the second law were somehow different and entropy "statistically always" decreased with time the way it "statistically always" increases now, then... well, it's hard to reason about such a universe because either it has very different laws than our own, or it's just our own universe with exactly that arbitrary t -t transformation. But in most logically-consistent interpretations of that scenario, that universe's version of Landauer's principle would also flip the arrow of time perceived by its local inhabitants, and they'd end up with only memories of their "future".
If I'm not quite making my point clear, try asking yourself why, if the laws of the universe are time reversible, why can't you remember the future the way you can remember the past? This gets into the mechanics of how memory works (as a general concept, not human memory specifically; it's easier to think about computer memory).
(Edit): Why isn't this a trivial point? Well, if you imagine a universe composed of a chain of of "linked states" that goes from (low entropy) - (high entropy) - (low entropy), you'd find that any inhabitants of that universe would perceive a universe with directional time that progresses in the entropy gradient, even though that universe has no consistent directional time.
Re: Entropy explained, with sheep (2016)
#36Earlier quoted context omitted.
I get your point about the asymptote, but I should have clarified: I was synthesizing two rules, "entropy always increases" and "matter cannot be created or destroyed" Beyond that, metaphysically, how does something increase without having an origin? "Everything just always was" seems to conveniently handwave away a very important line of inquiry. This line of inquiry might be uncomfortably close to religious thought…
>"Everything just always was" Or it wasn't and came into existence with a 'big bang'. So how did it come into existence? There's no scientific or religious answer for it. You'll still be skirting the question with the old 'who made the gods' problem. I know what you're getting at and trying to conflate science with religion. Spoilers here: Scientists don't know these answers and just because we don't know doesn't mea…
[deleted]
Re: Entropy explained, with sheep (2016)
#37So one thing I've never understood is how you can "count" microstates, or bits required to describe them, when the relevant physical parameters all seem to be real numbers. For instance, a gas of N atoms is described by 6N real numbers (3d position and velocity) regardless of how hot it is. The article talks about quanta of energy, but that seems like a simplification at best: a given interaction might be quantized,…
[deleted]
Re: Entropy explained, with sheep (2016)
#38excuse my naivete, but do black holes help reduce entropy by capturing/engulfing things around them? Is that the cycle how universe keeps creating and recreating itself?
Re: Entropy explained, with sheep (2016)
#39Earlier quoted context omitted.
Your reasoning is strange. Actually, higher entropy is what we may call "of lower complexity" requiring ever-shorter description length.
A higher entropy state has a longer description length. For example, let's say I have a magic electron microscope that can scan and record the exact position and velocity of each particle in some 1-cubic-micron volume, to within Heisenberg uncertainty limits and some finite digitization precision. If my sample is a 1-cubic-micron volume of flawless monocrystalline silicon at 0 Kelvin, I can 'zip' my recording and tra…
Your example of monocrystalline silicon at (almost) 0 Kelvin has actually higher entropy than your example of saltwater.
Re: Entropy explained, with sheep (2016)
#40This was really great. It's how I was taught entropy at college (biophysics and molecular biology) though without the sheep. "Statistical Mechanics" was the name our professor used. The only tiny change I'd like to make is to add a line or two near the end, something along the following lines: There's a lot fewer ways to arrange water molecules so that they form an ice cube than there are to arrange them as a liquid.…
[deleted]