Entropy: A little understood concept in physics [video] • Hacker News Board

Re: Entropy: A little understood concept in physics [video]

#141

Post by kergonath » Sun, Jul 02, 2023, 10:37 PM UTC

dekken_ wrote: post #95

credit_guy wrote: post #51

Earlier quoted context omitted.

The "heat death" of the universe is a concept that deserves to die. The second principle of thermodynamics is true only if you ignore gravity. In the presence of gravity, systems tend to go towards lower entropy, just see how a planetary system can form out of a gas cloud.

I think of it as a death cult. Thinking we know all that there is to know about the universe to the point where we can declare with 100% certainty that any particular thing will happen is not scientific.

Really? We are far from really understanding gravity, but I can very confidently tell you that if I kick a ball its trajectory will be a parabola (roughly, as a first order approximation and ignoring things like friction, which we can also calculate to a decent approximation). We can say where it will fall and give some confidence interval depending on the conditions and such. There is nothing unscientific about it.

Thermodynamics is not magic. In the same way that we can predict the evolution of climate without knowing where every single cloud will be, we can make statements about the evolution of large systems even though our knowledge of their state is imperfect. Again, nothing unscientific about it.

Re: Entropy: A little understood concept in physics [video]

#142

Post by kergonath » Sun, Jul 02, 2023, 10:40 PM UTC

gorhill wrote: post #53

hilbert42 wrote: post #7

That's an excellent overall summary as he covers almost every aspect of the subject albeit in brief. It would be good if he produced a second video dealing with the low entropy of incoming energy from the sun and the higher entropy of radiated energy from earth and relate that to global warming. In all the debate over global warming little is talked about why say CO2 and other greenhouse gasses increase the earth's t…

My understanding: Global warming occurs because the previous equilibrium between incoming and outgoing energy has been broken by changes in the composition of the atmosphere. So until we reach a new equilibrium long after the atmosphere composition ceases to change, the outgoing energy will be less than the incoming energy.

That’s exactly it. Except that equilibrium will never be reached, it’s more like tending towards a steady state.

Re: Entropy: A little understood concept in physics [video]

#143

Post by kergonath » Sun, Jul 02, 2023, 10:48 PM UTC

manojlds wrote: post #14

4ad wrote: post #2

I hate Veritasium's clickbait, and I think most of his videos are very poor, but this one is the exception. It's very well put together. The first ten minutes of the video is exactly how I introduce entropy to people. Of course I can't give him a pass on how crass it was telling that women he has a PhD in physics (he does not). The video would have been so much better without that two seconds of footage...

Most of his videos are GOOD, come on!

The problem is that on a given specific subject you can never be sure whether he’s exaggerating or misrepresenting things. Just this makes watching him a waste of time, because then you need to spend at least twice the time to fact check him. A bit like asking a question to ChatGPT. At least Wikipedia provides you links to proper sources.

Re: Entropy: A little understood concept in physics [video]

#144

Post by dekken_ » Sun, Jul 02, 2023, 11:16 PM UTC

kergonath wrote: post #141

dekken_ wrote: post #95

Earlier quoted context omitted.

I think of it as a death cult. Thinking we know all that there is to know about the universe to the point where we can declare with 100% certainty that any particular thing will happen is not scientific.

Really? We are far from really understanding gravity, but I can very confidently tell you that if I kick a ball its trajectory will be a parabola (roughly, as a first order approximation and ignoring things like friction, which we can also calculate to a decent approximation). We can say where it will fall and give some confidence interval depending on the conditions and such. There is nothing unscientific about it.…

If you read what I said, I said nothing about predictions. Predictions are fine. Stating things as certainties, not so much.

Re: Entropy: A little understood concept in physics [video]

#145

Post by staunton » Sun, Jul 02, 2023, 11:24 PM UTC

kergonath wrote: post #132

javajosh wrote: post #68

Earlier quoted context omitted.

yes, there are lots of quantitative details. I wanted to emphasize the key qualitative concept, from which the others can derive. In a similar way you can derive all of special relativity, and approach an intuition about the strangeness of spacetime, starting with only two ideas: the laws of physics are the same in all reference frames; the speed of light is constant. I prefer to start there and derive e.g. Lorentz f…

> starting with only two ideas: the laws of physics are the same in all reference frames; the speed of light is constant. Isn’t this redundant, though? The constant velocity for light in a vacuum comes directly from the laws of (classical) electromagnetism in the form of Maxwell’s equations. So “the laws of Physics are the same in all reference frames” implies “Maxwell’s equations are valid in all reference frames”,…

> So “the laws of Physics are the same in all reference frames” implies “Maxwell’s equations are valid in all reference frames”, which in turn implies “the velocity of light in vacuum is the same in all reference frames”

From the point of view of physicists before Einstein, this forces you to decide between Newtonian physics and Maxwell's theory, because the reference frames that are "equivalent" are irreconcilably different for those. The "irreconcilable" part is subtle and not obvious. Maxwell's theory "won", but it was the newer theory while Newton's was very well established. The contemporary physicists' efforts to reconcile the two using an "ether" were completely reasonable from their point of view. (And actually, you can't even completely exclude the existence of an ether, as some ether theories are consistent with the standard model to a reasonably high accuracy. What kills them is Occam's razor)

Re: Entropy: A little understood concept in physics [video]

#146

Post by kergonath » Sun, Jul 02, 2023, 11:36 PM UTC

dekken_ wrote: post #144

kergonath wrote: post #141

Earlier quoted context omitted.

Really? We are far from really understanding gravity, but I can very confidently tell you that if I kick a ball its trajectory will be a parabola (roughly, as a first order approximation and ignoring things like friction, which we can also calculate to a decent approximation). We can say where it will fall and give some confidence interval depending on the conditions and such. There is nothing unscientific about it.…

If you read what I said, I said nothing about predictions. Predictions are fine. Stating things as certainties, not so much.

It’s not a very useful point. Again, I can say with absolute certainty that a ball will follow a parabola and that an ice cube in a glass will melt.

Re: Entropy: A little understood concept in physics [video]

#147

Post by contravariant » Sun, Jul 02, 2023, 11:38 PM UTC

javajosh wrote: post #38

Entropy only made sense when I learned it from the perspective of statistical thermodynamics. It's a very programmerly understanding, IMHO, and it's quite intuitive. EXCEPT that the language used is ridiculous: grand canonical ensemble indeed! Anyway, the idea that a system can be in some number of specific states, and that equilibrium is that unique situation where the number of possible specific states is at its ma…

That intuition is still a bit shallow though. I don't mean that in a bad way, some intuition is better than none at all. However if you start to dig you'll find out the terminology goes out of wack.

Note that you're describing equilibrium as a unique situation where the number of possible states is at a maximum. Now how can a situation be unique if it has the maximum number of possible states? Clearly the situation is as far from unique as it can be.

To resolve the contradiction requires distinguishing between features of the probability distribution and features of a random sample (i.e. a possible state) and also needs an explanation how it even makes sense to view a deterministic physical system (leave quantum mechanics for now) as a random variable.

The theory that links everything together is ergodic theory, which has a couple of handy theorems. One is that for a certain kind of dynamical system the average over time and the average over the 'possible states' agree. Such a system can also be assigned an entropy. It even suggests that generally a system will be found around states with a probability close to 2^-entropy (this is not absolutely always true ..but close enough for physicists)

Now what does such a system look like? Well we need a state space (easy) and a measure on it which is constant as the system evolves (i.e. we can pick a region in the state space, evolve it and its volume will stay constant). The last part is tricky, but as it turns out classical mechanics gives us the phase space and the canonical volume on it (basically the standard notion of volume) which fit the bill. This gives a probability distribution on the state space and an entropy equal to log(volume in phase space), which matches the definitions in statistical physics but also gives a solid foundation for some of the seemingly arbitrary choices.

So there you have it, that's why a system can have a probability distribution attached to it, despite being deterministic, why 'high entropy states' are common, and why physical systems have a uniform distribution (and therefore an entropy which is the log of the number of states).

This also explains physicists got away with using a uniform distribution without worrying about which variables they used. By pure 'coincidence' the standard choice of variables that physicists use have this incredibly nice property that makes everything work out. I'm not sure if this is too well known so it might be worth abusing this to 'prove' a perpetuum mobile is possible to stop people using uniform distributions without due deliberation.

Re: Entropy: A little understood concept in physics [video]

#148

Post by Lichtso » Sun, Jul 02, 2023, 11:43 PM UTC

ithkuil wrote: post #130

Lichtso wrote: post #119

Earlier quoted context omitted.

I think you can very well extract work from having a membrane and selectively let one substance mix into the other but not the other in the first [0]. It is called Osmosis [1]. [0]: https://en.wikipedia.org/wiki/Semipermeable_membrane [1]: https://en.wikipedia.org/wiki/Osmosis

I guess what's confusing me in this scenario is that we're not saying that the two halves of the cylinder contain particles with different properties (e.g. different velocities) but only that we can "tell them apart" as if they were coloured differently, but otherwise behaving in exactly the same way. The former scenario is famously the setting for Maxwell's daemon. I was assuming this scenario is something else. I'm…

> only that we can "tell them apart"

That is irrelevant, we don't need to be able to tell them apart, the membrane needs to be able to. Besides that, they can be completely identical.

> I'm confused because on one hand I can see that it requires work to reorder the particles once they have been shuffled around. On the other hand I don't see how one could extract work while they get shuffled around if they all have the same momenta.

In the illustration with the cylinder from Wikipedia you can see that the level of the one fluid (which the other fluid is selected into) rises. It performs work against gravity and builds up potential energy / increases the pressure. You can harvest that.

> The former scenario is famously the setting for Maxwell's daemon. I was assuming this scenario is something else.

In Maxwell's daemon you start with a substance which is already mixed and separate it into its components. That requires work and is the exact opposite of what is happening here. In fact it is called reverse Osmosis [0]. Osmosis gives you pressure which you can harvest, so reverse osmosis needs pressure back to operate. That completes the cycle.

[0] https://en.wikipedia.org/wiki/Reverse_osmosis

Re: Entropy: A little understood concept in physics [video]

#149

Post by dekken_ » Sun, Jul 02, 2023, 11:46 PM UTC

kergonath wrote: post #146

dekken_ wrote: post #144

Earlier quoted context omitted.

If you read what I said, I said nothing about predictions. Predictions are fine. Stating things as certainties, not so much.

It’s not a very useful point. Again, I can say with absolute certainty that a ball will follow a parabola and that an ice cube in a glass will melt.

You can say what you like. Science is not about certainties. You can only control experiments to a particular degree and have no control of confounding factors which might interfere with your experiments. Do you really want to compare the totality of all universal processes to such trivial examples? I find it absurd.

Re: Entropy: A little understood concept in physics [video]

#150

Post by contravariant » Sun, Jul 02, 2023, 11:49 PM UTC

Balgair wrote: post #87

semi-extrinsic wrote: post #75

Earlier quoted context omitted.

No. Entropy can be used to explain the direction of time, as a kind of symmetry breaking of all the microscopic laws that are symmetric in time. But it does not say anything about the "speed of time". Relativity does tell us the speed of time - it's the speed of light.

To be suuuuuuper pedantic here: Relativity tells us that time is a dimension, one that is a bit unique. In that it has a constant attached to it. So, the 3 dimensions you're used to are just normal, they have no constants. (x,y,z) Meters of x are meters of z and meters of y. Relativity (and I'm really simplifying a lot by just saying 'relativity'), well relativity comes along as says that time is also a dimension, ju…

That constant is immaterial, it's just the conversion constant between two different units. It just turns out that for the units we're used the time unit is a lot larger than the space unit.

The real difference has to do with the metric on spacetime, but that gets tricky to explain. Suffice it to say that a rotation involving 2 of the spatial dimensions, and the equivalent of a rotation for time and a spatial dimension are quite different.