There are multiple different definitions of Entropy and usage. Boltzmann's and Gibbs's physical entropy is not strictly equivalent to information entropy of Shannon whereby legend says von Neumann told Shannon that call 'information capacity of a channel' entropy, as nobody knows it. A great reads from books of Arieh Ben-Naim is highly recommended.
Entropy: A little understood concept in physics [video]
151–160 of 178 posts
Re: Entropy: A little understood concept in physics [video]
#152Earlier quoted context omitted.
> 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 d…
I know. What I am saying is that the laws of physics being the same implies the velocity of light being the same. Of course it conflicts with Newton’s laws and Galilean transformations when changing reference frames. But what he demonstrated was that the apparent conflict could be solved in a logically consistent way, once you do away with the concept of universal time. From that point, Newton’s laws do not need to be invariant, because they were demonstrably incomplete, in contrast to Maxwell’s, which were verified as far as they could be with the experimental setups of the time.
Sure, postulating the existence of the ether was reasonable in a way at one point in time, I am not saying otherwise. But by 1905 it was on very shaky grounds, with no experimental result to support it. Saying that the theory can be tweaked to reproduce reality is not very useful: all theories can. What a theory needs to be verified is to predict things that the other established theories do not. And on that front, the ether theory is about as powerful as my pet theory that elementary particles are moved by tiny demons that we cannot see (I would make a joke about string theory but it’s way more serious than the ether one).
Re: Entropy: A little understood concept in physics [video]
#153I think the most unintuitive even unsettling aspect of entropy is that the entropy of black holes is proportional to their surface area, not their volume [0]. That is only briefly mentioned in the video and not discussed any further. [0] https://en.wikipedia.org/wiki/Holographic_principle#Black_ho...
To be fair black holes are just weird so that's not too damning on its own.
What makes it weird is that black holes must necessarily* have the maximum amount of entropy for a specific volume. So not only the entropy of a black hole is proportional to its surface area, but the entropy of some volume of space can not grow beyond that. In particular entropy cannot be proportional to volume without limit, the density must be 0 on average for a big enough region.
*: According to some people anyway.
Re: Entropy: A little understood concept in physics [video]
#154Earlier 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”,…
>That’s how Einstein himself explained it
Yes, I think we're violently agreeing then. The original 1905 paper is extremely readable.
Re: Entropy: A little understood concept in physics [video]
#155Earlier quoted context omitted.
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.
You did not qualify the complexity below which it is acceptable to be certain of something so this is unlikely to be productive. You said that certainty was impossible and I gave you examples of certain things. Besides, both a ball and a glass of water are insanely complex systems. I am not sure we have the same definition of science, to be honest.
Re: Entropy: A little understood concept in physics [video]
#156I loved this one too and I believe it is an excelent followup: I don't believe the 2nd law of thermodynamics. (The most uplifting video I'll ever make.) @ https://www.youtube.com/watch?v=89Mq6gmPo0s
Re: Entropy: A little understood concept in physics [video]
#157In the video, Derek says the sun provides "a more useful form of energy than earth gives back because it is more concentrated". I would argue this is not technically true. What makes the energy from the sun useful is that it emits blackbody radiation, and this has photons that are more energetic than heat (IR) radiated back into space. Light with wavelengths between 400-700 nm are used by plants for photosynthesis. Heat radiated back into the atmosphere is mostly in the IR spectrum. This is both quantitatively and qualitatively important due to the quantized properties of electrons orbiting nuclii (IR wavelengths cannot readily to elevate electrons into a greater energy state).
Re: Entropy: A little understood concept in physics [video]
#158Earlier 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…
Historically this caused a lot of confusion, so you aren't the only one. You may find E. Jaynes' classic paper on the Gibbs mixing paradox helpful, especially from page 7 onwards:
Re: Entropy: A little understood concept in physics [video]
#159Earlier quoted context omitted.
This is eye opening. Thanks a lot for this comment and linking the pdf. I loved E.T. Jayne's Probability Theory book, so looking forward to reading this pdf too.
There are a few chapters of an unpublished book on thermodynamics here: https://bayes.wustl.edu/etj/thermo.html This article is also interesting: "THE EVOLUTION OF CARNOT'S PRINCIPLE" https://bayes.wustl.edu/etj/articles/ccarnot.pdf Building on these ideas, the first five chapters of this (draft of a) book from Ariel Caticha are quite readable: https://www.arielcaticha.com/my-book-entropic-physics
I want to add this quote that I was originally looking for, and at last found in Jaynes's "Where do we Stand on Maximum Entropy?" (page 237 of http://ndl.ethernet.edu.et/bitstream/123456789/33178/1/R.%20...)
---
In the Summer of 1951, Professor G. Uhlenbeck gave his
famous course on Statistical Mechanics at Stanford, and fol-
lowing the lectures I had many conversations with him, over
lunch, about the foundations of the theory and current progress
on it. I had expected, naively, that he would be enthusiastic
about Shannon's work, and as eager as I to exploit these ideas
for Statistical Mechanics. Instead, he seemed to think that
the basic problems were, in principle, solved by the then
recent work of Bogoliubov and van Hove (which seemed to me
filling in details, but not touching at all on the real basic
problems)--and adamantly rejected all suggestions that there
is any connection between entropy and information.
His initial reaction to my remarks was exactly like my
initial reaction to Shannon's: "Whose information?" His
position, which I never succeeded in shaking one iota, was:
"Entropy cannot be a measure of 'amount of ignorance,' because
different people have different amounts of ignorance; entropy
is a definite physical quantity that can be measured in the
laboratory with thermometers and calorimeters." Although the
answer to this was clear in my own mind, I was unable, at the
time, to convey that answer to him. In trying to explain a
new idea I was, like Maxwell, groping for words because the
way of thinking and habits of language then current had to be
broken before I could express a different way of thinking.
Today, it seems trivially easy to answer Professor Uhlen-
beck's objection as follows: "Certainly, different people
have different amounts of ignorance. The entropy of a thermo-
dynamic system is a measure of the degree of ignorance of a
person whose sole knowledge about its microstate consists of
the values of the macroscopic quantities Xi which define its
thermodynamic state. This is a completely 'objective' quantity
in the sense that it is a function only of the Xi, and does not
depend on anybody's personality. There is then no reason why
it cannot be measured in the laboratory."Re: Entropy: A little understood concept in physics [video]
#160Earlier quoted context omitted.
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 dimensi…
Is it because of th minus sign?