alt Hacker NewsI don't get it.
To me, entropy is not a physical thing, but a measure of our imperfect knowledge about a system. We can only measure the bulk properties of matter, so we've made up a number to quantify how imperfect the bulk properties describe the true microscopic state of the system. But if we had the ability to zoom into the microscopic level, entropy would make no sense.
So I don't see how gravity or any other fundamental physical interaction could follow from entropy. It's a made-up thing by humans.
Replies
Good question. You are absolutely right that entropy is always fundamentally a way to describe are our lack of perfect knowledge of the system [0].
Nevertheless there is a distinct "reality" to entropic forces, in the sense that it is something that can actually be measured in the lab. If you are not convinced then you can look at:
https://en.wikipedia.org/wiki/Entropic_force
and in particular the example that is always used in a first class on this topic:
https://en.wikipedia.org/wiki/Ideal_chain
So when viewed in this way entropy is not just a "made-up thing", but an effective way to describe observed phenomena. That makes it useful for effective but not fundamental laws of physics. And indeed the wiki page says that entropic forces are an "emergent phenomenon".
Therefore, any reasonable person believing in entropic gravity will automatically call gravity an emergent phenomenon. They must conclude that there is a new, fundamental theory of gravity to be found, and this theory will "restore" the probabilistic interpretation of entropy.
The reason entropic gravity is exciting and exotic is that many other searches for this fundamental theory start with a (more or less) direct quantization of gravity, much like one can quantize classical mechanics to arrive at quantum mechanics. Entropic gravity posits that this is the wrong approach, in the same way that one does not try to directly quantize the ideal gas law.
[0] Let me stress this: there is no entropy without probability distributions, even in physics. Anyone claiming otherwise is stuck in the nineteenth century, perhaps because they learned only thermodynamics but not statistical mechanics.
Entropy isn't a function of imperfect knowledge. It's a function of the possible states of a system and their probability distributions. Quantum mechanics assumes, as the name implies, that reality at the smallest level can be quantised, so it's completely appropriate to apply entropy to describing things at the microscopic scale.
The way we use the word 'entropy' in computer science is different from how its used in physics. Here is a really good explanation in a great talk! https://youtu.be/Kr_S-vXdu_I?si=1uNF2g9OhtlMAS-G&t=2213
Entropy is certainly a physical “thing”, in the sense that it affects the development of the system. You can equally well apply your argument that it isn’t a physical thing because it doesn’t exist on a microscopic scale to temperature. Temperature doesn’t exist when you zoom in on single particles either.
There’s no reason to involve our knowledge of the system. Entropy is a measure of the number of possible micro states for a given system, and that number exists independently of us.
Something to consider is that entropy has units of measure. Why would a purely philosophical concept be given units of Joules per Kelvin?
I'm only reminded about this because, though I'm a physicist, I've been out of school for more than 3 decades, and decided that I owed myself a refresher on thermodynamics. This coincided with someone on HN recommending David Tong's textbook-quality lecture notes:
https://www.damtp.cam.ac.uk/user/tong/statphys.html
I think at least the first few pages are readable to a layperson, and address the issue of our imperfect knowledge of the precise configuration of a system containing, say, 1e23 particles.
But if we knew all of those relationships, the system would still have entropy.
This comment thread is exhibit N-thousand that "nobody really understands entropy". My basic understanding goes like this:
In thermodynamics, you describe a system with a massive number of microstates/dynamical variable according to 2-3 measurable macrostate variables. (E.g. `N, V, E` for an ideal gas.)
If you work out the dynamics of those macrostate variables, you will find that (to first order, i.e. in the thermodynamic limit) they depend only on the form of the entropy function of the system `S(E, N, V)`, e.g. Maxwell relations.
If you measured a few more macrostate variables, e.g. the variance in energy `sigma^2(E)` and the center of mass `m`, or anything else, you would be able to write new dynamical relations that depend on a new "entropy" `S(E, N, V, sigma^2(E), m)`. You could add 1000 more variables, or a million—e.g every pixel of an image—basically up until the point where the thermodynamic limit assumptions cease to hold.
The `S` function you'd get will capture the contribution of every-variable-you're-marginalizing-over to the relationships between the remaining variables. This is the sense in which it represents "imperfect knowledge". Entropy dependence arises mathematically in the relationships between macrostate variables—they can only couple to each by way of this function which summarizes all the variables you don't know/aren't measuring/aren't specifying.
That this works is rather surprising! It depends on some assumptions which I cannot remember (on convexity and factorizeabiltiy and things like that), but which apply to most or maybe all equilibrium thermodynamic-scale systems.
For the ideal gas, say, the classical-mechanics, classical-probability, and quantum-mechanic descriptions of the system all reduce to the same `S(N, V, E)` function under this enormous marginalization—the most "zoomed-out" view of their underlying manifold structures turns out to be identical, which is why they all describe the same thing. (It is surprising that seemingly obvious things like the size of the particles would not matter. It turns out that the asymptotic dynamics depend only on the information theory of the available "slots" that energy can go into.)
All of this appears as an artifact of the limiting procedure in the thermodynamic limit, but it may be the case that it's more "real" than this—some hard-to-characterize quantum decoherence may lead to this being not only true in an extraordinarily sharp first-order limit, but actually physically true. I haven't kept up with the field.
No idea how to apply this to gravity though.
Entropy can be defined as the logarithm of the number of microstates in a macrostate. Since transition between microstates is reversible, and therefore one-to-one (can't converge on any particular microstate, can't go in cycles, have to be something like a random walk) we're more likely to end up in a macrostate that holds a larger number of microstates.
For example, there are many more ways your headphone cord can be tangled than untangled, so when you pull it out of your pocket, and it's in a random state, then it's very likely to be tangled.
If entropy causes gravity, that means there are more somehow more microstates with all the mass in the universe smooshed together than microstates with all the mass in the universe spread apart.
Even if we take that view, gravity is still basically a similar case. What we call "gravity" is really an apparent force, that isnt a force at all when seen from a full 4d pov.
Imagine sitting outside the whole universe from t=0,t=end and observing one whole block. Then the trajectories of matter, unaffected by any force at all, are those we call gravitational.
From this pov, it makes a lot more sense to connect gravity with some orderly or disorderly features of these trajectories.
Inertia, on this view, is just a kind of hysteresis the matter distribution of the universe has -- ie., a kind of remembered deformation that persists as the universe evolves.
If you want to only have one possible past (i.e. can't destroy information) then when you end up in one branch of quantum state you need to "store" enough information to separate you form other branches and you really do need to have multiple possible microstates to differentiate them. If you look post-factum obviously you did end up in a specific state, but statistics do their work otherwise.
For years I thought the same for entropy. But now I believe it is fundamentaly impossible to know each micro state, irrespective our tools and methods. And this happens like and due to Heisenberg's uncertainty principle.
So all events are irreversible and entropy is always increasing. Perfection is only theoretical.
It sounds like you're talking about information entropy which to my understanding is analogue to but not the same as entropy in physics?
> It's a made-up thing by humans.
All of physics is made up by humans.
Your perspective is incorrect.
Physical entropy governs real physical processes. Simple example: why ice melts in a warm room. More subtle example: why cords get tangled up over time.
Our measures of entropy can be seen as a way of summarizing, at a macro level, the state of a system such as that warm room containing ice, or a tangle of cables, but the measure is not the same thing as the phenomenon it describes.
Boltzmann's approach to entropy makes the second law pretty intuitive: there are far more ways for a system to be disordered than ordered, so over time it tends towards higher entropy. That’s why ice melts in a warm room.