All of Physics in 9 Lines
motionmountain.net
motionmountain.net
For example, the derivation of General Relativity (quite a significant part of physics!) apparently follows from the author's own "Maximum Force" theory in Item (3).
ps. previously discussed:
That said, there IS a valid point to be made to highlight the inordinate success of modern physical theories. It's annoying when the only physics news is sensationalist psuedo-science "heresy" from those who don't even know what they're rebelling against. Sean Carrol does a great job of making this argument in an hour-long video "Quantum Field Theory and the Limits of Knowledge - Sean Carroll - 12/7/22": https://www.youtube.com/watch?v=REITVohWOO0
He makes a much more precise, and I think powerful, argument that we actually know quite a lot.
Do not try to learn anything from the submitted article, it promotes a, shall we say, "non-traditional" view of physics that is unlikely to be helpful.
https://arxiv.org/abs/2307.09914
It appears to be an example of argument by italics. I’m not convinced that it has any real content — it seems to be trying to say that the author thinks all systems are either being observed or they aren’t, and that there are therefore at least two microstates.
I think this is entirely missing the point and is mostly wrong. Even in the highly classical case of a gas, you have a box full of gas, with n particles and some volume V, etc. Those parameters form the macro state. Now you count microstates, take the log, and get the entropy. But nowhere in the count is a set of states where the gas is observed and a set where it isn’t. If you have a box of gas with n particle, etc, it’s implied that the gas exists!
So I don’t buy it. I’ll stick with S >= 0.
So does the "maximum force" argument, which is given in this paper:
https://arxiv.org/abs/physics/0309118
It is, to say the least, not generally accepted as a valid argument.
Maximum power seems especially odd — power is extensive. If you have two maximum power systems, don’t you end up with double the power?
So is force. Two maximum force systems should also end up with double the force.
Admittedly, power has much the the same problem. Saying that P <= P_max is some sort of physical law requires a lot more explanation of what it would mean than the paper even tries to give it.
S ≥ k ln2 is incorrect, as you say. A system whose state is fully known has no entropy. One can either see this through counting the number of microstates (which is 1) or by applying Shannon's definition of entropy to the trivial probability distribution which is 1 for precisely one state.
At some point you'll need math, I recommend https://www.amazon.com/No-bullshit-guide-linear-algebra/dp/0... (I actually started here), and for calculus, "No BS Guide to Math/Physics" by the same author. These books both include a review of high school math (i.e. trig) which i needed. For DiffEq I currently recommend Logan's "A First Course in Differential Equations", this is where I am now and I found this the most gentle after trying several textbooks recommended from r/math. Context: I am an adult with an engineering degree from 20 yrs ago.
(At the bottom, cf. “unworldliness”)
Physicist here, I don’t want to be too dismissive because reducing physics down to its basic principles is part of the game. However, I’m not sure this covers everything. We need a description or at least characterization of 4D Minkowski space. Continuity and even differentiability of functions is assumed. I also am not sure that canonical quantization is covered by this list. Quantizing the EM field, for example, is a big pain and not simply implied by the EM Lagrangian or even any quantization rules. I do not think you can go from this list to non-commuting Hermitian operators acting on a Hilbert space.
I think I'm okay with how opinionated this article is because, while I am not qualified to judge, it gives me an incredible sense of the wonder of physics. And I think opinionated intuitions, albeit somewhat wrong or imprecise, are useful for guiding ones understanding.
So why must thermodynamics be included in this list? Isn't all of macroscopic (thermodynamics) physics derived from the microscopic just like chemistry?
However, it is extremely valuable to also understand that the vast majority of thermodynamics (including our understanding of entropy) can be derived from completely independent axioms that have no relationship to information theory or the knowledge of discreteness of matter. You need to define temperature as an transitive observable (zeroth law of thermodynamics), you need to define heat as a type of energy (first law of thermodynamics), and you need some version of the second law (there are a few equivalent ones, but the easiest is that "heat flows only from high temperature to low temperature"). Lastly, you need equations of state as a starting point (instead of assumptions about the microscoping constituents of matter). Tadaaa, you have all that is necessary to derive all our knowledge of thermodynamics without knowing statistics or atoms.
Aesthetically this is incredibly pleasing and intellectually it is quite surprising that these two sets of axioms that look nothing alike produce the same self-consistent physics. To be productive in cutting edge research you usually need to be comfortable with both.
Edit: corrected associative -> transitive as pointed out below.
Why is that surprising? This sort of thing seems to be ubiquitous in our universe. F=ma is equivalent to the principle of least action. Turing machines are equivalent to the lambda calculus. Electrodynamics is equivalent to the existence of a finite reference velocity.
Also:
> You need to define temperature as an associative observable
Did you mean transitive? My understanding is that the required axiom is that if system A is in thermal equilibrium with system B, and B is in equilibrium with C, then A will be in equilibrium with C. That's transitivity, not associativity.
I corrected the wrong use of the word associative, thanks!
I submit: the qualification 'completely independent axioms' is incorrect. There is the observation: temperature is transitive. This transitive property is a statement of conservation (In terms of Carnot's thermodynamic it used to be thought of as conservation of Caloric.) The concept of Conservation of a quantity correlates with information.
We have that statistical mechanics subsumed Carnot's thermodynamics.
The laws of Carnot's thermodynamics are theorems of statistical mechanics. (Those theorems weren't necessarily stated explicitly. I'm saying the principles of statistical mechanics are sufficient to imply the laws of Carnot's thermodynamics.)
Years ago, in school, the physics teacher gave the following vivid demonstration:
The demonstration involved two beakers, stacked, the openings facing each other, initially a sheet of thin cardboard separated the two.
In the bottom beaker a quantity of Nitrogen dioxide gas had been had been added. The brown color of the gas was clearly visible. The top beaker was filled with plain air, so it was colorless.
Nitrogen dioxide is denser than air. If the gases would not mix then all of the Nitrogen dioxide would stay in the bottom beaker. But of course the two do mix.
When the separator was removed we saw the brown color of the Nitrogen dioxide rise to the top. In less than half a minute the combined space was an even brown color.
And then the teacher explained the significance: in the process of filling the entire space the heavier Nitrogen dioxide molecules had displaced lighter molecules. That is: a significant part of the population of Nitrogen dioxide had moved against the pull of gravity. This move against gravity is probability driven.
Statistical mechanics provides the means to treat this process quantitatively. You quantify by counting numbers of states. Mixed states outnumber separated states - by far.
The climbing of the Nitrogen dioxide molecules goes at the expense of the temperature of the combined gases. That is, if you make sure that in the initial state the temperature in the two compartments is the same then you can compare the final temperature with that. The temperature of the final mixture will be a bit lower than the starting temperature. That is, some kinetic energy has been converted to gravitational potential energy.
So in this particular demonstration probability was acting in a direction opposite to gravity, and overall probability had the upper hand.
Probability effects fall in the category of emergent phenomena. An emergent phenomenon is somewhat of an in-between category. Not quite as fundamental as the law of gravity, but there is no denying that it has an existence of its own.
> Action W = ∫ L dt is minimized in local motion. The lines below fix the two fundamental Lagrangians L.
that's my understanding as a non physicist .. but dW means local minima or maxima.. so i'm confused :)
And then you can go off the deep end and figure out how this all applies to quantum field theory :)
(L isn't a path. It's a scalar-valued function mapping the state of a system to a scaler. In C, with one classical particle, it might be double L(double t, double x, double v) where t is time, x is position, and v is velocity. IMO the simplest example from physics that actually makes sense as a minimization problem is the principle of least time: light going from point A to point B takes the fastest path. This seems a bit silly at first glance -- light travels along without having any idea where it's going. But it really is self-consistent: light propagates through space and through materials such that, wherever it ends up, it gets there by a locally fastest possible route. From this, you can derive specular reflection as well as Snell's Law (refraction) and you can start to understand mirages, e.g. why hot roads look shiny in the distance.)
[0] https://en.wikipedia.org/wiki/Calculus_of_variations is a so-so start -- IMO it's a bit rambly and doesn't do a great job of getting to the point.
If civilization were to collapse tomorrow and the survivors were left in the stone age with "All of Physics in 9 lines", it would arguably be useless. There's so much missing/buried context.
At school, I studied physics for 7 years. Nothing I was taught is hinted at by any of these 9 points, or at least in any way I'm able to recognise after receiving all that teaching, except perhaps some of the constants (they're not listed, but I assume there will be an overlap). Did I, in fact, learn absolutely nothing about physics in all those 7 years? It's much more likely to be the case that from a simple linguistics point of view, these 9 lines do not contain "all of physics", but rather than just the parts of physics that the author considers to be the most fundamental. Maybe if you have decades of highly specialised study you have a chance of remembering most of the rest of what's needed to fill in all the (known) gaps and assumptions those 9 lines are based on and hint at. And the fact that each "line" links to an entire volume that tries to fill in those gaps (I have no idea if they succeed in doing that or not), shows that this isn't anywhere close to what it claims to be.
It's about as vacuous a statement as trying to summarise all of maths as "the set of all possible sets" or all of philosophy as "cogito ergo sum".
Fundamental is what "contains all of physics" means in this context (key word: contains). The rest would be emergent properties.
A few equations being fundamental for big theories built upon them wouldn't be unheard of. Maxwell's equations for example cover several important fields of Physics. Newton's 3 laws cover classical mechanics.
Take something simple like "F=ma" which is in lots of textbooks. Nothing in those 9 lines seem to suggest anything that could be used to derive that.
I'm sure a domain expert, who already knows all this stuff, I'm sure they'd be useful as a memory aid to help them trot this stuff out, but do they "contain all present knowledge about nature, ..."? Not so much, if you need a ton of other knowledge to make use of them.
- action is extremized or at a saddle point, not necessarily minimized
- Action is not quantized in QM (and quantum-mechanical action is not quite the same as classical action). There's another very indirectly related notion of "action" which shows up in historical semiclassical approximations and which is quantized. The author has likely confused the two.
- SU(2) is not the gauge group of the weak interaction, because there is no such thing. A purely weak gauge theory with no EM is not possible, on account of having massive force carriers. The SU(2) and SU(1) in SU(3) x SU(2) x U(1) corresponds to weak isospin and weak hypercharge respectively, not weak charge and (EM) charge.
But even if all the errors were corrected there's a huge amount of missing context. (For instance, the actual content of the standard model Lagrangian - the fact that there are 19 free parameters is in no way sufficient to determine it) And even if you had all of that, a full reduction of macrophysics to microphysics is likely computationally intractable, even in principle.
(...) people asked what entropy was microscopically. The answer can be formulated in various ways. The two most extreme answers are:
Entropy measures the (logarithm of the) number 𝑊 of possible microscopic states. A given macroscopic state can have many microscopic realizations. The logarithm of this number, multiplied by the Boltzmann constant 𝑘, gives the entropy.*
Entropy is the expected number of yes-or-no questions, multiplied by 𝑘 ln 2, the answers of which would tell us everything about the system, i.e., about its microscopic state.
In short, the higher the entropy, the more microstates are possible. Through either of these definitions, entropy measures the quantity of randomness in a system. In other words, entropy measures the transformability of energy: higher entropy means lower transformability. Alternatively, entropy measures the freedom in the choice of microstate that a system has.
(...)
Before we complete our discussion of thermal physics we must point out in another way the importance of the Boltzmann constant 𝑘. We have seen that this constant appears whenever the granularity of matter plays a role; it expresses the fact that matter is made of small basic entities. The most striking way to put this statement is the following:
There is a characteristic entropy change in nature for single particles: Δ𝑆 ≈ 𝑘. This result is almost 100 years old; it was stated most clearly (with a different numerical factor) by Leo Szilard. The same point was made by Léon Brillouin (again with a different numerical factor. The statement can also be taken as the definition of the Boltzmann constant 𝑘.
The existence of a characteristic entropy change in nature is a powerful statement. It eliminates the possibility of the continuity of matter and also that of its fractality. A characteristic entropy implies that matter is made of a finite number of small components.
The existence of a characteristic entropy has numerous consequences. First of all, it sheds light on the third principle of thermodynamics. A characteristic entropy implies that absolute zero temperature is not achievable. Secondly, a characteristic entropy explains why entropy values are finite instead of infinite. Thirdly, it fixes the absolute value of entropy for every system; in continuum physics, entropy, like energy, is only defined up to an additive constant. The quantum of entropy settles all these issues.
Only that the codec needed to actually decompress (understand) it is huge.
Edit: from an information theory perspective.
Ω = 0Surely this is technically incorrect; there are countless observations that disagree with these 9 lines. We just suspect they are caused by measurement or operator error. There is evidence of all sorts of impossible things if you stick to just what is recorded. There can't be that many machines capable of measuring the extreme least-significant digit of these constants.
That's not his point though. Obviously those are not included in the observations that matter.
Same way "there can't be any evidence of a perpetual motion machine" is not refuted by people coming up with their "evidence".
We can't even be that confident they are constants. We've only had good measurements of them for a few centuries. He's right that proving that would be a big deal, but it isn't true to say that there are no inconsistent measurements.
Most of the other lines have terms/constants/variables that I've never heard of or don't remember from school, and usually it's "Lagrangian" again. I don't know what it means to fix, restrict, yield, or complete a Lagrangian. I could keep reading about that, but at this point I don't think I'm learning physics the right way. If there's one thing I remember from class, it's that there aren't many shortcuts here; usually you have to start at fundamentals and prove your way up.
Also, idk how entropy ≥ (some constant) implies thermodynamics, and seems the physicists here don't see it either.
It is arbitrary, in some sense: Lagrangians are specifications of a physical system in the same way that laws of motion are. Instead of directly describing a trajectory as the solution to some set of differential equations, the Lagrangian approach describes it as a stationary point (an extremum or a saddle point) of the action, which is the integral of the Lagrangian over time. The resulting equations of motion are then given by the Euler-Lagrange equation. L = K - V is (one formulation of) the Lagrangian for a system that obeys Newton's laws. Other systems have other Lagrangians, from which we get other laws of motion.
The other important formulation of classical mechanics is the Hamiltonian one, which very roughly speaking reparameterizes the Euler-Lagrange equation in terms of (generalized) positions and momenta, instead of just position. This turns your n-dimensional second order differential equation into a 2n-dimensional first order one, which is often more convenient to work with.
For simple "ideal billiard balls in a vacuum" situations it makes very little difference what approach you use, but Newtonian mechanics generalizes poorly. All of modern physics is based on the Lagrangian and Hamiltonian approaches.
If you genuinely believe in emergent phenomena, then these laws genuinely do not describe all the things that happen in the universe. I do not believe in emergence in this form, but some philosophers of science do.
That said, if that's what you mean, then it's been my belief for a long time that if we were given a book with all the true laws of physics at the lowest level we would still need to spend centuries deriving useful approximations for our practical concerns at the larger scales.
In the case of Descension the constraints are somewhat artificial and imposed by the artist. Arguably, the phenomena supervenes upon the physical structure of those constraints. But consider some living organism. It's various physical parts might be replaced by other parts with similar properties (with respect to their function) and the organism would keep existing as itself. But there isn't any particular substance which maintains the constraints which define the organism. Some philosophers of science (eg Terrance Deacon) uphold that this means emergent phenomenon do not supervene upon their material constituents per se, and are thus not determined by the laws of physics which dictate their properties. I don't buy it, but it is a position.
[1] https://www.thisiscolossal.com/2015/02/anish-kapoor-decensio...
It sort of reminds me of the Philosophy of Mathematics[1], where there are some schools of thought that I consider vaguely ridiculous too. Like some schools of Platonism suggesting mathematical objects actually exist somehow instead of it just being a convenient linguistic shorthand.
But what I ought to have asked is whether he thinks it's because the rules we know are incorrect or missing a few key features, or whether at some fundamental level they just can't do what he used to think they did. To my worldview, it borders on magical thinking to believe they couldn't describe everything in the universe. On the other hand, intuitively, it seems deeply unsatisfying (not to mention empirically unproven) to claim they do. It's a big question for sure.
That's kind of where physics is at, no? Until you succeed in building an apparatus that lets you see individual pixels, it's a continuous canvas for all intents & purposes.
Some discrete & deterministic layer underneath it all is a more elegant possibility imho. Might suit people who prefer "nature at its deepest level is math" worldview. But why would reality 'bother' to fit into that shoe? It just is. Whatever that is. Discrete or continuous, deterministic or probabilistic.
The real meaning of the commutation relation is not that there is a fundamental _relation_ between sets of observables but, I would argue, that at a deep level pairs of non-commuting observables like x and p, share a single ontological substance which we can view partially as either position or velocity depending on how we arrange our measuring apparatus.
That's a big if, which quickly shot down my then early and naive absolute determinism view when Heisenberg uncertainty principle reared its head:
σx•σp >= h/2π
so, can you go from these to predict the structure of DNA/RNA and predicting how they work?
also, I don't like the use of "nature" as some sort of concious entity that prefers some behaviors to others.
How would someone go from these to maxells equations?
Wondering just how big a leap is required?
For the Lagrangian and the derivation of Maxwell's equations see https://en.m.wikipedia.org/wiki/Covariant_formulation_of_cla... .
[0]: The author is being very sloppy – tons of additional structure and additional assumptions are silently implied by his "9 lines".
I'm not qualified to provide you with a more precise, still concise and (hopefully) still accurate description. However, if you want to dig further, the most beginner friendly introduction that I've stumbled upon is Susskind's The Theoretical Minimum - Classical Mechanics [1](there's a book & a series of videos).
There has been almost no definitive progress in fundamental physics in the past 50-100 years.
You could say the same of chemistry too. Or even about industrialization in general.
I would love if someone could elaborate this point.
Not a physicist, but from what I recall, the Planck length is presumed to be the smallest measurable distance before stuff turns into a black hole, which isn't very useful
Planck time is the time required for light in a vacuum to travel the Planck length.
Physics goes to shit if you try to go shorter on either measurement.
This is not correct. The Planck length happens to be very very roughly the scale at which we expect effective theories that ignore quantum-gravitational effects (i.e. the Standard Model) to break down. It has no special physical significance.
Toggle “ask for desktop version” doesn’t make any difference
Make 10 from 8 + 5... or ... reduce Maxwell's equations into U(1)?
There are a few comments here that explains the errors, and there are a few additional comments about other problems in the previous submission https://news.ycombinator.com/item?id=30733666
1. All of physics