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The Relation Between Mathematics and Physics by Paul Dirac
- rramadass 19d agoAlso see Relationship between Mathematics and Physics - https://en.wikipedia.org/wiki/Relationship_between_mathematics_and_physics https://en.wikipedia.org/wiki/Relationship_between_mathemati...
- wolfi1 16d agothere is a quote from Pauli about Dirac : 'There is no God and Dirac is his prophet' Heisenberg and Dirac had different opinions on the existence of a god and Pauli, asked for his opinion, had the former to say
- Tazerenix 16d agoThere's a quote Atiyah has about spin geometry which he heard from his advisor Hodge, who had an office next to Dirac at Cambridge. Only two people understand spinors: God, and Dirac. And Dirac's dead.
- general_reveal 16d ago[flagged]
- n4r9 16d agoThis is probably a reference to Hume's problem of induction, i.e. that observing a regularity in the past cannot justify assuming that it will hold in the future. It's vaguely related to the article, but talking about "time windows" and "Mathers" muddles the point.
- general_reveal 16d agoIs it vaguely related? He wondered why measuring anything even works. Why wouldn’t the measurement disappear, thus making all this measuring pointless? Because, apparently the measurement(s) are true each time-step, and it will be true for that time, until it’s not true. Why it reasonably works well for us? Well, God , I guess. Same way the Sun doesn’t burn our skin off (God, I guess, but some have issues with that). Sorry, I had to critique that immediately because I could already see that other second paragraph I quoted coming, as in, this author probably worships Math, Science, and those that do it, certainly not God, because he was unable to characterize the phenomena of it as related to God.
- n4r9 16d agoYes, vaguely related. Dirac is not wondering why measurement itself works, but why mathematical reasoning applies so effectively to the measurement results. I think it's valid to be surprised that all observations of a physical phenomena up until this point have obeyed a beautiful and (relatively) simple mathematical relationship, without even thinking about predicting the future.
- GoblinSlayer 15d agoMeasurement works because universe moves in a simple way. As Hume indicates, you need very complex motion for irregularity, maybe even sentient, but sentient universe is fairy tale.
- pixl97 15d ago> but sentient universe is fairy tale. Ehhhhh.... this is actually a much bigger claim than you realize and to immediately dismiss it leads to some problematic issues in the continuum of reality. Without a rigorous falsifiable definition of sentient at all scales it can apply at best the problem is undefined. Are brains sentient? Are neurons sentient? Are the actual algorithms these structures run sentient? Without those answers we can really only say "The universe is probably not sentient". Also, you are the universe experiencing itself.
- deleted 15d ago[deleted]
- GoblinSlayer 15d agoFor a regularity to be broken, the phenomenon causing this regularity should be sentient to break the regularity in an intelligently chosen way. It doesn't matter how sentient are neurons, they don't affect anything and might as well be absent. See https://en.wikipedia.org/wiki/Discovery_of_Neptune https://en.wikipedia.org/wiki/Discovery_of_Neptune - what neurons did there?
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- lolakutty 16d ago>There is no logical reason why the second method should be possible at all, One reason I can think of is if we consider that some regularity in the physical behavior is required for consciousness to evolve and so consciousness only forms in such worlds.
- rramadass 15d agoLater down in the essay, Dirac himself answers this; With this kind of cosmological picture one is led to suppose that there was a beginning of time, and that it is meaningless to inquire into what happened before then. One can get a rough idea of the geometrical relationships this involves by imagining the present to be the surface of a sphere, going into the past to be going in towards the centre of the sphere, and going into the future to be going outwards. There is then no limit to how far one may go into the future, but there is a limit to how far one can go into the past, corresponding to when one has reached the centre of the sphere. The beginning of time provides a natural origin from which to measure the time of any event. The result is usually called the epoch of that event. Thus the present epoch is 2 x 109 years [actually 2x10^9]. One further point in connection with the new cosmology is worthy of note. At the beginning of time the laws of Nature were probably very different from what they are now. Thus we should consider the laws of Nature as continually changing with the epoch, instead of as holding uniformly throughout space-time. This idea was first put forward by Milne, who worked it out on the assumptions that the universe at a given epoch is roughly everywhere uniform and spherically symmetrical. I find these assumptions not very satisfying, because the local departures from uniformity are so great and are of such essential importance for our world of life that it seems unlikely there should be a principle of uniformity overlying them. Further, as we already have the laws of Nature depending on the epoch, we should expect them also to depend on position in space, in order to preserve the beautiful idea of the theory of relativity there is fundamental similarity between space and time. This goes more drastically against Milne's assumptions than a mere lack of uniformity in the distribution of matter. Show respect to Mathematicians/Physicists/etc. many of whom had studied Philosophy and i dare say had a better understanding/insight of it than mere academic Philosophers. Why? Because they don't go off into la-la land but try very hard to have both observed evidence and a mathematical model of it match cleanly via a Theory. For your edification, read first "Meditations on First Philosophy by Rene Descartes" followed by "Physics and Philosophy by Werner Heisenberg".
- pixl97 15d agoThe difference between science and woo is science makes falsifiable predictions. I mean, go back 500 years. Tell everyone that everything is actually make of fields (no not the kind you grow things in). These fields manifest waves that carry certain amounts of energy. Those bits of energy build larger structures that are still so incredibly tiny the human imagination fails. But then you take those larger structures in a pattern and it builds atoms. Those atoms are actually 99.9999999% nothing but empty space end fields of force and electricity. This is why you don't pass thru things. Oh yea, these tiny empty things connect to each other in predictable ways creating molecules that are the basis of life. Just a tiny speck of them contains quadrillions of these molecules, crazy tiny. [The people you are talking to]: Get the wood, we're burning this witch.
- rramadass 15d agoRead my other comment here first which answers your first part - https://news.ycombinator.com/item?id=49738762 https://news.ycombinator.com/item?id=49738762 > Thorough worshipping of Math and “Mathers”, like as if they are a gift from God "There is no God and Dirac is his Prophet" -- Wolfgang Pauli. > Again, let’s stick with Hume, you’re the shit until you’re not. BS. Hume's ideas of Mathematics and their usage in Science were laughable (they predated modern mathematics and physics). The mathematics used in a theory has tremendous predictive power and does not depend on "miracles". So we know where it works and where it does not. > Einstein went to death not understanding Physics as he wanted to. No, that is not quite true. Einstein perfectly understood quantum physics/mechanics but considered it incomplete and philosophically abhorrent. > God loves that essay Hume wrote, truly. It’s all fun and games until God mindfucks your understanding. Nonsense.
- VorpalWay 16d agoShouldn't this have a "(1939)" suffix on the title according to HN rules? ;)
- sigmoid10 16d agoShould it though? I don't see such a rule. https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
- baxtr 15d agounwritten rules
- sigmoid10 15d agoWhy should anyone know or care about it then? This is not a static platform with a static userbase.
- baxtr 15d agoanother unwritten rule: don't take everything too serious that you read here ;)
- sigmoid10 14d agoThen you should adhere to yet another unwritten rule while we're at it: Don't use smileys. Especially not to change the meaning of your statements. You can just drop them and say what you mean, that makes communication easier and clearer. This is not facebook where people talk via emojis.
- delichon 15d agoKaffee: Corporal, would you turn to the page in this book that says where the mess hall is, please? Barnes: Lieutenant Kaffee, that’s not in the book, sir. Kaffee: You mean to say in all your time at Gitmo you’ve never had a meal?
- jdw64 16d ago[dead]
- GoblinSlayer 16d ago>but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which Nature has chosen This is quantifiable, right? Should be possible to measure how many mathematicians favor ideas like turbulence, macroscopic quantum physics, anthropic principle, analog geometry, finitism. I think, mathematics doesn't really try to match physics yet.
- huurtehoog 15d agoI think this passage is more about the fact that mathematics is a form of symbolic computation people create and it is weirdly congruent to the physical measurements and models of reality. Not that mathematicians see certain models and objects used in physical models in a favorable way. What favor even means here? It is quantifiable: several mathematical objects and categories people invented to do symbolic computation in letters and published papers are somehow very useful to model and understand data from physical measurements of reality. I highly recommend reading the "Unreasonable effectiveness of mathematics" essay by Wigner: https://www.hep.upenn.edu/~johnda/Papers/wignerUnreasonableEffectiveness.pdf https://www.hep.upenn.edu/~johnda/Papers/wignerUnreasonableE...
- GoblinSlayer 15d agoI don't see unreasonable effectiveness of mathematics. On one hand, it's a self fulfilling prophecy: if your math doesn't work, just make different math, and so on until it works (gravity was invented 6 times or so), so it's as effective as logic. On the other hand, it's fundamentally approximation limited by precision, so for any model we know when it breaks. And it's basically unworkable for chaotic or exponentially complex phenomena.
- podocarp 15d agoYou're just claiming it's effective. We know it's effective. But there's no reason it should be effective. It's primarily because philosophy has not caught up and we still can't explain the foundations of mathematics and causality. These things seem to be baked into our very nature. It is possible to image an alien race with different conceptions of logic and causality that are just unable however hard they try to formulate either proper mathematics or proper physical laws from mathematics. (Take for example the Pythagoreans who could not believe irrational numbers existed, so the famous cube root of 2 was fake news to them. They could never build their little cubic altar to whomever.)
- taaha47 15d ago"I would like to put forward a suggestion as to how such a scheme might be realized. If we express the present epoch, 2 x 109 years, in terms of a unit of time defined by the atomic constants, we get a number of the order 1039, which characterizes the present in an absolute sense. Might it not be that all present events correspond to properties of this large number, and, more generally, that the whole history of the universe corresponds to properties of the whole sequence of natural numbers? At first sight it would seem that the universe is far too complex for such a correspondence to be possible. But I think this objection cannot be maintained, since a number of the order 1039 is excessively complicated, just because it is so enormous. We have a brief way of writing it down, but this should not blind us to the fact that it must have excessivly complicated properties." this cannot be an early hint to the result made by chaitin; Chaitin’s Incompleteness Theorem?
- rramadass 15d agoRelated; From Heisenberg to Goedel via Chaitin - https://arxiv.org/abs/quant-ph/0402197 https://arxiv.org/abs/quant-ph/0402197
- rramadass 15d agoJust to clarify; The term "2 x 109" is actually "2 x 10^9" or 2 billion years which was considered the present epoch i.e. accepted age of the universe at that time. Dirac large numbers hypothesis - https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis https://en.wikipedia.org/wiki/Dirac_large_numbers_hypothesis
- DonaldFisk 15d agoCorrect (but now we know it should be somewhat higher than that), and 1039 should be 10^39, one of Dirac's Large Numbers, the size of the observable universe in atomic units, and also the ratio of electromagnetic to gravitational forces in the hydrogen atom.
- rramadass 15d agoRight. Added the wikipedia link to Dirac's LNH above. Also found this; The fundamental constants and their variation: observational status and theoretical motivations - https://arxiv.org/abs/hep-ph/0205340 https://arxiv.org/abs/hep-ph/0205340
- Xmd5a 15d ago> The dominating idea in this application of mathematics to physics is that the equations representing the laws of motion should be of a simple form. The whole success of the scheme is due to the fact that equations of simple form do seem to work. The physicist is thus provided with a principle of simplicity, which he can use as an instrument of research. https://arxiv.org/abs/math-ph/0009007 https://arxiv.org/abs/math-ph/0009007 > Occam's Razor as a Formal Basis for a Physical Theory > We introduce the principle of Occam's Razor in a form which can be used as a basis for economical formulations of physics. This allows us to explain the general structure of the Lagrangian for a composite physical system, as well as some other artificial postulates behind the variational formulations of physical laws. As an example, we derive Hamilton's principle of stationary action together with the Lagrangians for the cases of Newtonian mechanics, relativistic mechanics and a relativistic particle in an external gravitational field.
- anthk 15d agoNow dive down into Math with Penrose and David Bohm with the implicate order.
- rramadass 15d agoQuite independently of the Mathematics, Bohm's ideas of "Implicate and Explicate Order" are very interesting and comprehensible by the layman at a high-level - https://en.wikipedia.org/wiki/Implicate_and_explicate_order https://en.wikipedia.org/wiki/Implicate_and_explicate_order In particular, students of Hindu Philosophical Schools will find lots of parallels here. Bohm was heavily influenced by Jiddu Krishnamurti which inspired his take on quantum theory. Bohm also wrote a great book, "Quantum Theory" based on the Copenhagen Interpretation which contains separate parts on "Physical Formulation" and "Mathematical Formulation" of quantum theory.
- lioeters 15d agoGreat answer.
- thisisauserid 15d ago[dead]
- 3lambda 15d agoGiven its strength in mathematics, it seems likely that AI should be of great help with discovering new physics. We just need to teach it to ask interesting questions.
- jbmchuck 15d agoHow does this comment relate to the article?
- JimmyBuckets 15d agoDirac comments that he thinks a potential path to the discovery of new physics is to start with a mathematical domain and work outwards from there, guided by mathematical beauty. This is what I took OP's comment to be about - of course setting aside questions on an LLM's ability to recognize beauty
- goatlover 15d agoSuperstring theory has been based on the idea of mathematical beauty, but it's run into serious complications when it comes to empirical results. Science is empirical first and foremost, because we need to verify that theories actually predict the universe we live in by testing them. I don't know how LLMs would help sorting through the 10^500 possible universes when it comes to superstrings. You need to be able to run experiments or obtain observations.
- pixl97 15d agoActually there are people attempting to find new math via biological entities. Cells and such. The interesting thing here is it is easily falsifiable even though working at these scales is still insanely hard. Take the golden rule for example. It's a simple algorithm that shows up everywhere in nature. It represents the least amount of energy needed to assemble all kinds of structures. The gist here is nature finds these algorithms via evolution over billions of years and quadrillions of individual life experiments. We see life finding simple algorithms and platonic maths, how complex of algorithms has it found? You no longer have to do an impossible number of experiments, instead you have to tease apart gene expressions to turn them on and off. Now, that is still a monumental task, but it's still doable in a reasonable amount of time. Added: https://en.wikipedia.org/wiki/Xenobot https://en.wikipedia.org/wiki/Xenobot Individual cells like this can perform all kind of higher order operations that would appear to be intelligent actors.
- voxleone 15d agoThere's this little pet project of mine, the Functional Universe [0]. It explores a direction suggested by Dirac: treating mathematical structure and transformation not merely as a language for describing physical reality, but as potentially constitutive of it. FU models physical reality in terms of functional state evolution, with an emphasis on composition, aggregation, and transitions. In that sense, I think there's an interesting point of contact with Dirac's emphasis on transformations: Dirac points toward transformations as fundamental mathematical structures from which physics might be derived; FU asks what happens if physical reality itself is formulated in terms of transitions and their composition. [0] https://voxleone.github.io/FunctionalUniverse/ https://voxleone.github.io/FunctionalUniverse/
- deleted 15d ago[deleted]
- lioeters 15d agoCurious, in this model, is there any discussion on whether the mathematical structures underlying space-time are continuous or discrete? Usually the former is assumed, but it seems your "functional" approach may be able to accommodate the latter possibility.
- lerp-io 15d agouniverse is continuous / cant be proven otherwise but any measurement or simulation of it is discrete by nature same reason pi is computed infinitely and why calculus exists and why math exists at all to try and explain continuity of nature even if all of it is perceived discretely.
- pixl97 15d agoThe question is what exactly is continuous. The quantum fields themselves? And we have no evidence the the quantum fields are discrete quantum states themselves, but the particles they produce appear otherwise. It's always possible that continuous maths are a side effect of this field. Of course, the causality could be revered.
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- sahil50 15d ago[dead]
- jimbokun 15d agoDid Dirac’s prediction that studying “beautiful” mathematics would lead to breakthroughs in the understanding of Physics pan out?
- lacker 15d agoYes, quite well in fact. This lecture was in 1939. In the 50's, Lie groups (previously just a pure, beautiful mathematics) were used in particle physics. Gell-Mann used SU(3) to predict some new particles before anyone observed them. And then similar stuff happened later in quantum mechanics, with gauge theory, but I understand that only at a handwavy level. I think overall the "standard model" is a perfect example of what Dirac predicted. Whether this still holds up in the past 40 years is another question. I don't have a great example from my lifetime.
- GoblinSlayer 15d agoThe standard model is completely accidental, no? Also hierarchy problem.
- skew-aberration 14d agoAlso a layman but I have a different read of it. 1) Dirac actually developed big parts of Lie Theory and its application in relativistic particle physics, without using the mathematical formalisms at all (until later on). His work was subsumed/beautified by mathematicians after the fact (30s), an 'optimization' really which helped to extend and understand it further, not to discover it. The Gell-Mann prediction mirrors Dirac's own positron (non)prediction closely but was done without Lie formalisms. The applications of Lie theory in relativistic fields theories began even earlier, with the Noether/Klein/Hilbert/Einstein collaboration in 1910s. 2) Continuous symmetries are a convenience and not essential to particle physics IMHO. e.g. It's obvious we can swap positive and negative charge and get the same physics. That's a discrete symmetry. But in gauge theories the symmetry is not +ve <-> -ve, but rather the continuous rotation of the unit circle in a complex plane. electron becomes positron via complex numbers. It doesn't mean there's a complex electron with +-ie charge, but it does work better with relativistic Lagrangian fields theories where phase changes are continuous and frame dependent. Noether's methodology of using an invariant action integral leverages the Lie theory very effectively, but there are other ways to skin that cat though. 3) Beauty is in the eye of the beholder, but I doubt the standard model and the perturbative methods (renormalization, etc) underpinning it would be to Dirac's liking.
- viamiraia 15d agoas an example of this, pretend probability is a velocity: https://www.mathpages.com/home/kmath216/kmath216.htm https://www.mathpages.com/home/kmath216/kmath216.htm going beyond that page, think about beta distributions (and dirichlets). they are probability distributions about probabilities. try recentering the beta distribution between -1 and 1 first (representing c). going even further, recall the bernoulli-binomial-beta connection. treat the recentered beta distribution's parameters as bernoulli trials. try placing them in a light cone. let me know what interesting things you find ;)
- nikisweeting 14d agoFor those into deriving the laws of physics from pure math and game-of-life style iteration of simple rules, checkout the Wolfram Physics Project: https://www.wolframphysics.org/ https://www.wolframphysics.org/ https://github.com/pirate/wolfram-gauge-physics https://github.com/pirate/wolfram-gauge-physics