by Siva, June 16-17, 2015. Many thanks to Victor Chua for lending me his copy of the book.
As I read the book, I notice that the perspective in particle physics (which is captured well in Weinberg's voice) evolves through the chapters. For example, the significance of renormalizability, the attention given to string theory, etc.
Principles of symmetry unseat matter from the central role (as building blocks of modern physics).
- Comments
- I wonder if symmetry principles (as used in formulating QFT) are still a (semi)classical perspective with just enough quantum mechanics slapped on to them. For example, gauge symmetry is still a monstrosity as far as Feynman diagrams go.
- At least in cond-mat, symmetries form the basis of the Landau-Ginzburg paradigm, and notions of quantum order signify something deeper. HEP hasn't yet grasped the significance of this -- just as an example, this might prove to be the rolling stone that takes us forward on the quest for quantum gravity.
"[...]I have taught physics to liberal-arts undergraduates, I have felt that my most important task (and certainly the most difficult) was to give the students a taste of the power of being able to calculate in detail what happens under various circumstances in various physical systems [...] not because that is the sort of thing everyone needs to calculate but because in doing these calculations they could experience for themselves what the principles of physics really mean. Our knowledge of the principles that determine these and other notions is at the core of phyical science and a precious part of our civilization."
- Comments
- I'm not quite convinced that this is important for liberal-arts majors. Certainly, this is very very important for physics majors. I wish my education had exposed me more to the unity of physics in handling real world systems e.g. how you need all four forces for the sun to shine.
(Michelson, in 1894?) Believed that physics was soon to be complete, and the rest was all chemistry. (Lord Kelvin?)"[...] future truths of science are to be looked for in the sixth place of decimals."
- Comments
- In a sense, this is always quite true -- a question of what the expansion parameter to your effective theory is, in the regime that is experimentally accessible. Relativistic physics is a very small correction depending on your value of
$\sqrt{1 - \frac{v^2}{c^2}}$ . - However, so long as there are nonzero corrections, it seems plausible that one can find regimes where the corrections become extremely important (by looking at the functional dependence of the corrections on the parameters of the theory).
- In a sense, this is always quite true -- a question of what the expansion parameter to your effective theory is, in the regime that is experimentally accessible. Relativistic physics is a very small correction depending on your value of
(Dirac, 1929) "the underlying physical laws necessary for the mathematical theory of a larger part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the application of these laws leads to equations much too complicated to be soluble."
- Comments
- Today, I would characterize this a little differently -- what does it mean to understand something if you cannot compute? It consists of knowing the right questions to ask, and being able to compute/predict those answers.
- Having the "fundamental theory" is not the same as being able to calculate in every situation -- we need suitable effective theories for that (which might be hard or impossible to obtain by perturbing around a well-known situation). In effective theories we trust.
- Anderson: "More is different". I don't think Anderson and Dirac ever got along too well :P
- Also, we know of field theoretic examples where two descriptions are dual and neither is more fundamental than the other -- they are just better descriptions in different regimes!
"When proper care is given to the definition of masses and electric charges and other constants the infinities all cancel, but only in theories of certain special kinds."
- Comments
- Weinberg is promoting the idea of renormalizable theories (that has become a key tenet of particle physics: the SM is the most general renormalizable theory, given the gauge symmetry and the matter content, and a few physical constants)
- As a modern pragmatic EFTheorist, I would flip this around. A theory is a framework for spitting out predictions from (a finite number of) measurements. The idea of regulating/renormalizing tells you that in renormalizable theories you will not have much sensitivity to physics in the deep UV -- those are the only theories where you can get away with doing a finite number of measurements!
"I do not mean to suggest that the final theory will be deduced from pure mathematics [...] so rigid that it cannot be warped into some slightly different theory without introducing logical absurdities like infinite energies."
"Of course a final theory would not end scientific research, not even pure scientific research, nor even pure research in physics. Wonderful phenomena, from turbulence to thought, will still need explanation whatever final theory is discovered [...] A final theory will be final in only one sense -- it will bring to an end a certain sort of science, the ancient search for those principles that cannot be explained in terms of deeper principles."
- Let's play a child's game (examples on pushing the thread of "understanding")
- Why is glass transparent?
- Why does the sun shine?
"Why? Why? Why? [...] The word 'why' is notoriously slippery [...] Explanation, unlike deduction, carries a unique sense of direction [...] This 'because' does not have to do with our ability actually to deduce anything but reflects our view of the order of nature."
- In this chapter, Weinberg
- Takes a simple example from daily life, and shows how any question (Why?) that we can ask about it leads to the quantum mechanical and relativistic theory of 'elementary' degrees of freedom aka the Standard Model.
- Lists all the caveats (he can think of) to the notion of an ultimate theory and its power:
- Historical accidents (initial conditions)
- Complexity (sensitive dependence to initial conditions)
- Emergence (More is different)
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Weinberg defends his notion of reductionism (probably as an aftermath of dirty politics circa SSC)
- There is an undeniable hierarchy in how one field's output is another field's input. This is the (only) sense in which one is more fundamental than another. (Eg: Particle physics > Chemistry > Solid-state physics). This hierarchy of which is more elementary is how Weinberg uses the word "fundamental". One might quibble his use of the word, but one can certainly not take away his use of the meaning.
- Monotonicity theorems lend some support for this notion.
- After all, the value we attach to "elementary" is somewhat sentimental. He uses the word fundemantal/elementary in (merely?) this way.
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In my understanding, Weinberg does not say that the laws of chemistry follow from the laws of physics. Merely studying the building blocks of something does not explain to us how they are put together. However, he claims that the initial conditions of physics, combined with the laws of physics supply the initial conditions (building blocks) of chemistry. Somewhat confusingly, these building blocks could be actual blocks/objects, or rules/notions to start from. Eg: electrons and nuclei, and also the rules of electromagnetic interactions between charged particles.
- There is an undeniable hierarchy in the "flow" of physics through scale (much like renormalization group flow). For all practical purposes, the initial conditions of chemistry might be measured instead of predicted, and the practically important "laws of chemistry" might receive no inputs from the "laws of physics".
"We may formulate what we learn about mobs in the form of laws (such as the old saw that revolutions always eat their children), but, if we ask for an explanation of why such laws hold, we would not be very happy to know that these laws are not fundamental, without explanation in terms of anything else."
"I suspect that all working scientists (and perhaps most people in general) are in practice just as reductionist as I am [...He then goes on to give some wonderful illustrations...] The reductionist attitude provides a useful filter that saves scientists in all fields from wasting their time on ideas that are not worth pursuing. In this sense, we are all reductionists now." [Astrology, and para(foo) are his examples]
- Broader comments:
- In other words, Weinberg is the sort of guy who would like to keep the chain of "Why?"s going. It is no wonder then, that he is drawn to "elementary" physics (circa his time) -- he is not drawn to particle physics because he is dazzled by the beauty of particles. It is merely one more link in the chain of "Why?"s, whittling down the number of arbitrary facts needed to explain nature ab initio, not "explain" in a pragmatic sense.
- Anyone who explains something based on its parts is reductionist in that sense. It's literally a game of holier than thou!
- It is my opinion, that spending more time on notions of "fundamental" is splitting hairs. There are more interesting things to dwell on.
- Nothing a physicist wouldn't have heard before; nothing particularly insightful. Weinberg seems to have a fairly conservative/pragmatic viewpoint on quantum mechanics, and he finds the Copenhagen interpretation bearable. (His viewpoints might have changed in the intervening decades, and he's thought a bit of late about this matter)
This chapter is filled with some delightful historical anecdotes (particularly regarding the electroweak theory), and some interesting insights about what Weinberg calls the art of science.
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A physicist's sense of aesthetics has been instrumental in the acceptance of multiple fundamental breakthroughs in the past century. Acceptance of experimental confirmation has often been ambivalent!
- General relativity
- QED, renormalization of infinities
- Electroweak theory
- FTL neutrinos as being a false positive
- Never in the past century has experiment overthrown a well-accepted theory. Proven incomplete and provided new regimes, yes -- but never overthrown as invalid.
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Comments
- IMHO, the standard trope about theories being built on retrodictions and therefore requiring experimental confirmation of predictions applies to cases where "theories" are models which fit rules to prior observational data. OTOH, experimenters have a lot more discretionary capacity: Often, experiments are so hard to do right (human beings conducting it, and trying to guess and subtract all possible "backgrounds") that we distrust surprising experimental results.
- Without any compelling underlying principles, for mere "models" the rules could be tweaked to be slightly different (adding epicycles); there is no rigidity. OTOH, for well-motivated theory, the model is so rigid that it cannot easily be tweaked -- it is close to all or nothing.
"There is nothing in any single disagreement between theory and experiment that stands up and waves a flag and says, 'I am an important anomaly' [...] It took theory to explain which were the important observations."
"[..] half-serious maxim attributed to Eddington: One should never believe any experiment until it has been confirmed by theory."
"It appears that anything you say about the way that theory and experiment may interact is likely to be correct, and anything you say about the way that theory and experiment must interact is likely to be wrong. [...] I think that one should not hope for a science of science, the formulation of any definite rules about how scientists do or ought to behave, but only aim at a description of tha sort of behaviour that historically has led to scientific progress -- an art of science."
- Comments
- Beauty corresponds to a simplicity/elegance in the concepts and ideas underlying a theory.
- Occam's razor: It is wonderful when you postulate something very minimal and general, and quite acceptable, and the rest of the package comes along for consistency (a sense of inevitability/rigidity of not having too many knobs). Essentially low Kolmogrov complexity?
- Anything not forbidden will happen (Murphy's law)
- Ultimately, "beauty" is a judgement call on how likely a theory is to describe nature i.e. how likely is nature to obey a particular theory.
- Symmetry principles point to a "democracy/equality" in the organization of nature. It doesn't matter which of the symmetric options/perspectives you choose, the physics doesn't change! Physicists find this very beautiful for its minimality in sweeping away a whole range of arbitrariness corresponding to a choice.
- From Noether's theorem, every symmetry corresponds to a conserved quantity -- which gives us a handle on characterizing a system! (Invariants of a system that can be predicted by simply knowing the initial state)
- My personal favourite: locality
"The symmetries that are really important in nature are the not the symmetries of things, but the symmetries of laws."
- Comments
- Natural symmetry between the directions. Does not mean that up and down are the same, just that using either as the direction for counting displacements tells us that apples fall towards the earth in exactly the same way.
- Symmetries might sometimes be spontaneously broken by historical accidents (initial conditions). Eg: On the earth's surface, gravity breaks the symmetry between up and down.
"We do not want to discover a theory that is capable of describing all imaginable kinds of force among the particles of nature."
- Comments
- This is quite unlike other (applied) areas!
"not onle is out aesthetic judgement a means to the end of finding scientific explanations and judging their validity --- it is part of what we mean by an explanation."
"Deducing the consequences of a given set of well-formulated physical principles can be difficult or easy, but it is the sort of thing that physicists learn to do in graduate school and that they generally enjoy doing. The creation of new physical principles is agony and apparently cannot be taught."
- On why we have this sense of beauty
- We've been trained (evolved) by nature to find it beautiful
- Scientists tend to choose problems that have beautiful solutions (Eg: calculating critical exponents -vs- calculating the Curie temperature)
- We're historically used to discovering a simpler and more beautiful explanation on peeling back each layer.
"Sometimes when our sense of beauty lets us down, it is because we have overestimated the fundamental character of what we are trying to explain."
"I raised in the previous chapter the problem of what Wigner calls the 'nureasonable effectiveness' of mathematics; here I want to take up another equally puzzling phenomenon, the unreasonable ineffectiveness of philosophy."
- Positivism: Mach, Kaufmann, Einstein (Relativity vs QM), Pickering (quarks)
"No one would give a book about mountain climbing the title Constructing Everest."
- Against Kuhn's take on the absence of objective truths
"The danger they present to science comes from their possible influence on those who have not shared in the work of science but on whom we depend, especially on those in charge of funding science and on new generations of potential scientists."
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The phenomenon of spontaneously broken symmetry means that nature could have more symmetry than was apparent, and we might be able to find those principles to elucidate the structure in nature. This perspective has influenced the perspective in particle physics, over the last few decades.
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In this chapter, Weinberg elaborates on the main questions driving particle physics, at around the time of the book's publication (early 1990s),
- Quantum mechanical description of gravity (BH information paradox)
- Something different about the strong force
- What triggers electroweak symmetry breaking? (We found the Higgs! 2012)
- Baryogenesis
- GUTs, and the (big) hierarchy problem, SUSY
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EFTs (modern perspective on renormalizability) are consistent with tests done so far, but are an anathema since they break down when extrapolated to high energies. Like a hound on the scent of a trail, this seems like an avenue to dig deeper and come to terms with more fundamental physics (since fundamental physics must always give physically sensible answers)
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Comments: My take on major markers in the intervening decades (~20 years)
- The LEP paradox and the little hierarchy problem (now the LHC null surprise)
- Weinberg has barely a mention of string theory (so far in the book. There might be more in later chapters) The two string revolutions (the book was written around the time of the second) put string theory on a pedestal of beauty
- Holography! (implications for quantum gravity)
- IMHO, this is very very important, along with the appliaction of principles from quantum information/computation/complexity theory to fundamental physics.
- The discovery of the expanding universe brings a new naturalness/finetuning problem, and the anthropic solution. LambdaCDM as the standard model of cosmology calls for a microscopic description of dark matter.
- Weinberg also omits any mention of the theory of inflation, motivated by improving CMB observations. But this is theoretically ugly (ad hoc), even though it is somewhat minimal in the sense of rules to fit to data.
"It is a tribute to the fundamental importance of elementary particle physics that very bright students continue to come into the field when so little is going on."
I found that quote interesting. I say: "To pursue a PhD in theoretical high-energy physics, one needs to be half retarded and half advanced -- half-advanced for wanting to capture the excitement of the past, and half retarded for seeing a future in it."
- Expect quantum mechanics (resistance to deformation) and symmetry principles to play an important role.
[Strings, TaDa!] "It is not that someone suddenly had an inspiration that matter is composed of strings and then went on to develop a theory based on this idea; the theory of strings had been discovered before anyone realized that it was a theory of strings."
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String theory provides our first plausible candidate for a final theory.
- Strings are truly fundamental, and their vibrations cannot dissipate away into more elementary degrees of freedom. (Is the Hagedorn density of states a problem? Energy in strings should eventually accumulate into a few highly-excited strings?)
- SM+QuantumGravity+Extras(dark matter, dark energy, etc. you name it) as a low-energy EFT of lightest string states.
- Strings solve the problem of infinities. (Er... what about string field theory and integrations over the space of Riemanm surfaces, etc?)
- Quantum gravity (anomaly cancellation)
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Comments (some of these we've learned after the book was published)
- Belief: The most general S-matrix theory satisfying unitarity and Lorentz invariance is a theory of strings. (Is it local/causal in some particular sense?) Imposing locality/causality in a naive way leads us to QFT. It seems like we'll be lead to string theory if we're a little more subtle about it.
- After all, SYM is dual to a theory of strings. So QFTs might be dual to string theories :-?
- It boggles my mind that an S-Matrix (holographic) theory consistent with QM and Lorentz invariance must necessarily have gravity as a consequence :-?
- M-theory as the mother of all string theories (so uniqueness), but a zoo of compactifications (string multiverse/swampland)
- No more difference between internal and spacetime symmetries?
- Belief: The most general S-matrix theory satisfying unitarity and Lorentz invariance is a theory of strings. (Is it local/causal in some particular sense?) Imposing locality/causality in a naive way leads us to QFT. It seems like we'll be lead to string theory if we're a little more subtle about it.
"A fair fraction of today's young theoretical physicists are working on string theory [...] so far no detailed quantitative predictions have emerged that would allow a decisive test of string theory [...] impasse has led to an unfortunate split in the community of physicists. String theory is very demanding; few of the theorists who work on other problems have the background to nuderstand technical articles on string theory, and few of the string theorists have time to keep up with anything else in physics, least of all with high-energy experiments. Some of my colleagues have reacted to this unhappy predicament with some hostility to string theory. I do not share this feeling. String theory provides our only present source of candidates for a final theory -- how could anyone expect that many of the brightest young theorists would not work on it?"
"Once again I repeat: the aim of physics at its most fundamental level is not just to describe the world but to explain why it is the way it is."
"The idea of the anthropic principle began with the remark that the laws of nature seem surprisingly well suited to the existence of life [...] The energies of nuclear states depend in a complicated way on all the constants of physics, such as the masses and electric charges of the different types of elementary particles. It seems at first sight remarkable that these constants should take just the values that are needed to make it possible for carbon to be formed[..]" [Cop-out]
"A Soviet emigre physicist told me that a few years ago a joke was circulating in Moscow, to the effect that the anthropic principle explains why life is so miserable. There are many more ways for life to be miserable than happy; the anthropic principle only requires that laws of nature should allow the existence of intelligent beings, not that these beings should enjoy themselves."
"Perhaps there is a final theory [...] but humans are simply not intelligent enough. [...] A far more pressing worry is that the effort to discover the final laws may be stopped for want of money."
- Weinberg thinks that our best hope is to find something logically isolated (which cannot be deformed by a small amount). We might still not know why this theory is true, but we at least know why it cannot be slightly different. We might well be able to cook up theories which are wholesale different, but then look nothing like our universe -- so any simple observation would point out the only possible "ultimate" theory.
"The problem seems to be that we are trying to be logical about a question that is not really susceptible to logical argment: the question ofw hat should or should not engage our sense of wonder."
"about one thing we can be sure: the discovery of a final theory would not end the enterprise of science [...] we may regret that nature has become more ordinary, less full of wonder and mystery [...] There will be endless scientific problems and a whole universe left to explore, but I suspect that the scientists of the future may envy today's physicists a little, because we are still on the voyage to discover the final laws."
[Interesting comment]"The theologian Paul Tillich once observed that among scientists only physicists seem capable of using the word 'God' without embarrassment."
- Occam's razor: The only way science can proceed is to assume there is no divine intervention, and see how much purchase you get.
"For those who see no conflict between science and religion, the retreat of religion from the ground occupied by science is nearly complete."
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As we hone our understanding of nature, it seems more like nature by itself is not lending any purpose for humanity -- that seems to be up to us.
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Comments
- Weinberg has many things to say on this subject. Though I've read the words and paragraphs, I don't think I have a full grasp of what he is trying to convey. I do not intend to state everything he says; so I will say very little. I will go back and read this chapter some other time.
"the pain of confronting the prospect of our death and the deaths of those we love impels us to adopt beliefs that soften the pain. If we are able to manage to adjust our beliefs this way, then why not do so? [...] I can see no scientific or logical reason not to seel consolation by adjustment of our beliefs -- only a moral one, a point of honour [...] The honour of resisting this temptation is only a thin substitute for the consolations of religion, but it is not entirely without satisfactions of its own."
Comments: At this point, I guess that the story of the SSC is of chiefly historical interest, so I will not write much. To some extent, the book is an impassioned plea by Weinberg, in a time of crisis for particle physics, attempting to convey the desire to pursue a deeper understanding of the elementary building blocks of nature. The SSC was supposed to be the testing ground for those ideas -- an ambitious project that would have probably given us a glimpse of physics we never imagined. To this date (over 20 years since the cancellation of the project), we do not have a human endeavour that even comes close to achieving those ambitions. In 2012, the LHC (operating at about a fifth of the SSC's collision energy) announced the discovery of the Higgs boson as the particle responsible for triggering electroweak symmetry breaking. By now, the LHC has just stepped up to a third of the SSC's collision energy, and we eagerly await results as the machine gets going (circa mid-2015). This chapter portrays the story of the SSC's beginning, leading to the political climate surrounding the SSC's funding crisis circa 1992.
In the afterword to the Vintage edition (January 1994), Weinberg explains the situation, particularly the politics, surrounding the eventual termination of the program, and what it signifies for the future of research in fundamental science. I think that this chapter, in itself, is a gripping read. Weinberg also has some more (incisive) comments about, what he considers, 'The crisis of big science'.