Waves in an Impossible Sea

Going Beyond the Book

If you’re reading Waves in an Impossible Sea, and you have a question about a related subject that the book doesn’t directly cover, please ask it here!

46 Responses

  1. Thanks a lot for the book, it inspired me and made me think (I’ve recently had several intense half-nighters). I don’t want to spam your blog, so ask for an advice of how and with whom better to share:
    – Short fictional story illustrating the equivalence principle of GR (in English, characters excluding spaces – 4438)
    – Simple geometric derivation of Lorentz transformations, relativistic energy-momentum relation, invariant mass, for boson-like wavicles.

  2. Several questions about cosmic walls.
    – Does the wall of doom you described in The Wizardry of Quantum Fields run at the cosmic speed limit? I think so as you mentioned the “unsuspecting” universe, and we humans will just cede to exist if the wall reaches us, like unfortunate passengers of the Titan submersible for whom its catastrophic implosion went unnoticed.
    – The Hubble constant of 70 km/s/Mpc means that at ~4Gpc the expansion is superluminal and nothing which is father away now, including a wall of doom, could reach us. Therefore, we only need to worry about the local walls which have much lower probability to appear due to the restricted volume, right?
    – I’m thinking of a more benign version of the domain wall resembling the iron’s magnetic domains and their walls. Suppose the Higgs field acquired some constant non-zero value but with different potential phase across the universe (considering the Mexican hat shape). If so, are the different vacua “compatible” with each other, i.e. can a wavicle traverse the wall between phase domains? And how such a wall might look like?

    1. Excellent questions.

      1) In most models it approaches the cosmic speed limit closely after a short time, and yes, we don’t get much if any warning.

      2) Yes, what happens outside our cosmic horizon cannot hurt us, but there are some regions that are currently outside our horizon which might someday come within it. This depends in part on what “dark energy” really is and how it evolves.

      3) Domain walls of this sort are not possible with our Higgs field, because the different phases you are imagining are physically equivalent (“gauge equivalent” in the language of physicists.) This is different from a magnet where the different directions of pointing are physically inequivalent, making domains and domain walls possible. [Buzzwords: global symmetries can have inequivalent domains related by a symmetry; gauge symmetries are fakes — they are symmetries that act on the math used but not on the physics — so they cannot.] Other scalars fields could in principle have domains; but indeed, such domain walls have big effects on cosmology and so are sharply constrained by observation.

  3. Matt, the electron field interacts with the electromagnetic/photon field to produce an electron; but also an anti-electron, aka positron, to maintain charge conservation. The fact that the two charges are related by a sign change is something I find fascinating and, to my mind, appears to be saying something about (a) some property of the photon that needs to be conserved in the interaction or (b) to maintain a symmetry such as parity: Is this vaguely correct?

    1. It’s mainly just electric charge that’s at stake. The photon’s interaction with the electron field requires that whatever the former does to the latter, the total electric charge can’t change. Therefore, no matter what happens, a photon can only be transformed into n electrons and n positrons (where n is most commonly 1).

  4. Here’re a couple of ideas for the page’s name to discuss the book’s pedagogical choices. First is “Final Draft” and inspired by a recent addition to the Alan Wake computer game series. The game protagonist is an eponymous writer drawn to some kind of a parallel world by an obscure, powerful and evil entity called Dark Presence. And by reading your “strange space-suffusing entity, an enigmatic presence known as the Higgs’ field” passage it immediately stroked me how similar they are. Another is “Yoctosecond Edition” which plays with the double meaning of “second” and refers to the smallest timescale currently accessible.

  5. Hi Matt,
    Great book (and blog)! You clarify some major issues that, it is true, are left unanswered, or maybe are taken for granted, in most sources (eg. the fact that “particles” are wavicles, etc)!
    My question is this: you say, on the one hand, that mass is intransigence while, on the other, that mass doesn’t slow things down. How can these two statements be compatible with each other? And, in the end, what is it exactly that doesn’t allow objects to reach the cosmic speed limit? Mass or inertia? (I recently heard about an, as yet unverified, idea about “quantized inertia” that attempts to explain this fact)

  6. In 12 What Ears Can’ t Hear and Eyes Can’ t See you discuss the question of why a rainbow is narrow. Your explanation implies that dispersion spreads initially bright narrow arc to the spectrum and we see just a small portion of it. That’s true but not the whole story. The question is why that bright narrow arc appears in the first place. The sun has a finite angular diameter of half a degree, and its rays need to be redirected three times to reach an observer. Any initial misalignment would be amplified during the redirection within the constrained drop’s geometry, and we’ll end up seeing a wide band of light. But a thorough analysis shows that the deflection function has an extremum near the rainbow’s angle which acts like a lens focusing part of incoming light into the narrow band. There’s even another extremum having more complex optical path, which gives the outer, less bright arch with inverted dispersion.

  7. You were such a courageous boy jumping while flying in a jet. You might have expected that if you’d jumped high enough, you would have been tackled by the jet’s wall rushing at 500 mph! Here’s a fun exercise also playing with relativity principle, which I came up with many years ago during my long subway commutes. In a subway car take a seat for you to look sideways. Suppose the train goes to the right of you, and you’re in a long steady hop between two stations. Close your eyes. Without any visual clues, feeling just monotonous bumps and shaking, it’s rather easy to trick you mind thinking that the train goes in opposite direction, to the left of you, because by relativity principle they’re indistinguishable. And when the train starts braking, you’ll feel – quite opposite – rather intense speeding up! The feeling lasts until you realize that instead of intensifying, bumps and shaking subside. *Initially I posted it on “Got a Question” page, but now can’t find it there, so repost here.

  8. Can’t stop thinking about Lorentz-invariance. Here’s another toy/wild idea inspired by your latest posts on zero-point energy and standing waves. Starting points:
    – Cosmic fields (vacuum) energy density depends on the smallest scale of its constituent parts
    – Non-interacting wave excitations (particles) gradually spread
    – We have one example when the cosmic field(s) property – curvature – are influenced by matter-energy
    Let’s assume that a) the cosmic fields’ constituent parts are like non-interacting particles. Then in absence of other disturbances they will spread, overlap, and drive the smallest scale up suppressing the zero-point excitations. Then assume that b) in presence of any form of matter-energy these constituent particles interact with it and localize, driving the zero-point excitations to their usual level. Then it’s plausible that localization interaction is Lorentz-invariant because it happens due matter-energy presence, i.e. within its frame of reference. Another advantage that it might alleviate the vacuum energy problem as only induced zero-point excitations count.

    1. Concerning the vacuum energy and induced vs suppressed zero-point excitations. On intergalactic scale the suppressed zero-point excitations might still dominate as the space there is mostly empty. Then this model predicts the vacuum equation of state value as close to but still larger than minus one (due to dilution of the induced excitations during the expansion), which is vaguely consistent with the observed value.

      1. Ok, realized that the assumption for constituent particles to be non-interacting contradicts the need to provide a sort of stiffness in response to gravity.

  9. Dear Matt. I have tried to order your book using the discount code but I live in Spain and it only allows me to put a USA address. How can I get the book shipped to Spain?

    Kind regards,

    Julian Collins

    1. I’ll have to ask the publisher; the publication and shipping of books remains a black box to me. It may be that you have to go through their UK office and I’m not sure they are offering the discount there.

      1. Indeed, you can’t get the US discount, but the publisher says that Amazon in Spain is offering a comparable discount, and that is probably your best bet for the moment. I hope that works for you!

  10. It appears that the reason that 2 atoms cannot overlap is the same as the reason that we have white dwarves or neutron/quark stars. Could you expand on this topic in a blog post on this topic ?

  11. Hello Dr. Strassler, I’ve been a reader of your blog for several years (your series of posts culminating in measuring the distance to the Sun via meteor showers is fabulous) and I really enjoyed Waves in an Impossible Sea, so thank you for your writing!

    I have a question about confinement. In your post “A Half Century Since the Birth of QCD” from November 2023, you describe how confinement is the result of the dual Meissner effect. My question is, does this effect occur in classical Yang-Mills field theory, or is it strictly a quantum effect?

    1. Thanks for your kind comments about the blog and the book!

      Confinement is a quantum effect. In fact, the classical theory has a symmetry, known as a “scaling symmetry”, as does electromagnetism; that symmetry implies directly that the force between two particles at a distance r must be proportional to 1/r^2. Both quantum electromagnetism and quantum Yang-Mills theory violate that symmetry; in the former case the force is a little weaker than 1/r^2 at long distance, while in the latter case it is stronger at long distance. This part is easy to calculate in the quantum theory. What is hard to prove is that in the quantum theory the force eventually becomes constant — independent of r. It is this constancy of the force that represents true confinement. It is not only a quantum effect but a non-perturbative effect (i.e. not calculable using the simple techniques of Feynman diagrams or their equivalents.) It can only be caculated using computers — the numerical methods of lattice gauge theory. If someone can prove it using pure mathematics, they win a million dollars from the Clay foundation. Such motivation has not been enough to generate a solution, however.

  12. Dr.Strassler:
    I have a question inspired by one of your posts on one of your other sites, about the two slit experiment

    its my understanding, that in order to see this characteristic of wavicles, the two slits have to be very close together…..like less than a millimeter, does that sound correct?

    also, in the two slit experiment, say for a single photon, how is momentum conserved? in other words, if I fire my “photon gun” one photon, and the photon gun recoils in the negative X direction, the photon should, have momentum in the positive X direction. After it passes thru both slits, and ends up as a mark on the wall…..absorbed by an atom not directly behind the slits, what did it exchange momentum with? does it exchange momentum with the slits, as it passes thru both of them? If the photon gets absorbed by an atom, way off to the side, not directly behind the slits, it must have had sideways momentum given to it at one point. I watched a lecture by Dr. Susskind on this, and he seemed to indicate momentum was conserved, but didn’t say how…where was the momentum exchange?

    1. There is an interplay between the slit spacing, the wavelength of the light, and the size of the interference pattern, so your question doesn’t have an answer unless you are a lot more specific. Not also the interference pattern itself is not a sign of quantum physics; that happens with classical waves. It’s only when you see the interference pattern built up photon by photon that you are seeing quantum physics. [There are many wrong YouTube videos about this.]

      The photon can exchange momentum with the wall, just as a classical light wave can.

  13. Thank you so much for your book, which I just finished reading with great interest. Your use of the wavicle concept makes so much more sense to me than the Copenhagen interpretation. One question (of many):
    If a single photon is released that could be seen by two observers an equal distance away from the source, will only one of them see it, or both? Is this hypothetical similar to the two-slit experiment or different? Many thanks.

    1. Great question., I wish I could tell you that thinking in terms of wavicles resolves some of the puzzles in quantum physics, but it does not. It rephrases them, to some degree, and I think it prevents one from getting caught up in wrong ways of thinking (while the Copenhagen interpretation of “particle-wave duality” easily leads to unnecessary confusions.) Nevertheless, the puzzles are all still there. I carefully skirted them in the book because the story of wavicles and their rest masses does not require resolving them, and they would have been an enormous distraction from that story.

      As for your question: Only one observer (at most) will see your photon. And yes, it is very similar to the double slit experiment. The photon goes through both slits; it interferes with itself, creating a spread-out, complex pattern. Yet only one atom on the screen will grab it.

      However, this is not because a photon is a dot-like object when it is absorbed, as the Copenhagen interpretation would want you to imagine. The photon is still a wave, with a frequency. The absorbing atom, too, is not a dot; it has a radius of 1/3 of a billionth of a meter, which is not small on the scale of subatomic objects. The absorption process is an interaction among waves — or more precisely, an interaction among wavicles — that allow the photon to be absorbed by the electron wavicles that make up the outskirts of the atom.

      But the process by which the atom absorbs the spread-out photon, thereby making it impossible for any other atom to absorb it — and how this process is described in terms of probabilities rather than certainties — remains confusing. Either you use the many-world picture, in which the universe proliferates into a gazillion branches of possibilities, or you assert that the equations of quantum field theory leave something out, or… or like me, you sit back and hope someone smarter than you will come up with a better way to think about it.

      The many-worlds interpretation has the merit of being consistent with the equations (which the Copenhagen interpretation is not) but that does not make it intellectually or emotionally satisfying to most practitioners. It is popular, though, since it seems to be the best we have for now.

      1. Many thanks. This is very helpful. As between the many-worlds interpretation and confusion, I prefer the latter…

  14. Matt,
    Swimming with you through the wavey sea was great! No re-reading, except a paragraph here and there, was needed (although I am). You done good!
    As a non-physicist and non-mathematician, I have been reading to understand quantum mechanics for six decades. Ruth Kastner’s Transactional Interpretation finally makes sense to me (after four readings) so I would like to see if it is consistent with yours.
    While you offer many demurrals, I understand you to be describing that wavicles traverse trajectories in a pre-existing space-time container to translocate energy. Alternatively, Kastner’s (not Cramers’s) Transactional Interpretation proposes that instead, waves interact outside of space-time to translocate energy thereby creating events and their space-time separation. Note that this interpretation replaces particles, trajectories, and a space-time box with events, pre-space-time waves, and an evolving space-time.
    I wonder if your “demurrals” would make yours and Kastner’s interpretations compatible?
    Many thanks,
    Tony Way

    1. I’m afraid I can’t comment on that, since I don’t know Kastner’s interpretation well enough. But I am not taking a position on the interpretation of quantum physics in the book, just trying to give readers a useful picture without claiming that it is complete. I did make the remark that we don’t know if space exists or should be thought of as fundamental, and so for myself, as a scientist, I’m not assuming a space-time container in my research. But the picture I provided to readers does assume it, and might need for that very reason to be replaced someday — a point that I tried to make clear at the end of Chapter 14.

  15. Where can I find the Mathematica programs that you’ve used to make your blog animations, esp. the ones from “Fields and Their Particles: With Math?”

        1. I meant to ask where I can find your animation codes. I would like to try to reproduce you plot animations.

          1. Ah. This is all stuff I write myself and it’s kind of a mess — not commented or anything. And I have to think about what I do and don’t want to release. (Believe it or not, despite 10 years of animations, you’re the first one to ask.) Lemme think about it. There are more animations coming and you can remind me about it.

  16. Dr. Strassler:
    finished the book, absolutely loved it. I have placed it in my library right next to The Feynman Lectures on Physics. I would like, if possible, sometime in the future, a more detailed discussion of how a wavicle starts to spread out, but then collapses back to “point like” when it collides (exchanges momentum / energy) with another wavicle, and then starts spreading again.

    1. Great to hear you enjoyed the book!! Please leave a review on Amazon or GoodReads if you have the time.

      As for how to think about what happens when a wavicle collides with another wavicle — ah yes, I’d like a description of that too. This lies at the heart of perhaps the most difficult conceptual issue in physics. It’s a great question, but I’ll have to build up a whole infrastructure to even define and illustrate the question, so this will be something I probably won’t return to for months or even longer.

      1. I’m eager to get my hand on the book now, blame the recast site – the notion of science as “spectator sports” or since I rarely watch sports I don’t perform myself perhaps “spectator architecture” seems fitting. So seeing we have to wait for months or even longer perhaps some preliminaries to expand on the question or to have preliminary partial answers?

        In the following I may make the mistake of confusing the wavicle with the wavefunction but unless given hints I have to assume it is essentially the same interaction collapse. FWIW then here is a related question: Is the work “Answering Mermin’s challenge with conservation per no preferred reference frame” published in the less cited Nature Communications useful (does it survive basic criticism)? [Stuckey, W.M., Silberstein, M., McDevitt, T. et al. Answering Mermin’s challenge with conservation per no preferred reference frame. Sci Rep 10, 15771 (2020). https://doi.org/10.1038/s41598-020-72817-7%5D The conceptual issue does not seem testable but the work reinterprets “wavefunction collapse” as a relativistic effect. My naive view is that it adds to the wavepacket time dilation and length contraction the interaction collapse in order to conserve the wavefunction spin for the observer (here: interaction partner?). Then if we can familiarize ourselves with the first two effects, we could do the same with the potential third candidate.

        1. Well, this is not the type of question the book attempts to address; in fact, I deliberately skirt these issues.

          You are indeed at risk of confusing wavicle with wavefunction. But worse, it’s far from clear that wavefunctions collapse, or what it would mean for them to do so in a relativistic theory, or what would cause collapse, or how that collapse could be describable and predictable. This is why many of my colleagues either subscribe to Everett’s many-world view (as do Sean Carroll and Max Tegmark) or throw up their hands in dismay and confusion (as I do.) Someday I will try to explain the problem carefully; I have no solution.

          Regarding that specific paper (DOI number is wrong, but it is also here: https://www.nature.com/articles/s41598-020-72817-7 ), I would have to study it. Any serious papers trying to clarify how quantum physics really works have to be studied with care; otherwise one is likely to come away with the wrong impression. But real progress on a problem that has troubled us for a century is likely to require either a new experimental discovery or a profound new theoretical idea. This paper sounds potentially interesting, but not likely to be significant. I would expect bigger ideas to arise potentially from the interplay of quantum computing and quantum gravity research.

          1. Matt, thanks for the response! Yes, the paper discuss a relativistic consistent cause for collapse/Born postulate, which else is seen as a problem in search for bigger (likely testable) ideas.

    1. Thanks!! The book’s correct, but we have a missing redirect on the site. I’ve put in a temporary redirect and will make it automatic shortly. Try it again!

      1. Thanks. Just tried this and the redirect works great.

        [P.S. Just a quick note to tell how much I’m enjoying —and learning from— WiaIS.

        I’ve been (highly) recommending it to all my friends who find these things interesting.

        Finally, I very much enjoyed your appearance on Sean Carroll’s podcast.
        And I want to thank you for one specific point.

        That is, I’ve struggled for a long time to understand the precise mechanism as to how “the Higgs mechanism imparts mass to certain elementary particles”.

        During the episode you briefly mentioned, almost in passing, that the Higgs field affects (say) the electron field in such a way as to alter the form of the waves in the field, consequently changing its frequency, which in turn “determines the mass of the particle”.

        I can only tell you that when I heard this, simple as it may have been, lightbulbs went off all over the place. Thank you once again]

        Nichael Cramer
        Guilford VT

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