Waves in an Impossible Sea

Got a Question?

If you’re reading Waves in an Impossible Sea and you have a question about something in the book, ask it here! No question is too basic or elementary; whatever question you have, no doubt ten other readers have the same one.

Although I can’t hope to answer all of your questions in a timely fashion, I will be taking note of them, and gathering them into a list of Frequently Asked Questions for each chapter. Please consider mentioning the chapter or even the page that inspires your question, if there is one.

If you question is inspired by the book but is on a subject that the book doesn’t cover, consider putting your question on this page instead; it will help me keep things organized.

55 Responses

  1. Hi Matt, thank for an excellent book that covers field theory. It’s unique.
    How does a wavicle, like an electron wavicle, travel as a standing wave, say in a wire or as a beta particle? Is an electron wavicle a stable entity or constantly regenerating? Does it matter if they are identicle?
    How does a boson exchange take place to mediate a force? How does it know where to go to make the exchange?

    Thanks again!

    1. Thanks! Glad you liked it.

      Well, if an electron is traveling, it is *not* a standing wave. It’s only a standing wave if it is stationary (relative to you). If it travels past you, you will see it as having a different shape, more energy, and a higher frequency.

      An electron is a stable entity, in the sense that it never spontaneously decays away and need not regenerate. That’s because (a) it has energy and charge, both of which are conserved, and (b) because there is nothing into which it could spontaneously be transformed via the process known as “decay”. This is discussed in Chapter 21 or 22.

      Yes, it matters a lot that all electrons are identical. All of atomic physics depends on it. But maybe you mean something else by “does it matter”?

      The idea that forces come from “boson exchange” is one of the phibs I hate the most, because it leads to questions such as yours that are perfectly sensible, but have no answer. The notion of “boson exchange” is math that has been misrepresented as physics. Forces do not come from “boson exchange”, because the bosons involved are “virtual particles”, which are not particles (i.e. wavicles). No objects are being “exchanged”. Instead, what is happening does not involve wavicles, but rather the same general behavior of bosonic fields that one learns in first-year physics class — where one sees that electric forces come from electric fields. To express those fields in terms of virtual bosons is sometimes useful mathematically, but obscures the physics.

      The history of this notion arises from Feynman diagrams, a math technique for doing calculations that was once the most efficient method. But the amount of real physics behind Feynman diagrams is limited, to the point that the method is used less and less every year, having been superseded by more efficient and general techniques.

  2. Hello, while reading chapter 5, when I got the discussion of photons having a zero rest I wondered; how do we know that the rest mass is zero? If a photon is always moving, there is never an instance where we can be said to be stationary relative to it, right?
    I found the distinction between rest mass and other forms of mass especially interesting, for I remember reading years ago that ‘light can exert a pressure’ (I was probably reading this in the context of the idea of solar sails) and ‘photons have no mass’, statements that seemed contradictory as I know enough physics to know that common definitions for pressure is a force per unit area and force being defined as mass times acceleration, and so I couldn’t understand how something with zero mass could exert a force.

    1. Good questions. I do address the issue of a photon’s rest mass briefly in chapter 17, but it’s reasonable to ask it now.

      I’ll start with pressure because that is simpler. The problem is indeed that you are trying to use Newton’s laws in an Einsteinian world.

      Pressure is a measure of the momentum carried by the objects pounding a surface. While in Newton’s world, momentum is mass times velocity, this is not true in Einstein’s world (or even in Maxwell’s world of electromagnetic waves.) For Newton, one can write the relation KE = p^2/2m , where E is kinetic energy, p is momentum and m is mass. But in Einstein’s one writes a formula for total energy: TE = Sqrt[(mc^2)^2 + (pc)^2], and kinetic energy is then KE = TE – mc^2, which one can show becomes Newton’s formula when speeds are slow and TE is just a bit larger than mc^2. You will see from Einstein’s formula, however, that total energy for a zero-mass particle is TE = pc. Thus a photon does carry momentum equal to its total energy divided by c, and so it can therefore exert pressure.

      Now, how do we know a photon’s rest mass is zero? At the risk of being circular, one way we know is that photons travel at the cosmic speed limit, which is only possible for objects with zero rest mass. Another clue is that we do indeed measure that E = pc for photons.

      But all measurements have uncertainties. You should therefore ask how precisely we know that a photon’s mass is zero, and through what means. The best technique is different from what you might guess, putting to use yet another relation between photons and the electromagnetic fields in which they are ripples.

      There is a direct linkage between the rest mass of a photon and the range of the electromagnetic force (a point I do not discuss in the book, but I suppose I should add to the book’s supplemental material.) That is, instead of the force being the usual 1/r^2 that we learn in school, the force would instead be approximately e^(-mr)/r^2 if the photon had a mass m. Measurements of long range magnetic fields across large portions of the universe give a limit on the photon’s rest mass: planetary magnetic fields measured by space satellites show unambiguously that the photon’s rest mass can be no larger than 6 × 10^(−16) eV/c^2, and a 2007 argument puts the limit at 10^(-18) eV/c^2. (There are some less reliable methods which suggest it must be smaller than 10^(-26) eV/c^2.) These methods are much more powerful than trying to make precise measurements of a photon’s precise speed, energy and/or momentum.

  3. I’m only on Chapter 7, and you have answered so many questions I didn’t even realize were questions.
    A HUGE thank you for your careful and lucid explanations. Interweaving the vews from both ends of the telescope.
    And your insistence on precise use of language– So Very Important these days.
    Those phibs in sound bytes never sound right to me, even without much science background.

  4. A question. Note 2 of Chapter 22 says “there’ s no precise, unambiguous definition of the up, down, and strange quark rest masses. That’ s because the powerful forces keeping these quarks trapped never allow them to be stationary and isolated.” Is it an experimental or theoretical problem, i.e. whether the quark trapping makes precise measurement of their masses very hard, or the trapping makes the quark immediate surrounding very messy, and they can’t be described as well-defined ripples in their respective fields?

    1. It’s more the latter than the former. Since we never find these quarks isolated, they are always surrounded by and interacting with other particles, so we don’t get a chance to isolate one of them and do a crisp measurement of its energy and momentum. But even more profoundly, the mass of a particle which is never isolated turns out to be ill-defined mathematically. So in a way, the problem exists is at all levels, and the reasons at the different levels are closely related.

  5. Just from the symmetry argument Fig.34 can’t depict a travelling wave as the wind field is mirror-symmetric relative to the pressure crests/troughs there and could describe the wave travelling in the opposite direction as well, while they must definitely be different. And really, the figure and its explanation relate to the standing wave at half the amplitude. To find the correct wind field let’s consider the sound generator plane. It starts moving to the right followed by harmonic oscillations around the origin. For the sound wave moving to the right, the max right-wise plate speed which is reached at the origin corresponds to the max sound pressure (due to its ram pressure), and simultaneously to the max right-wise wind speed. In the same manner, max left-wise plate speed at the origin – min sound pressure – max left-wise wind speed. Therefore, the max wind arrows should be placed at the crests pointing right, and at troughs pointing left.

    1. Again, correct. (Similarly, spins precess in a magnetic field, rather than rocking back and forth.) But here the issue was to get the point across that the wind is a field and that sound is a wave in the wind. Putting in the correct figure would have required another layer of explanation, lengthening the discussion and provoking additional confusion for more readers. Instead, I decided I would give the correct explanation (and the figure) here on this website (to be added soon); this seems the best compromise between being clear about the points that matter and being 100% accurate about the points that don’t matter.

      1. Classic travelling wave is a core concept for a book on waves and fields. Yes, it requires some thinking, but I believe that good understanding of simple cases will help readers to grasp more complex concepts later. For example, here we encounter not three, but five interconnected entities – air, pressure field / wave, wind field / wave, and sound is equally a pressure and a wind wave. Pressure and wind wave influence and support each other during the wave propagation, here’s just one step from an electromagnetic wave. I think it’s possible to explain it not going to technical details (I have it for myself). And I would have avoided “At the center of a trough or crest, the wind field drops to zero” which is outright wrong.

        1. On your last point, fair enough. On the rest of it, I disagree. You have made a very simple point into a highly complex one, and I’m likely to delete it from here because you are again straying into things that the book does not cover. The purpose of this page is for people to ask about things they don’t understand, not for highly trained physicists to teach me that I should have done things differently, which only is more confusing for those who are not highly trained physicists. This page has an intended use, and I can’t let it be taken over for a completely different use.

          1. Sure delete it, sorry if I went too far. I’m not a trained physicist, just an engineer with math/physics background and an eye for details. I really enjoy reading your book and will post at Going Beyond thereafter.

        2. You’re trained enough! 🙂 Of course I’m glad you’re enjoying the book and I’m happy to discuss it. Maybe I should add a page to “Got a Question” and “Beyond the Book” that specifically allows us to discuss the pedagogical choices made. I’m having trouble thinking of a good name for it…

  6. At Fig.33 what you describe as “leaning” is actually shearing. Leaning implies rotating as a whole, like The Leaning Tower of Pisa, while shearing involves sliding layers as in the shifting stack of cards. I’m not aware of using the leaning and shearing terms interchangeably.

    1. This is not a technical book, and I did everything to avoid technical jargon. “Shear” does not mean in English what it means in physics, and so it is yet another word that would put a unnecessary barrier between reader and subject.

      1. Oh, sure. I learned shear from physics textbooks only. But may be sliding or shifting would work better? Their English meanings are closer to the actual process.

  7. Beautiful wind field at Fig.31. And the original animated map at hint.fm/wind is mesmerizing! For the figure, it would be great to have full directionality info, such as by adding small arrows to the lines. Without that info we need an additional input to fully decipher the map. Here we have two storms “draining” counter-clockwise – the larger over Pennsylvania and the smaller over Kansas. From them we can trace the wind field to other areas, and the pattern of the wind blowing from thinner end of the lines emerges. However, some areas are still hard, for example my initial guess for Arizona-Utah border area was wrong.

  8. In chapter 11 (The Waves of Knowing) you say: “This is also why you cannot surf a wave crest that isn’t breaking; it won’t take you with it”. Here by “surf” you mean “float freely along” I think. However, surfing usually means “riding a surfboard”. Riding a crest (“going into wave”) starts before it’s breaking. A surfer slides her surfboard down a coasting crest obliquely such as her forward speed is equal the crest’s coasting speed, staying roughly halfway down the crest.

  9. Great book. I learned a lot. Found a couple of typographical errors :
    (1) Chapter 19 (page 257) : “millibarns” should be millibars
    (2) “Library of Congress Cataloging-in-Publication Data” (no page number) says the author is Karl Sigmund” and the title is “The waltz of reason…”
    My hardcopy is “Printing 1, 2023”.
    Probably you made those errors on purpose, to see if people are reading carefully 🙂
    Keep up the good work.

    1. Oops! millibarns –> millibars, I’ve done that twice this year. Hah! The Library of Congress error is entirely the publisher’s, of course, and was noticed some time back; they are fixing it in future printings. Maybe your copy will someday be worth more than you paid for it 😉

      1. (1) FYI, my motivation to acquire your your book came from reading Don Lincoln’s review in Science (February 22). Unlike Lincoln, I like the way you used end notes. (2) My daughter is a geologist. She loved that, on page 3, you compared human existence to seismic waves in rock. She may never finish the book, but she will always be inspired by that metaphor.

        1. If the metaphor sticks, that’s a huge win! And yeah, endnotes are always an issue — I don’t like them much either, and in any case it was the publisher’s decision.
          I had always hoped this would be a 21st century book, with clickable endnotes, but publishers are still in the 19th century. But I’m going to put all the endnotes on a webpage, when I get a free minute, so one can have them available on one’s phone while reading the book.

  10. Hi Matt,
    Not sure if this is the place to post this question but it is related to the book and the “Sea”.
    On you recent interview with Sean Carroll you were talking about the Luminiferous Aether.
    Matt: “this magical substance which was called The luminiferous aether a name which has got lovely resonances”
    Sean: “it’s a great name compared to a lot of other dumb Names physicist came up with, Too bad it doesn’t exist”
    Matt: “or maybe it is, we’ll come back to that”
    But the conversation never returned to whether or not that aether exists.
    Can you give a little overview of what your comments on the subject would have been if you got back to it?
    I am a little over half way through the book and you seem to like the idea of a ‘space medium’ but so far don’t seem to committed.
    Peter Becher
    p.s. I did ask the same question of Sean for his AMA April ’24 on why he seemed so sure that it does not exist. Not sure if he will answer it.

  11. On pg 212 of WiaIS you write:
    “In short, we have a remarkably clear (if incomplete) picture of what the known elementary fields _do_. Despite this, we have barely any concept of what they _are_ —assuming that’s even a question we should be trying to answer.”

    My question is, should we be concerned that this seems to sound curiously similar to the debate over the “Copenhagen Interpretation of QM” [CI/QM]. That is, (to simplify the issue enormously) that those who support the CI/QM argue that QM is basically “merely” a highly-successful set of tools for calculating the outcome of experiments/measurements, and that asking “what’s really going on” is a fundamentally meaningless question.

    (Similarly, those who are uncomfortable with CI/QM argue that this approach is deeply unsatisfactory, in no small part because it deliberately ignores the underlying “Reality” —in the EPR sense— of the situation.)

    Now, I would never accuse you of being in the “Shut up and Calculate” camp 😉 . But does this seem like a reasonable characterization of the (current?) situation? And again, should we be concerned?

    1. I don’t think there’s reason (yet) for that level of conceptual concern. Quantum mechanics is inherently confusing to the human brain, and that’s why weird interpretations have emerged for it. By contrast, the issues on page 212 might be much simpler than that.

      If you didn’t understand what air was, you might have trouble interpreting what a barometer actually measures; “pressure” would be just a name, not an underlying concept. Once you had a better grasp of the nature of air, that would change. It’s possible that we can’t interpret what the electron field is because we don’t understand the full internal structure of the cosmos; once we learn that structure, perhaps the electron field’s nature will become clear. In some string theory constructions of imaginary universes, this is what would happen.

      Alternatively, it might turn out that space doesn’t exist after all, and both space and its fields will be interpreted in terms of, say, emergent phenomena in a completely different physical system.

      It’s true, though, that space and the relativity principle are sufficiently puzzling that we might end up with unresolvable confusions and the need for debateable interpretations. Too early to say, I think.

  12. Thanks for the detailed walk through of the basic concepts professor

    I am trying to understand how the gravitational mass varies with position/velocity of the observer.

    What is the formula for the same ? It seems different from relativistic mass obtained by relativistic version of E = mc^2.

    I also saw terms such as metric tensor & energy momentum tensor (in Wikipedia). How would they differ based on relative velocity ?

    Basically I am trying to visualize how space curves & influences motion based observer’s relative velocity/position.

    1. There is, in fact, no unambiguous definition of gravitational mass. In general relativity, the concept doesn’t really arise unless you force it to. This is why it is hard to find a clear definition of it on-line; there’s no clear definition in physics. Instead, in general relativity the question is subsumed into the equivalence principle: https://en.wikipedia.org/wiki/Equivalence_principle .

      The one thing that we can say is that if you are in a situation where Newton’s laws almost work, then it is clear that gravitational effects depend on motion in ways that Newton would not have expected, and that they grow as an object’s energy grows. But I haven’t been able to find any expert in general relativity who has been able to give me a reference in which it is shown that, in some limited situations, there’s a definition of gravitational mass that is clearly useful and widely agreed upon.

      I hope I’ll soon be able to understand this messy situation well enough that I can explain better why there’s no good answer. But up to this point, my efforts to resolve my own questions have run up against the fact that experts seem to disagree.

  13. When I read your discussion about the wave speed method of detection of motion, I was wishing you included an explanation about redshift. It seems like it should be related somehow.

    1. This is a bit intricate. There are different causes for redshift, which can be due both to relative velocity and to gravity. Let me just focus on the relative velocity case, as that’s more closely related to the wave-speed method.

      There is a “redshift” and “blueshift” in sound, too; that’s the Doppler effect. If the observer and the object emitting the sound wave are receding from each other, then the sound frequency drops. But the amount of the drop depends *both* on the speed of the object relative to the air *and* the speed of the observer relative to the air.

      The redshift for light is similar, yet different. If the observer and the object emitting the light wave are receding from each other, then the light-wave’s frequency drops. In this case, however, the amount of the drop depends *only* on the speed of the object relative to the observer.

      In short, as is the case over and over again, light resembles sound, yet differs from it in a crucial subtle way. The Doppler-like effect for light is arranged just so that it is independent of any motion relative to light’s medium — allowing it to be consistent with Galileo’s relativity. For sound, this is not the case; one can use the details of the Doppler effect to measure one’s motion relative to the air.

      This is the key conceptual point. I could go into more detail, but such details can be found in many places, such as Wikipedia. https://en.wikipedia.org/wiki/Doppler_effect https://en.wikipedia.org/wiki/Relativistic_Doppler_effect Let me know if my answer and the information on Wikipedia still leaves you wanting more information.

      1. I’ve seen it described something like this: light maintains its speed regardless of its frequency or wavelength, but an observer moving toward encounters the crests sooner and in a way more compacted, and therefore at an effectively higher frequency (blueshift); and the opposite for redshift. It’s not that the frequency actually changes, it’s the relative motion that makes it appear differently.

        So it seemed kind of similar to the wave speed method where you described watching the water waves pass by the boat — to determine if you’re moving, possibly how quickly, and in which relative direction.

        I’m a non-expert. In reading your book, I really appreciated your methodical examples throughout and consistent wording without relying on the usual seemingly inaccurate metaphors (Mrs Thatcher at a party).

        1. On the one hand, you are right, these issues are related. But you are imagining that there is a “true” — i.e., intrinsic — frequency. And this is a tricky point. Frequencies are generally relative, since they depend on speed, and speed is relative. For light waves, there is no intrinsic notion of frequency.

          This is already true in Sound. First, there is the wave frequency as seen by the sound emitter — for example, a violin plays a note on its G string, and that G is the note, right? Well, not so fast. If the violin is moving rapidly through the air, then the sound wave as seen by someone stationary with respect to the *air* may hear it as an F, not a G. There is no “true” frequency of the sound wave, unless you define truth in an arbitrary way… why should the violin’s perspective be truer than the air’s perspective? Meanwhile, someone else, moving throug the air in a different direction, may hear it as an A, or an F-sharp. Who is right? Everyone is right.

          In Light, it is even more true. Observers moving relative to one another see the light’s frequency as different. The light-emitter’s perspective is just that of one more observer; indeed, if the light scatters off some moving mirrors, the light-emitter may not even see the reflected light as having its original frequency. Again, everyone is correct. There is no true, intrinsic freuqency for a light wave. This is Einstein’s point.

          For an electron, things are otherwise. Observers moving relative to one another see the electron’s frequency as different; that’s all relative. But in this case there is a special perspective — the perspective of the electron, which an observer stationary with respect to the electron will share. In this case, we can define an intrinsic notion of frequency… that of the observer at rest with respect to the electron.

          By contrast, no one can ever be at rest with respect to a light wave, and so no light wave (and, more specifically, no photon) can have an intrinsic frequency. This lack of an intrinsic frequency is characteristic of any object with rest mass equal to zero.

          And so, yes, redshift and blueshift are relative. If you are moving toward me, and light is approaching us from the other direction, then, yes, you will encounter the light waves’ crests more often than I do — and so, yes, you will see the light as blueshifted relative to the way I see it. But we could say it the other way round; from your perspective, I am moving toward you, and the light approaches from behind me, and so I see the light as redshifted relative to the way you see it. Both viewpoints are correct. There is no “true” perspective. And so your statement “It’s not that the frequency actually changes, it’s the relative motion that makes it appear differently.”, which presupposes that there is a true frequency, is not correct, even though the picture for why redshift and blueshift occurs is correct.

          Gravitational blue- and red-shift are even more subtle. I don’t dare go into that today!

  14. Sincere thanks for this brilliant (and brilliantly written) book.

    I have a question about figure 37. I believe that this represents what happens for a laser beam, which makes sense given that a laser is coherent and all the photons are in phase with each other?

    But that raises the question of what happens if the photons aren’t coherent. If two photons are emitted from a light bulb out of phase with each other do they destructively interfere? It’s got me wondering how many non-coherent photons combine to create a high intensity light beam at all without cancelling each other out (they clearly don’t do so, but I can’t see how!).

    1. I’m glad you enjoyed the book!

      Each photon has energy E = h f, where f is its frequency and h is Planck’s constant. The energy of the two photons is 2 h f, and that cannot disappear.

      Locally there can be interference effects, but two incoherently emitted photons cannot be arranged to destructively interfere everywhere. There can only be an interference pattern which rearranges where the energy goes, but does not reduce it. The details depend on exactly how, when and where the photons are emitted.

      1. Thanks! The conservation of energy makes perfect sense. I’m not sure what stops two photons from destructively interfering everywhere though? What’s to stop two photons from being identical to each other apart from one being exactly the opposite phase of the other?

        I know I’m missing something, I’m just not sure what it is?

        1. 🙂 I don’t blame you for not being satisfied with my answer, even though it is correct.

          To resolve what’s puzzling you, I think I would need to take you into a bit of the math of the quantum field theory. You are thinking classically, in which electric fields from two waves are ordinary numbers and simply add, whereas in quantum physics we deal with states. Also there are subtle effects from the fact that a single photon emitted from a light bulb is not an infinite sine wave, and must instead be treated as a wave packet — a sine wave inside a finite envelope. At the moment I am not sure of the simplest way to show how this would work, but I will think about it and try to come up with a simple argument. It may not, in fact, be simple…

          [An example of something even more important, but not at all simple, involves the claim (even in classical physics) that no information travels faster than light-speed even though phase velocities, for certain types of fields, are generally faster than light-speed. Sometimes facts about waves really are subtle.]

          1. Thank you. I will take it on trust for now.

            It’s worth mentioning that the list of things I’m taking on trust is significantly smaller today than it was a week ago, entirely thanks to your book. I’m deeply grateful for all the hard work that clearly went into it.

  15. Big fan of yours and Lenny S’s classes. This refers to the kindle edition, chapter 15, no table 5. Not on iPad and not on pixel. Blank page on iPad, missing page number on pixel. Great book!!

    1. Thanks, I will let the publisher know immediately. You said Table 5; but Table 4 is on the same page. Is it also missing?!

      Tables 4 and 5 are now posted here: https://profmattstrassler.com/waves-in-an-impossible-sea/waves-in-an-impossible-sea-tables/

      Update: The publisher says: “If the table is missing, the most likely explanation is that his download got corrupted. He should contact Amazon and send them a screenshot to see if they can help him. The problem is not on our end.” Let me know if you get this resolved, or if you can’t.

  16. A question concerning note 4 of Chapt 7 in WiaIS (i.e. where you note that are “drastically abridging the complex prehistory I’d Einstein’s idea [concerning Special Relativy]):

    Rather than ask you to expand on that history here, can you suggest a good history-of-science reference that discusses this history?

    (For example, I know Pais’s excellent technical biography of the life and work of Einstein [“Subtle is the Lord”] and although the book gives an overview of these issues, it would be nice to find a book-length that covers this topic in depth.)

    Thank you

    1. Great question; I’ll have to put a good answer together and add it to the FAQ for chapter 7.

      Unfortunately, much of what I know has been cobbled together from many sources, including primary sources and historical research articles, and I can’t just now recall a source that goes into the depth you are asking for. (Moreover, I didn’t keep careful records since I never planned to cover this in the book.) One person who would probably know would be Peter Galison, and you might start with his books/articles (which I highly recommend) and the sources that he uses. It’s really worth learning a lot about the thinking of Lorentz and of Poincare’, who were close to the right ideas about relativity of space and time but never fully understood or accepted Einstein’s novel perspectives; also there are many interesting side stories involving people like Max Abraham and Fritz Hasenöhrl, who were able to recognize that there was probably something important about mc^2 but didn’t think big enough. Compared to the efforts of most others at the time, Einstein’s two remarkably short papers are blindingly clear and to the point; reading them is like drinking cool, fresh water.

      One article worth reading, based on a longer and more technical paper by Steve Boughn and Tony Rothman, is this summary by Rothman in Scientific American. I am not sure its claims all stand up to scrutiny, (and by “mass” Rothman always means “relativistic mass”, not “rest mass”, so be aware of that) but it does give some idea of how close the community was to figuring out relativity by 1905. If Einstein hadn’t existed, I suspect the main ideas of special relativity would probably have come together within ten years of 1905. Einstein short-circuited the process and moved everything along much faster. He wasn’t working in a vacuum, despite his relative isolation; he read a lot of the contemporary scientific papers, and so he probably encountered many of these confused ideas with little pieces of the truth. Nevertheless, the vision that what was involved was not limited to electrostatics, or electrons, or black body radiation, and instead was about literally everything — space, time, matter and motion — was bold and breathtaking, as well as correct.

      I will try to find you a couple of my sources and post them here, so please check back now and then, and let me know if you happen to find something particularly good.

      1. Thanks. I look forward to reading any further information when it’s available.
        (BTW, I knew Tony (way) back in grad school.)

        [Not a question, but I’ve often wondered about the follow-up question:

        That is, the general consensus concerning the origins of Special Relativity seems to be that while, as you say, Einstein pulled everything together in a crisp, elegant manner, it’s also true that lots of folks were flirting around the edges of SR and it’s likely it wouldn’t have been too long before it had come together.

        OTOH, it’s interesting to speculate that, if Einstein hadn’t lived, how long would it have been before we had _General_ Relativity. That’s certainly a whole different kettle of fish.]

  17. Just before I buy your book, will it help me (B.Sc. Eng with two years of physics in the late 70s) to understand what forces are – how do repulsion and attraction work?

    1. If you’re asking about forces in general, then that’s a tough question with a book-long answer, because forces come in great variety and can cause attraction and repulsion in a wide variety of ways.

      But if you’re asking specifically about the elementary forces — gravity, electromagnetism, strong nuclear, weak nuclear, and Higgs — then the book gives some insights. It does not give a complete answer, however, and that’s for a very simple reason: we don’t have one yet.

      What you learned in first-year university physics about electric forces has grown to become the universal story: across all known physics, there are elementary fields and particles, and these particles interact with each other via the fields, causing repulsion and attraction depending on the specific properties of the fields and the particles involved. In the case of gravity, we have a more complete story, thanks to Einstein, of how the gravitational field creates what we view as an attractive force; that’s through the notion of curved space, which I do describe in the book. But in the case of the other forces, there are many possible stories, none of which has been addressed by experiment, and the true story may be something we haven’t thought of yet. The most honest way to answer your question, then, is “we don’t fully know how repulsion and attraction work for the elementary forces of our universe.”

      This isn’t to say that physicists are completely at sea when it comes to these forces; far from it. We have various methods to calculate precisely the energy of two particles a certain distance apart. (Among them are the famous Feynman diagrams, which are often over-interpreted as explanatory, whereas in fact they are simply a method for calculation.) If that energy increases as the two particles approach each other, then there will be a repulsive force between them; if it decreases, there will be an attractive force.

      In other words, we physicsts have a very clear idea of what particles and fields do; we know the rules by which they operate. We can predict when a force will be attractive and when it will be repulsive, along with many other more subtle details, such as how the force changes with distance (which always differs from the 1/r^2 laws learned in first-year university physics).

      But knowing what fields do is very different from knowing what they are, and from knowing why they do what they do. My sense is that the latter questions are the ones you want to know the answers to. I want to know the answers too, but these are still open questions for coming generations to tackle.

      In short, the book won’t answer the question, but no scientist or author alive today could hope to do so. What the book does is explain what we know and delineate clearly what we don’t. I hope that will be, if not satisfying, at least profoundly clarifying.

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A decay of a Higgs boson, as reconstructed by the CMS experiment at the LHC