A Little Math; A Lot of Physics

One of my current goals is to explain how the Higgs field works to anyone who’s learned a bit of physics at the beginning-university or advanced pre-university level. As a step toward the goal, I am creating a set of pages that explain how fields work, why quantum mechanics implies that sufficiently simple fields have particles, and which aspect of a field’s behavior determines the masses of its particles.  You will find that knowing a little physics and a little math is helpful.

[I’m afraid that most of you who never had a beginning physics class at all will have to be patient. It’s an even greater challenge for me to explain the Higgs field to someone who’s allergic to math, or hasn’t had much math yet; I’m hoping my current efforts will help me see how surmount that challenge.  But meanwhile you might like to read my Higgs FAQ and my popular article on Why the Higgs Particle Matters.]

The first step is to remember how a ball on a spring works — one of the first things one learns in any physics class — and then learn a little bit about how quantum mechanics changes the answer — one of the first things one learns in a quantum mechanics class.  This is where the concept of a “quantum” first makes its appearance in physics.  Those articles are now ready for you to look at.  The next step [waves, both without and with quantum mechanics] will follow over the coming week.

Note: I’ve included, for the first time on this website, some animated gifs among the figures.  These should animate when you click on them.  I know they need improvement; over the next day I’ll be trying to make them faster to load and run.  Please be patient and let them load; but do let me know if you can’t make them work at all, and if so, what browser and hardware you’re using.  Update: they should be much faster now.

19 thoughts on “A Little Math; A Lot of Physics”

  1. Hi Matt. : in the start would you please answer this basic Q. :
    Can any thing in the physical be a necessity ?
    Are all fields , particles , constants , principles , rules……etc. contingents —can be otherwise –?
    Then what mechanism determines their properties ?

    • The answers to your questions aren’t known. A lot of what we’re doing in physics today is trying to get insight into these types of questions. So far it appears very little of what we observe in the universe is somehow necessary; in string theory, for instance, the number of possible types of worlds seems to be enormous. So it may be that just as the properties of the earth are contingent, most properties of the universe as a whole are contingent. But we just don’t know.

  2. Great, Tired of hearing about “molasses that slows things down”.
    Your particle explanation about Higgs causing oscillation between L/R version depending on the coupling makes a lot more sense.

  3. Love your site! I think you are a great physics writer and you help me understand these complex concepts very well 🙂 There is something floating around about some “Higgs Paradox” thing. Have you heard about it? Apparently there is something called entanglement occurring between detectors similar to what you illustrate in your quantum animation. Could you expand on this please?

    • Thanks! But — umm — I’m not sure what you’re referring to, so I can’t expand on it. “Higgs paradox”, entanglement among detectors and my quantum animation naively seem to me to be three unrelated issues. Can you point me to a link that might help me understand why you started thinking that maybe there’s some connection?

  4. Dr Strassler,

    You are doing a wonderful job as it is explaining physics to us “laymen”(does the word “laywoman” exist? I don’t know…) So you should not worry about “those who never had a beginning physics class”: they should have nothing to do with this site, and most of all with QFT!!!

  5. Jerry Coyne currently has a blog post entitled ‘A fish with gentials on its head’ which I couldn’t help but feel was a great title to grab people’s interest and get them reading. You seem to have chosen to go the other direction with ‘A little Math; A lot of Physics’! 🙂 But joking aside, thanks very much. Your work to explain these things is much appreciated.

  6. “the properties of the earth are contingent”

    Yes, The presence on earth of iron, silicium etc is also contingent. But what about the properties of iron, silicium etc. Are they contingent?

    • The answer simply isn’t known; but all evidence from theoretical considerations suggests that these properties are indeed contingent. There is nothing about the laws of nature that seems to require that the elementary particle masses and the strengths of the elementary forces take the values that they do. If you look at the equations we use for nature, and you imagine changing the masses of the quarks and electrons and the strengths of the strong nuclear and electromagnetic forces, you will find that doing so does not make our equations behave any worse or better than they normally do; they describe a different world than ours, but one that seems just as sensible. And if the particle masses and/or strengths of forces were different, then not only would the properties of iron and silicon be different, but in some cases either or both atoms might not exist at all [because their nuclei are then unstable.]

      So as far as we can tell at the moment, there appears to be something quite contingent about the specific properties of our universe. It is possible, of course, that this appearance is misleading. The only way forward is to learn more from experiments.

  7. What you just said is really great , allow me to add that any physical mechanism to generate all those properties is totally dependent on those same laws and constants and properties it assumed to generate , if we say that the mechanism could depend on extra cosmic laws and constants then we are in an impossible infinite regression…..
    Yes my friend our cosmos IS contingent , no other way.

  8. BUT what you said leads to a basic Q :
    What mechanism controls the electron field for ex. to ensure that billions upon billions of electrons on the cosmic scale have same mass and charge ?
    If mass and charge are contingent not necessary then something must control ALL field oscillations /ripples to have exactly same values .
    Then we are still waiting for your answer to : what are charges ,electric or color ?
    are we in the land of the unknowable ?

  9. Matt, thanks a million. It’s just what i need!
    Step by step.

    Michel Beekveld
    The Netherlands

  10. I am quite interested in the descriptions you have given and of others who may have shared perspective from a historical sense.

    Quotes in Brackets – “Let us see how these great physicists used harmonic oscillators to establish beachheads to new physics.

    Albert Einstein used harmonic oscillators to understand specific heats of solids and found that energy levels are quantized. This formed one of the key bridges between classical and quantum mechanics.

    Werner Heisenberg and Erwin Schrödinger formulated quantum mechanics. The role of harmonic oscillators in this process is well known.

    Paul A. M. Dirac was quite fond of harmonic oscillators. He used oscillator states to construct Fock space. He was the first one to consider harmonic oscillator wave functions normalizable in the time variable. In 1963, Dirac used coupled harmonic oscillators to construct a representation of the O(3,2) de Sitter group which is the basic scientific language for two-mode squeezed states.

    Hediki Yukawa was the first one to consider a Lorentz-invariant differential equation, with momentum-dependent solutions which are Lorentz-covariant but not Lorentz-invariant. He proposed harmonic oscillators for relativistic extended particles five years before Hofstadter observed that protons are not point particles in 1955. Some people say he invented a string-model approach to particle physics.

    Richard Feynman was also fond of harmonic oscillators. When he gave a talk at the 1970 Washington meeting of the American Physical Society, he stunned the audience by telling us not to use Feynman diagrams, but harmonic oscillators for quantum bound states. This figure illustrates what he said in 1970.

    We are still allowed to use Feynman diagrams for running waves. Feynman diagrams applicable to running waves in Einstein’s Lorentz-covariant world. Are Feynman’s oscillators Lorentz-covariant? Yes in spirit, but there are many technical problems. Then can those problems be fixed. This is the question. You may be interested in reading about this subject: Lorentz group in Feynman’s world.

    Can harmonic oscillators serve as a bridge between quantum mechanics and special relativity?”


    The Landscape “avant la lettre” by A.N. Schellekens- http://arxiv.org/abs/physics/0604134

    “The lowest harmonics correspond to the particles of the Standard Model, plus perhaps a few new particles. The higher harmonics correspond to an infinite series of particles that we can never observe, unless we can build a Planck Energy accelerator”

  11. I qualify as having an ‘advanced pre-university’ physics background, and I decided a year or so ago that I wanted to gain a greater understanding of modern particle physics. I’m not particularly driven to understand the Higgs field, per se, but I’ve found your site very helpful – articles such as that on virtual particles and the one that explains the quark make up of the proton have cleared up nagging questions that I had – so thank-you.

    In short, the conclusion that I’ve come to is that I really need to get to grips as much as possible with the maths behind at least some of the more basic physics.

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