Of Particular Significance

Additional Atomic Articles

POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON 01/15/2013

I’ve been adding to my series of layperson’s articles on The Structure of Matter, which eventually will serve as an introduction to particle physics for those coming to this site for the first time. You might recall that in early December I supplemented my older article on molecules with an article on atoms. I got some terrific reader feedback, in the form of incisive constructive criticism, which allowed me to greatly improve the latter article. Well, readers, you’ve got another chance to help me out if you would like to — or you can just enjoy the read. I have three new articles (two of them short) which were put up over the last few weeks. These are:

Incidentally, the next stage in this series will be to describe electrons, and then I will turn to atomic nuclei, to the neutrons and protons that they contain, and eventually to the quarks and gluons that make up the neutrons and protons.

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34 Responses

  1. This is a major theme of particle physics, and it is not a settled matter, that behaviours like the Uncertainty Principle, Non-locality or even Quantum Entanglement are really intrinsic to the very nature of stuff in our Universe.

  2. Dave Glyer, Kudzu, GEN — I happen right now to be sufficiently confused about these issues in the context of quantum field theory (which, more than quantum mechanics, is the language used for modern physics) that I don’t want to try to answer until I’ve had some time to think about this specifically. There is an element of truth in everything that each of you has been saying, but I don’t know (because I haven’t thought about it enough) how to make a complete summary of the issues.

    DG, it is certainly true that measurement itself is not the only issue to worry about — but to say exactly what the other issues are requires being very precise about what is actually real versus what we often take to be real but need not be. If you say that the only things that are real are things we measure, then… well, clearly measurement becomes the only issue. But that’s a radical position that you probably don’t want to take… should the uncertainty that determines the size of atoms on a distant planet depend on whether someone measures them? So it is probably better to think of uncertainty as resulting from properties intrinsic to the nature of real things in the world and how they interact with one another — and that this uncertainty becomes especially obvious to us when we try to measure things, which forces us to bring real things into interaction with one another in particular ways that highlight how different the world really is from how it appears to us in our daily lives.

    I’m not very satisfied with this answer. You shouldn’t be either. Over the coming year or two I hope to improve my command of this subject to the point that I can answer you more precisely.

    1. I look forward to that; it sounds like there is a deep understanding to be imparted and some subtle issues to be correctly described. My joy at my last increased understanding of this subject was significant and I feel I may be headed for another.

  3. Where I wrote “The Uncertainty Principle is a consequence of any type of measurement error”, I meant to say “The Uncertainty Principle is NOT a consequence of any type of measurement error”.

    Plural of “momentum” is “momenta”, my mistake.

  4. A comment above had what I believe is a confusion and when I asked a knowledgeable party the first time about my (mis-)conception they did not readily clarify it because they saw fro a different perspective and did not fully see that I did not understand the full concept.

    Thus, let me comment on how I previously thought about the uncertainty principle and that it is not the complete picture.

    My ‘understanding’ was that when you try to measure something you have to ‘send something to it and get back some signal. When you want to know where your pencil it, there is not much of a problem. However, when to get to things that are REALLY small — and atom is small in this context — you have to hit it with something that will interact with it (very high frequency radiation, say). Doing so will change its position and its vector of travel (and thus kinetic energy in a given reference frame). I saw the uncertainty as the total uncertainty that this measurement attempt has to deal with and that it cannot minimize below a certain level.

    However, this is not quite all there is and I think that it understates the total uncertainty involved.

    Hope this helps to see how the measurement issue arises and that it is not the whole picture, even though I have not really said a whit about WHY it is not the whole picture. I am hopeful that the learned physicists/expositor will explain enough to clarify for those of us without all of the tools. I do know a couple of places that I could look, but I am not at home and I am not sure which of four or five books laid it out so that I understood that my simpler ‘measurement’ conception is not the whole story.

    As an aside, I got to this site via Peter Woit’s Not Even Wrong site: http://www.math.columbia.edu/~woit/wordpress/ This (Strasser’s) is one of a number sites/blogs that he lists to see things, and one several that he typically cites as about the best to see (and he seems to be right, from my visits so far — I have started to block out time to go through his instructional materials, some of which I know reasonably well but not a lot of it and the linking together of what I “know” is what I have found best about this site.

    1. You are correct in stating that the uncertainty principle is more than a measurement error, if it was then it would not be a mathematical result, but would vary depending on what you used to measure. For the longest time however myself could see this as the only possible explanation.

      The principle itself arises from the wave nature of matter. While a classical solid particle (Or point particle) can have a definite speed and location, a wave’s position and speed are related.

      A wave that has a definite velocity, (momentum) that is, one which we know the speed of very accurately such as a single-moded plane wave has a very uncertain position (If we remember that the wave is a measure of probability of the particle being at a given point.) since it is a uniform distribution. Thus definite velocity comes with indefinite position.

      We can make a wave’s position more definite however if we make it a wave that is the sum of many other, simple, waves. (A superposition.) In this case we can add all possible plane waves together to make the resulting wave’s position as localized as we want. However as we increase the localization of the wave we are adding more simple waves, each with their own momentum. The resulting wave has a better specified position but a less specified momentum.

      So due to the properties of waves we cannot have a wave that is both extremely local in position and definite in momentum, there must always be a compromise, and that is the uncertainty principle. (I will note there are other ways of deriving this relationship, such as matrix mechanics, but I am very poorly versed in those.)

      1. It is not a ‘measurement error’ in the sense that things are not measured as well as they might be if you did a perfect job of it. etc., It is a measurement error in the sense that the nature of measurement requires that there be a minimum amount of uncertainty because you are going to disturb the thing you are measuring and that minimum is identifiable. At least that is how I understood it. And, this minimum measurement error is not the whole part of it (or not the crux of it, not the fundamental part).

        1. The Uncertainty Principle is a consequence of any type of measurement error.

          You can measure and determine the position of a particle with no problem.

          You can measure and determine the momentum (linear momentum) of a particle with no problem.

          But you can’t determine both magnitudes at the same time without having an uncertainty on both simultaneous determinations.

          You see, the same thing happens with large objects, like say, persons, but the uncertainty is so small in comparison to the size of a person and and linear momentum of a person that we did not discovered this principle until we started dealing with very small objects, like particles.

          To determine the position of a person, that is, to be able to see a person, we “throw” particles of light towards that person, wait for some of the particles to bounce off the person and be deflected towards us and we use our instruments (our eyes) to capture some of the deflected particles.

          Those particles bouncing off the person affect the person’s linear momentum according to Heisenberg’s principle, but the value of the uncertainty when compared to the overall value of linear momentum of the person is so neglegible that is just the same as if there was no uncertainty.

          When we do the same with a particle (for instance, a proton) as target instead of a person, we need high energy photons to throw at such a small object, so that the wavelength of the “bullet” particles is small enough that they will crash into the target particle instead of swiggling around it and missing it.

          When the bullet particles bounce off the target particle, such impact affects the value of linear momentum of the target particle. As the target particle is so small, the change in linear momentum of the target particle after the impact has a order of magnitude that corresponds to the value determined by the uncertainty principle.

          The effect is the same for all target objects and bullet particles, the main difference is in the relative values of linear momentums between small target objects to bullet particles and large target objects to bullet particles.

          Kind regards, GEN

        2. That is true, small objects are easily disturbed, however the uncertainty principle also applies when no measurement is being made, when multiple ‘measurements’ with opposite effects are made or a measurement that has a minimal effect on the target.

          Consider for example shining a laser light through a narrowing slit. As the slit narrows and becomes more precise, at first the beam of light narrows in step. But at a certain point it begins to widen again as the uncertainty principle requires. (A video can be seen here: http://www.youtube.com/watch?v=a8FTr2qMutA ) Why would this be a measurement error? Any particles that interacted with the slit would be stopped, and the uncertainty only increases in the dimension that is being restricted.

          Of course this makes perfect sense if you think of the beam as a wave, and this exact situation works with, as I have said, particles up to C60 clusters.

          Another situation is ‘optical tweezers’ where light interacts with particles to hold them in place rather than deflect them. Measurement errors are troublesome but in many cases can be mostly or even completely eliminated by good experimental design.

          1. Just a few comments.

            For any type of interference experiment with single particles, whether it be a double slit experiment or a crystal defraction experiment, to have a better and more complete understanding of such cases, we should use Quantum Electro Dynamics (QED) and its tools instead of 1920s Quantum Mechanics (QM).

            QED tools and calculations are much more complex that QM’s, but with QED we can have a satisfactory explanation of double slit experiments with single particles, while with QM we do not.

            Regarding the phrase “and the uncertainty only increases in the dimension that is being restricted”, let’s have a comment about it: this phrase is confusing, because it could give rise to the idea that the uncertainty principle happens to any given dimension of a particle that is being restricted by an experiment.

            This concept is not proper: the uncertainty principle shows up only when in an experiment you want to measure at the same time certain pairs of properties of a given particle: this will only happen with those certain pairs of properties and not to any given pair of properties, and this will not happen if you try to measure any given property alone.

            Those certain pairs of properties that exhibit this behaviour (the Uncertainty Principle) are called non commuters, just because in certain equations these pairs do not support commutative math properties that other pairs do..

            It is my understanding that what you want to imply regarding “funny behaviours” of properties when trying to restrict them in certain experiments is more related to non-locality of particles, and not necessarily with the Uncertainty Principle, like for instance, in the tunnel effect.

            If we are using a QM model, we need to use the time-dependent Schrodinger equation to obtain solutions (wave functions) that exhibit features like the tunnel effect.

            Kind regards, GEN

            1. Indeed some good points. Especially I should have phrased things to be clear that the uncertainty in the velocity in one dimension but not the other increases as the slit restricts the light beam’s location in one dimension and not the other.

      2. Werner Heisenberg, using matrix quantum mechanics equations, first bumped into the non-commuting pairs of properties, and he realized that this behaviour was rather significant of the nature of particles.

        This happened while he was developing matrix QM with Max Born and Pascual Jordan.

        The non-commuting equations did not offer him a useful expression for the value (order of magnitude) of the uncertainty that was evident that non-commuters implied.

        So, he resorted to use wave packets as wave analogy for particles, and with just a few calculations he was able to obtain the now famous expression(s) for his (also famous) Principle.

        Kind regards, GEN

  5. Thank you Professor, I start to learn. All start with to fix the position of a particle using Spherical trigonometry, start with z(t) = z0 + A cos [ 2 π ν t ] .

    I must learn something hard when approaching, “During the rotation movement of electron, circular of elliptical, the plan of movement tilts more or less against the proton, against its own orbital, against its own rotation axis, and against many other things.”

    But π = 3.1415926535897932384626433832795028841971693993751058209749445923078164062\

    The complete elliptic integral of the second kind E is proportional to the circumference of the ellipse c :
    c = 4aE(e), where a is the semi-major axis, and e is the eccentricity.

    1. Allow me to say this: most real cases of quantum mechanics problems regarding atoms involve atoms much larger than Hydrogen atoms, or even Hydrogen-liken atomic systems. Such systems are complex enough that they do not have an analythic solution (mainly because the problem in question is within the “many bodies’ system” kind of problem). So, such kinds of problems need to be solved by a numerical method, so, such a number of sigfigs for constants like PI makes no sense for a numerical method.

      Kind regards, GEN

      1. Thank you Mr.Nusimovich, I find not much time to go thru Prof Strassler’s very good explanations, Iam trying. My problem lies in very principle of
        profoundness itself, not “many bodies system”. It lies in quantization of physical information and energy(physical effect or quantumaction), which is
        very small(Amplitude = (1/2 π) √ 2 n h / ν M, and Energy = n h ν) – which is very large in our daily life that we can touch and feel – and the bridge in between them thru higgs like field.
        The uncertainty also lies in its measurement?. I mean, the linear momentum of physical information and energy cannot be shifted(or measured) to known particles unless we know why a transcendental field protrude(ripple) into circular closed system, by a negative transcendental pressure which produce that protrude(along the direction of propagation) – If the displacement(protrude) is positive, the force is negative? . We know mass and energy not the same – we see two different world – circular and linear- if we dive into one we must forget another ??

  6. Professor, you are correct Iam 😡 . I dont know Higgs equation. I cannot understand Gauge invariance. There is difference between two gauge field(goldstone bosons and Higgs h) of same phase(pi radians) – one is inside W and Z bosons and another outside matter system, broken by a condensate, giving no zero value. Photons had escape velocity from matter system, but simple Higgs not, Higgs h partially. where a complex scalar field Φ acquires a nonzero value, where the field energy has a minimum away from zero.
    The vector potential changes the phase of the quanta produced by the field when they move from point to point(Phi – pi/2).
    A particle less than speed of light c acquire mass means, less than escape velocity from matter system – not subjected to known physical effects like gravity ect. If a particle ≥ to c subjected to spacetime curvature. Neutrinos subjected to dark matter gravity, if it acquire mass come into matter system. ????

    1. So — reading your comments over time, I start to think you need to learn one thing at a time, and learn it well. What I hear from you is that many of the things you’ve learned are jumbled around and mixed up. I sometimes see this among graduate students, and I always urge them to sit down quietly, forget what they know, and start fresh.

      In particular, I think you need to set gravity aside, first, and learn particle physics in the absence of gravitational effects — which is just what graduate students do, because gravity isn’t necessary to understand particle physics. Now I don’t know if you have gone through my articles


      but if you have not, I suggest you do so. You will notice gravity never comes up. [You’ll also see that even special relativity comes up only partway through.] And I have also written the articles to de-emphasize gauge invariance, which is not nearly as big a deal as it is often made out to be, and is something you can come back to later. That said, these articles are not the complete story of the Higgs field and particle, but they will perhaps give you a bit more intuition and keep you focused on one subject for long enough to gain some clear understanding.

  7. The frequency of matter waves, as deduced by de Broglie, is directly proportional to the kinectic energy E(excluding its potential energy). So the action of particle = 1/2 m v^2 – V(x). Phi is commonly defined as the ratio of a circle’s circumference C to its diameter d: Phi = c/d. Energy E is F used to travel 2Phi radians. A complete circle spans an angle of 2Phi radians.
    Higgs-like field cannot shift mass in a partical travel in linear motion.
    So, F = -dV(x)/dx.
    We know the particles revolve spherically in closed systems. Newton’s first Law of motion in straight lines work with these particles in law of inertia, despite gravitation, air resistance ect. So, there must be some reference frame to reduce those known physical effects to negligible level. If, F = ( m + Phi0^2 ) a , then those known physical effects become prominent.

  8. /Professor Strassler’s above post gingerly leans toward being an exception, but the hesitancy speaks volumes. I would suggest that the failure to and the difficulty in “explaining” the behavior of atoms is that we really don’t know what it is. We have no consistent answer to the question, “how big is an electron?”/- article on atoms: Richard Benish.

    /3. the shifting of particles’ masses via a Higgs-like field/ – If there is no relation between this and relativity, I have no further questions ! 😳 😯 😡

    1. There’s no relation between shifting particle masses and relativity. Here is a Newtonian theory of a particle with a mass shifted by a Higgs-like field. A Newtonian particle can be described as moving according to Newton’s equations:

      F = m a

      This can be derived from an action principle if you like, where the action takes the form : 1/2 m v^2 – V(x), where V(x) is a potential energy and F = -dV(x)/dx.

      Now let’s imagine there is a Higgs-like field in nature, Phi(x). And let’s write the action

      1/2(m+ Phi(x)^2 ) v^2 – V(x)

      which gives the equation of motion

      F = (m + Phi(x)^2 ) a – v^2 Phi(x) dPhi(x)/dx

      where again F = -dV(x)/dx.

      If Phi(x) is a constant Phi0 across the universe, like the Higgs field is, then this new equation of motion becomes

      F = ( m + Phi0^2 ) a

      which is Newton’s equation again, but with the particle’s mass shifted from m to m + Phi0^2.

      There you have it: a Newtonian, non-relativistic, non-quantum theory with a shift in a particle’s mass due to a Higgs-like field.

  9. Uncertainty Principle is a practical experimental limitation or a physical reality ?
    What is its notion compared to “principles of special relativity say that any reference frame is valid” ?

    1. The uncertainty principle is a physical realty, not a simple matter of not being able to measure something accurately.

      It arises from the wave nature of particles and the way waves work. The uncertainty is a wave’s position and velocity are related, a wave with a well defined velocity cannot have a well defined position any more than it can have to separate energies. Thus if you can measure the position say, of something accurately then it has, by its nature an uncertain velocity.

      The mathematics behind this is really quite sublime. I am hoping we will get a post on it here sometime.

      1. Thank you Kudzu,
        but many-body systems (in a condensed matter context) treat particle as wave in QFT. It is particle or wave ? – particularly in gravitational field.
        In Special relativity, this subtleness is avoided by speed of light as reference frame. Definition of particle was related to its mass.
        So Uncertainty Principle didn’t give the intuition for giving mass through Higgs field – but Special relativity does ?

        1. You’re quite confused. The particle/wave nature of objects has nothing to do with gravity at all. Nor is there any connection even with special relativity; the definition of “particle” is not related to its mass by special relativity. It is simply a separate issue from relativity altogether. Moreover, there is no connection with the Higgs field of either relativity or particle/wave nature of objects.

          To say it again: there are three very different subjects here —

          1. the particle/wave nature of what we call “particles”
          2. relativity, both special and general
          3. the shifting of particles’ masses via a Higgs-like field

          These three things are unrelated; you can imagine a world (i.e. you can write down equations) in which any one or two of them is removed, leaving the other(s) intact. [Which isn’t to say this is a trivial point — you’ll have to give some things up if you do that. You won’t be able to have things like photons if you give up (2), for instance.]

            1. A world without (1) could have things like electrons, but those things would be very different from what we’re used to. They would behave the way electrons behave in freshman physics class… the way people thought electrons behaved in the 1890s.

  10. These are very good articles I enjoyed reading. Also your normal articles are very understandable for outsiders,

    A question I had while reading the part about the uncertainity principle, how was it being discovered (deeper reason for the behaviour). After a glance over Wikipedia I understood, it arises due to the circumstances of measurements in these small scales, e.g. it is simply a practical limitation you encounter everywhere. I believe one or two lines covering this would be useful for an outsider.

    Best regards,


    1. You know, I’m not 100% positive about the real history. The fake history which physicists teach their students is something like this: the Bohr model of the atom (which does look more like plantary orbits) led to an approach pioneered by Sommerfeld where the first hints (in retrospect) of uncertainty appeared. But not until Heisenberg developed his approach to quantum theory in the mid 1920s (in which measurable quantities were represented as matrices instead of as numbers — hence the name “matrix mechanics”) was it possible to see that certain pairs of quantities couldn’t simultaneously be predicted or measured with absolute precision. And Heisenberg was able to turn this into a clear and unambiguous mathematical statement on the limitations of what can be observed, which we call the Heisenberg Uncertainty Principle.

      Well, I’m sure the real history was both more complicated and messier than that… perhaps a historian can enlighten us.

      But I do believe it arose more out of the theoretical considerations of quantum mechanics than out of any experiments. Of course experiments were crucial in telling people that they had to invent something beyond Newtonian mechanics, and in testing whether the equations for quantum mechanics were right. But I don’t think the experiments led directly to the notion of uncertainty. Instead, uncertainty was recognized as a consequence of the theory which the experiments inspired.

  11. The articles are very well written, I do not see any need for corrections.

    Regarding the article on isotopes being almost identical from a chemical perspective, I would mention the fact that they are so identical, that when we need to isolate an certain isotope, we have to use physical operations instead of chemical processes to do that, like in the case of uranium enrichment with centrifuges.

    It is true that in that in uranium enrichment there are some chemical steps as it is used uranium hexafluoride instead of uranium in the centrifuges, as uranium hexafluoride is a gas (it is a solid at room temperature, but it has a very low boiling point of around 56 °C) and uranium is a solid, and the gas form is more useful for the centrifuge process, but the actual isolation process (the separation of isotopes) is a strictly physical operation.

    Kind regards, GEN

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