Celebrating the Standard Model: The Forces of Nature

A post for general readers:

This is the first of several posts celebrating the hugely successful Standard Model of particle physics, the concepts and equations that describe the basic bricks and mortar of the universe. In these posts, I’ll explain (without assuming readers have a science background) how we know some of its most striking features. We’ll look at simple facts that particle physicists have learned over the decades, and use them to infer basic features of the universe and to recognize deep questions that still trouble the experts.

The Elementary “Forces” of Physics: A Classification of Nature

Perhaps you’ve heard it said that “There are four fundamental forces in nature.” Whether you have or not, today I’ll show you how to verify this yourself. (Actually, there are five forces, though we’ll only see a hint of the fifth today.) The force everybody knows from daily life is gravity; ironically, this force has no measurable impact on particle physics, so it’s the only one we won’t be looking at in this post.

I’d better emphasize, though, that the word “force” is slippery. Normally, in everyday life, a force means something that will push or pull objects around. But when physicists say “force,” they often mean something much more general. Because of that they sometimes use the word “interaction” instead of “force”.

For example, static electricity that holds socks together when they come out of the dryer is an example of an honest electromagnetic force — the socks really are pulled together. So is the force that pulls a magnet to a refrigerator door. But when a light bulb glows, that doesn’t involve a force in the limited sense of a push or pull. Yet it still involves the “electromagnetic interaction”, i.e. the “electromagnetic force” in a generalized sense. That’s because, although it is far from obvious, the emission (or absorption) of light involves the same basic phenomena that govern the force between the socks.

[Physicists use “electromagnetic” rather than “electric” or “magnetic” separately because these two forces are so deeply intertwined that it is often impossible to distinguish them.]

So when physicists say there are “four forces” (or five), they are imposing a classification scheme on the world around us. They mean:

  • All fundamental physical processes in nature can be divided up into five classes.
  • Each class involves one of the following types of interactions:
    1. gravitational (holds the planet together and holds us to the ground),
    2. electromagnetic (creates light, controls chemistry and biology, and dominates daily life),
    3. weak-nuclear (essential in stars and in supernova explosions),
    4. strong-nuclear (forms protons, neutrons, and their agglomerations in atomic nuclei),
    5. Higgs-related (associated with the masses of all known elementary particles).

There are currently no verified exceptions to this classification scheme. And by examining basic facts about the various particles found in nature, we can see these classes (other than gravity) in operation.

Particle Lifetimes and Masses: A Tool for Understanding

The protons and electrons we’re made of last forever, as far as we know, as do neutrons inside of stable atoms. But most particles that particle physicists make in experiments have a short “lifetime”; they “decay” away, transformed into other particles, in less than a second. Even a neutron, left on its own, has a lifetime; it decays, on average, about 15 minutes after it was created.

Each particle’s decay involves one or more of the universe’s “forces”, and by examining their lifetimes, we can observe these “forces” at work. The figure below illustrates this; each dot indicates the mass (on the vertical scale) and average lifetime (on the horizontal scale) of a type of particle. Some of the particles shown are elementary, while others are “composite” objects made from multiple elementary particles. Most of the composites are “hadrons” (examples of which are protons and neutrons) which are made of quarks and anti-quarks.

I know the font is small, but as you’ll see, we don’t need the details, just the overall patterns. If you’re interested in the details, please note:

  • The masses are given in terms of “GeV/c2“. For scale, a single hydrogen atom has mass of roughly 1 GeV/c2, an electron has a mass of roughly 1/2000 GeV/c2, and the Higgs boson, the particle whose discovery we’re celebrating this week, has a mass of 125 GeV/c2.
  • The lifetimes are given in seconds; they are generally very short! [I am using scientific notation on this axis: “104” means a 1 with 4 zeroes after it (10000); 10-6, means a number smaller than 1 that has 6 zeroes, 0.000001; 10-16 similarly requires 16 zeroes, etc.]
Figure 1: Masses and lifetimes for assorted elementary and composite particles known to particle physicists. Details in the text. [h/t to Prof. Brian Shuve, who made a very similar plot, for inspiration.]

I’ve color-coded the particles in the following way:

  • At center, the elementary particles muon (μ) and tau (τ), two heavier cousins of the electron, are shown as blue dots.
  • At the upper left, with the largest masses and very short lifetimes, are four elementary particles: the top quark t (green), the W and Z bosons (light blue), and the Higgs boson H (red).
  • At the bottom, in purple, is positronium (ee), an exotic atom made from an electron and a positron (the electron’s antiparticle); it plays a central role in PET medical scans.
  • All of the other particles, shown in gray, black, and brown, are hadrons (particles made from quarks, antiquarks, and gluons) somewhat like the proton. Their names and the color scheme can be ignored for today.

These particles decay on time scales which vary widely, from trillionths of trillionths of seconds to millionths of a second, excepting the neutron (n) which looks quite unusual on this plot. Nevertheless, you can see that the dots aren’t randomly distributed. They cluster in interesting ways, and the question is: why?!

Learning From Particle Lifetimes

In the following figure, I’ve put some ovals around these clusters of dots, in order not only to draw your attention to the clustering but also to direct our thinking about their origins. In fact, each of these clusters reflects one of the forces of nature.

The one that’s most obvious is the cluster that lies along the blue dashed line. All of these particles are decaying by the weak nuclear “force”, in what we may call its “low-energy” or “virtual” manifestation, which we observe for particles of masses much below 50 GeV/c2. (Today I won’t discuss the origin of the blue dashed line, or why the particles lie along it; in my next post I’ll explain that it arises from so-called “virtual” W bosons.)

Figure 2: Same as in Figure 1, but with the particles clustered into classes according to the “force” that causes them to decay. The blue dashed line highlights a trend for weak-nuclear decays for particle masses below 50 GeV/c2; the lifetime of the neutron (n) secretly belongs on this line (star). The dotted red line shows the minimum lifetime a particle of that mass can have; a stronger force puts particles near this line, while a weaker one puts them well to the right.

Why do we call this the “weak nuclear force”? It is weak in the following sense: the cluster on the blue dashed line lies far to the right of the red dotted line. The red dotted line shows the minimum lifetime that a particle of a certain mass can have and yet still be called a particle. A particle with a shorter lifetime would fall apart before it could even form, so it’s no surprise that we don’t see anything to the left of that line. But the particles on the blue dashed line have lifetimes far, far longer than this minimum. That’s because the “force” that is causing them to decay is relatively ineffective — i.e., weak!

(For an advanced article on the forces and their relative strengths, see here.)

With this in mind, our eyes are now drawn to the next obvious cluster, circled in purple, which in contrast to the previous cluster lies very close to the red dashed line. These particles have lifetimes that are nearly as short as they possibly can be, which indicates they decay through a strong force — the strong nuclear force!

Then there are a few particles scattered between these two clusters, which I’ve circled in orange. They don’t organize themselves as easily as the previous two clusters, but roughly speaking they all involve the electromagnetic “force”, which is intermediate in strength. A sign of this is that these particles, as they decay, emit one or more gamma rays, which are high-energy “photons”, i.e. particles of (an invisible form of) light.

Also there’s a cluster of green and blue dots up in the upper left: the top quark t and the W and Z bosons. These elementary particles also decay by the weak nuclear force, not by its virtual manifestation but directly. This “high-energy” version of the weak nuclear force is quite a bit stronger than the low-energy version, so the lifetimes are relatively shorter, and lie to the left of the blue dashed line, if you were to extend it that far. In fact, these particles’ decays lie relatively close to the red dotted line, which tells us that for particles with masses near and above 100 GeV/c2, the weak nuclear “force” isn’t weak after all!

The Outliers

There are still a couple of notable outliers. First, there’s the red dot up at the top, the Higgs boson, discovered in 2012; this week marks the 10th anniversary of that discovery. (However, we’ve been making these particles for 34 years; see yesterday’s post.) The Higgs boson’s decay doesn’t occur by any of the forces that I’ve mentioned so far; indeed it’s the only particles known that decays mainly through the Higgs “force”. One thing you can see is that this force is a little weaker than the direct weak nuclear force, because the Higgs boson lies well to the right of the top quark and W boson. But there’s more to that story, which I’ll tell you more about in a later post.

Let’s now look at the neutron, n; it’s way off on the right, with a lifetime more than a billion times longer than its nearest rival. But actually, it’s not as mysterious as it first appears. The neutron does have a large mass, but it always decays to a proton, along with an electron and an anti-nutrino. The proton’s mass is very close to the neutron’s mass; their masses differ by only a part in a thousand. The tiny gap between the neutron’s mass and the proton’s mass (plus the electron’s little mass) suppresses the neutron’s decay rate, and makes its lifetime a million billion times longer than you’d expect! (We’ll see why in a future post.)

We can account for this by plotting the neutron’s dot not at the neutron’s mass, 0.939 GeV/c2, but at the the mass equal to the gap between the neutron’s mass and the sum of the proton’s mass and the electron’s mass. That gap is only 0.0007 GeV/c2, and so we move the neutron’s dot down, following the green arrow, to the location of the star. The star actually lies quite close to the blue dashed line! Thus we learn that, despite initial appearances, the neutron decays via the same virtual weak nuclear “force” as all the particles in the blue cluster!

Unification of Forces?

So, as claimed, all known particle decays can be easily classified as due to one of the known “forces”. What else can we learn from this plot?

Isn’t it interesting that everything seems to be converging towards the upper left? The electromagnetic “force”, the weak nuclear “force”, and the strong nuclear “force” all seem to be approaching one another, near that red dotted line. Even the Higgs force isn’t that far away.

The fact that all of these lines are converging is the first evidence (quite thin to be sure, but provocative and interesting) for what is sometimes called “grand unification”, or perhaps, somewhat less grandly, “coupling-constant unification” [i.e. unification of the strengths of the forces.] The idea is that the forces shown on this plot may all be manifestations of just a single force. Their identity may only become obvious far above this plot, at much higher masses than those of a top quark or Higgs boson. This is a speculative idea that’s very popular, and you can see why a plot like this helps make it compelling. Unfortunately we don’t have any clear evidence for it yet.

However, if it were right, could we fit gravity in with it? Maybe; in some versions of string theory, for instance, that’s what happens. But that’s even more speculative, and we’re not going to go into the stratosphere today. We can discuss that another time.

Still, not everything about this convergence of lines is speculative. The coming together of the weak-nuclear and electromagnetic forces turns out to reflect how the Standard Model is put together! The key step in the Standard Model’s construction is that these two “forces” represent a reorganization of two even more elementary “forces,” of comparable strength, which are called SU(2)-weak and U(1)-hypercharge. The experimental evidence for this smaller-scale quasi-unification is overwhelming. Indeed this reorganization of the forces is the main role of the Higgs field, whose ripples are Higgs bosons. But that’s a long story, not for today. (Readers who are game for some math, albeit pre-university math, could tackle my recent series explaining some of the details, both in the Standard Model and in an extension of it that could potentially explain a possible small shift in the W boson mass.)

So there you have it. Just by staring at the properties of the known particles, you can see for yourself what physicists and science writers always claim: that as far as we know today, there are four [well…, five] elementary “forces” of nature. And you can also see why scientists speculate about the possibility that these forces may, someday, prove to be fewer, and perhaps just one.

20 responses to “Celebrating the Standard Model: The Forces of Nature

  1. A comment for readers of books 🙂 : “There are things you find nothing about in books”(the skipper in Typhoon by Joseph Conrad)

  2. Does the Standard Model predict/allow for particles heavier than the top quark?

    Is the top quark, in essence, the top limits of the up and down quarks, the highest angular momentum that either the up or down quark can achieve?

    Finally, is the Higgs field the inherent instability, of nature (universe)? In other words, if the “anti” Higgs won at the Big Bang the universe would be composed of antimatter.

    • The Standard Model, by definition, involves the particles we know. There could certainly be ones with larger masses, but not within the current framework. In particular, any particle with a larger mass *which gets its mass entirely from the Standard Model Higgs field* is ruled out, not by theoretical argument, but by experiment; it would dramatically increase the Higgs boson production rate above current predictions.

      To your second question, the answer is no. The top quark is not an excited up quark. The six types of quarks are all independent particles, all of them elementary as far as we can tell. [And all the quarks have the same spin (intrinsic angular momentum).]

      To the third question the answer is also no; there is no “anti-Higgs field”, and no “anti-Higgs boson.”. From the Higgs field’s point of view, as for the photon’s, matter and anti-matter is much the same. So there are no instabilities associated with the Higgs field that have to do with matter and anti-matter.

      • Socrates Sophroniscus

        Exciting times we are living in, hey? Can’t wait to see the first images from the JWST next and, of course, what other particles/new physics comes out of CERN.

        BTW; IF the universe were to be a closed, spherical shell, then isn’t an aether the only thing required to create was we see today? The aether I am referring to is space itself. So, the “energy/mass/forces” we see and measure is the ripples traveling on different curvatures. Yes, the limit is c, the ripples that travel in a straight path, like photons. Hence, as the ripple travels on smaller radii will have heavier masses.

        I hope JWST can give us high-resolution images of BHs.

  3. So, I assume that we can do the ‘neutron trick’ with any particle and its decay products, but that for most the rest masses of the daughter products are minuscule compared to the parent. So the mass gap and the parent mass are essentially equal?

    Also, can we plot the proton’s supposed lifetime in this fashion, or is its decay governed by another factor?

    • Yes, the gap for the neutron is by far the narrowest relative to its mass. There are a couple of others with narrow gaps but usually one part in 10 or so, not 1/10^3. The proton lifetime is a different question but yes, I will get to it later. If the proton decays, it must be through a process that doesn’t appear in today’s discussion.

  4. “Standard Model of particle physics, [describes] the basic bricks and mortar of the universe.”

    As far as I know, all the data for the Standart Model comes from the collision of two electric beams created in the laboratory environment. For instance, Higgs field is a by-product of the collision of beams. What evidence do we have that what we observe in the collision of electric beams is also valid outside the electric beams? Can you clarify?

    Also, as you say, Standard Model excludes the portion of the world governed by gravity. How are we justified to claim that Standard Model based on data from electric beams reveals “the basic bricks and mortar of the universe”? There is more to the universe than electric beams created in the laboratory. Thanks!

    • Oh, gosh, it’s not just electron beams. It’s a wide variety of different processes, both artificial (e.g. proton proton collisions at the LHC, https://profmattstrassler.com/articles-and-posts/largehadroncolliderfaq/introduction-to-the-large-hadron-collider/, electron beams colliding into matter targets, precision atomic measurements, etc.) and natural (cosmic rays, radioactive decays, supernovas, etc.) I don’t have time to give you a complete list but it’s dozens and dozens of different strategies that all cross-check one another. Some things are better cross-checked than others, of course, but the recent measurement of the magnetic properties of the muon would be wildly off if you started messing with the Standard Model.

  5. kashyap vasavada

    Great article. I suppose the red line is the time required to travel its own Compton wavelength. If the particles in hidden jets decay in less than this time, how do you interpret them as particles. Do you just say that they are hidden fields which do not materialize as either wave or particle?!!

    • They don’t decay in less than this time; they would all be to the right of the red line, and the ones that decay to ordinary known particles would have quite long lifetimes, typically even to the right of the blue line. The fields are hidden from *us*, but they’re not hidden from each other, and from their point of view their behavior is just as ordinary as is the behavior of the fields and particles we know and love.

  6. Ok, thanks for your reply above: https://profmattstrassler.com/2022/07/06/celebrating-the-standard-model-the-forces-of-nature/#comment-445777

    There is another question about the Standard Model that I hope you can clarify. From my reading of popular sources over the years, I got the impression that Standart Model has free parameters that are tuned to explain new observations. If this is true, Standard Model is not a model or a theory but a fit. It is no different than fitting a line to points. Points are observations. If so, Standard Model will be tremendously successful because it cannot be otherwise, it is a fit. In a way it resembles the Ptolemaic model, but instead of epicycles, in Standard Model, symmetry mathematics is used to fit new observations to the model.

    This is how it looks to a layman from outside. Is there any truth to this?

    • There’s no real truth to it. To make the Standard Model, you fit only 20 numbers — not functions, just numbers. From there, you predict tens of thousands of measurements. For instance (as a tiny example), with those 20 numbers you predict the lifetimes and decay patterns of the W, Z, Higgs, top quark, bottom quark, etc and that represents hundreds of numbers. You also predict the angular patterns of the decays, which represents another large set of numbers. You predict the rate at which quarks, leptons, W and Z particles are produced in electron positron collisions, and also the angular patterns in the directions in which those particles travel after they are produced — another hundred measurements. You can also predict the mass spectrum of the “hadrons”, using a computer simulation of the equations that you’ve found; this requires, again, fitting two or three numbers and then predicting a dozen hadron masses. We can’t, unfortunately, compute the complicated properties of a proton, but we can measure them, using *electron-proton* collisions. This requires fitting a few functions, which have a few parameters each. Then, with that knowledge, we can study *proton-proton* collisions. The fit functions for the proton’s structure, combined with the Standard Model’s 20 fit numbers, gives thousands of correct measurements, including the 39 shown here (ignore the first column, that’s not really a prediction) https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PUBNOTES/ATL-PHYS-PUB-2022-009/fig_01a.png ; notice the predicted processes cover 7 orders of magnitude. You can look through the lists of hundreds of measurements, many of them of entire functions rather than just single numbers, made by the ATLAS experiment by clicking around in here: https://twiki.cern.ch/twiki/bin/view/AtlasPublic . CMS and LHCb have similar pages.

  7. Is not the use of the “force” misleading? Is not this kind of simplification or unification again in antinomy to the hierarchy problems? Should not the general aim be to avoid effective field concepts in physics at all? Is not it much better to search for a more detailed knowledge what new particles might be inside the circles and ovals, if any? Is not it possible that the only bit hint from this graphics is that the H might be similar to the star a decay state of an unknown new particle?

  8. Naively looking at the chart that groups the interactions, two things immediately jump out:

    1. The Higgs decay is on the same Weak Force line. In fact, it’s extremely close to where the EM and WF would merge.

    2. The Strong Force grouping is qualitatively different from the Electromagnetic and Weak Force groups. It’s more centered around a fixed point than points drawing out a line. One thing that does NOT show up is a graphical indicator of the force merging at higher energies like appears for the WF, EM (and possibly the Higgs).

    Are those observations worth anything or are they artifacts of the chosen measurements?

  9. Would it possible for an unknown force to have no “real” particles, in the sense that it’s W and Z would lie to the left of the red line?

    I get the argument for why this is impossible for something like the actual weak force. The strength of the force is directly proportional to the average mass, and therefore average lifetime, of the “real” W and Z particles. The only way to prevent a real W or Z from ever existing would be to dial its mass up to infinity, which in turn would send the force strength to 0 (AKA the force ceases to exist). The underlying quantum field is like a really stiff spring, only stretching or compressing (changing state) when a lot of energy is put in or pulled out. That is what the high rest mass, the high energy required to create an observable “real” W or Z, really means- you’ve got to seriously whack the underlying field to produce such a persistent and coherent disturbance in it, and all the rest of the physics follows from this.

    But what prevents me from having a new force, a new quantum field, where its “virtual all the way up”? As in, you can mathematically model it as if there are “real” particles like a Z or W at high energies, but they can’t actually physically exist, because they’d decay before they’d properly formed, or would violate some conservation law.

    For example, something like a new “color” force but with super-heavy ‘gluons’ and considerably lighter ‘quarks’. The super gluons can never exist as “real” particles because they would decay too quickly into the real quarks, and can’t ever be directly observed for the same reason familiar quarks can’t. But we still get a real super-glue force between super-quarks, because of ‘virtual’ super gluons. My total amateur hour intuition is that real quantum field theory precludes things like this, because there are deeper principles and math that would make it logically inconsistent. But I’d love to hear what those are, or if something like this is indeed theoretically possible.

    • This is an excellent question, and your intuition is pretty good. I think there is no unique answer. Once a “particle” has headed to the left of the line, there’s no clear sense in which it is heavy anymore; its mass is 100% uncertain, and really you should replace its effects by the effects of the objects to which it decays… which then makes the answer sensitive to the details of those objects. What this tells you is that super-strong forces can do all sorts of things, some of which we may not know of yet; as a recent example slightly related to your question, see this post: https://profmattstrassler.com/2022/03/20/a-prediction-from-string-theory/. By chance this issue hasn’t arisen in particle physics data, but it may someday, and it surely arises in the physics of condensed matter physics.

      • Thanks. I wasn’t aware that quantum fields with coupling constants above 1 were even physically possible, in principle, let alone that the LHC can search for a distinct interaction signature they’d produce.

        It makes sense that a “heavy particle” with a 100% uncertain mass is an oxymoron. And it sounds like the entire particle model for what the fields are doing is just a widely useful heuristic and calculation tool, which can (and does) break down in situations like a very strong force or chaotic & transient disturbances in the field.

        Which leads to the follow-up question: What the real rules are for identifying- or defining- the “fundamental particle” states of a quantum field, especially for something like a strong force where you may not be able to isolate & observe them? Because from what I can tell, the Standard Model’s rule is something like this: Nature’s collection of quantum fields implies a kind of vector space for the allowed states any given fundamental particle, wave, etc. can be in- such as having +-e electric charge or +-1/2 spin- and the “particle” states are simply the basis vectors of that vector space. This is where all the group theory and “irreducible group elements” stuff comes in.

        If that’s the case, then I can see how you could define a roster of “fundamental particles” for any new quantum field, even if none of them are directly observable. And why I’ve seen some people actually define ‘particles’ as these abstract mathematical objects rather than something more obviously physical.

        • You’re getting into some extremely subtle territory, stuff that only professional quantum field theorists tend to know. You can have field theories that have *no* particle states at all; these include “interacting conformal field theories”, which are what is used to describe, say, a metal at a 2nd-order phase transition. It is a fortuitous and perhaps fortunate fact that the Standard Model can be so easily discussed in terms of particles; that needn’t have been the case. How to handle the general situation is still not entirely known; conformal field theories can be formulated in terms of their correlation functions and critical exponents rather than particle states with masses. More general quantum field theories, such as those that have one conformal field theory in the ultraviolet and a different one in the infrared, can end up going beyond current mathematical techniques. But this takes us deep into the weeds of an advanced quantum field theory course, and a rarified atmosphere that I can’t really justify getting into within this blog. I don’t want to discourage you from learning more, but I’m not sure who is out there who has tackled these issues without relying heavily on mathematics.