The God Particle

By Sean Carroll | August 6, 2007 9:08 pm

Dennis Overbye does us all a huge favor by coming clean about “the God Particle.” The phrase refers to the hypothetical Higgs boson, long-time target of particle physics experiments. It was coined by Leon Lederman as a shameless ploy to sell books, and ever since has managed to appear in every single mention of the Higgs in the popular media — for example, in the headline of Dennis’s article from a couple of weeks ago.

Physicists, regardless of their stance toward timeless theological questions, hate this phrase. For one thing, it puts this particular boson on a much higher pedestal than it deserves, without conveying anything helpful about what makes it important. But more importantly, it loads an interesting but thoroughly materialist idea with absolutely useless religious overtones. Even harmful overtones — as Lederman himself notes, his coinage came about just around the time when creationism began to (once again) become a big problem, and this confusion was the last thing that anyone needed.

Furthermore, everyone knows that “the God particle” is misleading — even all of the journalists and headline writers who keep trotting it out. It’s just too damn irresistible. Particle physics is fascinating, but it takes some effort to convey the real excitement felt by experts to people who are watching from the sidelines, and a hook is a hook, shameless or not. If my job were writing about particle physics for a general audience, I doubt I’d be able to resist the temptation.

But, as Dennis notes, this God-talk is part of a venerable tradition on the part of physicists. We use “God” all the time to refer the workings of Nature, without meaning anything religious by it. Or at least, we used to; the nefarious encroachment of Intelligent Design and the religious right on our national discourse has given some of us pause. In the past I could have given a talk and said “Either you need a dynamical origin for the primordial cosmological perturbations, or you just have to accept that this is how God made the universe,” without any worry whatsoever that the physicists in the audience would have been confused. They would have known perfectly well that I was just using a colorful metaphor for “that’s just how the universe is,” in a purely cold-hearted and materialistic fashion. Nowadays I find myself avoiding such language, or substituting “Stephen Hawking” for “God” in a desperate attempt to preserve some of the humor.

All of which is to say: religion is impoverishing our language. I want God back, dammit.

CATEGORIZED UNDER: Science and the Media, Words
  • Moshe

    My issue with the term, beyond the religious overtones, is that it somehow gives the impression that the Higgs particle is in privileged position in the standard model, the origin of mass etc. etc., whereas the truth is that the VEV of the Higgs field does all those miracles. Those are simply two different (albeit related) objects with similar names.

  • Ulrich Mohrhoff

    How is the Higgs a “thoroughly materialist idea”?

    You may have a materialistic way of thinking about the Higgs, but that has something to do with you, not with the Higgs.

    The Higgs fits into any world view that can accommodate the Standard Model, including but not only materialism.

  • Ellipsis

    And as we also know, even the only-very-slightly-more-responsible statement that the “Higgs explains particle mass” is also utterly misleading. 1) The Higgs does not explain the values of rest masses of individual fundamental particles. 2) The Higgs also does not explain the old problem of why inertial mass is the same as gravitational mass. The Higgs just couples proportionally to mass and is needed to make the standard model make any sense at all (and not give infinite predictions just above the TeV scale).

    Maybe (just maybe…) the real Higgs might turn out to help us answer those two questions. But the predicted standard model one, as we know, does not.

  • George Musser

    OK, then, what *should* we journalists say about the Higgs? Can we at least say it’s why all particles don’t have the same (zero) mass?

  • Eric

    The Higgs mechanism does generate field-theoretic masses for the elementary particles. The actual values depend on the Yukawa couplings, and these are free parameters in the Standard Model. Thus, the Standard Model offers no explanation of the mass hierarchies and mixings between the different generations. However, the Yukawa couplings can be explained naturally within string theory.

  • Ellipsis

    Hi George — you definitely shouldn’t say that, as for example the proton would have mass even if the component valence and sea quarks were (somehow) massless — most of the proton’s (and neutron’s, and all light mesons’ and light quark baryons) rest mass is from the internal momenta of the quarks and gluons, not their rest masses.

    If you were to add a “fundamental” in front of “particles” it would be closer.

    But still not to my overly-critical liking, as it really doesn’t _explain_ “why” — the Higgs field just _relates to_ masses, it doesn’t really _explain_ them.

    Hmm, what’s a truly accurate and precise one-liner about the Higgs…?

    Good question.

  • Joseph Smidt

    Oh, so this particle is not what we are supposed to be worshiping? That New York Times always gets me.

  • Sean

    Moshe’s issue, although a real one, is sufficiently higher-order that I wouldn’t be upset to see it glossed over in popular presentations. It would be nice to appreciate the distinction between a field’s expectation value and its associated particle, but on most days I’m not that ambitious.

    The “explaining mass” issue is trickier. Within the standard model, if the Higgs didn’t exist, elementary particles would all have zero mass. That’s the sense in which the Higgs “explains mass” — the masses for particles in the Standard Model are all proportional to the Higgs expectation value. It doesn’t explain what the constants of proportionality are, true enough, but that’s another higher-level issue (in my personal hierarchy).

    The thing that bugs me about the “explains mass” business is that the particles responsible for most of the mass in you and me — protons and neutrons — are not elementary, and don’t get their mass from the Higgs at all. They get mass from the strong-interaction binding energies (QCD) holding the quarks and gluons together.

    A safe statement is “the Higgs is responsible for giving masses to the elementary particles of the Standard Model.” But that will never win any focus-group tests when placed against “the Higgs explains the origin of mass.”

  • Moshe

    I don’t see it as higher order effect, but it is a matter of taste. The point is that explaining the masses of elementary particles in terms of properties of the medium the propagate in, meaning in this case the Higgs VEV, is much less mysterious than relating them to some godly particle. It is intuitive and almost precisely correct to imagine the particles becoming massive because it is “more difficult” to move in the medium for which the Higgs field has acquired a VEV.

    (more generally, the elementary objects in our description of almost everything are quantum fields, not particles. Many times they don’t even have “associated particles”, would be nice if this was better appreciated, but that’s a different story…)

  • Aaron Bergman

    The problem with the phrase “the god particle” is that it reeks of condescension and disrespect. It pretty much epitomizes everything horrible one can perpetrate in “outreach”.

  • Jimbo

    I agree w/Sean re: Lederman’s shameless hype to sell his (I think) rather lowbrow rundown of particle physix and Higgsy…Or George Smoot’s post-COBE press conf., gushing, “Its like seeing god…”.
    Arthur C. Clarke(Isacc Asimov?) once quipped that any sufficiently advanced technology or species would appear `god-like’ to lower denizens of the galactic populace.
    If Holger Nielsen’s recent speculation that advanced effects from the future might manipulate discoveries at the LHC, then perhaps `WE’ in the future are playing god, with ourselves in the present, not unlike the `gods’ of Olympus, merrily throwing hints of Higgsy, sparticles,and black holes our way to confuse us, all to their perverse delight.
    Only a god could ignore causality in the interest of illusion and games….

  • God

    My major issue is that calling the Higgs the “God Particle” is like calling New York “America.” I made them all.

  • s. taylor

    “Materialist” is a term coined by supernaturalists. IIRC.. I’m sure your googlefu is as good as my own.

    There’s native framing to science. An example I’ve seen is “atheistic science”.

  • Quasar9

    I guess the COD or COLD particle hasn’t quite got the same ring
    How about the HID or Hidden particle
    but then it may as well be called the Higgs.

    Of course the gold particle to convey the excitement of a gold rush might have worked, or how about the bold particle – daring to go where particle (physicists) has never gone before

  • Quasar9

    Translate particle for field as and when required.

  • Ellipsis

    Best way I can think of how to properly explain the Higgs to a public audience? Read the stanzas III, VIII, and XII of Wallace Stevens’ “Thirteen Ways of Looking at a Blackbird”.

  • kapakapa

    Just as C.E. will slowly replace A.D., the scientists should first recoin a secular punch word until the rest of the world eventually catches on and drop g.p. as passe. Something as pithy as ‘black hole’.

    Besides what happens if LHC detects more exotic and heavier particles? If the god particle turns out to be not the ultimate IT, those lay people who bought the coinage for wrong reasons may turn against science irreparably.

    Sooner the better to reinvent a word, preferably before Higgs is found, if it ever will be found, and all the epoch making news can refer to the new name without a single mention of g.p. Hopefully that should rectify a misnomer. Good luck, scientists!

  • Haelfix

    My personal take: If it helps sway some confused politician to continue funding particle accelerators so that I can keep my job, im all for it.

    Theres plenty of famous religious phrases in Physics (many coined by Einstein), and honestly as atheist as we all are, who cares. I like to think of them as metaphorical.

    The public will continue to be just as confused about the actual science of it all, regardless if we call it the ‘God Particle’ or the ‘Anderson-Higgs particle’ or the ‘Globulator field’

  • Dan Geiger

    Einstein is also quoted as saying. “religion without science is dead, science without religion is blind.”
    While I’m under no illusion that Einstein was a “Christian” any more than Benjamin Franklin, there was no doubt that he (and Franklin) believed there was a supernatural,divine, intelligent being who created the universe “ex nihlo” from nothing. His belief in this “mystical/mythical” (today’s “scientific” viewpoint) did not impede his contributions to science any more than it did Issac newton, or Kepler who also openly enbraced a Creator-God.

  • Eric

    I propose that we start referring to supersymmetry as the God symmetry.

  • wolfgang

    > I propose that we start referring to supersymmetry as the God symmetry.
    Why? Because it does not exist ? 8-)

  • Blake Stacey

    Sean says,

    All of which is to say: religion is impoverishing our language. I want God back, dammit.

    We never had ‘im in the first place. Think about it: if the Spinozan use of the word were the original meaning, would anybody remember Spinoza today? The definition of God as a synonym for “cosmos” which rhymes with rod and sod is a modern invention, a brainchild of the physicists, and people won’t understand it until they’re all educated in physics.

    We do ourselves a great disservice by labeling the mysterious order of quarks and quasars with the name of a storm-bringer once worshiped on a patch of land beside the Mediterranean Sea. I suggest introducing more divine names into the physics meme-pool; we have, after all, thousands to choose from, of which a couple dozen have wide currency. Thus: “The good lady Isis is subtle but not malicious.” Or, “I cannot believe that Loki plays dice with the Universe.”

    From what I’ve read about string gas cosmology, in that model the reason the Universe has three spatial dimensions is essentially the same reason why knots can exist in 3D but not 2D or 4D.

    One of the successes of SGC is the possibility to explain the emergence of three large and isotropic spatial dimensions, while six remain stabilized near the string scale. In this way, SGC is the only cosmological model thus far that has attempted to explain the dimensionality of space-time dynamically5. The qualitative argument, due to Brandenberger and Vafa (Brandenberger and Vafa, 1989), was that winding string modes can maintain equilibrium in at most three spatial dimensions. This is based on the simple fact that p dimensional objects can generically intersect in at most 2p + 1 dimensions and the intuition that string interactions are due to intersections. They argued that once the winding modes annihilate with anti-winding modes, three spatial dimensions would be free to expand while the remaining six should remain confined by winding modes near the string scale. Winding modes were shown to possess such confining behavior quantitatively in (Tseytlin and Vafa, 1992).

    In neo-Einsteinian terms, perhaps the reason why we live in 3D space is because Aphrodite likes to get tied up in knots.

  • George Musser

    Oops, yes, I meant to say elementary particle.

    Sean, although the vast bulk of hadron mass is binding energy, isn’t it also the case that if quarks had zero mass, protons would outweigh neutrons and we wouldn’t be here to discuss all this?

    Why does attention typically focus on the question of fermion mass to the neglect of EW symmetry-breaking? Can I, in my journalistic capacity, describe the Higgs in terms of making photons and E&M what they are, flavor physics, etc.?


  • Blake Stacey

    Come to think of it, if you want to talk about symmetry breaking, “Babel particle” isn’t a bad turn of phrase. And as a book title, The Babel Particle sounds like a neat science-fiction novel, instead of yet another attempt to use modern science to give mouth-to-mouth resuscitation for ancient mythology.

    See, you put the Babel particle in your ear, and it instantly translates for you what the quarks and leptons are saying. . . .

  • dennis

    I like babel particle a lot.

  • mollishka

    “Babel particle” makes me think of Snow Crash.

  • Sean

    George, yes, lots of things would certainly be different if quarks were massless. But it nucleons would still have roughly 1GeV of mass.

    And every particle physicist in the world would put you on a pedestal if you chose to explain the Higgs (particle/field/mechanism) in terms of symmetry-breaking rather than mass-giving. The former is the real point, the latter is a spinoff that gets attention because it’s a bit easier to immediately grasp. It’s just hard to explain the symmetry-breaking business to your friend on the elevator. Especially when you’re breaking SU(2)xU(1) down to U(1), and people might be puzzled by what that means. (You would like to say “before EW symmetry breaking, W’s and Z’s were just like photons,” which is kind of true, but not exactly, because of the abelian vs. non-abelian thing.)

  • Moshe

    I seem to be playing the role of the pedant on this post, sorry…but one of the issues that came up for me in previous discussions (e.g on Clifford’s blog ) is trying to come up with a good explanation of the Higgs mechanism. I think there is actually a physics issue there…

    The problem is that gauge symmetry is no symmetry at all, just a redundancy in the description, so all the nice mental pictures one has from studying global symmetry and its breaking (for example in the theory of phase transition) are not quite right…technically speaking they are not gauge invariant. We also know that in some cases (following Fradkin- Shenker and others) there is no gauge invariant distinction between the Higgs mechanism and other mass-giving phenomena such as confinement.

    So, I for one would be grateful for an intuitive explanation of the Higgs mechanism. It may well be that the mass-giving, and not the symmetry-breaking, is the important aspect after all, but I am not sure.

  • Count Iblis

    Perhaps, if Leon Lederman had invented that term a few years earlier, Congress would not have killed the SSC?

  • Sean

    Moshe, true enough, and that would be even more awesome to get across. Except that I would still argue that mass-generating is not the important point, since other things also happen. Perhaps “phase-transitioning” is the real point.

  • Anne

    I much prefer the Oh my God particle.

  • Moshe

    Sean- that’s the thing, no other things are happening when the Higgs gets a VEV, no change in order parameter, no changes in global symmetry structure etc. etc., that’s why I am struggling to find a good intuitive explanation. Indeed, maybe the phase-transitioning is the only point, if that really is a word.

  • George Musser

    Moshe, Sean: can you put some flesh on the bones of the phase-transition description? That is, without one utterance of the term “gauge symmetry”, can you explain what exactly the phases in question are and why the transition cleaves the EW interaction?

  • Moshe

    I certainly cannot. The phase transition is simply the statement that the theory exists in two different phases, where the weak interactions are either long range or short range. The two phases are not distinguished by any other physical characteristics (order parameter) so it is difficult to come up with something that passes as an explanation. I’d really be happy to learn about such an intuitive explanation, but the things one usually hears conflate global and local symmetry breaking, which are mathematically similar but physically very different.

  • tyler

    So, I for one would be grateful for an intuitive explanation of the Higgs mechanism.

    Imagine how those of us who are trying to follow progress in this area from a lay perspective feel! I greatly appreciate all the effort put into making these difficult but important concepts more accessible.

    It’s very interesting to me that Moshe brings up the gauge symmetry (or non-symmetry) in this regard, as that has always been another plainly critical area in which I have had difficulty formulating an intuitive understanding. Indeed, it often seems to form the limit at which my understanding of a given subject fails, or becomes entirely metaphorical.

    I for one applaud the dogged “pedantry.”

    FWIW, this sort of issue is why I no longer rely on science journalists at all. No offense to George and the others who are working hard to get it right, but one information-lossy translation (from rigorous mathematical science to a non-expert-comprehensible english formulation) is bad enough. For that translation then to be re-filtered through a third party is simply too much. Thus the value I place on forums such as this one.

    It’s like running MP3 compression on a CD audio file – which is bad enough, it amazes me that people claim they can’t hear the difference – and then re-encoding the resulting MP3 file using another lossy codec. The end result is full of noise artifacts and lacks articulation in the details across the spectrum, especially at the limits. In many cases important aspects of the original idea (or song ;o) are completely lost.

  • Chris Oakley

    Deus ex machina particle could work.

    And it has “God” in it, albeit in Latin.

  • Jonathan Vos Post

    I thought that the Egyptians worshipped the Delta, Lemurians worsipped the Mu, sleepwalkers worshipped the Z, Hugh Hefner worshipped the Top, Simple Simon worshipped the Pi, Gell-Mann and Joyce worshippede the Quark, magicians worshipped the Charm, catfish worshipped the Bottom, H. P. Lovecraft and Charles Fort worshipped the Strange, Republicans worshipped the W, and Yiddish speakers worshipped the Nu.

  • Eugene

    I use the phrase “God gave us this/that” all the time. It seems funner and more engaging/forceful than the pedestrian “imagine we are given this by fiat….”.

    Personally, I don’t think I would change anyone’s minds about whether God exists or not. I am not so worried too about what the listener perceives what I believe in, as long as I get the point across.

  • Eugene

    As for the “God Particle” business, I propose a new name :

    The Uber-Particle.

    Take that LL!

  • Neil B.

    Well, they called it “The God Particle” because it (its field) supposedly gives other particles mass, which must be done to avoid some sort of chaos or undefined reality, I suppose. Would everything otherwise be like photons? But with the equivalence of mass-energy, would energy would still have an equivalent mass, or would even that be meaningless without the Higgs mechanism? In any case, it would be helpful to get a good middle-brow explanation of why there really, assuredly, needs to be something to provide a fundamental characteristic like mass, not just how it works. I mean, why can’t mass have been fundamental, or why not other ideas like acceleration coupling to the zero-point field, etc? As for extra implications, how does Higgs figure in now, to dark energy etc? Thanks.

  • Myhatma Gander

    I think that the point Moshe is raising is important, though I can’t help him find an intuitive explanation. His point that gauge “symmetry” isn’t a symmetry in any meaningful sense is the real blockbuster, because we have famous physicists going around saying things like “symmetry is all” blah blah blah. Long ago I attended a class on the differential geometry of gauge theory, and by the end it dawned on me that differential geometers don’t really care about gauge transformations, and the idea that connections exist “because” you “need to make gauge invariance local” just makes them giggle.

    Meanwhile, Sean said “in my personal hierarchy”….wasn’t he afraid that physicists would be confused by such religious language? By the way, are physicists confused by religious locutions like, “Holy shit!!” ?

  • Count Iblis

    The Higgs mechanism is often compared to superconductivity in introductory textbooks. And this is more than just an analogy, see e.g. here :)

  • Moshe

    Yeah, there is that, nicely summarized by Weinberg’s “Superconductivity For Particular Theorists”(Prog.Theor.Phys.Suppl.86:43,1986). This only pushes the issue one step back…

    (Also, probably should be obvious but I should say this issue definitely is nitpicking. I just wish I had better analogy to use, so I am asking…)

  • Greg Egan

    This is slightly OT, but … given that a hadron’s mass is dominated by binding effects, I wonder what the prospects are of experimentally measuring an anisotropy in, say, a proton’s acceleration in response to a force.

    My understanding is that the force required to accelerate a composite object will depend on the whole stress-energy tensor, not just the object’s total energy. Since the stress-energy tensor of a proton would not be isotropic, it ought to be a little bit harder to push around in some directions than others. Its spin axis would distinguish these directions, but the effect I’m talking about has nothing directly to do with spin; it’s a matter of how pressure and tension transform into changes of energy density under boosts.

    I don’t know anywhere near enough QCD even to guess the order of magnitude of this effect for a proton. Any experts care to comment?

  • Sean

    Greg, there are lots of equivalence-principle experiments that try to measure the different accelerations of objects made from different materials, and the people who do such experiments and make predictions for them definitely know that the baryon mass comes mostly from QCD, and are on the lookout for any deviations from the standard wisdom.

  • Greg Egan

    Sean, thanks for the reply. I’m still curious, though, as to whether anyone’s quantified the effect I mentioned, and if so whether or not it’s so ridiculously small as to be beyond all hope of measuring.

    Just to be clear, I’m certainly not suggesting any “deviations from the standard wisdom” here; unless I’ve misunderstood something basic in relativistic continuum mechanics (which is always possible), standard SR implies that anisotropic composite objects can have anisotropic responses to force. For example, an object under tension accelerates differently depending on whether the applied force is parallel to, or orthogonal to, the tension. What I’m far less clear about is whether the structure of a proton is such that there is a net effect of this nature, and if there is, whether it could conceivably come within the range of experimental measurement.

  • lfmorgan

    The current best in science is clearly an House of Word Definiton Mirrors that can only be notated in meaningful way by compex problematic math —which math has completed obscured local event detailed mechanics. A comletrion of Einstein’s deterministic universe is avaiable at my website for those who would like to quit playing with words and actually mind’s eye see ir all in infinite mechanical detail. The Universal Harmony (UH)=designer God real time self assembles and unasembles visible matter (VM)— as that VM is interactively immersed by ideal fluid dark matter that fills all space-time in a “no-force-at-a-distance-way” for an infinite, stable and closed, non-problematic universe. A gross simplification of Einstein’s field Equation does the trick G = R/3(v-squared) see details at website. That UH- Designer God allows organic matter to space-time build conizance that allows itself free will — and therefore problematic, trial & error existence.

  • Reginald Selkirk

    I’m a biologist. I’m glad that you are reluctant to use “God language” nowadays. Einstein used it, and look at how his quotes are misused, even in comments on this page. I hope the George Deutsch ‘Big Bang “Theory”‘ dust-up made physicists realize that the Fundagelicals are not just a threat to biology, but to all of science.

  • gs


    Can’t we take the asymptotic value of the Higgs doublet to be the order parameter? This is invariant under local gauge transformations, but I get confused about whether I should call this a “physical” quantity or not.

  • Ellipsis

    Greg Egan,

    Although I don’t know the answer to your question, the two places I would look first are limitations to the “emittance” of proton beams in accelerator physics (a brief check there indicated that other effects are much more dominant) and formation of antihydrogen (which I didn’t check, try for example the webpages of the ATHENA and ATRAP experiments at CERN) which is extraordinarily sensitive to (anti-)proton dynamics.

    Good luck. If anyone knows more please correct me.

  • Ms Chris

    “We do ourselves a great disservice by labeling the mysterious order of quarks and quasars with the name of a storm-bringer once worshiped on a patch of land beside the Mediterranean Sea.”

    Actually, the Mediterranean storm-bringer’s current followers are presumptuous to claim exclusive rights to the use of “god.” This is no more Yahweh’s name than it is Isis’ or Odin’s name.

    I’d think that calling it the “god particle” is irksome to fundies – though that’s not a good enough reason to keep doing it.

  • Cecil Kirksey

    For any HEP type: The Higgs field is a scalar field that is suppose to permeate all of space and interact with other particles (fields) to produce mass. Now does the Higgs field have a “constant value” for all space or does it vary? If it varies what causes the variation and how is it transmitted over space and at what speed? Does the Higgs particle have a mass? If so (I believe it is suppose to) what gives it its mass? A very nonlinear interaction?

  • Greg Egan

    Ellipsis, thanks for the tips! I’ve had no luck yet, but I’ll keep looking.

    FWIW, a naive back-of-the-envelope calculation (in which I trust Wikipedia that the force between gluons is of the order of 100 N, and I treat the mass and radius of the proton as being the relevant parameters for determining density and tension) implies that, in geometric units, the tension-to-density ratio is about 6 parts in 10^4. But I don’t know how that would vary with direction in a proton’s ground state, or how close it is to what a genuine QCD calculation would yield.

  • Ellipsis

    Cecil — please try Wikipedia and come back if you have questions. Any field that has a particle, i.e. a wave packet, associated with it, of course needs to vary in space

  • Ellipsis

    Greg — if a decent calculation (even a classical mechanics one) indicates that it might be an observable effect at an experiment similar to ATRAP or ATHENA, wait a few days to think (and make sure you haven’t made a mistake), and then send an e-mail to Gerry Gabrielse or one of his colleagues. They’ll probably correct you, but that’s OK.

  • Greg Egan

    Having looked at some recent research (Shape of the Proton, Gerald A. Miller), it seems the wave function is still so imperfectly understood that the kind of effect I’m envisaging would be swamped by the error bars in any current experiment.

  • Count Iblis

    Greg, the effect you are looking for simply doesn’t exists in a theory consistent with Special Relativity. Applying the same force in different directions for the same time will accelerate an anisotropic body to the same speeds in the respective directions, provided you start with the object at rest.

    The crucial thing here is that the momentum of the body is zero when you start to accelerate it…

  • Eric

    Yes, the Higgs vev can take different values at different points in space, giving rise to topological defects such as monopoles, cosmic strings, and domain walls.

  • marc

    In answer to your other question–the Higgs does have a mass, and it arises from a non-linear self-interaction

  • John Strong

    Religionism, the practice of religion in order to create more religion and gain power and wealth by it, is the problem, not the institution of religion itself.

    And now that this religionism can be manipulated for votes increases its power to disrupt the ordinary proceedings of society.

    The people who created ID, coordinate attacks on science, and try to legislate the Bible have a vested interest in doing so.

  • Cecil Kirksey

    I read the article(s). My questions apparently can be answered in the affirmative. However, I have a more general question concerning scalar fields that are suppose to permeate all of space. During inflation when space is expanding at several times the speed of light, the accepted wisdom is that the scalar field(s) will expand allong with space and maintain the same energy density, save quantum variations. Did the Higgs field exist during inflation? If not when did it come into existance? What caused it? Is the idea of a scalar field that permeates all of space and can travel faster than the speed of light bother anyone? If not why not? I know: no information is conveyed. That seems like a copout. Where are the dynamical equations that describe this field during inflation? Not space but this field.

    Thanks to everyone who wants to chime in and set me on the correct path of understanding this issue, which has troubled me every since inflation was predicted.

  • Ellipsis

    Hi Cecil — two of the world’s experts on that very issue are Mark and Sean (not me!)

  • Greg Egan

    Count Iblis, I’m about 80% sure I’m right, but I’m self-educated in this subject and if you can come up with a reference to a published result in relativistic continuum mechanics that contradicts my claim I’ll be very interested to read it.

    As I understand it, the nice simple formula they teach in elementary SR relating four-force, rest mass and four-acceleration, F=ma, is only strictly true for point particles (though in most situations it should be a very good approximation). A continuum object needs to be analysed with a stress-energy tensor, and if that tensor is anisotropic, the force needed to achieve acceleration of the body in different directions will be anisotropic too. (You emphasise the notion of “starting with the object at rest”, but that’s implicit in the whole idea of proper acceleration anyway: you measure proper acceleration in a frame co-moving with the body’s centre-of-mass.)

    To take one simple example, suppose you have an elastic string being trailed by a uniformly accelerating body. I’ve analysed this scenario for a simple linear model of elasticity on this page. It’s not hard to show that conservation of energy-momentum, i.e. setting the divergence of the stress-energy tensor of the material to zero, yields the equation:

    (1/s) [rho(s)+p(s)] + p’(s) = 0

    where s is a spatial coordinate measured orthogonal to the world lines of the Rindler frame for the accelerating body, rho(s) is the proper density of mass-energy in the material (including elastic potential energy), and p(s) is the pressure (which will be negative, as the string will be under tension).

    Now -p’(s) gives the net force on an infinitesimal element of the string, and (1/s) gives the acceleration of the hyperbolic world lines in a Rindler frame. So this equation resembles “F=ma”, but instead of rho(s) alone — the proper mass-energy of our element of string — we have rho(s)+p(s). This is due to the fact that the pressure/tension in an accelerating body is changing direction in space-time, and contributing to the momentum density.

    However, if we calculate the force/acceleration relationship for an acceleration in a direction in which there is no tension, we will get a different effective inertial mass: just rho(s). So there is an anisotropic response to applied force.

    Another example is the case of a rotating ring of elastic material. The total mass-energy of the ring in the centre-of-mass frame will be modified by kinetic and elastic potential energy, and if you compute the force needed to accelerate the ring with a given proper acceleration, a, in a direction orthogonal to the plane of the ring, it will simply be proportional to that total mass-energy. But if you accelerate the ring in the plane of rotation, the constant of proportionality, the effective inertial mass, will be different.

    Another way to look at all this is to think about boosts. When you have a point particle, it simply possesses an energy-momentum vector, P, and its total energy as measured by an observer with 4-velocity u is just E=P.u. If you start with a particle at rest, E will initially equal m=|P|, and if you apply a boost to P then E will transform in a very simple way, which will be independent of the direction of the boost.

    But when you have a composite system, E is found by integrating T^{00}, the time-time component of the system’s stress-energy tensor T. You can also integrate all four time components, T^{0a}, to get a total energy-momentum vector P. But even if you start with the centre-of-mass of the system at rest (i.e. the total momentum of the body in the observer’s reference frame is zero), if you apply a boost to T, there’s absolutely no guarantee that the change in E will be independent of the direction of the boost.

  • Greg Egan

    I wrote:

    Another way to look at all this is to think about boosts. [...] if you apply a boost to T, there’s absolutely no guarantee that the change in E will be independent of the direction of the boost.

    Sorry, that assertion was dead wrong. The total energy-momentum vector you get by integrating T^{0a} for a closed system will transform like an ordinary 4-vector (Misner, Thorne and Wheeler, page 145, makes this clear), so the change in E will be independent of the direction of the boost.

    This doesn’t change the rest of my argument. As I’ve said, I’m not 100% certain about any of this, but it seems clear that tension does modify the effective inertial mass of a composite object, and so anisotropic tension should give rise to an anisotropic effective inertial mass.

  • Count Iblis

    Hi Greg,

    It should be the case that the anisotropic effects are described by the angular momentum. So, mass and angular momentum are the two relevant parameters that you can extract from the energy-momebtum tensor.

    It may be more convenient to look at collisions instead of a steady force. It should be the case that you have conservation of momentum and angular momentum. Any anistropic effects should be a consequence of this…

  • Count Iblis

    Also, note that the angular momentum contributes to the energy. Therefore, the (invariant) mass of an object depends on its angular momentum.

  • Neil B.

    Iblis: That reminds me, to ask about to what extent the energy of rotation contributes to what we’d otherwise expect (if possible/available) for the masses of various fundamental particles. It is interesting because without a specific classical type mass distribution, we can’t say that the increase is to gamma times the rest value etc. And yet, note that there’s a magnetic field for the electron, which means charge distribution has at least an equivalent “radius” and “velocity.” I wonder if that can be compared, what we get when we pretend the electron is spinning as a shell of classical radius, etc, for any of that. I suppose it could mean something, but I hear little about it.

    Greg: I had an article in Physics Essays years ago about the problem of accelerating a mass at the end of a long string. The wild west of extended body dynamics in relativity is one of my favorite avocations, and surprisingly it has been argued and disagreed about for years in journals. Ken Nordtvedt wrote about the equivalent gravitational situation earlier, in AJP. His effect, that a mass suspending pulls less on the holding end than the mg measured locally at the mass, didn’t get the attention it deserved (for example, it never AFAIK appeared in writings as a cute implication of GR, like “You could hold up an elephant in earth-style gravity if you had a long enough cord.”) Maybe one reason is, the increasing magnitude of the hyperbolic gravity field just cancels that “red shift” of weight, so you hold things anyway with the mg using g where your hand is! This confuses the issue and got critic Ø Grøn of Norway all worked up, and in error in my view. That guy sure was a booger for me too later, as referee of my own paper.

    In any case, I’m sure you appreciate that stressed bodies in motion have a correction to the usual expressions for mass and momentum. (One illustration: if co-moving observes apply forces simultaneously to a rod seen by us in motion, the rod just sits there for them and no velocity increase for us. However, we see the rear force applied earlier. That puts “extra momentum” (f delta t) and energy (f dot v delta t) into the rod. The lateral shear version really explains the infamous “right-angle lever paradox.” When you apply those corrections to moving bodies, everything is supposed to work out (and per fundamental theorems), but it does make a mess when the stuff is accelerating. I finally got things to work out OK after the paper, where I couldn’t solve it at the time.

  • bjkeefe

    In Lederman’s defense, he did say in his book that the reason he chose the title he did is that the publisher wouldn’t let him use “The Goddam Particle.”

  • Greg Egan

    Count Iblis, Neil B., thanks for your comments.

    Count Iblis, I agree that if you do an experiment in which the incoming state for our system S is completely isolated from the environment, and the outgoing state for S is just a boosted copy of the ingoing state, then an identical force applied to S for an identical time will lead to an identical change in velocity, in whatever direction the force is applied. That follows from conservation of energy-momentum.

    Nevertheless, I believe it’s still possible to have anisotropic effects taking place during the interaction. If you imagine, say, a small square of elastic material subject to forces of 100 N and 101 N across the x-direction, and 200 N and 201 N across the y-direction, it will be subject to a net force of 1 N in both directions, but the different average tensions will give rise to small differences in its accelerations in the two directions. Given some complex anisotropic system, all that the conservation laws guarantee is an identical net effect over the course of the whole interaction, not a constant, direction-independent ratio between force and acceleration, holding moment by moment.

    That said, everything I’ve read about protons since first raising this question makes it seem unlikely that anyone will be measuring such an effect for a proton any time this century.

  • Rob Knop

    Creationism (particularly of the Intelligent Design sort) is impoverishing our language, not religion! Religion was the source of the metaphors you were using in the first place.

    And, yeah, I know, I will get hammered, “religion is mostly represented at least publicly by fundamentalists in the US today, yadda yadda yadda.” I get that every time I do this. But I think it very important to emphasize that creationism is not religion. As somebody who’s religious, I want God back, dammit, too! I want to take back religion so that folks like you don’t feel the need to hate it. I’m pissed at the fundamentalists for driving us to that. My way of fighting this is reminding everybody where possible that you don’t have to be a creationist to be religious… and that if you don’t feel the need to stupidly and literally interpret your religious text, perhaps you won’t feel the need to stupidly and literally interpret every metaphor spoken by a scientist.


  • Plato

    One talks about “Professor Einstein crossing the room” and I do not find it to farfetched to see this as a “intuitive principle” inherent in the term phase transition looking at our early universe.

    G -> H -> … -> SU(3) x SU(2) x U(1) -> SU(3) x U(1).

    Neither would I be to upset that what was illucive in terms of energy particle discriptions in Agasa was the continued struggle to describe what mathematics was approaching in terms of these new higher energy particles.

    This was the original, and applying to what remains illucive until actual experimentation is just something we do in descrbing the mystery. We understand the nature of the scientists work here.

    Some may have other agendas?

  • Plato

    The string landscape then would seem an appropriate and intuitive idea here in terms of the “hills and valleys” and what is “possible” in that early uiverse with regards to tunneling? “Mathematical building” with regards to genus figure calculated.

    Physically, the effect can be interpreted as an object moving from the “false vacuum” (where = 0) to the more stable “true vacuum” (where = v). Gravitationally, it is similar to the more familiar case of moving from the hilltop to the valley. IN the case of the Higg’s field the transformation is accompanied with a “phase change“, which endows mass to some of the particles


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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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