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I Why the speed of light is constant?

  1. Aug 17, 2015 #1
    Here is a question that might be somewhat more philosophical than this community cares for. If so, I apologize in advance.

    Are there any reputable theories as to why the speed of light is constant? I know that it is an empirical fact and therefore that it does not need to be proven. But on the other hand, the aim of physics has historically been to come up with satisfying theoretical explanations for empirical facts. Anyway, I'm just wondering if there are any reputable ideas out there that modern physicists are considering.
     
    Last edited: Aug 17, 2015
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  3. Aug 17, 2015 #2

    PeterDonis

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    The theory of relativity basically answers this question by saying that it's ill-formed; in the relativity view of spacetime, what we call "the speed of light" is really just a unit conversion factor between space units and time units, and since spacetime is unified in relativity, the unit conversion has to be the same everywhere.

    Or, to look at it another way, in the theory of relativity, there are three fundamentally different kinds of worldlines in spacetime: timelike, spacelike, and null. The proper way of saying that something travels "at the speed of light" is to say that it travels on null worldlines. This is a geometric property of the worldline, and again, it has to be "the same" everywhere--the geometric definition of a null worldline doesn't change.

    You could ask a different question, namely, why does light, the actual physical phenomenon, travel on null worldlines? Answering that requires going beyond the theory of relativity; it's a question about quantum field theory and why the quantum field describing light is massless (which is the QFT way of saying "travels on null worldlines"). In relativity, the fact that light travels on null worldlines is taken as a given, a property of light that doesn't have any further explanation within that theory.
     
  4. Aug 17, 2015 #3
    Can I ask to you explain what it means to say that the speed of light is a conversion factor between space and time units? I know the rudiments of special relativity, namely that c acts as a conversion factor when going from the space-time units of one reference frame to those of another, but I don't think I've learned how light speed acts as a conversion factor between the space and time units of a single reference frame.

    Yes, I think this is getting more to the heart of the kind of answer I would find satisfying. Only I would tack one more question in there between the lines (particularly, the question concerns your parenthetical). Not only would I ask why the quantum field describing light is massless, but also this: why does a massless field describe the phenomenon of "traveling on null worldlines"? In other words, what is the connection between having or not having mass and traveling at a speed that is independent of the speed of the source? Because even if we could answer the question of why light is massless, that would still leave open the question of why massless things travel at constant speed. Are there any stabs at an answer to that second question out there?
     
  5. Aug 17, 2015 #4
    Actually the aim of physics is to determine how things happen. i.e. to relate an initial state to a final state after an interaction. This may involve empirical facts or assumptions consistent with these facts.
     
  6. Aug 17, 2015 #5

    PeterDonis

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    In relativity, it is useful to use the same units for space and time. Any such system of units will relate space and time using the speed of light: for example, years for time and light-years for space (which is common in cosmology).

    No, that's not what ##c## does. Units of space and time (like years or light-years) aren't associated with any particular reference frame. See above.

    Because that's how the geometry of spacetime works. An object with mass (more precisely, one with nonzero rest mass, aka invariant mass) travels on a timelike worldline. An object that is massless (more precisely, one with zero rest mass aka invariant mass) travels on a null worldline. The property of invariant mass is what distinguishes these two types of worldlines.

    The fact that the speed of any massless object is independent of the speed of its source is a side effect of the way the geometry of spacetime works. The speed of any object moving on a null worldline is the same in all inertial frames; that's a fact of spacetime geometry. Since it's the same in all inertial frames, it must be independent of the speed of the source.

    If you ask, why is the speed of any object moving on a null worldline the same in all inertial frames, that is because the way Lorentz transformations act on timelike vectors is fundamentally different from the way they act on null vectors. Lorentz transformations change the "direction in spacetime" of timelike vectors; that corresponds to changing the "speed" associated with the vector, in the new frame, as compared to the old. In other words, Lorentz transformations "rotate" timelike vectors in spacetime (they are the hyperbolic geometry counterpart of ordinary rotations in 3-space).

    But Lorentz transformations don't rotate null vectors in spacetime; they only "dilate" them. What that means is that a Lorentz transformation doesn't change the speed of, say, a light beam; it only changes its frequency (or wavelength; they're equivalent). So a given light beam will have different frequencies (or wavelengths) in different frames, but not different speeds.
     
  7. Aug 17, 2015 #6

    Nugatory

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    A different (and less modern) way of thinking about it is to consider that the speed of light can be calculated from the classical laws of electricity and magnetism. Maxwell did exactly that in 1861, and his suggestion that light was an example of the electromagnetic radiation that his equations predicted was quickly accepted. However, we also expect that the laws of physics don't change just because you're in uniform motion - because of the earth's rotation, your speed changes by many kilometers a second between noon and midnight, but you don't expect the laws of physics in general or E&M in particular to change out from under you. You end up calculating the same speed of light at all hours of the day.

    That doesn't answer your "why?" question, it just transforms it into the question of why the laws of E&M are what they are.... But it was a pretty good hint from nature that we shouldn't be surprised to find that the speed of light is in fact constant. It took a half-century before Einstein picked up on this hint in 1905, and another decade or so after that to hammer out the modern mathematical formulation of special relativity, in which the constant speed of light appears as an experimentally supported fundamental assumption.
     
  8. Aug 17, 2015 #7
    Thanks so much for your generous replies. I have much to learn.

    Feel free to draw the line of demarcation here between legitimate question and crackpot question, but here goes one more. I hope that the following won't read as totally uninteresting and misguided babble, but I'd like to know what a physicist would make of this line of thought.

    The velocity of a rigid-body projectile (e.g. a tennis ball) is altered by the velocity of its source for the reason that the source communicates its own velocity to the projectile by means of a contact force, which (correct me if I'm wrong) is an electromagnetic interaction between charged particles. Light, however, unlike a rigid body, is not composed of charged particles, but rather of neutral photons. Therefore there can be no contact force and no communication of the velocity of the source to a light beam (and thus c is constant). Has this argument been made in the past, and if so why is it rejected?
     
  9. Aug 17, 2015 #8
  10. Aug 17, 2015 #9

    PeterDonis

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    This is sort of correct, but not completely. First, contact forces aren't purely electromagnetic repulsion between the electrons in neighboring atoms; part of it is also the Pauli exclusion principle, which makes atoms resist being compressed. (The uncertainty principle also plays a role here; the stability and behavior of solid objects is actually quite a bit more complicated than it appears on the surface.)

    Second, what the source "communicates" to the projectile by this means is momentum, not velocity. And the source itself also has to change momentum as a result, because of conservation of momentum (this is what "recoil" is, for example when firing a gun). In other words, when viewed from a fixed inertial frame, both the projectile and the source change velocity. So it's not just a simple "communication of velocity" from source to projectile; the kinematics is more complicated than that.

    Finally, this kind of analysis doesn't account for objects which cannot be viewed as "projectiles" fired from a "source". All objects with nonzero rest mass will have different velocities in different frames, regardless of how they got that way. So any analysis that is fully general must be based on something more fundamental than a specific mechanism for imparting velocity. That's why I cited the geometry of spacetime in my explanation.

    The problem with this is that it assumes that light is a pre-existing thing that is made to move at ##c## somehow. In fact, light gets created at its source--a given light beam doesn't exist at all until its source emits it. When it is emitted, it is emitted already in the state of "moving at ##c##", but a better way to say it is that it is emitted as a massless object, on a null worldline, and a null worldline is fundamentally different from a timelike one.

    Also, as rootone points out, light has momentum and can push against things; and sources that emit light show recoil, just as sources that emit timelike projectiles. So it's not correct to think of light as somehow not being subject to "contact forces"; light exchanges momentum with other things just like any other object.
     
  11. Aug 17, 2015 #10

    bcrowell

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    The answer to this question depends on what you take as fundamental assumptions. The 1905 approach is to take constancy of the speed of light as a fundamental assumption. A more modern approach is to take certain symmetry principles as your fundamental assumptions. If you do that, then it follows that there is an invariant speed, and that massless phenomena such as light travel at that speed. For an example of such a treatment, see Pal, "Nothing but relativity," http://arxiv.org/abs/physics/0302045 .
     
  12. Aug 17, 2015 #11

    Nugatory

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    As I am floating in space, you come rushing past in a spaceship moving at .5c. Just as you pass me, you switch on a light on the nose of your spaceship to send a flash of light forward in the direction of you motion. Your "no communication of the velocity" idea would explain why the flash of light ends up moving at c relative to me - but it fails to explain how the flash of light can then also be moving at the speed of light relative to you.

    (There are other problems with the idea as well: Photons aren't what you're thinking they are and light is not composed of them, at least not as the word "composed" is usually understood; light does exert a force on its source as it is emitted so there is a transfer of momentum from the source to the light; there are massive neutral particles and they don't travel at the speed of light and their speed is not independent of the source).

    The Physics Forums rules prohibit posting speculation and personal theories of this sort. Please don't do it any more.
     
  13. Aug 17, 2015 #12
    Thanks again for your replies. And sorry if my question was against regulations.

    Where can I read more about these particles?
     
  14. Aug 17, 2015 #13

    PeterDonis

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    The most common one is the neutron, which is in almost every atomic nucleus (the only exception is hydrogen-1) and is produced by a number of nuclear reactions.
     
  15. Aug 18, 2015 #14

    Gaz

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    I just think of it like say your going 80 mph and instead of the tennis ball you fire a rocket that's top speed is 100 mph that rocket isn't going to accelerate to 180 mph is it.
     
  16. Aug 18, 2015 #15

    vanhees71

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    That's again a tricky "why question". First of all I don't know, what you take as basis for an "explanation", because any "explanation" must start from something you consider as a fundamental law of nature, and we can only figure these out by observations and careful quantitative experiments.

    In my opinion, the status of the question, why electromagnetic fields are described by massless vector fields is not clear at all, and one must indeed take it as a fundamental law fitting all known observations so far with astonishing precision. So one could stop here, but it's anyway interesting to follow the question a bit.

    I try to answer it on the level of special relativity (i.e., leaving the general relativity and thus gravity out of this discussion, because then we really would leave safe ground ;-)). The most fundamental theory we have about the world is indeed the special-relativistic space-time model, describing space and time as a four-dimensional continuum, called the Minkowski space together with quantum-field theory based on it. Here the most comprehensive model we have is the Standard Model of elementary particles.

    So the question can be split in two questions: First of all, "why" is it the Minkowski space which describes the observed properties of what we call space and time well. Here the answer also is that of all space-time models it describes very many phenomena best (it's known that it must be modified again when taking into account gravity, leading to general relativity). You may argue in a bit more depth by invoking symmetry principles. One can start with the assumption that the principle of inertia holds, i.e., that there is a class of reference frames, where a body upon which no forces act, always move with constant velocity with respect to the corresponding observer who is at rest in one of these reference frames, the socalled inertial frames. Further, assuming that any inertial observer finds when measuring lengths of objects that are at rest relative to him that the corresponding geometry is Euclidean, implying that his space is homogeneous and isotropic. Further also time is assumed to be homogeneous, i.e., the laws of nature do not depend on the space and time where and when an inertial observer observes them. An analysis of the then following possible space-time symmetries shows that only two space-time models are left, namely the Galilei-Newton and the Einstein-Minkowski spacetime. The main difference is that in Einstein-Minkowski space time there is a fundamental "limiting speed", i.e., any object can only move with a velocity with respect to any inertial observer with at most this limiting speed ##c##, while in the case of Galilei-Newton space-time no such fundamental speed parameter exists. You can criticize this pretty complicated approach, however, because the assumptions going into it are pretty strong, but in my opinion it gives an idea, why there may exist space-time models with a fundamental limiting-speed parameter, independent of a concrete physical model like classical electrodynamics, which was the historical starting point for the theorists in the 19th century to think about these issues, with Einstein the one who has given the most convincing argument in terms of a space-time model (Einstein 1905).

    Now around 1925 it was discovered that the classical description of matter is inadequate too, and one discovered quantum theory as a better description. First attempts to formulate quantum theory within relativistic physics was not very successful and that's why first the non-relativistic theory was developed (Heisenberg+Born+Jordan 1925, Schrödinger 1926, Dirac 1926). Then of course, after having learnt to deal with non-relativistic quantum theory, also the relativistic theory was worked out. Soon it became clear that it is very hard to find a consistent theory which describes only a single interacting particle. This is understandable nowadays, because we deal with the creation and destruction of particles in accelerators of the highest energies on a quite familiar basis.

    Now it was also known from non-relativistic quantum theory that for many-body systems or systems with a non-fixed number of particles, there is an equivalent description of quantum theory, known as quantum field theory, because it can heuristically derived by taking the Schrödinger equation, formulating it with Hamilton's principle (analogous to canonical mechanics of point particles) and "quantize" it, i.e., making the fields operator valued, and the field describing annihilation and destruction processes of particles. This was the perfect starting point for a relativistic quantum field theory, and one can again use the powerful tool of group theory and the space-time symmetries of the Einstein-Minkowski spacetime, with the Poincare group as symmetry group (Wigner 1940). Together with some additional assumptions (locality, microcausality, existence of a state of lowest energy) you are lead to the local relativistic quantum field theories which are very successful (although not yet free of all mathematical obstacles for interacting particles).

    In this analysis it occured that there are two rough classes of fields, belonging to two posibilities to realize Poincare symmetry in the sense of quantum theory: the massive and the massless fields. Quantizing the non-interacting massive fields leads to massive particles with any type of spin 0, 1/2, 1,3/2,... The corresponding field equations are the Klein-Gordon equation, the Dirac equation, etc. These have a well-defined non-relativistic limit leading to non-relativistic quantum theory of the corresponding particles with spin.

    There's however also the class of field theories with massless fields. It's quantization is a bit more tricky, and they have no non-relativistic limit (this is also a deep property of the underlying space-time symmetries; while in Minkowski space massless fields (and even classical particles to some extent) make sense, massless particles make no sense in non-relativistic quantum theory, which is due to the different structure of the underlying space-time symmetry groups (Poincare group in the case of Einstein-Minkowski and the Galilei group in the case of the Galilei-Newton space-time).

    The standard model is built on these general QFT structure, but it took more discoveries of more symmetries concerning the whole zoo of particles found since the 1950ies. One of the most important discoveries is that of the socalled local gauge theories. The above mentioned analysis of the Poincare group reveals that massless particles with spin ##s \geq 1## cannot be simply described by fields but by classes of fields. This is known already from classical electrodynamics: Using the four-potential several four-potentials which just differ in a four-gradient field, describe the same situation. Taking this symmetry into account and quantizing it (which is a puzzling business and an interesting story of its own) leads among other things to the fact that a massless vector particle has not three spin states as a massive vector particle, but only two (represented by, e.g., helicity eigenstates with the helicity being the projection of the total angular momentum two the momentum direction of the particle and taking only the two values ##\pm 1##).

    The other way around, starting from gauge symmetry, it is most naural to assume that the corresponding vector field is massless. Of course, you also want to introduce charged matter particles to make a model for electromagnetically interacting charged particles and the electromagnetic field. Gauge invariance implies that necessarily electromagnetic charge must be conserved and that it is most simple to couple the vector field to a conserved current. The gauge transformation of the matter fields is invariance of the equations of motion under multiplication of these fields with a space-time dependent phase factor, with the phase (modulo multiplicative constants which represent the coupling strength between the particles and the vector field) being the same as in the gauge transformation of the vector field. Since the multiplication with a phase factor corresponds to symmetry under the Ablian group U(1), this is called an Abelian gauge theory, and it was pretty soon clear that such a theory describes electromagnetism very well, leading to quantum electrodynamics.

    However, as it turns out, you can as well formulate the theory with massive vector bosons, still keeping the theory gauge symmetric (Stueckelberg model). So gauge invariance is not a true "answer" to the question, why photons are massless quanta of a vector field. So it's still not answering the question, "why" photons are massless.

    Now the Standard Model rests on an even more general type of gauge symmetry. Already in the 1940ies Heisenberg discovered that one an describe also observed symmetries among particles with help of group theory. In his case he took the proton and the neutron which have (almost) the same mass as one and the same particle but just carrying another quantum number (called isospin). Thus he took proton and neutron as a isospin 1/2 doublet, i.e., the two eigenstates of the isospin-z component (with isospin +1/2 for the proton and isospin -1/2 for the neutron). As long as you consider only the strong interaction in scattering processes the isospin is (approximately) conserved.

    Then Yang and Mills had the brillant idea to ask what happens, if you "gauge" such non-Abelian symmetries (in this case under the isospin group SU(2)). "Gauging" means you assume that a global symmetry (you can rotate only with a constant SU(2) transformation in isospin space, but not locally, because the field theory contains derivatives which by themselves do not lead to simple transformation laws for the field derivatives when the SU(2) transformation is made space-time dependent) becomes global. It turns out that you can make a global symmetry of this kind a local symmetry by introducing appropriate vector fields, the gauge bosons of this symmetry. Although the original Yang-Mills model was not successful in describing the strong interactions, the gauge models turned out to be the key to build the Standard Model.

    Here it turned out that, contrary to the Abelian case, it is very difficult to give the gauge bosons a mass without distroying local gauge invariance. Only the famous Higgs mechanism could provide such a thing. So still you can make the non-Abelian gauge bosons massive, i.e., there is no real veto for massive vector bosons based on non-Abelian gauge symmetry.

    So the short conclusion of this long-wound try to "explain" the masslessness of the photon is: We don't have a better answer than the fact that all empirical observations are to a very high accuracy consistent with the assumption of a massless photon, being described in the standard model as a U(1) gauge theory with the gauge boson assumed to be massless.
     
  17. Aug 18, 2015 #16
    So what kind of force exists between a neutron and some ordinary piece of matter? Would the interaction be purely magnetic owing to the neutron's characteristic absence of charge but possession of a magnetic moment? I guess there is also the nuclear force.

    What about photons -- what kind of force exists between the photon and ordinary matter? If I remember correctly light is subject to gravity. Is there anything else? What, for instance, is responsible for the photon's ability to transfer momentum to a "solar sail".
     
    Last edited: Aug 18, 2015
  18. Aug 18, 2015 #17

    Nugatory

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    There is indeed a nuclear force, and it's most often responsible for fast-moving neutrons.

    I'll repeat what I said a few posts above: photons are not what you're thinking they are. You'll be properly introduced after you've worked through special relativity and then quantum mechanics, so have the background needed to take on quantum field theory which reconciles QM and SR. Until then, you will be better off working with the classical model of light as electromagnetic radiation; that's what SR is built on.

    And with that said: There's no meaningful way of talking about the force between a photon and ordinary matter - that's just not how photons work. However, electromagnetic radiation can carry energy and momentum; this is transferred to ordinary matter when the time-varying electrical and magnetic fields (that's what electromagnetic radiation is) act on the charged particles in the matter. So the force in question is electromagnetic, and a detailed explanation of how it works is built on Maxwell's equations of classical electrodynamics, discovered a half-century before relativity.
     
  19. Aug 18, 2015 #18
    You might want to refine your question because the speed of light is not constant ! The speed of light in a vacuum is constant.

    The speed of light through denser materials such as water or glass is slower.
     
  20. Aug 18, 2015 #19

    vanhees71

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    First of all everything that has energy and momentum (i.e., everything that exists at all) participates in the gravitational interaction, i.e., it is subject to gravitational force as well as a source of gravity (which is described as the curvature of space-time by Einstein's General Relativity Theory).

    The rest of the known matter is described by relativistic quantum-field theory in terms of the Standard model of elementary particle physics. According to this model, all known matter consists of the following particles (all described by Spin-1/2 quantum fields with the corresponding quantum particles being fermions):

    Leptons: (electron, e; Muon ##\mu##, Tauon ##\tau##) all carrying 1 negative electric charge unit and corresponding 3 sorts of neutrinos. These particles only participate in the electroweak interaction and gravity. In addition to the electric charge of the charged leptons both the charged leptons and their neutrino partners carry another charge, called "weak isospin".

    Quarks: [(up,down); (charm, strange); (bottom/beauty, top)] These participate in all interactions, i.e., the electroweak, the strong and the gravitational interaction. Each pair of quarks carries +2/3 and -1/3 elementary charges respectively. In addition they cary weak-isospin charge and the color charge of the strong interaction.

    Further there are the "force particles". A more scientific name is "the gauge bosons". They are described by fields, of which we best know the electromagnetic field, and only this electromagnetic field can be observed in a direct way also as a classical field (which from the point of view of quantum field theory are socalled coherent states of the electromagnetic quantum field). The gauge bosons all have spin 1 (that's why they must be bosons according to the spin-statistics theorem, which tells us that all particles with a half-integer spin number are fermions and those with an integer spin number are bosons). In a very rough sense (the full story is not so simple and involves some abstract mathematics, called group theory, for a complete understanding) we have the following gauge bosons in the standard model:

    Photons: Quanta of the electromagnetic field, coupling to anything that carries a non-zero electric charge (which is also not completely accurate, because quantum effects let them also interact via quantum fluctuations with uncharged particles, including themselves, but in the case of photons that's a very weak effect). The photons themselves are uncharged.

    3 weak gauge bosons: The W bosons (one carrying 1 positive and one carrying 1 negative elementary charge) and the Z bosons (having no electric charge); all couple to the weak-isospin charge and carry themselves also weak-isospin charge. The photons and weak gauge bosons are "carriers" of the electroweak interaction.

    8 gluons: they are electrically and iso-spin charge neutral and mediate the strong interaction and thus directly couple to everything that carries color charge (quarks and gluons themselves, which also carry (a different kind) of color charge).

    The strong force is special, because it shows confinement, i.e., we don't observe any objects carrying a non-vanishing color charge, but the quarks and gluons are always bound in color less composite objects. This is a very complicated state of affairs, which is not fully understood yet. We know from big computer simulations (called lattice-QCD calculations) that Quantumchromodynamics (on the fundamental level the theory describing the strong interactions among quarks and gluons as a gauge theory) seems to be the correct desription, particularly it is possible to calculate the masses of all known hadrons and predicts even the existence of some other hadrons not yet seen in experiments. Hadrons are the bound states of quarks and gluons. We know two types for sure today, namely the socalled mesons which consist of a valence quark and a valence antiquark and a lot of virtual quarks, antiquarks and gluons (as I said that's a hand-waving picture, not fully understood yet). The mesons carry all integer spin-quantum numbers and thus are bosons. They are all unstable. Then there are the baryons consisting of three valence quarks and a lot of virtual quarks, antiquarks, and gluons. The most prominent ones are the proton and the neutron, which themselves are the building blocks for all atomic nuclei of the every-day matter around us. The nuclei are hold together by the strong force. Although the hadrons are color neutral, there is still strong interaction left. You know this, e.g., from the analogous behavior of electrically neutral material, which still can interact electromagnetically, because the charged particles it is made up, are a bit distorted from the equilibrium positions due to some electric charges brought close to them. This "polarizes" the material leading to an electromagnetic interaction with the nearby charges. Even neutral molecules interact electromagnetically with each other, i.e., for composite neutral objects there's still some remnant electromagnetic interaction left.

    Then you are also right that the charged elementary particles not only carry this charge but also have a magnetic moment (which is due to their spin and the specific way each field, describing these particles, couple to the electromagnetic field). So it is understandable that the neutron also has a magnetic moment, which is due to the magnetic moments of the quarks and their "motion" (correctly their orbital angular momentum) within the hadronic bound state. The same is true for the proton, which carries one positive electric elementary charge and also has a magnetic moment. For the same reason neutral molecules still interact electromagnetically, also the neutrons do due to the charged valence down quarks and up quark as well as the virtual cloud of charged quarks contained in them.
     
  21. Aug 18, 2015 #20
    Woah. That is a lot to try to explain without pictures and tables ! :)

    Who has the best poster/picture of the Standard model these days?
    http://www.pha.jhu.edu/~dfehling/particle.gif [Broken]
    From: http://www.pha.jhu.edu/~dfehling/particle.gif [Broken]
     
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