[Paleopsych] Scientific American: The Mysteries of Mass

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The Mysteries of Mass
    June 27, 2005

    Physicists are hunting for an elusive particle that would reveal the
    presence of a new kind of field that permeates all of reality. Finding
    that Higgs field will give us a more complete understanding about how
    the universe works
    By Gordon Kane

    Most people think they know what mass is, but they understand only
    part of the story. For instance, an elephant is clearly bulkier and
    weighs more than an ant. Even in the absence of gravity, the elephant
    would have greater mass--it would be harder to push and set in motion.
    Obviously the elephant is more massive because it is made of many more
    atoms than the ant is, but what determines the masses of the
    individual atoms? What about the elementary particles that make up the
    atoms--what determines their masses? Indeed, why do they even have

    We see that the problem of mass has two independent aspects. First, we
    need to learn how mass arises at all. It turns out mass results from
    at least three different mechanisms, which I will describe below. A
    key player in physicists' tentative theories about mass is a new kind
    of field that permeates all of reality, called the Higgs field.
    Elementary particle masses are thought to come about from the
    interaction with the Higgs field. If the Higgs field exists, theory
    demands that it have an associated particle, the Higgs boson. Using
    particle accelerators, scientists are now hunting for the Higgs.

    The second aspect is that scientists want to know why different
    species of elementary particles have their specific quantities of
    mass. Their intrinsic masses span at least 11 orders of magnitude, but
    we do not yet know why that should be so. For comparison, an elephant
    and the smallest of ants differ by about 11 orders of magnitude of

    What Is Mass?
    Isaac newton presented the earliest scientific definition of mass in
    1687 in his landmark Principia: "The quantity of matter is the measure
    of the same, arising from its density and bulk conjointly." That very
    basic definition was good enough for Newton and other scientists for
    more than 200 years. They understood that science should proceed first
    by describing how things work and later by understanding why. In
    recent years, however, the why of mass has become a research topic in
    physics. Understanding the meaning and origins of mass will complete
    and extend the Standard Model of particle physics, the
    well-established theory that describes the known elementary particles
    and their interactions. It will also resolve mysteries such as dark
    matter, which makes up about 25 percent of the universe.

    Why is the Higgs field present throughout the universe? What is the
    Higgs field?

    The foundation of our modern understanding of mass is far more
    intricate than Newton's definition and is based on the Standard Model.
    At the heart of the Standard Model is a mathematical function called a
    Lagrangian, which represents how the various particles interact. From
    that function, by following rules known as relativistic quantum
    theory, physicists can calculate the behavior of the elementary
    particles, including how they come together to form compound
    particles, such as protons. For both the elementary particles and the
    compound ones, we can then calculate how they will respond to forces,
    and for a force F, we can write Newton's equation F = ma, which
    relates the force, the mass and the resulting acceleration. The
    Lagrangian tells us what to use for m here, and that is what is meant
    by the mass of the particle.

    But mass, as we ordinarily understand it, shows up in more than just F
    = ma. For example, Einstein's special relativity theory predicts that
    massless particles in a vacuum travel at the speed of light and that
    particles with mass travel more slowly, in a way that can be
    calculated if we know their mass. The laws of gravity predict that
    gravity acts on mass and energy as well, in a precise manner. The
    quantity m deduced from the Lagrangian for each particle behaves
    correctly in all those ways, just as we expect for a given mass.

    Fundamental particles have an intrinsic mass known as their rest mass
    (those with zero rest mass are called massless). For a compound
    particle, the constituents' rest mass and also their kinetic energy of
    motion and potential energy of interactions contribute to the
    particle's total mass. Energy and mass are related, as described by
    Einstein's famous equation, E = mc^2 (energy equals mass times the
    speed of light squared).

    An example of energy contributing to mass occurs in the most familiar
    kind of matter in the universe--the protons and neutrons that make up
    atomic nuclei in stars, planets, people and all that we see. These
    particles amount to 4 to 5 percent of the mass-energy of the universe.
    The Standard Model tells us that protons and neutrons are composed of
    elementary particles called quarks that are bound together by massless
    particles called gluons. Although the constituents are whirling around
    inside each proton, from outside we see a proton as a coherent object
    with an intrinsic mass, which is given by adding up the masses and
    energies of its constituents.

    The Standard Model lets us calculate that nearly all the mass of
    protons and neutrons is from the kinetic energy of their constituent
    quarks and gluons (the remainder is from the quarks' rest mass). Thus,
    about 4 to 5 percent of the entire universe--almost all the familiar
    matter around us--comes from the energy of motion of quarks and gluons
    in protons and neutrons.

    The Higgs Mechanism
    Unlike protons and neutrons, truly elementary particles--such as
    quarks and electrons--are not made up of smaller pieces. The
    explanation of how they acquire their rest masses gets to the very
    heart of the problem of the origin of mass. As I noted above, the
    account proposed by contemporary theoretical physics is that
    fundamental particle masses arise from interactions with the Higgs
    field. But why is the Higgs field present throughout the universe? Why
    isn't its strength essentially zero on cosmic scales, like the
    electromagnetic field? What is the Higgs field?

    The Higgs field is a quantum field. That may sound mysterious, but the
    fact is that all elementary particles arise as quanta of a
    corresponding quantum field. The electromagnetic field is also a
    quantum field (its corresponding elementary particle is the photon).
    So in this respect, the Higgs field is no more enigmatic than
    electrons and light. The Higgs field does, however, differ from all
    other quantum fields in three crucial ways.

    The first difference is somewhat technical. All fields have a property
    called spin, an intrinsic quantity of angular momentum that is carried
    by each of their particles. Particles such as electrons have spin 1/2
    and most particles associated with a force, such as the photon, have
    spin 1. The Higgs boson (the particle of the Higgs field) has spin 0.
    Having 0 spin enables the Higgs field to appear in the Lagrangian in
    different ways than the other particles do, which in turn allows--and
    leads to--its other two distinguishing features.

    The second unique property of the Higgs field explains how and why it
    has nonzero strength throughout the universe. Any system, including a
    universe, will tumble into its lowest energy state, like a ball
    bouncing down to the bottom of a valley. For the familiar fields, such
    as the electromagnetic fields that give us radio broadcasts, the
    lowest energy state is the one in which the fields have zero value
    (that is, the fields vanish)--if any nonzero field is introduced, the
    energy stored in the fields increases the net energy of the system.
    But for the Higgs field, the energy of the universe is lower if the
    field is not zero but instead has a constant nonzero value. In terms
    of the valley metaphor, for ordinary fields the valley floor is at the
    location of zero field; for the Higgs, the valley has a hillock at its
    center (at zero field) and the lowest point of the valley forms a
    circle around the hillock. The universe, like a ball, comes to rest
    somewhere on this circular trench, which corresponds to a nonzero
    value of the field. That is, in its natural, lowest energy state, the
    universe is permeated throughout by a nonzero Higgs field.

    The final distinguishing characteristic of the Higgs field is the form
    of its interactions with the other particles. Particles that interact
    with the Higgs field behave as if they have mass, proportional to the
    strength of the field times the strength of the interaction. The
    masses arise from the terms in the Lagrangian that have the particles
    interacting with the Higgs field.

    Our understanding of all this is not yet complete, however, and we are
    not sure how many kinds of Higgs fields there are. Although the
    Standard Model requires only one Higgs field to generate all the
    elementary particle masses, physicists know that the Standard Model
    must be superseded by a more complete theory. Leading contenders are
    extensions of the Standard Model known as Supersymmetric Standard
    Models (SSMs). In these models, each Standard Model particle has a
    so-called superpartner (as yet undetected) with closely related
    properties [see "The Dawn of Physics beyond the Standard Model," by
    Gordon Kane; Scientific American, June 2003]. With the Supersymmetric
    Standard Model, at least two different kinds of Higgs fields are
    needed. Interactions with those two fields give mass to the Standard
    Model particles. They also give some (but not all) mass to the
    superpartners. The two Higgs fields give rise to five species of Higgs
    boson: three that are electrically neutral and two that are charged.
    The masses of particles called neutrinos, which are tiny compared with
    other particle masses, could arise rather indirectly from these
    interactions or from yet a third kind of Higgs field.

    Theorists have several reasons for expecting the SSM picture of the
    Higgs interaction to be correct. First, without the Higgs mechanism,
    the W and Z bosons that mediate the weak force would be massless, just
    like the photon (which they are related to), and the weak interaction
    would be as strong as the electromagnetic one. Theory holds that the
    Higgs mechanism confers mass to the W and Z in a very special manner.
    Predictions of that approach (such as the ratio of the W and Z masses)
    have been confirmed experimentally.

    Second, essentially all other aspects of the Standard Model have been
    well tested, and with such a detailed, interlocking theory it is
    difficult to change one part (such as the Higgs) without affecting the
    rest. For example, the analysis of precision measurements of W and Z
    boson properties led to the accurate prediction of the top quark mass
    before the top quark had been directly produced. Changing the Higgs
    mechanism would spoil that and other successful predictions.

    Third, the Standard Model Higgs mechanism works very well for giving
    mass to all the Standard Model particles, W and Z bosons, as well as
    quarks and leptons; the alternative proposals usually do not. Next,
    unlike the other theories, the SSM provides a framework to unify our
    understanding of the forces of nature. Finally, the SSM can explain
    why the energy "valley" for the universe has the shape needed by the
    Higgs mechanism. In the basic Standard Model the shape of the valley
    has to be put in as a postulate, but in the SSM that shape can be
    derived mathematically.

    Testing the Theory
    Naturally, physicists want to carry out direct tests of the idea that
    mass arises from the interactions with the different Higgs fields. We
    can test three key features. First, we can look for the signature
    particles called Higgs bosons. These quanta must exist, or else the
    explanation is not right. Physicists are currently looking for Higgs
    bosons at the Tevatron Collider at Fermi National Accelerator
    Laboratory in Batavia, Ill.

    Second, once they are detected we can observe how Higgs bosons
    interact with other particles. The very same terms in the Lagrangian
    that determine the masses of the particles also fix the properties of
    such interactions. So we can conduct experiments to test
    quantitatively the presence of interaction terms of that type. The
    strength of the interaction and the amount of particle mass are
    uniquely connected.

    Third, different sets of Higgs fields, as occur in the Standard Model
    or in the various SSMs, imply different sets of Higgs bosons with
    various properties, so tests can distinguish these alternatives, too.
    All that we need to carry out the tests are appropriate particle
    colliders--ones that have sufficient energy to produce the different
    Higgs bosons, sufficient intensity to make enough of them and very
    good detectors to analyze what is produced.

    A practical problem with performing such tests is that we do not yet
    understand the theories well enough to calculate what masses the Higgs
    bosons themselves should have, which makes searching for them more
    difficult because one must examine a range of masses. A combination of
    theoretical reasoning and data from experiments guides us about
    roughly what masses to expect.

    The Large Electron-Positron Collider (LEP) at CERN, the European
    laboratory for particle physics near Geneva, operated over a mass
    range that had a significant chance of including a Higgs boson. It did
    not find one--although there was tantalizing evidence for one just at
    the limits of the collider's energy and intensity--before it was shut
    down in 2000 to make room for constructing a newer facility, CERN's
    Large Hadron Collider (LHC). The Higgs must therefore be heavier than
    about 120 proton masses. Nevertheless, LEP did produce indirect
    evidence that a Higgs boson exists: experimenters at LEP made a number
    of precise measurements, which can be combined with similar
    measurements from the Tevatron and the collider at the Stanford Linear
    Accelerator Center. The entire set of data agrees well with theory
    only if certain interactions of particles with the lightest Higgs
    boson are included and only if the lightest Higgs boson is not heavier
    than about 200 proton masses. That provides researchers with an upper
    limit for the mass of the Higgs boson, which helps focus the search.

    The LEP collider saw tantalizing evidence for the Higgs particle.

    For the next few years, the only collider that could produce direct
    evidence for Higgs bosons will be the Tevatron. Its energy is
    sufficient to discover a Higgs boson in the range of masses implied by
    the indirect LEP evidence, if it can consistently achieve the beam
    intensity it was expected to have, which so far has not been possible.
    In 2007 the LHC, which is seven times more energetic and is designed
    to have far more intensity than the Tevatron, is scheduled to begin
    taking data. It will be a factory for Higgs bosons (meaning it will
    produce many of the particles a day). Assuming the LHC functions as
    planned, gathering the relevant data and learning how to interpret it
    should take one to two years. Carrying out the complete tests that
    show in detail that the interactions with Higgs fields are providing
    the mass will require a new electron-positron collider in addition to
    the LHC (which collides protons) and the Tevatron (which collides
    protons and antiprotons).

    Dark Matter
    What is discovered about Higgs bosons will not only test whether the
    Higgs mechanism is indeed providing mass, it will also point the way
    to how the Standard Model can be extended to solve problems such as
    the origin of dark matter.

    With regard to dark matter, a key particle of the SSM is the lightest
    superpartner (LSP). Among the superpartners of the known Standard
    Model particles predicted by the SSM, the LSP is the one with the
    lowest mass. Most superpartners decay promptly to lower-mass
    superpartners, a chain of decays that ends with the LSP, which is
    stable because it has no lighter particle that it can decay into.
    (When a superpartner decays, at least one of the decay products should
    be another superpartner; it should not decay entirely into Standard
    Model particles.) Superpartner particles would have been created early
    in the big bang but then promptly decayed into LSPs. The LSP is the
    leading candidate particle for dark matter.

    The Higgs bosons may also directly affect the amount of dark matter in
    the universe. We know that the amount of LSPs today should be less
    than the amount shortly after the big bang, because some would have
    collided and annihilated into quarks and leptons and photons, and the
    annihilation rate may be dominated by LSPs interacting with Higgs

    As mentioned earlier, the two basic SSM Higgs fields give mass to the
    Standard Model particles and some mass to the superpartners, such as
    the LSP. The superpartners acquire more mass via additional
    interactions, which may be with still further Higgs fields or with
    fields similar to the Higgs. We have theoretical models of how these
    processes can happen, but until we have data on the superpartners
    themselves we will not know how they work in detail. Such data are
    expected from the LHC or perhaps even from the Tevatron.

    Neutrino masses may also arise from interactions with additional Higgs
    or Higgs-like fields, in a very interesting way. Neutrinos were
    originally assumed to be massless, but since 1979 theorists have
    predicted that they have small masses, and over the past decade
    several impressive experiments have confirmed the predictions [see
    "Solving the Solar Neutrino Problem," by Arthur B. McDonald, Joshua R.
    Klein and David L. Wark; Scientific American, April 2003]. The
    neutrino masses are less than a millionth the size of the next
    smallest mass, the electron mass. Because neutrinos are electrically
    neutral, the theoretical description of their masses is more subtle
    than for charged particles. Several processes contribute to the mass
    of each neutrino species, and for technical reasons the actual mass
    value emerges from solving an equation rather than just adding the

    Thus, we have understood the three ways that mass arises: The main
    form of mass we are familiar with--that of protons and neutrons and
    therefore of atoms--comes from the motion of quarks bound into protons
    and neutrons. The proton mass would be about what it is even without
    the Higgs field. The masses of the quarks themselves, however, and
    also the mass of the electron, are entirely caused by the Higgs field.
    Those masses would vanish without the Higgs. Last, but certainly not
    least, most of the amount of superpartner masses, and therefore the
    mass of the dark matter particle (if it is indeed the lightest
    superpartner), comes from additional interactions beyond the basic
    Higgs one.

    Finally, we consider an issue known as the family problem. Over the
    past half a century physicists have shown that the world we see, from
    people to flowers to stars, is constructed from just six particles:
    three matter particles (up quarks, down quarks and electrons), two
    force quanta (photons and gluons), and Higgs bosons--a remarkable and
    surprisingly simple description. Yet there are four more quarks, two
    more particles similar to the electron, and three neutrinos. All are
    very short-lived or barely interact with the other six particles. They
    can be classified into three families: up, down, electron neutrino,
    electron; charm, strange, muon neutrino, muon; and top, bottom, tau
    neutrino, tau. The particles in each family have interactions
    identical to those of the particles in other families. They differ
    only in that those in the second family are heavier than those in the
    first, and those in the third family are heavier still. Because these
    masses arise from interactions with the Higgs field, the particles
    must have different interactions with the Higgs field.

    Hence, the family problem has two parts: Why are there three families
    when it seems only one is needed to describe the world we see? Why do
    the families differ in mass and have the masses they do? Perhaps it is
    not obvious why physicists are astonished that nature contains three
    almost identical families even if one would do. It is because we want
    to fully understand the laws of nature and the basic particles and
    forces. We expect that every aspect of the basic laws is a necessary
    one. The goal is to have a theory in which all the particles and their
    mass ratios emerge inevitably, without making ad hoc assumptions about
    the values of the masses and without adjusting parameters. If having
    three families is essential, then it is a clue whose significance is
    currently not understood.

    Tying It All Together
    The standard model and the SSM can accommodate the observed family
    structure, but they cannot explain it. This is a strong statement. It
    is not that the SSM has not yet explained the family structure but
    that it cannot. For me, the most exciting aspect of string theory is
    not only that it may provide us with a quantum theory of all the
    forces but also that it may tell us what the elementary particles are
    and why there are three families. String theory seems able to address
    the question of why the interactions with the Higgs field differ among
    the families. In string theory, repeated families can occur, and they
    are not identical. Their differences are described by properties that
    do not affect the strong, weak, electromagnetic or gravitational
    forces but that do affect the interactions with Higgs fields, which
    fits with our having three families with different masses. Although
    string theorists have not yet fully solved the problem of having three
    families, the theory seems to have the right structure to provide a
    solution. String theory allows many different family structures, and
    so far no one knows why nature picks the one we observe rather than
    some other [see "The String Theory Landscape," by Raphael Bousso and
    Joseph Polchinski; Scientific American, September 2004]. Data on the
    quark and lepton masses and on their superpartner masses may provide
    major clues to teach us about string theory.
    One can now understand why it took so long historically to begin to
    understand mass. Without the Standard Model of particle physics and
    the development of quantum field theory to describe particles and
    their interactions, physicists could not even formulate the right
    questions. Whereas the origins and values of mass are not yet fully
    understood, it is likely that the framework needed to understand them
    is in place. Mass could not have been comprehended before theories
    such as the Standard Model and its supersymmetric extension and string
    theory existed. Whether they indeed provide the complete answer is not
    yet clear, but mass is now a routine research topic in particle

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