The Search for Relativity Violations

Home , Alan Kostelecky, CPT symmetry

VIOLATIONS OF RELATIVITY could be manifest in the ticking rates of mirror-image, antimatter clocks and the stretching of matter along specific directions.

To uncover evidence for an ultimate theory, scientists are looking for infractions of Einstein’s once sacrosanct physical principle By Alan Kosteleck´y

Relativity lies at the heart of the most fundamental theories of physics. Formulated by Albert Einstein in tempts to combine all the known forces and par- 1905, relativity is built on the key idea that phys- ticles into one ultimate unified theory, some ical laws take the same form for any inertial ob- physicists have been investigating the possibili- server—that is, for an observer oriented in any di- ty that relativity’s postulates provide only an ap- rection and moving at any constant speed. The proximation of nature’s workings. The hope is theory predicts an assortment of well-known ef- that small relativity violations might offer the OVERVIEW fects: among them, constancy of the speed of light first experimental signals of the long-sought ul- ■ Although special relativity for all observers, slowing of moving clocks, timate theory. is among the most length contraction of moving objects, and equiv- The unchanging quality, or invariance, of fundamental and well alence of mass and energy (E = mc2). These ef- physical laws for different observers represents verified of all physical fects have been confirmed in highly sensitive ex- a symmetry of space and time (spacetime), called theories, tiny violations of periments, and relativity is now a basic, everyday Lorentz symmetry after Dutch theoretical physi- it could be predicted by tool of experimental physics: particle colliders cist Hendrik Antoon Lorentz, who studied it be- theories that unify quantum take advantage of the increase in mass and life- ginning in the 1890s. A perfect sphere illustrates mechanics, gravity and the other forces of nature. time of fast particles; experiments with radioac- an ordinary symmetry, what is known as sym- ■ Numerous experiments tive isotopes depend on the conversion of mass metry under rotations: no matter how you turn are under way to uncover into energy. Even consumer electronics is affect- it, the sphere looks the same. Lorentz symmetry such effects, but so far ed—the Global Positioning System must allow is not based on objects looking the same but ex- none have proved sensitive for time dilation, which alters the rates of clocks presses instead the sameness of the laws of phys- enough to succeed. on its orbiting satellites. ics under rotations and also under boosts, which

DAVID EMMITE PHOTOGRAPHY In recent years, however, motivated by at- are changes of velocity. An observer sees the same

Lorentz symmetry is a fundamental property of the natural world that is of supreme importance for physics. It has two components: rotational symmetry and boost d symmetry. Imagine that we have two rods made of dissimilar materials but having identical lengths when placed side by side and two clocks operating by different mechanisms that keep identical time (a). Rotational symmetry states that if one rod Clock and one clock are rotated relative to the others, the rods nonetheless retain identical lengths and the clocks remain in sync (b). Boost symmetry considers what happens when one rod and one clock are “boosted” so that they move at a constant velocity relative to the other two, which here remain at rest. Boost symmetry predicts that the moving rod will be shorter and that the moving clock will run slower by amounts that depend in a precise way on the relative velocity (c). When space and time are combined Parity- to form spacetime, boost symmetry actually has almost identical mathematical form to inverted rotational symmetry. A closely related symmetry is CPT symmetry, where the letters antimatter stand for charge conjugation, parity inversion and time reversal. This predicts that if a clock clock is replaced by its antimatter equivalent (charge reversal), which is also inverted (parity) and running backward in time, the two will keep identical time (d). A mathematical theorem demonstrates that for a quantum field theory, CPT symmetry must hold whenever Lorentz symmetry is obeyed. Relativity Violated

Broken Lorentz symmetry can be represented by a field of relative to the vector field (left) may shrink or expand at vectors throughout spacetime. Particles and forces have another orientation (center). Similarly, two dissimilar clocks that interactions with this vector field (arrows) similar to the are synchronized at the first orientation may run slow or fast at interaction of charged particles with an electric field (which is the second orientation. In addition, dissimilar rods and clocks also a vector field). As a result, unlike the Lorentz symmetric that are boosted (right) may undergo different length case, all directions and all velocities are no longer equivalent. contractions and time dilations depending on their materials Two dissimilar rods that have equal lengths at one orientation and the direction and magnitude of the boost. DON FOLEY

94 SCIENTIFIC AMERICAN SEPTEMBER 2004 COPYRIGHT 2004 SCIENTIFIC AMERICAN, INC. laws of physics at play, no matter what Applied SPONTANEOUS SYMMETRY BREAKING occurs her orientation (rotation) and no mat- force when a completely symmetric set of conditions ter what her velocity (boost). When or underlying equations gives rise to an Lorentz symmetry holds, spacetime is asymmetric result. For example, consider a isotropic in the sense that all directions cylindrical stick with a force applied vertically and all uniform motions are equivalent, (left). The system is completely symmetrical so none are singled out as being special. with respect to rotations around the axis of the The Lorentz symmetry of spacetime stick. If a large enough force is applied, however, the system becomes unstable and forms the core of relativity. The details the stick will bend in some direction (right). of how boosts work produce all the The symmetry breaking can be represented by well-known relativistic effects. Before a vector, or an arrow (red), that indicates the Einstein’s 1905 paper, equations relat- direction and magnitude of the bending. ing to these effects had been developed Lorentz violation involves the emergence of by several other researchers, including such vector quantities throughout spacetime. Lorentz, but they typically interpreted the equations as describing physical changes in objects—for example, bond Lorentz symmetry. (The term “general” classic experiment in which cold neu- lengths between atoms becoming short- means that gravity is included, whereas trons rise against the earth’s gravita- er to generate length contraction. Ein- “special” relativity excludes it.) In gen- tional field, the gravity is incorporated stein’s great contributions included eral relativity, the laws of physics at any into the quantum description as an ex- combining all the pieces and realizing given location are the same for all ob- ternally applied force. That characteri- that the lengths and clock rates are in- server orientations and velocities, as be- zation models the experiment extreme- timately linked. The notions of space fore, but the effects of gravity make ly well, but it is unsatisfactory as a fun- and time merge into a single concept: comparisons between experiments at damental and consistent description. It spacetime. different locations more complicated. is like describing how a person can lift Lorentz symmetry is a key element General relativity is a classical theory a heavy object, with the bones’ mechan- in the very foundations of our best de- (that is, nonquantum), and no one ical strength and other properties accu- scription of the fundamental particles knows how to combine it with the ba- rately modeled and explained down to and forces. When combined with the sic Standard Model in a completely sat- the molecular level, but with the muscles principles of quantum mechanics, Lo- isfactory way. The two can be partially depicted as black-box machines that can rentz symmetry produces a framework combined, however, into a theory supply a specified range of forces. called relativistic quantum field theory. called “the Standard Model with grav- For these reasons and others, many In this framework, every particle or ity,” which describes all particles and all theoretical physicists believe that it force is described by a field that perme- four forces. must be possible to formulate an ulti- ates spacetime and has the appropriate mate theory—a complete and unified Lorentz symmetry. Particles such as Unification and description of nature that consistently electrons or photons exist as localized the Planck Scale combines quantum physics and gravity. excitations, or quanta, in the relevant TOGETHER THIS MELDING of the One of the first physicists to work on field. The Standard Model of particle Standard Model and general relativity is the idea of a unified theory was Einstein physics, which describes all known astonishingly successful in describing himself, who tackled this problem dur- particles and all known nongravita- nature. It describes all established fun- ing the last part of his life. His goal was tional forces (the electromagnetic, damental phenomena and experimental to find a theory that would describe not weak and strong forces), is a relativis- results, and no confirmed experimental only gravity but also electromagnetism. tic quantum field theory. The require- evidence for physics beyond it exists [see Alas, he had tackled the problem too ments of Lorentz symmetry strongly “The Dawn of Physics beyond the Stan- early. We now believe that electro- constrain how the fields in this theory dard Model,” by Gordon Kane; Scien- magnetism is closely related to the can behave and interact. Many interac- tific American, June 2003]. Never- strong and weak forces. (The strong tions that one could write down as theless, many physicists deem the com- force acts between quarks, which make plausible-looking terms to be added to bination unsatisfactory. One source of up particles such as protons and neu- the theory’s equations are excluded be- difficulty is that although quantum trons, whereas the weak force is re- cause they violate Lorentz symmetry. physics and gravity each have an elegant sponsible for some kinds of radioactiv- The Standard Model does not in- formulation, they seem mathematically ity and the decay of the neutron.) It was clude the gravitational interaction. Our incompatible in their present form. In only with experimental facts uncovered best description of gravity, Einstein’s situations where both gravity and quan- after Einstein’s death that the strong

DON FOLEY general relativity, is also founded on tum physics are important, such as the and weak forces became characterized

www.sciam.com SCIENTIFIC AMERICAN 95 COPYRIGHT 2004 SCIENTIFIC AMERICAN, INC. EARTH’S ROTATION will turn a tances, spacetime appears Lorentz in- Axis of rotation laboratory, such as this one variant, but this symmetry may be bro- involved in a hypothetical ken at sufficiently small distances as a experiment at Indiana University consequence of features of the unifica- (yellow dot), relative to any tion of quantum physics and gravity. relativity-violating vector field The observable effects of Planck- (arrows) that is present scale relativity violations are likely to lie throughout spacetime. In the lab in the range of 10–34 to 10–17. To gain frame of reference, the vector some feeling for these numbers, consid- field will seem to change direction over the course of a day, enabling er that the thickness of a human hair –30 the experiment to detect Lorentz is about 10 of the distance across –17 violations. For example, a the observable universe. Even 10 is comparison of two dissimilar roughly the ratio of a hair’s thickness to masses in the lab may see small the diameter of Neptune’s orbit. The periodic variations in their masses. detection of relativity violations therefore requires some of the most sensitive experiments ever performed. 6 A.M. Another fundamental spacetime symmetry that could be violated is so- 6 P.M. called CPT symmetry. This symmetry holds when the laws of physics are un- well enough for them to be understood cably intertwined at a fundamental affected when three transfomations are separately, let alone in combination length scale of about 10–35 meter, which all applied at once: interchange of par- with electromagnetism and gravity. is called the Planck length, after 19th- ticles and antiparticles (charge conju- One promising and comprehensive century German physicist Max Planck. gation, C), reflection in a mirror (parity approach to this ultimate theory is The Planck length is far too small to be inversion, P) and reversal of time (T). string theory, which is based on the idea within the direct reach of either con- The Standard Model obeys CPT sym- that all particles and forces can be de- ventional microscopes or less conven- metry, but theories with relativity vio- scribed in terms of one-dimensional ob- tional ones such as high-energy particle lations may break it. jects (“strings”), along with membranes colliders (which probe “merely” down of two dimensions and higher that are to about 10–19 meter). So not only is it Spontaneous Violations called branes [see “The String Theory very challenging to construct a con- HOW MIGHT RELATIVITY viola- Landscape,” by Raphael Bousso and vincing ultimate theory, but it is also tions emerge in the ultimate theory? Joseph Polchinski, on page 78]. Anoth- impractical to observe directly the new One natural and elegant mechanism is er approach, known as loop quantum physics it must surely predict. called spontaneous Lorentz violation. It gravity, seeks a consistent quantum in- Despite these obstacles, a route has similarities to the spontaneous terpretation of general relativity and may exist for obtaining experimental breaking of other kinds of symmetry, predicts that space is a patchwork of information about the unified theory at which occurs whenever the underlying discrete pieces (quanta) of volume and the Planck scale. Minuscule indirect ef- physical laws are symmetrical but the area [see “Atoms of Space and Time,” fects reflecting the new physics in the actual system is not. To illustrate the by Lee Smolin; Scientific American, unified theory may be detectable in ex- general idea of spontaneous symmetry January]. periments of sufficient sensitivity. An breaking, consider a slender cylindrical Whatever the eventual form of the analogy is the image on a television or stick, placed vertically with one end on ultimate theory, quantum physics and computer screen, which is composed of the floor [see illustration on preceding gravity are expected to become inextri- many small, bright pixels. The pixels page]. Imagine applying a force verti- are small compared with the distance cally downward on the stick. This situ- ALAN KOSTELECKÝ is professor of theoret- at which the screen is viewed, so the ation is completely symmetrical under ical physics at Indiana University. His pub- image appears smooth to the eye. But rotations around the axis of the stick: lications span a broad range of topics in in special situations, the pixels become the stick is cylindrical, and the force is particle physics, gravitation, string theory, evident—for example, when a news- vertical. So the basic physical equations mathematical physics and atomic physics. caster is wearing a tie with narrow for this situation are symmetrical under

THE AUTHOR His research on Lorentz and CPT symmetry stripes that trigger a Moiré pattern on rotation. But if sufﬁcient force is ap- triggered the recent flood of interest in rel- the screen. One class of such “Moiré plied, the stick will bend in some par- ativity violations and has led to many new patterns” from the Planck scale is rel- ticular direction, which spontaneously

experimental tests. ativity violations. At macroscopic dis- breaks the rotational symmetry. DON FOLEY

96 SCIENTIFIC AMERICAN SEPTEMBER 2004 COPYRIGHT 2004 SCIENTIFIC AMERICAN, INC. In the case of relativity violations, string theory and field theories with any experiment. With such a frame- the equations describing the stick and gravity was originally proposed in 1989 work, specific experimental parameters the applied force are replaced by the by me and Stuart Samuel of the City can be calculated, different experiments equations of the ultimate theory. In College of New York. It was extended can be compared, and predictions can place of the stick are the quantum fields in 1991 to include spontaneous CPT vi- be made for the kind of effects to be of matter and forces. The natural back- olation in string theory by me and expected. ground strength of such fields is usual- Robertus Potting of Algarve University Certain criteria guide our construc- ly zero. In certain situations, however, in Portugal. Since then, various addition of this framework. First, all physi- the background fields acquire a nonze- tional mechanisms have been proposed cal phenomena should be independent ro strength. Imagine that this happened for relativity violations arising in string of the particular coordinate system used for the electric field. Because the electric theory and in other approaches to quan- to map out space and time. Second, the field has a direction (technically, it is a tum gravity. If spontaneous Lorentz experimental successes of the Standard vector), every location in space will breaking or any other mechanisms do Model and general relativity mean that have a special direction singled out by turn out to be part of the ultimate fun- any Lorentz and CPT violations must the direction of the electric field. A damental theory, the concomitant rel- be small. By following these criteria and charged particle will accelerate in that ativity violations could provide the first using only the known forces and par- direction. Rotational symmetry is bro- experimental evidence for the theory. ticles, we are led to a set of possible ken (and so is boost symmetry). The terms—possible interactions—that could same reasoning applies for any nonzero Standard Model Extension be added to the equations of the theory. “tensor” field; a vector is a special case SUPPOSE THAT the fundamental the- Each term corresponds to a particular of a tensor. ory of nature does contain Lorentz vi- tensor field acquiring a nonzero back- Such spontaneous nonzero tensor olation, perhaps with CPT violation, ground value. The coefficients that fields do not arise in the Standard Mod- through some mechanism. How would specify the magnitudes of these terms el, but some fundamental theories, in- this manifest itself in experiments, and are unknown, and indeed many might cluding string theory, contain features how can it be related to known physics? be zero when the ultimate theory is that are favorable for spontaneous To answer these questions, we would known. Lorentz breaking. The idea that spon- like to have a general theoretical frame- The end result is a theory called the taneous Lorentz breaking and observ- work that encompasses all possible ef- Standard Model Extension, or SME. able relativity violations could occur in fects and that can be applied to analyze The beauty of this formulation is its

ORBITING LABORATORIES Studying Space in Space On satellites such as the space station will be experiments that seek evidence of Space station Lorentz violations in comparisons of clocks. The illustration shows the case where there are two relativity-violating vector ﬁelds (red and blue arrows) with different interactions with particles. Depicted below is a comparison between an atomic clock (represented by an atom) and a clock based on light or microwaves (wavy lines) in a resonant cavity. The light and electrons (red) interact with the red vectors, whereas protons (blue) interact with the blue vectors. As the space station rotates, these changing interactions cause the clocks to go in and out of sync, revealing the Lorentz violation. The 92-minute rotation of the space station provides for much faster and more sensitive data taking than a stationary earth-based experiment. Vector fields Electron

Neutron

Proton

Light in resonant Atom Resonant cavity cavity DON FOLEY

www.sciam.com SCIENTIFIC AMERICAN 97 COPYRIGHT 2004 SCIENTIFIC AMERICAN, INC. ICONOCLASTS Toppling the Giant Everyone wants to get a piece of Einstein. Two of the three most common crackpot missives received by scientists and science magazines involve Einstein: claims to have a unified theory (succeeding where Einstein failed) and claims to have proved his theories false. (The third big class of craziness: perpetual-motion machines and infinite-energy sources.) Like cannibals seeking the strength and life spirit of their victims, these misguided amateurs seem to think that by outdoing or disproving Einstein they will acquire all his prestige and acclaim. Of course, all that they disprove is their own competence with basic relativity. But the crazies are not the only iconoclasts. Many serious and well-qualified researchers also seek to go beyond Einstein, in the way that he went beyond Galileo and Newton. The accompanying article by Alan Kostelecký describes the experimental search for departures from Einsteinian relativity. The analysis he discusses is based on a general “Standard Model Extension” in which all plausible relativity- violating terms are added to the equations of particle physics. This all-encompassing model covers every possible deviation that could trickle down to everyday physics from the high-energy pinnacle of the (as yet undiscovered) ultimate unified theory. Yet certain putative breaches of relativity have attracted specific attention. One class of theories goes by the name “doubly special relativity,” which has been studied by Giovanni Amelino-Camelia of the University of Rome since 2000 and later by Lee Smolin of the Perimeter Institute for Theoretical Physics in Ontario, João Magueijo of Imperial College London and others. Magueijo, incidentally, fits the TOWERING FIGURE of Einstein provides a tempting target for physicists label “iconoclast” to a T—as is apparent from his argumentative book of all stripes. He would perhaps look with approval on these efforts Faster Than the Speed of Light. to go beyond his theories. Doubly special relativity is inspired by quantum gravity theories such as loop quantum gravity [see “Atoms of Space and Time,” by Lee of the speed of light in a vacuum, also known as c. The idea is that at Smolin; SCIENTIFIC AMERICAN, January], and it imposes a second kind of very short distances the smooth continuity of spacetime should “speed limit” that works in conjunction with the conventional barrier break down into something more granular—like grains of sand or the

generality: whatever your philosophical plings to these background fields, the relativity-violating behavior can depend or physical preferences for the origin of motions and interactions of particles on the size and orientation of the spin. relativity violations, the resulting effects acquire a directional dependence, like The particle can also fail to mirror its in nature must be described by the charged particles moving in an electric antiparticle (CPT violations). Each be- SME, because it contains all viable or a magnetic field. A similar visualiza- havior can vary depending on the spe- modifications and generalizations of tion works for CPT violation, but in cies of particle; for instance, protons relativity that are compatible with the this case the effects occur because par- might be affected more than neutrons, Standard Model and the known behav- ticles and antiparticles have different and electrons not at all. These effects ior of gravity. couplings to the background fields. combine to produce a plethora of inter- To visualize the effects of Lorentz The SME predicts that the behavior esting signals that can be sought in ex- violation, it is useful to think of space- of a particle can be affected by relativi- periments. A number of such experi- time as having an intrinsic orientation. ty violations in several ways. The par- ments have begun, but so far none has In the case of a vector field causing a ticle’s properties and interactions can provided conclusive evidence for rela- particular term in the SME equations, depend on the direction it is moving (ro- tivity violations. the orientation coincides with the di- tation violations) and on how fast it is Corbis rection of the vector field. The more going (boost violations). The particle Ancient Light general case of a tensor field is similar may have spin, an intrinsic quantity of ONE WAY TO OBTAIN exceptional

but more complicated. By virtue of cou- angular momentum, in which case the sensitivity to relativity violations is by LUCIEN AIGNER

98 SCIENTIFIC AMERICAN SEPTEMBER 2004 COPYRIGHT 2004 SCIENTIFIC AMERICAN, INC. network of a spider’s web. In quantum physics, short distances and depends on the precise structure of extra tiny dimensions that are short times correspond to high momenta and high energies. Thus, at appended to the four dimensions of space and time that we know sufficiently high energy—the so-called Planck energy—a particle and love [see “The String Theory Landscape,” by Raphael Bousso should “see” the graininess of spacetime. That violates relativity, and Joseph Polchinski, on page 78]. which depends on spacetime being smooth down to the tiniest size The possibility that alpha might change was considered as long scales. Reflecting this, in a doubly special theory, just as a particle ago as 1955, by the great Russian physicist Lev Landau. Today cannot be accelerated beyond c, it cannot be boosted beyond the physicists and astronomers are looking at ancient light from distant Planck energy. quasars for evidence that alpha was slightly different eons ago. Some of these models predict that extremely high frequency Changing alpha would subtly alter the frequency of light emitted or light should travel faster than lower-frequency light. Experimenters absorbed by atoms and ions. Most searches for such shifts have are looking for that effect in light from distant explosions called turned up empty thus far. One exception is the results of a group led gamma-ray bursts. by John K. Webb of the University of New South Wales in Australia. But skeptics are unconvinced that these theories are well Those researchers have used a novel method of analyzing the data founded. Some researchers argue, for example, that the equations to achieve finer precision and have reported evidence (albeit are physically equivalent to ordinary relativity, just dressed up in statistically somewhat weak) of shifts: between eight billion and enough complexities for that to be unobvious. The proof of the 11 billion years ago, alpha appears to have been about six parts in a pudding will have to come from a rigorous derivation of such a theory million feebler than it is today. Such a minute variation is hard to from something more fundamental, such as string theory or loop reconcile with the string theory explanation, which predicts long- quantum gravity. Not to mention experimental evidence. term stability of constants such as alpha, punctuated by occasional Another infraction that some have contemplated is that c itself catastrophic changes of great magnitude. has varied over the history of the universe. John W. Moffat of the Some researchers, however, assert that the precision claimed by University of Toronto studied models of this type in the early 1990s, the new method is not correct and that the “shifts” are just statistical and Magueijo has been a more recent champion of them. If c had fluctuations. In March of this year a team of astronomers led by been much greater in the very early moments of the big bang, certain Patrick Petitjean of the Institute of Astrophysics of Paris and the effects could have propagated at an extremely fast rate, which would Observatory of Paris and Raghunathan Srianand of the Inter- solve some cosmological puzzles. University Center for Astronomy and Astrophysics in Pune, India, If c varies, so, too, does the fine structure constant, alpha, which reported using the traditional methods pushed to the limit. They is a dimensionless number that specifies the strength of the concluded that as far back as 10 billion years, alpha has changed electromagnetic interaction. Alpha can be expressed in terms of c, by less than 0.6 part in a million, contradicting the claims of Webb Planck’s constant and the charge of the electron. Alpha can and company. therefore also change with c remaining constant, which might not So far then, Einstein has withstood all challengers. The infringe on relativity but would be equally seismic. Such variation in iconoclasts will have to keep looking for the first chink in his armor. alpha could occur in string theory, where the magnitude of alpha —Graham P. Collins, staff writer

studying the properties of polarized observable by measuring cosmological of light at right angles and verified that light that has traveled billions of light- polarization: the change in polarization their relative speed is independent of years across the cosmos. Certain rela- as the light travels would depend on the direction. The most sensitive experi- tivity-violating interactions in the SME color of the light. At Indiana Universi- ments nowadays use resonant cavities; will change the polarization of light as ty, Matthew Mewes and I have searched for example, rotating one on a turn- it travels through otherwise empty for this effect in polarization data of in- table and searching for changes in the space. The change grows as the light frared, visible and ultraviolet light from resonant frequency as it rotates. John travels greater distances. distant galaxies, obtaining a sensitivity A. Lipa’s group at Stanford University In the SME, the dominant relativi- of 10–32 on the coefficients controlling uses superconducting cavities to study ty violations involving light include these violations. the properties of microwave resonances. both ones that break CPT and ones The remaining relativity violations Achim Peters of Humboldt University that preserve it. Those that break CPT for light can be measured in the labora- in Berlin, Stephan Schiller of Düssel- are expected for technical theoretical tory using modern versions of experi- dorf University in Germany and their reasons to be absent or negligible, and ments similar to the classic Michelson- collaborators use laser light in sapphire studies of cosmological data have con- Morley test of relativity (named after crystal resonators. These experiments firmed this down to a sensitivity of physicist Albert Michelson and chemist and similar ones by other groups have 10–42. About half the CPT-preserving Edward Morley). The original Michel- already achieved sensitivities of 10–15 relativity violations for light would be son-Morley experiment sent two beams to 10–11.

www.sciam.com SCIENTIFIC AMERICAN 99 COPYRIGHT 2004 SCIENTIFIC AMERICAN, INC. Antimatter Experiments Antimatter ( invariance holds,antihydrogenandhydrogenshouldhaveidenticalemissionspectra (photons aretheirownantiparticles,soitisstillaphotonthatemitted).Thus,ifCPT left color orwavelengthwhenitselectrondropsfromahigherenergyleveltolowerone( hypothesis usingantihydrogenatoms.Ahydrogenatomemitslightwithacharacteristic called CPTinvarianceholds.TwoexperimentsatCERNnearGenevaaretestingthis Antimatter shouldbehaveinidenticalfashiontomatterifaformofspacetimesymmetry a signalofCPTviolation,whichinturnimpliesLorentzviolation. which shouldalsobeidenticalforhydrogenandantihydrogen.Anydiscrepancywould inverse oftheemissionprocessshownhere),andtransitionsinvolvingmicrowaves,all 410 434486565 bottom CPT SYMMETRY Hydrogen Antihydrogen 100 SENSITIVITY EXCEPTIONAL Experiments Clock-Comparison the tickingrate of thefirstone.Thesec- earth rotates.A secondclockmonitors the laboratoryandsorotates asthe magnetic field,whichisusually fixedin fined bythedirectionof applied field. Theorientationoftheclock isde- pends onthestrengthofmagnetic two oftheatom’senergylevelsthatde- the frequencyofatransitionbetween a magneticfield,andthetickingrateis The typicalbasic“clock”isanatomin a clockdependingonitsorientation. search forchangesinthetickingrateof in clock-comparisonexperiments,which ativity violationshasalsobeenachieved Electron ). Thesameprocessinantihydrogen( ). TheCERNexperimentswillactuallyuseabsorptionofultravioletlaserlight(the SCIENTIFIC AMERICAN Photon Proton Wavelength (nanometers) to rel- top right COPYRIGHT 2004 SCIENTIFIC AMERICAN, INC. 410 434486565 a difficulttechnical feat.Thefrequen- gases intomasers (microwavelasers), in asingleglassbulbandturns both worth’s groupmixesheliumand neon SME coefficientsforneutrons. Wals- 10 attained theremarkablesensitivity of Astrophysics. Theseexperimentshave the Harvard-Smithsonian in RonaldWalsworth’slaboratoryat ments ofthistypehavebeenperformed olation tobecomeapparent. fected bydifferentamountsforthevi- transition frequencies)havetobeaf- kind oftransition.Thetickingrates(the ent typeofatomundergoingthesame ond clockisoftentakentobeadiffer- ) shouldemitthesamecolorlight –31 To date,themostsensitiveexperi- to aspecificcombinationof Photon Antiproton Positron Center for top ing sensitivitiesof10 performed atotherinstitutions,achiev- ments withatomsasclockshavebeen cies ofthetwomasersarecompared. tion. Thisexperiment usedthegiant been achievedby theKTeVCollabora- Lorentz andCPTviolationinkaons has present, themostsensitiveconstraint on of kaonstosearchforCPTviolation. At laborations havestudiedtheoscillations ticeably. Severallargeexperimental col- CPT violationwouldchangethemno- so finelybalancedthatevenaminuscule back again.Thesekaonoscillationsare its antiparticle,theantikaon,andthen causes akaongraduallytoconvertinto It turnsoutthattheweakinteraction of fundamentalparticlecalledthekaon. of theclassicCPTtestsinvolvesatype erties ofparticlesandantiparticles.One can beperformedbycomparingprop- IETTSSFRCPT FOR TESTS DIRECT Antimatter well asorbitinginthattime.) and thusitrotatesevery92minutesas to keepthesamesidefacingearth, periment. (TheISSisoftenconfigured times asfastafixedearth-basedex- would allowdatatobetakenabout16 ISS’s orbitalperiodof92minutes sampled. Anotheradvantageisthatthe cesses, allspatialdirectionscouldbe ISS’s orbitalplaneisinclinedandpre- types ofrotationviolation.Becausethe tational axislimitssensitivitytosome use theearth’srotation,butfixedro- based clock-comparisonexperiments spatial directions.Typicalground- vantages, includingeasieraccesstoall would haveanumberofpotentialad- other satellites.Theseexperiments International SpaceStation(ISS)and clock-comparison experimentsonthe ing apositivemuonparticle). (an “atom”madeofanelectronorbit- in electromagnetictraps,andmuonium charged hydrogenionsandantiprotons positrons (antielectrons),negatively stead ofatoms)individualelectrons, trons. Otherexperimentshaveused(in- involving protons,neutronsandelec- ferent typesofrelativityviolations Various clock-comparisonexperi- Researchers haveplansforseveral –27 SEPTEMBER 2004 to 10 –23 violation for dif-

DON FOLEY Magnets

Electron spin

SPIN-COUPLED FORCES are investigated by a University of Washington experiment involving a torsion pendulum experiment (in which the hanging pendulum bob twists back and forth on its wire). The bob (photograph above) consists of rings of magnets made of two different outside the bob, reducing spurious signals caused by magnetic materials (red and blue at right). The field of each magnet type has the interactions. The electron spins, however, are unbalanced. If there is a same strength but is generated by a different quantity of electron spins sufficiently large relativity-violating vector field that interacts with (arrows). The magnetic field forms a closed loop with very little field electron spin, it will show up in perturbations of the bob’s oscillations.

Tevatron accelerator at Fermilab to cre- netic field [see illustration above]. The masses of neutrinos. But unusual oscil- ate vast numbers of kaons. The results ring is used as the bob in a torsion pen- lation properties for neutrinos are also yielded two independent measurements dulum, which twists back and forth predicted in the SME. Theorists have of SME coefficients at the level of 10–21. while suspended from a mounting on a shown that the description of neutrino Two experiments, ATHENA and rotating platform. A spin-dependent behavior in terms of relativity violations ATRAP, both at CERN (the European Lorentz violation would show up as a and the SME may be simpler than the laboratory for particle physics near perturbation of the pendulum’s oscil- conventional description in terms of Geneva), are under way to trap antihy- lations that depends on the pendulum’s masses. Future analyses of neutrino drogen and compare its spectroscopic orientation. This apparatus has been data could confirm this idea. properties with those of hydrogen, used to set the best current bounds on The experiments I have discussed which should be identical if CPT is pre- relativity violations involving electrons, have demonstrated that Planck-scale served [see box opposite page]. Any dif- at 10–29. sensitivities are attainable with existing ference uncovered would represent a It is possible that relativity viola- techniques. Although no compelling CPT violation and consequently a tions have already been detected but evidence for relativity violations has Lorentz violation. have not been recognized as such. In re- emerged to date, comparatively few High-sensitivity tests of relativity cent years, ghostly fundamental parti- types of relativity violations have been

) have also used objects made of materi- cles called neutrinos have been shown studied so far. The next few years will als in which the spins of many electrons to oscillate, which requires a modifica- see major improvements both in the combine to yield a net overall spin. tion of the minimal form of the Stan- scope of relativity tests (more coeffi- illustration (Think of each electron’s “spin” as be- dard Model [see “Solving the Solar cients measured) and in their depth ing a tiny compass needle. Opposite Neutrino Problem,” by Arthur B. Mc- (improved sensitivities). If relativity vi- pointing needles cancel, but parallel Donald, Joshua R. Klein and David L. olations are finally discovered, they will

); DON FOLEY ( ones add to give a larger total spin.) Wark; Scientific American, April signal a profound change in our un- Such materials are common—for ex- 2003]. The oscillations are usually as- derstanding of the universe at its most ample, an overall spin produces the cribed to small, previously unknown fundamental level. photograph ( magnetic field of a bar magnet. In searching for Lorentz violation, how- MORE TO EXPLORE ever, the presence of a strong magnet- Testing Times in Space. Steve K. Lamoreaux in Nature, Vol. 416, pages 803–804; April 25, 2002. ic field is a hindrance. To circumvent Back to the Future. Philip Ball in Nature, Vol. 427, pages 482–484; February 5, 2004. this, Eric Adelberger, Blayne Heckel Breaking Lorentz Symmetry. Robert Bluhm in Physics World, Vol. 17, No. 3, pages 41–46; and their colleagues at the University of March 2004. Available at physicsweb.org/article/world/17/3/7 Lorentz Invariance on Trial. Physics Today, University of Washington Maxim Pospelov and Michael Romalis in Vol. 57, No. 7, Washington have designed and built a pages 40–46; July 2004. spin-polarized ring of material that has Alan Kostelecký’s Web site on Lorentz and CPT violation is at

TED COOK a net electron spin but no external mag- www.physics.indiana.edu/~kostelec/faq.html