The Higgs Boson

artwork: CERN

When you get on the scale in the morning, you may be hoping that it registers a smaller number than the day before -- you may be hoping that you've lost weight. It's the quantity of mass in you, plus the force of gravity, that determines your weight. But what determines your mass?

That's one of the most-asked, most-hotly pursued questions in physics today. Many of the experiments circulating in the world's particle accelerators are looking into the mechanism that gives rise to mass. Scientists at CERN, as well as at Fermilab in Illinois, are hoping to find what they call the "Higgs boson." Higgs, they believe, is a particle, or set of particles, that might give others mass.

The idea of one particle giving another mass is a bit counter-intuitive... Isn't mass an inherent characteristic of matter? If not, how can one entity impart mass on all the others by simply floating by and interacting with them?

artwork: CERN Click on the image above for a helpful cartoon explanation of the Higgs Mechanism.

An oft-cited analogy describes it well: Imagine you're at a Hollywood party. The crowd is rather thick, and evenly distributed around the room, chatting. When the big star arrives, the people nearest the door gather around her. As she moves through the party, she attracts the people closest to her, and those she moves away from return to their other conversations. By gathering a fawning cluster of people around her, she's gained momentum, an indication of mass. She's harder to slow down than she would be without the crowd. Once she's stopped, it's harder to get her going again. This clustering effect is the Higgs mechanism, postulated by British physicist Peter Higgs in the 1960s. The theory hypothesizes that a sort of lattice, referred to as the Higgs field, fills the universe. This is something like an electromagnetic field, in that it affects the particles that move through it, but it is also related to the physics of solid materials. Scientists know that when an electron passes through a positively charged crystal lattice of atoms (a solid), the electron's mass can increase as much as 40 times. The same might be true in the Higgs field: a particle moving through it creates a little bit of distortion -- like the crowd around the star at the party -- and that lends mass to the particle.

photo: CERN Scientists at CERN use the enormous ALEPH detector in their search for the Higgs particle.

The question of mass has been an especially puzzling one, and has left the Higgs boson as the single missing piece of the Standard Model yet to be spotted. The Standard Model describes three of nature's four forces: electromagnetism and the strong and weak nuclear forces. Electromagnetism has been fairly well understood for many decades. Recently, physicists have learned much more about the strong force, which binds the elements of atomic nuclei together, and the weak force, which governs radioactivity and hydrogen fusion (which generates the sun's energy).

Electromagnetism describes how particles interact with photons, tiny packets of electromagnetic radiation. In a similar way, the weak force describes how two other entities, the W and Z particles, interact with electrons, quarks, neutrinos and others. There is one very important difference between these two interactions: photons have no mass, while the masses of W and Z are huge. In fact, they are some of the most massive particles known.
The first inclination is to assume that W and Z simply exist and interact with other elemental particles. But for mathematical reasons, the giant masses of W and Z raise inconsistencies in the Standard Model. To address this, physicists postulate that there must be at least one other particle -- the Higgs boson.

The simplest theories predict only one boson, but others say there might be several. In fact, the search for the Higgs particle(s) is some of the most exciting research happening, because it could lead to completely new discoveries in particle physics. Some theorists say it could bring to light entirely new types of strong interactions, and others believe research will reveal a new fundamental physical symmetry called "supersymmetry."

photo: CERN CERN scientists were unsure whether these events recorded by the ALEPH detector indicated the presence of a Higgs boson. Check out the links listed below for the latest information on the search for the Higgs Boson.

First, though, scientists want to determine whether the Higgs boson exists. The search has been on for over ten years, both at CERN's Large Electron Positron Collider (LEP) in Geneva and at Fermilab in Illinois. To look for the particle, researchers must smash other particles together at very high speeds. If the energy from that collision is high enough, it is converted into smaller bits of matter -- particles -- one of which could be a Higgs boson. The Higgs will only last for a small fraction of a second, and then decay into other particles. So in order to tell whether the Higgs appeared in the collision, researchers look for evidence of what it would have decayed into.

In August 2000, physicists working at CERN's LEP saw traces of particles that might fit the right pattern, but the evidence is still inconclusive. LEP was closed down in the beginning of November, 2000, but the search continues at Fermilab in Illinois, and will pick up again at CERN when the LHC (Large Hadron Collider) begins experiments in 2005.

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Extra Dimensions

Introduction

There has been a revolution in our thinking about extra dimensions. A new understanding of the feasibility oflocalizing four dimensional gauge theories in higher dimensionalspacetimes has led to a variety of phenomenologically viable models,and even to the possibility of localizing gravity. Unlike older theories ofextra dimensions, much of the focus now is on extra dimensions with sizes on the order of one thousandth of a proton width or larger! Thus, there is a potential for discovery at current and soon-to-be-completed colliders,and in some cases table-top experiments. In addition there are tremendous implications for cosmology.

Since Einstein forced physicists to think of time as a fourth dimensionthere have been speculations about a fifth and even higher dimensions. In order to avoid gross violations with experiment and even everyday experienceit was thought that any extra dimensions would have to be compact (like a circle or a sphere) and that their effects, if any, on present day experimentswould be unobservably small. There was the possibility that ordinary particles thatwe know are somehow restricted to a membrane with three spatial dimensions whichis embedded in a higher dimensional spacetime. This possibility was not taken veryseriously since it was not known how to realize this in a quantum field theory in arobust way. However recent developments in string theory show that such membranes arerequired for the consistency of string theory, and so they have acquired a new-foundrespectability and the nickname of branes. What is most exciting about this development is that when realistic models are built that incorporate such branesthere are often experimental signatures that can be seen at current and upcoming experiments.These signatures range from observing a change in the strength of gravity at sub-millimeter distances in table-top experimentsto the production of gravitons with momentum in an extra dimension at colliders. There are also important effects in cosmology which is about to undergo its own revolutiondue to an upcoming abundance of satellite data on the cosmic microwave background.
It is this potential for verification or elimination by experimental data thatis fueling the drive to understand the new possibilities of extra dimensions.

Background

Kaluza-Klein theories

Concrete proposals for the existence of extra dimensions date back to the 1920s, when Kaluzaand Klein attempted to unify gravity and electromagnetism in a five dimensional (5D) theory. If ahypothetical extra dimension were compact (a circle for example) then the propagation ofstandard model particles like the electron through this extra dimension would obviously havephysical consequences. However, if the size of the extra dimension was much smaller than thewavelength of the particles we were observing then the extra dimension could remain hidden.More specifically, with a compact extra dimension the momenta along this direction would bequantized, producing for each field a tower of momentum eigenstates (Kaluza-Klein modes) which wouldlook like massive excitations of the particle at the bottom of the tower which has no momentum in the extra dimension. Since we do not observe any such towers in nature, at least below a few hundred GeV inenergy, we can conclude that extra dimensions in which ordinary matter or gauge bosons can propagatemust have extremely small sizes (i.e. on the order of the inverse weak scale). On the theoreticalside, string theory actually requires extra dimensions, but their natural size, the Planck scale, is even smaller (1 followed by 15 zeroestimes smaller) than the direct experimental limit. Until quite recently it was thought that these arguments required extra dimensions to be irrelevantto long distance physics, however in the mid 1990s our understanding of string theory wasrevolutionized. Through the work of Polchinski and others it became clear that the consistency ofstring theory required the existence of new non-perturbative soliton-like objects called Dirichlet pbranes (Dp branes), which were generalizations of ordinary membranes with p spatial dimensions. Sincestrings could end on Dp branes with Dirichlet boundary conditions (hence the name) itsoon became clear that the low energy physics of N D3 branes was just an SU(N) gauge theory with N = 4 supersymmetry (SUSY)which was constrained to live in the four dimensional spacetime occupied by the D3branes.

Large extra dimensions

Very little time passed before phenomenologists used the idea of matter and gauge fields localized onbranes embedded in extra dimensions. Arkani-Hamed, Dimopoulos, and Dvali proposed thatthe standard model fields live on such a brane embedded in 2 to 6 extra dimensions. Sinceordinary particles did not propagate in the extra dimensions, the usual direct bounds did not apply,but since gravity cannot be restricted to the brane, gravitational effects provided thecrucial constraints. In this type of theory the observed Planck scale (1 followed by 18 zeroes times the proton mass) is only a low energy effectivecoupling that arises from integrating over the extra dimensions. With n extra dimensions the square of the Planck scale isrelated to the underlying gravitational scale (where gravity gets strong) to the 2+n power times the volume of the extra dimensions. At scales smaller than the size of the extradimensions, gravity can become much stronger, allowing for theradical possibility of identifyingthe scale where gravity gets strong with the weak scale (around 1000 times the proton mass). Somewhat surprising, with two extra dimensions the then-current gravitational bounds allowed the size of the extra dimensions to be as large as 1 mm with theunderlying gravitational scale (possibly the string scale!) to be at the weak scale. Refined table-top Cavendish experiments havealready been built and pushed the present direct experimental limit to 0.2 mm.Having three or more extradimensions allowed for a smaller extra-dimensional radius with same gravitational scale. Thus theproblem of explaining the huge hierarchy between Planck scale and the weak scaleis translated into the problem of explaining why the extra dimensions are stabilized at such largeradii relative to the weak scale.

Warped extra dimensions

The discussion so far assumes that the extra dimensions are flat or at least weakly curved, butanother startling possibility was suggested by Randall and Sundrum. They studied an extradimension that was strongly curved (or "warped") by a large negative cosmological constant.(This type of space is known in the literature as an anti-de Sitter (AdS) space, since de Sitter studieda universe with a positive cosmological constant.) They found models where the effective four dimensional (4D) cosmologicalconstant was zero, and where the massless 4D graviton mode was localized on a brane at oneend of the finite (or semi-infinite) extra dimension. Essentiallythe equation for the massless graviton mode is the precise analog of a Schrodinger equation with a binding potential.This provided a new way to make gravitymuch weaker than the weak interactions; if we happen to live on a brane where the graviton isnot localized, then its wavefunction on our brane can be exponentially suppressed. Again theproblem of understanding the hierarchy of Planck and weak scales is translated into understandingthe size of the extra dimension. The Randall-Sundrum (RS) scenario also has some motivation from string theory. A fewyears before Maldacena had proposed a correspondence between supergravity on AdSbackgrounds and conformal field theories (CFT). This AdS/CFT correspondence relatedsupergravity on AdS_5 x S^5 (AdS_5 is a 5 dimensional AdS space and S^5 is a 5 dimensional sphere that acts as a compactinternal space) to a 4D SU(N) gauge theory with N = 4 SUSY inthe large N limit. If one integrates out the KK modes of thesphere and truncates the "radial" direction of the AdS_5 space to a strip, this would yield a particular supersymmetric version of the RSscenario. In fact it is thought thatvariants of the Randall-Sundrum model correspond to some unknown, almost conformal, theoriescoupled to gravity. Subsequent work showed how to make precise calculations with the AdS/CFT correspondence (and its generalizations) which allows for many interesting predictions for4D gauge theories. For example using the correspondence between supergravity onblackhole AdS backgrounds and non-SUSY QCD, my collaborators and I calculated ratios ofglueball masses in three and four dimensions in a strong coupling, large N, limit ofQCD. Although the underlying theory is quite different from real QCD, we found that thesemass ratios are in good agreement with the available lattice data. One of the most remarkableaspects of this correspondence is that a non-perturbative quantum field theorycalculation is reduced to a simpleweakly coupled classical field theory problem. This means that the AdS/CFT correspondence maybe a useful calculational tool in the future for aspects of phenomenology that rely on non-perturbative dynamics (for example dynamical SUSY breaking).

Deconstruction

Recently another new tool for analyzing extra dimensions or reducing extra dimensionalmodels to relatively simple 4D models has been developed whichgoes by the name ``deconstruction". Essentially a 5D gauge theory is latticized in asequence of 4D gauge theories that are connected by link fields. The link fields connecttwo neighboring gauge groups by having gauge interactions under both groups. When the linkfield connecting N gauge groups get vacuum expectation values, the gauge groups break tothe diagonal group, leaving one massless gauge field and a tower of N-1 massivegauge fields. In the large N limit this tower reproduces the KK tower of a 5D gauge field belowthe energy scale associated with the lattice spacing.Since 5D gauge theories are not renormalizable, they must be equipped with a cutoff. Thedeconstruction (latticization) described above is the simplest way to introduce a gauge invariantcutoff and allow for reliable calculations. It also has the potential, by restrictingto a few lattice sites, to lead to new 4D theoriesthat mimic the low-energy behavior of a 5D theory. These 4D theories have more flexibilitythan 5D theories since they do not have to respect 5D Lorentz invariance, and thus theycan be further generalized to completely new 4D theories that can retain some of the moreinteresting qualities of 5D theories.

My recent research

Cosmology of extra dimensional theories

Cosmology offers particle physicists a method of testing models that is complementary to accelerator experiments. Particles that cannot be produced easily in accelerators can have drastic effects in the early universe. This can be seen in the new theories of gravity that involve sub-millimeter extra dimensions. My collaborators and I recently put severe constraints on a class of such theories. In these models, oscillations of the light field (the radion) that determines the size of the extra dimensions can over-close the universe. It had been proposed that a period of late inflation could solve this problem, however we found that the required inflaton scale is so low that it cannot successfully reheat the universe. We also found that in the 5D Randall-Sundrum scenario for solving the hierarchy problem, the extra dimensional gravity modes (in particular the radion)can make the universerapidly (on the scale of Planck times) unstable to collapse. We also showed that when the radion potential is stabilized (for exampleby a Goldberger-Wise mechanism) then a viable cosmology is possibleand as a result the radion has Higgs-like interactions. The radion istherefore potentially observable at the Tevatron and LHC.We also used string theory techniques (holographicrenormalization group) to analyze the model of Gregory, Rubakov, and Sibiryakov where gravity is four dimensional at intermediate distances, but five dimensional at long and short distance scales. In these models the massless 4D gravitonis quasi-localized, that is, it is localized but unstable with a very long lifetime (thespectrum of the analog Schrodinger problem is a continuum and a zero-energy resonance). The holographic renormalization grouptechnique enabled us to derive a low-energy effective theory that captured the long distancephysics (the physics below the renormalization scale). This enabled us to relate this model to a seemingly different (but equivalentat low energies) model proposed by Dvali, Gabadadze, and Porrati. Most importantly it allowed for a simple descriptionof the cosmology of a model with a quite complicated graviton propagator. Though such modelsturned out to be unstable, it is worthwhile trying to understand such extensions of gravityin light of the recent cosmological data favoring an accelerating universe.

Electroweak symmetry breaking

The Randall-Sundrum scenario for solving the hierarchy problem poses an interesting puzzle for electroweak symmetry breaking. It is widely believed that a morefundamental description of this scenario would involve a strongly-coupled, almost conformaltheory that breaks electroweak symmetry; but what could this theory be? In the 1980s andearly 1990s people considered the possibility that some strong (QCD-like) gauge dynamics(known as technicolor)does indeed perform such a breaking. I, among others , showed that the precisionelectroweak data on the S parameter essentially rules out the QCD-like technicolor scenario.In QCD-like theories it was possible to show that the contributions to S weregenerically large and had a positive sign, while experiment favors a small negative value forS.More recently Luty, Grant, and I considered whether or not some strongly-coupled SUSY gauge theories would be able to break electroweak symmetry without violating the experimental constraints. (This effort was quite distinct from previous attempts to combine SUSY and technicolor, since the realistic models all relied on non-SUSY dynamics to perform thesymmetry breaking.)Using Seiberg duality techniques we showed that a non-renormalization theorem holds for themodels we considered which forbids any contributions to the superpotential term which contributes to S, and that even afterSUSY breaking the contributions to S were so small as to be unobservable. However there are contributions to S from Kahler potential terms, which are of unknown sign. Theusual field theory dualities are not powerful enough to determine the sign of these contributions.After our paper appeared, Klebanov and Strassler showed thatthe large N limit of the models like the one we consideredcould be described (via a generalized AdS/CFT correspondence)by supergravity on a deformed conifold that asymptotically approaches AdS_5 with a compact internal space.The low-energy effective theory of this supergravity would be essentially a generalizedRS model.In principle one should be able to calculate the sign of S in the large N limit ofour models through a supergravity calculation in this generalized RS model.

GUT Breaking and extra dimensions

Most recently my collaborators and I realized that the Scherk-Schwarz mechanism ofsymmetry breaking could be applied not only to Grand UnifiedTheories in extra-dimensions but also tomodels with deconstructed extra dimensions. This led us to models with just a few gauge groups, which can easily solve the doublet-triplet splitting problem, suppress protondecay to the edge of detectability, and where gauge couplingunification could be reliably calculated without hard cutoffs. It also led to othermodels that shared these positive features but which could not be derived as a deconstructionof a 5D theory. These models also related the arrangement of lattice sitesto flavor physics: in particular, the hierarchies observed in the CKM matrix were related tothe number of lattice sites separating different generations.

Further Reading

1) T. Kaluza, Preus. Acad. Wiss. K1, 966 (1921) ;O. Klein, Z. Phys. 37, 895 (1926) .
2) The Hierarchy Problem and New Dimensions at a Millimeter,by N. Arkani-Hamed, S. Dimopoulos and G. Dvali,Phys. Lett. B429, 263 (1998) hep-ph/9803315
3) Weak Scale Superstrings,
by J. D. Lykken,Phys. Rev. D 54, 3693 (1996) hep-th/9603133
4) A Large Mass Hierarchy from a Small Extra Dimension,
by L. Randall and R. Sundrum,Phys. Rev. Lett. 83, 3370 (1999) hep-ph/9905221;
An Alternative to Compactification,by L. Randall and R. Sundrum,Phys. Rev. Lett. 83, 4690 (1999) hep-th/9906064
5)The shape of gravity,
by J. Lykken and L. Randall,JHEP 0006, 014 (2000) hep-th/9908076
6) The large N limit of superconformal field theories and supergravity,
by J. Maldacena,Adv. Theor. Math. Phys. 2, 231 (1998) hep-th/9711200
7)Gauge theory correlators from non-critical string theory,
by S. S. Gubser, I. R. Klebanov and A. M. Polyakov,Phys. Lett. B 428, 105 (1998) hep-th/9802109;
Anti-de Sitter space and holography,
by E. Witten,Adv. Theor. Math. Phys. 2, 253 (1998) hep-th/9802150
8) Glueball mass spectrum from supergravity,
by C. Csaki, H. Ooguri, Y. Oz and J. Terning,JHEP 9901, 017 (1999) hep-th/9806021;
Large N QCD from rotating branes,
by C. Csaki, Y. Oz, J. Russo and J. Terning,Phys. Rev. D 59, 065012 (1999) hep-th/9810186;
Supergravity models for 3+1 dimensional QCD,
by C. Csaki, J. Russo, K. Sfetsos and J. Terning,Phys. Rev. D 60, 044001 (1999) hep-th/9902067
9) (De) constructing dimensions,
by N. Arkani-Hamed, A. G. Cohen and H. Georgi,Phys. Rev. Lett. 86, 4757 (2001) hep-th/0104005;
Gauge invariant effective Lagrangian for Kaluza-Klein modes,
by C. T. Hill, S. Pokorski and J. Wang,Phys. Rev. D 64, 105005 (2001) hep-th/0104035
10) Late inflation and the moduli problem of sub-millimeter dimensions,
by C. Csaki, M. Graesser and J. Terning,Phys. Lett. B 456, 16 (1999) hep-ph/9903319
11) Cosmology of one extra dimension with localized gravity,
by C. Csaki, M. Graesser, C. Kolda and J. Terning,Phys. Lett. B 462, 34 (1999) hep-ph/9906513
12) Modulus stabilization with bulk fields,
by W. D. Goldberger and M. B. Wise,Phys. Rev. Lett. 83, 4922 (1999) hep-ph/9907447
13) Cosmology of brane models with radion stabilization,
by C. Csaki, M. Graesser, L. Randall and J. Terning,Phys. Rev. D 62, 045015 (2000) hep-ph/9911406
14) Holographic RG and cosmology in theories with quasi-localized gravity,
by C. Csaki, J. Erlich, T. J. Hollowood and J. Terning,Phys. Rev. D 63 (2001) 065019hep-th/0003076
15) Opening up extra dimensions at ultra-large scales,
by R. Gregory, V. A. Rubakov and S. M. Sibiryakov,Phys. Rev. Lett. 84, 5928 (2000) hep-th/0002072
16) 4D gravity on a brane in 5D Minkowski space,
by G. Dvali, G. Gabadadze and M. Porrati,Phys. Lett. B485, 208 (2000) hep-th/0005016
17) 4D models of Scherk-Schwarz GUT breaking via deconstruction,
by C. Csaki, G. D. Kribs and J. Terning,hep-ph/0107266
18) Radiative corrections to electroweak parameters in Technicolor theories,
by M. Golden and L. Randall,Nucl. Phys. B361, 3 (1991) ;
Large Corrections To Electroweak Parameters In Technicolor Theories,
by B. Holdom and J. Terning,Phys. Lett. B247, 88 (1990) ;
A new constraint on a strongly interacting Higgs sector,
by M. E. Peskin, T. Takeuchi, Phys. Rev. Lett. 65, 964 (1990) ;
Estimation of oblique electroweak corrections,
by M. E. Peskin, T. Takeuchi,Phys. Rev. D 46, 381 (1992).
19) Electroweak symmetry breaking by strong supersymmetric dynamics at the TeV scale,
by M. A. Luty, J. Terning and A. K. Grant,Phys. Rev. D 63, 075001 (2001) hep-ph/0006224
20) Supergravity and a confining gauge theory: Duality cascades and chiSB-resolution of naked singularities,
by I. R. Klebanov and M. J. Strassler,JHEP 0008, 052 (2000) hep-th/0007191
21) Locally localized gravity,
by A. Karch and L. Randall,JHEP 0105, 008 (2001) hep-th/0011156
22) Supergravity domain walls,
by M. Cvetic and H. H. Soleng,Phys. Rept. 282, 159 (1997) hep-th/9604090;
Supersymmetric domain wall world from D = 5 simple gauged supergravity,
by K. Behrndt and M. Cvetic,Phys. Lett. B 475, 253 (2000) hep-th/9909058

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Wormhole

A hypothetical "tunnel" connecting two different points in spacetime in such a way that a trip through the wormhole could take much less time than a journey between the same starting and ending points in normal space. The ends of a wormhole could, in theory, be intra-universe (i.e. both exist in the same universe) or inter-universe (exist in different universes, and thus serve as a connecting passage between the two).

Wormholes arise as solutions to the equations of Einstein's general theory of relativity. In fact, they crop up so readily in this context that some theorists are encouraged to think that real counterparts may eventually be found or fabricated and, perhaps, used for high-speed space travel and/or time travel. However, a known property of wormholes is that they are highly unstable and would probably collapse instantly if even the tiniest amount of matter, such as a single photon, attempted to pass through them. A possible way around this problem is the use of exotic matter to prevent the wormhole from pinching off.

A brief history of wormholes

The theory of wormholes goes back to 1916, shortly after Einstein published his general theory, when Ludwig Flamm, an obscure Austrian physicist, looked at the simplest possible solution of Einstein's field equations, known as the Schwarzschild solution (or Schwarzschild metric). This describes the gravitational field around a spherically-symmetric non-rotating mass. If the mass is sufficiently compact, the solution describes a particular form of the phenomenon now called a black hole – the Schwarzschild black hole. Flamm realized that Einstein's equations allowed a second solution, now known as a white hole, and that the two solutions, describing two different regions of (flat) spacetime were connected (mathematically) by a spacetime conduit.¹ Because the theory has nothing to say about where these regions of spacetime might be in the real world, the black hole "entrance" and white hole "exit" could be in different parts of the same universe or in entirely different universes.

In 1935, Einstein and Nathan Rosen further explored, it can be appreciated with hindsight, the theory of intra- or inter-universe connections in a paper² whose actual purpose was to try to explain fundamental particles, such as electrons, in terms of spacetime tunnels threaded by electric lines of force. Their work gave rise to the formal name Einstein-Rosen bridge for what the physicist John Wheeler would later call a "wormhole." (Wheeler also coined the terms "black hole" and "quantum foam".) Wheeler's 1955 paper³ discusses wormholes in terms of topological entities called geons and, incidentally, provides the first (now familiar) diagram of a wormhole as a tunnel connecting two openings in different regions of spacetime.

Traversable wormholes

Interest in so-called traversable wormholes gathered pace following the publication of a 1987 paper by Michael Morris, Kip Thorne, and Uri Yertsever (MTY) at the California Institute of Technology.^{4, 5} This paper stemmed from an inquiry to Thorne by Carl Sagan who was mulling over a way of conveying the heroine in his novel Contact across interstellar distances at trans-light speed. Thorne gave the problem to his Ph.D. students, Michael Morris and Uri Yertsever, who realized that such a journey might be possible if a wormhole could be held open long enough for a spacecraft (or any other object) to pass through. MTY concluded that to keep a wormhole open would require matter with a negative energy density and a large negative pressure – larger in magnitude than the energy density. Such hypothetical matter is called exotic matter.

Although the existence of exotic matter is speculative, a way is known of producing negative energy density: the Casimir effect. As a source for their wormhole, MTY turned to the quantum vacuum. "Empty space" at the smallest scale, it turns out, is not empty at all but seething with violent fluctuations in the very geometry of spacetime. At this level of nature, ultra-small wormholes are believed to continuously wink into and out of existence. MTY suggested that a sufficiently advanced civilization could expand one of these tiny wormholes to macroscopic size by adding energy. Then the wormhole could be stabilized using the Casimir effect by placing two charged superconducting spheres in the wormhole mouths. Finally, the mouths could be transported to widely-separated regions of space to provide a means of FTL communication and travel. For example, a mouth placed aboard a spaceship might be carried to some location many light-years away. Because this initial trip would be through normal spacetime, it would have to take place at sublight speeds. But during the trip and afterwards instantaneous communication and transport through the wormhole would be possible. The ship could even be supplied with fuel and provisions through the mouth it was carrying. Also, thanks to relativistic time-dilation, the journey need not take long, even as measured by Earth-based observers. For example, if a fast starship carrying a wormhole mouth were to travel to Vega, 25 light-years away, at 99.995% of the speed of light (giving a time-dilation factor of 100), shipboard clocks would measure the journey as taking just three months. But the wormhole stretching from the ship to Earth directly links the space and time between both mouths – the one on the ship and the one left behind on (or near) Earth. Therefore, as measured by Earthbound clocks too, the trip would have taken only three months – three months to establish a more-or-less instantaneous transport and communications link between here and Vega.

Star Trek's Deep Space 9 is located alongside a natural wormhole that leads to the other side of the Galaxy

Of course, the MTY scheme is not without technical difficulties, one of which is that the incredibly powerful forces needed to hold the wormhole mouths open might tear apart anything or anyone that tried to pass through. In an effort to design a more benign environment for travelers using a wormhole, Matt Visser of Washington University in St. Louis conceived an arrangement in which the spacetime region of a wormhole mouth is flat (and thus force-free) but framed by struts of exotic matter that contain a region of very sharp curvature.⁶ Visser envisages a cubic design, with flat-space wormhole connections on the square sides and cosmic strings as the edges. Each cube-face may connect to the face of another wormhole-mouth cube, or the six cube faces may connect to six different cube faces in six separated locations.

In 2011, Panagiota Kanti (University of Ioannina) and Burkhard Kleihaus (Universität Oldenburg) showed how it might be possible to construct traversable wormholes without using exotic matter by resorting to a form of string theory.¹⁰

Given that our technology is not yet up to the task of building a wormhole subway, the question arises of whether they might already exist. One possibility is that advanced races elsewhere in the Galaxy or beyond have already set up a network of wormholes that we could learn to use. Another is that wormholes might occur naturally. David Hochberg and Thomas Kephart of Vandebilt University have discovered that, in the earliest moments of the Universe, gravity itself may have given rise to regions of negative energy in which natural, self-stabilizing wormholes may have formed. Such wormholes, created in the Big Bang, might be around today, spanning small or vast distances in space.

References

1. Flamm, L. "Comments on Einstein's theory of gravity," Physikalische Zeitschrift, 17, 48 (1916).
2. Einstein, A., and Rosen, N. "The Particle Problem in the General Theory of Relativity", Physical Review, 48, 73 (1935)
3. Wheeler, J. A. "Geons," Physical Review, 97, 511–536 (1955).
4. Morris, M. S, Thorne, K. S., and Yurtsever, U. "Wormholes, time machines, and the weak energy condition," Phys. Rev. Letters, 61, 1446–1449 (1988).
5. Morris, M. S., and Thorne, K. S. "Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity", Am. J. Phys., 56, No. 5, 395–412 (1988).
6. Visser, M. "Wormholes, baby universes, and causality", Phys. Rev. D, 41, No. 4, 1116–1124 (1990).
7. Hochberg, D. and Visser, M. "Geometric structure of the generic static traversable wormhole throat", Phys. Rev. D, Phys. Rev D56, 4745 (1997).
8. Maccone, C. "Interstellar travel through magnetic wormholes", Journal of the British Interplanetary Society, 48, No. 11, 453–458 (1995).
9. Visser, M. (1995) Lorentzian Wormholes – From Einstein to Hawking, Woodbury, NY: AIP Press (1995).
10. Kantio, P. and Kleihaus, B., "Wormholes in dilatonic Einstein-Gauss-Bonnet theory." arXiv (2011).

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Active Galaxies and Quasars

Active galaxies are galaxies which have a small core of emission embedded in an otherwise typical galaxy. This core may be highly variable and very bright compared to the rest of the galaxy. Models of active galaxies concentrate on the possibility of a supermassive black hole which lies at the center of the galaxy. The dense central galaxy provides material which accretes onto the black hole releasing a large amount of gravitational energy. Part of the energy in this hot plasma is emitted as x-rays and gamma rays.
For "normal" galaxies, we can think of the total energy they emitas the sum of the emission from each of the stars found in the galaxy. Forthe "active" galaxies, this is not true. There is a great deal moreemitted energy than there should be... and this excess energy is found in theinfrared, radio, UV, and X-ray regions of the electromagnetic spectrum. Theenergy emitted by an active galaxy (or AGN) is anything but "normal". So what is happening in these galaxies to produce such an energetic output?
There are several types of active galaxies: Seyferts, quasars, andblazars. Most scientistsbelieve that, even though these types look very different to us, they arereally all the same thing viewed from different directions! Quasars are activegalaxies which are all very, very, very far away from us. Some of the quasarswe have seen so far are 12 billion light-years away! Blazars are verybright in the radio band, which results from looking directly down ajet which is emitting in synchrotron radiation. On the other hand, if the jet is not pointing toward youat all, and the dusty disk of material which lies in the plane of thegalaxy is in the way, you would see justwhat we see from the Seyferts. By measuring their redshifts, we findthat Seyferts are much closer to us thanquasars or blazars.
Active galaxies are intensely studied at all wavelengths. Since theycan change their behavior on short timescales, it is useful to studythem simultaneously at all energies. X-ray and gamma-ray observations haveproven to be important parts of this multiwavelength approach since manyhigh-energy quasars emit a large fraction of their power at such energies. X-rays can penetrate outward from very nearthe center of a galaxy. Since that is where the "engines" of AGN arelocated, X-rays provide scientists with unique insights into the physicalprocesses occurring there. In addition, gamma-ray observations alone canprovide valuable information on the nature of particle acceleration in thequasar jet, and clues as to how the particles interact with theirsurroundings.

A diagram of an active galaxy, showingthe primary components.

Seyfert Galaxies

Of the two types of Active Galactic Nuclei (AGN) which emit gamma rays, Seyfert galaxies are the low-energy gamma-ray sources. Seyfert galaxies typically emit most of their gamma rays up to energies of about100 keV and then fade as we observe them at higher energies. Early gamma-ray observations of Seyfert galaxies indicated that photons were detected up to MeV energies, but more sensitive observations have cast doubt on this possibility. At these low gamma-ray energies, the emission is usually a smooth continuation of the X-ray emission from such objects. This generally indicates that the physical processes creating the gamma rays are thermal processes similar to thoseresponsible for emission from galactic black hole sources. As a result, gamma-ray studies of the high-energy spectrum and variability can give scientists important information about the physical environment in the AGN.
Observations of Seyfert galaxies in gamma rays are also important for studies of the cosmic gamma-ray background. Even in regions of the sky wherethere are no point sources, a faint gamma-ray glow is detectable. It may be that this glow is the sum of many faint galaxies or perhaps a more exotic process. Studies of individual Seyfert galaxies can be combined with a model of how such objects are distributed in the Universe to compare to the diffuse gamma-ray background. In this way, astronomers not only learn about the interesting AGN phenomena, but learn more about the general nature of the Universe as a whole.

An artists concept of an active galactic nucleus

Quasars

One of the most remarkable trends in gamma-ray astronomy in recentyears has been the emergence of high-energy gamma-ray quasars as an important component of the gamma-ray sky. At gamma-ray energies, these active galaxies are bright; they are highly variable at all energies. Unlike the Seyfert type AGN, most of these sources arepreferentially detected at high energies, usually 100 MeV or more. In fact, they have been detected above 1 GeV, and some up to several TeV! Given the large distances to these objects and the strong emission of high-energy gamma rays, these are the most powerful particle accelerators in the Universe. Over 50 high-energy quasars are known at this time.Some appear as fuzzy stars that can be seen with large amateur telescopes. Many astronomers believe that Seyfert galaxies and high-energyquasars are basically the same type of objects, but we are simply viewingthem differently. Radio observations of AGN often show powerful jets, streamsof particles coming from the central source -- like water from a spigot.Charged particles are accelerated to nearly the speed of light in these jets. In the unified view of active galaxies,high-energy quasars are being viewed with the jet pointed towards uswhich allows us to see the resulting energetic radiation. With Seyfert galaxies, we are viewing from the side and do not see the very high-energyradiation which is traveling down the jet.

The region of the sky containing one of the high-energy quasars, PKS 0528+134, is shown at two different times using the EGRET instrument on the Compton Gamma-Ray Observatory. These active galaxies are highly variable, strongly emitting gamma-rays sometimes, disappearing at other times.

Blazars

The AGNs observed at higher energies form a subclass of AGNs known as blazars; a blazar is believed to be an AGN which has one of its relativistic jets pointed toward the Earth so that what we observe is primarily emission from the jet region. They arethus similar to quasars, but are not observed to be as luminous. The visible and gamma-ray emission from blazars is variable on timescales from minutes to days. Although theories exist as to thecauses of this variability, the sparse data do not yet allow any of theideas to be tested.To date more than 60 blazars have been detected by the EGRET experimentaboard the Compton Gamma-Ray Observatory. All these objects appear toemit most of their bolometricluminosity at gamma-ray energies and, inaddition, are strong extragalactic radio sources.

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Newton's three law of motion: Animated

According to Newton's first law...

An object at rest will remain at rest unless acted on by an unbalanced force.An object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force.This law is often called "the law of inertia".

What does this mean?This means that there is a natural tendency of objects to keep on doing what they're doing. All objects resist changes in their state of motion. In the absence of an unbalanced force, an object in motion will maintain this state of motion.

Let's study the "skater" to understand this a little better.
What is the motion in this picture?

What is the unbalanced force in this picture?

What happened to the skater in this picture?



This law is the same reason why you should always wear your seatbelt.




Now that you understand
Newton's First Law of Motion,
let's go on to his Second Law of Motion.    

According to Newton's second law...

Acceleration is produced when a force acts on a mass. The greater the mass (of the object being accelerated) the greater the amount of force needed (to accelerate the object).

What does this mean?Everyone unconsiously knows the Second Law. Everyone knows that heavier objects require more force to move the same distance as lighter objects.



However, the Second Law gives us an exact relationship between force,mass, and acceleration. It can be expressed as a mathematical equation:

or
FORCE = MASS times ACCELERATION



This is an example of how Newton's Second Law works:
Mike's car, which weighs 1,000 kg, is out of gas. Mike is trying to push the car to a gas station, and he makes the car go 0.05 m/s/s. Using Newton's Second Law, you can compute how much force Mike is applying to the car.


Answer = 50 newtons


This is easy, let's go on to
Newton's Third Law of Motion

  

According to Newton's third law...

For every action there is an equal and opposite re-action.

What does this mean?

This means that for every force there is a reaction force that is equal in size, but opposite in direction. That is to say that whenever an object pushes another object it gets pushed back in the opposite direction equally hard.



Let's study how a rocket works to understand
Newton's Third Law.

The rocket's action is to push down on the ground with the force of its powerful engines,and the reaction is that the ground pushes the rocket upwards with an equal force.

UP, UP, and AWAY!

You have just learned about
Newton's Three Laws of Motion.

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Newton's Three Laws of Motion

For Animated version See Newton's three law of motion: Animated



Let us begin our explanation of how Newton changed our understanding of the Universe by enumerating his Three Lawsof Motion.

Newton's First Law of Motion:

I. Every object in a state of uniform motion tends to remain in thatstate of motion unless an external force is applied to it.

This we recognize as essentially Galileo's concept of inertia, and this is oftentermed simply the "Law of Inertia".

Newton's Second Law of Motion:

II. The relationship between an object's mass m, its accelerationa, and the applied force F isF = ma.Acceleration and force are vectors (as indicated by their symbols beingdisplayed in slant bold font); in this law the direction of the forcevector is the same as the direction of the acceleration vector.

This is the most powerful of Newton's three Laws, because it allows quantitativecalculations of dynamics: how do velocities change when forces are applied.Notice the fundamental difference between Newton's 2nd Law and the dynamics ofAristotle: according to Newton, a force causes only a change invelocity (an acceleration); it does not maintain the velocity as Aristotleheld.
This is sometimes summarized by saying that under Newton, F =ma, but under Aristotle F = mv, where v is the velocity.Thus, according to Aristotle there is only a velocity if there is a force, butaccording to Newton an object with a certain velocity maintains thatvelocity unless a force acts on it to cause an acceleration (that is,a change in the velocity). As we have noted earlier in conjunction with thediscussion of Galileo, Aristotle's view seems to bemore in accord with common sense, but that is because of a failure toappreciate the role played by frictional forces. Once account is taken of all forcesacting in a given situation it is the dynamics of Galileo and Newton, not of Aristotle, that arefound to be in accord with the observations.

Newton's Third Law of Motion:

III. For every action there is an equal and opposite reaction.

This law is exemplified by what happens if we step off a boat onto the bank ofa lake: as we move in the direction of the shore, the boat tends to move inthe opposite direction (leaving us facedown in the water, if we aren'tcareful!).

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