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[sci.astro] Astrophysics (Astronomy Frequently Asked Questions) (4/9)

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Subject: Introduction sci.astro is a newsgroup devoted to the discussion of the science of astronomy. As such its content ranges from the Earth to the farthest reaches of the Universe. However, certain questions tend to appear fairly regularly. This document attempts to summarize answers to these questions. This document is posted on the first and third Wednesdays of each month to the newsgroup sci.astro. It is available via anonymous ftp from <URL:>, and it is on the World Wide Web at <URL:> and <URL:>. A partial list of worldwide mirrors (both ftp and Web) is maintained at <URL:>. (As a general note, many other FAQs are also available from <URL:>.) Questions/comments/flames should be directed to the FAQ maintainer, Joseph Lazio (
Subject: D.00 Astrophysics [Dates in brackets are last edit.] D.01 Do neutrinos have rest mass? What if they do? [2002-05-04] D.02 Have physical constants changed with time? [1997-02-04] D.03 What is gravity? [1998-11-04] D.04 Does gravity travel at the speed of light? [1998-05-06] D.05 What are gravitational waves? [1997-06-10] D.06 Can gravitational waves be detected? [2000-08-31] D.07 Do gravitational waves travel at the speed of light? [1996-07-03] D.08 Why can't light escape from a black hole? [1995-10-05] D.09 How can gravity escape from a black hole? [1996-01-24] D.10 What are tachyons? Are they real? [1995-10-02] D.11 What are magnetic monopoles? Are they real? [1996-07-03] D.12 What is the temperature in space? [1998-04-14] D.13 Saturn's rings, proto-planetary disks, accretion disks---Why are disks so common? [1999-07-18] [Interesting note: The Astrophysical Journal was founded in 1895 by George Hale and James Keeler. Professor Edward Wright points out that these men would not have understood most of these questions---let alone have known any of the answers.]
Subject: D.01 Do neutrinos have rest mass? What if they do? Author: Joseph Lazio <> First, it is worth remembering what a neutrino is. During early studies of radioactivity it was discovered that a neutron could decay. The decay products appeared to be just a proton and electron. However, if these are the only decay products, an ugly problem rears its head. If one considers a neutron at rest, it has a certain amount of energy. (Its mass is equivalent to a rest energy because of E = mc^2.) If one then sums the energies of the decay products---the masses of the electron and proton and their kinetic energy---it never equals that of the rest energy of a neutron. Thus, one has two choices, either energy is not conserved or there is a third decay product. Wolfgang Pauli was uncomfortable with abandoning the principle of energy conservation so he proposed, in 1930, that there was a third particle (which Enrico Fermi called the "little neutral one" or neutrino) produced in the decay of a neutron. It has to be neutral, i.e., carry no charge or have charge 0, because a neutron is neutral whereas an electron has charge -1 and a proton has a charge +1. In 1956 Pauli and Fermi were vindicated when a neutrino was detected directly by Reines & Cowan. (For his experimental work, Reines received the 1995 Nobel Prize in Physics.) The long gap between the Pauli's proposal and the neutrino's discovery is due to the way that a neutrino interacts. Unlike the electron and protron that can interact via the electromagnetic force, the neutrino interacts only via the weak force. (The electron can also interact via the weak force.) As its name suggests, weak force interactions are weak. A neutrino can pass through our planet without a problem. Indeed, as you read this, billions of neutrinos are passing through your body. As one might imagine, building an experimental appartus to detect neutrinos is challenging. Since 1956, additional kinds of neutrinos have been discovered. The electron has more massive counterparts, the muon and tau lepton. Each of these has an associated neutrino. Thus there is an electron neutrino, mu neutrino, and tau neutrino. (In addition, each has an anti-particle as well, so there is an electron anti-neutrino, mu anti-neutrino, and tau anti-neutrino. Furthermore, it was realized that in order to get the equations to balance, the decay of a neutron actually produces an electron, a protron, and electron anti-neutrino.) Early work assumed that the neutrino had no mass and experiments revealed quickly that, if the electron neutrino and anti-neutrino have any mass, it must be quite small. In the 1960s Raymond Davis, Jr., realized that the Sun should be a copious source of neutrinos, *if* it shines by nuclear fusion. Various fusion reactions that are thought to be important in producing energy in the core of the Sun produce neutrinos as a by-product. In a now-famous experiment at the Homestake Mine, he set out to detect some of these solar neutrinos. John Bahcall has collaborated with Davis to write a history of this experiment at <URL:>. Although quite difficult, in a few years, it became evident that there was a discrepancy. The number of neutrinos detected at Homestake was far lower than what models of the Sun predicted. Moreover, as new experiments came online in the late 1980s and early 1990s, the problem became even more severe. Not only was the number of neutrinos lower than expected, their energies were not what was predicted. There are three ways to resolve this problem. (1) Our models of the Sun are wrong. In particular, if the temperature of the Sun's core is just slightly lower than predicted that reduces the fusion reaction rates and therefore the number of neutrinos that should be detected at the Earth. (2) Our understanding of neutrinos is incomplete and, namely, the neutrino has mass. (3) Both. Astronomers were uncomfortable with explanation (1). The fusion reaction rate in the Sun's core is *quite* sensitive to its temperature. Adopting explanation (1) seemed to require some elaborate "fine-tuning" of the model. (Observations of the Sun in the 1990s have supported this initial reluctance of astronomers. Using helioseismology, <URL:>, astronomers have a second way of probing beneath the Sun's surface, and it does appear that the temperature of the Sun's core is just about what our best models predict.) In contrast explanation (2) seemed reasonable. After all, just detecting neutrinos was challenging. The possibility that they might have mass was not unreasonable. In the 1970s Vera Rubin and her collaborators were also demonstrating that spiral galaxies appeared to have a lot of unseen matter in them. If neutrinos has mass, one might be able to solve two problems at once, both matching the solar neutrino observations and accounting for some of the "missing matter" or dark matter. Explanation (2) is the following. Suppose the neutrino has mass. Then the neutrinos we observe, the electron neutrino, mu neutrino, and tau neutrino, might not be the "true" neutrinos. The true neutrinos, call them nu1, nu2, and nu3, would combine in various ways to produce the observed neutrinos. Moreover, various properties of quantum mechanics would allow the observed neutrinos to "oscillate" between the various flavors. Thus, an electron neutrino could be produced in the core of the Sun but oscillate to become a mu neutrino by the time it reached the Earth. Because the early experiments detected only electron neutrinos, if the electron neutrinos were changing to a different kind of neutrino, the apparent discrepancy would be resolved. This explanation is known as the MSW effect after the three physicists Mikheyev, Smirnov, and Wolfenstein who proposed it first. The second explanation now appears correct. Various terrestrial experiments, such as the Sudbury Neutrino Observatory (SNO), the Super-Kamiokande Observatory, the Liquid Scintillator Neutrino Detector (LSND) experiment, and Main Injector Neutrino Oscillation Search (MINOS), appear to be detecting neutrino oscillations directly. The mass required to explain neutrino oscillations is quite small. The mass is sufficiently small that all of the neutrinos in the Universe are unlikely to make a substantial contribution to the density of the Universe. However, it does appear to be sufficient to resolve the solar neutrino problem. Additional information on neutrinos is at <URL:>.
Subject: D.02 Have physical constants changed with time? Author: Steve Carlip <> The fundamental laws of physics, as we presently understand them, depend on about 25 parameters, such as Planck's constant h, the gravitational constant G, and the mass and charge of the electron. It is natural to ask whether these parameters are really constants, or whether they vary in space or time. Interest in this question was spurred by Dirac's large number hypothesis. The "large number" in question is the ratio of the electric and the gravitational force between two electrons, which is about 10^40; there is no obvious explanation of why such a huge number should appear in physics. Dirac pointed out that this number is nearly the same as the age of the Universe in atomic units, and suggested in 1937 that this coincidence could be understood if fundamental constants---in particular, G---varied as the Universe aged. The ratio of electromagnetic and gravitational interactions would then be large simply because the Universe is old. Such a variation lies outside ordinary general relativity, but can be incorporated by a fairly simple modification of the theory. Other models, including the Brans-Dicke theory of gravity and some versions of superstring theory, also predict physical "constants" that vary. Over the past few decades, there have been extensive searches for evidence of variation of fundamental "constants." Among the methods used have been astrophysical observations of the spectra of distant stars, searches for variations of planetary radii and moments of inertia, investigations of orbital evolution, searches for anomalous luminosities of faint stars, studies of abundance ratios of radioactive nuclides, and (for current variations) direct laboratory measurements. One powerful approach has been to study the "Oklo Phenomenon," a uranium deposit in Gabon that became a natural nuclear reactor about 1.8 billion years ago; the isotopic composition of fission products has permitted a detailed investigation of possible changes in nuclear interactions. Another has been to examine ratios of spectral lines of distant quasars coming from different types of atomic transitions (resonant, fine structure, and hyperfine). The resulting frequencies have different dependences on the electron charge and mass, the speed of light, and Planck's constant, and can be used to compare these parameters to their present values on Earth. Solar eclipses provide another sensitive test of variations of the gravitational constant. If G had varied, the eclipse track would have been different from the one we calculate today, so the mere fact that a total eclipse occurred at a particular location provides a powerful constraint, even if the date is poorly known. So far, these investigations have found no evidence of variation of fundamental "constants." The current observational limits for most constants are on the order of one part in 10^10 to one part in 10^11 per year. So to the best of our current ability to observe, the fundamental constants really are constant. References: For a good short introduction to the large number hypothesis and the constancy of G, see: C.M. Will, _Was Einstein Right?_ (Basic Books, 1986) For more technical analyses of a variety of measurements, see: L. L. Cowie & A. Songaila, Astrophysical Journal (1995) v. 453, p. 596 also available online at <URL:> P. Sisterna & H. Vucetich, Physical Review D41 (1990) 1034 and Physical Review D44 (1991) 3096 E.R. Cohen, in _Gravitational Measurements, Fundamental Metrology and Constants_, V. De Sabbata & V.N. Melnikov, editors (Kluwer Academic Publishers, 1988) "The Constants of Physics," Philosophical Transactions of the Royal Society of London A310 (1983) 209--363
Subject: D.03 What is gravity? Author: Steve Carlip <> Hundreds of years of observation have established the existence of a universal attraction between physical objects. In 1687, Isaac Newton quantified this phenomenon in his law of gravity, which states that every object in the Universe attracts every other object, with a force between any two bodies that is proportional to the product of their masses and inversely proportional to the square of the distance between them. If M and m are the two masses, r is the distance, and G is the gravitational constant, we can write: F = GMm/r^2 . The gravitational constant G can be measured in the laboratory and has a value of approximately 6.67x10^{-11} m^3/kg sec^2. Newton's law of gravity was one of the first great "unifications" of physics, explaining both the force we experience on Earth (the fall of the proverbial apple) and the force that causes the planets to orbit the Sun with a single, simple rule. Gravity is actually an extremely weak force. The electrical repulsion between two electrons, for example, is some 10^40 times stronger than their gravitational attraction. Nevertheless, gravity is the dominant force on the large scales of interest in astronomy. There are two reasons for this. First, gravity is a "long range" force---the strong nuclear interactions, for instance, fall off with distance much faster than gravity's inverse square law. Second, gravity is additive. Planets and stars are very nearly electrically neutral, so the forces exerted by positive and negative charges tend to cancel out. As far as we know, however, there is no such thing as negative mass, and no such cancellation of gravitational attraction. (Gravity may sometimes feel strong, but remember that you have the entire 6x10^24 kg of the Earth pulling on you.) For most purposes, Newton's law of gravity is extremely accurate. Newtonian theory has important limits, though, both observational (small anomalies in Mercury's orbit, for example) and theoretical (incompatibility with the special theory of relativity). These limits led Einstein to propose a revised theory of gravity, the general theory of relativity ("GR" for short), which states (roughly) that gravity is a consequence of the curvature of spacetime. Einstein's starting point was the principle of equivalence, the observation that any two objects in the same gravitational field that start with the same initial velocities will follow exactly the same path, regardless of their mass and internal composition. This means that a theory of gravity is really a theory of paths (strictly speaking, paths in spacetime), which picks out a "preferred" path between any two points in space and time. Such a description sounds vaguely like geometry, and Einstein proposed that it *was* geometry---that a body acting under the influence of gravity moves in the "straightest possible line" in a curved spacetime. As an analogy, imagine two ships starting at different points on the equator and sailing due north. Although the ships do not steer towards each other, they will find themselves drawn together, as if a mysterious force were pulling them towards each other, until they eventually meet at the North Pole. We know why, of course---the "straightest possible lines" on the curved surface of the Earth are great circles, which converge. According to general relativity, objects in gravitational fields similarly move in the "straightest possible lines" (technically, "geodesics") in a curved spacetime, whose curvature is in turn determined by the presence of mass or energy. In John Wheeler's words, "Spacetime tells matter how to move; matter tells spacetime how to curve." Despite their very different conceptual starting points, Newtonian gravity and general relativity give nearly identical predictions. In the few cases that they differ measurably, observations support GR. The three "classical tests" of GR are anomalies in the orbits of the inner planets (particularly Mercury), bending of light rays in the Sun's gravitational field, and the gravitational red shift of spectral lines. In the past few years, more tests have been added, including the gravitational time delay of radar and the observed motion of binary pulsar systems. Further tests planned for the future include the construction of gravitational wave observatories (see D.05) and the planned launch of Gravity Probe B, a satellite that will use sensitive gyroscopes to search for "frame dragging," a relativistic effect in which the Earth "drags" the surrounding space along with it as it rotates. References: For introductions to general relativity, try: K.S. Thorne, _Black Holes and Time Warps_ (W.W. Norton, 1994) R.M. Wald, _Space, Time, and Gravity_ (Univ. of Chicago Press, 1977) J.A. Wheeler, _A Journey into Gravity and Spacetime_ (Scientific American Library, 1990) For experimental evidence, see: C.M. Will, _Was Einstein Right?_ (Basic Books, 1986) or, for a more technical source, C.M. Will, _Theory and Experiment in Gravitational Physics, revised edition (Cambridge Univ. Press, 1993) You can find out about Gravity Probe B at <URL:> and <URL:>.
Subject: D.04 Does gravity travel at the speed of light? Author: Steve Carlip <>, Matthew P Wiener <> Geoffrey A Landis <> To begin with, the speed of gravity has not been measured directly in the laboratory---the gravitational interaction is too weak, and such an experiment is beyond present technological capabilities. The "speed of gravity" must therefore be deduced from astronomical observations, and the answer depends on what model of gravity one uses to describe those observations. In the simple Newtonian model, gravity propagates instantaneously: the force exerted by a massive object points directly toward that object's present position. For example, even though the Sun is 500 light seconds from the Earth, Newtonian gravity describes a force on Earth directed towards the Sun's position "now," not its position 500 seconds ago. Putting a "light travel delay" (technically called "retardation") into Newtonian gravity would make orbits unstable, leading to predictions that clearly contradict Solar System observations. In general relativity, on the other hand, gravity propagates at the speed of light; that is, the motion of a massive object creates a distortion in the curvature of spacetime that moves outward at light speed. This might seem to contradict the Solar System observations described above, but remember that general relativity is conceptually very different from Newtonian gravity, so a direct comparison is not so simple. Strictly speaking, gravity is not a "force" in general relativity, and a description in terms of speed and direction can be tricky. For weak fields, though, one can describe the theory in a sort of Newtonian language. In that case, one finds that the "force" in GR is not quite central---it does not point directly towards the source of the gravitational field---and that it depends on velocity as well as position. The net result is that the effect of propagation delay is almost exactly cancelled, and general relativity very nearly reproduces the Newtonian result. This cancellation may seem less strange if one notes that a similar effect occurs in electromagnetism. If a charged particle is moving at a constant velocity, it exerts a force that points toward its present position, not its retarded position, even though electromagnetic interactions certainly move at the speed of light. Here, as in general relativity, subtleties in the nature of the interaction "conspire" to disguise the effect of propagation delay. It should be emphasized that in both electromagnetism and general relativity, this effect is not put in _ad hoc_ but comes out of the equations. Also, the cancellation is nearly exact only for *constant* velocities. If a charged particle or a gravitating mass suddenly accelerates, the *change* in the electric or gravitational field propagates outward at the speed of light. Since this point can be confusing, it's worth exploring a little further, in a slightly more technical manner. Consider two bodies---call them A and B---held in orbit by either electrical or gravitational attraction. As long as the force on A points directly towards B and vice versa, a stable orbit is possible. If the force on A points instead towards the retarded (propagation-time-delayed) position of B, on the other hand, the effect is to add a new component of force in the direction of A's motion, causing instability of the orbit. This instability, in turn, leads to a change in the mechanical angular momentum of the A-B system. But *total* angular momentum is conserved, so this change can only occur if some of the angular momentum of the A-B system is carried away by electromagnetic or gravitational radiation. Now, in electrodynamics, a charge moving at a constant velocity does not radiate. (Technically, the lowest order radiation is dipole radiation, which depends on the acceleration.) So to the extent that that A's motion can be approximated as motion at a constant velocity, A cannot lose angular momentum. For the theory to be consistent, there *must* therefore be compensating terms that partially cancel the instability of the orbit caused by retardation. This is exactly what happens; a calculation shows that the force on A points not towards B's retarded position, but towards B's "linearly extrapolated" retarded position. Similarly, in general relativity, a mass moving at a constant acceleration does not radiate (the lowest order radiation is quadrupole), so for consistency, an even more complete cancellation of the effect of retardation must occur. This is exactly what one finds when one solves the equations of motion in general relativity. While current observations do not yet provide a direct model-independent measurement of the speed of gravity, a test within the framework of general relativity can be made by observing the binary pulsar PSR 1913+16. The orbit of this binary system is gradually decaying, and this behavior is attributed to the loss of energy due to escaping gravitational radiation. But in any field theory, radiation is intimately related to the finite velocity of field propagation, and the orbital changes due to gravitational radiation can equivalently be viewed as damping caused by the finite propagation speed. (In the discussion above, this damping represents a failure of the "retardation" and "non-central, velocity-dependent" effects to completely cancel.) The rate of this damping can be computed, and one finds that it depends sensitively on the speed of gravity. The fact that gravitational damping is measured at all is a strong indication that the propagation speed of gravity is not infinite. If the calculational framework of general relativity is accepted, the damping can be used to calculate the speed, and the actual measurement confirms that the speed of gravity is equal to the speed of light to within 1%. (Measurements of at least one other binary pulsar system, PSR B1534+12, confirm this result, although so far with less precision.) Are there future prospects for a direct measurement of the speed of gravity? One possibility would involve detection of gravitational waves from a supernova. The detection of gravitational radiation in the same time frame as a neutrino burst, followed by a later visual identification of a supernova, would be considered strong experimental evidence for the speed of gravity being equal to the speed of light. However, unless a very nearby supernova occurs soon, it will be some time before gravitational wave detectors are expected to be sensitive enough to perform such a test. References: There seems to be no nontechnical reference on this subject. For a technical reference, see T. Damour, in _Three Hundred Years of Gravitation_, S.W. Hawking and W. Israel, editors (Cambridge Univ. Press, 1987) For a good reference to the electromagnetic case, see R.P. Feynman, R.B. Leighton, and M. Sands, _The Feynman Lectures on Physics_, chapter II-21 (Addison-Wesley, 1989)
Subject: D.05 What are gravitational waves? Author: Bradford Holden <> General Relativity has a set of equations that give results for how a lump of mass-energy changes the space-time around it. (See D.03.) One of the solutions to these equations is the infamous black hole, another solution is the results used in modern cosmology, and the third common solution is one that leads to gravitational waves. Over a hundred years ago Maxwell realized that a solution to the equations governing electricity and magnetism would create waves. These waves move at the same speed that light does, and, hence, he realized that light is an electro-magnetic wave. In general, electromagnetic waves are created whenever a charge is accelerated, that is, whenever its velocity changes. Gravitational waves are analogous. However, instead of being disturbances in electric and magnetic fields, they are disturbances in spacetime. As such, they affect things like the distance between two points or the amount of time perceived to pass by an observer. Moreover, since there is no "negative mass," and momentum is conserved, any acceleration of mass is balanced by an equal and opposite change of momentum of some other mass. This implies that the lowest order gravitational wave is quadrupole, and gravitational waves are produced when an acceleration changes. Because gravitational waves are waves, they should exhibit many other properties of waves. For example, gravitational waves can, in principle, be scattered or exhibit a redshift. (But see the next question on the difficulty of testing this prediction.) [Note, *gravitational* waves...gravity waves are something else entirely (they occur in a medium when gravity is the restoring force) and are commonly seen in the atmosphere and oceans.]
Subject: D.06 Can gravitational waves be detected? Author: Bradford Holden <>, Steve Willner <> The effects of gravitational waves are ridiculously weak, and direct evidence for their existence has (probably) not been found with the detectors built to date. However, no known type of source would emit gravitational waves strong enough for detection, so no one is worried. In the 60's and early 70's, Joe Weber at the University of Maryland attempted to detect gravitational waves using large aluminum bars, which would vibrate if a gravitational wave came by. Because local causes also created vibrations, the technique was to look for coincidences between two or more detectors some distance apart. Weber claimed to see more coincidences than expected statistically and even to see a correlation with sidereal time. Unfortunately, other groups have used far more sensitive detectors operating on the same principles and found nothing. Two new experiments, far more sensitive than those using metal bars, are being built now. These are LIGO in the US and Virgo in Italy. They will work by detecting displacements between two elements separated by several kilometers. An indirect measurement of gravitational waves has been made, however. Gravitational waves are formed when a mass undergoes change of acceleration. They are stronger if the mass is dense and the acceleration changes rapidly. One place where this might happen would be two pulsars circling each other. A couple of systems like this exist, and one has been studied actively over the past 20 years or so. Pulsars make good clocks so you can time the orbital period of the pulsars quite easily. As the pulsars circle, they emit gravitational waves, and these waves remove energy (and angular momentum) from the system. The energy released has to come from somewhere, and that somewhere is the orbital energy of the pulsars themselves. This leads to the pulsars becoming closer and closer over time. A formula was worked out for this effect, and the observed pulsars match it amazingly well. So well, in fact, that if you plot the data on top of the prediction, there is no apparent deviation. (It's actually rather disgusting, none of my results ever come out that well.) Anyway, Joe Taylor of Princeton and a student of his, Russell Hulse, shared the Nobel Prize in Physics for, in part, this work. Useful references are given in section D.03. V. M. Kaspi discusses pulsar timing in 1995 April Sky & Telescope, p. 18. The conference proceedings volume _General Relativity and Gravitation 1989_, eds. Ashby, Bartlett, & Wyss, (Cambridge U. Press 1990) contains a summary of the aluminum bar results. _General Relativity and Gravitation 1992_, eds. Gleiser, Kozameh, & Moreschi (IOP Publishing 1993) contains an article by Joe Taylor summarizing the pulsar results. An example of recent pulsar research is the article by Kaspi, Taylor, and Ryba, 1994 ApJ 428, 713, who give instructions for obtaining their archival timing data via Internet. Some references to Weber's work are: 1969 Phys. Rev. Lett. 22, 1320. 1970 Phys. Rev. Lett. 24, 276. 1971 Nuovo Cimento 4B, 199. Information on gravitational wave detection experiments can be found on the Web for LIGO <URL:>, VIRGO <URL:>, GEO 600 <URL:>, and TAMA <URL:>.
Subject: D.07 Do gravitational waves travel at the speed of light? See sci.physics FAQ part 2, <URL:>, (for North American sites) <URL:>, <URL:>, <URL:>, (European sites) <URL:>, and (Australia) <URL:>. Short answer: yes in GR, not necessarily in other theories of gravity; experimental limits require speed very close to c.
Subject: D.08 Why can't light escape from a black hole? Author: William H. Mook, Jr. <wm0@s1.GANet.NET> P.S. Laplace wrote in 1798: "A luminous star, of the same density of Earth, and whose diameter should be two hundred and fifty times larger than that of the Sun would not in consequence of its attraction, allow any of its rays to arrive at us; it is therefore possible that the largest luminous bodies in the universe may, through this cause, be invisible." _Gravitation_ by Misner, Thorne & Wheeler presents a dialog explaining why black holes deserve their name. (It is on pp 872--875 in the 1978 paperback edition, ISBN 0-7167-0344-0.) As explained in D.03, light rays follow geodesics in spacetime. To describe things fully you need Eddington-Finkelstein coordinates. In these coordinates it's pretty easy to see there is a 'surface of last influence'. In fact, page 873 of MTW has a pretty good graphic showing just that. The surface of last influence is the 'birthpoint' of the black hole. It's also clear that in the normal sense of things, 'up' doesn't exist on the surface of a black hole. As a matter of fact, black holes don't really have solid surfaces as you might be thinking. Black holes have horizons, but that's a region in space, not a solid surface. If you draw various world lines of observers travelling in and around black holes you will see that the light cones of observers who don't cross the event horizon have some segment of those cones above the horizon. Those observers who do cross the event horizon of a black hole are constrained to fall toward the center eventually. There simply are not any geodesics that cross the horizon in the outward direction. At the center there is a region of infinite density and zero volume where everything ends up. This is a problem in the classical understanding of black holes. Recent attempts to understand black holes on a quantum level have indicated that they radiate thermally (they have a finite temperature, though one incredibly low if the black hole is of reasonable size) that is proportional to the gradient of the gravity field. This is due to the capture of virtual particles decaying from the vacuum at the horizon. These are created in pairs and one of them is caught in the black hole and the other is radiated externally. This has been interpreted by Hawking as a tunneling effect and as a form of Unruh radiation. This may give some clever and knowledgeable researcher enough information to figure out what's happening at the center someday. Another way to think about things is to consider basic geometry. The surface area of a ball is related to its diameter by pi. A = pi*d^2. But any gravitating body distorts space so that a light beam travelling through the center of the body measures a diameter slightly larger than that indicated by the surface from which it is measured. In the case of a black hole the diameter measured in this way is infinite, while the surface area is finite.
Subject: D.09 How can gravity escape from a black hole? Author: Matthew P Wiener <>, Steve Carlip <> In a classical point of view, this question is based on an incorrect picture of gravity. Gravity is just the manifestation of spacetime curvature, and a black hole is just a certain very steep puckering that captures anything that comes too closely. Ripples in the curvature travel along in small undulatory packs (radiation---see D.05), but these are an optional addition to the gravitation that is already around. In particular, black holes don't need to radiate to have the fields that they do. Once formed, they and their gravity just are. In a quantum point of view, though, it's a good question. We don't yet have a good quantum theory of gravity, and it's risky to predict what such a theory will look like. But we do have a good theory of quantum electrodynamics, so let's ask the same question for a charged black hole: how can a such an object attract or repel other charged objects if photons can't escape from the event horizon? The key point is that electromagnetic interactions (and gravity, if quantum gravity ends up looking like quantum electrodynamics) are mediated by the exchange of *virtual* particles. This allows a standard loophole: virtual particles can pretty much "do" whatever they like, including travelling faster than light, so long as they disappear before they violate the Heisenberg uncertainty principle. The black hole event horizon is where normal matter (and forces) must exceed the speed of light in order to escape, and thus are trapped. The horizon is meaningless to a virtual particle with enough speed. In particular, a charged black hole is a source of virtual photons that can then do their usual virtual business with the rest of the universe. Once again, we don't know for sure that quantum gravity will have a description in terms of gravitons, but if it does, the same loophole will apply---gravitational attraction will be mediated by virtual gravitons, which are free to ignore a black hole event horizon. See R Feynman QED (Princeton, ???) for the best nontechnical account of how virtual photon exchange manifests itself as long range electrical forces.
Subject: D.10 What are tachyons? Are they real? Author: William H. Mook, Jr. <wm0@s1.GANet.NET> See also the sci.physics FAQ part 4: sci.physics_Frequently_Asked_Questions_(4_4)] Tachyons are theoretical particles that always travel faster than light. Tachy meaning "swift." There is a formula that relates mass to speed in the special theory of relativity: m = m0 / SQR(1 - v^2/c^2) where m = energy divided by c^2 (sometimes called "relativistic mass") m0 = rest mass v = velocity of mass relative to you c = velocity of light (constant in all frames of reference) So, as you see an object moving faster and faster, its mass increases. A simple experiment with electrons in a vacuum tube can convince you that mass increases in this way. So you get something like: v/c m/m0 0.0 1.000 .2 1.021 .4 1.091 .6 1.250 .8 1.667 .9 2.294 .95 3.203 .99 7.089 .995 10.013 .999 22.366 1.000 infinity This led Einstein and others to conclude that it was impossible for any material object to travel at or beyond the speed of light. Because as you increase speed mass increases. With increased mass, there's a requirement for increased energy to accelerate the mass. In the end, an infinite amount of energy is needed to move any object *at* the speed of light. Nothing would move you faster than the speed of light, according to this type of analysis. But, some researchers noted that light has no trouble moving at the speed of light. Furthermore, objects with mass have no trouble converting to light. Light has no trouble converting to objects with mass. So, you have tardyons and photons. Tardy meaning slow. These classes of objects can easily be converted into one another. Now, in terms of the equation given above, if you start out with *any* mass you are constrained to moving less than the speed of light. If you start out with zero mass, you stay at zero mass. This describes the situation with respect to photons. You have zero over zero, and end up with zero.... But, what if you started out faster than the speed of light? Then the equation above would give you an imaginary mass, since v^2 / c^2 would be greater than 1 and that would be subtracted from 1 to produce a negative number. Then you'd take the square root of the negative number and end up with an imaginary number. So, normal matter moving faster than the speed of light ends up with imaginary mass, whatever that may be. Imaginary mass travelling faster than the speed of light would show up as regular mass to an observer at rest. v/c m/m0 (m/m0)*i infinity 0+0.000i 0.000 1,000 0-0.001i 0.001 100 0-0.010i 0.010 10 0-0.101i 0.101 8 0-0.126i 0.126 6 0-0.169i 0.169 4 0-0.258i 0.258 2 0-0.577i 0.577 1.5 0-1.118i 1.118 1.1 0-2.182i 2.182 1.05 0-3.123i 3.123 1.01 0-7.053i 7.053 1.000 0-inf*i infinity So, if there was such a thing as imaginary mass, it would look like normal mass but it would always travel *faster* than c, the speed of light. When it lost energy it would move faster. When it gained energy it would move slower. So, in addition to tardyons and photons, there might exist tachyons. Description Tardyon Photon Tachyon Gain energy faster c slower Lose energy slower c faster Zero energy rest c infinity Infinite energy c c c Now, do tachyons exist? If tachyons exist they can easily be detected by the presence of Cerenkov radiation in a vacuum. Cerenkov radiation is radiation emitted when a charged particle travels through a medium at a speed greater than the velocity of light in the medium. This occurs when the refractive index of the medium is high. Cerenkov radiation is like the bow wave of a boat, or the shock wave of a supersonic airplane. Photons bunch up in front of the tachyon and they're radiated away at an angle determined by the speed of the tachyon. Cerenkov detectors are useful in atomic physics for determining the speed of particles moving through a medium. Light slows as it passes through a medium. That's what's responsible for optical effects. There's nothing mysterious about Cerenkov radiation in a medium. So, folks know how to make an operate Cerenkov detectors because they're a useful speedometer when you're working with subatomic particles Now, there have been a few studies looking for Cerenkov radiation in a vacuum. This would indicated the reality of tachyons. Cerenkov radiation has never been detected in vacuum. So, most people believe that tachyons don't exist.
Subject: D.11 What are magnetic monopoles? Are they real? Short answer is that magnetic monopoles are the magnetic equivalent of point electric charges. Like the electron and positron (which can be considered to carry one unit of electric charge, negative and positive, respectively), one could imagine that there might be magnetic particles which have only a north or south magnetic pole. See J. D. Jackson, _Classical Electrodynamics_, for an extensive discussion.
Subject: D.12 What is the temperature in space? Author: Steve Willner <> Empty space itself cannot have a temperature, unless you mean some abstruse question about quantum vacuums. However, if you put a physical object into space, it will reach a temperature that depends on how efficiently it absorbs and emits radiation and on what heating sources are nearby. For example, an object that both absorbs and emits perfectly, put at the Earth's distance from the Sun, will reach a temperature of about 280 K or 7 C. If it is shielded from the Sun but exposed to interplanetary and interstellar radiation, it reaches about 5 K. If it were far from all stars and galaxies, it would come into equilibrium with the microwave background at about 2.7 K. Spacecraft (and spacewalking astronauts) often run a bit hotter than 280 K because they generate internal energy. Arranging for them to run at the desired temperature is an important aspect of design. Some people also consider the "temperature" of high energy particles like the solar wind or cosmic rays or the outer parts of the Earth's atmosphere. These particles are not in thermal equilibrium, so it's not correct to speak of a single temperature for them, but their energies correspond to temperatures of thousands of kelvins or higher. Generally speaking, these particles are too tenuous to affect the temperature of macroscopic objects. There simply aren't enough particles around to transfer much energy. (It's the same on the ground. There are cosmic rays going through your body all the time, but there aren't enough to keep you warm if the air is cold. The air at the Earth's surface is dense enough to transfer plenty of heat to or from your body.)
Subject: D.13 Saturn's rings, proto-planetary disks, accretion disks---Why are disks so common? Author: Michael Richmond <>, Peter R. Newman Disks are common in astronomical objects: The rings around the giant planets, most notably Saturn; the disks surrounding young stars; and the disks thought to surround neutron stars and black holes. Why are they so common? First a simple explanation, then a more detailed one. Consider a lot of little rocks orbiting around a central point, with orbits tilted with respect to each other. If two rocks collide, their vertical motions will tend to cancel out (one was moving downwards, one upwards when they hit), but, since they were both orbiting around the central point in roughly the same direction, they typically are moving in the same direction "horizontally" when they collide. Over a long enough period of time, there will be so many collisions between rocks that rocks will lose their "vertical" motions---the average vertical motion will approach zero. But the "horizontal" motion around the central point, i.e., a disk, will remain. A more detailed explanation starts with the following scenario: Consider a "gas" of rubber balls (molecules) organized into a huge cylindrical shape rotating about the axis of the cylinder. Make some astrophysically-reasonable assumptions: - The laws of conservation of angular momentum and conservation of linear momentum hold (this is basic, well-tested Newtonian mechanics). - The cylinder is held together by gravity, so the gas doesn't just dissipate into empty space. - The main motion of each ball is in rotation about the cylinder's axis, but each ball has some random motion too, so the balls all run into each other occasionally. The sum of the angular momentum of the whole system is thus not zero, but the sum of the linear momentum is zero (relative to the centre of mass of the entire cylinder). - The balls are not perfectly bouncy, so that collisions between balls results in some of the energy of collision going to heating each ball. Now, consider the motion of the balls in two directions: perpendicular to the cylinder axis, and parallel to the axis. First, perpendicular to the axis: conservation of the non-zero angular momentum will tend to keep the diameter of the cylinder stay relatively constant. When the balls bounce off each other, some are thrown towards the axis and some away. In a more realistic model, some balls are, indeed, ejected from the system entirely, and others (to conserve angular momentum) will fall into the center (i.e., the central object). Parallel to the axis, however, the net linear momentum is zero, and this, too, is conserved. Balls falling from the top and bottom (due to the gravity of all the other balls) will again hit each other and get heated. They don't bounce back as far as they fall, so the length of the axis is continuously (if slowly) shortened. Continue with both sets of changes for long enough, and the cylinder collapses to a disk (i.e., a cylinder with small height). A similar explanation works for a rotating gas organized into any initial shape such as a sphere. The subsequent evolution of the initial disk starts to get complicated in the astrophysical setting, because of things like magnetic fields, stellar wind, and so on. So, in short, what makes the disk is the rotation. If an initial spherical cloud were not rotating, it would simple collapse as a sphere and no disk would form.
Subject: Copyright This document, as a collection, is Copyright 1995--2000 by T. Joseph W. Lazio ( The individual articles are copyright by the individual authors listed. All rights are reserved. Permission to use, copy and distribute this unmodified document by any means and for any purpose EXCEPT PROFIT PURPOSES is hereby granted, provided that both the above Copyright notice and this permission notice appear in all copies of the FAQ itself. Reproducing this FAQ by any means, included, but not limited to, printing, copying existing prints, publishing by electronic or other means, implies full agreement to the above non-profit-use clause, unless upon prior written permission of the authors. This FAQ is provided by the authors "as is," with all its faults. Any express or implied warranties, including, but not limited to, any implied warranties of merchantability, accuracy, or fitness for any particular purpose, are disclaimed. If you use the information in this document, in any way, you do so at your own risk.

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