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From: jlazio@patriot.net
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Subject: [sci.astro] Astrophysics (Astronomy Frequently Asked Questions) (4/9)
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Summary: This posting addresses frequently asked questions about
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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 ,
and it is on the World Wide Web at
and
. A partial list of
worldwide mirrors (both ftp and Web) is maintained at
. (As a general note,
many other FAQs are also available from
.)
Questions/comments/flames should be directed to the FAQ maintainer,
Joseph Lazio (jlazio@patriot.net).
------------------------------
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
. 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, ,
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
.
------------------------------
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
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
and
.
------------------------------
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 , VIRGO
, GEO 600
, and TAMA
.
------------------------------
Subject: D.07 Do gravitational waves travel at the speed of light?
See sci.physics FAQ part 2,
,
(for North American sites)
,
,
,
(European sites)
, and
(Australia)
.
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.
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.
See also the sci.physics FAQ part 4:
ftp://rtfm.mit.edu/pub/usenet-by-hierarchy/sci/physics/
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
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