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Subject: Sci.physics Frequently Asked Questions - December 1993  - Part 2/2
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Summary: This posting contains a list of Frequently Asked Questions
    (and their answers) about physics, and should be read by anyone who
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Keywords: Sci.physics FAQ December 1993 Part 2/2
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Archive-name: physics-faq/part2
Last-modified: 1993/11/18

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               FREQUENTLY ASKED QUESTIONS ON SCI.PHYSICS - Part 2/2
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Item 15.

Some Frequently Asked Questions About Black Holes   updated 2-JUL-1993 by MM
-------------------------------------------------   original by Matt McIrvin

Contents:

1. What is a black hole, really?
2. What happens to you if you fall in?
3. Won't it take forever for you to fall in?  Won't it take forever
   for the black hole to even form?
4. Will you see the universe end?
5. What about Hawking radiation?  Won't the black hole evaporate
   before you get there?
6. How does the gravity get out of the black hole?
7. Where did you get that information?

1. What is a black hole, really?

    In 1916, when general relativity was new, Karl Schwarzschild worked
out a useful solution to the Einstein equation describing the evolution of
spacetime geometry.  This solution, a possible shape of spacetime, would
describe the effects of gravity *outside* a spherically symmetric,
uncharged, nonrotating object (and would serve approximately to describe
even slowly rotating objects like the Earth or Sun).  It worked in much the
same way that you can treat the Earth as a point mass for purposes of
Newtonian gravity if all you want to do is describe gravity *outside* the
Earth's surface.

    What such a solution really looks like is a "metric," which is a
kind of generalization of the Pythagorean formula that gives the length of
a line segment in the plane.  The metric is a formula that may be used to
obtain the "length" of a curve in spacetime.  In the case of a curve
corresponding to the motion of an object as time passes (a "timelike
worldline,") the "length" computed by the metric is actually the elapsed
time experienced by an object with that motion.  The actual formula depends
on the coordinates chosen in which to express things, but it may be
transformed into various coordinate systems without affecting anything
physical, like the spacetime curvature.  Schwarzschild expressed his metric
in terms of coordinates which, at large distances from the object,
resembled spherical coordinates with an extra coordinate t for time.
Another coordinate, called r, functioned as a radial coordinate at large
distances; out there it just gave the distance to the massive object.

    Now, at small radii, the solution began to act strangely.  There
was a "singularity" at the center, r=0, where the curvature of spacetime
was infinite.  Surrounding that was a region where the "radial" direction
of decreasing r was actually a direction in *time* rather than in space.
Anything in that region, including light, would be obligated to fall toward
the singularity, to be crushed as tidal forces diverged. This was separated
from the rest of the universe by a place where Schwarzschild's coordinates
blew up, though nothing was wrong with the curvature of spacetime there.
(This was called the Schwarzschild radius.  Later, other coordinate systems
were discovered in which the blow-up didn't happen; it was an artifact of
the coordinates, a little like the problem of defining the longitude of the
North Pole.  The physically important thing about the Schwarzschild radius
was not the coordinate problem, but the fact that within it the direction
into the hole became a direction in time.)

    Nobody really worried about this at the time, because there was no
known object that was dense enough for that inner region to actually be
outside it, so for all known cases, this odd part of the solution would not
apply.  Arthur Stanley Eddington considered the possibility of a dying star
collapsing to such a density,  but rejected it as aesthetically unpleasant
and proposed that some new physics must intervene.  In 1939, Oppenheimer
and Snyder finally took seriously the possibility that stars a few times
more massive than the sun might be doomed to collapse to such a state at
the end of their lives.

    Once the star gets smaller than the place where Schwarzschild's
coordinates fail (called the Schwarzschild radius for an uncharged,
nonrotating object, or the event horizon) there's no way it can avoid
collapsing further.  It has to collapse all the way to a singularity for
the same reason that you can't keep from moving into the future! Nothing
else that goes into that region afterward can avoid it either, at least in
this simple case.  The event horizon is a point of no return.

    In 1971 John Archibald Wheeler named such a thing a black hole,
since light could not escape from it.  Astronomers have many candidate
objects they think are probably black holes, on the basis of several kinds
of evidence (typically they are dark objects whose large mass can be
deduced from their gravitational effects on other objects, and which
sometimes emit X-rays, presumably from infalling matter).  But the
properties of black holes I'll talk about here are entirely theoretical.
They're based on general relativity, which is a theory that seems supported
by available evidence.

2. What happens to you if you fall in?

    Suppose that, possessing a proper spacecraft and a self-destructive
urge, I decide to go black-hole jumping and head for an uncharged,
nonrotating ("Schwarzschild") black hole.  In this and other kinds of hole,
I won't, before I fall in, be able to see anything within the event
horizon.  But there's nothing *locally* special about the event horizon;
when I get there it won't seem like a particularly unusual place, except
that I will see strange optical distortions of the sky around me from all
the bending of light that goes on.  But as soon as I fall through, I'm
doomed.  No bungee will help me, since bungees can't keep Sunday from
turning into Monday.  I have to hit the singularity eventually, and before
I get there there will be enormous tidal forces-- forces due to the
curvature of spacetime-- which will squash me and my spaceship in some
directions and stretch them in another until I look like a piece of
spaghetti.  At the singularity all of present physics is mute as to what
will happen, but I won't care.  I'll be dead.

    For ordinary black holes of a few solar masses, there are actually
large tidal forces well outside the event horizon, so I probably wouldn't
even make it into the hole alive and unstretched.  For a black hole of 8
solar masses, for instance, the value of r at which tides become fatal is
about 400 km, and the Schwarzschild radius is just 24 km.  But tidal
stresses are proportional to M/r^3.  Therefore the fatal r goes as the cube
root of the mass, whereas the Schwarzschild radius of the black hole is
proportional to the mass.  So for black holes larger than about 1000 solar
masses I could probably fall in alive, and for still larger ones I might
not even notice the tidal forces until I'm through the horizon and doomed.

3. Won't it take forever for you to fall in?  Won't it take forever
   for the black hole to even form?

    Not in any useful sense.  The time I experience before I hit the
event horizon, and even until I hit the singularity-- the "proper time"
calculated by using Schwarzschild's metric on my worldline -- is finite.
The same goes for the collapsing star; if I somehow stood on the surface of
the star as it became a black hole, I would experience the star's demise in
a finite time.

    On my worldline as I fall into the black hole, it turns out that
the Schwarzschild coordinate called t goes to infinity when I go through
the event horizon.  That doesn't correspond to anyone's proper time,
though; it's just a coordinate called t.  In fact, inside the event
horizon, t is actually a *spatial* direction, and the future corresponds
instead to decreasing r.  It's only outside the black hole that t even
points in a direction of increasing time.  In any case, this doesn't
indicate that I take forever to fall in, since the proper time involved is
actually finite.

    At large distances t *does* approach the proper time of someone who
is at rest with respect to the black hole.  But there isn't any
non-arbitrary sense in which you can call t at smaller r values "the proper
time of a distant observer," since in general relativity there is no
coordinate-independent way to say that two distant events are happening "at
the same time."  The proper time of any observer is only defined locally.

    A more physical sense in which it might be said that things take
forever to fall in is provided by looking at the paths of emerging light
rays.  The event horizon is what, in relativity parlance, is called a
"lightlike surface"; light rays can remain there.  For an ideal
Schwarzschild hole (which I am considering in this paragraph) the horizon
lasts forever, so the light can stay there without escaping.  (If you
wonder how this is reconciled with the fact that light has to travel at the
constant speed c-- well, the horizon *is* traveling at c! Relative speeds
in GR are also only unambiguously defined locally, and if you're at the
event horizon you are necessarily falling in; it comes at you at the speed
of light.)  Light beams aimed directly outward from just outside the
horizon don't escape to large distances until late values of t.  For
someone at a large distance from the black hole and approximately at rest
with respect to it, the coordinate t does correspond well to proper time.

    So if you, watching from a safe distance, attempt to witness my
fall into the hole, you'll see me fall more and more slowly as the light
delay increases.  You'll never see me actually *get to* the event horizon.
My watch, to you, will tick more and more slowly, but will never reach the
time that I see as I fall into the black hole.  Notice that this is really
an optical effect caused by the paths of the light rays.

    This is also true for the dying star itself.  If you attempt to
witness the black hole's formation, you'll see the star collapse more and
more slowly, never precisely reaching the Schwarzschild radius.

    Now, this led early on to an image of a black hole as a strange
sort of suspended-animation object, a "frozen star" with immobilized
falling debris and gedankenexperiment astronauts hanging above it in
eternally slowing precipitation.  This is, however, not what you'd see. The
reason is that as things get closer to the event horizon, they also get
*dimmer*.  Light from them is redshifted and dimmed, and if one considers
that light is actually made up of discrete photons, the time of escape of
*the last photon* is actually finite, and not very large.  So things would
wink out as they got close, including the dying star, and the name "black
hole" is justified.

    As an example, take the eight-solar-mass black hole I mentioned
before.  If you start timing from the moment the you see the object half a
Schwarzschild radius away from the event horizon, the light will dim
exponentially from that point on with a characteristic time of about 0.2
milliseconds, and the time of the last photon is about a hundredth of a
second later.  The times scale proportionally to the mass of the black
hole.  If I jump into a black hole, I don't remain visible for long.

    Also, if I jump in, I won't hit the surface of the "frozen star."
It goes through the event horizon at another point in spacetime from
where/when I do.

    (Some have pointed out that I really go through the event horizon a
little earlier than a naive calculation would imply.  The reason is that my
addition to the black hole increases its mass, and therefore moves the
event horizon out around me at finite Schwarzschild t coordinate.  This
really doesn't change the situation with regard to whether an external
observer sees me go through, since the event horizon is still lightlike;
light emitted at the event horizon or within it will never escape to large
distances, and light emitted just outside it will take a long time to get
to an observer, timed, say, from when the observer saw me pass the point
half a Schwarzschild radius outside the hole.)

    All this is not to imply that the black hole can't also be used for
temporal tricks much like the "twin paradox" mentioned elsewhere in this
FAQ.  Suppose that I don't fall into the black hole-- instead, I stop and
wait at a constant r value just outside the event horizon, burning
tremendous amounts of rocket fuel and somehow withstanding the huge
gravitational force that would result.  If I then return home, I'll have
aged less than you.  In this case, general relativity can say something
about the difference in proper time experienced by the two of us, because
our ages can be compared *locally* at the start and end of the journey.

4. Will you see the universe end?

    If an external observer sees me slow down asymptotically as I fall,
it might seem reasonable that I'd see the universe speed up
asymptotically-- that I'd see the universe end in a spectacular flash as I
went through the horizon.  This isn't the case, though.  What an external
observer sees depends on what light does after I emit it.  What I see,
however, depends on what light does before it gets to me.  And there's no
way that light from future events far away can get to me.  Faraway events
in the arbitrarily distant future never end up on my "past light-cone," the
surface made of light rays that get to me at a given time.

    That, at least, is the story for an uncharged, nonrotating black
hole.  For charged or rotating holes, the story is different.  Such holes
can contain, in the idealized solutions, "timelike wormholes" which serve
as gateways to otherwise disconnected regions-- effectively, different
universes.  Instead of hitting the singularity, I can go through the
wormhole.  But at the entrance to the wormhole, which acts as a kind of
inner event horizon, an infinite speed-up effect actually does occur.  If I
fall into the wormhole I see the entire history of the universe outside
play itself out to the end.  Even worse, as the picture speeds up the light
gets blueshifted and more energetic, so that as I pass into the wormhole an
"infinite blueshift" happens which fries me with hard radiation.  There is
apparently good reason to believe that the infinite blueshift would imperil
the wormhole itself, replacing it with a singularity no less pernicious
than the one I've managed to miss.  In any case it would render wormhole
travel an undertaking of questionable practicality.

5. What about Hawking radiation?  Won't the black hole evaporate
   before you get there?

    (First, a caveat: Not a lot is really understood about evaporating
black holes.  The following is largely deduced from information in Wald's
GR text, but what really happens-- especially when the black hole gets very
small-- is unclear.  So take the following with a grain of salt.)

Short answer:  No, it won't.  This demands some elaboration.

    From thermodynamic arguments Stephen Hawking realized that a black
hole should have a nonzero temperature, and ought therefore to emit
blackbody radiation.  He eventually figured out a quantum- mechanical
mechanism for this.  Suffice it to say that black holes should very, very
slowly lose mass through radiation, a loss which accelerates as the hole
gets smaller and eventually evaporates completely in a burst of radiation.
This happens in a finite time according to an outside observer.

    But I just said that an outside observer would *never* observe an
object actually entering the horizon!  If I jump in, will you see the black
hole evaporate out from under me, leaving me intact but marooned in the
very distant future from gravitational time dilation?

    You won't, and the reason is that the discussion above only applies
to a black hole that is not shrinking to nil from evaporation. Remember
that the apparent slowing of my fall is due to the paths of outgoing light
rays near the event horizon.  If the black hole *does* evaporate, the delay
in escaping light caused by proximity to the event horizon can only last as
long as the event horizon does!  Consider your external view of me as I
fall in.

    If the black hole is eternal, events happening to me (by my watch)
closer and closer to the time I fall through happen divergingly later
according to you (supposing that your vision is somehow not limited by the
discreteness of photons, or the redshift).

    If the black hole is mortal, you'll instead see those events happen
closer and closer to the time the black hole evaporates.  Extrapolating,
you would calculate my time of passage through the event horizon as the
exact moment the hole disappears!  (Of course, even if you could see me,
the image would be drowned out by all the radiation from the evaporating
hole.)  I won't experience that cataclysm myself, though; I'll be through
the horizon, leaving only my light behind. As far as I'm concerned, my
grisly fate is unaffected by the evaporation.

    All of this assumes you can see me at all, of course.  In practice
the time of the last photon would have long been past.  Besides, there's
the brilliant background of Hawking radiation to see through as the hole
shrinks to nothing.

    (Due to considerations I won't go into here, some physicists think
that the black hole won't disappear completely, that a remnant hole will be
left behind.  Current physics can't really decide the question, any more
than it can decide what really happens at the singularity. If someone ever
figures out quantum gravity, maybe that will provide an answer.)

6. How does the gravity get out of the black hole?

    Purely in terms of general relativity, there is no problem here.
The gravity doesn't have to get out of the black hole.  General relativity
is a local theory, which means that the field at a certain point in
spacetime is determined entirely by things going on at places that can
communicate with it at speeds less than or equal to c.  If a star collapses
into a black hole, the gravitational field outside the black hole may be
calculated entirely from the properties of the star and its external
gravitational field *before* it becomes a black hole. Just as the light
registering late stages in my fall takes longer and longer to get out to
you at a large distance, the gravitational consequences of events late in
the star's collapse take longer and longer to ripple out to the world at
large.  In this sense the black hole *is* a kind of "frozen star": the
gravitational field is a fossil field.  The same is true of the
electromagnetic field that a black hole may possess.

    Often this question is phrased in terms of gravitons, the
hypothetical quanta of spacetime distortion.  If things like gravity
correspond to the exchange of "particles" like gravitons, how can they get
out of the event horizon to do their job?

    First of all, it's important to realize that gravitons are not as
yet even part of a complete theory, let alone seen experimentally.  They
don't exist in general relativity, which is a non-quantum theory.  When
fields are described as mediated by particles, that's quantum theory, and
nobody has figured out how to construct a quantum theory of gravity.  Even
if such a theory is someday built, it may not involve "virtual particles"
in the same way other theories do.  In quantum electrodynamics, the static
forces between particles are described as resulting from the exchange of
"virtual photons," but the virtual photons only appear when one expresses
QED in terms of a quantum- mechanical approximation method called
perturbation theory.  It currently looks like this kind of perturbation
theory doesn't work properly when applied to quantum gravity.  So although
quantum gravity may well involve "real gravitons" (quantized gravitational
waves), it may well not involve "virtual gravitons" as carriers of static
gravitational forces.

    Nevertheless, the question in this form is still worth asking,
because black holes *can* have static electric fields, and we know that
these may be described in terms of virtual photons.  So how do the virtual
photons get out of the event horizon?  The answer is that virtual particles
aren't confined to the interiors of light cones: they can go faster than
light!  Consequently the event horizon, which is really just a surface that
moves at the speed of light, presents no barrier.

    I couldn't use these virtual photons after falling into the hole to
communicate with you outside the hole; nor could I escape from the hole by
somehow turning myself into virtual particles.  The reason is that virtual
particles don't carry any *information* outside the light cone.  That is a
tricky subject for another (future?) FAQ entry.  Suffice it to say that the
reasons virtual particles don't provide an escape hatch for a black hole
are the same as the reasons they can't be used for faster-than-light travel
or communication.

7. Where did you get that information?

    The numbers concerning fatal radii, dimming, and the time of the
last photon came from Misner, Thorne, and Wheeler's _Gravitation_ (San
Francisco: W. H. Freeman & Co., 1973), pp. 860-862 and 872-873. Chapters 32
and 33 (IMHO, the best part of the book) contain nice descriptions of some
of the phenomena I've described.

    Information about evaporation and wormholes came from Robert Wald's
_General Relativity_ (Chicago: University of Chicago Press, 1984). The
famous conformal diagram of an evaporating hole on page 413 has resolved
several arguments on sci.physics (though its veracity is in question).

    Steven Weinberg's _Gravitation and Cosmology_ (New York: John Wiley
and Sons, 1972) provided me with the historical dates.  It discusses some
properties of the Schwarzschild solution in chapter 8 and describes
gravitational collapse in chapter 11.

********************************************************************************
Item 16.

Below Absolute Zero - What Does Negative Temperature Mean?   updated 24-MAR-1993
----------------------------------------------------------

Questions:  What is negative temperature?  Can you really make a system
which has a temperature below absolute zero?  Can you even give any useful
meaning to the expression 'negative absolute temperature'?

Answer:  Absolutely. :-)

    Under certain conditions, a closed system *can* be described by a
negative temperature, and, surprisingly, be *hotter* than the same system
at any positive temperature.  This article describes how it all works.

Step I: What is "Temperature"?
------------------------------

    To get things started, we need a clear definition of "temperature."
Our intuitive notion is that two systems in thermal contact should exchange
no heat, on average, if and only if they are at the same temperature.  Let's
call the two systems S1 and S2. The combined system, treating S1 and S2
together, can be S3.  The important question, consideration of which
will lead us to a useful quantitative definition of temperature, is "How will
the energy of S3 be distributed between S1 and S2?"  I will briefly explain
this below, but I recommend that you read K&K, referenced below, for a
careful, simple, and thorough explanation of this important and fundamental
result.

    With a total energy E, S has many possible internal states
(microstates).  The atoms of S3 can share the total energy in many ways.
Let's say there are N different states.  Each state corresponds to a
particular division of the total energy in the two subsystems S1 and S2.
Many microstates can correspond to the same division, E1 in S1 and E2 in
S2. A simple counting argument tells you that only one particular division
of the energy, will occur with any significant probability.  It's the one
with the overwhelmingly largest number of microstates for the total system
S3. That number, N(E1,E2) is just the product of the number of states
allowed in each subsystem, N(E1,E2) = N1(E1)*N2(E2), and, since E1 + E2 =
E, N(E1,E2) reaches a maximum when N1*N2 is stationary with respect to
variations of E1 and E2 subject to the total energy constraint.

    For convenience, physicists prefer to frame the question in terms
of the logarithm of the number of microstates N, and call this the entropy,
S. You can easily see from the above analysis that two systems are in
equilibrium with one another when (dS/dE)_1 = (dS/dE)_2, i.e., the rate of
change of entropy, S, per unit change in energy, E, must be the same for
both systems.  Otherwise, energy will tend to flow from one subsystem to
another as S3 bounces randomly from one microstate to another, the total
energy E3 being constant, as the combined system moves towards a state of
maximal total entropy.  We define the temperature, T, by 1/T = dS/dE, so
that the equilibrium condition becomes the very simple T_1 = T_2.

    This statistical mechanical definition of temperature does in fact
correspond to your intuitive notion of temperature for most systems. So
long as dS/dE is always positive, T is always positive.  For common
situations, like a collection of free particles, or particles in a harmonic
oscillator potential, adding energy always increases the number of
available microstates, increasingly faster with increasing total energy. So
temperature increases with increasing energy, from zero, asymptotically
approaching positive infinity as the energy increases.

Step II: What is "Negative Temperature"?
----------------------------------------

    Not all systems have the property that the entropy increases
monotonically with energy.  In some cases, as energy is added to the system,
the number of available microstates, or configurations, actually decreases
for some range of energies.  For example, imagine an ideal "spin-system", a
set of N atoms with spin 1/2 one a one-dimensional wire.  The atoms are not
free to move from their positions on the wire.  The only degree of freedom
allowed to them is spin-flip:  the spin of a given atom can point up or
down.  The total energy of the system, in a magnetic field of strength B,
pointing down, is (N+ - N-)*uB, where u is the magnetic moment of each atom
and N+ and N- are the number of atoms with spin up and down respectively.
Notice that with this definition, E is zero when half of the spins are
up and half are down.  It is negative when the majority are down and
positive when the majority are up.

    The lowest possible energy state, all the spins will point down,
gives the system a total energy of -NuB, and temperature of absolute zero.
There is only one configuration of the system at this energy, i.e., all the
spins must point down.  The entropy is the log of the number of
microstates, so in this case is log(1) = 0.  If we now add a quantum of
energy, size uB, to the system, one spin is allowed to flip up.  There are
N possibilities, so the entropy is log(N).  If we add another quantum of
energy, there are a total of N(N-1)/2 allowable configurations with two
spins up.  The entropy is increasing quickly, and the temperature is rising
as well.

    However, for this system, the entropy does not go on increasing
forever.  There is a maximum energy, +NuB, with all spins up.  At this
maximal energy, there is again only one microstate, and the entropy is
again zero.  If we remove one quantum of energy from the system, we allow
one spin down.  At this energy there are N available microstates.  The
entropy goes on increasing as the energy is lowered.  In fact the maximal
entropy occurs for total energy zero, i.e., half of the spins up, half
down.

    So we have created a system where, as we add more and more energy,
temperature starts off positive, approaches positive infinity as maximum
entropy is approached, with half of all spins up.  After that, the
temperature becomes negative infinite, coming down in magnitude toward
zero, but always negative, as the energy increases toward maximum. When the
system has negative temperature, it is *hotter* than when it is has
positive system.  If you take two copies of the system, one with positive
and one with negative temperature, and put them in thermal contact, heat
will flow from the negative-temperature system into the positive-temperature
system.

Step III:  What Does This Have to Do With the Real World?
---------------------------------------------------------

    Can this system ever by realized in the real world, or is it just a
fantastic invention of sinister theoretical condensed matter physicists?
Atoms always have other degrees of freedom in addition to spin, usually
making the total energy of the system unbounded upward due to the
translational degrees of freedom that the atom has.  Thus, only certain
degrees of freedom of a particle can have negative temperature.  It makes
sense to define the "spin-temperature" of a collection of atoms, so long as
one condition is met:  the coupling between the atomic spins and the other
degrees of freedom is sufficiently weak, and the coupling between atomic
spins sufficiently strong, that the timescale for energy to flow from the
spins into other degrees of freedom is very large compared to the timescale
for thermalization of the spins among themselves.  Then it makes sense to
talk about the temperature of the spins separately from the temperature of
the atoms as a whole. This condition can easily be met for the case of
nuclear spins in a strong external magnetic field.

    Nuclear and electron spin systems can be promoted to negative
temperatures by suitable radio frequency techniques.   Various experiments
in the calorimetry of negative temperatures, as well as applications of
negative temperature systems as RF amplifiers, etc., can be found in the
articles listed below, and the references therein.

References:

        Kittel and Kroemer,_Thermal Physics_, appendix E.
        N.F. Ramsey, "Thermodynamics and statistical mechanics at negative
        absolute temperature,"  Phys. Rev. _103_, 20 (1956).
        M.J. Klein,"Negative Absolute Temperature," Phys. Rev. _104_, 589 (1956).

********************************************************************************
Item 17.

Which Way Will my Bathtub Drain?                updated 16-MAR-1993 by SIC
--------------------------------                original by Matthew R. Feinstein

Question: Does my bathtub drain differently depending on whether I live
in the northern or southern hemisphere?

Answer: No.  There is a real effect, but it is far too small to be relevant
when you pull the plug in your bathtub.

    Because the earth rotates, a fluid that flows along the earth's
surface feels a "Coriolis" acceleration perpendicular to its velocity.
In the northern hemisphere low pressure storm systems spin counterclockwise.
In the southern hemisphere, they spin clockwise because the direction
of the Coriolis acceleration is reversed.  This effect leads to the
speculation that the bathtub vortex that you see when you pull the plug
from the drain spins one way in the north and the other way in the south.

    But this acceleration is VERY weak for bathtub-scale fluid
motions.  The order of magnitude of the Coriolis acceleration can be
estimated from size of the "Rossby number" (see below).  The effect of the
Coriolis acceleration on your bathtub vortex is SMALL.  To detect its
effect on your bathtub, you would have to get out and wait until the motion
in the water is far less than one rotation per day.  This would require
removing thermal currents, vibration, and any other sources of noise.  Under
such conditions, never occurring in the typical home, you WOULD see an
effect.  To see what trouble it takes to actually see the effect, see the
reference below.  Experiments have been done in both the northern and
southern hemispheres to verify that under carefully controlled conditions,
bathtubs drain in opposite directions due to the Coriolis acceleration from
the Earth's rotation.

    Coriolis accelerations are significant when the Rossby number is
SMALL.     So, suppose we want a Rossby number of 0.1 and a bathtub-vortex
length scale of 0.1 meter.  Since the earth's rotation rate is about
10^(-4)/second, the fluid velocity should be less than or equal to
2*10^(-6) meters/second.  This is a very small velocity.  How small is it?
Well, we can take the analysis a step further and calculate another, more
famous dimensionless parameter, the Reynolds number.

    The Reynolds number is = L*U*density/viscosity

    Assuming that physicists bathe in hot water the viscosity will be
about 0.005 poise and the density will be about 1.0, so the Reynolds Number
is about 4*10^(-2).

    Now, life at low Reynolds numbers is different from life at high
Reynolds numbers.  In particular, at low Reynolds numbers, fluid physics is
dominated by friction and diffusion, rather than by inertia: the time it
would take for a particle of fluid to move a significant distance due to an
acceleration is greater than the time it takes for the particle to break up
due to diffusion.

    The same effect has been accused of responsibility for the
direction water circulates when you flush a toilet.  This is surely
nonsense.  In this case, the water rotates in the direction which the pipe
points which carries the water from the tank to the bowl.

Reference: Trefethen, L.M. et al, Nature 207 1084-5 (1965).

********************************************************************************
Item 18.

Why do Mirrors Reverse Left and Right?          updated 16-MAR-1993 by SIC
--------------------------------------

    The simple answer is that they don't.  Look in a mirror and wave
your right hand.  On which side of the mirror is the hand that waved?  The
right side, of course.

    Mirrors DO reverse In/Out.  Imaging holding an arrow in your hand.
If you point it up, it will point up in the mirror.  If you point it to the
left, it will point to the left in the mirror.  But if you point it toward
the mirror, it will point right back at you.  In and Out are reversed.

    If you take a three-dimensional, rectangular, coordinate system,
(X,Y,Z), and point the Z axis such that the vector equation X x Y = Z is
satisfied, then the coordinate system is said to be right-handed.  Imagine
Z pointing toward the mirror.  X and Y are unchanged (remember the arrows?)
but Z will point back at you.  In the mirror, X x Y = - Z.  The image
contains a left-handed coordinate system.

    This has an important effect, familiar mostly to chemists and
physicists. It changes the chirality, or handedness of objects viewed in
the mirror. Your left hand looks like a right hand, while your right hand
looks like a left hand.  Molecules often come in pairs called
stereoisomers, which differ not in the sequence or number of atoms, but
only in that one is the mirror image of the other, so that no rotation or
stretching can turn one into the other.  Your hands make a good laboratory
for this effect.  They are distinct, even though they both have the same
components connected in the same way. They are a stereo pair, identical
except for "handedness".

    People sometimes think that mirrors *do* reverse left/right, and
that the effect is due to the fact that our eyes are aligned horizontally
on our faces.  This can be easily shown to be untrue by looking in any
mirror with one eye closed!

Reference:  _The Left Hand of the Neutrino_, by Isaac Asimov, contains
a very readable discussion of handedness and mirrors in physics.

********************************************************************************
Item 19.

What is the Mass of a Photon?                   updated 24-JUL-1992 by SIC
                                                original by Matt Austern

Or, "Does the mass of an object depend on its velocity?"

    This question usually comes up in the context of wondering whether
photons are really "massless," since, after all, they have nonzero energy.
The problem is simply that people are using two different definitions of
mass.  The overwhelming consensus among physicists today is to say that
photons are massless.  However, it is possible to assign a "relativistic
mass" to a photon which depends upon its wavelength.  This is based upon
an old usage of the word "mass" which, though not strictly wrong, is not
used much today.

    The old definition of mass, called "relativistic mass," assigns
a mass to a particle proportional to its total energy E, and involved
the speed of light, c, in the proportionality constant:

                m = E / c^2.                                        (1)

This definition gives every object a velocity-dependent mass.

    The modern definition assigns every object just one mass, an
invariant quantity that does not depend on velocity.  This is given by

                m = E_0 / c^2,                                      (2)

where E_0 is the total energy of that object at rest.

    The first definition is often used in popularizations, and in some
elementary textbooks.  It was once used by practicing physicists, but for
the last few decades, the vast majority of physicists have instead used the
second definition.  Sometimes people will use the phrase "rest mass," or
"invariant mass," but this is just for emphasis: mass is mass.  The
"relativistic mass" is never used at all.  (If you see "relativistic mass"
in your first-year physics textbook, complain! There is no reason for books
to teach obsolete terminology.)

    Note, by the way, that using the standard definition of mass, the
one given by Eq. (2), the equation "E = m c^2" is *not* correct.  Using the
standard definition, the relation between the mass and energy of an object
can be written as

                E   = m c^2 / sqrt(1 -v^2/c^2),                     (3)
or as

                E^2 = m^2 c^4  +  p^2 c^2,                          (4)

where v is the object's velocity, and p is its momentum.

    In one sense, any definition is just a matter of convention.  In
practice, though, physicists now use this definition because it is much
more convenient.  The "relativistic mass" of an object is really just the
same as its energy, and there isn't any reason to have another word for
energy: "energy" is a perfectly good word.  The mass of an object, though,
is a fundamental and invariant property, and one for which we do need a
word.

    The "relativistic mass" is also sometimes confusing because it
mistakenly leads people to think that they can just use it in the Newtonian
relations
                F = m a                                             (5)
and
                F = G m1 m2 / r^2.                                  (6)

In fact, though, there is no definition of mass for which these
equations are true relativistically: they must be generalized.  The
generalizations are more straightforward using the standard definition
of mass than using "relativistic mass."

    Oh, and back to photons: people sometimes wonder whether it makes
sense to talk about the "rest mass" of a particle that can never be at
rest.  The answer, again, is that "rest mass" is really a misnomer, and it
is not necessary for a particle to be at rest for the concept of mass to
make sense.  Technically, it is the invariant length of the particle's
four-momentum.  (You can see this from Eq. (4).)  For all photons this is
zero. On the other hand, the "relativistic mass" of photons is frequency
dependent. UV photons are more energetic than visible photons, and so are
more "massive" in this sense, a statement which obscures more than it
elucidates.

    Reference: Lev Okun wrote a nice article on this subject in the
June 1989 issue of Physics Today, which includes a historical discussion
of the concept of mass in relativistic physics.

********************************************************************************
Item 20.
                                                updated 16-MAR-1992 by SIC
                                                Original by John Blanton
Why Do Stars Twinkle While Planets Do Not?
-----------------------------------------

    Stars, except for the Sun, although they may be millions of miles
in diameter, are very far away.  They appear as point sources even when
viewed by telescopes.  The planets in our solar system, much smaller than
stars, are closer and can be resolved as disks with a little bit of
magnification (field binoculars, for example).

    Since the Earth's atmosphere is turbulent, all images viewed up
through it tend to "swim."  The result of this is that sometimes a single
point in object space gets mapped to two or more points in image space, and
also sometimes a single point in object space does not get mapped into any
point in image space.  When a star's single point in object space fails to
map to at least one point in image space, the star seems to disappear
temporarily. This does not mean the star's light is lost for that moment.
It just means that it didn't get to your eye, it went somewhere else.

    Since planets represent several points in object space, it is
highly likely that one or more points in the planet's object space get
mapped to a points in image space, and the planet's image never winks out.
Each individual ray is twinkling away as badly as any star, but when all of
those individual rays are viewed together, the next effect is averaged out
to something considerably steadier.

    The result is that stars tend to twinkle, and planets do not.
Other extended objects in space, even very far ones like nebulae, do not
twinkle if they are sufficiently large that they have non-zero apparent
diameter when viewed from the Earth.

********************************************************************************
Item 21.                                           original by David Brahm

Baryogenesis - Why Are There More Protons Than Antiprotons?
-----------------------------------------------------------

(I) How do we really *know* that the universe is not matter-antimatter
symmetric?

(a) The Moon:  Neil Armstrong did not annihilate, therefore the moon
is made of matter.
(b) The Sun:  Solar cosmic rays are matter, not antimatter.
(c) The other Planets:  We have sent probes to almost all.  Their survival
demonstrates that the solar system is made of matter.
(d) The Milky Way:  Cosmic rays sample material from the entire galaxy.
In cosmic rays, protons outnumber antiprotons 10^4 to 1.
(e) The Universe at large: This is tougher.  If there were antimatter
galaxies then we should see gamma emissions from annihilation.  Its absence
is strong evidence that at least the nearby clusters of galaxies (e.g., Virgo)
are matter-dominated.  At larger scales there is little proof.
    However,  there is a problem, called the "annihilation catastrophe"
which probably eliminates the possibility of a matter-antimatter symmetric
universe.  Essentially, causality prevents the separation of large chucks
of antimatter from matter fast enough to prevent their mutual annihilation
in in the early universe.  So the Universe is most likely matter dominated.

(II) How did it get that way?

    Annihilation has made the asymmetry much greater today than in the
early universe.  At the high temperature of the first microsecond, there
were large numbers of thermal quark-antiquark pairs.  K&T estimate 30
million antiquarks for every 30 million and 1 quarks during this epoch.
That's a tiny asymmetry.  Over time most of the antimatter has annihilated
with matter, leaving the very small initial excess of matter to dominate
the Universe.

    Here are a few possibilities for why we are matter dominated today:

a) The Universe just started that way.
   Not only is this a rather sterile hypothesis, but it doesn't work under
   the popular "inflation" theories, which dilute any initial abundances.
b) Baryogenesis occurred around the Grand Unified (GUT) scale (very early).
   Long thought to be the only viable candidate, GUT's generically have
   baryon-violating reactions, such as proton decay (not yet observed).
c) Baryogenesis occurred at the Electroweak Phase Transition (EWPT).
   This is the era when the Higgs first acquired a vacuum expectation value
   (vev), so other particles acquired masses.  Pure Standard Model physics.

    Sakharov enumerated 3 necessary conditions for baryogenesis:

    (1)  Baryon number violation.  If baryon number is conserved in all
reactions, then the present baryon asymmetry can only reflect asymmetric
initial conditions, and we are back to case (a), above.
    (2) C and CP violation.  Even in the presence of B-violating
reactions, without a preference for matter over antimatter the B-violation
will take place at the same rate in both directions, leaving no excess.
    (3) Thermodynamic Nonequilibrium.  Because CPT guarantees equal
masses for baryons and antibaryons, chemical equilibrium would drive the
necessary reactions to correct for any developing asymmetry.

    It turns out the Standard Model satisfies all 3 conditions:

    (1) Though the Standard Model conserves B classically (no terms in
the Lagrangian violate B), quantum effects allow the universe to tunnel
between vacua with different values of B.  This tunneling is _very_
suppressed at energies/temperatures below 10 TeV (the "sphaleron mass"),
_may_ occur at e.g. SSC energies (controversial), and _certainly_ occurs at
higher temperatures.

    (2) C-violation is commonplace.  CP-violation (that's "charge
conjugation" and "parity") has been experimentally observed in kaon
decays, though strictly speaking the Standard Model probably has
insufficient CP-violation to give the observed baryon asymmetry.

    (3) Thermal nonequilibrium is achieved during first-order phase
transitions in the cooling early universe, such as the EWPT (at T = 100 GeV
or so).  As bubbles of the "true vacuum" (with a nonzero Higgs vev)
percolate and grow, baryogenesis can occur at or near the bubble walls.

    A major theoretical problem, in fact, is that there may be _too_
_much_ B-violation in the Standard Model, so that after the EWPT is
complete (and condition 3 above is no longer satisfied) any previously
generated baryon asymmetry would be washed out.

References: Kolb and Turner, _The Early Universe_;
  Dine, Huet, Singleton & Susskind, Phys.Lett.B257:351 (1991);
  Dine, Leigh, Huet, Linde & Linde, Phys.Rev.D46:550 (1992).

********************************************************************************
Item 22.

TIME TRAVEL - FACT OR FICTION?                  updated 18-NOV-1993
------------------------------                  original by Jon J. Thaler

    We define time travel to mean departure from a certain place and
time followed (from the traveller's point of view) by arrival at the same
place at an earlier (from the sedentary observer's point of view) time.
Time travel paradoxes arise from the fact that departure occurs after
arrival according to one observer and before arrival according to another.
In the terminology of special relativity time travel implies that the
timelike ordering of events is not invariant.  This violates our intuitive
notions of causality.  However, intuition is not an infallible guide, so we
must be careful.  Is time travel really impossible, or is it merely another
phenomenon where "impossible" means "nature is weirder than we think?"  The
answer is more interesting than you might think.

THE SCIENCE FICTION PARADIGM:

    The B-movie image of the intrepid chrononaut climbing into his time
machine and watching the clock outside spin backwards while those outside
the time machine watch the him revert to callow youth is, according to
current theory, impossible.  In current theory, the arrow of time flows in
only one direction at any particular place.  If this were not true, then
one could not impose a 4-dimensional coordinate system on space-time, and
many nasty consequences would result. Nevertheless, there is a scenario
which is not ruled out by present knowledge.  This usually requires an
unusual spacetime topology (due to wormholes or strings in general
relativity) which has not not yet seen, but which may be possible.  In
this scenario the universe is well behaved in every local region; only by
exploring the global properties does one discover time travel.

CONSERVATION LAWS:

    It is sometimes argued that time travel violates conservation laws.
For example, sending mass back in time increases the amount of energy that
exists at that time.  Doesn't this violate conservation of energy?  This
argument uses the concept of a global conservation law, whereas
relativistically invariant formulations of the equations of physics only
imply local conservation.  A local conservation law tells us that the
amount of stuff inside a small volume changes only when stuff flows in or
out through the surface.  A global conservation law is derived from this by
integrating over all space and assuming that there is no flow in or out at
infinity.  If this integral cannot be performed, then global conservation
does not follow.  So, sending mass back in time might be alright, but it
implies that something strange is happening.  (Why shouldn't we be able to
do the integral?)

GENERAL RELATIVITY:

    One case where global conservation breaks down is in general
relativity. It is well known that global conservation of energy does not
make sense in an expanding universe.  For example, the universe cools as it
expands; where does the energy go?  See FAQ article #1 - Energy
Conservation in Cosmology, for details.

    It is interesting to note that the possibility of time travel in GR
has been known at least since 1949 (by Kurt Godel, discussed in [1], page
168). The GR spacetime found by Godel has what are now called "closed
timelike curves" (CTCs).  A CTC is a worldline that a particle or a person
can follow which ends at the same spacetime point (the same position and
time) as it started.   A solution to GR which contains CTCs cannot have a
spacelike embedding - space must have "holes" (as in donut holes, not holes
punched in a sheet of paper).  A would-be time traveller must go around or
through the holes in a clever way.

    The Godel solution is a curiosity, not useful for constructing a
time machine.  Two recent proposals, one by Morris, et al. [2] and one by
Gott [3], have the possibility of actually leading to practical devices (if
you believe this, I have a bridge to sell you).   As with Godel, in these
schemes nothing is locally strange; time travel results from the unusual
topology of spacetime.  The first uses a wormhole (the inner part of a
black hole, see fig. 1 of [2]) which is held open and manipulated by
electromagnetic forces.  The second uses the conical geometry generated by
an infinitely long string of mass.  If two strings pass by each other, a
clever person can go into the past by traveling a figure-eight path around
the strings.  In this scenario, if the string has non-zero diameter and
finite mass density, there is a CTC without any unusual topology.

GRANDFATHER PARADOXES:

    With the demonstration that general relativity contains CTCs,
people began studying the problem of self-consistency.  Basically, the
problem is that of the "grandfather paradox:"  What happens if our time
traveller kills her grandmother before her mother was born?  In more
readily analyzable terms, one can ask what are the implications of the
quantum mechanical interference of the particle with its future self.
Boulware [5] shows that there is a problem - unitarity is violated. This is
related to the question of when one can do the global conservation integral
discussed above.  It is an example of the "Cauchy problem" [1, chapter 7].

OTHER PROBLEMS (and an escape hatch?):

    How does one avoid the paradox that a simple solution to GR has
CTCs which QM does not like?  This is not a matter of applying a theory in
a domain where it is expected to fail.  One relevant issue is the
construction of the time machine.  After all, infinite strings aren't
easily obtained.  In fact, it has been shown [4] that Gott's scenario
implies that the total 4-momentum of spacetime must be spacelike.  This
seems to imply that one cannot build a time machine from any collection of
non-tachyonic objects, whose 4-momentum must be timelike.  There are
implementation problems with the wormhole method as well.

TACHYONS:

Finally, a diversion on a possibly related topic.

    If tachyons exist as physical objects, causality is no longer
invariant. Different observers will see different causal sequences.  This
effect requires only special relativity (not GR), and follows from the fact
that for any spacelike trajectory, reference frames can be found in which
the particle moves backward or forward in time.  This is illustrated by the
pair of spacetime diagrams below.  One must be careful about what is
actually observed; a particle moving backward in time is observed to be a
forward moving anti-particle, so no observer interprets this as time
travel.

                t
One reference   |                    Events A and C are at the same
frame:          |                    place.  C occurs first.
                |
                |                    Event B lies outside the causal
                |          B         domain of events A and C.
     -----------A----------- x       (The intervals are spacelike).
                |
                C                    In this frame, tachyon signals
                |                    travel from A-->B and from C-->B.
                |                    That is, A and C are possible causes
                                     of event B.

Another         t
reference       |                    Events A and C are not at the same
frame:          |                    place.  C occurs first.
                |
                |                    Event B lies outside the causal
     -----------A----------- x       domain of events A and C. (The
                |                    intervals are spacelike)
                |
                |   C                In this frame, signals travel from
                |                    B-->A and from B-->C.  B is the cause
                |             B      of both of the other two events.

    The unusual situation here arises because conventional causality
assumes no superluminal motion.  This tachyon example is presented to
demonstrate that our intuitive notion of causality may be flawed, so one
must be careful when appealing to common sense.  See FAQ article # 6 -
Tachyons, for more about these weird hypothetical particles.

CONCLUSION:

    The possible existence of time machines remains an open question.
None of the papers criticizing the two proposals are willing to
categorically rule out the possibility.  Nevertheless, the notion of time
machines seems to carry with it a serious set of problems.

REFERENCES:

1: S.W. Hawking, and G.F.R. Ellis, "The Large Scale Structure of Space-Time,"
   Cambridge University Press, 1973.
2: M.S. Morris, K.S. Thorne, and U. Yurtsever, PRL, v.61, p.1446 (1989).
   --> How wormholes can act as time machines.
3: J.R. Gott, III, PRL, v.66, p.1126 (1991).
   --> How pairs of cosmic strings can act as time machines.
4: S. Deser, R. Jackiw, and G. 't Hooft, PRL, v.66, p.267 (1992).
   --> A critique of Gott.  You can't construct his machine.
5: D.G. Boulware, University of Washington preprint UW/PT-92-04.
   Available on the [e-mail] bulletin board: item number 9207054.
   --> Unitarity problems in QM with closed timelike curves.
6: "Nature", May 7, 1992
   --> Contains a very well written review with some nice figures.

********************************************************************************
Item 23.

The EPR Paradox and Bell's Inequality Principle    updated 31-AUG-1993 by SIC
-----------------------------------------------    original by John Blanton

    In 1935 Albert Einstein and two colleagues, Boris Podolsky and
Nathan Rosen (EPR) developed a thought experiment to demonstrate what they
felt was a lack of completeness in quantum mechanics.  This so-called "EPR
paradox" has lead to much subsequent, and still on-going, research. This
article is an introduction to EPR, Bell's inequality, and the real
experiments which have attempted to address the interesting issues raised
by this discussion.

    One of the principle features of quantum mechanics is that not all
the classical physical observables of a system can be simultaneously known,
either in practice or in principle.  Instead, there may be several sets of
observables which give qualitatively different, but nonetheless complete
(maximal possible) descriptions of a quantum mechanical system.  These sets
are sets of "good quantum numbers," and are also known as "maximal sets of
commuting observables."  Observables from different sets are "noncommuting
observables."

    A well known example of noncommuting observables are position and
momentum.  You can put a subatomic particle into a state of well-defined
momentum, but then you cannot know where it is - it is, in fact, everywhere
at once.  It's not just a matter of your inability to measure, but rather,
an intrinsic property of the particle.  Conversely, you can put a particle
in a definite position, but then it's momentum is completely ill-defined.
You can also create states of intermediate knowledge of both observables:
If you confine the particle to some arbitrarily large region of space,
you can define the momentum more and more precisely.  But you can never
know both, exactly, at the same time.

    Position and momentum are continuous observables.  But the same
situation can arise for discrete observables such as spin.  The quantum
mechanical spin of a particle along each of the three space axes are a set
of mutually noncommuting observables.  You can only know the spin along one
axis at a time.  A proton with spin "up" along the x-axis has undefined
spin along the y and z axes.  You cannot simultaneously measure the x and y
spin projections of a proton. EPR sought to demonstrate that this
phenomenon could be exploited to construct an experiment which would
demonstrate a paradox which they believed was inherent in the
quantum-mechanical description of the world.

    They imagined two physical systems that are allowed to interact
initially so that they subsequently will be defined by a single Schrodinger
wave equation (SWE).   [For simplicity, imagine a simple physical
realization of this idea - a neutral pion at rest in your lab, which decays
into a pair of back-to-back photons.  The pair of photons is described
by a single two-particle wave function.]  Once separated, the two systems
[read: photons] are still described by the same SWE, and a measurement of
one observable of the first system will determine the measurement of the
corresponding observable of the second system.  [Example:  The neutral pion
is a scalar particle - it has zero angular momentum.  So the two photons
must speed off in opposite directions with opposite spin. If photon 1
is found to have spin up along the x-axis, then photon 2 *must* have spin
down along the x-axis, since the total angular momentum of the final-state,
two-photon, system must be the same as the angular momentum of the intial
state, a single neutral pion.  You know the spin of photon 2 even without
measuring it.] Likewise, the measurement of another observable of the first
system will determine the measurement of the corresponding observable of the
second system, even though the systems are no longer physically linked in
the traditional sense of local coupling.

    However, QM prohibits the simultaneous knowledge of more than one
mutually noncommuting observable of either system.  The paradox of EPR is
the following contradiction:  For our coupled systems, we can measure
observable A of system I [for example, photon 1 has spin up along the
x-axis; photon 2 must therefore have x-spin down.] and observable B of
system II [for example, photon 2 has spin down along the y-axis; therefore
the y-spin of photon 1 must be up.] thereby revealing both observables for
both systems, contrary to QM.

    QM dictates that this should be impossible, creating the
paradoxical implication that measuring one system should "poison" any
measurement of the other system, no matter what the distance between
them. [In one commonly studied interpretation, the mechanism by which
this proceeds is 'instantaneous collapse of the wavefunction'.  But
the rules of QM do not require this interpretation, and several
other perfectly valid interpretations exist.]  The second system
would instantaneously be put into a state of well-defined observable A,
and, consequently, ill-defined observable B, spoiling the measurement.
Yet, one could imagine the two measurements were so far apart in
space that special relativity would prohibit any influence of one
measurement over the other.  [After the neutral-pion decay, we can wait until
the two photons are a light-year apart, and then "simultaneously" measure
the x-spin of photon 1 and the y-spin of photon 2.  QM suggests that if,
for example, the measurement of the photon 1 x-spin happens first, this
measurement must instantaneously force photon 2 into a state of ill-defined
y-spin, even though it is light-years away from photon 1.

    How do we reconcile the fact that photon 2 "knows" that the x-spin
of photon 1 has been measured, even though they are separated by
light-years of space and far too little time has passed for information
to have travelled to it according to the rules of Special Relativity?
There are basically two choices.  You can accept the postulates of QM"
as a fact of life, in spite of its seemingly uncomfortable coexistence
with special relativity, or you can postulate that QM is not complete,
that there *was* more information available for the description of the
two-particle system at the time it was created, carried away by both
photons, and that you just didn't know it because QM does not properly
account for it.

    So, EPR postulated the existence of hidden variables, some so-far
unknown properties, of the systems should account for the discrepancy.
Their claim was that QM theory is incomplete; it does not completely
describe the physical reality.  System II knows all about System I
long before the scientist measures any of the observables, and thereby
supposedly consigning the other noncommuting observables to obscurity.
No instantaneous action-at-a-distance is necessary in this picture,
which postulates that each System has more parameters than are
accounted by QM. Niels Bohr, one of the founders of QM, held the opposite
view and defended a strict interpretation, the Copenhagen Interpretation,
of QM.

    In 1964 John S. Bell proposed a mechanism to test for the existence
of these hidden parameters, and he developed his inequality principle as
the basis for such a test.

    Use the example of two photons configured in the singlet state,
consider this:  After separation, each photon will have spin values for
each of the three axes of space, and each spin can have one of two values;
call them up and down.  Call the axes A, B and C and call the spin in the A
axis A+ if it is up in that axis, otherwise call it A-.  Use similar
definitions for the other two axes.

    Now perform the experiment.  Measure the spin in one axis of one
particle and the spin in another axis of the other photon.  If EPR were
correct, each photon will simultaneously have properties for spin in each
of axes A, B and C.

    Look at the statistics.  Perform the measurements with a number of
sets of photons.  Use the symbol N(A+, B-) to designate the words "the
number of photons with A+ and B-."  Similarly for N(A+, B+), N(B-, C+),
etc.  Also use the designation N(A+, B-, C+) to mean "the number of photons
with A+, B- and C+," and so on.  It's easy to demonstrate that for a set of
photons

(1)    N(A+, B-) = N(A+, B-, C+) + N(A+, B-, C-)

because all of the (A+, B-, C+) and all of the (A+, B-, C-) photons are
included in the designation (A+, B-), and nothing else is included in N(A+,
B-).  You can make this claim if these measurements are connected to some
real properties of the photons.

    Let n[A+, B+] be the designation for "the number of measurements of
pairs of photons in which the first photon measured A+, and the second
photon measured B+."  Use a similar designation for the other possible
results.  This is necessary because this is all it is possible to measure.
You can't measure both A and B of the same photon.  Bell demonstrated that
in an actual experiment, if (1) is true (indicating real properties), then
the following must be true:

(2)    n[A+, B+] <= n[A+, C+] + n[B+, C-].

    Additional inequality relations can be written by just making the
appropriate permutations of the letters A, B and C and the two signs.  This
is Bell's inequality principle, and it is proved to be true if there are
real (perhaps hidden) parameters to account for the measurements.

        At the time Bell's result first became known, the experimental
record was reviewed to see if any known results provided evidence against
locality. None did. Thus an effort began to develop tests of Bell's
inequality. A series of experiments was conducted by Aspect ending with one
in which polarizer angles were changed while the photons were `in flight'.
This was widely regarded at the time as being a reasonably conclusive
experiment confirming the predictions of QM.

    Three years later Franson published a paper showing that the timing
constraints in this experiment were not adequate to confirm that locality
was violated. Aspect measured the time delays between detections of photon
pairs. The critical time delay is that between when a polarizer angle is
changed and when this affects the statistics of detecting photon pairs.
Aspect estimated this time based on the speed of a photon and the distance
between the polarizers and the detectors. Quantum mechanics does not allow
making assumptions about *where* a particle is between detections. We
cannot know *when* a particle traverses a polarizer unless we detect the
particle *at* the polarizer.

    Experimental tests of Bell's inequality are ongoing but none has
yet fully addressed the issue raised by Franson. In addition there is an
issue of detector efficiency. By postulating new laws of physics one can
get the expected correlations without any nonlocal effects unless the
detectors are close to 90% efficient. The importance of these issues is a
matter of judgement.

    The subject is alive theoretically as well.  In the 1970's
Eberhard derived Bell's result without reference to local hidden variable
theories; it applies to all local theories.  Eberhard also showed that the
nonlocal effects that QM predicts cannot be used for superluminal
communication.  The subject is not yet closed, and may yet provide more
interesting insights into the subtleties of quantum mechanics.

REFERENCES:

1.  A. Einstein, B. Podolsky, N. Rosen:  "Can quantum-mechanical
description of physical reality be considered complete?"
Physical Review 41, 777 (15 May 1935).  (The original EPR paper)

2.  D. Bohm:  Quantum Theory, Dover, New York (1957).  (Bohm
discusses some of his ideas concerning hidden variables.)

3.  N. Herbert:  Quantum Reality, Doubleday.  (A very good
popular treatment of EPR and related issues)

4.  M. Gardner: Science - Good, Bad and Bogus, Prometheus Books.
(Martin Gardner gives a skeptics view of the fringe science
associated with EPR.)

5.  J. Gribbin:  In Search of Schrodinger's Cat, Bantam Books.
(A popular treatment of EPR and the paradox of "Schrodinger's
cat" that results from the Copenhagen interpretation)

6.  N. Bohr:  "Can quantum-mechanical description of physical
reality be considered  complete?" Physical Review 48, 696 (15 Oct
1935).  (Niels Bohr's response to EPR)

7.  J. Bell:  "On the Einstein Podolsky Rosen paradox" Physics 1
#3, 195 (1964).

8.  J. Bell:  "On the problem of hidden variables in quantum
mechanics" Reviews of  Modern Physics 38 #3, 447 (July 1966).

9.  D. Bohm, J. Bub:  "A proposed solution of the measurement
problem in quantum  mechanics by a hidden variable theory"
Reviews of Modern Physics 38  #3, 453 (July 1966).

10.  B. DeWitt:  "Quantum mechanics and reality" Physics Today p.
30 (Sept 1970).

11.  J. Clauser, A. Shimony:  "Bell's theorem: experimental
tests and implications" Rep.  Prog. Phys. 41, 1881 (1978).

12.  A. Aspect, Dalibard, Roger:  "Experimental test of Bell's
inequalities using time- varying analyzers" Physical Review
Letters 49 #25, 1804 (20 Dec 1982).

13.  A. Aspect, P. Grangier, G. Roger:  "Experimental realization
of Einstein-Podolsky-Rosen-Bohm gedankenexperiment; a new
violation of Bell's inequalities" Physical  Review Letters 49
#2, 91 (12 July 1982).

14.  A. Robinson: "Loophole closed in quantum mechanics test"
Science 219, 40 (7 Jan 1983).

15.  B. d'Espagnat:  "The quantum theory and reality" Scientific
American 241 #5 (November 1979).

16. "Bell's Theorem and Delayed Determinism", Franson, Physical Review D,
pgs. 2529-2532, Vol. 31, No. 10, May 1985.

17. "Bell's Theorem without Hidden Variables", P. H. Eberhard, Il Nuovo
Cimento, 38 B 1, pgs. 75-80, (1977).

18. "Bell's Theorem and the Different Concepts of Locality", P. H.
Eberhard, Il Nuovo Cimento 46 B, pgs. 392-419, (1978).
********************************************************************************
Item 24.

The Nobel Prize for Physics (1901-1993)         updated 15-OCT-1993 by SIC
---------------------------------------

The following is a complete listing of Nobel Prize awards, from the first
award in 1901.  Prizes were not awarded in every year.  The description
following the names is an abbreviation of the official citation.

1901    Wilhelm Konrad Rontgen          X-rays
1902    Hendrik Antoon Lorentz          Magnetism in radiation phenomena
        Pieter Zeeman
1903    Antoine Henri Bequerel          Spontaneous radioactivity
        Pierre Curie
        Marie Sklowdowska-Curie
1904    Lord Rayleigh                   Density of gases and
        (a.k.a. John William Strutt)     discovery of argon
1905    Pilipp Eduard Anton von Lenard  Cathode rays
1906    Joseph John Thomson             Conduction of electricity by gases
1907    Albert Abraham Michelson        Precision metrological investigations
1908    Gabriel Lippman                 Reproducing colors photographically
                                         based on the phenomenon of interference
1909    Guglielmo Marconi               Wireless telegraphy
        Carl Ferdinand Braun
1910    Johannes Diderik van der Waals  Equation of state of fluids
1911    Wilhelm Wien                    Laws of radiation of heat
1912    Nils Gustaf Dalen               Automatic gas flow regulators
1913    Heike Kamerlingh Onnes          Matter at low temperature
1914    Max von Laue                    Crystal diffraction of X-rays
1915    William Henry Bragg             X-ray analysis of crystal structure
        William Lawrence Bragg
1917    Charles Glover Barkla           Characteristic X-ray spectra of elements
1918    Max Planck                      Energy quanta
1919    Johannes Stark                  Splitting of spectral lines in E fields
1920    Charles-Edouard Guillaume       Anomalies in nickel steel alloys
1921    Albert Einstein                 Photoelectric Effect
1922    Niels Bohr                      Structure of atoms
1923    Robert Andrew Millikan          Elementary charge of electricity
1924    Karl Manne Georg Siegbahn       X-ray spectroscopy
1925    James Franck                    Impact of an electron upon an atom
        Gustav Hertz
1926    Jean Baptiste Perrin            Sedimentation equilibrium
1927    Arthur Holly Compton            Compton effect
        Charles Thomson Rees Wilson     Invention of the Cloud chamber
1928    Owen Willans Richardson         Thermionic phenomena, Richardson's Law
1929    Prince Louis-Victor de Broglie  Wave nature of electrons
1930    Sir Chandrasekhara Venkata Raman Scattering of light, Raman effect
1932    Werner Heisenberg               Quantum Mechanics
1933    Erwin Schrodinger               Atomic theory
        Paul Adrien Maurice Dirac
1935    James Chadwick                  The neutron
1936    Victor Franz Hess               Cosmic rays
    Carl D. Anderson        The positron
1937    Clinton Joseph Davisson         Crystal diffraction of electrons
        George Paget Thomson
1938    Enrico Fermi                    New radioactive elements
1939    Ernest Orlando Lawrence         Invention of the Cyclotron
1943    Otto Stern                      Proton magnetic moment
1944    Isador Isaac Rabi               Magnetic resonance in atomic nuclei
1945    Wolfgang Pauli                  The Exclusion principle
1946    Percy Williams Bridgman         Production of extremely high pressures
1947    Sir Edward Victor Appleton      Physics of the upper atmosphere
1948    Patrick Maynard Stuart Blackett Cosmic ray showers in cloud chambers
1949    Hideki Yukawa                   Prediction of Mesons
1950    Cecil Frank Powell              Photographic emulsion for meson studies
1951    Sir John Douglas Cockroft       Artificial acceleration of atomic
        Ernest Thomas Sinton Walton      particles and transmutation of nuclei
1952    Felix Bloch                     Nuclear magnetic precision methods
        Edward Mills Purcell
1953    Frits Zernike                   Phase-contrast microscope
1954    Max Born                        Fundamental research in QM
        Walther Bothe                   Coincidence counters
1955    Willis Eugene Lamb              Hydrogen fine structure
        Polykarp Kusch                  Electron magnetic moment
1956    William Shockley                Transistors
        John Bardeen
        Walter Houser Brattain
1957    Chen Ning Yang                  Parity violation
        Tsung Dao Lee
1958    Pavel Aleksejevic Cerenkov      Interpretation of the Cerenkov effect
        Il'ja Mickajlovic Frank
        Igor' Evgen'evic Tamm
1959    Emilio Gino Segre               The Antiproton
        Owen Chamberlain
1960    Donald Arthur Glaser            The Bubble Chamber
1961    Robert Hofstadter               Electron scattering on nucleons
        Rudolf Ludwig Mossbauer         Resonant absorption of photons
1962    Lev Davidovic Landau            Theory of liquid helium
1963    Eugene P. Wigner                Fundamental symmetry principles
        Maria Goeppert Mayer            Nuclear shell structure
        J. Hans D. Jensen
1964    Charles H. Townes               Maser-Laser principle
        Nikolai G. Basov
        Alexander M. Prochorov
1965    Sin-Itiro Tomonaga              Quantum electrodynamics
        Julian Schwinger
        Richard P. Feynman
1966    Alfred Kastler                  Study of Hertzian resonance in atoms
1967    Hans Albrecht Bethe             Energy production in stars
1968    Luis W. Alvarez                 Discovery of many particle resonances
1969    Murray Gell-Mann                Quark model for particle classification
1970    Hannes Alfven                   Magneto-hydrodynamics in plasma physics
        Louis Neel                      Antiferromagnetism and ferromagnetism
1971    Dennis Gabor                    Principles of holography
1972    John Bardeen                    Superconductivity
        Leon N. Cooper
        J. Robert Schrieffer
1973    Leo Esaki                       Tunneling in superconductors
        Ivar Giaever
        Brian D. Josephson              Super-current through tunnel barriers
1974    Antony Hewish                   Discovery of pulsars
        Sir Martin Ryle                 Pioneering radioastronomy work
1975    Aage Bohr                       Structure of the atomic nucleus
        Ben Mottelson
        James Rainwater
1976    Burton Richter                  Discovery of the J/Psi particle
        Samual Chao Chung Ting
1977    Philip Warren Anderson          Electronic structure of magnetic and
        Nevill Francis Mott             disordered solids
        John Hasbrouck Van Vleck
1978    Pyotr Kapitsa                   Liquifaction of helium
        Arno A. Penzias                 Cosmic Microwave Background Radiation
        Robert W. Wilson
1979    Sheldon Glashow                 Electroweak Theory, especially
        Steven Weinberg                  weak neutral currents
        Abdus Salam
1980    James Cronin                    Discovery of CP violation in the
        Val Fitch                        asymmetric decay of neutral K-mesons
1981    Kai M. Seigbahn                 High resolution electron spectroscopy
        Nicolaas Bleombergen            Laser spectroscopy
        Arthur L. Schawlow
1982    Kenneth G. Wilson               Critical phenomena in phase transitions
1983    Subrahmanyan Chandrasekhar      Evolution of stars
        William A. Fowler
1984    Carlo Rubbia                    Discovery of W,Z
        Simon van der Meer              Stochastic cooling for colliders
1985    Klaus von Klitzing              Discovery of quantum Hall effect
1986    Gerd Binning                    Scanning Tunneling Microscopy
        Heinrich Rohrer
        Ernst August Friedrich Ruska    Electron microscopy
1987    Georg Bednorz                   High-temperature superconductivity
        Alex K. Muller
1988    Leon Max Lederman               Discovery of the muon neutrino leading
        Melvin Schwartz                  to classification of particles in
        Jack Steinberger                 families
1989    Hans Georg Dehmelt              Penning Trap for charged particles
        Wolfgang Paul                   Paul Trap for charged particles
        Norman F. Ramsey                Control of atomic transitions by the
                                         separated oscillatory fields method
1990    Jerome Isaac Friedman           Deep inelastic scattering experiments
        Henry Way Kendall                leading to the discovery of quarks
        Richard Edward Taylor
1991    Pierre-Gilles de Gennes         Order-disorder transitions in liquid
                                         crystals and polymers
1992    Georges Charpak                 Multiwire Proportional Chamber
1993    Russell A. Hulse                Discovery of the first binary pulsar
        Joseph H. Taylor                 and subsequent tests of GR

********************************************************************************
Item 25.

Open Questions                                  updated 01-JUN-1993 by SIC
--------------                                  original by John Baez

    While for the most part a FAQ covers the answers to frequently
asked questions whose answers are known, in physics there are also plenty
of simple and interesting questions whose answers are not known. Before you
set about answering these questions on your own, it's worth noting that
while nobody knows what the answers are, there has been at least a little,
and sometimes a great deal, of work already done on these subjects. People
have said a lot of very intelligent things about many of these questions.
So do plenty of research and ask around before you try to cook up a theory
that'll answer one of these and win you the Nobel prize!  You can expect to
really know physics inside and out before you make any progress on these.

    The following partial list of "open" questions is divided into two
groups, Cosmology and Astrophysics, and Particle and Quantum Physics.
However, given the implications of particle physics on cosmology, the
division is somewhat artificial, and, consequently, the categorization is
somewhat arbitrary.

    (There are many other interesting and fundamental questions in
fields such as condensed matter physics, nonlinear dynamics, etc., which
are not part of the set of related questions in cosmology and quantum
physics which are discussed below.  Their omission is not a judgement
about importance, but merely a decision about the scope of this article.)

Cosmology and Astrophysics
--------------------------

1.  What happened at, or before the Big Bang?  Was there really an initial
singularity?  Of course, this question might not make sense, but it might.
Does the history of universe go back in time forever, or only a finite
amount?

2.  Will the future of the universe go on forever or not?  Will there be a
"big crunch" in the future?  Is the Universe infinite in spatial extent?

3.  Why is there an arrow of time; that is, why is the future so much
different from the past?

4.  Is spacetime really four-dimensional?   If so, why - or is that just a
silly question?  Or is spacetime not really a manifold at all if examined
on a short enough distance scale?

5.  Do black holes really exist?  (It sure seems like it.)  Do they really
radiate energy and evaporate the way Hawking predicts?  If so, what happens
when, after a finite amount of time, they radiate completely away?  What's
left?  Do black holes really violate all conservation laws except
conservation of energy, momentum, angular momentum and electric charge?
What happens to the information contained in an object that falls into a
black hole?  Is it lost when the black hole evaporates?  Does this require
a modification of quantum mechanics?

6.  Is the Cosmic Censorship Hypothesis true?  Roughly, for generic
collapsing isolated gravitational systems are the singularities that might
develop guaranteed to be hidden beyond a smooth event horizon?  If Cosmic
Censorship fails, what are these naked singularities like?  That is, what
weird physical consequences would they have?

7.  Why are the galaxies distributed in clumps and filaments?  Is most of
the matter in the universe baryonic?  Is this a matter to be resolved by
new physics?

8.  What is the nature of the missing "Dark Matter"?  Is it baryonic,
neutrinos, or something more exotic?

Particle and Quantum Physics
----------------------------

1.  Why are the laws of physics not symmetrical between left and right,
future and past, and between matter and antimatter?  I.e., what is the
mechanism of CP violation, and what is the origin of parity violation in
Weak interactions?  Are there right-handed Weak currents too weak to have
been detected so far?  If so, what broke the symmetry?  Is CP violation
explicable entirely within the Standard Model, or is some new force or
mechanism required?

2.  Why are the strengths of the fundamental forces (electromagnetism, weak
and strong forces, and gravity) what they are?  For example, why is the
fine structure constant, which measures the strength of electromagnetism,
about 1/137.036?  Where did this dimensionless constant of nature come from?
Do the forces really become Grand Unified at sufficiently high energy?

3.  Why are there 3 generations of leptons and quarks?  Why are there mass
ratios what they are?  For example, the muon is a particle almost exactly
like the electron except about 207 times heavier.  Why does it exist and
why precisely that much heavier?   Do the quarks or leptons have any
substructure?

4.  Is there a consistent and acceptable relativistic quantum field theory
describing interacting (not free) fields in four spacetime dimensions?  For
example, is the Standard Model mathematically consistent?  How about
Quantum Electrodynamics?

5.  Is QCD a true description of quark dynamics?  Is it possible to
calculate masses of hadrons (such as the proton, neutron, pion, etc.)
correctly from the Standard Model?  Does QCD predict a quark/gluon
deconfinement phase transition at high temperature?  What is the nature of
the transition?  Does this really happen in Nature?

6.  Why is there more matter than antimatter, at least around here? Is
there really more matter than antimatter throughout the universe?

7.  What is meant by a "measurement" in quantum mechanics?  Does
"wavefunction collapse" actually happen as a physical process?  If so, how,
and under what conditions?  If not, what happens instead?

8.  What are the gravitational effects, if any, of the immense (possibly
infinite) vacuum energy density seemingly predicted by quantum field
theory?  Is it really that huge?  If so, why doesn't it act like an
enormous cosmological constant?

9.  Why doesn't the flux of solar neutrinos agree with predictions?  Is the
disagreement really significant?  If so, is the discrepancy in models of
the sun, theories of nuclear physics, or theories of neutrinos?  Are
neutrinos really massless?

The Big Question (TM)
---------------------

This last question sits on the fence between the two categories above:

    How do you merge Quantum Mechanics and General Relativity to create a
quantum theory of gravity?  Is Einstein's theory of gravity (classical GR)
also correct in the microscopic limit, or are there modifications
possible/required which coincide in the observed limit(s)?  Is gravity
really curvature, or what else -- and why does it then look like curvature?
An answer to this question will necessarily rely upon, and at the same time
likely be a large part of, the answers to many of the other questions above.

********************************************************************************
Item 26.                                        updated 24-MAY-1993 by SIC

Accessing and Using Online Physics Resources
--------------------------------------------

(I) Particle Physics Databases

    The Full Listings of the Review of Particle Properties (RPP), as
well as other particle physics databases, are accessible on-line.  Here is
a summary of the major ones, as described in the RPP:

(A) SLAC Databases

PARTICLES   - Full listings of the RPP
HEP         - Guide to particle physics preprints, journal articles, reports,
              theses, conference papers, etc.
CONF        - Listing of past and future conferences in particle physics
HEPNAMES    - E-mail addresses of many HEP people
INST        - Addresses of HEP institutions
DATAGUIDE   - Adjunct to HEP, indexes papers
REACTIONS   - Numerical data on reactions (cross-sections, polarizations, etc)
EXPERIMENTS - Guide to current and past experiments

Anyone with a SLAC account can access these databases.  Alternately, most
of us can access them via QSPIRES.  You can access QSPIRES via BITNET with
the 'send' command ('tell','bsend', or other system-specific command) or by
using E-mail.  For example, send QSPIRES@SLACVM FIND TITLE Z0 will get you
a search of HEP for all papers which reference the Z0 in the title.  By
E-mail, you would send the one line message "FIND TITLE Z0" with a blank
subject line to [e-mail] or [e-mail].
QSPIRES is free.  Help can be obtained by mailing "HELP" to QSPIRES.

For more detailed information, see the RPP, p.I.12, or contact: Louise
Addis ([e-mail]) or Harvey Galic ([e-mail]).

(B) CERN Databases on ALICE

LIB         - Library catalogue of books, preprints, reports, etc.
PREP        - Subset of LIB containing preprints, CERN publications, and
              conference papers.
CONF        - Subset of LIB containing upcoming and past conferences since 1986
DIR         - Directory of Research Institutes in HEP, with addresses, fax,
              telex, e-mail addresses, and info on research programs

ALICE can be accessed via DECNET or INTERNET.  It runs on the CERN library's
VXLIB, alias ALICE.CERN.CH (IP# 128.141.201.44).  Use Username ALICE (no
password required.)  Remote users with no access to the CERN Ethernet can
use QALICE, similar to QSPIRES.  Send E-mail to [e-mail], put
the query in the subject field and leave the message field black.  For
more information, send the subject "HELP" to QALICE or contact CERN
Scientific Information Service, CERN, CH-1211 Geneva 23, Switzerland,
or E-mail [e-mail].

Regular weekly or monthly searches of the CERN databases can be arranged
according to a personal search profile.  Contact David Dallman, CERN SIS
(address above) or E-mail [e-mail].

DIR is available in Filemaker PRO format for Macintosh.  Contact Wolfgang
Simon ([e-mail]).

(C) Particle Data Group Online Service

    The Particle Data Group is maintaining a new user-friendly computer
database of the Full Listings from the Review of Particle Properties. Users
may query by paper, particle, mass range, quantum numbers, or detector and
can select specific properties or classes of properties like masses or
decay parameters. All other relevant information (e.g. footnotes and
references) is included. Complete instructions are available online.

    The last complete update of the RPP database was a copy of the Full
Listings from the Review of Particle Properties which was published as
Physical Review D45, Part 2 (1 June 1992). A subsequent update made on 27
April 1993 was complete for unstable mesons, less complete for the W, Z, D
mesons, and stable baryons, and otherwise was unchanged from the 1992
version.

DECNET access: SET HOST MUSE or SET HOST 42062
TCP/IP access: TELNET MUSE.LBL.GOV or TELNET 131.243.48.11
Login to: PDG_PUBLIC with password HEPDATA.

Contact: Gary S. Wagman, [phone].  Email: ([e-mail]).

(D) Other Databases

Durham-RAL and Serpukhov both maintain large databases containing Particle
Properties, reaction data, experiments, E-mail ID's, cross-section
compilations (CS), etc.  Except for the Serpukhov CS, these databases
overlap SPIRES at SLAC considerably, though they are not the same and may
be more up-to-date.  For details, see the RPP, p.I.14, or contact:
For Durham-RAL, Mike Whalley ([e-mail],[e-mail]) or
Dick Roberts ([e-mail]).  For Serpukhov, contact Sergey Alekhin
([e-mail]) or Vladimir Exhela ([e-mail]).

(II) Online Preprint Sources

There are a number of online sources of preprints:

[e-mail] (algebraic geometry)
[e-mail]           (astrophysics)
[e-mail]           (condensed matter)
[e-mail]           (functional analysis)
[e-mail]            (computational and lattice physics)
[e-mail]                 (high energy physics phenomenological)
[e-mail]                 (high energy physics theoretical)
[e-mail]              (liquid crystals, optical materials)
[e-mail]                  (general relativity, quantum cosmology)
[e-mail],               (nuclear physics theory)
[e-mail]               (nonlinear science)

    To get things if you know the preprint number, send a message to
the appropriate address with subject header "get (preprint number)" and
no message body. If you *don't* know the preprint number, or want to get
preprints regularly, or want other information, send a message with
subject header "help" and no message body.

(III) The World Wide Web

    There is a wealth of information, on all sorts of topics, available
on the World Wide Web [WWW], a distributed HyperText system (a network of
documents connected by links which can be activated electronically).
Subject matter includes some physics areas such as High Energy Physics,
Astrophysics abstracts, and Space Science, but also includes such diverse
subjects as bioscience, musics, and the law.

* How to get to the Web

       If you have no clue what WWW is, you can go over the Internet with
telnet to info.cern.ch (no login required) which brings you to the WWW
Home Page at CERN. You are now using the simple line mode browser. To move
around the Web, enter the number given after an item.

* Browsing the Web

    If you have a WWW browser up and running, you can move around
more easily. The by far nicest way of "browsing" through WWW uses the
X-Terminal based tool "XMosaic". Binaries for many platforms (ready for use)
and sources are available via anonymous FTP from ftp.ncsa.uiuc.edu in directory
Web/xmosaic.  The general FTP repository for browser software is info.cern.ch
(including a hypertext browser/editor for NeXTStep 3.0)

* For Further Information

    For questions related to WWW, try consulting the WWW-FAQ: Its most
recent version is available via anonymous FTP on rtfm.mit.edu in
/pub/usenet/news.answers/www-faq , or on WWW at
http://www.vuw.ac.nz:80/overseas/www-faq.html

    The official contact (in fact the midwife of the World Wide Web)
is Tim Berners-Lee, [e-mail]. For general matters on WWW, try
[e-mail] or Robert Cailliau (responsible for the "physics"
content of the Web, [e-mail]).

(IV) Other Archive Sites

    There is an FTP archive site of preprints and programs
for nonlinear dynamics, signal processing, and related subjects on node
lyapunov.ucsd.edu (132.239.86.10) at the Institute for Nonlinear Science,
UCSD.  Just login anonymously, using your host id as your password. Contact
Matt Kennel ([e-mail]) for more information.

********************************************************************************
END OF FAQ