From: harigaya@etl.go.jp (Kikuo Harigaya)
Subject: Sci.Physics Frequently Asked Questions - January 1993 - Part 2/2
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Date: Wed, 30 Dec 1992 20:58:28 GMT

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 	      FREQUENTLY ASKED QUESTIONS ON SCI.PHYSICS - Part 2/2
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Item 12.

Which Way Will my Bathtub Drain? 		updated 11-May-1192 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 high pressure storm systems spin clockwise.
In the southern hemisphere, they spin counterclockwise 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".  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. 

	Therefore 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.

	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 13.

Why are Golf Balls Dimpled?			updated 14-May-1992 by SIC
---------------------------			original by Craig DeForest

	The dimples, paradoxically, *do* increase drag slightly.  But they 
also increase `Magnus lift', that peculiar lifting force experienced by 
rotating bodies travelling through a medium.  Contrary to Freshman physics, 
golf balls do not travel in inverted parabolas.  They follow an 'impetus 
trajectory':

                                    *    *       
                              *             *
(golfer)                *                    *
                  *                          * <-- trajectory
 \O/        *                                *
  |   *                                      *
-/ \-T---------------------------------------------------------------ground

	This is because of the combination of drag (which reduces
horizontal speed late in the trajectory) and Magnus lift, which supports
the ball during the initial part of the trajectory, making it relatively
straight.  The trajectory can even curve upwards at first, depending on
conditions!  Here is a cheesy diagram of a golf ball in flight, with some
relevant vectors: 

                             F(magnus)
                             ^
                             |
                F(drag) <--- O -------> V 
                          \     
                           \----> (sense of rotation)

	The Magnus force can be thought of as due to the relative drag on
the air on the top and bottom portions of the golf ball: the top portion is
moving slower relative to the air around it, so there is less drag on the
air that goes over the ball.  The boundary layer is relatively thin, and
air in the not-too-near region moves rapidly relative to the ball.  The
bottom portion moves fast relative to the air around it; there is more drag
on the air passing by the bottom, and the boundary (turbulent) layer is
relatively thick; air in the not-too-near region moves more slowly relative
to the ball. The Bernoulli force produces lift. (alternatively, one could
say that `the flow lines past the ball are displaced down, so the ball is
pushed up.') 

	The difficulty comes near the transition region between laminar
flow and turbulent flow.  At low speeds, the flow around the ball is
laminar.  As speed is increased, the bottom part tends to go turbulent
*first*.  But turbulent flow can follow a surface much more easily than
laminar flow. 

	As a result, the (laminar) flow lines around the top break away
from the surface sooner than otherwise, and there is a net displacement
*up* of the flow lines.  The magnus lift goes *negative*. 

	The dimples aid the rapid formation of a turbulent boundary layer
around the golf ball in flight, giving more lift.  Without 'em, the ball
would travel in more of a parabolic trajectory, hitting the ground sooner.
(and not coming straight down.) 

a paper in American Journal of Physics by one Lyman Briggs, c. 1947. 
Briggs was trying to explain the mechanism behind the `curve ball' in
baseball, using specialized apparatus in a wind tunnel at the NBS.  He
stumbled on the reverse effect by accident, because his model `baseball'
had no stitches on it. The stitches on a baseball create turbulence in
flight in much the same way that the dimples on a golf ball do. 

********************************************************************************
Item 14.

Why do Mirrors Reverse Left and Right?        	updated 11-JUN-1992 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.  The further behind you an object is,
the further in front of you it appears in the mirror.  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 15.

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 16.
						updated 4-SEP-1992 by SIC
						Original by Bill Johnson
How to Change Nuclear Decay Rates
---------------------------------

"I've had this idea for making radioactive nuclei decay faster/slower than
they normally do.  You do [this, that, and the other thing].  Will this work?" 

Short Answer: Possibly, but probably not usefully.

Long Answer:

	"One of the paradigms of nuclear science since the very early days
of its study has been the general understanding that the half-life, or
decay constant, of a radioactive substance is independent of extranuclear
considerations."  (Emery, cited below.)  Like all paradigms, this one is
subject to some interpretation. Normal decay of radioactive stuff proceeds
via one of four mechanisms: 

	* Emission of an alpha particle -- a helium-4 nucleus -- reducing
	the number of protons and neutrons present in the parent nucleus 
	by two each; 
	* "Beta decay," encompassing several related phenomena in which a
	neutron in the nucleus turns into a proton, or a proton turns into 
	a neutron -- along with some other things including emission of 
	a neutrino.  The "other things", as we shall see, are at the bottom
	of several questions involving perturbation of decay rates; 
	* Emission of one or more gamma rays -- energetic photons -- that
	take a nucleus from an excited state to some other (typically
	ground) state; some of these photons may be replaced by 
	"conversion electrons," of which more shortly; or 
	*Spontaneous fission, in which a sufficiently heavy nucleus simply
	breaks in half.  Most of the discussion about alpha particles will
	also apply to spontaneous fission.

Gamma emission often occurs from the daughter of one of the other decay
modes.  We neglect *very* exotic processes like C-14 emission or double
beta decay in this analysis. 

	"Beta decay" refers most often to a nucleus with a neutron excess,
which decays by converting a neutron into a proton:

	n ----> p + e- + anti-nu(e),

where n means neutron, p means proton, e- means electron, and anti-nu(e) 
means an antineutrino of the electron type.  The type of beta decay which
involves destruction of a proton is not familiar to many people, so
deserves a little elaboration.  Either of two processes may occur when this
kind of decay happens: 

	p ----> n + e+ + nu(e), 

where e+ means positron and nu(e) means electron neutrino; or

	p + e- ----> n + nu(e),

where e- means a negatively charged electron, which is captured from the
neighborhood of the nucleus undergoing decay.  These processes are called
"positron emission" and "electron capture," respectively.  A given nucleus
which has too many protons for stability may undergo beta decay through
either, and typically both, of these reactions. 

	"Conversion electrons" are produced by the process of "internal
conversion," whereby the photon that would normally be emitted in gamma
decay is *virtual* and its energy is absorbed by an atomic electron.  The
absorbed energy is sufficient to unbind the electron from the nucleus
(ignoring a few exceptional cases), and it is ejected from the atom as a
result. 

	Now for the tie-in to decay rates.  Both the electron-capture and
internal conversion phenomena require an electron somewhere close to the
decaying nucleus.  In any normal atom, this requirement is satisfied in
spades: the innermost electrons are in states such that their probability
of being close to the nucleus is both large and insensitive to things in
the environment.  The decay rate depends on the electronic wavefunctions,
i.e, how much of their time the inner electrons spend very near the 
nucleus -- but only very weakly. For most nuclides that decay by electron 
capture or internal conversion, most of the time, the probability of 
grabbing or converting an electron is also insensitive to the environment, 
as the innermost electrons are the ones most likely to get grabbed/converted. 

	However, there are exceptions, the most notable being the
the astrophysically important isotope beryllium-7.  Be-7 decays purely
by electron capture (positron emission being impossible because of
inadequate decay energy) with a half-life of somewhat over 50 days.  It has
been shown that differences in chemical environment result in half-life
variations of the order of 0.2%, and high pressures produce somewhat
similar changes. Other cases where known changes in decay rate occur are
Zr-89 and Sr-85, also electron capturers; Tc-99m ("m" implying an excited
state), which decays by both beta and gamma emission; and various other
"metastable" things that decay by gamma emission with internal conversion. 
With all of these other cases the magnitude of the effect is less than is
typically the case with Be-7. 

	What makes these cases special?  The answer is that one or another
of the usual starting assumptions -- insensitivity of electron wave
function near the nucleus to external forces, or availability of the
innermost electrons for capture/conversion -- are not completely valid. 
Atomic beryllium only has 4 electrons to begin with, so that the "innermost
electrons" are also practically the *outermost* ones and therefore much
more sensitive to chemical effects than usual.  With most of the other
cases, there is so little energy available from the decay (as little as a
few electron volts; compare most radioactive decays, where hundreds or
thousands of *kilo*volts are released), courtesy of accidents of nuclear
structure, that the innermost electrons can't undergo internal conversion. 
Remember that converting an electron requires dumping enough energy into it
to expel it from the atom (more or less); "enough energy," in context, is
typically some tens of keV, so they don't get converted at all in these
cases.  Conversion therefore works only on some of the outer electrons,
which again are more sensitive to the environment. 

	A real anomaly is the beta emitter Re-187.  Its decay energy is
only about 2.6 keV, practically nothing by nuclear standards.  "That this
decay occurs at all is an example of the effects of the atomic environment
on nuclear decay: the bare nucleus Re-187 [i.e., stripped of all orbital
electrons -- MWJ] is stable against beta decay and it is the difference of
15 keV in the total electronic binding energy of osmium [to which it decays
-- MWJ] and rhenium ... which makes the decay possible" (Emery).  The
practical significance of this little peculiarity, of course, is low, as
Re-187 already has a half life of over 10^10 years. 

	Alpha decay and spontaneous fission might also be affected by
changes in the electron density near the nucleus, for a different reason. 
These processes occur as a result of penetration of the "Coulomb barrier"
that inhibits emission of charged particles from the nucleus, and their
rate is *very* sensitive to the height of the barrier.  Changes in the
electron density could, in principle, affect the barrier by some tiny
amount.  However, the magnitude of the effect is *very* small, according to
theoretical calculations; for a few alpha emitters, the change has been
estimated to be of the order of 1 part in 10^7 (!) or less, which would be
unmeasurable in view of the fact that the alpha emitters' half lives aren't
known to that degree of accuracy to begin with. 

	All told, the existence of changes in radioactive decay rates due
to the environment of the decaying nuclei is on solid grounds both
experimentally and theoretically.  But the magnitude of the changes is
nothing to get very excited about. 

Reference: The best review article on this subject is now 20 years old: G.
T. Emery, "Perturbation of Nuclear Decay Rates," Annual Review of Nuclear
Science vol. 22, p. 165 (1972).  Papers describing specific experiments are
cited in that article, which contains considerable arcane math but also
gives a reasonable qualitative "feel" for what is involved. 

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

  Dine, Huet, Singleton & Susskind, Phys.Lett.B257:351 (1991);
  Dine, Leigh, Huet, Linde & Linde, Phys.Rev.D46:550 (1992).

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

TIME TRAVEL - FACT OR FICTION?                  updated 25-Nov-1992
------------------------------			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.  It 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. 

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
physical objects, whose 4-momentum must be timelike unless tachyons exist. 
Similar objections apply to the wormhole method. 

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 hep-th@xxx.lanl.gov bulletin board: item number 9207054.
   --> Unitarity problems in QM with closed timelike curves.

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

Gravity and the Radiation of Charged Particles  updated 26-DEC-1992 by SIC
----------------------------------------------	original by Kurt Sonnenmoser

Three oft-asked questions about the Equivalence Principle and the
radiation of charged particles in a gravitational field according to GR:

A)  DOES THE GRAVITATIONAL FIELD OF A STATIC MASSIVE BODY CAUSE
    RADIATION FROM A CHARGED PARTICLE AT REST ON ITS SURFACE?
    (Or: "According to the Equivalence Principle, the electron on my
    desk should radiate!")

    Answer: No, it doesn't. Reason: Static situation --> no magnetic
fields --> vanishing field energy current, i.e. no radiation. The
Equivalence Principle only leads you to the conclusion that if you
put the particle on the bottom of an accelerated elevator in gravity
free space, you will observe no radiation (in the reference frame of
the elevator).

B ) DOES A CHARGED STABLE PARTICLE IN FREE FALL IN THE GRAVITATIONAL
    FIELD OF A MASSIVE BODY RADIATE? (Or: "According to the Equivalence
    Principle, my electron should not radiate if it falls to the
    ground!")

    Answer: Yes, it does. Reason: It's like with any accelerated motion
of a charged particle: The acceleration causes "kinks" in the field
lines that propagate with the velocity of light and carry off
energy. This energy comes from the orbital energy of the particle
and not from its mass. As before, trying to apply the Equivalence
Principle is misleading: the free falling particle is only _locally_
equivalent to one at rest in gravity free space, but in order to
calculate the energy radiated off, you have to integrate the energy
flux of the electromagnetic field over a sphere going to infinity
(in a fixed reference frame), which is, of course, not a local
procedure. The Equivalence Principle only tells you that if you go
very close to the particle, you see no radiation.

C)  DOES A UNIFORMLY ACCELERATED CHARGE RADIATE? (Or: "Ok, let's forget
    about the Equivalence Principle! What happens globally?")

    Answer: David Boulware [Ann.Phys. 124, 169-188 (1980) ("Radiation
from a Uniformly Accelerated Charge")] has shown that a uniformly
accelerated charge in gravity-free space does in fact radiate
(contrary to earlier beliefs, e.g. of Pauli), but also that it is
_not_ globally equivalent to a charge at rest in a static
gravitational field. More specifically, there are regions of
space-time where there is no coordinate frame in which the
accelerated charge is at rest and the gravitational field static. So
there is no contradiction to the fact that charges at rest in a
gravitational field do not radiate.

********************************************************************************
Item 20.

The Nobel Prize for Physics (1901-1992)		updated 29-Nov-1992 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
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 Alven                    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
********************************************************************************
Item 21.

Open Questions					updated 13-OCT-1992 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? 

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 to 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 22.					updated 15-OCT-1992 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 QSPIRES@SLACVM.BITNET or QSPIRES@VM.SLAC.STANFORD.EDU.
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 (ADDIS@SLACVM.BITNET) or Harvey Galic (GALIC@SLACVM.BITNET).

(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 QALICE@VXLIB.CERN.CH, 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 MALICE@VXLIB.CERN.CH.

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 CALLMAN@CERNVM.CERN.CH.

DIR is available in Filemaker PRO format for Macintosh.  Contact Wolfgang
Simon (ISI@CERNVM.CERN.CH).

(C) 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 (MRW@UKACRL.BITNET,MRW@CERNVM.BITNET) or 
Dick Roberts (RGR@UKACRL.BITNET).  For Serpukhov, contact Sergey Alekhin 
(ALEKHIN@M9.IHEP.SU) or Vladimir Exhela (EZHELA@M9.IHEP.SU). 

(II) Online Preprint Sources

There are a number of online sources of preprints:

alg-geom@publications.math.duke.edu (algebraic geometry)
astro-ph@babbage.sissa.it           (astrophysics)
cond-mat@babbage.sissa.it           (condensed matter)
funct-an@babbage.sissa.it           (functional analysis)
hep-lat@ftp.scri.fsu.edu            (computational and lattice physics)
hep-ph@xxx.lanl.gov                 (high energy physics phenomenological)
hep-th@xxx.lanl.gov                 (high energy physics theoretical)
lc-om@alcom-p.cwru.edu              (liquid crystals, optical materials)
gr-qc@xxx.lanl.gov                  (general relativity, quantum cosmology)

	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. 

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


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