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Subject: Sci.Physics Frequently Asked Questions - January 1993 - Part 1/2
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Editor's Note:

The FAQ has expanded beyond the 100K limit set by my mailer.  To facilitate
distribution, as well as future expansion, it has been divided, abritrarily,
into a two-part posting.

--------------------------------------------------------------------------------
           FREQUENTLY ASKED QUESTIONS ON SCI.PHYSICS - Part 1/2
--------------------------------------------------------------------------------

    This Frequently Asked Questions List is posted monthly, at or near
the first of the month, to the Usenet newsgroup sci.physics in an attempt
to provide good answers to frequently asked questions and other reference
material which is worth preserving. If you have corrections or answers to
other frequently asked questions that you would like included in this
posting, send E-mail to [e-mail] (Scott I. Chase).

    The FAQ is distributed to all interested parties whenever sufficient
changes have accumulated to  warrant such a mailing.  To request that your
address be added to the list, send mail to my address, above, and include
the words "FAQ Mailing List" in  the subject header of your message.  To
faciliate mailing, the FAQ is now being distributed as a multi-part posting.

    If you are a new reader of sci.physics, please read item #1, below.
If you do not wish to read the FAQ at all, add "Frequently Asked Questions"
to your .KILL file.

    A listing of new items can be found above the subject index, so
that you can quickly identify new subjects of interest.  To locate old
items which have been updated since the last posting, look for the stars (*)
in the subject index, which indicate new material.

    Items which have been submitted by a single individual are
attributed to the original author.  All other contributors have been thanked
privately.

New Items: 19. Gravity and the Radiation of Charged Particles

Index of Subjects
-----------------
 1. An Introduction to Sci.Physics
 2. Gravitational Radiation
 3. Energy Conservation in Cosmology and Red Shift
 4. Effects Due to the Finite Speed of Light
 5. The Top Quark
 6. Tachyons
 7. Special Relativistic Paradoxes
    (a) The Barn and the Pole
    (b) The Twin Paradox
 8. The Particle Zoo
 9. Olbers' Paradox
10. What is Dark Matter?
11. Hot Water Freezes Faster than Cold!
12. Which Way Will my Bathtub Drain?
13. Why are Golf Balls Dimpled?
14. Why do Mirrors Reverse Left and Right?
15. What is the Mass of a Photon?
16. How to Change Nuclear Decay Rates
17. Baryogenesis - Why Are There More Protons Than Antiprotons?
18. Time Travel - Fact or Fiction?
19.*Gravity and the Radiation of Charged Particles
20. The Nobel Prize for Physics
21. Open Questions
22. Accessing and Using Online Physics Resources

********************************************************************************
Item 1.                        updated 4-AUG-1992 by SIC

An Introduction to Sci.Physics
------------------------------

    Sci.Physics is an unmoderated newsgroup dedicated to the discussion
of physics, news from the physics community, and physics-related social
issues.  People from a wide variety of non-physics backgrounds, as well
as students and experts in all areas of physics participate in the ongoing
discussions on sci.physics.  Professors, industrial scientists, graduate
students, etc., are all on hand to bring physics expertise to bear on
almost any question.   But the only requirement for participation is
interest in physics, so feel free to post -- but before you do, please do
the following:

(1) Read this posting, a.k.a., the FAQ.  It contains good answers,
contributed by the readership,  to some of the most frequently asked
questions.

(2) Understand "netiquette."  If you are not sure what this means,
subscribe to news.announce.newusers and read the excellent discussion of
proper net behavior that is posted there periodically.

(3) Be aware that there is another newsgroup dedicated to the discussion of
"alternative" physics.  It is alt.sci.physics.new-theories, and is the
appropriate forum for discussion of physics ideas which are not widely
accepted by the physics community.  Sci.Physics is not the group for such
discussions.  A quick look at items posted to both groups will make the
distinction apparent.

(4) Read the responses already posted in the thread to which you want to
contribute.  If a good answer is already posted, or the point you wanted
to make has already been made, let it be.  Old questions have probably been
thoroughly discussed by the time you get there - save bandwidth by posting
only new information.  Post to as narrow a geographic region as is
appropriate.  If your comments are directed at only one person, try E-mail.

(5) Get the facts right!  Opinions may differ, but facts should not.  It is
very tempting for new participants to jump in with quick answers to physics
questions posed to the group.  But it is very easy to end up feeling silly
when people barrage you with corrections.  So before you give us all a
physics lesson you'll regret - look it up.

(6) Be prepared for heated discussion.  People have strong opinions about
the issues, and discussions can get a little "loud" at times. Don't take it
personally if someone seems to always jump all over everything you say.
Everyone was jumping all over everybody long before you got there!  You
can keep the discussion at a low boil by trying to stick to the facts.
Clearly separate facts from opinion - don't let people think you are
confusing your opinions with scientific truth.  And keep the focus of
discussion on the ideas, not the people who post them.

(7) Tolerate everyone.  People of many different points of view, and widely
varying educational backgrounds from around the world participate in this
newsgroup.  Respect for others will be returned in kind.  Personal
criticism is usually not welcome.

********************************************************************************
Item 2.

Gravitational Radiation                updated: 4-May-1992 by SIC
-----------------------

    Gravitational Radiation is to gravity what light is to
electromagnetism. It is produced when massive bodies accelerate.  You can
accelerate any body so as to produce such radiation, but due to the feeble
strength of gravity, it is entirely undetectable except when produced by
intense astrophysical sources such as supernovae, collisions of black
holes, etc.  These are quite far from us, typically, but they are so
intense that they dwarf all possible laboratory sources of such radiation.

    Gravitational waves have a polarization pattern that causes objects
to expand in one direction, while contracting in the perpendicular
direction. That is, they have spin two.  This is because gravity waves are
fluctuations in the tensorial metric of space-time.

    All oscillating radiation fields can be quantized, and in the case
of gravity,  the intermediate boson is called the "graviton" in analogy
with the photon. But quantum gravity is hard, for several reasons:
    (1) The quantum field theory of gravity is hard, because gauge
interactions of spin-two fields are not renormalizable.  See Cheng and Li,
Gauge Theory of Elementary Particle Physics (search for "power counting").
    (2) There are conceptual problems - what does it mean to quantize
geometry, or space-time?

    It is possible to quantize weak fluctuations in the gravitational
field.  This gives rise to the spin-2 graviton.  But full quantum gravity
has so far escaped formulation.  It is not likely to look much like the
other quantum field theories.  In addition, there are models of gravity
which include additional bosons with different spins.  Some are the
consequence of non-Einsteinian models, such as Brans-Dicke which has a
spin-0 component. Others are included by hand, to give "fifth force"
components to gravity. For example, if you want to add a weak repulsive
short range component, you will need a massive spin-1 boson.  (Even-spin
bosons always attract.  Odd-spin bosons can attract or repel.)  If
antigravity is real, then this has implications for the boson spectrum as
well.

    The spin-two polarization provides the method of detection.  All
experiments to date use a "Weber bar."  This is a cylindrical, very
massive, bar suspended  by fine wire, free to oscillate in response to a
passing graviton.   A high-sensitivity, low noise, capacitive transducer
can turn the oscillations of the bar into an electric signal for analysis.
So far such searches have failed.  But they are expected to be
insufficiently sensitive for typical  radiation intensity from known types
of sources.

    A more sensitive technique uses very long baseline laser
interferometry.  This is the principle of LIGO (Laser Interferometric
Gravity wave Observatory).  This is a two-armed detector, with
perpendicular laser beams each travelling several km before meeting to
produce an interference pattern which fluctuates if a gravity wave distorts
the geometry of the detector.  To eliminate noise from seismic effects as
well as human noise sources, two detectors separated by hundreds to
thousands of miles are necessary.  A coincidence measurement then provides
evidence of gravitational radiation.  In order to determine the source of
the signal, a third detector, far from either of the first two, would be
necessary.  Timing differences in the arrival of the signal to the three
detectors would allow triangulation of the angular position in the sky of
the signal.

    The first stage of LIGO, a two detector setup in the U.S., has been
approved by Congress in 1992.  LIGO researchers have started designing a
prototype detector, and are hoping to enroll another nation, probably in
Europe, to fund and be host to the third detector.

    The speed of gravitational radiation (C_gw) depends upon the
specific model of Gravitation that you use.  There are quite a few
competing models (all consistent with all experiments to date) including of
course Einstein's but also Brans-Dicke and several families of others.
All metric models can support gravity waves.  But not all predict radiation
travelling at C_gw = C_em.  (C_em is the speed of electromagnetic waves.)

    There is a class of theories with "prior geometry", in which, as I
understand it, there is an additional metric which does not depend only on
the local matter density.  In such theories, C_gw != C_em in general.

    However, there is good evidence that C_gw is in fact at least
almost C_em. We observe high energy cosmic rays in the 10^20-10^21 eV
region.  Such particles are travelling at up to (1-10^-18)*C_em.  If C_gw <
C_em, then particles with C_gw < v < C_em will radiate Cerenkov
gravitational radiation into the vacuum, and decelerate from the back
reaction.  So evidence of these very fast cosmic rays good evidence that
C_gw >= (1-10^-18)*C_em, very close indeed to C_em.  Bottom line: in a
purely Einsteinian universe, C_gw = C_em. However, a class of models not
yet ruled out experimentally does make other predictions.

    A definitive test would be produced by LIGO in coincidence with
optical measurements of some catastrophic event which generates enough
gravitational radiation to be detected.  Then the "time of flight" of both
gravitons and photons from the source to the Earth could be measured, and
strict direct limits could be set on C_gw.

    For more information, see Gravitational Radiation (NATO ASI -
Les Houches 1982), specifically the introductory essay by Kip Thorne.

********************************************************************************
Item 3.

ENERGY CONSERVATION IN COSMOLOGY AND RED SHIFT    updated: 10-May-1992 by SIC
----------------------------------------------

IS ENERGY CONSERVED IN OUR UNIVERSE? NO

    Why?  Every conserved quantity is the result of some symmetry of
nature. This is known as Noether's theorem.  For example, momentum
conservation is the result of translation invariance, because position  is
the variable conjugate to momentum.  Energy would be conserved due to
time-translation invariance. However, in an expanding or contracting
universe, there is no time-translation invariance.  Hence energy is not
conserved.  If you want to learn more about this, read Goldstein's
Classical Mechanics, and look up Noether's theorem.

DOES RED-SHIFT LEAD TO ENERGY NON-CONSERVATION:  SOMETIMES

There are three basic cosmological sources of red-shifted light:
(1) Very massive objects emitting light
(2) Very fast objects emitting light
(3) Expansion of the universe leading to CBR (Cosmic Background
    Radiation) red-shift

About each:
(1) Light has to climb out the gravitational well of a very massive object.
 It gets red-shifted as a result.  As several people have commented, this
does not lead to energy non-conservation, because the photon had negative
gravitational potential energy when it was deep in the well.  No problems
here.  If you want to learn more about this read Misner, Thorne, and
Wheeler's Gravitation, if you dare.

(2) Fast objects moving away from you emit Doppler shifted light.  No
problems here either.  Energy is only one part a four-vector, so it
changes from frame to frame.  However, when looked at in a Lorentz
invariant way, you can convince yourself that everything is OK here too.
If you want to learn more about this, read Taylor and Wheeler's
Spacetime Physics.

(3) CBR has red-shifted over billions of years.  Each photon gets redder
and redder.  And the energy is lost.  This is the only case in which
red-shift leads to energy non-conservation.  Several people have speculated
that radiation pressure "on the universe" causes it to expand more quickly,
and attempt to identify the missing energy with the speed at which the
universe is expanding due to radiation pressure.  This argument is
completely specious.  If you add more radiation to the universe you add
more energy, and the universe is now more closed than ever, and the
expansion rate slows.

    If you really MUST construct a theory in which something like
energy is conserved (which is dubious in a universe without
time-translation invariance), it is possible to arbitrarily define things
so that energy has an extra term which compensates for the loss.  However,
although the resultant quantity may be a constant, it is of questionable
value, and certainly is not an integral associated with time-invariance, so
it is not what everyone calls energy.

********************************************************************************
Item 4.

EFFECTS DUE TO THE FINITE SPEED OF LIGHT    updated 28-May-1992 by SIC
----------------------------------------

    There are two well known phenomena which are due to the finite
speed of electromagnetic radiation, but are essentially classical in
nature, requiring no other facts of special relativity for their
understanding.

(1) Apparent Superluminal Velocity of Galaxies

    A distant object can appear to travel faster than the speed of
light relative to us, provided that it has some component of motion towards
us as well as perpendicular to our line of sight.  Say that on Jan. 1 you
make a position measurement of galaxy X.  One month later, you measure it
again. Assuming you know it's distance from us by some independent
measurement, you derive its linear speed, and conclude that it is moving
faster than the speed of light.

    What have you forgotten?  Let's say that on Jan. 1, the object is D
km from us, and that between Jan. 1 and Feb. 1, the object has moved d km
closer to us.  You have assumed that the light you measured on Jan. 1 and
Feb. 1 were emitted exactly one month apart.  Not so.  The first light beam
had further to travel, and was actually emitted (1 + d/c) months before the
second measurement, if we measure c in km/month.  The object has traveled
the given angular distance in more time than you thought.  Similarly, if
the object is moving away from us, the apparent angular velocity will be
too slow, if you do not correct for this effect, which becomes significant
when the object is moving along a line close to our line of sight.

    Note that most extragalactic objects are moving away from us due to
the Hubble expansion.  So for most objects, you don't get superluminal
apparent velocities.  But the effect is still there, and you need to take
it into account if you want to measure velocities by this technique.

References:

Considerations about the Apparent 'Superluminal Expansions' in
Astrophysics, E. Recami, A. Castellino, G.D. Maccarrone, M. Rodono,
Nuovo Cimento 93B, 119 (1986).

Apparent Superluminal Sources, Comparative Cosmology and the Cosmic
Distance Scale, Mon. Not. R. Astr. Soc. 242, 423-427 (1990).

(2) Terrell Rotation

    Consider a cube moving across your field of view with speed near
the speed of light.  The trailing face of the cube is edge on to your line
of sight as it passes you.  However, the light from the back edge of that
face (the edge of the square farthest from you) takes longer to get to your
eye than the light from the front edge.  At any given instant you are
seeing light from the front edge at time t and the back edge at time
t-(L/c), where L is the length of an edge.  This means you see the back
edge where it was some time earlier. This has the effect of *rotating* the
*image* of the cube on your retina.

    This does not mean that the cube itself rotates.  The *image* is
rotated. And this depends only on the finite speed of light, not any other
postulate or special relativity.  You can calculate the rotation angle by
noting that the side face of the cube is Lorentz contracted to L' =
L/gamma. This will correspond to a rotation angle of arccos(1/gamma).

    It turns out, if you do the math for a sphere, that the amount of
apparent rotation exactly cancels the Lorentz contraction.  The object
itself is flattened, but then you see *behind* it as it flies by just
enough to restore it to its original size.  So the image of a sphere is
unaffected by the Lorentz flattening that it experiences.

    Another implication of this is that if the object is moving at
nearly the speed of light, although it is contracted into an
infinitesimally thin pancake, you see it rotated by almost a full 90
degrees, so you see the complete backside of the object, and it doesn't
disappear from view.  In the case of the sphere, you see the transverse
cross-section (which suffers no contraction), so that it still appears to
be exactly a sphere.

    That it took so long historically to realize this is undoubtedly
due to the fact that although we were regularly accelerating particle beams
in 1959 to relativistic speeds, we still do not have the technology to
accelerate any macroscopic objects to speeds necessary to reveal the
effect.

References: J. Terrell, Phys Rev. _116_, 1041 (1959).  For a textbook
discussion, see Marion's _Classical Dynamics_, Section 10.5.

********************************************************************************
Item 5.

TOP QUARK                    updated: 10-May-1992 by SIC
---------

    The top quark is the hypothetical sixth fundamental strongly
interacting particle (quark).  The known quarks are up (u), down (d),
strange (s), charm (c) and  bottom (b).  The Standard Model requires quarks
to come in pairs in order to prevent mathematical inconsistency due to
certain "anomalous" Feynman diagrams, which cancel if and only if the
quarks are paired.  The pairs are (d,u),(s,c) and (b,?).  The missing
partner of the b is called "top".

    In addition, there is experimental evidence that the b quark has an
"isodoublet" partner, which is so far unseen.  The forward-backward
asymmetry in the reaction e+ + e- -> b + b-bar and the absence of
flavor-changing neutral currents in b decays imply the existence of the
isodoublet partner of the b. ("b-bar", pronounced "bee bar", signifies the
b antiquark.)

    The mass of the top quark is restricted by a variety of
measurements. Due to radiative corrections which depend on the top quark
circulating as a virtual particle inside the loop in the Feynman diagram,
a number of experimentally accessible processes depend on the top quark
mass.  There are about a dozen such measurements which have been made so
far, including the width of the Z, b-b-bar mixing (which historically gave
the first hints that the top quark was very massive), and certain aspects
of muon decay.  These results collectively limit the top mass to roughly
140 +/- 30 GeV.  This uncertainty is a "1-sigma" error bar.

    Direct searches for the top quark have been performed, looking for
the expected decay products in both p-p-bar and e+e- collisions.  The best
current limits on the top mass are:
    (1) From the absence of Z -> t + t-bar, M(t) > M(Z)/2 = 45 GeV.
This is a "model independent" result, depending only on the fact that the
top quark should be weakly interacting, coupling to the Z with sufficient
strength to have been detected at the current resolution of the LEP
experiments which have cornered the market on Z physics in the last several
years.
    (2) From the absence of top quark decay products in the reaction p
+ p-bar -> t + t-bar -> hard leptons + X at Fermilab's Tevatron collider,
the CDF (Collider Detector at Fermilab) experiment.  Each top quark is
expect to decay into a W boson and a b quark.  Each W subsequently decays
into either a charged lepton and a neutrino or two quarks.  The cleanest
signature for the production and decay of the t-t-bar pair is the presence
of two high-transverse-momentum (high Pt) leptons (electron or muon) in the
final state.  Other decay modes have higher branching ratios, but have
serious experimental backgrounds from W bosons produced in association with
jets.  The current lower limit on M(t) from such measurements is 91 GeV
(95% confidence), 95 GeV (90% confidence).  However, these limits assume
that the top quark has the expected decay products in the expected branching
ratios, making these limits "model dependent," and consequently not as
"hard" as the considerably lower LEP limit of ~45 GeV.

    The future is very bright for detecting the top quark.  LEP II, the
upgrade of CERN's e+e- collider to E >= 2*Mw = 160 GeV by 1994, will allow
a hard lower limit of roughly 90 GeV to be set.  Meanwhile, upgrades to
CDF, start of a new experiment, D0,  and upgrades to the accelerator
complex at Fermilab have recently allowed higher event rates and better
detector resolution, should allow production of standard model top quarks of
mass < 150 GeV in the next two years, and even higher mass further in the
future, at high enough event rate to identify the decays and give rough mass
measurements.

References: Phys. Rev. Lett. _68_, 447 (1992) and the references therein.

********************************************************************************
Item 6.

Tachyons                    updated: 4-May-1992 by SIC
--------

        There was a young lady named Bright,
        Whose speed was far faster than light.
        She went out one day,
        In a relative way,
        And returned the previous night!

            -Reginald Buller


    It is a well known fact that nothing can travel faster than the
speed of light. At best, a massless particle travels at the speed of light.
But is this really true?  In 1962, Bilaniuk, Deshpande, and Sudarshan, Am.
J. Phys. _30_, 718 (1962), said "no".  A very readable paper is Bilaniuk
and Sudarshan, Phys. Today _22_,43 (1969).  I give here a brief overview.

    Draw a graph, with momentum (p) on the x-axis, and energy (E) on
the y-axis.  Then draw the "light cone", two lines with the equations E =
+/- p. This divides our 1+1 dimensional space-time into two regions.  Above
and below are the "timelike" quadrants, and to the left and right are the
"spacelike" quadrants.

    Now the fundamental fact of relativity is that E^2 - p^2 = m^2.
(Let's take c=1 for the rest of the discussion.)  For any non-zero value of
m (mass), this is an hyperbola with branches in the timelike regions.  It
passes through the point (p,E) = (0,m), where the particle is at rest.  Any
particle with mass m is constrained to move on the upper branch of this
hyperbola.  (Otherwise, it is "off-shell", a term you here in association
with virtual particles - but that's another topic.) For massless particles,
E^2 = p^2, and the particle moves on the light-cone.

    These two cases are given the names tardyon (or bradyon in more
modern usage) and luxon, for "slow particle" and "light particle".  Tachyon
is the name given to the supposed "fast particle" which would move with v>c.

    Now another familiar relativistic equation is E =
m*[1-(v/c)^2]^(-.5).  Tachyons (if they exist) have v > c.  This means that
E is imaginary!  Well, what if we take the rest mass m, and take it to be
imaginary?  Then E is negative real, and E^2 - p^2 = m^2 < 0.  Or, p^2 -
E^2 = M^2, where M is real.  This is a hyperbola with branches in the
spacelike region of spacetime.  Tachyons are constrained to move on this
hyperbola.

    You can now deduce many interesting properties of tachyons.  For
example, they accelerate (p goes up) if they lose energy (E goes down).
Futhermore, a zero-energy tachyon is "transcendent," or infinitely fast.
This has profound consequences.  For example, let's say that there are
electrically charged tachyons.  Since they move faster than the speed of
light in the vacuum, they produce Cerenkov radiation.  This lowers their
energy, and they accelerate. So any charged tachyon in the region of
spacetime where you might choose to put a "charged tachyon detector" will
quickly accelerate off to the edge of the universe, to be lost forever.
You will never find a charged tachyon, whether they exist or not.

    However, tachyons are not entirely invisible.  You can imagine that
you might produce them in some exotic nuclear reaction.  If they are
charged, you could "see" them by detecting the Cerenkov light they produce
as they speed away faster and faster.  Such experiments have been done.  So
far, no tachyons have been found.  Even neutral tachyons can scatter off
normal matter with experimentally observable consequences.  Again, no such
tachyons have been found.

    Once you move away from relativistic kinematics and start talking
about the quantum field theory or particle physics of tachyons, things get
much more complicated.  It is not easy to summarize results here.  However,
one reasonably modern reference is _Tachyons, Monopoles, and Related
Topics_, E. Recami, ed. (North-Holland, Amsterdam, 1978).

    One little-publicized fact is that in the framework of field
theory, one CANNOT transmit information faster than the speed of light with
tachyons.  Since this may be controversial let us be more precise.
It's easiest to begin by looking at the wave equation for a free
scalar particle, the so-called Klein-Gordon equation:

        (BOX + m^2)phi = 0

where BOX is the D'Alembertian, which in 1+1 dimensions is just

        BOX = (d/dt)^2 - (d/dx)^2.

(For four-dimensional space-time just throw in -(d/dy)^2 -(d/dz)^2.)
In field theory, noninteracting massive particles (tardyons) are
described by this equation with the mass m being real.   Non-interacting
tachyons would be described by this equation with m imaginary.
Regardless of m, any solution is a linear combination, or superposition,
of solutions of the form

                exp(-iEt + ipx)

where E^2 - p^2 = m^2.   By actually solving the equation this way, one
notices a strange thing.  If the solution phi and its time derivative
are zero outside the interval [-L,L] when t = 0, they will be zero
outside the interval [-L-|t|, L+|t|] at any time t.  In other words,
disturbances do not spread with speed faster than 1 (the speed of
light).

However, there are lots of problems with tachyons in quantum field
theory.  A lot of mathematically rigorous work on quantum field theory
uses the Garding-Wightman axioms for quantum fields.  These rule out
tachyons for other reasons because they require that all states satisfy
E^2 - p^2 >= 0.   This allows one to define the vacuum as the state
minimizing E^2 - p^2 (required by these axioms to be unique).   As
described above, theories with tachyons violate this axiom.  In fact, if
one has a bunch of tachyons around, one can make E^2 - p^2 as negative
as you like.   Heuristically, this is bad because it means that the
vacuum is unstable: spontaneous creation of tachyon-antitachyon pairs
will tend to occur, reducing the total energy of the system.

********************************************************************************
Item 7. Special Relativistic Paradoxes - part (a)

The Barn and the Pole            updated 4-AUG-1992 by SIC
---------------------            original by Robert Firth

    These are the props.  You own a barn, 40m long, with automatic
doors at either end, that can be opened and closed simultaneously by a
switch. You also have a pole, 80m long, which of course won't fit in the
barn.

    Now someone takes the pole and tries to run (at nearly the speed of
light) through the barn with the pole horizontal.  Special Relativity (SR)
says that a moving object is contracted in the direction of motion: this is
called the Lorentz Contraction.  So, if the pole is set in motion
lengthwise, then it will contract in the reference frame of a stationary
observer.

    You are that observer, sitting on the barn roof.  You see the pole
coming towards you, and it has contracted to a bit less than 40m. So, as
the pole passes through the barn, there is an instant when it is completely
within the barn.  At that instant, you close both doors.  Of course, you
open them again pretty quickly, but at least momentarily you had the
contracted pole shut up in your barn.  The runner emerges from the far door
unscathed.

    But consider the problem from the point of view of the runner.  She
will regard the pole as stationary, and the barn as approaching at high
speed. In this reference frame, the pole is still 80m long, and the barn
is less than 20 meters long.  Surely the runner is in trouble if the doors
close while she is inside.  The pole is sure to get caught.

    Well does the pole get caught in the door or doesn't it?  You can't
have it both ways.  This is the "Barn-pole paradox."  The answer is buried
in the misuse of the word "simultaneously" back in the first sentence of
the story.  In SR, that events separated in space that appear simultaneous
in one frame of reference need not appear simultaneous in another frame of
reference. The closing doors are two such separate events.

    SR explains that the two doors are never closed at the same time in
the runner's frame of reference.  So there is always room for the pole.  In
fact, the Lorentz transformation for time is t'=(t-v*x/c^2)/sqrt(1-v^2/c^2).
It's the v*x term in the numerator that causes the mischief here.  In the
runner's frame the further event (larger x) happens earlier.  The far door
is closed first.  It opens before she gets there, and the near door closes
behind her. Safe again - either way you look at it, provided you remember
that simultaneity is not a constant of physics.

References:  Taylor and Wheeler's _Spacetime Physics_ is the classic.
Feynman's _Lectures_ are interesting as well.

********************************************************************************
Item 7. Special Relativistic Paradoxes - part (b)

The Twin Paradox                 updated 17-AUG-1992 by SIC
----------------                original by Kurt Sonnenmoser

A Short Story about Space Travel:

    Two twins, conveniently named A and B, both know the rules of
Special Relativity.  One of them, B, decides to travel out into space with
a velocity near the speed of light for a time T, after which she returns to
Earth. Meanwhile, her boring sister A sits at home posting to Usenet all
day.  When A finally comes home, what do the two sisters find?  Special
Relativity (SR) tells A that time was slowed down for the relativistic
sister, B, so that upon her return to Earth, she knows that B will be
younger than she is, which she suspects was the the ulterior motive of the
trip from the start.

    But B sees things differently.  She took the trip just to get away
from the conspiracy theorists on Usenet, knowing full well that from her
point of view, sitting in the spaceship, it would be her sister, A, who
was travelling ultrarelativistically for the whole time, so that she would
arrive home to find that A was much younger than she was.  Unfortunate, but
worth it just to get away for a while.

    What are we to conclude?  Which twin is really younger?  How can SR
give two answers to the same question?  How do we avoid this apparent
paradox? Maybe twinning is not allowed in SR?  Read on.

Paradox Resolved:

    Much of the confusion surrounding the so-called Twin Paradox
originates from the attempts to put the two twins into different frames ---
without the useful concept of the proper time of a moving body.

    SR offers a conceptually very clear treatment of this problem.
First chose _one_ specific inertial frame of reference; let's call it S.
Second define the paths that A and B take, their so-called world lines. As
an example, take (ct,0,0,0) as representing the world line of A, and
(ct,f(t),0,0) as representing the world line of B (assuming that the the
rest frame of the Earth was inertial). The meaning of the above notation is
that at time t, A is at the spatial location (x1,x2,x3)=(0,0,0) and B is at
(x1,x2,x3)=(f(t),0,0) --- always with respect to S.

    Let us now assume that A and B are at the same place at the time t1
and again at a later time t2, and that they both carry high-quality clocks
which indicate zero at time t1. High quality in this context means that the
precision of the clock is independent of acceleration. [In principle, a
bunch of muons provides such a device (unit of time: half-life of their
decay).]

    The correct expression for the time T such a clock will indicate at
time t2 is the following [the second form is slightly less general than the
first, but it's the good one for actual calculations]:

         t2          t2      _______________
            /           /      /             2 |
      T  =  | d\tau  =  | dt \/  1 - [v(t)/c]              (1)
        /           /
        t1          t1

where d\tau is the so-called proper-time interval, defined by

              2         2      2      2      2
     (c d\tau)  = (c dt)  - dx1  - dx2  - dx3 .

Furthermore,
                   d                          d
           v(t) = -- (x1(t), x2(t), x3(t)) = -- x(t)
                  dt                         dt

is the velocity vector of the moving object. The physical interpretation
of the proper-time interval, namely that it is the amount the clock time
will advance if the clock moves by dx during dt, arises from considering
the inertial frame in which the clock is at rest at time t --- its
so-called momentary rest frame (see the literature cited below). [Notice
that this argument is only of a heuristic value, since one has to assume
that the absolute value of the acceleration has no effect. The ultimate
justification of this interpretation must come from experiment.]

    The integral in (1) can be difficult to evaluate, but certain
important facts are immediately obvious. If the object is at rest with
respect to S, one trivially obtains T = t2-t1. In all other cases, T must
be strictly smaller than t2-t1, since the integrand is always less than or
equal to unity. Conclusion: the traveling twin is younger. Furthermore, if
she moves with constant velocity v most of the time (periods of
acceleration short compared to the duration of the whole trip), T will
approximately be given by      ____________
                  /          2 |
                    (t2-t1) \/  1 - [v/c]    .             (2)

The last expression is exact for a round trip (e.g. a circle) with constant
velocity v. [At the times t1 and t2, twin B flies past twin A and they
compare their clocks.]

    Now the big deal with SR, in the present context, is that T (or
d\tau, respectively) is a so-called Lorentz scalar. In other words, its
value does not depend on the choice of S. If we Lorentz transform the
coordinates of the world lines of the twins to another inertial frame S',
we will get the same result for T in S' as in S. This is a mathematical
fact. It shows that the situation of the traveling twins cannot possibly
lead to a paradox _within_ the framework of SR. It could at most be in
conflict with experimental results, which is also not the case.

    Of course the situation of the two twins is not symmetric, although
one might be tempted by expression (2) to think the opposite. Twin A is
at rest in one and the same inertial frame for all times, whereas twin B
is not.  [Formula (1) does not hold in an accelerated frame.]  This breaks
the apparent symmetry of the two situations, and provides the clearest
nonmathematical hint that one twin will in fact be younger than the other
at the end of the trip.  To figure out *which* twin is the younger one, use
the formulae above in a frame in which they are valid, and you will find
that B is in fact younger, despite her expectations.

    It is sometimes claimed that one has to resort to General
Relativity in order to "resolve" the Twin "Paradox". This is not true. In
flat, or nearly flat space-time (no strong gravity), SR is completely
sufficient, and it has also no problem with world lines corresponding to
accelerated motion.

References:
    Taylor and Wheeler, _Spacetime Physics_  (An *excellent* discussion)
    Goldstein, _Classical Mechanics_, 2nd edition, Chap.7 (for a good
    general discussion of Lorentz transformations and other SR basics.)

********************************************************************************
Item 8.

The Particle Zoo                updated 9-OCT-1992 by SIC
----------------                original by Matt Austern

    If you look in the Particle Data Book, you will find more than 150
particles listed there.  It isn't quite as bad as that, though...

    The particles are in three categories: leptons, mesons, and
baryons. Leptons are particle that are like the electron: they are
spin-1/2, and they do not undergo the strong interaction.  There are three
charged leptons, the electron, muon, and tau, and three neutral leptons, or
neutrinos.  (The muon and the tau are both short-lived.)

    Mesons and baryons both undergo strong interactions.  The
difference is that mesons have integral spin (0, 1,...), while baryons have
half-integral spin (1/2, 3/2,...).  The most familiar baryons are the
proton and the neutron; all others are short-lived.  The most familiar
meson is the pion; its lifetime is 26 nanoseconds, and all other mesons
decay even faster.

    Most of those 150+ particles are mesons and baryons, or,
collectively, hadrons.  The situation was enormously simplified in the
1960s by the "quark model," which says that hadrons are made out of
spin-1/2 particles called quarks.  A meson, in this model, is made out of a
quark and an anti-quark, and a baryon is made out of three quarks.  We
don't see free quarks (they are bound together too tightly), but only
hadrons; nevertheless, the evidence for quarks is compelling. Quark masses
are not very well defined, since they are not free particles, but we can
give estimates.  The masses below are in GeV; the first is current mass
and the second constituent mass (which includes some of the effects of the
binding energy):

      Generation:       1             2            3
      U-like:     u=.006/.311   c=1.50/1.65   t=91-200/91-200
      D-like:     d=.010/.315   s=.200/.500   b=5.10/5.10

    In the quark model, there are only 12 elementary particles, which
appear in three "generations."  The first generation consists of the up
quark, the down quark, the electron, and the electron neutrino. (Each of
these also has an associated antiparticle.)  These particle make up all of
the ordinary matter we see around us.  There are two other generations,
which are essentially the same, but with heavier particles.  The second
consists of the charm quark, the strange quark, the muon, and the muon
neutrino; and the third consists of the top quark, the bottom quark, the
tau, and the tau neutrino.  (The top has not been directly observed; see
the "Top Quark" FAQ entry for details.)  These three generations are
sometimes called the "electron family", the "muon family", and the "tau
family."

    Finally, according to quantum field theory, particles interact by
exchanging "gauge bosons," which are also particles.  The most familiar on
is the photon, which is responsible for electromagnetic interactions.
There are also eight gluons, which are responsible for strong interactions,
and the W+, W-, and Z, which are responsible for weak interactions.

The picture, then, is this:

            FUNDAMENTAL PARTICLES OF MATTER
  Charge        -------------------------
    -1          |  e    |  mu   |  tau  |
     0          | nu(e) |nu(mu) |nu(tau)|
                -------------------------       + antiparticles
   -1/3         | down  |strange|bottom |
    2/3         |  up   | charm |  top  |
                -------------------------

            GAUGE BOSONS
  Charge                        Force
     0            photon                electromagnetism
     0            gluons (8 of them)        strong force
    +-1            W+ and W-            weak force
     0            Z                weak force

    The Standard Model of particle physics also predict the
existence of a "Higgs boson," which has to do with breaking a symmetry
involving these forces, and which is responsible for the masses of all the
other particles.  It has not yet been found.  More complicated theories
predict additional particles, including, for example, gauginos and sleptons
and squarks (from supersymmetry), W' and Z' (additional weak bosons), X and
Y bosons (from GUT theories), Majorons, familons, axions, paraleptons,
ortholeptons, technipions (from technicolor models), B' (hadrons with
fourth generation quarks), magnetic monopoles, e* (excited leptons), etc.
None of these "exotica" have yet been seen.  The search is on!

REFERENCES:

    The best reference for information on which particles exist, their
masses, etc., is the Particle Data Book.  It is published every two years;
the most recent edition is Physical Review D Vol.45 No.11 (1992).

    There are several good books that discuss particle physics on a
level accessible to anyone who knows a bit of quantum mechanics.  One is
_Introduction to High Energy Physics_, by Perkins.  Another, which takes a
more historical approach and includes many original papers, is
_Experimental Foundations of Particle Physics_, by Cahn and Goldhaber.

    For a book that is accessible to non-physicists, you could try _The
Particle Explosion_ by Close, Sutton, and Marten.  This book has fantastic
photography.

********************************************************************************
Item 9.

Olbers' Paradox                    updated: 2-JUL-1992 by SIC
---------------

    Why isn't the night sky as uniformly bright as the surface of the
Sun? If the Universe has infinitely many stars, then it should be.  After
all, if you move the Sun twice as far away from us, we will intercept
one-fourth as many  photons, but the Sun will subtend one-fourth of the
angular area.  So the areal intensity remains constant.  With infinitely
many stars, every angular element of the sky should have a star, and the
entire heavens should be a bright as the sun.  We should have the
impression that we live in the center of a hollow black body whose
temperature is about 6000 degrees Centigrade.   This is Olbers' paradox.
It can be traced as far back as Kepler in 1610.  It was rediscussed by
Halley and Cheseaux in the eighteen century, but was not popularized as
a paradox until Olbers took up the issue in the nineteenth century.

    There are many possible explanations which have been considered.
Here are a few:
    (1) There's too much dust to see the distant stars.
    (2) The Universe has only a finite number of stars.
    (3) The distribution of stars is not uniform.  So, for example,
        there could be an infinitely of stars, but they hide behind one
        another so that only a finite angular area is subtended by them.
    (4) The Universe is expanding, so distant stars are red-shifted into
        obscurity.
    (5) The Universe is young.  Distant light hasn't even reached us yet.

    The first explanation is just plain wrong.  In a black body, the
dust will  heat up too.  It does act like a radiation shield, exponentially
damping the  distant starlight.  But you can't put enough dust into the
universe to get rid of enough starlight without also obscuring our own Sun.
So this idea is bad.

    The second might have been correct, but estimates of the total
matter in the universe are too large to allow this escape.  The number of
stars is close enough to infinite for the purpose of lighting up the sky.
The third explanation might be partially correct.  We just don't know.  If
the stars are distributed fractally, then there could be large patches of
empty space, and the sky could appear dark except in small areas.

    But the final two possibilities are are surely each correct and
partly responsible.  There are numerical arguments that suggest that the
effect of the finite age of the Universe is the larger effect.  We live
inside a spherical shell of "Observable Universe" which has radius equal to
the lifetime of the Universe.  Objects more than about 15 billions years
old are too far away for their light ever to reach us.

    Historically, after Hubble discovered that the Universe was
expanding, but before the Big Bang was firmly established by the discovery
of the cosmic background radiation, Olbers' paradox was presented as proof
of special relativity.  You needed the red-shift (an SR effect) to get rid
of the starlight.  This effect certainly contributes.  But the finite age
of the Universe is the most important effect.

References:  Ap. J. _367_, 399 (1991). The author, Paul Wesson, is said to
be on a personal crusade to end the confusion surrounding Olbers' paradox.

_Darkness at Night: A Riddle of the Universe_, Edward Harrison, Harvard
University Press, 1987

********************************************************************************
Item 10.

What is Dark Matter?                 updated 11-May-1991 by SIC
--------------------

    The story of dark matter is best divided into two parts.  First we
have the reasons that we know that it exists.  Second is the collection of
possible explanations as to what it is.

Why the Universe Needs Dark Matter
----------------------------------

    We believe that that the Universe is critically balanced between
being open and closed.  We derive this fact from the observation of the
large scale structure of the Universe.  It requires a certain amount of
matter to accomplish this result.  Call it M.

    You can estimate the total BARYONIC matter of the universe by
studying big bang nucleosynthesis.  The more matter in the universe, the
more slowly the universe should have expanded shortly after the big bang.
The longer the "cooking time" allowed, the higher the production of helium
from primordial hydrogen.  We know the He/H ratio of the universe, so we
can estimate how much baryonic matter exists in the universe.  It turns out
that you need about 0.05 M total baryonic matter to account for the known
ratio of light isotopes.  So only 1/20 of the total mass of they Universe
is baryonic matter.

    Unfortunately, the best estimates of the total mass of everything
that we can see with our telescopes is roughly 0.01 M.  Where is the other
99% of the stuff of the Universe?  Dark Matter!

    So there are two conclusions.  We only see 0.01 M out of 0.05 M
baryonic matter in the Universe.  The rest must be in baryonic dark matter
halos surrounding galaxies.  And there must be some non-baryonic dark matter
to account for the remaining 95% of the matter required to give omega, the
mass of universe, in units of critical mass, equal to unity.

    For those who distrust the conventional Big Bang models, and don't
want to rely upon fancy cosmology to derive the presence of dark matter,
there are other more direct means.   It has been observed in clusters of
galaxies that the motion of galaxies within a cluster suggests that they
are bound by a total gravitational force due to about 5-10 times as much
matter as can be accounted for from luminous matter in said galaxies.  And
within an individual galaxy, you can measure the rate of rotation of the
stars about the galactic center of rotation.  The resultant "rotation
curve" is simply related to the distribution of matter in the galaxy.  The
outer stars in galaxies seem to rotate too fast for the amount of matter
that we see in the galaxy.  Again, we need about 5 times more matter than
we can see via electromagnetic radiation.  These results can be explained
by assuming that there is a "dark matter halo" surrounding every galaxy.

What is Dark Matter
-------------------

    This is the open question.  There are many possibilities, and
nobody really knows much about this yet.  Here are a few of the many
published suggestions, which are being currently hunted for by
experimentalists all over the world:

(1) Normal matter which has so far eluded our gaze, such as
    (a) dark galaxies
    (b) brown dwarfs
    (c) planetary material (rock, dust, etc.)

(2) Massive Standard Model neutrinos.  If any of the neutrinos are massive,
then this could be the missing mass.  Note that the possible 17 KeV tau
neutrino would give far too much mass creating almost as many problems as
it solves in this regard.

(3) Exotica (See the "Particle Zoo" FAQ entry for some details)

    Massive exotica would provide the missing mass.  For our purposes,
these fall into two classes: those which have been proposed for other
reasons but happen to solve the dark matter problem, and those which have
been proposed specifically to provide the missing dark matter.

    Examples of objects in the first class are axions, additional
neutrinos, supersymmetric particles, and a host of others. Their properties
are constrained by the theory which predicts them, but by virtue of their
mass, they solve the dark matter problem if they exist in the correct
abundance.

    Particles in the second class are generally classed in loose groups.
Their properties are not specified, but they are merely required to be
massive and have other properties such that they would so far have eluded
discovery in the many experiments which have looked for new particles.
These include WIMPS (Weakly Interacting Massive Particles), CHAMPS, and a
host of others.

References:  _Dark Matter in the Universe_ (Jerusalem Winter School for
Theoretical Physics, 1986-7), J.N. Bahcall, T. Piran, & S. Weinberg editors.
_Dark Matter_ (Proceedings of the XXIIIrd Recontre de Moriond) J. Audouze and
J. Tran Thanh Van. editors.

********************************************************************************
Item 11.

Hot Water Freezes Faster than Cold!        updated 11-May-1992 by SIC
-----------------------------------        original by Richard M. Mathews

    You put two pails of water outside on a freezing day.  One has hot
water (95 degrees C) and the other has an equal amount of colder water (50
degrees C).  Which freezes first?  The hot water freezes first!  Why?

    It is commonly argued that the hot water will take some time to
reach the initial temperature of the cold water, and then follow the same
cooling curve.  So it seems at first glance difficult to believe that the
hot water freezes first.  The answer lies mostly in evaporation. The effect
is definitely real and can be duplicated in your own kitchen.

    Every "proof" that hot water can't freeze faster assumes that the
state of the water can be described by a single number.  Remember that
temperature is a function of position.  There are also other factors
besides temperature, such as motion of the water, gas content, etc. With
these multiple parameters, any argument based on the hot water having to
pass through the initial state of the cold water before reaching the
freezing point will fall apart.  The most important factor is evaporation.

    The cooling of pails without lids is partly Newtonian and partly by
evaporation of the contents.  The proportions depend on the walls and on
temperature.  At sufficiently high temperatures evaporation is more
important.  If equal masses of water are taken at two starting
temperatures, more rapid evaporation from the hotter one may diminish its
mass enough to compensate for the greater temperature range it must cover
to reach freezing.  The mass lost when cooling is by evaporation is not
negligible. In one experiment, water cooling from 100C lost 16% of its mass
by 0C, and lost a further 12% on freezing, for a total loss of 26%.

    The cooling effect of evaporation is twofold.  First, mass is
carried off so that less needs to be cooled from then on.  Also,
evaporation carries off the hottest molecules, lowering considerably the
average kinetic energy of the molecules remaining. This is why "blowing on
your soup" cools it.  It encourages evaporation by removing the water vapor
above the soup.

    Thus experiment and theory agree that hot water freezes faster than
cold for sufficiently high starting temperatures, if the cooling is by
evaporation.  Cooling in a wooden pail or barrel is mostly by evaporation.
In fact, a wooden bucket of water starting at 100C would finish freezing in
90% of the time taken by an equal volume starting at room temperature. The
folklore on this matter may well have started a century or more ago when
wooden pails were usual.  Considerable heat is transferred through the
sides of metal pails, and evaporation no longer dominates the cooling, so
the belief is unlikely to have started from correct observations after
metal pails became common.

References:
    "Hot water freezes faster than cold water.  Why does it do so?",
    Jearl Walker in The Amateur Scientist, Scientific American,
    Vol. 237, No. 3, pp 246-257; September, 1977.

    "The Freezing of Hot and Cold Water", G.S. Kell in American
    Journal of Physics, Vol. 37, No. 5, pp 564-565; May, 1969.

*******************
END OF FAQ PART 1/2
  ********************
Date: Wed, 30 Dec 92 11:10:39 PST
From: [e-mail]
Message-Id: <[e-mail]>
Subject: Sci.Physics Frequently Asked Questions - January 1993 - Part 2/2
To: distribution:@Csa2.LBL.Gov; (see end of body)
X-St-Vmsmail-To: @[-]MAILING_LIST.FAQ

Archive-name: physics-faq
Last-modified: 1992/12/26

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

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.)

References: Perhaps the best (and easy-to-read) reference on this effect is
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.

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 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 [e-mail] 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 [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) 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)

    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