Editor's note:  

	FAQ #19, on the Equivalence Principle and the radiation of 
charged particles, has opened a proverbial can of worms.  It has been
brought to my attention by people who's expertise far exceeds my own
that many serious issues are glossed over or perhaps even misrepresented
in the article as I had previously editted it.
	I have attempted to address some of these concerns in a modified
article, but some of the problems are beyond my ability to handle.  Please
note that the changes are entirely my own, not the original author's, and
are based upon my own, probably naive, new understanding of the issues based
upon input from concerned readers.
	It has been suggested that I simply pull the article until I can
prove its assertions or give adequate references to accepted literature.
However, that is likely never to happen if it depends only upon my 
(non-existent) expertise on GR.  So I have warily decided to keep it in the
public view in the hope that it will act as an irritant, and perhaps
induce some qualified expert to produce some pearls of wisdom which I can
use to fix its obvious deficiencies.

	The other articles which I have indicated have been modified for this 
posting contain only cosmetic changes.
						-Scott

--------------------------------------------------------------------------------
 	      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 sichase@csa2.lbl.gov (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: NONE

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: 24-JAN-1993 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 infinity 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 premise of the second explanation may technically be correct.
But the number of stars, finite as it might be, is still large enough to 
light up the entire sky, i.e., the total amount of luminous matter  in the 
Universe is 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


