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- Subject: Sci.physics Frequently Asked Questions - December 1993 - Part 2/2
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- Date: 2 Dec 1993 14:10 PST
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- --------------------------------------------------------------------------------
- FREQUENTLY ASKED QUESTIONS ON SCI.PHYSICS - Part 2/2
- --------------------------------------------------------------------------------
-
- Item 15.
-
- Some Frequently Asked Questions About Black Holes updated 2-JUL-1993 by MM
- ------------------------------------------------- original by Matt McIrvin
-
- Contents:
-
- 1. What is a black hole, really?
- 2. What happens to you if you fall in?
- 3. Won't it take forever for you to fall in? Won't it take forever
- for the black hole to even form?
- 4. Will you see the universe end?
- 5. What about Hawking radiation? Won't the black hole evaporate
- before you get there?
- 6. How does the gravity get out of the black hole?
- 7. Where did you get that information?
-
- 1. What is a black hole, really?
-
- In 1916, when general relativity was new, Karl Schwarzschild worked
- out a useful solution to the Einstein equation describing the evolution of
- spacetime geometry. This solution, a possible shape of spacetime, would
- describe the effects of gravity *outside* a spherically symmetric,
- uncharged, nonrotating object (and would serve approximately to describe
- even slowly rotating objects like the Earth or Sun). It worked in much the
- same way that you can treat the Earth as a point mass for purposes of
- Newtonian gravity if all you want to do is describe gravity *outside* the
- Earth's surface.
-
- What such a solution really looks like is a "metric," which is a
- kind of generalization of the Pythagorean formula that gives the length of
- a line segment in the plane. The metric is a formula that may be used to
- obtain the "length" of a curve in spacetime. In the case of a curve
- corresponding to the motion of an object as time passes (a "timelike
- worldline,") the "length" computed by the metric is actually the elapsed
- time experienced by an object with that motion. The actual formula depends
- on the coordinates chosen in which to express things, but it may be
- transformed into various coordinate systems without affecting anything
- physical, like the spacetime curvature. Schwarzschild expressed his metric
- in terms of coordinates which, at large distances from the object,
- resembled spherical coordinates with an extra coordinate t for time.
- Another coordinate, called r, functioned as a radial coordinate at large
- distances; out there it just gave the distance to the massive object.
-
- Now, at small radii, the solution began to act strangely. There
- was a "singularity" at the center, r=0, where the curvature of spacetime
- was infinite. Surrounding that was a region where the "radial" direction
- of decreasing r was actually a direction in *time* rather than in space.
- Anything in that region, including light, would be obligated to fall toward
- the singularity, to be crushed as tidal forces diverged. This was separated
- from the rest of the universe by a place where Schwarzschild's coordinates
- blew up, though nothing was wrong with the curvature of spacetime there.
- (This was called the Schwarzschild radius. Later, other coordinate systems
- were discovered in which the blow-up didn't happen; it was an artifact of
- the coordinates, a little like the problem of defining the longitude of the
- North Pole. The physically important thing about the Schwarzschild radius
- was not the coordinate problem, but the fact that within it the direction
- into the hole became a direction in time.)
-
- Nobody really worried about this at the time, because there was no
- known object that was dense enough for that inner region to actually be
- outside it, so for all known cases, this odd part of the solution would not
- apply. Arthur Stanley Eddington considered the possibility of a dying star
- collapsing to such a density, but rejected it as aesthetically unpleasant
- and proposed that some new physics must intervene. In 1939, Oppenheimer
- and Snyder finally took seriously the possibility that stars a few times
- more massive than the sun might be doomed to collapse to such a state at
- the end of their lives.
-
- Once the star gets smaller than the place where Schwarzschild's
- coordinates fail (called the Schwarzschild radius for an uncharged,
- nonrotating object, or the event horizon) there's no way it can avoid
- collapsing further. It has to collapse all the way to a singularity for
- the same reason that you can't keep from moving into the future! Nothing
- else that goes into that region afterward can avoid it either, at least in
- this simple case. The event horizon is a point of no return.
-
- In 1971 John Archibald Wheeler named such a thing a black hole,
- since light could not escape from it. Astronomers have many candidate
- objects they think are probably black holes, on the basis of several kinds
- of evidence (typically they are dark objects whose large mass can be
- deduced from their gravitational effects on other objects, and which
- sometimes emit X-rays, presumably from infalling matter). But the
- properties of black holes I'll talk about here are entirely theoretical.
- They're based on general relativity, which is a theory that seems supported
- by available evidence.
-
- 2. What happens to you if you fall in?
-
- Suppose that, possessing a proper spacecraft and a self-destructive
- urge, I decide to go black-hole jumping and head for an uncharged,
- nonrotating ("Schwarzschild") black hole. In this and other kinds of hole,
- I won't, before I fall in, be able to see anything within the event
- horizon. But there's nothing *locally* special about the event horizon;
- when I get there it won't seem like a particularly unusual place, except
- that I will see strange optical distortions of the sky around me from all
- the bending of light that goes on. But as soon as I fall through, I'm
- doomed. No bungee will help me, since bungees can't keep Sunday from
- turning into Monday. I have to hit the singularity eventually, and before
- I get there there will be enormous tidal forces-- forces due to the
- curvature of spacetime-- which will squash me and my spaceship in some
- directions and stretch them in another until I look like a piece of
- spaghetti. At the singularity all of present physics is mute as to what
- will happen, but I won't care. I'll be dead.
-
- For ordinary black holes of a few solar masses, there are actually
- large tidal forces well outside the event horizon, so I probably wouldn't
- even make it into the hole alive and unstretched. For a black hole of 8
- solar masses, for instance, the value of r at which tides become fatal is
- about 400 km, and the Schwarzschild radius is just 24 km. But tidal
- stresses are proportional to M/r^3. Therefore the fatal r goes as the cube
- root of the mass, whereas the Schwarzschild radius of the black hole is
- proportional to the mass. So for black holes larger than about 1000 solar
- masses I could probably fall in alive, and for still larger ones I might
- not even notice the tidal forces until I'm through the horizon and doomed.
-
- 3. Won't it take forever for you to fall in? Won't it take forever
- for the black hole to even form?
-
- Not in any useful sense. The time I experience before I hit the
- event horizon, and even until I hit the singularity-- the "proper time"
- calculated by using Schwarzschild's metric on my worldline -- is finite.
- The same goes for the collapsing star; if I somehow stood on the surface of
- the star as it became a black hole, I would experience the star's demise in
- a finite time.
-
- On my worldline as I fall into the black hole, it turns out that
- the Schwarzschild coordinate called t goes to infinity when I go through
- the event horizon. That doesn't correspond to anyone's proper time,
- though; it's just a coordinate called t. In fact, inside the event
- horizon, t is actually a *spatial* direction, and the future corresponds
- instead to decreasing r. It's only outside the black hole that t even
- points in a direction of increasing time. In any case, this doesn't
- indicate that I take forever to fall in, since the proper time involved is
- actually finite.
-
- At large distances t *does* approach the proper time of someone who
- is at rest with respect to the black hole. But there isn't any
- non-arbitrary sense in which you can call t at smaller r values "the proper
- time of a distant observer," since in general relativity there is no
- coordinate-independent way to say that two distant events are happening "at
- the same time." The proper time of any observer is only defined locally.
-
- A more physical sense in which it might be said that things take
- forever to fall in is provided by looking at the paths of emerging light
- rays. The event horizon is what, in relativity parlance, is called a
- "lightlike surface"; light rays can remain there. For an ideal
- Schwarzschild hole (which I am considering in this paragraph) the horizon
- lasts forever, so the light can stay there without escaping. (If you
- wonder how this is reconciled with the fact that light has to travel at the
- constant speed c-- well, the horizon *is* traveling at c! Relative speeds
- in GR are also only unambiguously defined locally, and if you're at the
- event horizon you are necessarily falling in; it comes at you at the speed
- of light.) Light beams aimed directly outward from just outside the
- horizon don't escape to large distances until late values of t. For
- someone at a large distance from the black hole and approximately at rest
- with respect to it, the coordinate t does correspond well to proper time.
-
- So if you, watching from a safe distance, attempt to witness my
- fall into the hole, you'll see me fall more and more slowly as the light
- delay increases. You'll never see me actually *get to* the event horizon.
- My watch, to you, will tick more and more slowly, but will never reach the
- time that I see as I fall into the black hole. Notice that this is really
- an optical effect caused by the paths of the light rays.
-
- This is also true for the dying star itself. If you attempt to
- witness the black hole's formation, you'll see the star collapse more and
- more slowly, never precisely reaching the Schwarzschild radius.
-
- Now, this led early on to an image of a black hole as a strange
- sort of suspended-animation object, a "frozen star" with immobilized
- falling debris and gedankenexperiment astronauts hanging above it in
- eternally slowing precipitation. This is, however, not what you'd see. The
- reason is that as things get closer to the event horizon, they also get
- *dimmer*. Light from them is redshifted and dimmed, and if one considers
- that light is actually made up of discrete photons, the time of escape of
- *the last photon* is actually finite, and not very large. So things would
- wink out as they got close, including the dying star, and the name "black
- hole" is justified.
-
- As an example, take the eight-solar-mass black hole I mentioned
- before. If you start timing from the moment the you see the object half a
- Schwarzschild radius away from the event horizon, the light will dim
- exponentially from that point on with a characteristic time of about 0.2
- milliseconds, and the time of the last photon is about a hundredth of a
- second later. The times scale proportionally to the mass of the black
- hole. If I jump into a black hole, I don't remain visible for long.
-
- Also, if I jump in, I won't hit the surface of the "frozen star."
- It goes through the event horizon at another point in spacetime from
- where/when I do.
-
- (Some have pointed out that I really go through the event horizon a
- little earlier than a naive calculation would imply. The reason is that my
- addition to the black hole increases its mass, and therefore moves the
- event horizon out around me at finite Schwarzschild t coordinate. This
- really doesn't change the situation with regard to whether an external
- observer sees me go through, since the event horizon is still lightlike;
- light emitted at the event horizon or within it will never escape to large
- distances, and light emitted just outside it will take a long time to get
- to an observer, timed, say, from when the observer saw me pass the point
- half a Schwarzschild radius outside the hole.)
-
- All this is not to imply that the black hole can't also be used for
- temporal tricks much like the "twin paradox" mentioned elsewhere in this
- FAQ. Suppose that I don't fall into the black hole-- instead, I stop and
- wait at a constant r value just outside the event horizon, burning
- tremendous amounts of rocket fuel and somehow withstanding the huge
- gravitational force that would result. If I then return home, I'll have
- aged less than you. In this case, general relativity can say something
- about the difference in proper time experienced by the two of us, because
- our ages can be compared *locally* at the start and end of the journey.
-
- 4. Will you see the universe end?
-
- If an external observer sees me slow down asymptotically as I fall,
- it might seem reasonable that I'd see the universe speed up
- asymptotically-- that I'd see the universe end in a spectacular flash as I
- went through the horizon. This isn't the case, though. What an external
- observer sees depends on what light does after I emit it. What I see,
- however, depends on what light does before it gets to me. And there's no
- way that light from future events far away can get to me. Faraway events
- in the arbitrarily distant future never end up on my "past light-cone," the
- surface made of light rays that get to me at a given time.
-
- That, at least, is the story for an uncharged, nonrotating black
- hole. For charged or rotating holes, the story is different. Such holes
- can contain, in the idealized solutions, "timelike wormholes" which serve
- as gateways to otherwise disconnected regions-- effectively, different
- universes. Instead of hitting the singularity, I can go through the
- wormhole. But at the entrance to the wormhole, which acts as a kind of
- inner event horizon, an infinite speed-up effect actually does occur. If I
- fall into the wormhole I see the entire history of the universe outside
- play itself out to the end. Even worse, as the picture speeds up the light
- gets blueshifted and more energetic, so that as I pass into the wormhole an
- "infinite blueshift" happens which fries me with hard radiation. There is
- apparently good reason to believe that the infinite blueshift would imperil
- the wormhole itself, replacing it with a singularity no less pernicious
- than the one I've managed to miss. In any case it would render wormhole
- travel an undertaking of questionable practicality.
-
- 5. What about Hawking radiation? Won't the black hole evaporate
- before you get there?
-
- (First, a caveat: Not a lot is really understood about evaporating
- black holes. The following is largely deduced from information in Wald's
- GR text, but what really happens-- especially when the black hole gets very
- small-- is unclear. So take the following with a grain of salt.)
-
- Short answer: No, it won't. This demands some elaboration.
-
- From thermodynamic arguments Stephen Hawking realized that a black
- hole should have a nonzero temperature, and ought therefore to emit
- blackbody radiation. He eventually figured out a quantum- mechanical
- mechanism for this. Suffice it to say that black holes should very, very
- slowly lose mass through radiation, a loss which accelerates as the hole
- gets smaller and eventually evaporates completely in a burst of radiation.
- This happens in a finite time according to an outside observer.
-
- But I just said that an outside observer would *never* observe an
- object actually entering the horizon! If I jump in, will you see the black
- hole evaporate out from under me, leaving me intact but marooned in the
- very distant future from gravitational time dilation?
-
- You won't, and the reason is that the discussion above only applies
- to a black hole that is not shrinking to nil from evaporation. Remember
- that the apparent slowing of my fall is due to the paths of outgoing light
- rays near the event horizon. If the black hole *does* evaporate, the delay
- in escaping light caused by proximity to the event horizon can only last as
- long as the event horizon does! Consider your external view of me as I
- fall in.
-
- If the black hole is eternal, events happening to me (by my watch)
- closer and closer to the time I fall through happen divergingly later
- according to you (supposing that your vision is somehow not limited by the
- discreteness of photons, or the redshift).
-
- If the black hole is mortal, you'll instead see those events happen
- closer and closer to the time the black hole evaporates. Extrapolating,
- you would calculate my time of passage through the event horizon as the
- exact moment the hole disappears! (Of course, even if you could see me,
- the image would be drowned out by all the radiation from the evaporating
- hole.) I won't experience that cataclysm myself, though; I'll be through
- the horizon, leaving only my light behind. As far as I'm concerned, my
- grisly fate is unaffected by the evaporation.
-
- All of this assumes you can see me at all, of course. In practice
- the time of the last photon would have long been past. Besides, there's
- the brilliant background of Hawking radiation to see through as the hole
- shrinks to nothing.
-
- (Due to considerations I won't go into here, some physicists think
- that the black hole won't disappear completely, that a remnant hole will be
- left behind. Current physics can't really decide the question, any more
- than it can decide what really happens at the singularity. If someone ever
- figures out quantum gravity, maybe that will provide an answer.)
-
- 6. How does the gravity get out of the black hole?
-
- Purely in terms of general relativity, there is no problem here.
- The gravity doesn't have to get out of the black hole. General relativity
- is a local theory, which means that the field at a certain point in
- spacetime is determined entirely by things going on at places that can
- communicate with it at speeds less than or equal to c. If a star collapses
- into a black hole, the gravitational field outside the black hole may be
- calculated entirely from the properties of the star and its external
- gravitational field *before* it becomes a black hole. Just as the light
- registering late stages in my fall takes longer and longer to get out to
- you at a large distance, the gravitational consequences of events late in
- the star's collapse take longer and longer to ripple out to the world at
- large. In this sense the black hole *is* a kind of "frozen star": the
- gravitational field is a fossil field. The same is true of the
- electromagnetic field that a black hole may possess.
-
- Often this question is phrased in terms of gravitons, the
- hypothetical quanta of spacetime distortion. If things like gravity
- correspond to the exchange of "particles" like gravitons, how can they get
- out of the event horizon to do their job?
-
- First of all, it's important to realize that gravitons are not as
- yet even part of a complete theory, let alone seen experimentally. They
- don't exist in general relativity, which is a non-quantum theory. When
- fields are described as mediated by particles, that's quantum theory, and
- nobody has figured out how to construct a quantum theory of gravity. Even
- if such a theory is someday built, it may not involve "virtual particles"
- in the same way other theories do. In quantum electrodynamics, the static
- forces between particles are described as resulting from the exchange of
- "virtual photons," but the virtual photons only appear when one expresses
- QED in terms of a quantum- mechanical approximation method called
- perturbation theory. It currently looks like this kind of perturbation
- theory doesn't work properly when applied to quantum gravity. So although
- quantum gravity may well involve "real gravitons" (quantized gravitational
- waves), it may well not involve "virtual gravitons" as carriers of static
- gravitational forces.
-
- Nevertheless, the question in this form is still worth asking,
- because black holes *can* have static electric fields, and we know that
- these may be described in terms of virtual photons. So how do the virtual
- photons get out of the event horizon? The answer is that virtual particles
- aren't confined to the interiors of light cones: they can go faster than
- light! Consequently the event horizon, which is really just a surface that
- moves at the speed of light, presents no barrier.
-
- I couldn't use these virtual photons after falling into the hole to
- communicate with you outside the hole; nor could I escape from the hole by
- somehow turning myself into virtual particles. The reason is that virtual
- particles don't carry any *information* outside the light cone. That is a
- tricky subject for another (future?) FAQ entry. Suffice it to say that the
- reasons virtual particles don't provide an escape hatch for a black hole
- are the same as the reasons they can't be used for faster-than-light travel
- or communication.
-
- 7. Where did you get that information?
-
- The numbers concerning fatal radii, dimming, and the time of the
- last photon came from Misner, Thorne, and Wheeler's _Gravitation_ (San
- Francisco: W. H. Freeman & Co., 1973), pp. 860-862 and 872-873. Chapters 32
- and 33 (IMHO, the best part of the book) contain nice descriptions of some
- of the phenomena I've described.
-
- Information about evaporation and wormholes came from Robert Wald's
- _General Relativity_ (Chicago: University of Chicago Press, 1984). The
- famous conformal diagram of an evaporating hole on page 413 has resolved
- several arguments on sci.physics (though its veracity is in question).
-
- Steven Weinberg's _Gravitation and Cosmology_ (New York: John Wiley
- and Sons, 1972) provided me with the historical dates. It discusses some
- properties of the Schwarzschild solution in chapter 8 and describes
- gravitational collapse in chapter 11.
-
- ********************************************************************************
- Item 16.
-
- Below Absolute Zero - What Does Negative Temperature Mean? updated 24-MAR-1993
- ----------------------------------------------------------
-
- Questions: What is negative temperature? Can you really make a system
- which has a temperature below absolute zero? Can you even give any useful
- meaning to the expression 'negative absolute temperature'?
-
- Answer: Absolutely. :-)
-
- Under certain conditions, a closed system *can* be described by a
- negative temperature, and, surprisingly, be *hotter* than the same system
- at any positive temperature. This article describes how it all works.
-
- Step I: What is "Temperature"?
- ------------------------------
-
- To get things started, we need a clear definition of "temperature."
- Our intuitive notion is that two systems in thermal contact should exchange
- no heat, on average, if and only if they are at the same temperature. Let's
- call the two systems S1 and S2. The combined system, treating S1 and S2
- together, can be S3. The important question, consideration of which
- will lead us to a useful quantitative definition of temperature, is "How will
- the energy of S3 be distributed between S1 and S2?" I will briefly explain
- this below, but I recommend that you read K&K, referenced below, for a
- careful, simple, and thorough explanation of this important and fundamental
- result.
-
- With a total energy E, S has many possible internal states
- (microstates). The atoms of S3 can share the total energy in many ways.
- Let's say there are N different states. Each state corresponds to a
- particular division of the total energy in the two subsystems S1 and S2.
- Many microstates can correspond to the same division, E1 in S1 and E2 in
- S2. A simple counting argument tells you that only one particular division
- of the energy, will occur with any significant probability. It's the one
- with the overwhelmingly largest number of microstates for the total system
- S3. That number, N(E1,E2) is just the product of the number of states
- allowed in each subsystem, N(E1,E2) = N1(E1)*N2(E2), and, since E1 + E2 =
- E, N(E1,E2) reaches a maximum when N1*N2 is stationary with respect to
- variations of E1 and E2 subject to the total energy constraint.
-
- For convenience, physicists prefer to frame the question in terms
- of the logarithm of the number of microstates N, and call this the entropy,
- S. You can easily see from the above analysis that two systems are in
- equilibrium with one another when (dS/dE)_1 = (dS/dE)_2, i.e., the rate of
- change of entropy, S, per unit change in energy, E, must be the same for
- both systems. Otherwise, energy will tend to flow from one subsystem to
- another as S3 bounces randomly from one microstate to another, the total
- energy E3 being constant, as the combined system moves towards a state of
- maximal total entropy. We define the temperature, T, by 1/T = dS/dE, so
- that the equilibrium condition becomes the very simple T_1 = T_2.
-
- This statistical mechanical definition of temperature does in fact
- correspond to your intuitive notion of temperature for most systems. So
- long as dS/dE is always positive, T is always positive. For common
- situations, like a collection of free particles, or particles in a harmonic
- oscillator potential, adding energy always increases the number of
- available microstates, increasingly faster with increasing total energy. So
- temperature increases with increasing energy, from zero, asymptotically
- approaching positive infinity as the energy increases.
-
- Step II: What is "Negative Temperature"?
- ----------------------------------------
-
- Not all systems have the property that the entropy increases
- monotonically with energy. In some cases, as energy is added to the system,
- the number of available microstates, or configurations, actually decreases
- for some range of energies. For example, imagine an ideal "spin-system", a
- set of N atoms with spin 1/2 one a one-dimensional wire. The atoms are not
- free to move from their positions on the wire. The only degree of freedom
- allowed to them is spin-flip: the spin of a given atom can point up or
- down. The total energy of the system, in a magnetic field of strength B,
- pointing down, is (N+ - N-)*uB, where u is the magnetic moment of each atom
- and N+ and N- are the number of atoms with spin up and down respectively.
- Notice that with this definition, E is zero when half of the spins are
- up and half are down. It is negative when the majority are down and
- positive when the majority are up.
-
- The lowest possible energy state, all the spins will point down,
- gives the system a total energy of -NuB, and temperature of absolute zero.
- There is only one configuration of the system at this energy, i.e., all the
- spins must point down. The entropy is the log of the number of
- microstates, so in this case is log(1) = 0. If we now add a quantum of
- energy, size uB, to the system, one spin is allowed to flip up. There are
- N possibilities, so the entropy is log(N). If we add another quantum of
- energy, there are a total of N(N-1)/2 allowable configurations with two
- spins up. The entropy is increasing quickly, and the temperature is rising
- as well.
-
- However, for this system, the entropy does not go on increasing
- forever. There is a maximum energy, +NuB, with all spins up. At this
- maximal energy, there is again only one microstate, and the entropy is
- again zero. If we remove one quantum of energy from the system, we allow
- one spin down. At this energy there are N available microstates. The
- entropy goes on increasing as the energy is lowered. In fact the maximal
- entropy occurs for total energy zero, i.e., half of the spins up, half
- down.
-
- So we have created a system where, as we add more and more energy,
- temperature starts off positive, approaches positive infinity as maximum
- entropy is approached, with half of all spins up. After that, the
- temperature becomes negative infinite, coming down in magnitude toward
- zero, but always negative, as the energy increases toward maximum. When the
- system has negative temperature, it is *hotter* than when it is has
- positive system. If you take two copies of the system, one with positive
- and one with negative temperature, and put them in thermal contact, heat
- will flow from the negative-temperature system into the positive-temperature
- system.
-
- Step III: What Does This Have to Do With the Real World?
- ---------------------------------------------------------
-
- Can this system ever by realized in the real world, or is it just a
- fantastic invention of sinister theoretical condensed matter physicists?
- Atoms always have other degrees of freedom in addition to spin, usually
- making the total energy of the system unbounded upward due to the
- translational degrees of freedom that the atom has. Thus, only certain
- degrees of freedom of a particle can have negative temperature. It makes
- sense to define the "spin-temperature" of a collection of atoms, so long as
- one condition is met: the coupling between the atomic spins and the other
- degrees of freedom is sufficiently weak, and the coupling between atomic
- spins sufficiently strong, that the timescale for energy to flow from the
- spins into other degrees of freedom is very large compared to the timescale
- for thermalization of the spins among themselves. Then it makes sense to
- talk about the temperature of the spins separately from the temperature of
- the atoms as a whole. This condition can easily be met for the case of
- nuclear spins in a strong external magnetic field.
-
- Nuclear and electron spin systems can be promoted to negative
- temperatures by suitable radio frequency techniques. Various experiments
- in the calorimetry of negative temperatures, as well as applications of
- negative temperature systems as RF amplifiers, etc., can be found in the
- articles listed below, and the references therein.
-
- References:
-
- Kittel and Kroemer,_Thermal Physics_, appendix E.
- N.F. Ramsey, "Thermodynamics and statistical mechanics at negative
- absolute temperature," Phys. Rev. _103_, 20 (1956).
- M.J. Klein,"Negative Absolute Temperature," Phys. Rev. _104_, 589 (1956).
-
- ********************************************************************************
- Item 17.
-
- Which Way Will my Bathtub Drain? updated 16-MAR-1993 by SIC
- -------------------------------- original by Matthew R. Feinstein
-
- Question: Does my bathtub drain differently depending on whether I live
- in the northern or southern hemisphere?
-
- Answer: No. There is a real effect, but it is far too small to be relevant
- when you pull the plug in your bathtub.
-
- Because the earth rotates, a fluid that flows along the earth's
- surface feels a "Coriolis" acceleration perpendicular to its velocity.
- In the northern hemisphere low pressure storm systems spin counterclockwise.
- In the southern hemisphere, they spin clockwise because the direction
- of the Coriolis acceleration is reversed. This effect leads to the
- speculation that the bathtub vortex that you see when you pull the plug
- from the drain spins one way in the north and the other way in the south.
-
- But this acceleration is VERY weak for bathtub-scale fluid
- motions. The order of magnitude of the Coriolis acceleration can be
- estimated from size of the "Rossby number" (see below). The effect of the
- Coriolis acceleration on your bathtub vortex is SMALL. To detect its
- effect on your bathtub, you would have to get out and wait until the motion
- in the water is far less than one rotation per day. This would require
- removing thermal currents, vibration, and any other sources of noise. Under
- such conditions, never occurring in the typical home, you WOULD see an
- effect. To see what trouble it takes to actually see the effect, see the
- reference below. Experiments have been done in both the northern and
- southern hemispheres to verify that under carefully controlled conditions,
- bathtubs drain in opposite directions due to the Coriolis acceleration from
- the Earth's rotation.
-
- Coriolis accelerations are significant when the Rossby number is
- SMALL. So, suppose we want a Rossby number of 0.1 and a bathtub-vortex
- length scale of 0.1 meter. Since the earth's rotation rate is about
- 10^(-4)/second, the fluid velocity should be less than or equal to
- 2*10^(-6) meters/second. This is a very small velocity. How small is it?
- Well, we can take the analysis a step further and calculate another, more
- famous dimensionless parameter, the Reynolds number.
-
- The Reynolds number is = L*U*density/viscosity
-
- Assuming that physicists bathe in hot water the viscosity will be
- about 0.005 poise and the density will be about 1.0, so the Reynolds Number
- is about 4*10^(-2).
-
- Now, life at low Reynolds numbers is different from life at high
- Reynolds numbers. In particular, at low Reynolds numbers, fluid physics is
- dominated by friction and diffusion, rather than by inertia: the time it
- would take for a particle of fluid to move a significant distance due to an
- acceleration is greater than the time it takes for the particle to break up
- due to diffusion.
-
- The same effect has been accused of responsibility for the
- direction water circulates when you flush a toilet. This is surely
- nonsense. In this case, the water rotates in the direction which the pipe
- points which carries the water from the tank to the bowl.
-
- Reference: Trefethen, L.M. et al, Nature 207 1084-5 (1965).
-
- ********************************************************************************
- Item 18.
-
- Why do Mirrors Reverse Left and Right? updated 16-MAR-1993 by SIC
- --------------------------------------
-
- The simple answer is that they don't. Look in a mirror and wave
- your right hand. On which side of the mirror is the hand that waved? The
- right side, of course.
-
- Mirrors DO reverse In/Out. Imaging holding an arrow in your hand.
- If you point it up, it will point up in the mirror. If you point it to the
- left, it will point to the left in the mirror. But if you point it toward
- the mirror, it will point right back at you. In and Out are reversed.
-
- If you take a three-dimensional, rectangular, coordinate system,
- (X,Y,Z), and point the Z axis such that the vector equation X x Y = Z is
- satisfied, then the coordinate system is said to be right-handed. Imagine
- Z pointing toward the mirror. X and Y are unchanged (remember the arrows?)
- but Z will point back at you. In the mirror, X x Y = - Z. The image
- contains a left-handed coordinate system.
-
- This has an important effect, familiar mostly to chemists and
- physicists. It changes the chirality, or handedness of objects viewed in
- the mirror. Your left hand looks like a right hand, while your right hand
- looks like a left hand. Molecules often come in pairs called
- stereoisomers, which differ not in the sequence or number of atoms, but
- only in that one is the mirror image of the other, so that no rotation or
- stretching can turn one into the other. Your hands make a good laboratory
- for this effect. They are distinct, even though they both have the same
- components connected in the same way. They are a stereo pair, identical
- except for "handedness".
-
- People sometimes think that mirrors *do* reverse left/right, and
- that the effect is due to the fact that our eyes are aligned horizontally
- on our faces. This can be easily shown to be untrue by looking in any
- mirror with one eye closed!
-
- Reference: _The Left Hand of the Neutrino_, by Isaac Asimov, contains
- a very readable discussion of handedness and mirrors in physics.
-
- ********************************************************************************
- Item 19.
-
- What is the Mass of a Photon? updated 24-JUL-1992 by SIC
- original by Matt Austern
-
- Or, "Does the mass of an object depend on its velocity?"
-
- This question usually comes up in the context of wondering whether
- photons are really "massless," since, after all, they have nonzero energy.
- The problem is simply that people are using two different definitions of
- mass. The overwhelming consensus among physicists today is to say that
- photons are massless. However, it is possible to assign a "relativistic
- mass" to a photon which depends upon its wavelength. This is based upon
- an old usage of the word "mass" which, though not strictly wrong, is not
- used much today.
-
- The old definition of mass, called "relativistic mass," assigns
- a mass to a particle proportional to its total energy E, and involved
- the speed of light, c, in the proportionality constant:
-
- m = E / c^2. (1)
-
- This definition gives every object a velocity-dependent mass.
-
- The modern definition assigns every object just one mass, an
- invariant quantity that does not depend on velocity. This is given by
-
- m = E_0 / c^2, (2)
-
- where E_0 is the total energy of that object at rest.
-
- The first definition is often used in popularizations, and in some
- elementary textbooks. It was once used by practicing physicists, but for
- the last few decades, the vast majority of physicists have instead used the
- second definition. Sometimes people will use the phrase "rest mass," or
- "invariant mass," but this is just for emphasis: mass is mass. The
- "relativistic mass" is never used at all. (If you see "relativistic mass"
- in your first-year physics textbook, complain! There is no reason for books
- to teach obsolete terminology.)
-
- Note, by the way, that using the standard definition of mass, the
- one given by Eq. (2), the equation "E = m c^2" is *not* correct. Using the
- standard definition, the relation between the mass and energy of an object
- can be written as
-
- E = m c^2 / sqrt(1 -v^2/c^2), (3)
- or as
-
- E^2 = m^2 c^4 + p^2 c^2, (4)
-
- where v is the object's velocity, and p is its momentum.
-
- In one sense, any definition is just a matter of convention. In
- practice, though, physicists now use this definition because it is much
- more convenient. The "relativistic mass" of an object is really just the
- same as its energy, and there isn't any reason to have another word for
- energy: "energy" is a perfectly good word. The mass of an object, though,
- is a fundamental and invariant property, and one for which we do need a
- word.
-
- The "relativistic mass" is also sometimes confusing because it
- mistakenly leads people to think that they can just use it in the Newtonian
- relations
- F = m a (5)
- and
- F = G m1 m2 / r^2. (6)
-
- In fact, though, there is no definition of mass for which these
- equations are true relativistically: they must be generalized. The
- generalizations are more straightforward using the standard definition
- of mass than using "relativistic mass."
-
- Oh, and back to photons: people sometimes wonder whether it makes
- sense to talk about the "rest mass" of a particle that can never be at
- rest. The answer, again, is that "rest mass" is really a misnomer, and it
- is not necessary for a particle to be at rest for the concept of mass to
- make sense. Technically, it is the invariant length of the particle's
- four-momentum. (You can see this from Eq. (4).) For all photons this is
- zero. On the other hand, the "relativistic mass" of photons is frequency
- dependent. UV photons are more energetic than visible photons, and so are
- more "massive" in this sense, a statement which obscures more than it
- elucidates.
-
- Reference: Lev Okun wrote a nice article on this subject in the
- June 1989 issue of Physics Today, which includes a historical discussion
- of the concept of mass in relativistic physics.
-
- ********************************************************************************
- Item 20.
- updated 16-MAR-1992 by SIC
- Original by John Blanton
- Why Do Stars Twinkle While Planets Do Not?
- -----------------------------------------
-
- Stars, except for the Sun, although they may be millions of miles
- in diameter, are very far away. They appear as point sources even when
- viewed by telescopes. The planets in our solar system, much smaller than
- stars, are closer and can be resolved as disks with a little bit of
- magnification (field binoculars, for example).
-
- Since the Earth's atmosphere is turbulent, all images viewed up
- through it tend to "swim." The result of this is that sometimes a single
- point in object space gets mapped to two or more points in image space, and
- also sometimes a single point in object space does not get mapped into any
- point in image space. When a star's single point in object space fails to
- map to at least one point in image space, the star seems to disappear
- temporarily. This does not mean the star's light is lost for that moment.
- It just means that it didn't get to your eye, it went somewhere else.
-
- Since planets represent several points in object space, it is
- highly likely that one or more points in the planet's object space get
- mapped to a points in image space, and the planet's image never winks out.
- Each individual ray is twinkling away as badly as any star, but when all of
- those individual rays are viewed together, the next effect is averaged out
- to something considerably steadier.
-
- The result is that stars tend to twinkle, and planets do not.
- Other extended objects in space, even very far ones like nebulae, do not
- twinkle if they are sufficiently large that they have non-zero apparent
- diameter when viewed from the Earth.
-
- ********************************************************************************
- Item 21. original by David Brahm
-
- Baryogenesis - Why Are There More Protons Than Antiprotons?
- -----------------------------------------------------------
-
- (I) How do we really *know* that the universe is not matter-antimatter
- symmetric?
-
- (a) The Moon: Neil Armstrong did not annihilate, therefore the moon
- is made of matter.
- (b) The Sun: Solar cosmic rays are matter, not antimatter.
- (c) The other Planets: We have sent probes to almost all. Their survival
- demonstrates that the solar system is made of matter.
- (d) The Milky Way: Cosmic rays sample material from the entire galaxy.
- In cosmic rays, protons outnumber antiprotons 10^4 to 1.
- (e) The Universe at large: This is tougher. If there were antimatter
- galaxies then we should see gamma emissions from annihilation. Its absence
- is strong evidence that at least the nearby clusters of galaxies (e.g., Virgo)
- are matter-dominated. At larger scales there is little proof.
- However, there is a problem, called the "annihilation catastrophe"
- which probably eliminates the possibility of a matter-antimatter symmetric
- universe. Essentially, causality prevents the separation of large chucks
- of antimatter from matter fast enough to prevent their mutual annihilation
- in in the early universe. So the Universe is most likely matter dominated.
-
- (II) How did it get that way?
-
- Annihilation has made the asymmetry much greater today than in the
- early universe. At the high temperature of the first microsecond, there
- were large numbers of thermal quark-antiquark pairs. K&T estimate 30
- million antiquarks for every 30 million and 1 quarks during this epoch.
- That's a tiny asymmetry. Over time most of the antimatter has annihilated
- with matter, leaving the very small initial excess of matter to dominate
- the Universe.
-
- Here are a few possibilities for why we are matter dominated today:
-
- a) The Universe just started that way.
- Not only is this a rather sterile hypothesis, but it doesn't work under
- the popular "inflation" theories, which dilute any initial abundances.
- b) Baryogenesis occurred around the Grand Unified (GUT) scale (very early).
- Long thought to be the only viable candidate, GUT's generically have
- baryon-violating reactions, such as proton decay (not yet observed).
- c) Baryogenesis occurred at the Electroweak Phase Transition (EWPT).
- This is the era when the Higgs first acquired a vacuum expectation value
- (vev), so other particles acquired masses. Pure Standard Model physics.
-
- Sakharov enumerated 3 necessary conditions for baryogenesis:
-
- (1) Baryon number violation. If baryon number is conserved in all
- reactions, then the present baryon asymmetry can only reflect asymmetric
- initial conditions, and we are back to case (a), above.
- (2) C and CP violation. Even in the presence of B-violating
- reactions, without a preference for matter over antimatter the B-violation
- will take place at the same rate in both directions, leaving no excess.
- (3) Thermodynamic Nonequilibrium. Because CPT guarantees equal
- masses for baryons and antibaryons, chemical equilibrium would drive the
- necessary reactions to correct for any developing asymmetry.
-
- It turns out the Standard Model satisfies all 3 conditions:
-
- (1) Though the Standard Model conserves B classically (no terms in
- the Lagrangian violate B), quantum effects allow the universe to tunnel
- between vacua with different values of B. This tunneling is _very_
- suppressed at energies/temperatures below 10 TeV (the "sphaleron mass"),
- _may_ occur at e.g. SSC energies (controversial), and _certainly_ occurs at
- higher temperatures.
-
- (2) C-violation is commonplace. CP-violation (that's "charge
- conjugation" and "parity") has been experimentally observed in kaon
- decays, though strictly speaking the Standard Model probably has
- insufficient CP-violation to give the observed baryon asymmetry.
-
- (3) Thermal nonequilibrium is achieved during first-order phase
- transitions in the cooling early universe, such as the EWPT (at T = 100 GeV
- or so). As bubbles of the "true vacuum" (with a nonzero Higgs vev)
- percolate and grow, baryogenesis can occur at or near the bubble walls.
-
- A major theoretical problem, in fact, is that there may be _too_
- _much_ B-violation in the Standard Model, so that after the EWPT is
- complete (and condition 3 above is no longer satisfied) any previously
- generated baryon asymmetry would be washed out.
-
- References: Kolb and Turner, _The Early Universe_;
- Dine, Huet, Singleton & Susskind, Phys.Lett.B257:351 (1991);
- Dine, Leigh, Huet, Linde & Linde, Phys.Rev.D46:550 (1992).
-
- ********************************************************************************
- Item 22.
-
- TIME TRAVEL - FACT OR FICTION? updated 18-NOV-1993
- ------------------------------ original by Jon J. Thaler
-
- We define time travel to mean departure from a certain place and
- time followed (from the traveller's point of view) by arrival at the same
- place at an earlier (from the sedentary observer's point of view) time.
- Time travel paradoxes arise from the fact that departure occurs after
- arrival according to one observer and before arrival according to another.
- In the terminology of special relativity time travel implies that the
- timelike ordering of events is not invariant. This violates our intuitive
- notions of causality. However, intuition is not an infallible guide, so we
- must be careful. Is time travel really impossible, or is it merely another
- phenomenon where "impossible" means "nature is weirder than we think?" The
- answer is more interesting than you might think.
-
- THE SCIENCE FICTION PARADIGM:
-
- The B-movie image of the intrepid chrononaut climbing into his time
- machine and watching the clock outside spin backwards while those outside
- the time machine watch the him revert to callow youth is, according to
- current theory, impossible. In current theory, the arrow of time flows in
- only one direction at any particular place. If this were not true, then
- one could not impose a 4-dimensional coordinate system on space-time, and
- many nasty consequences would result. Nevertheless, there is a scenario
- which is not ruled out by present knowledge. This usually requires an
- unusual spacetime topology (due to wormholes or strings in general
- relativity) which has not not yet seen, but which may be possible. In
- this scenario the universe is well behaved in every local region; only by
- exploring the global properties does one discover time travel.
-
- CONSERVATION LAWS:
-
- It is sometimes argued that time travel violates conservation laws.
- For example, sending mass back in time increases the amount of energy that
- exists at that time. Doesn't this violate conservation of energy? This
- argument uses the concept of a global conservation law, whereas
- relativistically invariant formulations of the equations of physics only
- imply local conservation. A local conservation law tells us that the
- amount of stuff inside a small volume changes only when stuff flows in or
- out through the surface. A global conservation law is derived from this by
- integrating over all space and assuming that there is no flow in or out at
- infinity. If this integral cannot be performed, then global conservation
- does not follow. So, sending mass back in time might be alright, but it
- implies that something strange is happening. (Why shouldn't we be able to
- do the integral?)
-
- GENERAL RELATIVITY:
-
- One case where global conservation breaks down is in general
- relativity. It is well known that global conservation of energy does not
- make sense in an expanding universe. For example, the universe cools as it
- expands; where does the energy go? See FAQ article #1 - Energy
- Conservation in Cosmology, for details.
-
- It is interesting to note that the possibility of time travel in GR
- has been known at least since 1949 (by Kurt Godel, discussed in [1], page
- 168). The GR spacetime found by Godel has what are now called "closed
- timelike curves" (CTCs). A CTC is a worldline that a particle or a person
- can follow which ends at the same spacetime point (the same position and
- time) as it started. A solution to GR which contains CTCs cannot have a
- spacelike embedding - space must have "holes" (as in donut holes, not holes
- punched in a sheet of paper). A would-be time traveller must go around or
- through the holes in a clever way.
-
- The Godel solution is a curiosity, not useful for constructing a
- time machine. Two recent proposals, one by Morris, et al. [2] and one by
- Gott [3], have the possibility of actually leading to practical devices (if
- you believe this, I have a bridge to sell you). As with Godel, in these
- schemes nothing is locally strange; time travel results from the unusual
- topology of spacetime. The first uses a wormhole (the inner part of a
- black hole, see fig. 1 of [2]) which is held open and manipulated by
- electromagnetic forces. The second uses the conical geometry generated by
- an infinitely long string of mass. If two strings pass by each other, a
- clever person can go into the past by traveling a figure-eight path around
- the strings. In this scenario, if the string has non-zero diameter and
- finite mass density, there is a CTC without any unusual topology.
-
- GRANDFATHER PARADOXES:
-
- With the demonstration that general relativity contains CTCs,
- people began studying the problem of self-consistency. Basically, the
- problem is that of the "grandfather paradox:" What happens if our time
- traveller kills her grandmother before her mother was born? In more
- readily analyzable terms, one can ask what are the implications of the
- quantum mechanical interference of the particle with its future self.
- Boulware [5] shows that there is a problem - unitarity is violated. This is
- related to the question of when one can do the global conservation integral
- discussed above. It is an example of the "Cauchy problem" [1, chapter 7].
-
- OTHER PROBLEMS (and an escape hatch?):
-
- How does one avoid the paradox that a simple solution to GR has
- CTCs which QM does not like? This is not a matter of applying a theory in
- a domain where it is expected to fail. One relevant issue is the
- construction of the time machine. After all, infinite strings aren't
- easily obtained. In fact, it has been shown [4] that Gott's scenario
- implies that the total 4-momentum of spacetime must be spacelike. This
- seems to imply that one cannot build a time machine from any collection of
- non-tachyonic objects, whose 4-momentum must be timelike. There are
- implementation problems with the wormhole method as well.
-
- TACHYONS:
-
- Finally, a diversion on a possibly related topic.
-
- If tachyons exist as physical objects, causality is no longer
- invariant. Different observers will see different causal sequences. This
- effect requires only special relativity (not GR), and follows from the fact
- that for any spacelike trajectory, reference frames can be found in which
- the particle moves backward or forward in time. This is illustrated by the
- pair of spacetime diagrams below. One must be careful about what is
- actually observed; a particle moving backward in time is observed to be a
- forward moving anti-particle, so no observer interprets this as time
- travel.
-
- t
- One reference | Events A and C are at the same
- frame: | place. C occurs first.
- |
- | Event B lies outside the causal
- | B domain of events A and C.
- -----------A----------- x (The intervals are spacelike).
- |
- C In this frame, tachyon signals
- | travel from A-->B and from C-->B.
- | That is, A and C are possible causes
- of event B.
-
- Another t
- reference | Events A and C are not at the same
- frame: | place. C occurs first.
- |
- | Event B lies outside the causal
- -----------A----------- x domain of events A and C. (The
- | intervals are spacelike)
- |
- | C In this frame, signals travel from
- | B-->A and from B-->C. B is the cause
- | B of both of the other two events.
-
- The unusual situation here arises because conventional causality
- assumes no superluminal motion. This tachyon example is presented to
- demonstrate that our intuitive notion of causality may be flawed, so one
- must be careful when appealing to common sense. See FAQ article # 6 -
- Tachyons, for more about these weird hypothetical particles.
-
- CONCLUSION:
-
- The possible existence of time machines remains an open question.
- None of the papers criticizing the two proposals are willing to
- categorically rule out the possibility. Nevertheless, the notion of time
- machines seems to carry with it a serious set of problems.
-
- REFERENCES:
-
- 1: S.W. Hawking, and G.F.R. Ellis, "The Large Scale Structure of Space-Time,"
- Cambridge University Press, 1973.
- 2: M.S. Morris, K.S. Thorne, and U. Yurtsever, PRL, v.61, p.1446 (1989).
- --> How wormholes can act as time machines.
- 3: J.R. Gott, III, PRL, v.66, p.1126 (1991).
- --> How pairs of cosmic strings can act as time machines.
- 4: S. Deser, R. Jackiw, and G. 't Hooft, PRL, v.66, p.267 (1992).
- --> A critique of Gott. You can't construct his machine.
- 5: D.G. Boulware, University of Washington preprint UW/PT-92-04.
- Available on the hep-th@xxx.lanl.gov bulletin board: item number 9207054.
- --> Unitarity problems in QM with closed timelike curves.
- 6: "Nature", May 7, 1992
- --> Contains a very well written review with some nice figures.
-
- ********************************************************************************
- Item 23.
-
- The EPR Paradox and Bell's Inequality Principle updated 31-AUG-1993 by SIC
- ----------------------------------------------- original by John Blanton
-
- In 1935 Albert Einstein and two colleagues, Boris Podolsky and
- Nathan Rosen (EPR) developed a thought experiment to demonstrate what they
- felt was a lack of completeness in quantum mechanics. This so-called "EPR
- paradox" has lead to much subsequent, and still on-going, research. This
- article is an introduction to EPR, Bell's inequality, and the real
- experiments which have attempted to address the interesting issues raised
- by this discussion.
-
- One of the principle features of quantum mechanics is that not all
- the classical physical observables of a system can be simultaneously known,
- either in practice or in principle. Instead, there may be several sets of
- observables which give qualitatively different, but nonetheless complete
- (maximal possible) descriptions of a quantum mechanical system. These sets
- are sets of "good quantum numbers," and are also known as "maximal sets of
- commuting observables." Observables from different sets are "noncommuting
- observables."
-
- A well known example of noncommuting observables are position and
- momentum. You can put a subatomic particle into a state of well-defined
- momentum, but then you cannot know where it is - it is, in fact, everywhere
- at once. It's not just a matter of your inability to measure, but rather,
- an intrinsic property of the particle. Conversely, you can put a particle
- in a definite position, but then it's momentum is completely ill-defined.
- You can also create states of intermediate knowledge of both observables:
- If you confine the particle to some arbitrarily large region of space,
- you can define the momentum more and more precisely. But you can never
- know both, exactly, at the same time.
-
- Position and momentum are continuous observables. But the same
- situation can arise for discrete observables such as spin. The quantum
- mechanical spin of a particle along each of the three space axes are a set
- of mutually noncommuting observables. You can only know the spin along one
- axis at a time. A proton with spin "up" along the x-axis has undefined
- spin along the y and z axes. You cannot simultaneously measure the x and y
- spin projections of a proton. EPR sought to demonstrate that this
- phenomenon could be exploited to construct an experiment which would
- demonstrate a paradox which they believed was inherent in the
- quantum-mechanical description of the world.
-
- They imagined two physical systems that are allowed to interact
- initially so that they subsequently will be defined by a single Schrodinger
- wave equation (SWE). [For simplicity, imagine a simple physical
- realization of this idea - a neutral pion at rest in your lab, which decays
- into a pair of back-to-back photons. The pair of photons is described
- by a single two-particle wave function.] Once separated, the two systems
- [read: photons] are still described by the same SWE, and a measurement of
- one observable of the first system will determine the measurement of the
- corresponding observable of the second system. [Example: The neutral pion
- is a scalar particle - it has zero angular momentum. So the two photons
- must speed off in opposite directions with opposite spin. If photon 1
- is found to have spin up along the x-axis, then photon 2 *must* have spin
- down along the x-axis, since the total angular momentum of the final-state,
- two-photon, system must be the same as the angular momentum of the intial
- state, a single neutral pion. You know the spin of photon 2 even without
- measuring it.] Likewise, the measurement of another observable of the first
- system will determine the measurement of the corresponding observable of the
- second system, even though the systems are no longer physically linked in
- the traditional sense of local coupling.
-
- However, QM prohibits the simultaneous knowledge of more than one
- mutually noncommuting observable of either system. The paradox of EPR is
- the following contradiction: For our coupled systems, we can measure
- observable A of system I [for example, photon 1 has spin up along the
- x-axis; photon 2 must therefore have x-spin down.] and observable B of
- system II [for example, photon 2 has spin down along the y-axis; therefore
- the y-spin of photon 1 must be up.] thereby revealing both observables for
- both systems, contrary to QM.
-
- QM dictates that this should be impossible, creating the
- paradoxical implication that measuring one system should "poison" any
- measurement of the other system, no matter what the distance between
- them. [In one commonly studied interpretation, the mechanism by which
- this proceeds is 'instantaneous collapse of the wavefunction'. But
- the rules of QM do not require this interpretation, and several
- other perfectly valid interpretations exist.] The second system
- would instantaneously be put into a state of well-defined observable A,
- and, consequently, ill-defined observable B, spoiling the measurement.
- Yet, one could imagine the two measurements were so far apart in
- space that special relativity would prohibit any influence of one
- measurement over the other. [After the neutral-pion decay, we can wait until
- the two photons are a light-year apart, and then "simultaneously" measure
- the x-spin of photon 1 and the y-spin of photon 2. QM suggests that if,
- for example, the measurement of the photon 1 x-spin happens first, this
- measurement must instantaneously force photon 2 into a state of ill-defined
- y-spin, even though it is light-years away from photon 1.
-
- How do we reconcile the fact that photon 2 "knows" that the x-spin
- of photon 1 has been measured, even though they are separated by
- light-years of space and far too little time has passed for information
- to have travelled to it according to the rules of Special Relativity?
- There are basically two choices. You can accept the postulates of QM"
- as a fact of life, in spite of its seemingly uncomfortable coexistence
- with special relativity, or you can postulate that QM is not complete,
- that there *was* more information available for the description of the
- two-particle system at the time it was created, carried away by both
- photons, and that you just didn't know it because QM does not properly
- account for it.
-
- So, EPR postulated the existence of hidden variables, some so-far
- unknown properties, of the systems should account for the discrepancy.
- Their claim was that QM theory is incomplete; it does not completely
- describe the physical reality. System II knows all about System I
- long before the scientist measures any of the observables, and thereby
- supposedly consigning the other noncommuting observables to obscurity.
- No instantaneous action-at-a-distance is necessary in this picture,
- which postulates that each System has more parameters than are
- accounted by QM. Niels Bohr, one of the founders of QM, held the opposite
- view and defended a strict interpretation, the Copenhagen Interpretation,
- of QM.
-
- In 1964 John S. Bell proposed a mechanism to test for the existence
- of these hidden parameters, and he developed his inequality principle as
- the basis for such a test.
-
- Use the example of two photons configured in the singlet state,
- consider this: After separation, each photon will have spin values for
- each of the three axes of space, and each spin can have one of two values;
- call them up and down. Call the axes A, B and C and call the spin in the A
- axis A+ if it is up in that axis, otherwise call it A-. Use similar
- definitions for the other two axes.
-
- Now perform the experiment. Measure the spin in one axis of one
- particle and the spin in another axis of the other photon. If EPR were
- correct, each photon will simultaneously have properties for spin in each
- of axes A, B and C.
-
- Look at the statistics. Perform the measurements with a number of
- sets of photons. Use the symbol N(A+, B-) to designate the words "the
- number of photons with A+ and B-." Similarly for N(A+, B+), N(B-, C+),
- etc. Also use the designation N(A+, B-, C+) to mean "the number of photons
- with A+, B- and C+," and so on. It's easy to demonstrate that for a set of
- photons
-
- (1) N(A+, B-) = N(A+, B-, C+) + N(A+, B-, C-)
-
- because all of the (A+, B-, C+) and all of the (A+, B-, C-) photons are
- included in the designation (A+, B-), and nothing else is included in N(A+,
- B-). You can make this claim if these measurements are connected to some
- real properties of the photons.
-
- Let n[A+, B+] be the designation for "the number of measurements of
- pairs of photons in which the first photon measured A+, and the second
- photon measured B+." Use a similar designation for the other possible
- results. This is necessary because this is all it is possible to measure.
- You can't measure both A and B of the same photon. Bell demonstrated that
- in an actual experiment, if (1) is true (indicating real properties), then
- the following must be true:
-
- (2) n[A+, B+] <= n[A+, C+] + n[B+, C-].
-
- Additional inequality relations can be written by just making the
- appropriate permutations of the letters A, B and C and the two signs. This
- is Bell's inequality principle, and it is proved to be true if there are
- real (perhaps hidden) parameters to account for the measurements.
-
- At the time Bell's result first became known, the experimental
- record was reviewed to see if any known results provided evidence against
- locality. None did. Thus an effort began to develop tests of Bell's
- inequality. A series of experiments was conducted by Aspect ending with one
- in which polarizer angles were changed while the photons were `in flight'.
- This was widely regarded at the time as being a reasonably conclusive
- experiment confirming the predictions of QM.
-
- Three years later Franson published a paper showing that the timing
- constraints in this experiment were not adequate to confirm that locality
- was violated. Aspect measured the time delays between detections of photon
- pairs. The critical time delay is that between when a polarizer angle is
- changed and when this affects the statistics of detecting photon pairs.
- Aspect estimated this time based on the speed of a photon and the distance
- between the polarizers and the detectors. Quantum mechanics does not allow
- making assumptions about *where* a particle is between detections. We
- cannot know *when* a particle traverses a polarizer unless we detect the
- particle *at* the polarizer.
-
- Experimental tests of Bell's inequality are ongoing but none has
- yet fully addressed the issue raised by Franson. In addition there is an
- issue of detector efficiency. By postulating new laws of physics one can
- get the expected correlations without any nonlocal effects unless the
- detectors are close to 90% efficient. The importance of these issues is a
- matter of judgement.
-
- The subject is alive theoretically as well. In the 1970's
- Eberhard derived Bell's result without reference to local hidden variable
- theories; it applies to all local theories. Eberhard also showed that the
- nonlocal effects that QM predicts cannot be used for superluminal
- communication. The subject is not yet closed, and may yet provide more
- interesting insights into the subtleties of quantum mechanics.
-
- REFERENCES:
-
- 1. A. Einstein, B. Podolsky, N. Rosen: "Can quantum-mechanical
- description of physical reality be considered complete?"
- Physical Review 41, 777 (15 May 1935). (The original EPR paper)
-
- 2. D. Bohm: Quantum Theory, Dover, New York (1957). (Bohm
- discusses some of his ideas concerning hidden variables.)
-
- 3. N. Herbert: Quantum Reality, Doubleday. (A very good
- popular treatment of EPR and related issues)
-
- 4. M. Gardner: Science - Good, Bad and Bogus, Prometheus Books.
- (Martin Gardner gives a skeptics view of the fringe science
- associated with EPR.)
-
- 5. J. Gribbin: In Search of Schrodinger's Cat, Bantam Books.
- (A popular treatment of EPR and the paradox of "Schrodinger's
- cat" that results from the Copenhagen interpretation)
-
- 6. N. Bohr: "Can quantum-mechanical description of physical
- reality be considered complete?" Physical Review 48, 696 (15 Oct
- 1935). (Niels Bohr's response to EPR)
-
- 7. J. Bell: "On the Einstein Podolsky Rosen paradox" Physics 1
- #3, 195 (1964).
-
- 8. J. Bell: "On the problem of hidden variables in quantum
- mechanics" Reviews of Modern Physics 38 #3, 447 (July 1966).
-
- 9. D. Bohm, J. Bub: "A proposed solution of the measurement
- problem in quantum mechanics by a hidden variable theory"
- Reviews of Modern Physics 38 #3, 453 (July 1966).
-
- 10. B. DeWitt: "Quantum mechanics and reality" Physics Today p.
- 30 (Sept 1970).
-
- 11. J. Clauser, A. Shimony: "Bell's theorem: experimental
- tests and implications" Rep. Prog. Phys. 41, 1881 (1978).
-
- 12. A. Aspect, Dalibard, Roger: "Experimental test of Bell's
- inequalities using time- varying analyzers" Physical Review
- Letters 49 #25, 1804 (20 Dec 1982).
-
- 13. A. Aspect, P. Grangier, G. Roger: "Experimental realization
- of Einstein-Podolsky-Rosen-Bohm gedankenexperiment; a new
- violation of Bell's inequalities" Physical Review Letters 49
- #2, 91 (12 July 1982).
-
- 14. A. Robinson: "Loophole closed in quantum mechanics test"
- Science 219, 40 (7 Jan 1983).
-
- 15. B. d'Espagnat: "The quantum theory and reality" Scientific
- American 241 #5 (November 1979).
-
- 16. "Bell's Theorem and Delayed Determinism", Franson, Physical Review D,
- pgs. 2529-2532, Vol. 31, No. 10, May 1985.
-
- 17. "Bell's Theorem without Hidden Variables", P. H. Eberhard, Il Nuovo
- Cimento, 38 B 1, pgs. 75-80, (1977).
-
- 18. "Bell's Theorem and the Different Concepts of Locality", P. H.
- Eberhard, Il Nuovo Cimento 46 B, pgs. 392-419, (1978).
- ********************************************************************************
- Item 24.
-
- The Nobel Prize for Physics (1901-1993) updated 15-OCT-1993 by SIC
- ---------------------------------------
-
- The following is a complete listing of Nobel Prize awards, from the first
- award in 1901. Prizes were not awarded in every year. The description
- following the names is an abbreviation of the official citation.
-
- 1901 Wilhelm Konrad Rontgen X-rays
- 1902 Hendrik Antoon Lorentz Magnetism in radiation phenomena
- Pieter Zeeman
- 1903 Antoine Henri Bequerel Spontaneous radioactivity
- Pierre Curie
- Marie Sklowdowska-Curie
- 1904 Lord Rayleigh Density of gases and
- (a.k.a. John William Strutt) discovery of argon
- 1905 Pilipp Eduard Anton von Lenard Cathode rays
- 1906 Joseph John Thomson Conduction of electricity by gases
- 1907 Albert Abraham Michelson Precision metrological investigations
- 1908 Gabriel Lippman Reproducing colors photographically
- based on the phenomenon of interference
- 1909 Guglielmo Marconi Wireless telegraphy
- Carl Ferdinand Braun
- 1910 Johannes Diderik van der Waals Equation of state of fluids
- 1911 Wilhelm Wien Laws of radiation of heat
- 1912 Nils Gustaf Dalen Automatic gas flow regulators
- 1913 Heike Kamerlingh Onnes Matter at low temperature
- 1914 Max von Laue Crystal diffraction of X-rays
- 1915 William Henry Bragg X-ray analysis of crystal structure
- William Lawrence Bragg
- 1917 Charles Glover Barkla Characteristic X-ray spectra of elements
- 1918 Max Planck Energy quanta
- 1919 Johannes Stark Splitting of spectral lines in E fields
- 1920 Charles-Edouard Guillaume Anomalies in nickel steel alloys
- 1921 Albert Einstein Photoelectric Effect
- 1922 Niels Bohr Structure of atoms
- 1923 Robert Andrew Millikan Elementary charge of electricity
- 1924 Karl Manne Georg Siegbahn X-ray spectroscopy
- 1925 James Franck Impact of an electron upon an atom
- Gustav Hertz
- 1926 Jean Baptiste Perrin Sedimentation equilibrium
- 1927 Arthur Holly Compton Compton effect
- Charles Thomson Rees Wilson Invention of the Cloud chamber
- 1928 Owen Willans Richardson Thermionic phenomena, Richardson's Law
- 1929 Prince Louis-Victor de Broglie Wave nature of electrons
- 1930 Sir Chandrasekhara Venkata Raman Scattering of light, Raman effect
- 1932 Werner Heisenberg Quantum Mechanics
- 1933 Erwin Schrodinger Atomic theory
- Paul Adrien Maurice Dirac
- 1935 James Chadwick The neutron
- 1936 Victor Franz Hess Cosmic rays
- Carl D. Anderson The positron
- 1937 Clinton Joseph Davisson Crystal diffraction of electrons
- George Paget Thomson
- 1938 Enrico Fermi New radioactive elements
- 1939 Ernest Orlando Lawrence Invention of the Cyclotron
- 1943 Otto Stern Proton magnetic moment
- 1944 Isador Isaac Rabi Magnetic resonance in atomic nuclei
- 1945 Wolfgang Pauli The Exclusion principle
- 1946 Percy Williams Bridgman Production of extremely high pressures
- 1947 Sir Edward Victor Appleton Physics of the upper atmosphere
- 1948 Patrick Maynard Stuart Blackett Cosmic ray showers in cloud chambers
- 1949 Hideki Yukawa Prediction of Mesons
- 1950 Cecil Frank Powell Photographic emulsion for meson studies
- 1951 Sir John Douglas Cockroft Artificial acceleration of atomic
- Ernest Thomas Sinton Walton particles and transmutation of nuclei
- 1952 Felix Bloch Nuclear magnetic precision methods
- Edward Mills Purcell
- 1953 Frits Zernike Phase-contrast microscope
- 1954 Max Born Fundamental research in QM
- Walther Bothe Coincidence counters
- 1955 Willis Eugene Lamb Hydrogen fine structure
- Polykarp Kusch Electron magnetic moment
- 1956 William Shockley Transistors
- John Bardeen
- Walter Houser Brattain
- 1957 Chen Ning Yang Parity violation
- Tsung Dao Lee
- 1958 Pavel Aleksejevic Cerenkov Interpretation of the Cerenkov effect
- Il'ja Mickajlovic Frank
- Igor' Evgen'evic Tamm
- 1959 Emilio Gino Segre The Antiproton
- Owen Chamberlain
- 1960 Donald Arthur Glaser The Bubble Chamber
- 1961 Robert Hofstadter Electron scattering on nucleons
- Rudolf Ludwig Mossbauer Resonant absorption of photons
- 1962 Lev Davidovic Landau Theory of liquid helium
- 1963 Eugene P. Wigner Fundamental symmetry principles
- Maria Goeppert Mayer Nuclear shell structure
- J. Hans D. Jensen
- 1964 Charles H. Townes Maser-Laser principle
- Nikolai G. Basov
- Alexander M. Prochorov
- 1965 Sin-Itiro Tomonaga Quantum electrodynamics
- Julian Schwinger
- Richard P. Feynman
- 1966 Alfred Kastler Study of Hertzian resonance in atoms
- 1967 Hans Albrecht Bethe Energy production in stars
- 1968 Luis W. Alvarez Discovery of many particle resonances
- 1969 Murray Gell-Mann Quark model for particle classification
- 1970 Hannes Alfven Magneto-hydrodynamics in plasma physics
- Louis Neel Antiferromagnetism and ferromagnetism
- 1971 Dennis Gabor Principles of holography
- 1972 John Bardeen Superconductivity
- Leon N. Cooper
- J. Robert Schrieffer
- 1973 Leo Esaki Tunneling in superconductors
- Ivar Giaever
- Brian D. Josephson Super-current through tunnel barriers
- 1974 Antony Hewish Discovery of pulsars
- Sir Martin Ryle Pioneering radioastronomy work
- 1975 Aage Bohr Structure of the atomic nucleus
- Ben Mottelson
- James Rainwater
- 1976 Burton Richter Discovery of the J/Psi particle
- Samual Chao Chung Ting
- 1977 Philip Warren Anderson Electronic structure of magnetic and
- Nevill Francis Mott disordered solids
- John Hasbrouck Van Vleck
- 1978 Pyotr Kapitsa Liquifaction of helium
- Arno A. Penzias Cosmic Microwave Background Radiation
- Robert W. Wilson
- 1979 Sheldon Glashow Electroweak Theory, especially
- Steven Weinberg weak neutral currents
- Abdus Salam
- 1980 James Cronin Discovery of CP violation in the
- Val Fitch asymmetric decay of neutral K-mesons
- 1981 Kai M. Seigbahn High resolution electron spectroscopy
- Nicolaas Bleombergen Laser spectroscopy
- Arthur L. Schawlow
- 1982 Kenneth G. Wilson Critical phenomena in phase transitions
- 1983 Subrahmanyan Chandrasekhar Evolution of stars
- William A. Fowler
- 1984 Carlo Rubbia Discovery of W,Z
- Simon van der Meer Stochastic cooling for colliders
- 1985 Klaus von Klitzing Discovery of quantum Hall effect
- 1986 Gerd Binning Scanning Tunneling Microscopy
- Heinrich Rohrer
- Ernst August Friedrich Ruska Electron microscopy
- 1987 Georg Bednorz High-temperature superconductivity
- Alex K. Muller
- 1988 Leon Max Lederman Discovery of the muon neutrino leading
- Melvin Schwartz to classification of particles in
- Jack Steinberger families
- 1989 Hans Georg Dehmelt Penning Trap for charged particles
- Wolfgang Paul Paul Trap for charged particles
- Norman F. Ramsey Control of atomic transitions by the
- separated oscillatory fields method
- 1990 Jerome Isaac Friedman Deep inelastic scattering experiments
- Henry Way Kendall leading to the discovery of quarks
- Richard Edward Taylor
- 1991 Pierre-Gilles de Gennes Order-disorder transitions in liquid
- crystals and polymers
- 1992 Georges Charpak Multiwire Proportional Chamber
- 1993 Russell A. Hulse Discovery of the first binary pulsar
- Joseph H. Taylor and subsequent tests of GR
-
- ********************************************************************************
- Item 25.
-
- Open Questions updated 01-JUN-1993 by SIC
- -------------- original by John Baez
-
- While for the most part a FAQ covers the answers to frequently
- asked questions whose answers are known, in physics there are also plenty
- of simple and interesting questions whose answers are not known. Before you
- set about answering these questions on your own, it's worth noting that
- while nobody knows what the answers are, there has been at least a little,
- and sometimes a great deal, of work already done on these subjects. People
- have said a lot of very intelligent things about many of these questions.
- So do plenty of research and ask around before you try to cook up a theory
- that'll answer one of these and win you the Nobel prize! You can expect to
- really know physics inside and out before you make any progress on these.
-
- The following partial list of "open" questions is divided into two
- groups, Cosmology and Astrophysics, and Particle and Quantum Physics.
- However, given the implications of particle physics on cosmology, the
- division is somewhat artificial, and, consequently, the categorization is
- somewhat arbitrary.
-
- (There are many other interesting and fundamental questions in
- fields such as condensed matter physics, nonlinear dynamics, etc., which
- are not part of the set of related questions in cosmology and quantum
- physics which are discussed below. Their omission is not a judgement
- about importance, but merely a decision about the scope of this article.)
-
- Cosmology and Astrophysics
- --------------------------
-
- 1. What happened at, or before the Big Bang? Was there really an initial
- singularity? Of course, this question might not make sense, but it might.
- Does the history of universe go back in time forever, or only a finite
- amount?
-
- 2. Will the future of the universe go on forever or not? Will there be a
- "big crunch" in the future? Is the Universe infinite in spatial extent?
-
- 3. Why is there an arrow of time; that is, why is the future so much
- different from the past?
-
- 4. Is spacetime really four-dimensional? If so, why - or is that just a
- silly question? Or is spacetime not really a manifold at all if examined
- on a short enough distance scale?
-
- 5. Do black holes really exist? (It sure seems like it.) Do they really
- radiate energy and evaporate the way Hawking predicts? If so, what happens
- when, after a finite amount of time, they radiate completely away? What's
- left? Do black holes really violate all conservation laws except
- conservation of energy, momentum, angular momentum and electric charge?
- What happens to the information contained in an object that falls into a
- black hole? Is it lost when the black hole evaporates? Does this require
- a modification of quantum mechanics?
-
- 6. Is the Cosmic Censorship Hypothesis true? Roughly, for generic
- collapsing isolated gravitational systems are the singularities that might
- develop guaranteed to be hidden beyond a smooth event horizon? If Cosmic
- Censorship fails, what are these naked singularities like? That is, what
- weird physical consequences would they have?
-
- 7. Why are the galaxies distributed in clumps and filaments? Is most of
- the matter in the universe baryonic? Is this a matter to be resolved by
- new physics?
-
- 8. What is the nature of the missing "Dark Matter"? Is it baryonic,
- neutrinos, or something more exotic?
-
- Particle and Quantum Physics
- ----------------------------
-
- 1. Why are the laws of physics not symmetrical between left and right,
- future and past, and between matter and antimatter? I.e., what is the
- mechanism of CP violation, and what is the origin of parity violation in
- Weak interactions? Are there right-handed Weak currents too weak to have
- been detected so far? If so, what broke the symmetry? Is CP violation
- explicable entirely within the Standard Model, or is some new force or
- mechanism required?
-
- 2. Why are the strengths of the fundamental forces (electromagnetism, weak
- and strong forces, and gravity) what they are? For example, why is the
- fine structure constant, which measures the strength of electromagnetism,
- about 1/137.036? Where did this dimensionless constant of nature come from?
- Do the forces really become Grand Unified at sufficiently high energy?
-
- 3. Why are there 3 generations of leptons and quarks? Why are there mass
- ratios what they are? For example, the muon is a particle almost exactly
- like the electron except about 207 times heavier. Why does it exist and
- why precisely that much heavier? Do the quarks or leptons have any
- substructure?
-
- 4. Is there a consistent and acceptable relativistic quantum field theory
- describing interacting (not free) fields in four spacetime dimensions? For
- example, is the Standard Model mathematically consistent? How about
- Quantum Electrodynamics?
-
- 5. Is QCD a true description of quark dynamics? Is it possible to
- calculate masses of hadrons (such as the proton, neutron, pion, etc.)
- correctly from the Standard Model? Does QCD predict a quark/gluon
- deconfinement phase transition at high temperature? What is the nature of
- the transition? Does this really happen in Nature?
-
- 6. Why is there more matter than antimatter, at least around here? Is
- there really more matter than antimatter throughout the universe?
-
- 7. What is meant by a "measurement" in quantum mechanics? Does
- "wavefunction collapse" actually happen as a physical process? If so, how,
- and under what conditions? If not, what happens instead?
-
- 8. What are the gravitational effects, if any, of the immense (possibly
- infinite) vacuum energy density seemingly predicted by quantum field
- theory? Is it really that huge? If so, why doesn't it act like an
- enormous cosmological constant?
-
- 9. Why doesn't the flux of solar neutrinos agree with predictions? Is the
- disagreement really significant? If so, is the discrepancy in models of
- the sun, theories of nuclear physics, or theories of neutrinos? Are
- neutrinos really massless?
-
- The Big Question (TM)
- ---------------------
-
- This last question sits on the fence between the two categories above:
-
- How do you merge Quantum Mechanics and General Relativity to create a
- quantum theory of gravity? Is Einstein's theory of gravity (classical GR)
- also correct in the microscopic limit, or are there modifications
- possible/required which coincide in the observed limit(s)? Is gravity
- really curvature, or what else -- and why does it then look like curvature?
- An answer to this question will necessarily rely upon, and at the same time
- likely be a large part of, the answers to many of the other questions above.
-
- ********************************************************************************
- Item 26. updated 24-MAY-1993 by SIC
-
- Accessing and Using Online Physics Resources
- --------------------------------------------
-
- (I) Particle Physics Databases
-
- The Full Listings of the Review of Particle Properties (RPP), as
- well as other particle physics databases, are accessible on-line. Here is
- a summary of the major ones, as described in the RPP:
-
- (A) SLAC Databases
-
- PARTICLES - Full listings of the RPP
- HEP - Guide to particle physics preprints, journal articles, reports,
- theses, conference papers, etc.
- CONF - Listing of past and future conferences in particle physics
- HEPNAMES - E-mail addresses of many HEP people
- INST - Addresses of HEP institutions
- DATAGUIDE - Adjunct to HEP, indexes papers
- REACTIONS - Numerical data on reactions (cross-sections, polarizations, etc)
- EXPERIMENTS - Guide to current and past experiments
-
- Anyone with a SLAC account can access these databases. Alternately, most
- of us can access them via QSPIRES. You can access QSPIRES via BITNET with
- the 'send' command ('tell','bsend', or other system-specific command) or by
- using E-mail. For example, send QSPIRES@SLACVM FIND TITLE Z0 will get you
- a search of HEP for all papers which reference the Z0 in the title. By
- E-mail, you would send the one line message "FIND TITLE Z0" with a blank
- subject line to QSPIRES@SLACVM.BITNET or QSPIRES@VM.SLAC.STANFORD.EDU.
- QSPIRES is free. Help can be obtained by mailing "HELP" to QSPIRES.
-
- For more detailed information, see the RPP, p.I.12, or contact: Louise
- Addis (ADDIS@SLACVM.BITNET) or Harvey Galic (GALIC@SLACVM.BITNET).
-
- (B) CERN Databases on ALICE
-
- LIB - Library catalogue of books, preprints, reports, etc.
- PREP - Subset of LIB containing preprints, CERN publications, and
- conference papers.
- CONF - Subset of LIB containing upcoming and past conferences since 1986
- DIR - Directory of Research Institutes in HEP, with addresses, fax,
- telex, e-mail addresses, and info on research programs
-
- ALICE can be accessed via DECNET or INTERNET. It runs on the CERN library's
- VXLIB, alias ALICE.CERN.CH (IP# 128.141.201.44). Use Username ALICE (no
- password required.) Remote users with no access to the CERN Ethernet can
- use QALICE, similar to QSPIRES. Send E-mail to QALICE@VXLIB.CERN.CH, put
- the query in the subject field and leave the message field black. For
- more information, send the subject "HELP" to QALICE or contact CERN
- Scientific Information Service, CERN, CH-1211 Geneva 23, Switzerland,
- or E-mail MALICE@VXLIB.CERN.CH.
-
- Regular weekly or monthly searches of the CERN databases can be arranged
- according to a personal search profile. Contact David Dallman, CERN SIS
- (address above) or E-mail CALLMAN@CERNVM.CERN.CH.
-
- DIR is available in Filemaker PRO format for Macintosh. Contact Wolfgang
- Simon (ISI@CERNVM.CERN.CH).
-
- (C) Particle Data Group Online Service
-
- The Particle Data Group is maintaining a new user-friendly computer
- database of the Full Listings from the Review of Particle Properties. Users
- may query by paper, particle, mass range, quantum numbers, or detector and
- can select specific properties or classes of properties like masses or
- decay parameters. All other relevant information (e.g. footnotes and
- references) is included. Complete instructions are available online.
-
- The last complete update of the RPP database was a copy of the Full
- Listings from the Review of Particle Properties which was published as
- Physical Review D45, Part 2 (1 June 1992). A subsequent update made on 27
- April 1993 was complete for unstable mesons, less complete for the W, Z, D
- mesons, and stable baryons, and otherwise was unchanged from the 1992
- version.
-
- DECNET access: SET HOST MUSE or SET HOST 42062
- TCP/IP access: TELNET MUSE.LBL.GOV or TELNET 131.243.48.11
- Login to: PDG_PUBLIC with password HEPDATA.
-
- Contact: Gary S. Wagman, (510)486-6610. Email: (GSWagman@LBL.GOV).
-
- (D) Other Databases
-
- Durham-RAL and Serpukhov both maintain large databases containing Particle
- Properties, reaction data, experiments, E-mail ID's, cross-section
- compilations (CS), etc. Except for the Serpukhov CS, these databases
- overlap SPIRES at SLAC considerably, though they are not the same and may
- be more up-to-date. For details, see the RPP, p.I.14, or contact:
- For Durham-RAL, Mike Whalley (MRW@UKACRL.BITNET,MRW@CERNVM.BITNET) or
- Dick Roberts (RGR@UKACRL.BITNET). For Serpukhov, contact Sergey Alekhin
- (ALEKHIN@M9.IHEP.SU) or Vladimir Exhela (EZHELA@M9.IHEP.SU).
-
- (II) Online Preprint Sources
-
- There are a number of online sources of preprints:
-
- alg-geom@publications.math.duke.edu (algebraic geometry)
- astro-ph@babbage.sissa.it (astrophysics)
- cond-mat@babbage.sissa.it (condensed matter)
- funct-an@babbage.sissa.it (functional analysis)
- hep-lat@ftp.scri.fsu.edu (computational and lattice physics)
- hep-ph@xxx.lanl.gov (high energy physics phenomenological)
- hep-th@xxx.lanl.gov (high energy physics theoretical)
- lc-om@alcom-p.cwru.edu (liquid crystals, optical materials)
- gr-qc@xxx.lanl.gov (general relativity, quantum cosmology)
- nucl-th@xxx.lanl.gov, (nuclear physics theory)
- nlin-sys@xyz.lanl.gov (nonlinear science)
-
- To get things if you know the preprint number, send a message to
- the appropriate address with subject header "get (preprint number)" and
- no message body. If you *don't* know the preprint number, or want to get
- preprints regularly, or want other information, send a message with
- subject header "help" and no message body.
-
- (III) The World Wide Web
-
- There is a wealth of information, on all sorts of topics, available
- on the World Wide Web [WWW], a distributed HyperText system (a network of
- documents connected by links which can be activated electronically).
- Subject matter includes some physics areas such as High Energy Physics,
- Astrophysics abstracts, and Space Science, but also includes such diverse
- subjects as bioscience, musics, and the law.
-
- * How to get to the Web
-
- If you have no clue what WWW is, you can go over the Internet with
- telnet to info.cern.ch (no login required) which brings you to the WWW
- Home Page at CERN. You are now using the simple line mode browser. To move
- around the Web, enter the number given after an item.
-
- * Browsing the Web
-
- If you have a WWW browser up and running, you can move around
- more easily. The by far nicest way of "browsing" through WWW uses the
- X-Terminal based tool "XMosaic". Binaries for many platforms (ready for use)
- and sources are available via anonymous FTP from ftp.ncsa.uiuc.edu in directory
- Web/xmosaic. The general FTP repository for browser software is info.cern.ch
- (including a hypertext browser/editor for NeXTStep 3.0)
-
- * For Further Information
-
- For questions related to WWW, try consulting the WWW-FAQ: Its most
- recent version is available via anonymous FTP on rtfm.mit.edu in
- /pub/usenet/news.answers/www-faq , or on WWW at
- http://www.vuw.ac.nz:80/overseas/www-faq.html
-
- The official contact (in fact the midwife of the World Wide Web)
- is Tim Berners-Lee, timbl@info.cern.ch. For general matters on WWW, try
- www-request@info.cern.ch or Robert Cailliau (responsible for the "physics"
- content of the Web, cailliau@cernnext.cern.ch).
-
- (IV) Other Archive Sites
-
- There is an FTP archive site of preprints and programs
- for nonlinear dynamics, signal processing, and related subjects on node
- lyapunov.ucsd.edu (132.239.86.10) at the Institute for Nonlinear Science,
- UCSD. Just login anonymously, using your host id as your password. Contact
- Matt Kennel (mbk@inls1.ucsd.edu) for more information.
-
- ********************************************************************************
- END OF FAQ
-
-