(127) Sun 17 May 92 0:29 By: Don Allen To: Jerry Woody Re: Physics-FAQ 1/9 St: @EID:116b 0

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(127) Sun 17 May 92 0:29 By: Don Allen To: Jerry Woody Re: Physics-FAQ 1/9 St: ------------------------------------------------------------ @EID:116b 01d0e979 @MSGID: 1:363/29 458106d3 ** Forwarded from Usenet ** =========================================================================== Article 15701 of sci.physics: From: sichase@csa3.lbl.gov (SCOTT I CHASE) Newsgroups: sci.physics Subject: Frequently Asked Questions List - Special Mid-Month Posting Keywords: frequently asked questions Message-ID: <23416@dog.ee.lbl.gov> Date: 15 May 92 20:03:36 GMT Reply-To: sichase@csa3.lbl.gov Organization: Lawrence Berkeley Laboratory - Berkeley, CA, USA Lines: 1050 NNTP-Posting-Host: News-Software: VAX/VMS VNEWS 1.3-4 --------------------------------------------------------------------------- FREQUENTLY ASKED QUESTIONS ON SCI.PHYSICS --------------------------------------------------------------------------- To the Reader, This special mid-month posting of the faq is due to rapid developments, which I feel justify more feedback from the readership. The faq has more than doubled in size, thanks to the comments, suggestions, and text sent to me by many people. This release has also been spell checked and grammatically improved. Again thanks to those who did exactly what I would have done - picked nits. The processing of all the information and suggestions that I have received is still not complete. Please be patient if you have already had your say but do not see any changes yet. The best form of criticism a replacement! If you don't like what you see, give it *your* best shot. New paragraphs, or entire entries are welcome from brave readers. -Scott -------------------- Scott I. Chase SICHASE@CSA2.LBL.GOV --------------------------------------------------------------------------- Facts about the FAQ: This FAQ is posted monthly, near the first of the month. If you do not wish to read the FAQ at all, add "Frequently Asked Questions" to your KILL file. A listing of new items will be posted above the subject index, so that you can quickly identify new subjects of interest. If an old item has been modified in a substantial way, the 'update' date will be later than May 3, the last release date. Entries are long - full of facts, figures, and references. That's the way I like it. As someone has urged me to publicize, "It's my FAQ. If you don't like it, write your own." Since the number of items is still small, I will post the entirely of each summary. In the future, length restrictions may require that I post only excerpts. Topics include those which are truly "frequently asked questions" along with several personal favorites and interesting items submitted by others. When the majority of material for an entry comes from one person, I have attributed the entry to them. Otherwise, contributors have been thanked privately. I have attempted to adhere to a consistent technical level which will make the FAQ accessible to educated newcomers, but still remain interesting to the cognoscenti. I hope that the specific references will provide access points into the literature for those who with to pursue any topic further. Last modified: 15-May-1992 New Items: 5. Tachyons 6. Special Relativistic Paradoxes (a) The Barn and the Pole 7. The Particle Zoo 8. Olber's Paradox 9. What is Dark Matter? 10. Hot Water Freezes Faster than Cold! 11. Which Way Will my Bathtub Drain? 12. Why are Golf Balls Dimples? 13. The Nobel Prize for Physics Index of Subjects ----------------- 1. Gravitational Radiation 2. Energy Conservation in Cosmology and Red Shift 3. Effects Due to the Finite Speed of Light 4. The Top Quark 5. Tachyons 6. Special Relativistic Paradoxes (a) The Barn and the Pole 7. The Particle Zoo 8. Olber's Paradox 9. What is Dark Matter? 10. Hot Water Freezes Faster than Cold! 11. Which Way Will my Bathtub Drain? 12. Why are Golf Balls Dimples? 13. The Nobel Prize for Physics ------Cont in Physics-FAQ pt 2------------------------------------------- Don --- RemoteAccess 0.03+ * Origin: Odyssey UFO Echo -*- Gourmet Delight (407)649-4136 (1:363/29) SEEN-BY: 10/45 19/19 123/19 138/136 154/414 203/123 238/300 260/233 268/102 SEEN-BY: 323/109 363/29 42 95 107 153 1000/210 1010/0 2600/140 3607/20 SEEN-BY: 3800/8 @PATH: 363/29 3607/20 268/102 ------------------------------------------------------------ (128) Sun 17 May 92 0:30 By: Don Allen To: Jerry Woody Re: Physics-FAQ 2/9 St: ------------------------------------------------------------ @EID:116b 01d0e972 @MSGID: 1:363/29 458106dc ----Physics-FAQ part 2---------------------------------------------------- *************************************************************************** Item 1. 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. 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. -----Cont in Physics-FAQ pt 3---------------------------------------------- Don --- RemoteAccess 0.03+ * Origin: Odyssey UFO Echo -*- Gourmet Delight (407)649-4136 (1:363/29) SEEN-BY: 10/45 19/19 123/19 138/136 154/414 203/123 238/300 260/233 268/102 SEEN-BY: 323/109 363/29 42 95 107 153 1000/210 1010/0 2600/140 3607/20 SEEN-BY: 3800/8 @PATH: 363/29 3607/20 268/102 ------------------------------------------------------------ (129) Sun 17 May 92 0:32 By: Don Allen To: Jerry Woody Re: Physics-FAQ 3/9 St: ------------------------------------------------------------ @EID:116b 01d0e97b @MSGID: 1:363/29 458106e5 ------Physics-FAQ part 3--------------------------------------------------- *************************************************************************** Item 2. 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 3. EFFECTS DUE TO THE FINITE SPEED OF LIGHT updated 4-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 galaxy 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 galaxy is D km from us, and that between Jan. 1 and Feb. 1, the galaxy 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 galaxy has traveled the given angular distance in more time than you thought. Similarly, if the galaxy 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 galaxy 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: I have not located any yet. If you know of some, please let me know. (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 Mechanics_, Section 10.5. ------Cont in Physics-FAQ pt 4--------------------------------------------- Don --- RemoteAccess 0.03+ * Origin: Odyssey UFO Echo -*- Gourmet Delight (407)649-4136 (1:363/29) SEEN-BY: 10/45 19/19 123/19 138/136 154/414 203/123 238/300 260/233 268/102 SEEN-BY: 323/109 363/29 42 95 107 153 1000/210 1010/0 2600/140 3607/20 SEEN-BY: 3800/8 @PATH: 363/29 3607/20 268/102 ------------------------------------------------------------ (130) Sun 17 May 92 0:32 By: Don Allen To: Jerry Woody Re: Physics-FAQ 4/9 St: ------------------------------------------------------------ @EID:116b 01d0e974 @MSGID: 1:363/29 458106ee ----Physics-FAQ part 4----------------------------------------------------- *************************************************************************** Item 4. 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 pairs. 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, 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 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-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 which allow higher event rates and better detector resolution, should allow production of standard model top quarks of mass < 170 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. -----Cont in Physics-FAQ pt 5---------------------------------------------- Don --- RemoteAccess 0.03+ * Origin: Odyssey UFO Echo -*- Gourmet Delight (407)649-4136 (1:363/29) SEEN-BY: 10/45 19/19 123/19 138/136 154/414 203/123 238/300 260/233 268/102 SEEN-BY: 323/109 363/29 42 95 107 153 1000/210 1010/0 2600/140 3607/20 SEEN-BY: 3800/8 @PATH: 363/29 3607/20 268/102 ------------------------------------------------------------ (131) Sun 17 May 92 0:33 By: Don Allen To: All Re: Physics-FAQ 5/9 St: ------------------------------------------------------------ @EID:116b 01d0e97d @MSGID: 1:363/29 458106f7 -------Physics-FAQ part 5-------------------------------------------------- *************************************************************************** Item 5. 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, Bilanuik, Deshpande, and Sudarshan, Am. J. Phys. _30_, 718 (1962), said "no". A very readable paper is Bilanuik 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 loose 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 Cerenkov radiate. 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. -----Cont in Physics-FAQ pt 6--------------------------------------------- Don --- RemoteAccess 0.03+ * Origin: Odyssey UFO Echo -*- Gourmet Delight (407)649-4136 (1:363/29) SEEN-BY: 10/45 19/19 123/19 138/136 154/414 203/123 238/300 260/233 268/102 SEEN-BY: 323/109 363/29 42 95 107 153 1000/210 1010/0 2600/140 3607/20 SEEN-BY: 3800/8 @PATH: 363/29 3607/20 268/102 ------------------------------------------------------------ (132) Sun 17 May 92 0:34 By: Don Allen To: Jerry Woody Re: Physics-FAQ 6/9 St: ------------------------------------------------------------ @EID:116b 01d0e976 @MSGID: 1:363/29 45810700 -----Physics-FAQ part 6--------------------------------------------------- *************************************************************************** Item 6. The Barn and the Pole updated 5-May-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, for example, only 32 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. The Particle Zoo updated 15-May-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. 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 mu 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 2/3 | down |strange|bottom | -1/3 | 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 in Physics Letters B239 (1990). 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. ----Cont in Physics-FAQ pt 7---------------------------------------------- Don --- RemoteAccess 0.03+ * Origin: Odyssey UFO Echo -*- Gourmet Delight (407)649-4136 (1:363/29) SEEN-BY: 10/45 19/19 123/19 138/136 154/414 203/123 238/300 260/233 268/102 SEEN-BY: 323/109 363/29 42 95 107 153 1000/210 1010/0 2600/140 3607/20 SEEN-BY: 3800/8 @PATH: 363/29 3607/20 268/102 ------------------------------------------------------------ (133) Sun 17 May 92 0:36 By: Don Allen To: Jerry Woody Re: Physics-FAQ 7/9 St: ------------------------------------------------------------ @EID:116b 01d0e97f @MSGID: 1:363/29 45810709 ----Physics-FAQ part 7----------------------------------------------------- *************************************************************************** Item 8. Olber's Paradox updated: 5-May-1992 by SIC --------------- Why isn't the night sky as uniformly bright as the surface of the Sun? If the Universe has infinitely many stars, then it should be. After all, if you move the Sun twice as far away from us, we will intercept one-fourth as many photons, but the Sun will subtend one-fourth of the angular area. So the areal intensity remains constant. With infinitely many stars, every angular element of the sky should have a star, and the entire heavens should be a bright as the sun. We should have the impression that we live in the center of a hollow black body whose temperature is about 6000 degrees Centigrade. This is Olber's 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 Olber took up the issue in the nineteenth century. There are many possible explanations which have been considered. Here are a few: (1) There's too much dust to see the distant stars. (2) The Universe has only a finite number of stars. (3) The distribution of stars is not uniform. So, for example, there could be an infinitely of stars, but they hide behind one another so that only a finite angular area is subtended by them. (4) The Universe is expanding, so distant stars are red-shifted into obscurity. (5) The Universe is young. Distant light hasn't even reached us yet. The first explanation is just plain wrong. In a black body, the dust will heat up too. It does act like a radiation shield, exponentially damping the distant starlight. But you can't put enough dust into the universe to get rid of enough starlight without also obscuring our own Sun. So this idea is bad. The second might have been correct, but estimates of the total matter in the universe are too large to allow this escape. The number of stars is close enough to infinite for the purpose of lighting up the sky. The third explanation might be partially correct. We just don't know. If the stars are distributed fractally, then there could be large patches of empty space, and the sky could appear dark except in small areas. But the final two possibilities are are surely each correct and partly responsible. There are numerical arguments that suggest that the effect of the finite age of the Universe is the larger effect. We live inside a spherical shell of "Observable Universe" which has radius equal to the lifetime of the Universe. Objects more than about 15 billions years old are too far away for their light ever to reach us. Historically, after Hubble discovered that the Universe was expanding, but before the Big Bang was firmly established by the discovery of the cosmic background radiation, Olber's 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 Olber's paradox. *************************************************************************** Item 9. 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 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. ----Cont in Physics-FAQ pt 8----------------------------------------------- Don --- RemoteAccess 0.03+ * Origin: Odyssey UFO Echo -*- Gourmet Delight (407)649-4136 (1:363/29) SEEN-BY: 10/45 19/19 123/19 138/136 154/414 203/123 238/300 260/233 268/102 SEEN-BY: 323/109 363/29 42 95 107 153 1000/210 1010/0 2600/140 3607/20 SEEN-BY: 3800/8 @PATH: 363/29 3607/20 268/102 ------------------------------------------------------------ (134) Sun 17 May 92 0:37 By: Don Allen To: Jerry Woody Re: Physics-FAQ 8/9 St: ------------------------------------------------------------ @EID:116b 01d0e978 @MSGID: 1:363/29 45810712 ----Physics-FAQ part 8----------------------------------------------------- *************************************************************************** Item 10. Hot Water Freezes Faster than Cold! updated 11-May-1992 ----------------------------------- 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 cold 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 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. *************************************************************************** Item 11. Which Way Will my Bathtub Drain? updated 11-May-1192 by SIC -------------------------------- original by Matthew R. Feinstein Question: Does my bathtub drain differently depending on whether I live in the northern or southern hemisphere? Answer: No. There is a real effect, but it is far too small to be relevant when you pull the plug in your bathtub. Because the earth rotates, a fluid that flows along the earth's surface feels a "Coriolis" acceleration perpendicular to its velocity. In the northern hemisphere high pressure storm systems spin clockwise. In the southern hemisphere, they spin counterclockwise because the direction of the Coriolis acceleration is reversed. This effect leads to the speculation that the bathtub vortex that you see when you pull the plug from the drain spins one way in the north and the other way in the south. But this acceleration is --very-- weak for bathtub-scale fluid motions. The order of magnitude of the Coriolis acceleration can be estimated from size of the "Rossby number". Coriolis accelerations are significant when the Rossby number is --small--. So, suppose we want a Rossby number of 0.1 and a bathtub-vortex length scale of 0.1 meter. Since the earth's rotation rate is about 10^(-4)/second, the fluid velocity should be less than or equal to 2*10^(-6) meters/second. This is a very small velocity. How small is it? Well, we can take the analysis a step further and calculate another, more famous dimensionless parameter, the Reynolds number. The Reynolds number is = L*U*density/viscosity Assuming that physicists bathe in hot water the viscosity will be about 0.005 poise and the density will be about 1.0, so the Reynolds Number is about 4*10^(-2). Now, life at low Reynolds numbers is different from life at high Reynolds numbers. In particular, at low Reynolds numbers, fluid physics is dominated by friction and diffusion, rather than by inertia: the time it would take for a particle of fluid to move a significant distance due to an acceleration is greater than the time it takes for the particle to break up due to diffusion. Therefore the effect of the Coriolis acceleration on your bathtub vortex is --SMALL--. To detect its effect on your bathtub, you would have to get out and wait until the motion in the water is far less than one rotation per day. This would require removing thermal currents, vibration, and any other sources of noise. Under such conditions, never occurring in the typical home, you WOULD see an effect. To see what trouble it takes to actually see the effect, see the reference below. Experiments have been done in both the northern and southern hemispheres to verify that under carefully controlled conditions, bathtubs drain in opposite directions due to the Coriolis acceleration from the Earth's rotation. The same effect has been accused of responsibility for the direction water circulates when you flush a toilet. This is surely nonsense. In this case, the water rotates in the direction which the pipe points which carries the water from the tank to the bowl. Reference: Trefethen, L.M. et al, Nature 207 1084-5 (1965). ----Cont in Physics-FAQ pt 9----------------------------------------------- Don --- RemoteAccess 0.03+ * Origin: Odyssey UFO Echo -*- Gourmet Delight (407)649-4136 (1:363/29) SEEN-BY: 10/45 19/19 123/19 138/136 154/414 203/123 238/300 260/233 268/102 SEEN-BY: 323/109 363/29 42 95 107 153 1000/210 1010/0 2600/140 3607/20 SEEN-BY: 3800/8 @PATH: 363/29 3607/20 268/102 ------------------------------------------------------------ (135) Sun 17 May 92 0:38 By: Don Allen To: Jerry Woody Re: Physics-FAQ 9/9 St: ------------------------------------------------------------ @EID:116b 01d0e971 @MSGID: 1:363/29 4581071b ------Physics-FAQ part 9--------------------------------------------------- *************************************************************************** Item 12. Why are Golf Balls Dimpled? updated 14-May-1992 by SIC --------------------------- original by Craig DeForest The dimples, paradoxically, *do* increase drag slightly. But they also increase `Magnus lift', that peculiar lifting force experienced by rotating bodies travelling through a medium. Contrary to Freshman physics, golf balls do not travel in inverted parabolas. They follow an 'impetus trajectory': * * * * (golfer) * * * * <-- trajectory \O/ * * | * * -/ \-T---------------------------------------------------------------ground This is because of the combination of drag (which reduces horizontal speed late in the trajectory) and Magnus lift, which supports the ball during the initial part of the trajectory, making it relatively straight. The trajectory can even curve upwards at first, depending on conditions! Here is a cheesy diagram of a golf ball in flight, with some relevant vectors: F(magnus) ^ | F(drag) <--- O -------> V \ \----> (sense of rotation) The Magnus force can be thought of as due to the relative drag on the air on the top and bottom portions of the golf ball: the top portion is moving slower relative to the air around it, so there is less drag on the air that goes over the ball. The boundary layer is relatively thin, and air in the not-too-near region moves rapidly relative to the ball. The bottom portion moves fast relative to the air around it; there is more drag on the air passing by the bottom, and the boundary (turbulent) layer is relatively thick; air in the not-too-near region moves more slowly relative to the ball. The Bernoulli force produces lift. (alternatively, one could say that `the flow lines past the ball are displaced down, so the ball is pushed up.') The difficulty comes near the transition region between laminar flow and turbulent flow. At low speeds, the flow around the ball is laminar. As speed is increased, the bottom part tends to go turbulent *first*. But turbulent flow can follow a surface much more easily than laminar flow. As a result, the (laminar) flow lines around the top break away from the surface sooner than otherwise, and there is a net displacement *up* of the flow lines. The magnus lift goes *negative*. The dimples aid the rapid formation of a turbulent boundary layer around the golf ball in flight, giving more lift. Without 'em, the ball would travel in more of a parabolic trajectory, hitting the ground sooner. (and not coming straight down.) References: Perhaps the best (and easy-to-read) reference on this effect is a paper in American Journal of Physics by one Lyman Briggs, c. 1947. Briggs was trying to explain the mechanism behind the `curve ball' in baseball, using specialized apparatus in a wind tunnel at the NBS. He stumbled on the reverse effect by accident, because his model `baseball' had no stitches on it. The stitches on a baseball create turbulence in flight in much the same way that the dimples on a golf ball do. *************************************************************************** Item 13. The Nobel Prize for Physics (1901-1932) updated 11-May-1992 by SIC --------------------------------------- The following is a complete listing of Nobel Prize awards, from the first award in 1901, until I got tired of typing. More will follow. 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 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 *************************************** ***************************************** END OF FAQ Don --- RemoteAccess 0.03+ * Origin: Odyssey UFO Echo -*- Gourmet Delight (407)649-4136 (1:363/29) SEEN-BY: 10/45 19/19 123/19 138/136 154/414 203/123 238/300 260/233 268/102 SEEN-BY: 323/109 363/29 42 95 107 153 1000/210 1010/0 2600/140 3607/20 SEEN-BY: 3800/8 @PATH: 363/29 3607/20 268/102


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