Physics Facts

submitted by Patrick Nikkolai A. Persia

(2003-06-23) The tai-chi mandala:  Taiji or Yin-Yang symbol.
Niels Bohr's coat of arms: "Argent, a taiji Gules and Azure."

The Chinese Taiji symbol dates back to the Song dynasty (960–1279).  Known in the West as the Yin-Yang symbol, it appears in the ancient I Ching (or YiJing; the so-called "Book of Changes"). It is meant to depict the two traditional types of complementary principles from which all things are supposed to be produced, Yin and Yang, whirling within an eternally turning circle representing the primordial void (the Tao).  Yin and Yang are each divided into greater and lesser "phases" (or "elements"), whereas the fifth central phase (earth) represents a perfect balance.  To a Western mind, this traditional Taoist classification may seem entirely arbitrary, especially when extended to modern physics (see below).  The reason could be that it really is totally arbitrary, at least for the part about physics:  The traditional Chinese taiji symbol became a sort of scientific icon when Niels Bohr adopted it for his coat of arms in 1947, but it was never meant to convey any precise scientific meaning...

The Origin of Yin-Yang

by Patrick Nikkolai A. Persia

Please click the link below to view the file.

yin-yang origin.doc

Here’s info about that intriguing particle that is theorized to exceed the speed of light…

Tachyons

                There was a young lady named Bright,

                Whose speed was far faster than light.

                She went out one day,

                In a relative way,

                And returned the previous night!

                        -Reginald Buller

It is a well known fact that nothing can travel faster than the speed of light.  At best, a massless particle travels at the speed of light.  But is this really true?  In 1962, Bilaniuk, Deshpande, and Sudarshan, Am. J. Phys. 30, 718 (1962), said "no".  A very readable paper is Bilaniuk and Sudarshan, Phys. Today 22,43 (1969).  I give here a brief overview.

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

Now the fundamental fact of relativity is that E² - p² = m².  (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 hear in association with virtual particles - but that's another topic.)  For massless particles, E² = p², 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. (Tachyons were first introduced into physics by Gerald Feinberg, in his seminal paper "On the possibility of faster-than-light particles" [Phys.Rev. v.159, pp.1089--1105 (1967)]).

Now another familiar relativistic equation is E = m*[1-(v/c)²]^-1/2.  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 E² - p² = m² < 0.  Or, p² - E² = M², where M is real.  This is a hyperbola with branches in the spacelike region of spacetime.  The energy and momentum of a tachyon must satisfy this relation.

You can now deduce many interesting properties of tachyons.  For example, they accelerate (p goes up) if they lose energy (E goes down).  Furthermore, a zero-energy tachyon is "transcendent," or infinitely fast.  This has profound consequences.  For example, let's say that there were electrically charged tachyons.  Since they would move faster than the speed of light in the vacuum, they should produce Cherenkov radiation.  This would lower their energy, causing them to accelerate more!  In other words, charged tachyons would probably lead to a runaway reaction releasing an arbitrarily large amount of energy.  This suggests that coming up with a sensible theory of anything except free (noninteracting) tachyons is likely to be difficult.  Heuristically, the problem is that we can get spontaneous creation of tachyon-antitachyon pairs, then do a runaway reaction, making the vacuum unstable.  To treat this precisely requires quantum field theory, which gets 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).

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 Cherenkov 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.

How about using tachyons to transmit information faster than the speed of light, in violation of Special Relativity?  It's worth noting that when one considers the relativistic quantum mechanics of tachyons, the question of whether they "really" go faster than the speed of light becomes much more touchy!  In this framework, tachyons are waves that satisfy a wave equation.  Let's treat free tachyons of spin zero, for simplicity.  We'll set c = 1 to keep things less messy.  The wavefunction of a single such tachyon can be expected to satisfy the usual equation for spin-zero particles, the Klein-Gordon equation:

                (BOX + m2)phi = 0

where BOX is the D'Alembertian, which in 3+1 dimensions is just

                BOX = (d/dt)2 - (d/dx)2 - (d/dy)2 - (d/dz)2.

The difference with tachyons is that m² is negative, and m is imaginary.

To simplify the math a bit, let's work in 1+1 dimensions, with co-ordinates x and t, so that

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

Everything we'll say generalizes to the real-world 3+1-dimensional case.  Now - regardless of m, any solution is a linear combination, or superposition, of solutions of the form

                phi(t,x) = exp(-iEt + ipx)

where E² - p² = m².  When m² is negative there are two essentially different cases.  Either |p| >= |E|, in which case E is real and we get solutions that look like waves whose crests move along at the rate |p|/|E| >= 1, i.e., no slower than the speed of light.  Or |p| < |E|, in which case E is imaginary and we get solutions that look waves that amplify exponentially as time passes!

We can decide as we please whether or not we want to consider the second sort of solutions.  They seem weird, but then the whole business is weird, after all.

1) If we do permit the second sort of solution, we can solve the Klein-Gordon equation with any reasonable initial data - that is, any reasonable values of phi and its first time derivative at t = 0.  (For the precise definition of "reasonable," consult your local mathematician.)  This is typical of wave equations.  And, also typical of wave equations, we can prove the following 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, localized disturbances do not spread with speed faster than the speed of light!  This seems to go against our notion that tachyons move faster than the speed of light, but it's a mathematical fact, known as "unit propagation velocity".

2) If we don't permit the second sort of solution, we can't solve the Klein-Gordon equation for all reasonable initial data, but only for initial data whose Fourier transforms vanish in the interval [-|m|,|m|].  By the Paley-Wiener theorem this has an odd consequence: it becomes impossible to solve the equation for initial data that vanish outside some interval [-L,L]!  In other words, we can no longer "localize" our tachyon in any bounded region in the first place, so it becomes impossible to decide whether or not there is "unit propagation velocity" in the precise sense of part 1).  Of course, the crests of the waves exp(-iEt + ipx) move faster than the speed of light, but these waves were never localized in the first place!

The bottom line is that you can't use tachyons to send information faster than the speed of light from one place to another.  Doing so would require creating a message encoded some way in a localized tachyon field, and sending it off at superluminal speed toward the intended receiver.  But as we have seen you can't have it both ways: localized tachyon disturbances are subluminal and superluminal disturbances are nonlocal.

SOURCE:

     This article was taken from: http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html Updated March 1993 by SIC; Original by Scott I. Chase. © 1992--2002 by Scott Chase, Michael Weiss, Philip Gibbs, Chris Hillman, and Nathan Urban.  The individual articles are © 1992--2002 by the individual authors credited.  All rights are reserved.

Neutron Bombs

“And this shall be the plague wherewith the LORD will smite all the people that have fought against Jerusalem; Their flesh shall consume away while they stand upon their feet, and their eyes shall consume away in their holes, and their tongue shall consume away in their mouth.” - the ancient Israeli prophet Zechariah, in the Tenakh, ca 500 BC

The ancients never cease to amaze.  Zechariah’s strange prophecy made no scientific sense at all for 2,500 years after he uttered it.  Before the 1970s, the only way to conceive of this scenario occurring was by the direct supernatural intervention of Zechariah’s God, the God of Abraham, Isaac, and Jacob.  In the last 20 years, however, humans have figured out a technical way to achieve similar results.

Zechariah’s foreboding apocalyptic prose, quite remarkably, is an accurate description of the effects of a neutron bomb.  A neutron is simply a component of every atomic nucleus (except plain hydrogen).  As we all learned in physics class, an atom consists of a nucleus, made of positively charged protons clinging to neutrons with a neutral (no) electrical charge.  A negatively charged electron “cloud” surrounds the nucleus.  In general, every proton must have a companion neutron and an offsetting electron to form a stable element.  Neutrons are critical building blocks of every material thing in our universe.

When neutrons are where they are supposed to be, clinging to protons in atomic nuclei, they are vital for the existence of matter.  When they are freed, however, they make an extremely lethal form of radiation.  The neutron bomb exploits this deadly characteristic of free neutrons.  A neutron bomb is a third generation nuclear weapon.  In a first generation nuclear fission bomb, heavy atomic nuclei are split apart, and the power released from these large atoms is tremendous.  In its much more powerful second generation descendant, the fusion bomb, or thermonuclear bomb, light hydrogen isotopes are fused together to form heavier atoms, releasing unfathomable amounts of energy.  Fusion bombs make fission bombs look like firecrackers.

In one of these deadly thermonuclear bombs, the hydrogen isotopes of tritium and deuterium are fused together to form heavier elements, releasing about half the initial energy of the device.  The fusion core of the bomb is wrapped in a blanket of very heavy uranium 238 atoms.  The U-238 isotopes are split by the searing energy released from the fusion core, initiating a secondary fission explosion that can be more powerful than all the munitions ever expended in the history of humanity.  Extremely devastating and lethal, these hydrogen bombs are very messy, vaporizing or burning everything, and leaving the very earth itself contaminated with radiation that can last for millennia.  God forbid we ever decide to pull the red doomsday trigger and use these hell-spawned beasts on fellow humans.

The neutron bomb is another generation beyond a thermonuclear device.  It has the same core of a fusion bomb, but the blanket of heavy U-238 isotopes is removed, so only the energy released from the fusion core comprises the total explosive yield.  This energy is in the form of a massive flux of neutrons, combined with some gamma radiation.  Neutrons are highly lethal to humans and animals, and the N-bomb instantly kills everything in its radius of lethality.  Any living creatures that receive non-lethal doses of the neutrons will be dead within a day or two from radiation sickness.  Neutron radiation literally vaporizes the soft flesh of humans at close range, and Zechariah’s remarkable prophecy, regardless of what he was really prophesying, is an extraordinary description of the effects of a neutron bomb on human beings. 

Neutron bombs are also much cleaner than conventional nukes.  A neutron blast only kills living things, leaving all buildings and weapons intact.  It is the ultimate weapon to use against massed troops and armor, as all the enemies die instantly, no structures or vehicles are damaged, and, most importantly, no radioactive fallout is left behind.  Unlike fission or fusion nukes, neutron bombsites are safe to walk into immediately after the explosion.  Neutron technology has been developed to such a level that these devices can be produced in as small a package as the size of a common baseball!  They can be used in field artillery and small rockets, and even soldiers dug in behind several feet of earth are not safe from a neutron blast.  Until the Clinton/Gore Administration, only two nations wielded this fearful weapon, the United States and Israel.  Thanks to the DNC/Chinagate scandal, however, China is now known to possess neutron devices, and several other countries are rumored to be actively pursuing this technology.  Many global intelligence analysts believe that small neutron bombs may unfortunately become the weapon of choice for the discerning terrorist in the 21st century.  It IS an ironic and sad commentary on humanity that the most intelligent humans (nuclear physicists) build weapons that the most power-hungry and unaccountable humans (politicians) use to kill the most courageous humans (patriotic soldiers).  We truly live in a crazy world.

SOURCE:

    Excerpts from: http://www.gold-eagle.com/gold_digest_00/hamilton100900pv.html Adam Hamilton, CPA, MCSE aka Zelotes 9 October 2000 Copyright 2000 Zeal Research