Alternate View Column AV-07
Keywords: optics, reversal, 4-wave mixer, time-reverse, thermodynamics, 2nd Law
Published in the June-1985 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 12/1/84 and is copyrighted © 1984, John G. Cramer. All rights reserved.
No part may be reproduced in any form without the explicit permission of the author.
The purpose of this AV Column is to describe a physical paradox involving what seems to be an loophole in a well established physical law, the famous Second Law of Thermodynamics. The 2nd Law states that the amount of disorder (entropy) always either increases or remains constant for any isolated system of particles, whether they are gas molecules or light photons. An yet, as we will see, laser physicists seem to have provided us with a way of making the 2nd Law work backwards for a system of photons, so that the disorder decreases.
Everyday experience tells us that there are some processes which once done can be undone while others cannot. For example, a padlock can be repeatedly locked and unlocked, but an egg once scrambled can never be unscrambled. In physics we call the first kind of process reversible and the second irreversible. The essential difference between reversible and irreversible processes is related to the 2nd Law and the increase in disorder. In a system which is designed to limit the amount of disorder which can occur (like the padlock) the growth of this disorder may be so small as to go unnoticed, and the process seems to be reversible. In a system where few limits are placed on the disorder (like an egg) the system may grow very disordered indeed, and and the process is clearly irreversible.
As an example of a simple irreversible process, let's allow the gas to escape from a sealed steel cylinder full of gas molecules into a surrounding vacuum. At the start we open a valve holding the molecules in. The cylinder then contains 100% of the molecules and the surrounding space contains none. We will call this situation State A. Now we let this system evolve with time until it reaches State B in which 1/2 of the molecules are still in the cylinder and 1/2 of them have emerged into the surrounding space. After a while longer the system reaches State C in which almost all of the molecules have left the essentially empty cylinder. The disorder has grown progressively in this sequence. The system was "perfectly" ordered in State A, less well ordered in State B, and minimally ordered in State C. And somehow, when the system was in State B the molecules "knew" that they should proceed to State C rather than State A. The probability of the system returning to State A through the random motion of the molecules is negligibly small. This is the essence of the 2nd Law.
But suppose that by some magical process we could intervene when the system was in State B so as to instantaneously "flip" the velocity direction of each individual gas molecule. Then (at least in the opinion of most physicists) the gas would do a most unusual thing: all of the molecules would retrace their steps and go back into the cylinder, returning to State A. The order of the system, instead of decreasing as the 2nd Law requires, would increase in violation of the 2nd Law. In principle if we could perform the same "velocity flip" operation on more complicated system, for example an egg and its immediate surroundings, the disorder of that system would also be reduced and in the scrambled egg would be unscrambled and would retreat into an unbroken shell.
But the 2nd Law is a well established physical principle which has never been found wanting in a century of experimental testing. Surely natural laws can't be broken with such abandon; there must be something funny about the operation of reversing velocities. Physicists have considered this point carefully and have concluded that this operation is indeed impossible. Velocity reversal is an example of what is called a "fine grain" process. A "fine grain" process requires detailed information about each individual molecule, as opposed to a "coarse grain" process which requires only average overall information such as pressure, temperature, etc. The famous Maxwell's Demon, a little man equipped with a little tennis racquet with which he bats fast molecules in one direction and slow molecules in another, is also an example of a fine grain process. It has become a physics dogma, supported by the success of the 2nd Law, that fine grain processes are impossible (except in cases where the mechanism behind the process increases disorder more than the process reduces it), and that only coarse grain processes are allowed without restriction.
Recent work in laser physics, moreover, seems to have created an annoying flea presently nipping at the back of this dogma. Light photons should in principle obey the same thermodynamic principles (including the 2nd Law) as gas molecules. And laser physicists seem to have provided us with a means of performing the operation of perfect velocity reversal on a system of light photons. The apparatus for performing this thermodynamic miracle is called the four-wave conjugate mirror.
To understand what this device does, let us first consider what an ordinary mirror does. Basically, a mirror reflects light by reversing the component of the light's electric field which is perpendicular to the mirror surface. This makes the light change direction, moving away from the mirror but usually also away from the direction from which it came. If you wanted to bounce a laser beam back in exactly the reverse direction, you could use tricky mirror arrangement called a "cube corner" reflector. You may recall that the Apollo astronauts left some on these on the surface of the moon for use in laser ranging. But even with a cube-corner reflector, if the light beam is spreading out before it hits the mirror (as it usually is), it will continue to spread.
The four-wave conjugate mirror which laser physicists have recently devised is quite different from an ordinary mirror in that instead of reflecting the incident beam is space, it reflects it in time. The incoming light wave is mixed with two other oppositely directed light waves generated by lasers within the apparatus. These three waves interact with a transparent medium through which they pass to produce a fourth wave which is the time reverse of the wave which came in. A way of thinking about what happens is that the incoming light wave and one of the laser waves combine to inscribe a temporary hologram on the medium, and that the other laser wave then interacts with this hologram to produce the fourth time-reversed wave.
Since the fourth wave is the time-reverse of the incoming wave it will go back along precisely the same path taken by the incoming wave. If the original wave was spreading out from a source point, the new wave will converge back to that source point. If the original wave was distorted and diffused by irregularities and dust particles in the intervening air, the new wave will travel back through the same irregularities and undo the distortions to produce a wave just like the one which originally emerged from the source. The photons comprising the fourth wave are just velocity flipped counterparts of those which entered the apparatus.
This trick may have "space war" applications of both the science-fictional and the DOD variety. If someone tries to zap your space ship with a laser beam you can return fire right up his gun barrel. A four-wave mixer will "shoot back" with perfect aim and accuracy, automatically compensating for distortion, etc. There is another laser-based device called a light amplifier which effectively "Xeroxes(TM)" light waves passing through it to produce multiple copies. If we place a light amplifier in front of the conjugate mirror, the beam which shoots back can be given much more power than the original beam, so an assailant can be out-gunned. And it also possible to shoot first. Instead of precisely aiming a laser beam one can send out a weak wide-angle beam which reflects from a "target", and then use the reflected wave after four-wave conjugation and amplification to send a vast quantity of light power back to the target. (A note of warning to would-be Star Warriors however: this technique will not work over sattelite-scale distances because most potential targets will have changed positions during the transit time of the light.)
Of course physicists are, for the most part, not particularly interested in target practice with ray guns and have other reasons for being interested in conjugate mirrors. An example is laser-produced inertial fusion, which may one day provide a solution to our energy problems. The trick here is to hit a tiny pellet containing tritium with as much laser energy as possible, causing thermonuclear reactions. Focusing and aiming the high power lasers through windows which may be distorted by the reactions is a serious problem. Amplified conjugate mirrors may provide an answer to that problem. The trick mentioned above is used here. A "guide laser" is flashed at the pellet. Waves reflected from the pellet are amplified, sent back by conjugate reflection, and amplified again up to an enormous power level. Since the original reflected waves were diverging from the tiny pellet, the amplified time-reversed waves will be converging on the pellet and will score a "direct hit" on it from many directions at once. Even if the windows introduce distortions, the aim and convergence of the waves is still perfect.
But let's return to the original point: the application of the 2nd Law to devices involving four-wave conjugate mirrors. It would seem that this device is the velocity reverser, and as such has the capability of reversing an "irreversible" process which involves light photons. Of course, the machinery behind the four-wave mirror may increase disorder more than it is decreased for the photon system, but I can think of ideal arrangements where this does not seem to be true. Since the four-wave mirror is a wave device perhaps there is a subtle connection between the 2nd Law and the particle-wave duality of light which has not up to now been appreciated. In any case, I am not presently able to offer a solution to this thermodynamic paradox. Solutions from you readers will be read with interest. I would like to think that perhaps we have a handle on a way of building a truly "fine grain" device and that perhaps the progressive increase of entropy isn't as inevitable as we had believed.
Four Wave Conjugate Mirrors:
Concetto R. Giuliano, Physics Today 34 #4, 27-35 (April, 1982).
The 2nd Law and Maxwell's Demon:
W. Ehring, Scientific American 217 #11, 103-110 (November, 1967).
Results of the "Name The Universe" Contest:
I want to thank all of you who took the time and effort to write and enter the Name The Universe Contest which was announced in my AV column of September, 1984. There were a surprisingly large number of entries (more than I can possibly acknowledge individually), they are still coming in, and there were lots of interesting suggestions. I'm sorry that only one person can win, ... but that's the way our universe works.
And now ... (drumroll) ... the Winnah is ... (the envelope please) ... Colin R. Leslie of Victoria, British Columbia!! Colin complains that, in the case of galaxies, while others have exciting names like "Andromeda" our own galaxy is stuck with "Milky Way", with its implications of candy bar wrappers and cholesterol collected from four-legged animals with udders. He feels that we need to do better for our universe and suggests the name Gaea. Gaea (with apologies to John Varley) refers to the primal Earth-Mother goddess of Greek mythology, worshipped at a time when the Earth _was the universe as far as its inhabitants were concerned. And so Gaea is appropriate as the name of our universe-mother, sustaining all of us and making like possible against all odds.
The first runner up is Linda L. Clements of Fremont, California, a Professor of Materials Engineering who suggests that "Technicium-43" is an appropriate name for our universe because technetium, element number 43, is the first element in the periodic table (aside from the neutron which may or may not belong there) which has no stable nuclear isotopes. In an H-space containing a multiplicity of bubble universes with slightly different force strengths this characteristic should uniquely distinguish our universe from others. I like that is a quick way of identifying our universe, but I find it less appealing than Gaea as a name.
The second runner up is my friend Gene Wolfe, who hasn't been daunted by my
rejection of his "Malkuth" and has persisted by suggesting that "BOB" is the
appropriate name for our universe. He explains that at the time of the Big
Bang the universe was named "BB" (a small hard pellet-like object), that its
name has now expanded to BOB, and that when it expands further it will become
BOOB (or maybe even BOOOOB). He then goes on to make allusions to the filling
of a Size D Cup which I will, in the interest of decorum, refrain from
repeating here. SF
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