Alternate View Column AV-82
Keywords: space drive phased array amplitude intensity
HBT interferometry photon particle wave
Published in the January-1997 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 7/23/96 and is copyrighted © 1996, John G. Cramer. All rights reserved.
No part may be reproduced in any form without the explicit permission of the author.
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When I was about 16 years old I found a remarkable Letter-to-the-Editor printed in the "Brass Tacks" section of John W. Campbell's _Astounding Science Fiction_ (the previous incarnation of this magazine). The letter described a "magnetic space drive" that seemed very likely to actually work. This column is about interferometry, but I will start by describing that space drive, which, in a sense, is an interferometer.
Here's the magnetic space drive setup. We place two bar magnets, each one perhaps one inch long, at a center-to-center separation of 6 inches, with the bar magnets' long axes lying on the same straight line. We arrange the magnet poles so the north pole of magnet A is closest to the south pole of magnet B. In this configuration each magnet experiences an attractive force, pulling it toward the other magnet. These forces cancel, so that there is no net force on the two-magnet system.
Now the trick: we rapidly flip magnet A, so that its poles are reversed. Magnet A is in the field of magnet B and now experiences a repulsive force in the direction away from B. However, magnetic disturbances travel at the speed of light. Until the field change arrives about half a nanosecond after the flip, magnet B remains in the unreversed field of magnet A and will still experience an attractive force in the direction of A. Thus, B is attracted to A while A is repelled from B. Therefore, the two-magnet system has a net force on it, pushing it in the direction from B to A.
This net force is transitory, but it can be maintained indefinitely by repeated flipping. Just as the field change from A arrives at magnet B, we flip the polarity of B. Since arrival of the field change and the polarity flip happen simultaneously, B is still attracted to A. And for the next half nanosecond while B's field change propagates to A, the magnet A continues to be repelled by B. Again the two-magnet system experiences a net force in the direction from B to A. And when the news of B's reversed field reaches A, we flip A. And so on ...
The result of this programmed magnet-flipping is that the isolated two-magnet system has a roughly constant net force acting on it. If isolated in space, the system will accelerate, gaining velocity, momentum, and kinetic energy. It is therefore indeed a "magnetic space drive". It also appears to present a physical paradox, in that it seems to be violating Newton's 3rd Law of Motion (momentum conservation) with extreme prejudice.
I carried this puzzle around with me for several years in high school and college before I finally worked out what was going on. I was a physics major in college and struggled to learn enough mathematics and electromagnetic theory to analyze this magnetic space drive properly. Finally I succeeded.
One can view the system as a pair of magnetic dipole loop antennas that are driven 90 degrees out of phase and spaced a quarter of a wavelength apart. Careful analysis of the forces shows that the overall system will indeed experience a definite (but small) net force. But there is also another effect: each of the magnetic dipoles is an antenna that emits radio waves, and because of their separation and phasing, the waves on one side along their mutual axis will tend to cancel, while the waves on the other side will tend to reinforce. It is a "beaming" antenna system, known in radio lingo as an "end-fire antenna" It has the property of transmitting radio waves in a particular direction in space. The beamed waves travel in the direction opposite that of the net force, and the force is the "radiative reaction" to the momentum carried away by the radio waves.
Therefore, the magnetic space drive will work. It uses radio waves in place of a rocket exhaust and recoils in the opposite direction, just as Newton's 3rd Law says it should. The down-side of this device is that the force you get for a given amount of expended electrical power is extremely small. The reaction force is the net radio wave power divided by the velocity of light so developing a thrust of one Newton requires 300 megawatts of power, about the output of a medium size nuclear power plant. The magnetic space drive works, at least on paper, but requires too much power to be of any practical interest as a propulsion system.
However, the device is interesting for another purpose. If we use the two-dipole antenna system as a receiver instead of a transmitter, it is sensitive to incoming waves coming from the same direction in which it tends to broadcast. The directional effect can be enhanced by adding more antennas to the system and mixing their received signals with appropriately chosen phases. Such a phased array of antennas is standard in radio astronomy and can be used to transmit or receive radio waves with pinpoint accuracy.
Combining the amplitudes of the signals from such an antenna array is called amplitude interferometry. It is a very powerful and widely used technique. The directional accuracy of such an array is limited by diffraction, the tendency of waves to distort and spread at the edges of an aperture. Two radio sources (e.g., quasars) separated by an angle X can distinguished if X is greater than about w/d, where w is the wavelength of the radio waves and d is the diameter of the system of antennas used to detect the waves. The same relation holds for optical telescopes, where w is the wavelength of the light observed and d is the diameter of the telescope aperture. This places a large premium on having a large value of d, since this makes the angular resolution X very small. In radio astronomy, "antenna farms" radio telescopes like the Very Large Array at Socorro, New Mexico, an array of 27 dish antennas configured in a large "Y" 20 km on a side, are used to obtain very good angular resolution. [For more information, see the VLA web site.] On a larger scale, widely separated antenna complexes record radio waves with precise timing and phase information. The recordings are later combined to provide the equivalent of a radio telescope with an Earth-diameter aperture. Optical telescopes are now being developed that will extend this kind of amplitude interferometry into the optical domain.
The amplitude interferometry techniques however, apply only to sources of coherent waves, e. g., radio waves from a single antenna (or light from a laser), that comes from a single source and maintains a continuous phase across a broad wave front. This limits its uses in optical astronomy, because most stars are incoherent light sources (like a light bulb). The light from different parts of the star's surface has no consistent phase relation. Fortunately, there is another kind of interferometry that can be used with incoherent light sources. It was invented by the radio astronomers Hanbury-Brown and Twiss, and it is called intensity (or HBT) interferometry.
The Hanbury-Brown-Twiss trick is to multiply the signals from two dish-antenna detectors instead of adding them, as would be done in amplitude interferometry. This is equivalent to imposing a requirement that photons from the source are detected by both detectors simultaneously, in good time coincidence. They showed mathematically that the strength of the multiplied signal depends on (D.S), the product of the diameter D of the star producing the observed radio waves and the separation S of the detectors receiving the waves.
Hanbury-Brown and Twiss mounted their antennas on a carriage that allow them to be moved to change their spacing S and pointed them at a nearby star. They found, as expected, that when the dishes were close together and S was small, the multiplied signal was strong. But as the dishes were moved apart and S was increased, the signal decreased. The disk separation S(1/2) at which they receive a signal that was half the maximum value was used to infer the diameter of the star. Using this technique, the diameters of many nearby stars were measured.
HBT interferometry works only with incoherent light sources. As the source becomes coherent, the multiplied signal drops to the background level. It works best when the ratio (D.S)/(L.w) has a value near 1, where L is the distance to the star and w is the wavelength of the radio waves used in the measurements, and when the detected particles are identical bosons, i.e., particles like photons that have integer rather than half-integer spins. [See my AV column in the March-1995 Analog for a discussion of quantum spin statistics.]
HBT interferometry teaches an interesting lesson about photons. Particles like photons cannot consistently be described as a blob of mass-energy which travels through space from point A to point B. The enhancement observed in HBT interferometry implies a more complex picture. The detection of waves from source points at the right and left edges of the disc of a star can be considered as removing one energy quantum (hc/w) from each of the two source points and delivering one energy quantum (hc/w) to each of the two detectors. For many combinations of source and detector separation distances, the detected waves are nearly opposite in phase, so that the composite wave is very weak and the detection event is very improbable. For a few ideal combinations of source and detector separation distances, however all of the composite waves are strong because their components coherently reinforce. In this case the detection event is much more probable, as predicted by quantum mechanics.
However, neither of the photons detected at A or B can be said to have originated uniquely at one of the two sources. Each detected photon originated partly in each of the two sources. It might be said that each source produced two partial photons and that fractions from two sources combined at a detector to make a full size photon. Thus, photons are not little baseball-like energy packets that travel in a straight line at the speed of light. They must split and combine as waves. Their particle aspect is an illusion created by the quantum boundary conditions for emission and absorption. Photons have no unique identity except when they are emitted or detected. That's part of the weirdness of quantum mechanics.
HBT interferometry also has another application, in a completely different area of physics. My field of research is ultra-relativistic heavy ion physics. I and my co-workers study collisions between heavy nuclei accelerated to the highest energies we can manage, which at the moment is 33 TeV lead nuclei accelerated at the CERN SPS accelerator.
In these collisions thousands of pi mesons are created. Pi mesons have a spin of zero and are therefore bosons. If we use the wavelength of a pi meson for w, the size of the colliding nuclear system for D, and the size and separation of components of our particle detectors at CERN (a few meters) for S and L, the ratio (D.S)/(L.w) is around 1, just as in the radio wave case. This allows us to use HBT interferometry to measure the sizes of the ultra-hot fireballs produced in our nucleus-nucleus collisions. We've been using this technique on our data for some time with good results. The ultra-hot fireballs we produce show very interesting size and expansion characteristics.
And there's another interesting quantum moral here. The pion "particles" we detect are usually considered to be tiny combinations of a quark and an anti-quark locked in a strong-interaction embrace. But they are also identical bosons.
The fact that HBT interferometry works with pi mesons tell us that they are no more baseball-like particles that are photons. They are also manifestations of quantum boundary conditions for emission and absorption, and detected pion are being assembled from particle "slices" supplied by many separate and incoherent emission points.
Particles are an illusion. That's part of the weird and wonderful universe in which we live.
This page was created by John G. Cramer on 7/23/96.