By John Walsh 10 Jan 1999
Exploitation of interstellar space has three major hurdles - distance, resources and time. These pose insuperable technical problems unless politically acceptable solutions are found. There are problems. One is the vast distances to be crossed, the next - the enormous risk to human life, the next - retrieving the information within a reasonable time frame, and the last is the resources needed to achieve the result. These problems are not as difficult to solve today as it may once have appeared. This partially speculative paper exposes a way to decimate the problem and create new industries for the future while securing a foothold in space. I have previously discussed one of the problems of interstellar travel which poses further technical problems (20) yet possibly solves the most crucial ones for human travel. This paper explores the possibility of the creation of an interstellar network grid with instantaneous communications facility. Some technologies exist already, others are looming on the horizon of existing technology. No warp drives or wormholes needed to provide the solutions. This proposal attempts to solve all the major objections to human risk, distance, time, and resource utilizing a superficially similar variant of "Bell’s Telephone". The problem also requires major technical advances in exploiting ZPE with comparatively minor advances in other technologies to make it a reality in the near future. Some preliminary implications involving the SETI Program and the possibility of encountering an existing "alien" network are canvassed. |
Of all the problems that stand in the way of travel to the stars the most difficult ones to solve are those of the politics involved with massive conventional distances and vast voids in time to span. In our century we have already seen what near instantaneous global communications can do with bringing people together. Imagine for a moment what could be facilitated with interstellar communications without delays in time. This may at first seem impossible but recent practical developments in communications and quantum theory indicate that instantaneous quantum "teleportation" can occur provided a suitable "carrier" is laid down for the flow of information across cosmic distances. Recent experiments avoid direct mention of this effect but the thrust of the experiments is to verify that the information that was "teleported" is indeed the original unread signal. Further enhancements appears to inevitably lead to long distance instantaneous communication by a separation of source of signal and its uploading into the entangled carrier and production of the entangled carrier. A further decoder would be available at the destination. One form of the experiment is as shown here from a Reuters News Source. This is fully discussed in H.J.Kimble’s References (15,18) below
1. Without looking at the input signal, the sender -- Alice -- combines the original beam of light with a special beam of 'entangled light.' The result is something that looks like complete gibberish.
2. Alice sends the gibberish information to the recipient, Bob. The information looks like complete gibberish to him, too.
3. However, Bob has his own copy of the special entangled light. Combining it with the gibberish he got from Alice reproduces the original beam of light.
The requirement of the experiment is to prove that the signal is decoded faithfully over benchtop scale of distance. Though this is a fantastic advance it cannot provide faster than light communication. Indeed the encrypted beam must be sent to the recieving post and decoded.
I will apologize for the form of this conceptual and speculative paper. I believe that a simple technique for discription leads to wider perusal and in this case no essential ingredient is lost because of it’s transparent treatment. I feel that it actually renders it a service that a mathematical approach cannot provide.
I also wish to thank R.F.Werner for use of his section on Bell’s Telephone, a better expose of this process could not be found anywhere. A further apology is in order for the speculation and lack of conciseness and informality of the References. I also wish to thank H. Puthoff for his description of Zero Point Energy and it’s origins.
Clearly the experiment could also be performed with the source of entangled beams half way between "Alice" and "Bob". This problem has been partially dealt with in the literature as "Bell’s Telephone" which is one class of ‘impossible machines". One beam is analysed with "Original" signal destroying the "Original" information and "coding" one end of the beam, while an EPR Bridge "connects" the other to its reciprocal twin beam. The information cannot be sent along the beam at supraliminal speed because, though the entangled beam responds to the instantaneous analysis of one end of the beam with collapse of the wave packet into a complementary state at the other, the remote end cannot decipher any messages. Messaging would require predicting the coding before it’s complementary signal arrives. Since the actual code would depend on the appropriate superposition of quantum states from the original beam, this appears to put an end to this conjecture. All appears lost for the case of supraliminal signaling except there is one loophole. The two entangled beams do not need to have encoded information on them, at least they do not need to have quantum information encoded on them. How is it possible to send information without encoding information on the beam from one end then decoding it off at the other?
Consider the frame of reference of the photon. In its "rest frame" the instant a photon or photons are created they are destroyed as they undergo the most extreme form of "twin paradox" relativistic time slowing possible. No time passes in the photon’s frame of reference. This would mean that all points on the photon or photons in the Singlet State are in effect - contiguous. From our frame of reference we "see" a distorted photon or photons as an expanding wave packet occupying an ever-increasing "spherical" shell of space (actually we see nothing since the act of "seeing" this phenomena will destroy the quantum character of the wave packet). Encoded on each photon is half of the information necessary for constructing an information retrieval system as indicated in the Quantum Beam Teleportation Experiment as devised by Kimble (above). What we know about this shell is that the photons are in an uncollapsed state. That is the complex quantities required to describe the state are intact and are propagating through "our" space at the speed of light. After a "long" period of time each photon is well and truly spatially separated from its anti-twin. If one or both of the photons were allowed to fall on a narrow slit, a screen on the remote side of that slit will show a set of interference fringes. Consider a symmetric arrangement of slits with or without a screen. Both opposite Singlet State photons will diffract through their respective slits. This is the normal optical effect noted with unentangled monochromatic light. Supposing one half of this Singlet State was interrupted (absorbed). This would need to occur on the near side of the slit from the radiation source, this is where the distance to the slit was sufficiently small to invoke the non-local effects of the Bell inequality. This event could not be so close to the slit that there was any argument as to which side of the slit the photon was. What would happen?
Since the two photons are entangled in one Singlet State then the destruction of one of the photons would disturb the twin photon sufficiently to instantly collapse it’s state. The later consequence of this would be as it passed the slit no interference pattern could be formed at the screen. The photon would be a ballistic without the 2 qubits of data encoded. Sure it would have complementary properties to the other now extinct photon, but without it’s twin the Singlet State of the two particles is lost. A telescope viewing the screen where a minima or maxima was previously being ‘built up" would suddenly lose the pattern (stochastic illumination) and a change of brightness would occur. This is equivalent to ‘bursting the wave front’s bubble. In a transverse direction to the direction of propagation the state would instantly collapse leaving the second photon without it’s linked Twin State. It is inconceivable that half a wave front could continue to propagate under energy considerations alone. Localization of the second photon must instantly follow. This is not information being sent as a "packet" along with photons. This information is unique to the Singlet State that has just collapsed. To put this clearly just waving my hand if front of one slit causes the interference pattern at the other slit to vanish and reform in synchronization with my actions. Who cares about sending data on the photons anyway?
The entangled signal will be instantly communicated over the distance as a semaphore. Entanglement occurs over any distance instantaneously, even kilometers (perhaps light years) as recent experiments have indicated. A problem as to slit alignment still persists. All that is required is to wait sufficiently long until the beams ‘arrive" at the respective locations of source and destination, then communication begins to be possible. The technical problem resolves itself to producing "clean" entanglement beams and the accurate placement of these three instruments the source, and two detectors. Note that if two-way communications is required two separate systems will be needed for full duplex communication and there can be only one screen - at the receiving end.
In a practical system all three instrument would be located at each platform in multiples to perform several tasks with several channels, however the entanglement beams would be vectored towards the next platforms up and down the network. A receiver and detector combination would be used to detect signals from the next stations up and down the network. There would be full duplex semaphore systems operating at each site. Destination information would be decoded and new destination information would be placed onto the beam so that routing could occur at network bridges. Redundant information could be used to route packets of semaphore data. Sufficient channel capacity would be required to perform all housekeeping tasks as well as the sending of signals. Lost packets could be instantly resent to maintain real-time connectivity. Multiple streams could also be sent to recover lost data and for error checking. As the network grew increased bandwidth would need to be added. This does not sound as elegant as encoding the data on the stream as quanta but I doubt if anything is lost other than a requirement to send this analog "morse code" as relatively long dots and dashes compared with photon streams sent.
Two figures illustrate the current situation. Not to scale and not supposed to be a faithful representation, merely a conceptual model. The convention of Alice and Bob is continued with a third distinct source equidistant from both Alice and Bob.
POINTS ARISING
Quantum entanglement brings a possibility for the deployment of a "grid" that performs the same function philosophically as the Iridium Global Communications Network but taken a step further into the heavens. Recent demonstrations of long distance communications using quantum entanglement over tens of kilometers followed by the "teleportation" of a continuous beam of light foreshadow a new age of instantaneous communications. There are formidable problems to be solved but I propose that the overall problem may be taken apart into sections and dealt with piecemeal. I will assume that the reader is familiar with several concepts, some of which are still some ways off in their final development. These are:
The basic theory of quantum teleportation was outlined in 1993 by IBM physicist Charles Bennett and his colleagues. Anton Zeilinger from Innsbruck performed Early experimental work - the first reported Quantum Teleportation of a single Photon. Based on work by Dr. Jeff Kimble, a physics professor at the California Institute of Technology, Anton Zeilinger and others, the possibility exists for the construction of a signaling system (possibly full duplex) that allows end to end communication - instantaneously - using beams of photons whose properties are being teleported. According to the theory particles are created in pairs such that the two beams are "twinned" in a quantum sense. Encoding one end of the dual beam system with information immediately leads to the appearance of the complementary quantum state at the remote end of the system. In order that this process begins, a period of time must elapse to establish the particle streams to the remote ends of the beam at light speed. The encoding process is unconventional as the system is reduced to a semaphore and optical detection via interferometry. The main problem then resolves itself into establishment of "outposts" relatively equidistant between source and destination. These would need to be "stationary" sources of suitable particles for the primary purpose of communication. Since there are no stationary points in space the outposts would need continuous communication with other such stations (grid) to facilitate continuous communication to enable reportioning. These devices would take many years to be put into place, even at high velocity, to span the large distances between the stars but owing to telepresence and ZPE this may not be as difficult as once thought.
Because communications would be instantaneous across these platforms, I propose that they be "manned" by machines that allow a telepresence at the remote locality. Such telepresence will mean that self motivating machines would be an overkill and the telepresence will lead to far more versatility than a mere machine could be expected to be able to accomplish autonomously. They would be able to repair their defective parts and to continually take advantage of technological advances of developments on the home world. They would be equipped with adequate fabrication facilities to enable the creation of anything that could conceivably be needed for manufacture on site, even new outposts would be constructible using local materials. The beacons would be adequately provided with energy to perform all tasks. These include repair of the telepresence robots and support machinery. Maneuvering power for the platforms sustained for decades, maybe even centuries to maintain a "constant" position equidistant between other similar outposts. Workers on the home world would communicate with their "twin" telepresence unit for daily work on board the vessels. You would not need to "commute" as communication would be instantaneous along the channel and they would remain in the safety of the home world. Some thought discovers that, the beam itself can be used to "fix" positional errors over time. Navigational Computers would be used to monitor the end-to-end beam positioning via feedback.
Some velocity modulation of the optical beams would be necessary for maneuvering and repositioning of the platforms. This may involve dielectric materials. The energy requirements would be considerable. These would be for powering of all systems as well as the provision of the acquisition of raw materials from "nearby sources" on an irregular basis to allow for building of facilities and machines at the outpost. I propose the only form of energy that will allow this protracted energetic process would be the harnessing of zero point energy. This would allow arbitrary high velocities to be reached in realistic time frames if sufficient energy were made available. I quote from Hal Puthoff’s Paper "Quantum Vacuum Fluctuations: A New Rosetta stone of Physics" where it refers to the origin of this energy in part, as to it’s existence - this has already been confirmed on the small scale.
"As to where the ubiquitous electromagnetic zero-point energy comes from, historically there have been two schools of thought: existence by fiat as part of the boundary conditions of the universe, or generation by the (quantum-fluctuation) motion of charged particles that constitute matter. A straightforward calculation of the latter’s possibility has recently been carried out by the author. It was assumed that zero-point fields drive particle motion, and that the sum of particle motions throughout the universe in turn generate the zero-point fields, in the form of a self-regenerating cosmological feedback cycle not unlike a cat chasing its own tail. This self-consistent approach yielded the known zero-point field distribution, thus indicating a dynamic-generation process for the zero-point fields. Now as to the question of why quantum theory.." thus ends the quote.
A conservative estimate recently by Putoff of the amount of energy at the disposal of an advanced technological civilization would approximate to the amount of energy needed to evaporate all the oceans of the Earth from an empty space equivalent to the void in an ordinary coffee mug. This energy would be available from this space regeneratively from the universe time after time. It is not perpetual motion. The suggestion is that civilizations will have plenty of energy at their disposal but not for use on the home world owing to thermodynamic considerations. This would be that our planet’s civilization would rapidly cook itself with waste heat if commercial enterprise were allowed to exploit this source of relatively free energy on the surface of the earth. This would not be a problem in empty space where such energies would find enormous use, waste heat could be radiated harmlessly away into space.
What would we do with this energy? Space Propulsion for positioning the platform would be accomplished by the use of matter - antimatter creation and annihilation. Dual beams could be used for ion propulsion using steerable jets. Practical system are presently being used on space missions, these could be scaled up to the task. The two streams would be accelerated through twin systems - one for matter particles the other for antimatter particles. These beams could be allowed to meet at some distance away from the vessel (a safe distance). A small vessel could be propelled by the same system to allow the drones to gather material from asteroids or comets in order to produce product for use by the platforms.
.In principle the grid could be as wide as we choose as communication would be instantaneous but would probably follow corridors of resource through the galaxy. It is not inconceivable that a platform could be positioned in a spatial void. This is not very likely as there is little point in positioning a platform there because of little material to exploit other than it provide an ideal location for positioning a beacon between two highly interesting sites. These sites would be equally accessible via several other platforms sited along corridors of resource. How would these sites communicate? A packet communication system similar to present internet technology would be used with routing according to address of the packets. With optimum positioning of the platforms the packets would reach their intended destinations almost instantly. There may be Von Neumann Machines on the platforms that could be used to duplicate systems when presented with resources thus extending the grid. The grid could be made tighter in time bringing more points within contact of the grids realtime control range.
Because communication and information transfer was instantaneous as well as at no risk to human life via the benefit of telepresence, politically this becomes a do-able problem. Some benefits would be gained immediately in exploiting near earth materials such as local asteroids and comets. The grid would expand as resources permitted thriving on dead interplanetary and interstellar material. The amount of resource required would not be very large since there are no life support systems or colonies to provide for. All that would be needed would be communication platforms, small resource vehicles, telepresence devices and all the support systems to accompany them including the ZPE energy exploitation system and matter - antimatter particle machines.
If we encountered other civilizations this would enable a non-threatening commerce to be set up and surrogate meetings could be arranged between our telepresence machines and the other civilizations. An exchange of ideas could be made in real time without the threat of an ‘invasion". We could "sell" Network Access as a batering item in exchange for new technologies and thus spread our intellectual influence without spreading our diseases or requiring us to dominate and terraform these other worlds. Our machines would wait for first contact, setting up tight networks around inhabited worlds with accompanying tight grids. Our remote machines could investigate those worlds using our surrogate telepresences. Close in around these worlds "radio" and laser communication would fill the short gap to the nearest beacon so the home world could be kept informed of progress and in realtime contact. Temporary communications beacons could be placed half way between source and destination while exploration was underway to enhance telepresence and reduce phase delays in instrumentation.
An intriguing possibility exists that this process may have already occurred and such grids may already exist in our region of the galaxy. It goes without saying... not produced by we earthlings! It awaits our interest such that we could become an integral part of a spreading Galactic Civilization by "applying" for membership. This is similar to the sentinel concept proposed by Arthur C. Clarke in the epic motion picture 2001 - A Space Odyssey. No stargate though but something safer - telepresence. Possible through virtual reality we could visit their home world, and telepresence will also allow our "neighbours" to visit us in complete safety.
This throws a new light on SETI’s Investigations. Maybe we should be looking for "hot infra-red nearby objects that may be a source of particle radiation. These objects would also be communications ports for civilizations making initial contact via radio or laser communication, and hence not the distant star systems, which are the origin of the communication signals themselves. There are interesting cases in the annals of communications which involve the retransmission of radio or television signals - are these first contact attempts?. The initial communications would be to arouse the interloper and ask this "ISP" for access. This would be "cheap membership" but there would then be "barriers to access" for getting a piece of the local action. We do not have ZPE or Spacecraft capable of installing such systems ourselves in competition with a potentially existing system in order to negotiate "fair" access rights.
This interpretation of Quantum Entanglement that I have proposed may appear to violate axioms previously laid down by pundits. I apologize in advance if this conjecture turns out to be wrong, the proof of the pudding is in the eating and I do not have resources to carry out this simple test.
The long-term survival of our culture will depend on having the local rights to this high tech merchandise if it turns out that this is the special case we would all like to see. The alternative might be our culture being eventually submerged by contact with a more creative and dynamic civilization. It would appear that it could be suprisingly simple for our culture to perform all of these "Labors of Hercules" when you compare them with the tasks already demonstrated by our Civilization. Alternatively we can saturate "them" with our soapies and other trash television and bring them down to our level? Perhaps we can get them on breach of Copyright by they watching our transmissions. Time will tell.
The reference section below is a compilation of existing references from Hal Putoff’s Papers and others from Kimble and Associates but does not refect all resources relating to this matter.
with apologies
I believe that to fully understand the problem this source needs to be quoted almost in full to elucidate the problem and to distinguish it from my treatment.
"Bell's Telephone
We have shown the impossibility of all the devices in our list from the impossibility of the first, the joint measurements. So we must ask how fundamental this impossibility statement is. Is it perhaps an accidental feature of the quantum theoretical formalism, and not a law of nature, as hidden variable theorist would have us believe? At least a partial answer is provided by yet another impossible machine, which would come even before the joint measuring device in the logical order of impossible machines, namely Bell's Telephone. It is named, of course, after John Bell, the inventor of the correlation inequalities bearing his name. These inequalities refer to a source preparing pairs of quantum particles. The particles fly apart, and are independently subject to measurements by two physicists traditionally named Alice and Bob.
Each one has two measuring devices to choose from, which produce a yes/no result in each individual experiment. Hence there are four yes/no measuring devices involved, which can be combined in four different ways into a correlation experiment. A certain linear combination of the four correlations is a quantity known as the Bell correlation. What Bell showed was that if we assume that the data can be accounted for by a hidden variable theory, in which each one of the separated particles is described by its own variable (a so-called local hidden variable theory), the Bell correlation cannot be larger than 2. The fascinating point about this is that experiments have been made in which values significantly larger than 2 (around 2.8) were measured (in perfect agreement with quantum mechanical predictions). So, remarkably, a question of the foundations of quantum mechanics has been directly decided by experiment. Here we want to rearrange Bell's locality assumption a bit, so that it takes the form of an impossible machine assumption. We will assume exactly the same situation as in an experiment testing the violation of Bell's inequality. Let us assume that Bob has a joint measuring device for the two devices used in the actual experiment, in the sense described above. Then we claim that Alice can send signals to Bob, by encoding her message in her choice of measuring device (say A or B). Bob can read her message by looking at his joint measuring device. If he sees two equal results (yes/yes or no/no) he guesses that Alice has been sending A, otherwise he guesses B. The crucial question is whether his guesses come out better than chance: in that case we have a proper transmission of information (albeit on a noisy channel), and we will call this device "Bell's telephone". It is easy to derive a lower bound for the probability that Bob guesses right (see web page for reference) , and it comes out as the Bell correlation, divided by 4. Hence as soon as Bell's inequalities are violated, the probability is better than 1/2, and the telephone works. Note that it works over arbitrarily large distances, if we just let the two particles travel apart far enough. This is (eventually) in contradiction with Einstein causality. So if we accept the experimental evidence of Bell correlation’s larger than 2, Bell's telephone is forbidden by an important fundamental physical principle outside quantum mechanics. But the only assumption in this derivation is Bob's ownership of a joint measuring device, so the non-existence of such a device, and with it the non-existence of the other machines in our list, follows ultimately from causality. It should be mentioned that we do not really have to resort to the Theory of Relativity to find the impossibility of Bell's Telephone. Quantum Theory or, more precisely, the standard way of describing composite systems in a tensor product Hilbert space rules out Bell's Telephone, too. So Bell's Telephone is also properly an "impossible machine of quantum mechanics".
Of course, nobody can be forced to accept Einstein causality as a fundamental principle. To someone like that our impossibility proof for all the devices above will hardly be convincing. And indeed there is a large community of hidden variable theorists who suggest modifications of quantum mechanics discarding causality, or "locality". Quantum Theory (in its statistical interpretation, which I will consistently adopt) is a local theory in the sense that Bell's Telephone is excluded in this theory. So be warned that whenever you read about the alleged non-locality of quantum theory (and the literature abounds with this claim), you are really reading about the non-locality of a hidden variable add-on to quantum mechanics, often invoked implicitly."
Point taken...(26)
1.R. Podolny, "Something Called Nothing" (Mir Publ., Moscow,1986)
2.W. E. Lamb, Jr., and R. C. Retherford, "Fine Structure of the Hydrogen Atom by a Microwave Method," Phys. Rev. 72, 241 (1947)
3.P. W. Milonni, R. J. Cook and M. E. Goggin, "Radiation Pressure from the Vacuum : Physical Interpretation of the Casimir Force," Phys. Rev. A 38, 1621 (1988)
4.R. L. Forward, "Extracting Electrical Energy from the Vacuum by Cohesion of Charged Foliated Conductors," Phys. Rev. B 30, 1700 (1984)
5.H. E. Puthoff, "Ground State of Hydrogen as a Zero-Point Fluctuation-Determined State," Phys. Rev. D 35, 3266
(1987) See also science news article, "Why Atoms Don't Collapse," in New Scientist, p. 26 (9 July 1987)
6.A. D. Sakharov, "Vacuum Quantum Fluctuations in Curved Space and the Theory of Gravitation, Dokl. Akad. Nauk.
SSSR (Sov. Phys. - Dokl. 12, 1040 (1968). See also discussion in C. W. Misner, K. S. Thorne and J. A. Wheeler,
Gravitation (Freeman, San Francisco, 1973), p. 426
7.H. E. Puthoff, "Gravity as a Zero-Point Fluctuation Force," Phys. Rev. A 39, 2333 (1989)
8.H. E. Puthoff, "Source of Vacuum Electromagnetic Zero-Point Energy," subm. to Phys. Rev. A, (March 1989)
9.See review of SED by T. H. Boyer, "A Brief Survey of Stochastic Electrodynamics," in Foundations of Radiation Theory and Quantum Electrodynamics, edited by A. O. Barut (Plenum, New York, 1980) See also the very readable account "The Classical Vacuum," in Scientific American, p. 70 (August 1985)
10.E. P. Tryon, "Is the Universe a Vacuum Fluctuation?" Nature 246, 396 (1973)
11.A. Vilenkin, "Creation of Universes from Nothing," Phys. Lett. 117B, 25 (1982)
12.R. Podolny, Ref. 1, p. 211
13 H. Puthoff : "Quantum Vacuum Fluctuations: A New Rosetta Stone of Physics" from http://www.clas.ufl.edu/anthro/ZPE.html later than January 7, 1989
..14 R. Soderlind "It’s beam me up a spooky memory",The Australian Jan 27, 1998
..15 H.J.Kimble Quantum Teleportation page:http://www.cco.caltech.edu/~qoptics/teleport.html
..16 S.L.Braunstein and H.J.Kimble, "Teleportation of Broad Bandwidth Quantum Information", Phys. Rev. Lett. 80,869 (1998)
..17 L.Vaidman, "Unconditional Quantum Teleportation", Phys Rev. A 49. 1473 (1994)
..18 A.Furusawa,J.L.Sørensen,S.L.Braunstein,C.A.Fuchs,H.J.Kimble,and E.S.Polzik Science 1998 October 23; 282: 706-709
..19 IBM Page on Quantum Teleportation :http://www.research.ibm.com/quantuminfo/teleportation/
..20 J. Walsh, "Considerations in Relativity Yielding a Novel Result in the Interpretation of the "Clock Paradox" Phenomena". Sept 1975
..21 M.Pavcic,J.Summhammer "Interferometry with Two Pairs of Spin Correlated Photons", Physical Review Letters 73, 3191-3194, 1991
..22 G. Krenn, A. Zeilinger, "Entangled Entanglement", Austrian Fonds zur Forderung.. (FWF) Project No.S65-02,S65-11
..23 G.Krenn, K.Svosil, "Stronger than quantum correlations", Austrian Fonds zur Forderung.. (FWF) Project S65-11
..24 M.Michler,K.Mattle,H.Weinfurter,A.Zeillinger,"Interferometric Bell-state Analysis", Austrian Fonds zur Forderung.. (FWF) Project S65-02 and NSF Grant No. PHY92-13964, February 13,1996
..25 S.L.Braunstein,H.J.Kimble,"A posterori teleportation",quant-ph/980001, 01 Oct 1998
..26 R.F.Werner, "Appendix. : Bell’s Telephone",Web page at or near http://nostromo.physik.uni-osnabrueck.de/~rwerner/QInf/qinf12.html, Mailto einardt.Werner@physik.uni-osnbrueck.de Dec. 17, 1996