This page deals with aspects of quantum theory that have not yet received the attention they deserve from either theorists or practical researchers.
The conventional wisdom has it that quantum effects, such as wave/particle duality, are only noticeable when dealing with atomic-sized or smaller objects. To express it in simple terms, all particles have an associated wavelength, which roughly equates to the distance around the notional position of the object where its quantum behaviour may be observed. The wavelength gets shorter as either the mass or the energy - which are basically the same thing expressed in different ways - gets larger. For a not particularly energetic electron, the wavelengths are of atomic size, which is how we get stable atomic structures and all the wonderful phenomena of chemical bonding, and tunnel diodes and LEDs and other cool shit. For a more massive particle like a proton, its wavelength is of nuclear size, and we get all the nuclear phenomena which are a bit like chemical ones only smaller and more energetic.
I mentioned "tunnel diodes"; these are electronic devices used as microwave oscillators, which make use of the interesting quantum phenomenon known as "tunnelling". An electron may be presented with a potential barrier, analogous to a wall, which it does not have enough energy to climb over. But if its wave function extends to the other side of the barrier, it can effectively disappear from one side and appear on the other side without ever having gone over the top of the barrier. It is said to have "tunnelled" through the barrier. In a tunnel diode, it is electrons which exhibit tunnelling behaviour, but any entity capable of exhibiting wave/particle duality can tunnel.
As the theory is usually stated, objects of everyday size - macro-sized objects - also display wave/particle behaviour, but they have wavelengths so immensely smaller than an atomic nucleus that we never notice their wavelike aspect and view them entirely as particles. However, it turns out that there is an additional component to the wave function which gives rise to extra maxima in the curve, much further out than those dealt with by current theories. This means that a tunnelling particle can disappear and reappear at a much greater distance from its original position than is usually deemed possible. In the frequently-studied cases of subatomic particles, the additional maxima are so small and at such immense distances that not only is the probability of observing an event very small, the "other end of the tunnel" is nowhere near the apparatus, so all that is noticed is that on rare occasions a particle is not detected when expected, or one is detected when not expected. These anomalies are put down to experimental error and indeed are usually swamped by other sources of noise. For this reason, few researchers have produced any results that would lead the theorists to perceive a need for the theory to be modified.
The function describing the size and distance of the extra maxima varies in a complicated way but the general trend is for the maxima to get larger and closer. The curve is not smooth, but has spikes here and there; there is a particularly large spike for objects with masses between about 0.1g and 10kg. Let us consider an object around the middle of this range, such as a socket, as in socket set, thing for undoing bolts with. In the case of an object the size of a socket the maxima are at distances of a few metres from the object, and consequently sockets can exhibit tunnelling behaviour and appear at random locations a few metres away from where you thought they were, usually when you're on your back underneath the car, holding up the gearbox with one rapidly-tiring arm and flailing about with the other looking for the socket which is no longer there despite the fact that you were using it only a minute ago.
By storing sockets neatly in their compartmented box, one can take advantage of a "filled shell" effect related to that which causes the extreme stability of "magic number" nuclei or the chemical inertness of the noble gases, and inhibit the sockets from tunnelling out. It is easy to demonstrate that this is a "filled shell" effect by forgetting to put one socket back in the box; once there is a gap in the shell, the stability is destroyed and the other sockets begin to disappear as well.
For a slightly less massive object, such as a CD, the maxima are smaller but at greater distances. It is well known that once a CD has been lost it is rarely found again; this is because it has tunnelled to a distant point well out of the owner's usual orbit. Again, filled shell stabilisation effects can be made use of by putting the CD in its case; however this sometimes results in the whole CD+case combination tunnelling as a single particle, so it is less useful than in the case of sockets. Also, since the "shell" has only a single occupant when filled, its stability is not very great, and it is still possible for the CD to tunnel out of its case. I suspect the technique's utility is greater with double CDs, but I don't have many of them, so the sample is too small to be useful.
My CD of The Final Cut, by Pink Floyd, tunnelled out of my room the other day; fortuitously I had some detector apparatus running at the time, the results from which lead me to suspect that it is now somewhere south of the M4 / Brunel's main line, possibly approximately along the line of the M3 / the LSWR main line (the Waterloo-Bournemouth route). If anyone in this area has discovered a Final Cut CD, in its case, with the original CD rather badly scratched and tucked inside the booklet, and its place in the designated area of the case taken by a CD-R labelled "The Final Cut" in black marker, please get in touch. (This event is described in more detail as background to my article on fitting a Volvo Amazon with a straight-six B30 engine.)
Stabilisation effects do not appear to operate on pieces of paper stored in a folder. I am not certain whether this is because there is no well-defined "filled" state for a folder or because for stabilisation to be effective it would require all the pieces of paper to be carrying a very similar kind of information. I incline towards the latter, following observation of such events as the piece of paper carrying the original circuit diagram for my Volvo 164's electric fan thermostat tunnelling out of the folder of Volvo-related documents in which it was being kept. The other documents were all legal-type stuff, insurance and MoTs and the like; the one which disappeared was (obviously) of an engineering nature. As with the CDs, if you have found my circuit I would appreciate it if you would let me know.
For objects the size of human beings, the anomalously large maxima associated with socket-sized objects have reverted to the general trend of the curve, and while still present are much smaller, so human beings rarely exhibit tunnelling behaviour. It is not entirely unknown, though, as shown by the occasions when you suddenly realise you're standing on the other side of the room and you haven't got a fucking clue what you're doing there. People usually attribute this to a lapse of memory, but in fact it is often an instance of a macroscopic tunnelling event. Again, the proximity of other objects of similar mass - such as other human beings - gives rise to a stabilising effect, so that it is most uncommon for one person to observe another tunnelling. It is, however, possible - though incredibly rare - for an entire group of human beings to tunnel as a unit entity, and such an event has indeed been recorded, in the shape of the "mystery" of the Marie Celeste. It is a little-known fact that the mysteriously missing men and women reappeared equally mysteriously on a volcanic tropical island blessed with abundant fruit and fish and a rich growth of herb. Quite understandably, once they'd explored the island they weren't too bothered about trying to get home, and instead spent an enjoyable time getting stoned and shagging, until one day the volcano erupted and blew them all to shit. (Moral: when stranded on a tropical island, build a boat before you build a spliff.) A diary kept by one of the castaways, chipped into a rock face, survived the eruption and was discovered during the Second World War by US forces using the island as a base, but the information was immediately classified due to the nature of the military activities on the island, and the rock face was later used for target practice and destroyed. The information would have been buried forever in the military archives were it not for the fact that pigeons are in the ideal mass range to exhibit tunnelling behaviour, having evolved to make use of it to gain access to secluded nest sites; a flock of us penetrated the mainland base next up the chain of command from the island one night and read all the secret files, just for the crack. Some years later we sold it all to the Russians for ten tons of pigeon food, but since by that time they were importing grain from the US they renegotiated the price to 100kg of fissile material. The fuckers haven't delivered yet, so one day we're going to toodle over there and half-inch one of their nuclear subs, which are not designed to defend themselves against a mass attack by quantum-tunnelling pigeons. All we have to do is tunnel into the sub, have a shit, and tunnel out again. With several thousand pigeons all depositing their every turd inside the sub but never actually staying there long enough to be caught, the crew have a choice between suffocating under a pile of pigeon shit or abandoning ship, and once they've gone we invade all at once, chuck all the shit out again and drive off in the sub. If anyone tries to stop us we can threaten to nuke them. I don't think they'll take too much comfort from thinking we can't bypass the safety systems on the missiles; I think they're more likely to think that a flock of pigeons capable of stealing a nuclear submarine is capable of doing anything.
Ahem. Where was I? Oh yeah, quantum stuff.
Another quantum phenomenon which has received insufficient study - although it has received considerably more than macroscopic tunnelling has - is entanglement, the "non-local connection", the "spooky action at a distance" that even Einstein balked at, though despite the great man's misgivings the effect has been proven to exist and is currently the focus of a fair bit of research aimed at producing a workable system of quantum cryptography. Indeed, working transmission links using the techniques required to implement quantum cryptography have been built, though as yet they are highly experimental, and have an impractically low bit rate and an impractically high error rate.
What's this phenomenon all about? To cut out a lot of waffle, once any two quantum entities have interacted they are forever connected (by what is known as a "non-local connection"). The quantum cryptography experiments referred to above use a single pair of connected particles. I am more interested in the more complex case when those particles are allowed to interact with other particles. If A is connected to B, and B interacts with C, then A is now, indirectly, connected to C. If Z then interacts with A, there is an indirect connection between Z and C. And so on. We have a chain of non-local connections built up from successive particle interactions.
An interesting consequence of this can be seen if we consider a case such as that of a photograph being distributed on the Internet (it could be text or music or software or any kind of data, but a frequently-used example in classical steganography is the concealment of data in the noise of a digital image; Bin Laden's lot have been suspected of communicating by means of data embedded in photos of stuff for sale on Ebay). Every stage of the distribution involves interactions between quantum entities. The reflection of light photons off the subject of the photograph is a quantum process, as is the interaction of those photons with electrons in the film emulsion of a proper camera or the image sensor of a digital one. Further quantum processes transfer the image to a computer, upload it to a web server and distribute it across the net. Quantum processes mediate the transfer of the image all the way down the line, right up to the interactions of the photons making up the visible image at the receiving end with their target - and indeed, on from there into any image processing done by the target.
There is therefore a chain of non-local connections linking subject and target, and it is theoretically possible to make use of this chain of connections as a communications channel. Despite the "broadcast" nature of the example given, the channel is extremely secure; the nature of the encoding inherent in the transmission process renders the spectrum of the transmitted information inherently Gaussian, so that any possible random receiver is not only unable to decode it, but cannot even determine that it is there at all, as without the appropriate key data it cannot be distinguished from the random noise present on an unused channel. Traffic analysis is impossible - all transmissions of information carry such quantum channels as a matter of course but it is impossible for any random receiver to determine whether the channels are being used or not. Only a receiver "in the know" - having suitable key data - can detect the presence of the information and decode it. (And, of course, reply, or attempt to.)
This form of quantum steganography is extremely versatile and useful. It requires no modification to any of the equipment used in the transmission and storage of the carrier data (the photograph, in this example); the bandwidth available for transmission of the carrier data is unaffected; it is entirely unaffected by the use of lossy compression methods; only the intended recipient is even aware of the presence of the steganographic data; and the channel can be set up well in advance of when it will be used and then left dormant until the required time (again following the example, the photograph can be taken and distributed about the Internet years before the channel is made active).
Most remarkably, it requires neither sender nor receiver to have any form of apparatus, nor even to make any particular effort to set up a quantum steganographic communications channel. As mentioned above, all transmitted information carries such channels as a matter of course. All that is required is for sender and receiver to have matching key data, and the channel will become active once the chain of quantum non-local connections between sender and receiver is complete.
In the example given, it is entirely possible that the chain might indeed take years to complete, and I think it is safe to say that the effect of the sudden activation of the channel years after its initiation could be considered to be a little weird - an approximate, not particularly good, analogy would be making a phone call without realising you're doing it, then having the actual conversation some years later without being anywhere near a phone - or the other person - at the time. Actually, it's not really any more weird than nuclear fission would seem to someone from a thousand years ago. Both fission and quantum steganography are simple consequences of the laws of physics. They're just things that happen, only not very often, because the conditions required are not common. Uranium ore deposits do not undergo chain-reaction fission except in exceptional cases such as Oklo, because the correct combination of nuclear properties in the ore and the surrounding rock very rarely arises by chance; similarly out of the zillions of possible quantum communications channels set up every day by every transmission of information, very few are ever activated because it is so rare that a sender and receiver have matching key data.
There is even the intriguing possibility that the channel may be active across time, as the particles comprising the sender and receiver are naturally quantum-connected with all previous states of the sender and receiver. The result is that a sender-receiver pair are connected as soon as both sender and receiver exist, as long as they manage to activate the channel at some point during their existence. Data on this phenomenon is unfortunately sparse, since its study is hindered by the fact that though the channel may already exist, until it is activated its existence may not be immediately apparent and so the thought of communicating through it does not arise. The available data is therefore limited to sporadic bursts of information that make it into the channel anyway and appear at the other end unexpectedly, and quite possibly unrecordably as a result. (A very bad analogy might be of two people telephoning each other but instead of speaking putting the phones on the table and wandering off and doing other stuff leaving the phones connected, only coming back to pick the phones up at some later time. While the phones are both on the table it is possible that one person may do some sufficiently noisy thing that the person at the other end might hear some faint noise from the phone on the table and forget it, or might just not notice it. If one person picks the phone up and shouts the person at the other end might hear some distorted and largely unintelligible crackle. Coherent communication is not possible until both people have picked up the phone. The problem with this analogy is, of course, that the two people telephoning each other should take place when they actually pick the phones up, the phones having been connected anyway because they were going to be connected at some point.) What little data is available, however, does seem to suggest that an active connection probably is active over the entire coexistence of sender and receiver regardless of when the connection is actually made.
This, then, is another phenomenon which has received insufficient study due to its nature. Its dependence on the extremely rare match between sender and receiver makes it not amenable to scientific study, because the chance of any study selecting a pair at random which turn out to be matched is so low that any attempt at experimental verification is almost bound to yield a negative result. There is also the tendency of people to assume that it can't happen because of the usual confusion between "impossible" and "just really unusual/weird" (such assumptions are usually inappropriate where quantum physics is concerned, but almost all thinkers about quantum physics, even great thinkers like Einstein, have fallen into such traps at some point). However, matched pairs of sender and receiver do exist and given such an unusual combination the phenomenon can be demonstrated; I am of the opinion that an active, working quantum non-local steganographic communications channel is a great gift from God, and should therefore, with Jesus's guidance, be put to its fullest good use.
No communication method is perfect, and while this method has some very great advantages, there are certain difficulties as well. Current research seems to indicate that the lowest error rates are achieved when the information being transmitted has a high degree of redundancy - interestingly, unlike most comms links, the redundancy must be in the information itself rather than in its encoding; ECC schemes do not work well. Natural language is quite highly redundant and can be transmitted without too much loss, especially if the concepts being discussed are fairly fundamental and well-known; something like a telephone number, on the other hand, has zero redundancy and is almost impossible to transmit without errors. It could be described as a low-bit-rate communications system which is more suited to sending love letters than battlefield situation reports. This is, of course, not necessarily a bad thing... make love not war, and all that.
Feel free to email me if you wish to exchange any information on quantum non-local steganographic communication.
