The wireless spectrum auction is wrapping up as I type, launching a new era of … more of the same.  This auction ended up nearly tripling expectations — the good news: three times as much revenue to apply against the Canadian national debt; the bad news: after shelling out so much dough, who’s going to want to lower the cost of wireless for consumers?  Those extra payments are going to be passed on to — you guessed it! — us.

What a sad state of affairs.  The unavoidable problem at the heart of wireless is limited bandwidth, which has to be licensed at great cost to wireless providers, meaning only a select few companies have the resources to operate wireless networks.  This lack of resources and resulting lack of competition means service is bad and costs are high.  If only there was a way to communicate wirelessly without using bandwidth ….

Of course, there’s lots of different frequencies.  The electromagnetic spectrum includes radiation with wavelengths ranging from as high as a mountain (radio waves) to smaller than the nucleus of an atom (gamma rays), and everything in between, including visible light.  The shift from analogue to digital has allowed the finite number of different frequencies to be used in exponentially more efficient ways, freeing up the extra space to carry more information.  But not all frequencies can be used to carry information, and even those that can still have their limits.

Non-wireless communication isn’t restricted by bandwidth, but by infrastructure.  Fibre optic cable, for example, carries a lot of information — and two fibre optic cables carry twice as much information.  In fact, by using a single fibre optic cable to transmit information encoded using different transverse modes of visible light, a single cable can be retrofit to relay several times as much information as a single-frequency cable.  But while fibre optic is great for relaying information between hubs, it doesn’t help with wireless devices; nobody wants a fibre optic cable connected to their cellphone.  That would be messy.

Is there another way to relay information wirelessly over great distances, without using electromagnetic radiation?  Maybe.  Probably not.  But maybe …. One of the stranger offshoots of quantum theory is an effect known as quantum entanglement:

“When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own …. By the interaction, the two representatives have become entangled.” (Schrödinger, Proceedings of the Cambridge Philosophical Society, 1935)

The author of the link above continues:

“What Schrödinger showed was that if two particles are prepared in a quantum state such that there is a matching correlation between two ‘canonically conjugate’ dynamical quantities — quantities like position and momentum whose values suffice to specify all the properties of a classical system — then there are infinitely many dynamical quantities of the two particles for which there exist similar matching correlations: every function of the canonically conjugate pair of the first particle matches with the same function of the canonically conjugate pair of the second particle.”

Great, eh?  Essentially, what that means is that if you understand the relationship between to particles when they’re directly interacting, their properties are “linked.”  Even when the two particles are separated, they continue to remain linked, and their properties of momentum and direction continue to bear relation to one another.  In fact, altering one aspect of direction or momentum in one particle produces a predictable change in the entangled partner particle.  Essentially, you can poke one particle and the other one will feel it (I’m oversimplifying greatly, but that’s sort of the net effect).  This change is simultaneous, so information relayed into one particle is passed on to the mate instantly, no matter how far apart they are.  This means information could, theoretically, be moved from one particle to the other across expanses of space faster than the speed of light — in violation of the law of relativity.

Unfortunately, there are a couple of problems with this.  The first problem arises from the fact that you can only measure one aspect of direction or momentum, and only once.  After that, the alteration made to one particle affects the synchronicity of the pair; the link is broken.

To use an analogy: imagine two roommates, Alice and Bob, who have lived together for so long that they have picked up each other’s habits, sense of humour, etc.  After a while, Bob moves out.  One day, a mutual acquaintance stops Bob on the street and asks him if he thinks Alice likes paintings by Chagall.  Due to the many years they spent together, Bob answers “yes” with total accuracy.  The acquaintance asks a second question about whether Alice likes Brahams.  But answering the first question has so jarred Bob’s memory that he is incapable of ever answering correctly again.

Even so, subatomic particles are very, very small, so stacking a device with a few trillion atoms, each of which conveys a single bit of information, isn’t really a dealbreaker.  Each particle can be used once, to relay a bit of information from a sender to a receiver, and then tossed aside.  Zillions of Alices could live with zillions of Bobs!

But there is another problem.  While it’s true that changes to one particle can affect another, it’s not entirely clear whether this can be used to relay information.  The way information passes from one particle to another is actually quite inscrutable; rather than being as straightforward as “poke one particle and the other one feels it,” it’s more like “if you have two entangled particles, and a third particle with unknown properties, one entangled particle can poke the unknown particle in such a way that the unknown properties become identifiable to the other entangled particle.”  But while that’s more complicated, it doesn’t necessarily preclude the transfer of information from one particle to the other.  If that’s all that stood between us and quantum communication, there would still be no theoretical barrier between us and the day when we use linked particles to communicate vast amounts of information, instantly, wirelessly, without cancer-causing radiation, over cosmic distances.

Unfortunately, that’s not all that stands between us and quantum communication.  Probably.  Bell’s theorem, published by John S. Bell in the 1960s, includes the no-communication theorem, which says, in a nutshell, that while information can be sent, communication is not possible; if the no-communication theorem is proven, the theory of relativity will remain safe.  If disproven, well … all bets are off.  To quote another blogger, John Gordon:

“Bell’s Theorem showed that if non-locality (‘spooky action at a distance,’ instantaneous correlation of polarization states, etc.) were found to occur, irregardless of any interpretation of quantum mechanics, then physics had to abandon one of two cherished beliefs:

“1. That the world exists independently of our observations of it.
“2. That there is no communication faster than the speed of light.

“Subsequently non-locality has been shown, several times, to occur. That means we have to give up on either the ‘persistent world’ or faster than light communications. Not surprisingly, physicists have decided the lesser evil is to accept a faster than light communication — as long as that communication carries no ‘meaning.’ In other words, ‘meaning’ cannot travel faster than light.”

I’m not a mathemetician, so I can’t parse the mathematics demonstrating the statistical impossibility of discerning signal from noise in quantum communication for you, but I think Gordon puts it pretty well: if Bell’s no-communication theorem is correct, either relativity has to go, or quantum communication does.  As current accepted wisdom stands, the superluminal transfer of information is possible, but stripped of significance; from a statistical perspective, it’s so insignificant it’s as if there was no link between the two entangled particles at all.

But if the no-communication theorem is not disproven, then quantum communication is theoretically possible: a panacea that will solve all our bandwidth (and distance-lag) problems.  The communication industry will be changed forever.  If there were no limits to who could offer communication services, or how much?  The mind reels.  All the hassles of dealing with telecoms — high prices, bandwidth caps, traffic throttling, government spying, being forced to use limited applications or devices — would evaporate overnight.  I could go on for days about how great that would be, but considering that it will most likely never happen, I won’t.  But wouldn’t it be great?  Wouldn’t it?