Quantum pigeons

It will come as no particular shock to regular readers of Skeptophilia that I have a fascination for quantum physics.  Not that I can say I understand it that well; but no less than Nobel laureate and generally brilliant guy Richard Feynman said (in his lecture "The Character of Physical Law"), "If you think you understand quantum mechanics, you don't understand quantum mechanics."  I have a decent, if superficial, grasp of such loopy ideas as quantum indeterminacy, superposition, entanglement, and so on.  Which is why I find the following joke absolutely hilarious:

Heisenberg and Schrödinger were out for a drive one day, and they got pulled over by a cop. The cop says to Heisenberg, who was driving, "Hey, buddy, do you know how fast you were going?"

 
Heisenberg says, "No, but I know exactly where I am."

 
The cop says, "You were doing 85 miles per hour!"

 
Heisenberg throws his hands in the air and responds, "Great!  Now I'm lost."

 
The cop scowls at him.  "All right, pal, if you're going to be a smartass, I'm going to search your car."  So he opens the trunk, and there's a dead cat inside it.  He says, in some alarm, "There's a dead cat in your trunk."

 
Schrödinger says, "Well, there is now."

Thanks, you're a great audience. I 'll be here all week.

In any case, there's a recent paper in Proceedings of the National Academy of Sciences called, "Experimental Demonstration of the Quantum Pigeonhole Paradox," by a team of physicists at China's University of Science and Technology, which was enough to make my brain explode.  Here's the gist of it, although be forewarned that if you ask me for further explanation, you're very likely to get very little besides an expression of puzzled bewilderment, similar to the one my puppy gives me when I tell him something that is beyond his capacity to understand, such as why he should stop eating the sofa.

There's something called the pigeonhole principle in number theory, that seems kind of self-evident to me but apparently is highly profound to number theorists and other people who delve into things like sets, one-to-one correspondences, and mapping.  It goes like this: if you try to put three pigeons into two pigeonholes, one of the pigeonholes must be shared by two pigeons.

See, I told you it was self-evident.  Maybe you have to be a number theorist before you find these kind of things remarkable.

[Image licensed under the Creative Commons Razvan Socol, Rock Pigeon (Columba livia) in Iași, CC BY-SA 3.0]

In any case, what the recent paper showed is that on the quantum level, the pigeonhole principle doesn't hold true.  In the experiment, photons take the place of pigeons, and polarization states (either horizontal or vertical) take the place of the pigeonholes.  And when you do this, you find...

... that when you compare the polarization states of the three photons, no two of them are alike.

Hey, don't yell at me.  I didn't discover this stuff, I'm just telling you about it.

"The quantum pigeonhole effect challenges our basic understanding…  So a clear experimental verification is highly needed," study co-authors Chao-Yang Lu and Jian-Wei Pan wrote in an e-mail.  "The quantum pigeonhole may have potential applications to find more complex and fundamental quantum effects."

It's not that I distrust them or am questioning their results (I'm hardly qualified to do so), but I feel like what they're saying makes about as much sense as saying that 2 + 2 = 5 for large values of 2.  Every time I'm within hailing distance of getting it, my brain goes, "Nope.  If the first two photons are, respectively, horizontally polarized and vertically polarized, the third has to be either horizontal or vertical."

But apparently that's not true. Emily Conover, writing for Science News,writes:

The mind-bending behavior is the result of a combination of already strange quantum effects.  The photons begin the experiment in an odd kind of limbo called a superposition, meaning they are polarized both horizontally and vertically at the same time.  When two photons’ polarizations are compared, the measurement induces ethereal links between the particles, known as quantum entanglement.  These counterintuitive properties allow the particles to do unthinkable things.

Which helps.  I guess.  Me, I'm still kind of baffled, which is okay.  I love it that science is capable of showing us wonders, things that stretch our minds, cause us to question our understanding of the universe.  How boring it would be if every new scientific discovery led us to say, "Meh.  Confirms what I already thought."

****************************************

Spookier action

One of the downsides of being a layperson rather than a scientist (and I very much consider myself to be the former, despite having been a science teacher for over three decades) is that my understanding is hampered simply because it's impossible to know all the details of research by people who are way smarter than I am.

This is worst in completely counter-intuitive disciplines like quantum physics.

That doesn't prevent me from being really interested in all this stuff.  I was just discussing quantum entanglement with a dear friend a couple of days ago (as one does), and his question was, "Could you use it to communicate information?"  On the surface, it seems like it should be possible, right?

It's not -- at least as far as our current understanding goes.  But the reason isn't obvious on first glance.  In entanglement, a pair of particles is created which can be described by a single wave function; this means that their states are correlated, and knowing the state of one of them automatically tells you the state of the other, regardless of how far apart they are.  Let's say you and I create an entangled pair that has a net spin of zero.  You take your particle to Tokyo and I take mine to Lisbon.  Then you measure yours, and find it has a spin axis pointing upward.  I know immediately that if I measure mine, it will have a spin axis pointing downward.

Graph of the wave function of a single particle [Image is in the Public Domain]

So far, it seems like, "what's so weird about that?"  It doesn't seem any more remarkable than having a matched pair of gloves each in its own sealed box, and if you open your box in Tokyo and find it's a left-handed glove, mine in Lisbon has to be a right-handed glove.  The reality of the particles is weirder -- the members of the entangled pair are neither spin-up nor spin-down until they're measured, but in a state of superposition -- existing in a field of probabilities of both states at the same time.  Only once one of them is measured does it lock in to a particular state, and that measurement is what locks in the other particle simultaneously -- something Einstein famously called "spooky action at a distance."

Okay, so why couldn't that be used for communication?  The reason is rather subtle.  Let's say you want to communicate something simple, something that can be answered "yes" or "no."  So you and I take the two particles in our entangled pair to Tokyo and Lisbon, respectively.  We agree ahead of time that once you get there, you are going to go outside to see if it's a clear day and whether you can see Mount Fuji.  If you can, you will force your particle into a spin-up state; won't that force mine into a spin-down state, thus communicating the information to me instantaneously, thousands of miles away?

The answer is no.  The reason is, you didn't just measure your particle's state, you changed it.  And this breaks the entanglement.  The moment you do anything to alter the state of your particle, it decouples it from mine, and my particle now has a 50/50 chance of being spin-up or spin-down; it's no longer affected by what happens to yours.  Every kind of information transfer known requires changing the state of the particles you're using to carry the information, and that transfer can only travel at the speed of light or slower.

So it seems like the faster-than-light "subspace communication" used in Star Trek is impossible, right?

Well... maybe.

This is where I skate out over very thin ice, because what got all this started (besides the conversation with my friend) was a paper last week in Quantum Science and Technology which -- if I'm reading it right, and I might well not be -- suggests that there might be a way around this, by sending information (1) without using particles, and (2) by having the information go directly from sender to receiver without traveling through the intervening space.

If you're thinking, "That sounds like a wormhole" -- exactly.  Hatim Salih, of the University of Bristol, says he's found a way to create a "traversable wormhole" that could transfer quantum information instantaneously.

Salih calls this even-spookier-action-at-a-distance counterportation.  "Here’s the sharp distinction," he said in a news release.  "While counterportation achieves the end goal of teleportation, namely disembodied transport, it remarkably does so without any detectable information carriers traveling across.  If counterportation is to be realized, an entirely new type of quantum computer has to be built: an exchange-free one, where communicating parties exchange no particles.  By contrast to large-scale quantum computers that promise remarkable speed-ups, which no one yet knows how to build, the promise of exchange-free quantum computers of even the smallest scale is to make seemingly impossible tasks – such as counterportation – possible, by incorporating space in a fundamental way alongside time."

"We experience a classical world which is actually built from quantum objects," said John Rarity, Salih's colleague at the University of Bristol.  "The proposed experiment can reveal this underlying quantum nature showing that entirely separate quantum particles can be correlated without ever interacting.  This correlation at a distance can then be used to transport quantum information (qbits) from one location to another without a particle having to traverse the space, creating what could be called a traversable wormhole."

Okay... that's just nifty, but... but... Einstein?  Speed of light?  How do you avoid the paradoxes that come with faster-than-light information transfer?

Maybe there's something I'm not understanding, here.  All right, to be fair, I'm sure there's a gazillion things I'm not understanding, here.  Cf. my aforementioned layperson status.  But it sure seems like if you can do this, you're talking about something that would break the cosmic speed limit for information transfer, and shake physics down to its roots.

Much as I'd love to see the world of Star Trek realized, I'm pretty certain that I'm missing something critical, and this isn't going to turn out to be what it sounds like.  There's probably some subtlety -- like the measuring-versus-changing distinction in entanglement -- that isn't apparent.

What that might be, however, escapes me.  If any physicists read this post, do enlighten me.  While I don't relish the idea of my hopes being dashed, I'm virtually certain they will be.  And as Carl Sagan so trenchantly put it, "For me, it is far better to grasp the Universe as it really is than to persist in delusion, however satisfying and reassuring."

****************************************

Nonlocal and unreal

This year, the Nobel Prize in Physics went to three scientists who have proven beyond a shadow of a doubt that our common-sense perception of how the universe works is very, very far off from the reality.

What that reality actually is remains to be seen.

John Clauser, Alain Aspect, and Anton Zeilinger were the recipients of the award this year "for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science."  Their experiments established a mind-boggling fact: the universe is not locally real.

What that means, in non-technical language, is harder to pin down.  In physics, the concept of locality has to do with the fact that information transfer has a speed limit -- the speed of light.  If an event occurs at one point in space, then that event can only affect another point in space if it's nearby enough that light has enough time to travel between one and the other.  Reality means that an object's properties are independent of observation; it's a hard-science version of the time-honored question, "if a tree falls in the forest, and no one is there, does it make a sound?"

While the "locality" piece isn't perhaps something that impacts us on a daily basis -- light travels so fast that on the scales we usually deal with, it may as well be instantaneous -- "reality" certainly does.  Even the physicists balked for decades against the hints they were getting that locality and reality were on shaky ground.  No less a luminary than Albert Einstein said, "Do you really believe that the Moon is not there when you are not looking at it?"  But ever since Northern Irish physicist John Stewart Bell first proposed that there was something at the heart of quantum mechanics that called local reality into question, way back in 1962, the loopholes for avoiding that bizarre conclusion have been closing one by one.

The heart of the problem lies with entanglement.  The idea here is that you can create a pair of particles such that you know if one has a particular property (such as a spin axis pointing up) the other will have the opposite property (spin axis pointing down).  So far, nothing too weird about that.  It's no odder than putting each of a pair of gloves into a sealed box, and handing a box to your friend; if when your friend opens his box, he finds a left-handed glove, you automatically know your box must contain the right-handed one.  The system was set up that way.

But what Bell implied was that this wasn't the case.  The gloves were neither right nor left until you opened one of the boxes; if your friend did that, and observed a left-handed glove, the glove in your box "sensed that" (whatever the hell that means!) and instantaneously became right-handed, regardless of how far apart they were at the time.  The measurement process somehow created the state of the system, even if the parts of it were separated by a distance too great for light to cross.

For a long time, the prevailing approach amongst physicists was just to pretend it wasn't happening, an approach David Mermin summed up as "shut up and calculate."  Perhaps there were "hidden variables" that made some sort of locally real explanation account for the strange phenomenon of entanglement; using our analogy, that the gloves were what they were even though they hadn't been observed yet, no superluminal communication necessary.  And for a while, they kind of got away with it.  But with a series of ingenious experiments, Clauser, Aspect, and Zeilinger conclusively showed that there are no hidden variables; the universe, it seems, is not locally real.

What exactly is happening is another matter.  The three recipients of this year's Nobel Prize in Physics have shown that what John Stewart Bell proposed sixty years ago is spot-on correct, as crazy as it sounds.  There is something about the process of observation that does lock the observed object into a particular state faster than should be possible; Schrödinger's long-suffering cat seems to be not a wild metaphor but how the universe actually works.

I find this whole thing fascinating but a little overwhelming.  It's hard to imagine how our physical surroundings can behave in a manner so completely opposite to our common-sense notions.  But Clauser, Aspect, and Zeilinger have demonstrated conclusively that they do -- and it lies with the rest of the physics community to tell us laypeople exactly what that means.

****************************************

A smile without a cat

Every time I hear some new discovery in quantum physics, I think, "Okay, it can't get any weirder than this."

Each time, I turn out to be wrong.

A few of the concepts I thought had blown my mind as much as possible:

• Quantum superposition -- a particle being in two states at once until you observe it, at which point it apparently decides on one of them (the "collapse of the wave function")
• The double-slit experiment -- if you pass light through a closely-spaced pair of slits, it creates a distinct interference pattern -- an alternating series of parallel bright and dark bands.  The same interference pattern occurs if you shoot the photons through one of the slits, one photon at a time.  If you close the other slit, the pattern disappears.  It's as if the photons passing through the left-hand slit "know" if the right-hand slit is open or closed.
• Quantum entanglement -- two particles that somehow are "in communication," in the sense that altering one of them instantaneously alters the other, even if it would require superluminal information transfer to do so (what Einstein called "spooky action-at-a-distance")
• The pigeonhole paradox -- you'd think that if you passed three photons through polarizing filters that align their vibration plane either horizontally or vertically, there'd be two of them polarized the same way, right?  It's a fundamental idea from set theory; if you have three gloves, it has to be the case that either two are right-handed or two are left-handed.  Not so with photons.  Experiments showed that you can polarize three photons in such a way that no two of them match.

Bizarre, counterintuitive stuff, right there.  But wait till you hear the latest:  three physicists, Yakim Aharonov of Tel Aviv University, Sandu Popescu of the University of Bristol, and Eliahu Cohen of Bar Ilan University, have demonstrated something they're calling a quantum Cheshire Cat.  Apparently under the right conditions, a particle's properties can somehow come unhooked from the particle itself and move independently of it -- a bit like Lewis Carroll's cat disappearing but leaving behind its disembodied grin.

The Cheshire Cat from John Tenniel's illustrations for Alice in Wonderland (1865) [Image is in the Public Domain]

I'll try to explain how it works, but be aware that I'm dancing right along the edge of what I'm able to understand, so if you ask for clarification I'll probably say, "Damned if I know."  But here goes.

Imagine a box containing a particle with a spin of 1/2.  (Put more simply, this means that if you measure the particle's spin along any of the three axes (x, y, and z), you'll find it in an either-or situation -- right or left, up or down, forward or backward.)  The box has a partition down the middle that is fashioned to have a small, but non-zero, probability of the particle passing through.  At the other end of the box is a second partition -- if the particle is spin-up, it passes through; if not, it doesn't and is reflected back into the box.

With me so far?  'Cuz this is where it gets weird.

In quantum terms, the fact that there's a small but non-zero chance of the particle leaking through means that part of it does leak through; this is a feature of quantum superposition, which boils down to particles being in two places at once (or, more accurately, their positions being fields of probabilities rather than one specific location).  If the part that leaks through is spin-up, it passes through the right-hand partition and out of the box; otherwise it reflects back and interacts with the original particle, causing its spin to flip.

The researchers found that this flip occurs even if measurements show that the particle never left the left-hand side of the box.

So it's like the spin of the particle becomes unhooked from the particle itself, and is free to wander about -- then can come back and alter the original particle.  See why they call it a quantum Cheshire Cat?  Like Carroll's cat's smile, the properties of the particle can somehow come loose.

Whatever a "loose property" actually means.

The researchers have suggested that this bizarre phenomenon might allow counterfactual communication -- communication between two observers without any particle or energy being transferred between them.  In the setup I described, the observer left of the box would know if the observer on the right had turned the spin-dependent barrier on or off by watching to see if the particle in the left half of the box had altered its spin.  More spooky action-at-a-distance, that.

What I have to keep reminding myself is that none of this is some kind of abstract idea or speculation of what could be; these findings have been experimentally verified over and over.  Partly because it's so odd and counterintuitive, the theories of quantum physics have been put through rigorous tests, and each time they've passed with flying colors.  As crazy as it sounds, this is what reality is, despite how hard it is to wrap our minds around it.

"What is the most important for us is not a potential application – though that is definitely something to look for – but what it teaches us about nature," said study co-author Sandu Popescu.  "Quantum mechanics is very strange, and almost a hundred years after its discovery it continues to puzzle us.  We believe that unveiling even more puzzling phenomena and looking deeper into them is the way to finally understand it."

Indeed.  I keep coming back to the fact that everything you look at -- all the ordinary stuff we interact with on a daily basis -- is made of particles and energy that defy our common sense at every turn.  As the eminent biologist J. B. S. Haldane famously put it, "The universe is not only queerer than we imagine -- it is queerer than we can imagine."

**********************************

Some of the most enduring mysteries of linguistics (and archaeology) are written languages for which we have no dictionary -- no knowledge of the symbol-to-phoneme (or symbol-to-syllable, or symbol-to-concept) correspondences.

One of the most famous cases where that seemingly intractable problem was solved was the near-miraculous decipherment of the Linear B script of Crete by Alice Kober and Michael Ventris, but it bears keeping in mind that this wasn't the first time this kind of thing was accomplished.  In the early years of the nineteenth century, this was the situation with the Egyptian hieroglyphics -- until the code was cracked using the famous Rosetta Stone, by the dual efforts of Thomas Young of England and Jean-François Champollion of France.

This herculean, but ultimately successful, task is the subject of the fascinating book The Writing of the Gods: The Race to Decode the Rosetta Stone, by Edward Dolnick.  Dolnick doesn't just focus on the linguistic details, but tells the engrossing story of the rivalry between Young and Champollion, ending with Champollion beating Young to the solution -- and then dying of a stroke at the age of 41.  It's a story not only of a puzzle, but of two powerful and passionate personalities.  If you're an aficionado of languages, history, or Egypt, you definitely need to put this one on your to-read list.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]