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."

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The fork in the road

One of the most bizarre (and misunderstood) features of quantum physics is indeterminacy.

This is because we live in a macroscopic universe that -- most of the time, at least -- behaves in a determinate fashion.  Now, that doesn't mean we necessarily know everything about it.  For example, if we drop balls into a Galton board -- a device with a grid of pegs to deflect the ball's path -- eventually we'll get a normal distribution:

[Image licensed under the Creative Commons Matemateca (IME USP), Galton box, CC BY-SA 4.0]

With a device like a Galton board, we can accurately predict the probability of any given ball landing in a particular slot, but the actual path of the ball can't be predicted ahead of time.

Here's where the difficulty starts, though.  When people talk about quantum phenomena and describe them as probabilities, there's a way in which the analogy to macroscopic probability breaks down.  With a Galton board, the problem with predicting a ball's path doesn't mean it's not completely deterministic; it has to do with our (very) incomplete knowledge about the ball's initial state.  If you knew every last detail about the game -- each ball's mass, spin, air resistance, elasticity, the angle and speed of release, the angle at which it strikes the first peg, as well as the position, shape, and composition of every peg -- at least in theory, you could predict with one hundred percent accuracy which slot it would land in.  The ball's path is completely controlled by deterministic Newtonian physics; it's only the complexity of the system and our lack of knowledge that makes it impossible to parse.

This is not the situation with quantum systems.

When a particle travels from its source to a detector -- such as in the famous double-slit experiment -- it's not that the particle really and truly went through either slit A or slit B, and we simply don't happen to know which.  The particle, or more accurately, the wave function of the particle, took both paths at the same time, and how the detector is set up determines what we end up seeing.  Prior to being observed at the detector, the particle literally existed in all possible paths simultaneously, including ones passing through Bolivia and the Andromeda Galaxy.

To summarize the difference -- in a determinate system, we may not be able to predict an outcome, but that's only because we have incomplete information about it.  In an indeterminate system, the probability field itself is the reality.  However tempting it is to say that a particle, prior to being observed, took a specific fork in the road, and we just don't know which, completely misses the truth -- and misses how utterly bizarre the quantum world actually is.

People who object to this admittedly weird model of the world usually fall back on a single question, which is surprisingly hard to answer.  Okay, so on the one hand we have deterministic but complex systems, whose outcome is sensitively dependent on initial conditions (like the Galton board).  On the other, we have quantum systems which are probabilistic by nature.  How could we tell the difference?  Maybe in a quantum system there are hidden variables -- information about the system we don't have access to -- that make it appear indeterminate.  (This was Einstein's opinion, which he summed up in his famous statement that "God does not play dice with the universe.")

Unfortunately for Einstein, and for anyone else who is uncomfortable with the fact that the microscopic basis of reality is fundamentally at odds with our desire for a mechanistic, predictable universe, research at the Vienna University of Technology, which was described in a paper this week in Physical Review Letters, has shown conclusively that there are no hidden variables.  Our reality is indeterminate.  The idea of particles having definite positions and velocities, independent of observation and measurement, is simply wrong.

The experiment hinges on something called the Leggett-Garg Inequality -- described in a 1985 paper by physicists Anthony James Leggett and Anupam Garg -- which clearly distinguishes between how classical (determinate) and quantum (indeterminate) systems evolve over time.  Correlations between three different time measurements of the same system would show a different magnitude depending on whether it was behaving in a classical or quantum fashion.

The problem is, no one was able to figure out how to create a real-world test of it -- until now.  The team developed a neutron interferometer, which splits a neutron beam into two parts and then recombines it at a detector.  And the results of the experiment showed conclusively that contrary to our mental image of neutrons as hard little b-bs, that of course have to take either the left or the right hand path, every single neutron took both paths at the same time.  This violates the Leggett-Garg Inequality and is a crystal-clear hallmark of an inherently indeterminate system.

"Our experiment shows that nature really is as strange as quantum theory claims," said study co-author Stephan Sponar.  "No matter which classical, macroscopically realistic theory you come up with, it will never be able to explain reality.  It doesn't work without quantum physics."

Now, mind you, I'm not saying I completely understand this.  As Richard Feynman himself put it, "I think we can safely say that no one understands quantum physics."  (And if the great Feynman could say this, it doesn't leave much room for a rank amateur like me to pontificate about it.)  But perhaps the most fitting way to end is with a quote by the brilliant biologist J. B. S. Haldane: "The world is not only queerer than we suppose, it is queerer than we can suppose."

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Quantum pigeons

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," so I figure I have a pretty good excuse for my lack of deep comprehension.  I have a decent, if superficial, grasp of such loopy ideas as quantum indeterminacy, superposition, entanglement, and so on, but that's about the best I can do.  At least I understand enough to 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, "Did you know 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, the topic comes up because of a 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 be out of luck.

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 research 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 claiming 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."

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Wibbly-wobbly...

Have I told you my favorite joke?

Heisenberg and Schrödinger are out for a drive, and a cop pulls them over.

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 70 miles per hour!"

Heisenberg throws his hands up in annoyance and says, "Great!  Now I'm lost."

The cop scowls and says, "Okay, if you're going to be a wiseguy, I'm gonna search your car."  So he opens the trunk, and there's a dead cat inside.

The cop says, "Did you know there's a dead cat in your trunk?"

Schrödinger says, "Well, there is now."

*brief pause so you can all stop chortling*

The indeterminate nature of reality at the smallest scales always tends to make people shake their head in wonderment at how completely weird the universe is, if they don't simply disbelieve it entirely.  The Uncertainty Principle, peculiar as it sounds, is a fact.  It isn't a limitation of our measurement technique, as if you were trying to find the size of something small and had a poorly-marked ruler, so you could get a more accurate number if you found a better one.  This is something fundamental and built-in about reality.  There are pairs of measurements for which precision is mutually exclusive, such as velocity and position -- the more accurate your information is about one of them, the less you can even theoretically know about the other.

Likewise, the collapse of the wave function, which gave rise to the story of the famous (but ill-fated) cat, is an equally counterintuitive part of how reality is put together.  Outcomes of purely physical questions -- such as where a particular electron is at a given time -- are probabilities, and only become certainties when you measure them.  Again, this isn't a problem with measurement; it's not that the electron really is in a specific location, and you just don't know for sure where until you look.  Before you measure it, the electron's reality is that it's a spread-out field of probabilities.  Something about interacting with it using a measuring device makes that field of probabilities collapse into a specific location -- and no one knows exactly why.

But if you want your mind blown further -- last week in a paper in Physical Review Letters we found out how long it takes.

It turns out the wave function collapse isn't instantaneous.  In "Tracking the Dynamics of an Ideal Quantum Measurement," by a team led by Fabian Pokorny of Stockholm University, the researchers describe a set of experiments involving "nudging" a strontium atom with a laser to induce the electrons to switch orbits (i.e. making them assume a particular energy, which is one of those quantum-indeterminate things like position).  The fidelity of the measurement goes down to the millionths of a second, so the scientists were able to keep track of what happened in fantastically short time intervals.

And the more they homed in on what the electron was doing, the fuzzier things got.  The theory is that as you get down on those scales, time itself becomes blurred -- so the shorter the time interval, the less certain you are about when exactly something happened.

"People assume that time is a strict progression from cause to effect, but actually, from a non-linear non-subjective viewpoint, it's more of a big ball of wibbly-wobbly timey-wimey... stuff." -- The Tenth Doctor, "Blink"

I don't know about you, but I thought I had kinda sorta wrapped my brain around the quantum indeterminacy of position thing, but this just blew my mind all over again.  Even time is fuzzy?  I shouldn't be surprised; for something so damn familiar, time itself is really poorly understood.  With all of the spatial dimensions, you can move any direction you want; why is time one-way?  It's been explained using the Second Law of Thermodynamics, looking at ordered states and disordered states -- the explanation goes something like this:

Start with an ordered state, such as a hundred pennies all heads-up.  Give them a quick shake.  A few will flip, but not many.  Now you might have 83 heads and 17 tails.  There are a great many possible ways you could have 83 heads and 17 tails as long as you don't care which pennies are which.  Another shake, and it might be 74/26, a configuration that there are even more possibilities for.  And so on.  Since at each turn there are a huge number of possible disordered states and a smaller number of ordered ones, each time you perturb the system, you are much more likely to decrease orderliness than to increase it.  You might shake a 50/50 distribution of pennies and end up with all heads -- but it's so fantastically unlikely that the probability might as well be zero.  This push toward disorder gives an arrow to the direction of time.

Well, that's all well and good, but there's also the problem I wrote about last week, about physical processes being symmetrical -- there are a great many of them that are completely time-reversible.  Consider, for example, watching a ten-second clip of a single billiard ball bouncing off the side of a pool table.  Could you tell if you were watching the clip backward or forwards?  It's unlikely.  Such interactions look as sensible physically in real time or time-reversed.

So what time actually is, and why there's an arrow of time, is still a mystery.  Because we certainly feel the passage of time, don't we?  And not from any probabilistic perception of "well, I guess it's more likely time's flowing this way today because things have gotten more disorderly."  It feels completely real -- and completely fixed and invariable.

As Einstein put it, "The distinction between past, present, and future is an illusion, but it is a stubbornly persistent one."

Anyhow, that's our bizarre scientific discovery of the day.  But I better get this post finished up.  Time's a wasting.

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This week's Skeptophilia book recommendation of the week is a classic -- Martin Gardner's wonderful Did Adam and Eve Have Navels?

Gardner was a polymath of stupendous proportions, a mathematician, skeptic, and long-time writer of Scientific American's monthly feature "Mathematical Games."  He gained a wonderful reputation not only as a puzzle-maker but as a debunker of pseudoscience, and in this week's book he takes on some deserving targets -- numerology, UFOs, "alternative medicine," reflexology, and a host of others.

Gardner's prose is light, lucid, and often funny, but he skewers charlatans with the sharpness of a rapier.  His book is a must-read for anyone who wants to work toward a cure for gullibility -- a cure that is desperately needed these days.

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

The library of possibilities

In the brilliant Doctor Who episode "Turn Left," the Doctor's companion Donna Noble finds out that a single decision she made on a single day -- whether to turn right or left at an intersection -- creates two possible futures, one of them absolutely horrific.

It's a common trope in science fiction (although in my opinion, it's seldom been done as well, nor as poignantly, as in "Turn Left"), to look at how our futures could have been significantly different than they are.  I even riffed on this in one of my own novels -- Lock & Key -- in which there are not only multiple possible outcomes for each decision, there's a library (and a remarkably grumpy Head Librarian) that keeps track of not only what has happened, but what could have happened.  For every human being who ever existed, or who ever might have existed.

If you want to know how I handled the idea, you'll just have to read the book.

In reality, of course, the number of possible outcomes for even a simple series of choices increases exponentially with each successive decision, so in any realistic situation the possibilities are about as close to infinite as you can get.  Which makes a paper that came out in Nature last week even more extraordinary.

In order to see how amazing it is, a brief lesson in quantum mechanics for the non-physics-types in the studio audience.

One of the basic concepts in quantum physics is superposition: any measurable property of a wave (or subatomic particle) exists in multiple states at the same time.  The distribution of these states -- more specifically, the probability that the particle is in a specific state -- can be described by its wave function.  And the completely counterintuitive outcome of this model is that prior to observation, the particle is in all possible states at once, and only drops into a particular one (in a process called "collapsing the wave function") when it's observed.  (Regular readers of Skeptophilia may recall that I did a post on a particular part of this theory, Wigner's paradox, a few weeks ago.)

So that's amazing enough.  Particles and waves exist as a multitude of present possibilities, all at the same time.  But now, a collaboration between physicists at Griffith University (Queensland, Australia) and Nanyang Technological University (Singapore) have gone a step further:

They have developed a prototype device that generates a quantum state embodying all of the particle's future states simultaneously.

 My first thought was, "That can't possibly mean what it sounds like."  But yes, that turns out to be exactly what it means.  "When we think about the future, we are confronted by a vast array of possibilities," said Mile Gu of Nanyang Technological University, who led the study.  "These possibilities grow exponentially as we go deeper into the future. For instance, even if we have only two possibilities to choose from each minute, in less than half an hour there are 14 million possible futures.  In less than a day, the number exceeds the number of atoms in the universe."

So having even a simple system that generates all possible futures at the same time is somewhere beyond amazing, and into the realm of the nearly incomprehensible.

"Our approach is to synthesize a quantum superposition of all possible futures for each bias," said Farzad Ghafari, of Griffith University.  "By interfering these superpositions with each other, we can completely avoid looking at each possible future individually.  In fact, many current artificial intelligence (AI) algorithms learn by seeing how small changes in their behavior can lead to different future outcomes, so our techniques may enable quantum enhanced AIs to learn the effect of their actions much more efficiently."

"The functioning of this device is inspired by the Nobel Laureate Richard Feynman," added Dr Jayne Thompson, a member of the Singapore team.  "When Feynman started studying quantum physics, he realized that when a particle travels from point A to point B, it does not necessarily follow a single path.  Instead, it simultaneously transverses all possible paths connecting the points.  Our work extends this phenomenon and harnesses it for modeling statistical futures."

So I'm sitting here, trying to wrap my brain around the implication of this research.  Quantum indeterminacy indicates that we don't live in a completely deterministic universe; there's always some uncertainty, built into the actual fabric of the universe.  But the idea that we could, even in principle, create a system from which we could analyze all of the possible futures is stunning.

As Maggie Carmichael, the Assistant Librarian in Lock & Key, puts it:

All of our actions, even the smallest ones, make a difference.  Most of us never find out what that difference is.  All choices have consequences, however insignificant they seem at the time.  However, the truth of that statement is only evident here in the Library, where we can see what would have happened if we had acted otherwise.  Without that information, what happens simply… happens.

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This week's Skeptophilia book recommendation is a fun one; Atlas Obscura by Joshua Foer, Dylan Thuras, and Ella Morton.  The book is based upon a website of the same name that looks at curious, beautiful, bizarre, frightening, or fascinating places in the world -- the sorts of off-the-beaten-path destinations that you might pass by without ever knowing they exist.  (Recent entries are an astronomical observatory in Zweibrücken, Germany that has been painted to look like R2-D2; the town of Story, Indiana that is for sale for a cool $3.8 million; and the Michelin-rated kitchen run by Lewis Georgiades -- at the British Antarctic Survey’s Rothera Research Station, which only gets a food delivery once a year.)

This book collects the best of the Atlas Obscura sites, organizes them by continent, and tells you about their history.  It's a must-read for anyone who likes to travel -- preferably before you plan your next vacation.

(If you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!)