Reality vs. allegory

When I was about twenty, I stumbled upon the book The Dancing Wu-Li Masters by Gary Zukav.  The book provides a non-mathematical introduction to the concepts of quantum mechanics, which is good, I suppose; but then it attempts to tie it to Eastern mysticism, which is troubling to anyone who actually understands the science.

But as a twenty-year-old -- even a twenty-year-old physics major -- I was captivated.  I went from there to Fritjof Capra's The Tao of Physics, which pushes further into the alleged link between modern physics and the wisdom of the ancients.  In an editorial review of the book, we read:

First published in 1975, The Tao of Physics rode the wave of fascination in exotic East Asian philosophies.  Decades later, it still stands up to scrutiny, explicating not only Eastern philosophies but also how modern physics forces us into conceptions that have remarkable parallels...  (T)he big picture is enough to see the value in them of experiential knowledge, the limits of objectivity, the absence of foundational matter, the interrelation of all things and events, and the fact that process is primary, not things.  Capra finds the same notions in modern physics.

In part, I'm sure my positive reaction to these books was because I was in the middle of actually taking a class in quantum mechanics, and it was, to put not too fine a point on it, really fucking hard.  I had thought of myself all along as quick at math, but the math required for this class was brain-bendingly difficult.  It was a relief to escape into the less rigorous world of Capra and Zukav.

To get a feel for the difference, first read a quote from the Wikipedia article on quantum electrodynamics, chosen because it was one of the easier ones to understand:

(B)eing closed loops, (they) imply the presence of diverging integrals having no mathematical meaning.  To overcome this difficulty, a technique called renormalization has been devised, producing finite results in very close agreement with experiments.  It is important to note that a criterion for theory being meaningful after renormalization is that the number of diverging diagrams is finite.  In this case the theory is said to be renormalizable.  The reason for this is that to get observables renormalized one needs a finite number of constants to maintain the predictive value of the theory untouched.  This is exactly the case of quantum electrodynamics displaying just three diverging diagrams.  This procedure gives observables in very close agreement with experiment as seen, e.g. for electron gyromagnetic ratio.

Compare that to Capra's take on things, in a quote from The Tao of Physics:

Modern physics has thus revealed that every subatomic particle not only performs an energy dance, but also is an energy dance; a pulsating process of creation and destruction.  The dance of Shiva is the dancing universe, the ceaseless flow of energy going through an infinite variety of patterns that melt into one another.  For the modern physicists, then Shiva’s dance is the dance of subatomic matter.  As in Hindu mythology, it is a continual dance of creation and destruction involving the whole cosmos; the basis of all existence and of all natural phenomenon.  Hundreds of years ago, Indian artists created visual images of dancing Shivas in a beautiful series of bronzes.  In our times, physicists have used the most advanced technology to portray the patterns of the cosmic dance.

[Image licensed under the Creative Commons Arpad Horvath, CERN shiva, CC BY-SA 3.0]

It all sounds nice, doesn't it?  No need for hard words like "renormalization" and "gyromagnetic ratio," no messy mathematics.  Just imagining particles dancing, waving around their four little quantum arms, just like Shiva.

The problem here, though, isn't just laziness; and I've commented on the laziness inherent in the woo-woo movement often enough that I don't need to write about it further.  But there's a second issue, one often overlooked by laypeople, and that is "mistaking analogy for reality."

Okay, I'll go so far as to say that the verbal descriptions of quantum mechanics sound like some of the "everything that happens influences everyone and everything, all the time" stuff from Buddhism and Hinduism -- the interconnectedness of all, a concept that is explained in the beautiful allegory of "Indra's Net:"

Far away in the heavenly abode of the great god Indra, there is a wonderful net which has been hung by some cunning artificer in such a manner that it stretches out infinitely in all directions.  In accordance with the extravagant tastes of deities, the artificer has hung a single glittering jewel in each "eye" of the net, and since the net itself is infinite in dimension, the jewels are infinite in number.  There hang the jewels, glittering like stars in the first magnitude, a wonderful sight to behold.  If we now arbitrarily select one of these jewels for inspection and look closely at it, we will discover that in its polished surface there are reflected all the other jewels in the net, infinite in number.  Not only that, but each of the jewels reflected in this one jewel is also reflecting all the other jewels, so that there is an infinite reflecting process occurring. [Francis Cook, Hua-Yen Buddhism, 1977]

But does this mean what some have claimed, that the Hindus discovered the underlying tenets of quantum mechanics millennia ago?

Hardly.  Just because two ideas have some similarities doesn't mean that they are, at their basis, saying the same thing.  You could say that Hinduism has some parallels to quantum mechanics -- parallels that I would argue are accidental, and not really all that persuasive when you dig into them more deeply.  But those parallels don't mean that Hinduism as a whole is true, or that the mystics who devised it were somehow prescient.

In a way, we science teachers are at fault for this, because so many of us teach by analogy.  I did it all the time: antibodies are like cellular trash tags; enzyme/substrate interactions are like keys and locks; the Krebs cycle is like a merry-go-round where two kids get on and two kids get off at each turn.  But hopefully, our analogies are transparent enough that no one comes away with the impression that they are describing what is really happening.  Fortunately, I can say that I never saw a student begin an essay on the Krebs cycle by talking about merry-go-rounds and children.

The line gets blurred, though, when the reality is so odd, and the actual description of it (i.e. the mathematics) so abstruse, that most non-scientists can't really wrap their brain around it.  Then there is a real danger of substituting a metaphor for the truth.  It's not helped by persuasive, charismatic writers like Capra and Zukav, nor the efforts of True Believers to cast the science as supporting their religious ideas, because it helps to prop up their own worldview (you can read an especially egregious example of this here).

After a time in my twenties when I was seduced by pretty allegories, I finally came to the conclusion that the reality was better -- and, in its own way, breathtakingly beautiful (albeit still really fucking hard).  Take the time to learn what the science actually says, and I think you'll find it a damnsight more interesting and elegant than Shiva and Indra and the rest of 'em.  And best of all: it's actually true.

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A plea on behalf of Schrödinger's cat

I'm going to make a dual plea to all y'all:

1. Before you accept a paranormal or supernatural explanation for something, make sure you've ruled out all the normal and natural ones first.
2. Before you try to apply a scientific explanation to an alleged paranormal phenomenon, make sure you understand the science itself first.

I stumbled on an especially good (well, bad, actually) example of what happens when you break both of these rules of thumb with "paranormal explorer, investigator, and researcher" Ashley Knibb's piece, "Into the Multiverse to Search for Ghosts: Are We Seeing Parallel Realities?"  The entire article could have been replaced by the word "No," which would represent a substantial gain in both terseness and accuracy, but unfortunately Knibb seems to think that the multiverse model might actually explain a significant chunk of supernatural claims.

Let's start out with the fact that he joins countless others in misusing the word dimension to mean "some place other than the regular world we see around us."  To clear this up, allow me to quote the first line of the damn Wikipedia article on the topic: "the dimension of a mathematical space (or object) is defined as the minimum number of coordinates needed to specify any point within it."  We live in a three-dimensional space because three measurements -- up/down, right/left, forward/backward -- are necessary to pinpoint where exactly something is.

So saying that something is "in another dimension" makes about as much sense as saying your Uncle Fred lives in "horizontal."

Then he goes on to mention the quantum multiverse (also known as the Many-Worlds Interpretation), the bubble universe model, and brane theory as possible scientific bases for explaining the paranormal.  First off, I'll give him as much as to say that these are all legitimate theoretical models, although the three have little to nothing to do with each other.  The Many-Worlds Interpretation of quantum theory arises because of the puzzle of the collapse of the wave function, which (in the Copenhagen Interpretation) seems strangely connected to the concept of an observer.  Physicist Hugh Everett postulated that observer-dependency could be eliminated if every quantum collapse results in a split -- every possible outcome of a quantum collapse is realized in some universe.

[Image licensed under the Creative Commons Christian Schirm, Schroedingers cat film, CC0 1.0]

Then there's the bubble universe model, which comes from the cosmological concept of inflation.  This theory suggests that our current universe was created by the extremely rapid expansion of a "bubble" of inflating spacetime, and that such bubbles could occur again and create new universes.  Finally, brane theory is an offshoot of string theory, where a brane is a higher-dimensional structure whose properties might be used to explain the apparent free parameters in the Standard Model of Particle Physics.

These three models do have one thing in common, though.  None of them has been supported by experimental evidence or observation (yet).  For the first two, it very much remains to be seen if they could be.  In Everett's Many-Worlds Interpretation, the different timelines are afterward completely and permanently sealed off from one another; we don't have access to the timeline in which a particular electron zigged instead of zagging, much less the one where you married your childhood sweetheart and lived happily ever after.  The theory, as far as it goes, appears to be completely untestable and unfalsifiable.  (This is what led to Wolfgang Pauli's brilliantly acerbic quip, "This isn't even wrong.")  

And as far as the bubble universe goes, any newly-formed bubbles would expand away from everything else at rates faster than the speed of light (it's believed that space itself isn't subject to the Universal Speed Limit -- thus keeping us science fiction aficionados in continuing hopes for the development of a warp drive).  Because information maximally travels at the speed of light, any knowledge of the bubble next door will be forever beyond our reach.

Be that as it may, Knibb blithely goes on to suggest that one of these models, or some combination, could be used to explain not only ghosts, but poltergeists, "audible phenomena," déjà vu, the Mandela Effect, sleep paralysis, and cryptid sightings.

Whoo-wee.  Sir, you are asking three speculative theories to do some awfully heavy lifting.

But now we get to the other piece, which is deciding that all of the listed phenomena are, in fact, paranormal in nature.  Ghosts and poltergeists -- well, like I've said many times before, I'm doubtful, but convincible.  However, I'm in agreement with C. S. Lewis's character MacPhee, who said, "If anything wants Andrew MacPhee to believe in its existence, I’ll be obliged if it will present itself in full daylight, with a sufficient number of witnesses present, and not get shy if you hold up a camera or a thermometer."  A lot of "audible phenomena" can be explained by the phenomenon of priming -- when the mind is already anticipating a particular input (such as a creepy voice on a static-y recording) we're more likely to perceive it even if there's nothing there in actuality.  (As skeptic Crispian Jago put it, "You can't miss it when I tell you what's there.")  Déjà vu is still a bit of a mystery, but some research out of Colorado State University a few years ago suggests that it's also a brain phenomenon, in this case stemming from a misinterpretation of familiar sensory stimuli.  The Mandela Effect is almost certainly explained by the plasticity of human memory.  Sleep paralysis is a thoroughly studied, and reasonably well understood, neurological phenomenon (although apparently scary as hell).

As far as cryptid sightings -- well, y'all undoubtedly know what I think of most of those.

So the first step with all of these is to establish that there's anything there to explain.  The second is to demonstrate that the scientific explanations we do have are inadequate to explain them.

The third is to learn some fucking science before you try to apply quantum physics, inflationary cosmology, and string theory to why you got creeped out in a haunted pub.

Okay, I'm probably coming across as being unwarrantedly snarky, here.  But really.  There's no excuse for this kind of thing.  Even if you're not up to reading peer-reviewed science papers on the topics, a cursory glance at the relevant Wikipedia pages should be enough to convince you that (for example) the bubble universe model cannot explain ghosts.  Misrepresenting the science in this way isn't doing anyone any favors, most especially the people who seriously investigate claims of the supernatural, such as the generally excellent Society for Psychical Research.

As far as whether there's anything to any of these allegedly paranormal claims -- well, I'm not prepared to answer that categorically.  All I can say is that of the ones I've looked into, none of them meet the minimum standard of evidence that it would take to convince someone whose mind isn't already made up.  But I'm happy to hear about it if you think you've got a case that could change my mind.

Just make sure to tell the ghost not to get shy if I hold up a camera or a thermometer.

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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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Quantum homeopathy

In response to a post I did a while back about the tendency of people to believe loony ideas if they're couched in ten-dollar vocabulary, a loyal reader of Skeptophillia sent me a link to a paper by one Lionel Milgrom, of Imperial College (London), that has turned this phenomenon into an art form.

The name of the paper?

"'Torque-Like' Action of Remedies and Diseases on the Vital Force and Their Consequences for Homeopathic Treatment."

ln it, we witness something pretty spectacular: an attempt to explain homeopathy based on quantum mechanics.

[Image is in the Public Domain]

I'm not making this up, and it doesn't seem like a spoof; in fact, the paper appeared in the open-access Journal of Alternative and Complementary Medicine.  Here's the opening paragraph:

Within the developing theoretical context of quantum macroentanglement, a mathematical model of the Vital Force (Vf) has recently been formulated.  It describes the Vf in terms of a hypothetical gyroscope with quantized angular momentum.  This enables the Vf's state of health to be represented in terms of a "wave function" derived solely from secondary symptom observables produced in response to disease or homeopathic remedies.  So far, this approach has illustrated the biphasal action of remedies, resonance phenomena arising out of homeopathic provings, and aspects of the therapeutic encounter.

So right out of the starting gate, he's talking about using the quantum interactions of a force no one has ever detected to explain a treatment modality that has been repeatedly found to be completely worthless.  This by itself is pretty impressive, but it gets better as it goes along:

According to this model, symptom expression corresponds to precession of the Vf "gyroscope."  Conversely, complete removal of symptoms is equivalent to cessation of Vf "precession."  However, if overprescribed or given in unsuitable potency, the curative remedy (which may also be formulated as a wave function but this time derived solely from changes in Vf secondary symptom observables) may cause the Vf to express proving symptoms.  Thus, with only observation of symptoms and changes in them to indicate, indirectly, the state of a patient's Vf, the safest treatment strategy might be for the practitioner to proceed via gradual removal of the symptoms.

When I read the last line, I was lucky that I wasn't drinking anything, because it would have ended up splattered all over my computer.  Yes!  By all means, if a sick person comes in to visit a health professional, the health professional should proceed by removing the sick person's symptoms!

Because proceeding by making the symptoms worse is kind of counterproductive, you know?

His talk about "overprescription" made me chuckle, too.  Because if you'll recall, the late James Randi demonstrated dozens of times that the result of consuming a whole bottle of a homeopathic remedy is... nothing.  On the other hand, since the homeopaths believe that the more dilute a substance is, the stronger it gets, maybe "overprescribing" means "prescribing less."

Which reminds me of the story about the guy who forgot to take his homeopathic remedy, and as a result died of an overdose.

*rimshot*

And if this isn't enough, Dr. Milgrom (yes, he has a Ph.D., astonishingly enough) has also published other papers, including "The Thermodynamics of Health, Healing, and Love" and "Toward a Topological Description of the Therapeutic Process."

What's next, "The Three-Body Problem: A Classical Mechanics Approach to Handling Love Affairs?"

I have to admit, though, that there's something almost charming about this guy's attempt to bring pseudoscience under the lens of physics.  His blathering on about imaginary "vital forces" and the precession of microscopic gyroscopes as a mechanism for disease is, if nothing else, creative.  While what he's claiming is complete bollocks, Dr. Milgrom's determination to keep soldiering on is kind of adorable.

The good news, of course, is that his papers are unlikely to convince anyone who isn't already convinced.  The only danger is the undeserved veneer of credibility that this sort of thing gives homeopathy in people whose minds aren't yet made up.  One can only hope that the thorough debunking of this fraudulent practice that has been done by actual scientific researchers will prove, in the end, to be more persuasive.

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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 -- or that a photon can, somehow, go through both slits simultaneously and interfere with itself.  Whatever that means.
• 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.  How could it get any stranger than that?

Wait till you hear about this one.

In 2021, three physicists, Yakim Aharonov of Tel Aviv University, Sandu Popescu of the University of Bristol, and Eliahu Cohen of Bar Ilan University, said they'd demonstrated something they called 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 the first barrier means that in a sense, 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.

When this idea was proposed in 2021, it sounded so completely bizarre that it couldn't possibly be correct.  And earlier this year, a paper in Nature by Jonte Hance of Hiroshima University et al. seemed to rule out the phenomenon; but now, a second experiment described in the same journal by Armin Danner of Atominstitut Wien et al. appears to show conclusively that it does, in fact, occur.  So it looks like however counterintuitive the quantum Cheshire Cat is -- like the outrageously odd Bell's theorem, we're stuck with it.  It may twist our brain into knots, but it seems to be how reality works.

What I have to keep reminding myself is that none of this weirdness is some kind of abstract idea or speculation of what could be; these findings have been experimentally verified over and over.  Partly because they're so odd and counterintuitive, the theories of quantum physics have been put through rigorous tests, and each time they've passed with flying colors.  If these concepts sound crazy -- well, maybe the universe is crazy.

"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 Sandu Popescu, co-author of the 2021 paper that got the smile-without-a-cat idea started.  "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."

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Quantum foams and tiny wormholes

One of the most frustrating things for insatiably curious laypeople like myself is to find that despite our deep and abiding interest in a topic, there's simply a limit to what we're capable of understanding.

I know that happened to me with mathematics.  All through grade school, and even into college, I found math to be one of my easiest subjects.  I never had to struggle to understand it, and got high grades without honestly trying all that hard.

Then I hit Calculus 3.

I use the word "hit" deliberately, because it felt like running into a brick wall.  I think the problem was that this was the point where I stopped being able to visualize what was going on, and without that concrete sense of why things worked the way they did, it turned into memorization and application of a set of what appeared to be randomly-applied rules, a technique that only worked when I remembered them accurately.  I lost the intuitiveness of my earlier experience.  It returned to some extent when I took Differential Equations (partly due to a stupendous teacher), but I went from there to Vector Calculus, and it was all over.

That was the moment I decided that I am a Bear Of Very Little Brain, and the effect of the experience (combined with a similar unfortunate roadblock in Classical Mechanics) convinced me that a career as a physicist was not in the cards.

That feeling came back to me full-force when I ran across a paper in the journal Physical Review D entitled "Dark Energy from Topology Change Induced by Microscopic Gauss-Bonnet Wormholes," by Stylianos A. Tsilioukas, Emmanuel N. Saridakis, and Charalampos Tzerefos, of the University of Thessaly.  Even reading the abstract left me with an expression rather like the one my puppy has when I try to explain a concept to him that is simply beyond his comprehension, like why he shouldn't eat my gym socks.  You can tell he's trying to understand, he clearly wants to understand, but it's just not getting through.

But as far as the paper goes, at least I can tell that the idea is really cool, so I'm going to attempt to tell you about it.  If there are any physics boffins in the studio audience who want to correct my misapprehensions or misstatements, please feel free to let me know in the comments.

About seventy percent of the mass/energy content of the universe is something called dark energy.  (It's entirely unrelated to dark matter; the potential confusion between the two has led to a push to rename it vacuum energy.)  Dark energy is a bit of a placeholder name anyhow, given that we don't really know what it is; all we see is its effect, which is the measured increasing expansion rate of the universe.

The current best guess about its nature is that dark energy is a property of space itself (i.e., not something that space contains, but an inherent characteristic of the fabric of spacetime).  This energy manifests as a repulsive force, but because it's intrinsic, it doesn't dilute as space expands, the way a cloud might dissipate into air; its content per unit volume remains constant, so as space expands, the total amount of dark energy in the universe increases, resulting in a steady acceleration of the expansion rate.  At the moment, at least on the local level, gravity is still stronger than the expansion, so we're safe enough; but eventually (we're talking a long way in the future) space will have expanded so much that dark energy will overwhelm all other forces, and matter itself will be torn to shreds.

But despite this, we still have no idea what causes it, or even what it really is.

The Tsilioukas et al. paper -- once again, as far as I can understand it -- proposes a solution to that.

On the smallest scales, spacetime seems to be a "quantum foam" -- a roiling, bubbling ferment of virtual particles and antiparticles, constantly being created and destroyed.  That these virtual particles are real has been demonstrated experimentally, despite their existing for such a short time that most physicists would question even using the word "existing" as a descriptor.  So these incredibly quick fluctuations in spacetime -- even in a complete vacuum -- can have a discernible effect despite the fact that detecting the particles themselves is theoretically impossible.

What Tsilikouas et al. suggest is that there's a feature of the quantum foam that, described mathematically, is basically a network of tiny wormholes -- tunnels through spacetime connecting two separate points.  They're (1) as quick to appear and vanish as the aforementioned virtual particles, and (2) extremely submicroscopic, so don't get your hopes up about visiting Deep Space Nine any time soon.

The mathematics of these wormholes is described by a principle from topology called the Gauss-Bonnet theorem, named after mathematicians Carl Friederich Gauss and Pierre Ossian Bonnet (no relation), and when you include a Gauss-Bonnet term in the equations of General Relativity, you get something that seems to act just like the observed effects of dark energy.

So the runaway expansion of the universe might be due to tiny wormholes forming from the quantum foam of the vacuum -- and those minuscule fluctuations in spacetime add up to seventy percent of the total mass/energy content of the universe.

Like I said, it's not like I'm any more qualified to analyze whether they're on to something than Jethro is to explain why chewing up my gym socks makes him a Very Bad Puppy.  And it must be said that these theoretical models sometimes run into the sad truth from Thomas Henry Huxley, that "the great tragedy of science is the slaying of a beautiful hypothesis by an ugly fact."

But given that up till now, dark energy has been nothing more than a mysterious, undetectable, unanalyzable something that nevertheless outweighs all other kinds of matter and energy put together -- a rather embarrassing situation for physicists to find themselves in -- the new explanation seems to be a significant step in the right direction.

At least to a Bear Of Very Little Brain.

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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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Cosmological conundrums

Three of the most vexing problems in physics -- and ones I've hit on a number of times here at Skeptophilia -- are:

1. dark matter -- the stuff that (by its gravitational influence) seems to make up 26% of the mass/energy of the universe, and yet has resisted every effort at detection or inquiry into what other properties it might have.
2. dark energy -- a mysterious "something" that is said to be responsible for the apparent runaway expansion of the universe, and which (like dark matter) has defied detection or explanation in any other way.  This makes up 69% of the universe's mass/energy -- meaning the ordinary matter we're made of comprises only 5% of the apparent content of the universe.
3. the conflict between the general theory of relativity (i.e. the theory of gravitation) and quantum physics.  In the realm of the very small (or at high energies), the theory of relativity falls apart -- it's irreconcilable with the nondeterministic model of quantum mechanics.  Despite over a century of the best minds in theoretical physics trying to find a quantum theory of gravity, the two most fundamental underpinnings of our understanding of the universe just don't play well together.

A while back I was discussing this with the fiddler in my band, who also happened to be a Cornell physics lecturer.  Her comment was that the mess physics is currently in suggests we're missing something major -- the same way that the apparent constancy of the speed of light in a vacuum, regardless of reference frame, created an intractable nightmare for physicists at the end of the nineteenth century.  It took Einstein coming up with the Theories of Relativity to show that the problem wasn't a problem at all, but a fundamental reality about how space and time work, to resolve it all.

"We're still waiting for this century's Einstein," Kathy said.

[Image licensed under the Creative Commons ESA/Hubble, Collage of six cluster collisions with dark matter maps, CC BY 4.0]

There's no shortage of physicists working on stepping into those shoes -- and just last week, two papers came out suggesting possible solutions for the first two problems.

One claims to solve all three simultaneously.

Both of them start with a similar take on dark matter and dark energy as Einstein did about the luminiferous aether, the mysterious substance that nineteenth-century physicists thought was the medium through which light propagated; they simply don't exist.  

The first one, from Rajendra Gupta of the University of Ottawa, proposes that the need for both dark matter and dark energy in the model comes from a misconception about how the laws of physics change on a cosmological time scale.  The prevailing wisdom has been "they don't;" the laws now are the same as the laws thirteen billion years ago, not long after the Big Bang.  Gupta suggests that making two modifications to the model -- assuming that the strength of the four fundamental forces of nature (gravity, electromagnetism, and the weak and strong nuclear forces) have decreased over time, and that light loses energy as it travels over long distances, explain all the astrophysical observations we've made, and obviates the need for dark matter and dark energy.

"The study's findings confirm that our previous work -- JWST early-universe observations and ΛCDM cosmology -- about the age of the universe being 26.7 billion years [rather than the usually accepted value of 13.8 billion years] has allowed us to discover that the universe does not require dark matter to exist," Gupta said.  "In standard cosmology, the accelerated expansion of the universe is said to be caused by dark energy but is in fact due to the weakening forces of nature as it expands, not due to dark energy."

The second, by Jonathan Oppenheim and Andrea Russo of University College London, suggests a different solution that (if correct) not only gets rid of dark matter and dark energy, but in one fell swoop resolves the conflict between relativity and quantum physics.  They propose that the problem is the deterministic nature of gravity; if a quantum-like uncertainty is introduced into gravitational models, the whole shebang works without the need for some mysterious dark matter and dark energy that no one has ever been able to find experimentally.

The mathematics of the model -- which, I must admit up front, are beyond me -- introduce new terms to explain the behavior of gravity at low accelerations, which are (not coincidentally) the regime where the effects of dark matter become apparent.  It's a striking approach; physicist Sabine Hossenfelder, who is generally reluctant to hop on the latest Grand Unified Theory bandwagon (and whose pessimism has been, unfortunately, justified in the past) writes in an essay on the new theory, "Reading Oppenheim’s new papers—published in the journals Nature Communications and Physical Review X—about what he dubs 'Post-Quantum Gravity,' I have been impressed by how far he has pushed the approach.  He has developed a full-blown framework that combines quantum physics with classical physics, and he tells me that he has another paper in preparation which shows that he can solve the problem of infinites that plague the Big Bang and black holes."

Despite this, Hossenfelder is still dubious about Post-Quantum Gravity.  "I don’t want to withhold from you that I think Oppenheim’s theory is wrong, because it remains incompatible with Einstein’s cherished principle of locality, which says that causes should only travel from one place to its nearest neighbours and not jump over distances," she writes.  "I suspect that this is going to cause problems sooner or later, for example with energy conservation.  Still, I might be wrong...  If Oppenheim’s right, it would mean Einstein was both right and wrong: right in that gravity remained a classical, non-quantum theory, and wrong in that God did play dice indeed.  And I guess for the good Lord, we would have to be both sorry and not sorry."

So we'll just have to wait and see.  If either of these theories is right, we're talking Nobel Prize material.  If the second one is right, it'd be the physics discovery of the century.  Like Sabine Hossenfelder, I'm not holding my breath; attempts to solve definitively the three problems I started this post with are, thus far, batting zero.  And I'm hardly qualified to make a judgment about what the chances are for these two.  But like many interested laypeople, I'll be fascinated to see which way it goes -- and to see if we might, in the words of my bandmate/physicist friend, be "looking at the twenty-first century's Einstein."

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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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