Bubbles, dimensions, and black holes

One of the weirder claims of modern physics, which I first ran into when I was reading about string theory a few years ago, is that the universe could have more than three spatial dimensions -- but the extra ones are "curled up" and are (extremely) sub-microscopic.

I've heard it explained by an analogy of an ant walking on a string.  There are two ways the ant can go -- back and forth on the string, or around the string.  The "around the string" dimension is curled into a loop, whereas the back-and-forth one has a much greater spatial extent.

Scale that up, if your brain can handle it, to three dimensions of the back-and-forth variety, and as many as nine or ten of the around-the-string variety, and you've got an idea of what the claim is.

The problem is, those extra dimensions have proven to be pretty thoroughly undetectable, which has led critics to quote Wolfgang Pauli's quip, that it's a theory that "is not even wrong," it's unverifiable -- which is synonymous to saying "it isn't science."  But the theorists are still trying like mad to find an indirect method to show the existence of these extra dimensions.

To no avail at the present, although we did have an interesting piece added to the puzzle a while back that I somehow missed the first time 'round.  Astronomers Katie Mack of North Carolina State University and Robert McNees of Loyola University published a paper in arXiv that puts a strict limit on the number of macroscopic dimensions -- and that limit is three.

So sorry, fans of A Wrinkle in Time, there's no such thing as the tesseract.  The number of dimensions is three, and three is the number of dimensions.  Not four.  Nor two, unless thou proceedest on to three. 

Five is right out.

The argument by Mack and McNees -- which, although I have a B.S. in physics, I can't begin to comprehend fully -- boils down to the fact that the universe is still here.  If there were extra macroscopic spatial dimensions (whether or not we were aware of them) it would be possible that two cosmic particles of sufficient energy could collide and generate a miniature black hole, which would then give rise to a universe with different physical laws.  This new universe would expand like a bubble rising in a lake, its boundaries moving at the speed of light, ripping apart everything down to and including atoms as it went.

"If you’re standing nearby when the bubble starts to expand, you don’t see it coming," Mack said.  "If it’s coming at you from below, your feet stop existing before your mind realizes that."

This has been one of the concerns about the Large Hadron Collider, since the LHC's entire purpose is to slam together particles at enormous velocities.  Ruth Gregory of Durham University showed eight years ago that there was a non-zero possibility of generating a black hole that way, which triggered the usual suspects to conjecture that the scientists were trying to destroy the universe.  Why they would do that, when they inhabit said universe, is beyond me.  In fact, since they'd be standing right next to the Collider when it happened, they'd go first, before they even had a chance to cackle maniacally and rub their hands together about the fate of the rest of us.

"The black holes are quite naughty," Gregory said, which is a sentence that is impossible to hear in anything but a British accent.  "They really want to seed vacuum decay.  It’s a very strong process, if it can proceed."

"No structures can exist," Mack added.  "We’d just blink out of existence."

Of course, it hasn't happened, so that's good news.  Although I suppose this wouldn't be a bad way to go, all things considered.  At least it would be over quickly, not to mention being spectacular.  "Here lies Gordon, killed during the formation of a new universe," my epitaph could read, although there wouldn't be anyone around to write it, nor anything to write it on.

Which is kind of disappointing.

Anyhow, what Mack and McNees have shown is that this scenario could only happen if there was a fourth macroscopic dimension, and since it hasn't happened in the universe's 13.8 billion year history, it probably isn't going to.

So don't cancel your meetings this week.  Mack and McNees have shown that any additional spatial dimensions over the usual three must be smaller than 1.6 nanometers, which is about three times the diameter of your average atom; bigger than that, and we would already have become victims of "vacuum decay," as the expanding-bubble idea is called.

A cheering notion, that.  Although I have to say, it's an indication of how bad everything else has gotten that "We're not dead yet" is the best I can do for good news.

That's our news from the world of scientific research -- particle collisions, expanding black holes, and vacuum decay.  Myself, I'm not going to worry about it.  I figure if it happens, I'll be gone so fast I won't have time to be upset at my imminent demise, and afterwards none of my loved ones will be around to care.  Another happy thought is that I'll take Nick Fuentes, Tucker Carlson, Elon Musk, Stephen Miller, and Andrew Tate along with me, which might almost make destroying the entire universe worth it.

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Brane teaser

After my diatribe a couple of days ago about the misuse of the word dimension, I got into a discussion with a friend that can be summed up as, "Okay, then how are we supposed to picture spaces with more than three dimensions?"

Well, the simple answer is that we can't.  Our brains are equipped to manage pictorial representations of three dimensions or fewer.  We can try to get a handle on it via analogy -- a particularly masterful example is Edwin Abbott's Flatland: A Romance of Many Dimensions, which considers a two-dimensional character named A. Square, who has as hard a time picturing a third dimension as we do a fourth.  When a three-dimensional sphere passes through Flatland, A. Square perceives it as a series of successive two-dimensional slices -- a circle that appears out of nowhere, grows larger, then shrinks and finally vanishes.  The implication is that if a four-dimensional object -- a hypersphere, perhaps -- were to pass through our three-dimensional world, we'd see something similar; a projection of successive "slices," a sphere popping into existence, expanding, then contracting and vanishing.

But the fact remains that these are ways of thinking about a concept that is, honestly, beyond our ken.  It's the problem that plagues many of the deep models of physics -- something that can be described clearly and accurately by the math is nevertheless impossible to visualize.  It's a bit like the situation with quantum mechanics; the math is astonishingly precise and makes spot-on predictions, but if you ask most physicists, "So what physical reality is the math describing?" the answer you'll get is a slightly embarrassed "we don't know."  (If they don't say "Shut up and calculate.")

It's a serious sticking point with people like myself, who understand best when we can picture what's going on.  It was when I hit that spot in my undergraduate studies -- when the professor said, basically, "The math is what's real, here, don't bother trying to visualize it because you can't" -- that I decided that a career in physics was not in the cards for me.

Despite that, I have continued to be intrigued with notions like quantum indeterminacy and higher-dimensional space, even though when I read about them I often have an expression on my face like the one my puppy has when I explain a complex concept that is beyond his comprehension, such as why he shouldn't eat the sofa.  I'm currently reading a wonderful book about the topic of extra dimensions, by the brilliant theoretical physicist Lisa Randall, called Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions, which does an outstanding job of bringing the topic down to a level we eager-but-not-so-bright puppies can understand.  (And if you want more, she has an appendix with mathematical notes elucidating the topic in a deeper and more precise fashion.)  

One of the more fascinating topics she goes into is the concept of a brane -- a cross-section of a higher-dimensional space a bit like A. Square's expanding-and-contracting circles.  The name comes from the word membrane, because (like a cell membrane) a two-dimensional brane can be a boundary on a three-dimensional space.  The surface of the Earth's ocean, for example, can be seen as a two-dimensional brane (not only acting as a boundary, but oscillating up and down into the three-dimensional space on either side).

Of course, you're not limited to two-dimensional branes in three-dimensional space.  A generalized name for branes in p dimensions is called a p-brane, which was one of my father's favorite insults (albeit spelled differently).  

A two-dimensional representation of a three-dimensional projection of a six-dimensional structure called a Calabi-Yau manifold.  Yeah, my head hurts, too. [Image licensed under the Creative Commons Andrew J. Hanson, Indiana University., CalabiYau5, CC BY-SA 3.0]

Where it becomes more interesting, and unfortunately far harder to picture, is when you consider the idea from some physicists -- Randall has been one of the lead researchers in this field -- that our own three-dimensional universe is a three-brane within a higher-dimensional space.  There is a tantalizing suggestion that this model may explain some of physics's most persistent mysteries, such as why the gravitational force is so weak compared to the other three.  If we are actually living in a three-dimensional slice, the gravitational force within our bit of space may leak across into the higher dimensions,  weakening its intensity and perhaps influencing other branes within the space (which might give physicists a way of finding evidence for the conjecture).

There's even the suggestion that the Big Bang may have occurred because of collision between two three-branes in a multi-dimensional hyperspace -- a model called ekpyrotic cosmology.  

But we're still up against the problem that it's impossible to answer the question, "But what does it actually look like?"  The mathematics is crisp and clear; any picture we come up with is, by comparison, incomplete and inaccurate.  Take, for example, a hypercube, a symmetrical four-dimensional structure that can be described mathematically but is impossible to visualize.  All we can do is consider what projections of it -- shadows, so to speak -- look like in three dimensions.  Here's a particularly mesmerizing projection of a rotating hypercube:

[Image licensed under the Creative Commons Jason Hise, 8-cell-orig, CC0 1.0]

So we're kind of ending where we started.  All of this is just a teaser, really -- a brief excursion into a subject that is just now being investigated by some of the most brilliant minds on the planet.  If the mathematics of branes and higher dimensions and whatnot is beyond you -- it certain is me -- we're left with trying to get a faint glimmer of understanding via analogy.  Which only gets you so far.

But at least it gives us something our branes -- um, brains -- can handle.

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Dimensional analysis

As long-time readers of Skeptophilia know, it really torques my lug nuts when people take perfectly good scientific terms, re-define them however the fuck they like, and then pretend what they're saying makes sense.

The list of terms this has happened to is a long one, and includes frequency, resonance, quantum (lord, how they do love the word quantum), and vibration, to name a few.  But there's none that bothers me quite as much as the rampant misuse of the word dimension.

Part of the reason this one gets to me is that the concept of a dimension is so simple that you'd think it'd be hard to get wrong.  If you go to the Wikipedia article about the term, you will read in the very first line, "In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it."  The space we live in is three-dimensional because to define the location of a point, you need to know where it lies referent to three directions -- up/down, back/front, and right/left.

This hasn't stopped people from taking the term and running right off the cliff with it.  And it's not a new phenomenon.  I remember an episode of the abysmal 1960s science-fiction series (heavy on the fiction, light on the science) Lost in Space called "Invaders from the Fifth Dimension," wherein Will Robinson was kidnapped by a pair of evil aliens who looked like the love children of Matt Gaetz and Herman Munster.

These aliens told Will they were "from the fifth dimension," which makes about as much sense as if your Uncle Fred told you he was from "horizontal."  Be that as it may, after they captured Will they revealed to him their nefarious plan, which was to use his brain to power their spaceship.  Things looked bad, but Will defeated them by (I swear I am not making this up) feeling sad at them, which caused their spaceship to blow up.

So using the word "dimension" as a fancy way of saying "a mysterious place somewhere" goes back a long way.  But because of a loyal reader of Skeptophilia, I just read what has to be the single most ridiculous example of this I've ever seen.

And that includes "Invaders from the Fifth Dimension."

It's an article in Your Tango called "The Theory That Claims We Visit Other Dimensions While We Sleep," by NyRee Ausler.  Which brings up another misused word that really bothers me, which is "theory."  A theory is not "this crazy idea I dreamed up just now," and nor does it mean "a guess that could just as easily be right as wrong."  A theory is model with strong explanatory and predictive power, and which fits all the available data and evidence we have at hand.  When the creationists say, breezily, "Evolution is just a theory," that is not some kind of point in their favor; all it shows is that they have no idea what the word actually means.

After all, we call it "music theory" and that's not because we think music may not exist.

But I digress.

Anyhow, back to NyRee Ausler.  It will come as no shock to find out that she answers her question, "do we visit other dimensions while we dream?" with, "Yes, of course we do."  The way we know, she says, is that the laws of physics aren't the same in dreams as they are in reality.  I can vouch at least for that much.  I dreamed last night that I was out working in my garden, and I kept accidentally digging up plants and knocking things over and generally wreaking havoc, but then when I was done not only was everything back to normal, but all the flowers were blooming despite the fact that it's currently December and the high temperature today is supposed to be 13 F.

In any case, her point that "dreams are fucking weird" hardly needs further elucidation, but she goes on to say that the reason for all this is that dreams take place in another dimension.  And then she launches into a brief description of -- I shit you not -- string theory, which is a mathematical model of subatomic physics requiring ten spatial dimensions, all but three of which are thought to be (very) submicroscopic and "curled up."  The analogy commonly used is an ant on a garden hose -- it can go along the hose (one stretched-out dimension), or around the hose's circumference (one curled-up dimension).  The string theorists claim that three of the dimensions in our universe are of the stretched-out variety, and seven are curled up so tightly that we don't experience them on a macroscopic scale, but influence quantum phenomena such as how particles interact at very high energies. 

And yes, what NyRee Ausler is saying is that when you dream, you are somehow visiting these extremely tiny, curled-up dimensions, and that's why dreams are peculiar.  Once again, acting as if these extra dimensions were places, not just mathematical constructs describing spatial coordinates.

But it gets even better than that, because she goes on to tell us what each of those dimensions are like, one by one.  I direct you to the original link if you want to read about them all, but here's one, just to give you the flavor:

The sixth dimension consists of a straight line of possible worlds. Here, you get an opportunity to access all possible worlds that started with the same original conditions, like the Big Bang Theory.  It is known as the "phase space" in a set of parallel universes where everything that could have happened in our pasts, but did not, occurred in some other universe.  The sixth dimension exists in the same space and time as the one we occupy, an overlay of our universe or a 3-D space containing every possible world.

Right!  Exactly!  What?

What made me laugh the hardest is that she tried to give her article an extra soupçon of scienc-y-ness by mentioning Calabi-Yau manifolds, an extremely complex concept from higher-dimensional algebraic geometry, because lobbing in a technical term you obviously don't understand clearly strengthens your argument.

I know it's probably a waste of energy for me to spend my time railing about this, but there are people who will read this and think it's actual science.  And that bugs the absolute hell out of me.  The thing is, her article is not just wrong, it's lazy.  As I demonstrated above, all you have to do is to take the time to read the first paragraph of a damn Wikipedia page to see that what Ausler is claiming is blatant horse waste.

But science is hard, and technical, and to really understand it requires reading peer-reviewed journal articles and learning terminology and mathematics.  Easier to blather on about string theory and dimensions and (*snerk*) Calabi-Yau manifolds as if you knew what you were talking about, and hope that enough people click on the link that the ad revenue will pay for your groceries next month.

So anyhow, thanks to the reader who sent me the article.  I did get a couple of good laughs out of it, but the overall teeth-grinding I did while reading it probably resulted in net damage to my emotional state.  Pseudoscience will be with us always, springing up like mushrooms after a summer rain.  Or like my garden on a frigid day in December, at least in my sixth-dimensional dreams.

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A lens into the dark sector

I don't really regret the weird, meandering path I took through the educational system -- but I have to admit to a bit of envy when it comes to people who are true experts in their field.

My inveterate dilettantism means I'm reasonably conversant in a lot of areas, but don't really have a deep understanding of anything.  Being a dabbler is neither a bad background to have as a high school teacher nor as a blogger, but it does mean that I often run into topics and think, "Wow, I really wish I could wrap my brain around this."

This happened just yesterday when I happened upon a paper in The European Physical Journal C called, "A Warped Scalar Portal to Fermionic Dark Matter."  My Bachelor of Science diploma in physics should have come with a sticky note appended to it that says, "... yeah, but he pretty much sucked as a physics student."  I struggled in virtually all of my upper-level physics classes, due to a combination of lack of focus and troubles with mathematics that I never figured my way out of.  The result is that I have a degree in physics, but reading an academic paper on the topic loses me after the first couple of paragraphs.

But so much of physics is so incredibly cool that I wish I understood it better.  The paper I took a look at yesterday (it'd be a vast exaggeration to say I "read" it) is a real coup -- if its findings bear out, it stands a good chance of solving two of the most perplexing questions of subatomic physics.

The first is akin to the planetary spacing issue I dealt with here a couple of days ago.  It asks a curious question: why do the fundamental particles have the masses they do?  Photons are massless; neutrinos damn close, but have a very tiny amount of mass; electrons are next (along with their relatives, muons), then protons and neutrons, and on up the scale to very heavy (and short-lived) particles like the "double-charmed xi baryon" which has four times the rest mass of a proton and a half-life so short it hasn't been measured yet, but is probably less than 10 ^-14 seconds (that's a decimal point, followed by thirteen zeros and a one -- better known to us non-physicists as "really, really short").

The other question is one I've looked at here before; the nature of the mysterious "dark matter" that makes up something like a quarter of the known mass of the universe, but thus far has resisted all detection by anything but its mysterious gravitational signature.  We don't know what it's made of, nor how (or if) it interacts with itself or other forms of matter.

I've commented about it that just as the odd constancy of the speed of light in a vacuum regardless of the reference frame of the observer waited around for a genius -- in this case, Einstein -- to explain it, the baffling dark matter is waiting for this century's Einstein to have the requisite insight.

[Image licensed under the Creative Commons Illustris Collaboration, Illustris Dark Matter and Gas, CC BY-SA 4.0]

Well, the waiting may be over.  A trio of physicists at Johannes Gutenberg University Mainz -- Adrian Carmona, Javier Castellano Ruiz, and Matthias Neubert -- have come up with a theoretical framework that, if it bears out, explains both the fundamental particle masses and the nature of dark matter in one fell swoop, by proposing an additional fundamental particle and force that act on matter through a tightly-coiled extra spatial dimension.

A press release at Science Daily describes their research this way:

In a recent paper published in the European Physical Journal C, the researchers found a spectacular resolution to this dilemma.  They discovered that their proposed particle would necessarily mediate a new force between the known elementary particles (our visible universe) and the mysterious dark matter (the dark sector).  Even the abundance of dark matter in the cosmos, as observed in astrophysical experiments, can be explained by their theory.  This offers exciting new ways to search for the constituents of the dark matter -- literally via a detour through the extra dimension -- and obtain clues about the physics at a very early stage in the history of our universe, when the dark matter was produced.

"After years of searching for possible confirmations of our theoretical predictions, we are now confident that the mechanism we have discovered would make the dark matter accessible to forthcoming experiments, because the properties of the new interaction between ordinary matter and dark matter -- which is mediated by our proposed particle -- can be calculated accurately within our theory," said study co-author Matthias Neubert.  "In the end -- so our hope -- the new particle may be discovered first through its interactions with the dark sector."

This, gentle readers, is what is known as "Nobel Prize material."

If, of course, it is confirmed by further research and investigation.  The thing that makes me hopeful is that the theories with the greatest likelihood of success are the ones that explain several problems at once; consider, for example, how the quantum mechanical model simultaneously accounted for the energy levels in hydrogen atoms, the bizarre double-slit experiment, Heisenberg's Uncertainty Principle, and the collapse of the wave function (most famous for being responsible for the Schrödinger's Cat phenomenon).  A really powerful model has enormous breadth, depth, and explanatory power, and this one -- at least from a preliminary look -- seems to have all three.

But, as I pointed out at the beginning, that's from the point of view of a dilettante.  I'm hardly qualified to assess whether the Carmona et al. paper will withstand scrutiny from the experts or will end up as another in the very long list of ideas that didn't pan out.  So keep your eyes on the news.

It might be that we are about to turn the lights on in the dark sector for the first time ever.

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Science fiction enthusiasts will undoubtedly know the classic 1973 novel by Arthur C. Clarke, Rendezvous with Rama.  In this book, Earth astronomers pick up a rapidly approaching object entering the Solar System, and quickly figure out that it's not a natural object but an alien spacecraft.  They put together a team to fly out to meet it as it zooms past -- and it turns out to be like nothing they've ever experienced.

Clarke was a master at creating alien, but completely consistent and believable, worlds, and here he also creates a mystery -- because just as if we really were to find an alien spacecraft, and had only a limited amount of time to study it as it crosses our path, we'd be left with as many questions as answers.  Rendezvous with Rama reads like a documentary -- in the middle of it, you could easily believe that Clarke was recounting a real rendezvous, not telling a story he'd made up.

In an interesting example of life imitating art, in 2017 astronomers at an observatory in Hawaii discovered an object heading our way fast enough that it has to have originated outside of our Solar System.  Called 'Oumuamua -- Hawaiian for "scout" -- it had an uncanny, if probably only superficial, resemblance to Clarke's Rama.  It is long and cylindrical, left no gas or dust plume (as a comet would), and appeared to be solid rather than a collection of rubble.  The weirdest thing to me was that backtracking its trajectory, it seems to have originated near the star Vega in the constellation Lyra -- the home of the superintelligent race that sent us a message in the fantastic movie Contact.

The strangeness of the object led some to speculate that it was the product of an extraterrestrial intelligence -- although in fairness, a team in 2019 gave their considered opinion that it wasn't, mostly because there was no sign of any kind of internal energy source or radio transmission coming from it.  A noted dissenter, though, is Harvard University Avi Loeb, who has laid out his case for 'Oumuamua's alien technological origin in his new book Extraterrestrial: The First Sign of Intelligent Life Beyond Earth.

His credentials are certainly unimpeachable, but his book is sure to create more controversy surrounding this odd visitor to the Solar System.  I won't say he convinced me -- I still tend to side with the 2019 team's conclusions, if for no other reason Carl Sagan's "Extraordinary Claims Require Extraordinary Evidence" rule-of-thumb -- but he makes a fascinating case for the defense.  If you are interested in astronomy, and especially in the question of whether we're alone in the universe, check out Loeb's book -- and let me know what you think.

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