The constancy of constants

One of the most enduring mysteries of physics is why the fundamental constants have the values they do.

I remember first thinking about this when I was a freshman in college, and we were looking at the Special Theory of Relativity in my intro-to-physics class.  The speed of light in a vacuum -- the ultimate speed limit, whatever Star Trek would have you believe -- is 299,792,458 meters per second.

What occurred to me was why it was exactly that number and not something else.  What if the speed of light was, say, twenty miles per hour?  Automobile travel would be a different game, and we'd have serious relativistic effects even riding a bicycle.  (Races would be an interesting affair; faster runners' clocks would move more slowly than slower runners' would, so by the end of the race, it'd be hard to get anyone to agree on what everyone's time was.)

All of which was delightfully silly stuff but didn't really get at the original question, which is why the speed of light has the value it does.  And it's not just the speed of light; in Martin Rees's wonderful book Just Six Numbers, he looks at how a handful of fundamental constants -- the gravitational flatness of the universe, the strength of the strong nuclear force, the ratio between the strength of the electromagnetic force and the gravitational force, the number of spatial dimensions, the ratio between the rest mass energy of matter and the gravitational field energy, and the cosmological constant -- have combined to produce the universe around us.  Alter any of these, even by a little bit, and you have a universe that would be profoundly hostile to life, if not to stable matter in general.

This has led some of the more religious-minded folks to what is called the Strong Anthropic Principle, sometimes called the "fine-tuning argument" -- that the universe has been fine-tuned for life, presumably by a Higher Power tweaking the dials on those constants to make them juuuuuuust right for us.  Which runs into two unfortunate counterarguments: (1) the vast majority of the universe is completely hostile to life regardless, including much of our home planet; and (2) the fact that we live in a universe where the important constants have those particular values isn't that surprising, because if they didn't, we wouldn't be around to remark upon it.

The latter is something known as the Weak Anthropic Principle, a stance that doesn't tell you much except for the unremarkable fact that the only kind of universe we could live in is one that has the conditions in which we could live.

[Image is in the Public Domain]

What I find intriguing is that none of these universal constants is derivable -- none come out of calculations based upon known physical laws... yet.  It might be that some of them are derivable and we just haven't figured out how.  Thus far, though, they seem completely arbitrary (except, as noted, that they have to have the values that they do in order for us to be here to consider the question).

A subtler question, and one that (unlike the fine-tuning argument) is actually testable, is whether those constants are the same everywhere in the universe, and whether they're constant over time.  Because if not -- if they vary either in time or space -- that strongly implies that they're not arbitrary, but derive from some underlying characteristic of matter, energy, and space/time that we have yet to uncover, and therefore in altered conditions could have a different value.  So a lot of time is being spent to determine whether any of these constants might be not so constant after all.

We at least have results for one of them, one that is not on Rees's List of Six but is nonetheless pretty damn important; the fine-structure constant, usually written as the Greek letter alpha.  The fine-structure constant is a measure of the strength of interaction between electrons and photons, and is equal to 1/137 (it's a dimensionless number, so it doesn't matter what units you use).

The fine-structure constant is one of the numbers whose value is instrumental in the formation of atoms, so (like Rees's numbers) if it were much different, the universe would be a very different place.  It's one that can be studied at a distance, because one outcome of the fine-structure constant having the value it does is that it creates the spread between the spectral lines of hydrogen.

So a team of physicists looked at the spectrum of hydrogen emitted in the vicinity of a supermassive black hole -- a place where the fabric of space/time is highly contorted because of the enormous gravitational field.  In a paper in Physical Review Letters, we find out that the fine-structure constant in that extremely different and hostile region of space is...

... 1/137.

The authors write:

Searching for space-time variations of the constants of Nature is a promising way to search for new physics beyond General Relativity and the standard model motivated by unification theories and models of dark matter and dark energy.  We propose a new way to search for a variation of the fine-structure constant using measurements of late-type evolved giant stars from the S-star cluster orbiting the supermassive black hole in our Galactic Center.  A measurement of the difference between distinct absorption lines (with different sensitivity to the fine structure constant) from a star leads to a direct estimate of a variation of the fine structure constant between the star’s location and Earth.  Using spectroscopic measurements of 5 stars, we obtain a constraint on the relative variation of the fine structure constant below 10^−5.

So the variation between the fine-structure constant and the fine-structure constant near a humongous black hole is less than a factor of 0.00001.

Note that this still doesn't tell us anything about why the fundamental constants have the values they do, all it does is suggest pretty strongly that they are constant regardless of the conditions pertaining in the region of space where they're measured.  So I guess we're still in the same boat as physicist Wolfgang Pauli, who said, "When I die, the first question I'm going to ask the Devil is, 'What is the meaning of the fine-structure constant?'"

The universe is a strange and mysterious place, and we're only beginning to figure out how it all works.  I mean, think about it; while I don't want to denigrate the scientific accomplishments of our forebears, we've really only begun to parse how the fundamental laws of nature work in the last 150 years.  It's an exciting time -- even if we don't yet have answers to a lot of the most basic questions in physics, at least we're figuring out which questions to ask.

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Order out of chaos

When I was an undergraduate, I sang in the University of Louisiana Choir in a production of Franz Josef Haydn's spectacular choral work The Creation.

The opening is a quiet, eerie orchestral passage called "The Representation of Chaos" -- meant to evoke the unformed "void" that made up the universe prior to the moment of creation.  Then the Archangel Raphael sings, "In the beginning, God made Heaven and Earth; and the Earth was without form and void, and darkness was upon the face of the deep."  The chorus joins in -- everything still in a ghostly pianissimo -- "In the spirit, God moved upon the face of the waters; and God said, "Let there be light.  And... there... was...

...LIGHT!"

The last word is sung in a resounding, major-chord fortissimo, with the entire orchestra joining in -- trumpets blaring, tympanis booming, the works.  

Even if you don't buy the theology, it's a moment that sends chills up the spine.  (You can hear it yourself here.)

Of course, the conventional wisdom amongst the cosmologists has been that the universe didn't begin in some kind of chaotic, dark void; quite the opposite.  The Big Bang -- or at least, the moment after it -- is usually visualized as a searingly hot, dense fireball, which expanded and cooled, leading to a steady entropy increase.  So by our current models, we're heading toward chaos, not away from it.

Well, maybe.

A recent paper by the pioneering Portuguese physicist and cosmologist João Magueijo has proposed a new model for the origins of the universe that overturns that entire scenario -- and far from being ridiculed off the stage, he's captured the attention even of hard-nosed skeptics like Sabine Hossenfelder, who did a video on her YouTube channel about his paper a few days ago that is well worth watching in its entirety.  But the gist, as far as a layperson like myself can understand it, goes like this.

It's long been a mystery why the fundamental constants of physics have the values they do, and why they actually are constant.  A handful of numbers -- the speed of light, the strength of the electromagnetic interaction, the strength of the gravitational force, the fine-structure constant, and a few others -- govern the behavior of, well, pretty much everything.  None seem to be derivable from more fundamental principles; i.e., they appear to be arbitrary.  None have ever been observed to shift, regardless how far out in space (and therefore how far back in time) you look.  And what's curious is that most of them have values that are tightly constrained, at least from our perspective.  Even a percent or two change in either direction, and you'd have situations like stars burning out way too fast to host stable planetary systems, atoms themselves falling apart, or matter not generating sufficient gravity to clump together.

So to many, the universe has appeared "fine-tuned," as if some omnipotent deity had set the dials just right at the moment of creation of the universe to favor everything we see around us (including life).  This is called the anthropic principle -- the strong version implying a master fine-tuner, the weak version being the more-or-less tautological statement that if those numbers had been any different, we wouldn't be here to ask the question.

But that doesn't get us any closer to figuring out why the fundamental constants are what they are.  Never one to shy away from the Big Questions, that's exactly what Magueijo has undertaken -- and what he's come up with is, to put it mildly, intriguing.

What he did was to start from the assumption that the fundamental constants aren't... constant.  That In The Beginning (to stick with our original Book of Genesis metaphor), the universe was indeed chaos -- the constants could have had more or less any values.  The thing is, the constants aren't all independent of each other.  Just as numbers in our mundane life can push and pull on each other -- to give a simple example, if you alter housing prices in a town, other numbers such as average salaries, rates of people moving in and moving out, tax rates, and funding for schools will shift in response -- the fundamental constants of physics affect each other.  What Magueijo did was to set some constraints on how those constants can evolve, then let the model run to see what kind of universe eventually came out.

And what he found was that after jittering around for a bit, the constants eventually found stable values and settled into an equilibrium.  In Hossenfelder's video, she uses the analogy of sand grains on a vibration plate being jostled into spots that have the highest stability (the most resistance to motion).  At that point, the pattern that emerges doesn't change again no matter how long you vibrate the plate.  What Magueijo suggests is that the current configuration of fundamental constants may not be the only stable one, but the range of what the constants could be might be far narrower than we'd thought -- and it also explains why we don't see the constants changing any more.

Why they are, in fact, constant.

Stable pattern of grains on a vibrating pentagonal Chladni plate [Image licensed under the Creative Commons Matemateca (IME USP), Chladni plate 16, CC BY-SA 4.0]

Magueijo's work might be the first step toward solving one of the most vexing questions of physics -- why the universe exists with these particular laws and constants, despite there not seeming to be any underlying reason for it.  Perhaps we've been looking at the whole thing the wrong way.  The early universe really may have been without substance and void -- but instead of a voice crying "let there be light!", things simply evolved until they reached a stable configuration that then generated everything around us.

It might not be as audibly dramatic as Haydn's vision of The Creation, but it's just as much of an eye-opener.

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The constancy of constants

One of the most enduring mysteries of physics is why the fundamental constants have the values they do.

I remember first thinking about this when I was a freshman in college, and we were looking at the Special Theory of Relativity in my intro-to-physics class.  The speed of light in a vacuum -- the ultimate speed limit, whatever Star Trek would have you believe -- was 299,792,458 meters per second.

What occurred to me was why it was exactly that number and not something else.  What if the speed of light was, say, twenty miles per hour?  Automobile travel would be a different game, and we'd have serious relativistic effects even riding a bicycle.  (Races would be an interesting affair; faster runners' clocks would move more slowly than slower runners' would, so by the end of the race, it'd be hard to get anyone to agree on what everyone's time was.)

All of which was delightfully silly stuff but didn't really get at the original question, which is why the speed of light has the value it does.  And it's not just the speed of light; in Martin Rees's wonderful book Just Six Numbers, he looks at how a handful of fundamental constants -- the gravitational flatness of the universe, the strength of the strong nuclear force, the ratio between the strength of the electromagnetic force and the gravitational force, the number of spatial dimensions, the ratio between the rest mass energy of matter and the gravitational field energy, and the cosmological constant -- have combined to produce the universe around us.  Alter any of these, even by a little bit, and you have a universe that would be profoundly hostile to life, if not to stable matter in general.

This has led some of the more religious-minded folks to what is called the Strong Anthropic Principle, sometimes called the "fine-tuning argument" -- that the universe has been fine-tuned for life, presumably by a Higher Power tweaking the dials on those constants to make them juuuuuuust right for us.  Which runs into two unfortunate counterarguments: (1) the vast majority of the universe is completely hostile to life, including much of our home planet; and (2) the fact that we live in a universe where the important constants have those particular values is unremarkable, because if they didn't, we wouldn't be around to remark upon it.

The latter is something known as the "Weak Anthropic Principle," a stance that doesn't tell you much except for the fact that the only kind of universe we could live in is one that has the conditions in which we could live.

[Image is in the Public Domain]

What I find intriguing is that none of these universal constants is derivable -- none come out of calculations based upon known physical laws... yet.  It might be that some of them are derivable and we just haven't figured out how.  Thus far, though, they seem completely arbitrary (except, as noted, that they have to have the values that they do in order for us to be here to consider the question).

A subtler question, and one that (unlike the fine-tuning argument) is actually testable, is whether those constants are the same everywhere in the universe, and whether they're constant over time.  Because if not -- if they vary either in time or space -- that strongly implies that they're not arbitrary, but derive from some underlying characteristic of matter, energy, and space/time that we have yet to uncover, and therefore in altered conditions could have a different value.  So a lot of time is being spent to determine whether any of these constants might be not so constant after all.

Just last week the results came in for one of them, one that is not on Rees's List of Six but is nonetheless pretty damn important; the fine-structure constant, usually written as the Greek letter alpha.  The fine-structure constant is a measure of the strength of interaction between electrons and photons, and is equal to 1/137 (it's a dimensionless number, so it doesn't matter what units you use).

The fine-structure constant is one of the numbers whose value is instrumental in the formation of atoms, so (like Rees's numbers) if it were much different, the universe would be a very different place.  It's one that can be studied at a distance, because one outcome of the fine-structure constant having the value it does is that it creates the spread between the spectral lines of hydrogen.

So a team of physicists looked at the spectrum of hydrogen emitted in the vicinity of a supermassive black hole -- a place where the fabric of space/time is highly contorted because of the enormous gravitational field.  In a paper in Physical Review Letters, we find out that the fine-structure constant in that extremely different and hostile region of space is...

... 1/137.

The authors write:

Searching for space-time variations of the constants of Nature is a promising way to search for new physics beyond General Relativity and the standard model motivated by unification theories and models of dark matter and dark energy.  We propose a new way to search for a variation of the fine-structure constant using measurements of late-type evolved giant stars from the S-star cluster orbiting the supermassive black hole in our Galactic Center.  A measurement of the difference between distinct absorption lines (with different sensitivity to the fine structure constant) from a star leads to a direct estimate of a variation of the fine structure constant between the star’s location and Earth.  Using spectroscopic measurements of 5 stars, we obtain a constraint on the relative variation of the fine structure constant below 10^−5.

So the variation between the fine-structure constant and the fine-structure constant near a humongous black hole is less than a factor of 0.00001.

Note that this still doesn't tell us anything about why the fundamental constants have the values they do, all it does is suggest pretty strongly that they are constant regardless of the conditions pertaining in the region of space where they're measured.

The universe is a strange and mysterious place, and we're only beginning to figure out how it all works.  I mean, think about it; while I don't want to denigrate the scientific accomplishments of our forebears, we've really only begun to parse how the fundamental laws of nature work in the last 150 years.  It's an exciting time -- even if we don't yet have answers to a lot of the most basic questions in physics, at least we're figuring out which questions to ask.

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One of my favorite people is the indefatigable British science historian James Burke.  First gaining fame from his immensely entertaining book and television series Connections, in which he showed the links between various historical events that (seen as a whole) play out like a centuries-long game of telephone, he went on to wow his fans with The Day the Universe Changed and a terrifyingly prescient analysis of where global climate change was headed, filmed in 1989, called After the Warming.

One of my favorites of his is the brilliant book The Pinball Effect.  It's dedicated to the role of chaos in scientific discovery, and shows the interconnections between twenty different threads of inquiry.  He's posted page-number links at various points in his book that you can jump to, where the different threads cross -- so if you like, you can read this as a scientific Choose Your Own Adventure, leaping from one point in the web to another, in the process truly gaining a sense of how interconnected and complex the history of science has been.

However you choose to approach it -- in a straight line, or following a pinball course through the book -- it's a fantastic read.  So pick up a copy of this week's Skeptophilia book of the week.  You won't be able to put it down.

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

Unique, just like everyone else

There's this idea that the creationists just love, and it's called the Strong Anthropic Principle.  The idea of the Strong Anthropic Principle is that there are a lot of seemingly arbitrary parameters in the universe, all of which appear to be underivable from other basic principles, and which are uniquely set to generate a universe in which stable matter and life can exist.  The speed of light, the strength of the strong nuclear force, the fine structure constant, the strength of gravity, the strength of the electromagnetic force -- all of them are at values which, if you tweaked them a little bit in either direction, would result in an uninhabitable universe.

The problem is, the Strong Anthropic Principle seems to breeze right past two inherent flaws in reasoning.  The first is that the fundamental constants seem underivable from first principles -- emphasis on the word seem.  In other words, the conjecture that they are arbitrary, and that their value is an example of an intelligent deity's fine tuning, rests on our current state of ignorance about physics.

The second, of course, is that it's a completely untestable proposition.  Unless you're assuming your conclusion (that a creator exists) you can't tell anything from the fundamental physical constants except that they are what they are.  After all, we only have the one universe accessible to study.  It could equally well be that other universes are just as likely as this one, and have other physical constants (and thus are uninhabitable) -- and that we can ask the question only because if the constants in this universe were other than they are, we wouldn't be here to consider it.  (This latter framing of the problem is called the "Weak Anthropic Principle," and is usually the stance taken by non-theists.)

The general weakness of the Strong Anthropic Principle hasn't stopped it from being embraced wholeheartedly by people who are trying to bolster the creationist worldview, and it's the essence of the article that appeared on Answers in Genesis a while back called "Not Just Another Star."  The whole thing, really, can be summed up as "Aren't we special?"  Here's a sampling:

While the sun has many characteristics similar to stars, the Bible never refers to it as a star. This suggests that the sun may have some unique characteristics. Could that refer to its composition? The sun’s composition is a bit unusual—it has far less lithium than most stars do. Lithium isn’t very common in stars anyway, but the sun is among the most lithium-poor stars. Though this statistic is interesting, it isn’t clear whether it is significant... 

By God’s gracious design, the earth has a protective magnetic field that prevents the sun’s flares from disrupting life. The particles racing from the sun interact with the magnetic field, which deflects most of the particles. Yet we are periodically reminded about such imminent danger when the flares overload the ability of the earth’s magnetic field to protect us. Astronauts on the Space Station must enter protected sections of the station after a solar flare. 

Not all planets have strong enough magnetic fields to protect living organisms on their surfaces. Even on planets that do, the situation would be dire if the star’s magnetic activity were far higher than the sun’s. The much more frequent and far more powerful flares probably would compromise any reasonable magnetic field that a planet would have. Because this particle radiation would be harmful to living things, even secular astronomers recognize that variable stars probably can’t support living things... 

Our sun is just a tiny yellow star in a vast collection that could support life. You’ll hear this more and more. Don’t believe it. The minimum requirement of a life-supporting star is missing from all the other stars. Our God-given sun appears to be unique.

What makes this wryly amusing that the creationists are choosing this week to post the article all over the place (it was actually written a few months ago, but I've just seen it on evangelical websites in the last week or so) -- because two days ago, a study appeared over at Phys.org that suggests that not only might the Earth not be unique, we might be one of (get this) 100 million inhabitable planets in the Milky Way alone.

That, friends, is a lot of places to look for alien life.  And a pretty strong blow to anyone's impression that the Earth is The Chosen Place.  Here's what one of the paper's authors, Alberto Farién of Cornell University, had to say:

This study does not indicate that complex life exists on that many planets. We're saying that there are planetary conditions that could support it. Origin of life questions are not addressed – only the conditions to support life.  Complex life doesn't mean intelligent life – though it doesn't rule it out or even animal life – but simply that organisms larger and more complex than microbes could exist in a number of different forms.  For example, organisms that form stable food webs like those found in ecosystems on Earth.

Add that to the fact that as nice as the Earth is, even here we have a great many places that are pretty hostile to human life -- Antarctica, large parts of the Great Rift Valley, Australia's Nullarbor Plain, most of the Sahara -- not to mention 71% of the surface area of the Earth (i.e. the oceans) -- and the Strong Anthropic Principle is looking weaker and weaker.

So, yeah.  Nice try, but not so much.

It's been a continuous move out of the center for us, hasn't it?  First Copernicus knocks down geocentrism; then Kepler says that the planets don't move in perfect circles.  Darwin punches a hole in the uniqueness of Homo sapiens with The Ascent of Man, and various geneticists in the 20th century show that all life, down to the simplest, pretty much encodes information the same way.  Now, we find out that there may be 100 million places kind of like the Earth out there in space.

Some people may find that depressing, but I don't.  I actually think it's awesome.  For one thing, it would mean we're almost certainly not alone in the universe.  For another, I think that a lot of humanity's missteps have come from a false sense of superiority -- over the environment, over other species, even over other human groups.  Maybe this kind of thing is good for us; there's nothing wrong with adopting a little humility as a species, not to mention perspective.

The argument from design

I received a response to a recent post in the form of an (actually quite friendly) email that posed a question I've been asked before, and that I thought might deserve a post of its own.  Here is an excerpt of the email:

Many atheist/skeptics base their disbelief on a lack of evidence for a deity.  If God exists, there should be evidence in the world around us.  A universe created by an omnipotent power should be different than one that was created by random processes.  If you're being honest, you have to admit that the universe we live in seems pretty fine-tuned for life, isn't it?  Scientists have identified dozens of fundamental numbers whose values are just right for the existence of matter, space, planets, stars, and life.  If any of those numbers were any different, life couldn't exist.  Doesn't it look very much like some intelligence set the values of the dials just right so as to produce a universe that we could live in?

This argument has been widely trumpeted by Christians who are not biblical literalists -- who may, in fact, accept such empirically supported models as the Big Bang and organic evolution, and who buy that the Earth is not six thousand years old, as the biblical chronology would have you believe, but six-some-odd billion years old.  But despite these non-fundamentalists' buying the whole scientific process (which is all to the good), they still can't quite let go of the idea that a higher power must be behind the whole thing.  And the "fine-tuning of the universe" is one of their main arguments.

It's called the strong anthropic principle.  The universe is such a hospitable place, they say, that god has to have set it up just for us.  But there's just one flaw in the whole thing; the central contention, that the universe is hospitable... just isn't true.

I mean, it all sounds very nice, doesn't it?  God created the universe with us in mind, and this produced awesome places like Maui and the Florida Keys.  The problem is, even here on our home planet, things aren't all that... friendly.  Much of the Earth's land surface has a climate or topography that makes it pretty unsuitable for human life.  (Being that it's midwinter in upstate New York, I'd throw my own home town into that category.)  Even some of the more congenial places, places that are warm enough and have enough water and fertile soil to keep us alive, are prone to natural disasters like hurricanes, tornadoes, earthquakes, volcanoes, and mudslides.  And if you leave the Earth, things only get worse; most of the universe is damn near a vacuum, and what's not is filled with black holes, quasars, asteroid belts, supernovae, neutron stars, and Wolf-Rayet gamma ray bursters -- the last-mentioned being capable of emitting an outburst of radiation so powerful that it could blast an entire solar system into oblivion.

Yes, well, what about the fact that all of the fundamental constants are set just right to produce matter?  This was the subject of Sir Martin Rees' book Just Six Numbers, in which he describes what the universe would be like if fundamental constants such as the curvature of space, the fine-structure constant, Planck's constant, the speed of light, and so on, were different -- and all of these alterations produce a universe that would be inhospitable to the formation of stars and planets, much less life.  And because we can't at the moment see any other reason why the constants are what they are -- i.e., there is no fundamental principle from which they can be derived, they seem arbitrary -- Rees and others argue that this is evidence of fine tuning.

I see two problems with this.  The first is that it is an argument from ignorance; because we have not yet come up with a unified theory that shows why the speed of light is three hundred million meters per second, and not (for example) 25 miles per hour, doesn't mean that we won't eventually do so.  You can't prove anything from a lack of knowledge.

Second, it seems to me that the strong anthropic principle is a backwards argument; it's taking what did happen, and arguing that there's a reason that it must have happened that way, that if it weren't designed, it wouldn't have happened that way.  It's as if I were dealt a straight flush in poker (an exceedingly unlikely occurrence) and I argued that because it's unlikely, someone must have rigged the deck.

All we know, honestly, is that it did happen, for the very good reason that if it hadn't happened that way, we wouldn't be here to talk about it.  This is called the weak anthropic principle -- even if the fundamental physical constants are arbitrary, there's no design implied, because in a universe with different physical constants, we wouldn't exist to discuss the matter.  The only place such arguments are possible are universes where life can occur.  Physicist Bob Park summarizes this viewpoint with the Yogi Berra-like statement, "If things were different, then things would not be like things are."  Put that way, it's hard to see how it's an argument for a deity, much less an omnipotent one with our best interests in mind.

Anyhow, that's my response to the Argument from Design.  Like I said, the person who wrote to me was really quite friendly about the whole thing, which (although we disagree about some fundamental ideas) is certainly an improvement from the spittle-flecked responses I sometimes get that suggest Satan is, as we speak, sharpening up his torture equipment with me in mind.  So, for that, I'll just say, "Thanks for writing."  Civilized discussion is, as always, the goal around here.