Seeing the light

Picture this: you're walking down a road on a dark, moonless night.  In the distance, you see a light.  How far away is the light?

The problem is obvious.  You can only make a good guess about the distance between you and the light source if you know how bright the light actually is.  A close-by dim light will have the same apparent brightness as a faraway bright light.  (The opposite would be true, too, of course.  You could only estimate the light source's intrinsic brightness if you knew how far away it was.)

That, in a nutshell, is the difficulty with making distance measurements of astronomical objects.  There are three tools, though, that can help to get around this problem.

The first only works for relatively nearby objects.  It's called parallax, and it has to do with the apparent motion of objects when you are actually what's moving.  You've all seen this; when you're driving down the freeway, nearby objects (such as the fence running along the side of the road) seem to zoom past a lot faster than distant ones (such as the mountain in the distance).  To figure out something's distance using parallax, you need two measurements of its apparent position relative to the unmoving background.  Then, using the distance you know that you have traveled, it's a matter of simple trigonometry to figure out how far away the object is.

Even nearby stars, though, exhibit such a tiny parallax that it requires a very long baseline -- such as the position of the Earth between June 21 and December 21.  By that time, it's halfway around its orbit, and the baseline is the orbit's circumference -- about three hundred million kilometers.  However, objects farther away than about ten light years have such a minuscule parallax that it's effectively undetectable.

The second, discovered by astronomer Henrietta Swan Leavitt in the early twentieth century, is a peculiarity of a type of variable star called a Cepheid variable.  Cepheid variables have a regular rise and fall in brightness, and Leavitt discovered (using fairly nearby ones) that their pulsation rate is directly proportional to how bright they actually are.  And, as I pointed out above, once you know how bright a light source is, you can estimate how far away it is.  (Making Cepheids one of the most commonly used "standard candles" in astronomy.)

The third sprang right from Leavitt's discovery.  When the light from distant galaxies was analyzed, astronomer Edwin Hubble observed something strange; it was red shifted.  Red shift is the electromagnetic version of the Doppler effect -- the wavelengths of light get stretched out (move toward the red end of the spectrum) if an object is moving away from you.  The more the shift, the greater the velocity.  But the kicker occurred when Hubble used  Leavitt's discovery of the relationship between a Cepheid variable's pulsation rate and intrinsic brightness to figure out how far away these galaxies were, and found another interesting correlation; the farther away the galaxy was, the greater the red shift -- and therefore, the faster it was moving away from us.  This led directly to the Big Bang/expanding universe model, and marks the origin of modern cosmology.

There's a fourth method, though, only recently discovered, but which was the technique used in a study that appeared last week in the Astrophysical Journal to determine the distance to five hundred distant galaxies.  It's called echo mapping, and it works like this.

Many, if not all, galaxies have a massive black hole at the center.  Black holes are not amenable to any of the standard methods of distance calculation.  They don't emit light, so even the red shift method won't work.  But one feature of most massive black holes is that they are surrounded by a torus-shaped dust cloud of debris.  The intense gravitational pull of the black hole draws matter into it, heats it up, and causes it to emit radiation in sudden bursts.  That radiation flashes outward and is absorbed by the inner surface of the dust cloud, warming it and creating an infrared signal that is detectable by telescopes on Earth.

Well, we know that light travels at three hundred thousand kilometers per second, and also that light's intensity drops off as a function of the inverse square of the distance from the source (twice as far means four times dimmer, three times as far means nine times dimmer, and so on).  Dust only forms if the temperature is below twelve hundred degrees Celsius -- any hotter and the molecules are torn apart by the thermal energy.  So a large black hole, with a large radiation output, would generate a dust cloud with a larger inner radius -- just as campers sitting around a campfire need to be closer to a smaller fire to be as warm as someone farther from a bigger fire.

So that's all the pieces.  If you know the time between the initial flash of radiation from the black hole and the subsequent infrared signal emitted by the dust cloud, you can figure out the circumference of the dust cloud.  Knowing the circumference tells you how intense the radiation source is (bigger circumference = more intense radiation source).  This gives you the actual luminosity of the accretion disc around the black hole -- and therefore how far away it is.

What never fails to impress me about scientists, and science in general, is the cleverness with which problems are approached.  Some of the best solutions to scientific questions have come from completely out-of-the-box ideas, or (as in the case of Henrietta Swan Leavitt's discovery about Cepheid variables) using something that at first appears to be a trivial factoid to illuminate something truly enormous.

I don't know about you, but whenever I see stuff like this, I always think, "I would never have thought of doing that."  I know that part of it is that, being a non-scientist, I haven't been steeped in one subject for years.  But I think the really successful scientists, the ones who make the major breakthroughs, are the ones whose brains are able to bring together what initially appear to be entirely disparate bits of information, and generate a synthesis that is way bigger than the sum of the parts.

In other words, science is primarily a creative act.

A fitting way to end this post is a quote from the brilliant Austrian physicist Lise Meitner:

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One of my favorite TED talks is by the neurophysiologist David Eagleman, who combines two things that don't always show up together; intelligence and scientific insight, and the ability to explain complex ideas in a way that a layperson can understand and appreciate.

His first book, Incognito, was a wonderful introduction to the workings of the human brain, and in my opinion is one of the best books out there on the subject.  So I was thrilled to see he had a new book out -- and this one is the Skeptophilia book recommendation of the week.

In Livewired: The Inside Story of the Ever-Changing Brain, Eagleman looks at the brain in a new way; not as a static bunch of parts that work together to power your mind and your body, but as a dynamic network that is constantly shifting to maximize its efficiency.  What you probably learned in high school biology -- that your brain never regenerates lost neurons -- is misleading.  It may be true that you don't grow any new neural cells, but you're always adding new connections and new pathways.

Understanding how this happens is the key to figuring out how we learn.

In his usual fascinating fashion, Eagleman lays out the frontiers of neuroscience, giving you a glimpse of what's going on inside your skull as you read his book -- which is not only amusingly self-referential, but is kind of mind-blowing.  I can't recommend his book highly enough.

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

A window on the deep past

When I was a kid, I always enjoyed going on walks with my dad.  My dad wasn't very well educated -- barely finished high school -- but was incredibly wise and had an amazing amount of solid, practical common sense.  His attitude was that God gave us reasoning ability and we had damn well better use it -- that most of the questions you run into can be solved if you just get your opinions and ego out of the way and look at them logically.

The result was that despite never having had a physics class in his life, he was brilliant at figuring things out about how the world works.  Like the mind-blowing (well, to ten-year-old kid, at least) idea he told me about because we saw a guy pounding in a fence post with a sledgehammer.

The guy was down the street from us -- maybe a hundred meters away or so -- and I noticed something weird.  The reverberating bang of the head of the sledge hitting the top of the post was out of sync with what we were seeing.  We'd see the sledge hit the post, then a moment later, bang.

I asked my dad about that.  He thought for a moment, and said, "Well, it's because it takes time for the sound to arrive.  The sound is slower than light is, so you see the hammer hit before you hear it."  He told me about how his father had taught him tell how close a thunderstorm is by counting the seconds between the lightning flash and the thunderclap, and that the time got shorter the closer it was.  He pointed at the guy pounding in the fence post, and said, "So the closer we get to him, the shorter the delay should be between seeing the hammer hit and hearing it."

Which, of course, turned out to be true.

But then, a crazy thought occurred to me.  "So... we're always hearing things in the past?"

"I suppose so," he said.  "Even if you're really close to something, it still takes some time for the sound to get to you."

Then, an even crazier thought.  "The light takes some time, too, right?  A shorter amount of time, but still some time.  So we're seeing things in the past, too?"

He shrugged.  "I guess so.  Light is always faster than sound."  Then he grinned.  "I guess that's why some people appear bright until you hear them talk."

It was some years later that I recognized the implications of this -- that the farther away something is, the further back into the past we're looking.  The Sun is far enough away that the light from it takes eight minutes and twenty seconds to get here, so you are always seeing the Sun not as it is now, but as it was, eight minutes and twenty seconds ago.  The closest star to us other than the Sun is Proxima Centauri, which is 4.3 light years away -- so here, you're looking at a star as it was 4.3 years ago.  There is, in fact, no way to know what it looks like now -- the Special Theory of Relativity showed that the speed of light is the fastest speed at which information can travel.  Any of the stars you see in the night sky might be exploding right now (not that it's likely, mind you), and not only would we have no way to know, the farther away they are, the longer it would take us to find out about it.

This goes up to some unimaginably huge distances.  Consider quasars, which are peculiar beasts to say the least.  When first discovered in the 1950s, they were such anomalies that they were nicknamed quasi-stellar radio sources mainly because no one knew what the hell they were.  Astrophysicist Hong-Yee Chiu contracted that clumsy appellation to quasar in 1964, and it stuck.

The funny thing about them was on first glance, they just looked like ordinary stars -- points of light.  Not even spectacular ones -- the brightest quasar has a magnitude just under +13, meaning it's not even visible in small telescopes.  But when the astronomers looked at the light coming from them, they found something extraordinary.

The light was wildly red-shifted.  You probably know that red-shift occurs because of the Doppler effect -- just as the sound of a siren from an ambulance moving away from you sounds lower in pitch because the sound waves are stretched out by the ambulance's movement, the light from something moving away from you gets stretched -- and the analog to pitch in sound is frequency in light.  The faster an object is moving away from you, the more its light drops in frequency (moves toward the red end of the spectrum).  And, because of Hubble's law and the expansion of space, the faster an object in deep space is moving away from you, the farther away it is.

So that meant two things: (1) if Hubble's law was being applied correctly, quasars were ridiculously far away (the nearest ones estimated at about a billion light years); and (2) if they really were that far away, they were far and away the most luminous objects in the universe (an average quasar, if placed thirty light years away, would be as bright as the Sun).

But what on earth (or outside of it, actually) could generate that much energy?  And why weren't there any nearby ones?  Whatever process resulted in a quasar evidently stopped happening a billion or more years ago -- otherwise we'd see ones closer to us (and therefore, ones that had occurred more recently; remember, farther away in space, further back in time).

Speculation ran wild, mostly because the luminosities and distances were so enormous that it seemed like there must be some other explanation.  Quasars, some said, were red-shifted not because the light was being stretched not by the expansion of space, but because it was escaping a gravity well -- so maybe they weren't far away, they were simple off-the-scale massive.  Maybe they were the output-end of a stellar wormhole.  Maybe they were some kind of chain reaction of millions of supernovas all at once.

See?  I told you they didn't look that interesting.  [Image licensed under the Creative Commons ESO, Quasar (24.5 mag ;z~4) in MS 1008 Field, CC BY 4.0]

Further observations confirmed the crazy velocities, and found that they were consistent with the expansion of space -- quasars are, in fact, billions of light years away, receding from us at what in Spaceballs would definitely qualify as ludicrous speed, and therefore had a luminosity that was unlike anything else.  But what could be producing such an energy output?

The answer, it seems, is that what we're seeing is the light emitted as gas and dust makes its last suicidal plunge into a galaxy-sized black hole -- as it speeds up, friction heats it up, and it emits light on a scale that boggles the mind.  Take that energy output and drag it out as space expands, and you get the longest-wavelength light there is -- radio waves -- but produced at at a staggering intensity.

All of this comes up because of a series of six papers last week in The Astronomical Journal about a discovery of three quasars that are the most energetic ever discovered (and therefore, the most energetic objects in the known universe).  The most luminous of the three is called SDSS J1042+1646, which brings up the issue of how astrophysicists name the objects they study.  I'm sorry, but "SDSS J1042+1646" just does not capture the gravitas and magnitude of this thing.  There should be a new naming convention that will give the interested layperson an idea of the scale we're talking about here.  I propose renaming it "Abso-fucking-lutely Enormous Glowing Thing, No, Really, You Don't Even Understand How Big It Is."  Although that's a little cumbersome, I maintain that it's better than SDSS J1042+1646.

But I digress.

Anyhow, the energy output of this thing is 5x10^30 gigawatts.  That's five million trillion trillion gigawatts.  By comparison, your average nuclear reactor puts out one gigawatt.  Even all the stars in the Milky Way put together are a hundred times less energetic than this one quasar.

See?  I told you.  Abso-fucking-lutely enormous.

These quasars have also given astrophysicists some insight into why we don't see any close by.  They are blowing radiation -- and debris -- out of the core of the quasar at such high rates that eventually they run out of gas.  The matter loss slows down star formation, and over time a quasar transforms into an ordinary, stable galaxy.

So billions of years ago, the Milky Way was probably a quasar, and to a civilization on a planet a billion light years away, that's what it would look like now.  If you wanted your mind blown further.

The universe is a big place, and we are by comparison really tiny.  Some people don't like that, but for me, it re-emphasizes the fact that our little toils and troubles down here are minor and transitory.  The glory of what's out there will always outshine anything we do -- which is, I think, a good thing.

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In the midst of a pandemic, it's easy to fall into one of two errors -- to lose focus on the other problems we're facing, and to decide it's all hopeless and give up.  Both are dangerous mistakes.  We have a great many issues to deal with besides stemming the spread and impact of COVID-19, but humanity will weather this and the other hurdles we have ahead.  This is no time for pessimism, much less nihilism.

That's one of the main gists in Yuval Noah Harari's recent book 21 Lessons for the 21st Century.  He takes a good hard look at some of our biggest concerns -- terrorism, climate change, privacy, homelessness/poverty, even the development of artificial intelligence and how that might impact our lives -- and while he's not such a Pollyanna that he proposes instant solutions for any of them, he looks at how each might be managed, both in terms of combatting the problem itself and changing our own posture toward it.

It's a fascinating book, and worth reading to brace us up against the naysayers who would have you believe it's all hopeless.  While I don't think anyone would call Harari's book a panacea, at least it's the start of a discussion we should be having at all levels, not only in our personal lives, but in the highest offices of government.

The problem with Hubble

In my Critical Thinking classes, I did a unit on statistics and data, and how you tell if a measurement is worth paying attention to.  One of the first things to consider, I told them, is whether a particular piece of data is accurate or merely precise -- two words that in common parlance are used interchangeably.

In science, they don't mean the same thing.  A piece of equipment is said to be precise if it gives you close to the same value every time.  Accuracy, though, is a higher standard; data are accurate if the values are not only close to each other when measured with the same equipment, but agree with data taken independently, using a different device or a different method.

A simple example is that if my bathroom scale tells me every day for a month that my mass is (to within one kilogram either way) 239 kilograms, it's highly precise, but very inaccurate.

This is why scientists always look for independent corroboration of their data.  It's not enough to keep getting the same numbers over and over; you've got to be certain those numbers actually reflect reality.

This all comes up because of some new information about one of the biggest scientific questions known -- the rate of expansion of the entire universe.

[Image is in the Public Domain, courtesy of NASA]

A few months ago, I wrote about some recent experiments that were allowing physicists to home in on the Hubble constant, a quantity that is a measure of how fast everything in the universe is flying apart.  And the news appeared to be good; from a range of between 50 and 500, physicists had been able to narrow down the value of the Hubble constant to between 65.3 and 75.6.

The problem is, nobody's been able to get closer than that -- and in fact, recent measurements have widened, not narrowed, the gap.

There are two main ways to measure the Hubble constant.  The first is to use information like red shift and Cepheid variables (stars whose period of brightness oscillation varies predictably with their intrinsic brightness, making them a good "standard candle" to determine the distance to other galaxies) to figure out how fast the galaxies we see are receding from each other.  The other is to use the cosmic microwave background radiation -- the leftovers from the radiation produced by the Big Bang -- to determine the age of the universe, and therefore, how fast it's expanding.

So this is a little like checking my bathroom scale by weighing myself on it, then comparing my weight as measured by the scale at the gym and seeing if I get the same answer.

And the problem is, the measurement of the Hubble constant by these two methods is increasingly looking like it's resulting in two irreconcilably different values.

The genesis of the problem is that our measurement ability has become more and more precise -- the error bars associated with data collection have shrunk considerably.  And if the two measurements were not only precise, but also accurate, you would expect that our increasing precision would result in the two values getting closer and closer together.

Exactly the opposite has happened.

"Five years ago, no one in cosmology was really worried about the question of how fast the universe was expanding.  We took it for granted," said astrophysicist Daniel Mortlock of Imperial College London.  "Now we are having to do a great deal of head scratching – and a lot of research...  Everyone’s best bet was that the difference between the two estimates was just down to chance, and that the two values would converge as more and more measurements were taken.  In fact, the opposite has occurred.  The discrepancy has become stronger.  The estimate of the Hubble constant that had the lower value has got a bit lower over the years and the one that was a bit higher has got even greater."

The discovery of dark matter and dark energy, the first by Vera Rubin, Kent Ford, and Ken Freeman in the 1970s, and the second by Adam Riess and Saul Perlmutter in the 1990s, accounted for the fact that the rate of expansion seemed wildly out of whack with the amount of observable matter in the universe.  The problem is, since the discovery of the effects of dark matter and dark energy, we haven't gotten any closer to finding out what they actually are.  Every attempt to directly detect either one has resulted in zero success.

Now, it appears that the problems run even deeper than that.

"Those two discoveries [dark matter and dark energy] were remarkable enough," said Riess.  "But now we are facing the fact there may be a third phenomenon that we had overlooked – though we haven’t really got a clue yet what it might be."

"The basic problem is that having two different figures for the Hubble constant measured from different perspectives would simply invalidate the cosmological model we made of the universe," Mortlock said.  "So we wouldn’t be able to say what the age of the universe was until we had put our physics right."

It sounds to me a lot like the situation in the late 1800s, when physicists were trying to determine the answer to a seemingly simple question -- in what medium do light waves propagate?  Every wave has to be moving through something; water waves come from regular motion of water molecules, sound waves from oscillation of air molecules, and so on.  With light waves, what was "waving?"

Because the answer most people accepted was, "something has to be waving even if we don't know what it is," scientists proposed a mysterious substance called the "aether" that permeated all of space, and was the medium through which light waves were propagating.  All attempts to directly detect the aether were failures, but this didn't discourage people from saying that it must be there, because otherwise, how would light move?

Then along came the brilliant (and quite simple -- in principle, anyhow) Michelson-Morley experiment, which proved beyond any doubt that the aether didn't exist.  Light traveling in a vacuum appeared to have a constant speed in all frames of reference, which is entirely unlike any other wave ever studied.  And it wasn't until Einstein came along and turned our entire understanding upside down with the Special Theory of Relativity that we saw the piece we'd been missing that made sense of all the weird data.

What we seem to be waiting for is this century's Einstein, who will explain the discrepancies in the measurements of the Hubble constant, and very likely account for the mysterious, undetectable dark matter and dark energy (which sound a lot like the aether, don't they?) at the same time.  But until then, we're left with a mystery that calls into question one of the most fundamental conclusions of modern physics -- the age of the universe.

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This week's Skeptophilia book recommendation is a fun book about math.

Bet that's a phrase you've hardly ever heard uttered.

Jordan Ellenberg's amazing How Not to Be Wrong: The Power of Mathematical Thinking looks at how critical it is for people to have a basic understanding and appreciation for math -- and how misunderstandings can lead to profound errors in decision-making.  Ellenberg takes us on a fantastic trip through dozens of disparate realms -- baseball, crime and punishment, politics, psychology, artificial languages, and social media, to name a few -- and how in each, a comprehension of math leads you to a deeper understanding of the world.

As he puts it: math is "an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength."  Which is certainly something that is drastically needed lately.

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

Revising Hubble

If I had to pick the most paradigm-changing discovery of the twentieth century, a strong contender would be the discovery of red shift by astronomer Edwin Hubble.

What Hubble found was that when he analyzed the spectral lines from stars in distant galaxies, the lines -- representing wavelengths of light emitted by elements in the stars' atmospheres -- had slid toward the red (longer-wavelength) end of the spectrum.  Hubble realized that this meant that the galaxies were receding from us at fantastic speeds, resulting in a Doppler shift of the light coming from them.

What was most startling, though, is that the further away a galaxy was, the faster it was moving.  This observation led directly to the theory of the Big Bang, that originally all matter in the universe was coalesced into a single point, then -- for reasons still unclear -- began to expand outward at a rate that defies comprehension.

There's a simple quantity (well, simple to define, anyhow) that describes the relationship that Hubble discovered.  It's called the Hubble constant, and is defined at the ratio between the velocity of a galaxy and its distance from us.  The relationship seems to be linear (meaning the constant isn't itself dependent upon distance), but the exact value has proven extremely difficult to determine.  Measurements have varied between 50 and 500 kilometers per second per megaparsec, which is a hell of a range for something that's supposed to be a constant.

And the problem is, the value has varied depending on how it's calculated.  Measurements based upon the cosmic microwave background radiation give one range of values; measurements using Type 1A supernovae (a commonly-used "standard candle" for calculating the distances to galaxies) give a different range.

Enter Kenta Hotokezaka of Princeton University, who has decided to tackle this problem head-on.  “The Hubble constant is one of the most fundamental pieces of information that describes the state of the universe in the past, present and future," Hotokezaka said in a press release.  "So we’d like to know what its value is...  either one of [the accepted calculations of the constant] is incorrect, or the models of the physics which underpin them are wrong.  We’d like to know what is really happening in the universe, so we need a third, independent check."

Hotokezaka and his team have found the check they were looking for in the collision of two neutron stars in a distant galaxy.  The measurements made of the gravitational waves emitted by this collision were so precise it kind of boggles the mind.  Adam Deller, of Swinburne University of Technology in Australia, who co-authored the paper, said, "The resolution of the radio images we made was so high, if it was an optical camera, it could see individual hairs on someone’s head 3 miles away."

[Image licensed under the Creative Commons ESA, Colliding neutron stars ESA385307, CC BY-SA 3.0 IGO]

Using this information, the researchers were able to narrow in on the Hubble constant -- reducing the uncertainty to between 65.3 and 75.6 kilometers per second per megaparsec.

Quite an improvement over 50 to 500, isn't it?

"This is the first time that astronomers have been able to measure the Hubble constant by using a joint analysis of a gravitational-wave signals and radio images,"  Hotokezaka said about the accomplishment of his team.  "It is remarkable that only a single merger event allows us to measure the Hubble constant with a high precision — and this approach relies neither on the cosmological model (Planck) nor the cosmic-distance ladder (Type Ia)."

I'm constantly astonished by what we can learn of our universe as we sit here, stuck on this little ball of spinning rock around an average star in one arm of an average galaxy.  It's a considerable credit to our ingenuity, persistence, and creativity, isn't it?  From our vantage point, we're able to gain an understanding of the behavior of the most distant objects in the universe -- and from that, deduce how everything began.

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This week's Skeptophilia book recommendation is pure fun for anyone who (like me) appreciates both plants and an occasional nice cocktail -- The Drunken Botanist by Amy Stewart.  Most of the things we drink (both alcohol-containing and not) come from plants, and Stewart takes a look at some of the plants that have provided us with bar staples -- from the obvious, like grapes (wine), barley (beer), and agave (tequila), to the obscure, like gentian (angostura bitters) and hyssop (Bénédictine).

It's not a scientific tome, more a bit of light reading for anyone who wants to know more about what they're imbibing.  So learn a little about what's behind the bar -- and along the way, a little history and botany as well.

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