Lost horizon

While our knowledge of the origin of the universe has grown tremendously in the past hundred years, there are still plenty of cosmological mysteries left to solve.

One of the most vexing is called the horizon problem.

It's one of those situations where at first, it seems like "where's the problem?"  Then you look into it a little more, and kind of go, "... oh."  The whole thing has to do with how fast a change can percolate through a system.  Amongst the (many) outcomes of the General Theory of Relativity, we are reasonably certain that the upper bound at which disturbances of any kind can propagate is the speed of light.

So if a change of some sort happens in region A, but it is so far away from region B that there hasn't been enough time for light to travel between the two, it is fundamentally impossible for that change to have any effect at all in region B.  Such regions are said to be causally disconnected.

So far, so good.  The thing is, though, there are plenty of sets of causally disconnected regions in the universe.  If at midnight in the middle of winter you were to aim a very powerful telescope straight up into the sky, the farthest objects you could see are on the order of ten billion light years away.  Do the same six months later, in midsummer, and you'd be looking at objects ten billion light years away in the other direction.  The distance between the two is therefore on the order of twenty billion light years (and this is ignoring the expansion of the universe, which makes the problem even worse).  Since the universe is only something like 13.8 billion years old, there hasn't been enough time for light to travel between the objects you saw in winter and those you saw in summer.

Therefore, they can't affect each other in any way.  Furthermore, they've always been causally disconnected, at least as far back as we have good information.  By our current models, they were already too far apart to communicate three hundred thousand years after the Big Bang, the point at which decoupling occurred and the 2.7 K cosmic microwave background radiation formed. 

Herein lies the problem.  The cosmic microwave background (CMB for short) is very nearly isotropic -- it's the same no matter which direction you look.  There are minor differences in the temperature, thought to be due to quantum fluctuations at the moment of decoupling, but those average out to something very close to uniformity.  It seems like some process homogenized it, a bit like stirring the cream into a cup of coffee.  But how could that happen, if opposite sides of the universe were already causally disconnected from each other at the point when it formed?

A map of the CMB from the Wilkinson Microwave Anisotrophy Probe [Image is in the Public Domain courtesy of NASA]

It's worse still, however, which I just found out about when I watched a video by the awesome physicist and science educator Sabine Hossenfelder a couple of days ago.  Because a 2003 paper found that the CMB isn't isotropic after all.

I'm not talking about the CMB dipole anisotropy -- the fact that one region of the sky has CMB a little warmer than average, and the opposite side of the sky a little cooler than average.  That much we understand pretty well.  The Milky Way Galaxy is itself moving through space, and that creates a blue shift on one side of the sky and a red shift on the other, accounting for the measurably warmer and cooler regions, respectively.

What Hossenfelder tells us about is that there's an anisotropy in the sizes of the warm and cool patches.  It's called the hemispherical power spectrum asymmetry, and simply put, if you sort out the sizes of the patches at different temperatures, you find that one side of the sky is "grainier" than the other.  Like I said, we've known about this since 2003, but there was nothing in any of the models that could account for this difference, so cosmologists kind of ignored the issue in the hopes that better data would make the problem go away.

It didn't.  A recent paper using newly-collected data from the Planck mission found that the hemispherical power spectrum asymmetry is real.

And we haven't the first idea what could have caused it.

In a way, of course, this is tremendously exciting.  A great many scientific discoveries have started with someone looking at something, frowning, and saying, "Okay, hang on a moment."  Here we have something we already didn't understand (CMB isotropy and the horizon problem) gaining an added layer of weirdness (it's not completely isotropic after all, but is anisotropic in a really strange way).  What this shows us is that our current models of the origins of the universe are still incomplete.

Looks like it's a good time to go into cosmology.  In what other field is there a universe-sized problem waiting to be solved?

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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!]

Paradoxes within paradoxes

Sometimes the simplest, most innocuous-seeming questions can lead toward mind-blowingly profound answers.

I remember distinctly running into one of these when I was in -- I think -- 8th grade science class.  It was certainly pre-high-school; whether it was from Mrs. Guerin at Paul Breaux Junior High School, or another of my teachers, is a memory that has been lost in the sands of time and middle-aged forgetfulness.

What I have never forgotten is the sudden, pulled-up-short response I had to what has been nicknamed Olbers' Paradox, named after 18th century German astronomer Heinrich Wilhelm Matthias Olbers, who first thought to ask the question -- if the universe is infinite, as it certainly seems to be, why isn't the night sky uniformly and dazzlingly bright?

I mean, think about it.  If the universe really is infinite, then no matter what direction you look, your line of sight is bound to intersect with a star eventually.  So there should be light coming from every direction at once, and the night sky shouldn't be dark.  Why isn't it?

The first thought was that there was something absorptive in the way -- cosmic dust, microscopic or submicroscopic debris left behind by stars and blown outward by stellar wind.  The problem is, there doesn't seem to be enough of it; the average density of cosmic dust in interstellar space is less than a millionth of a gram per cubic meter.

When the answer was discovered, it was nothing short of mind-boggling.  It turns out Olbers' paradox isn't a paradox at all, because there is light coming at us from all directions, and the night sky is uniformly bright -- it's just that it's shining in a region of the spectrum our eyes can't detect.  It's called the three-degree cosmic microwave background radiation, and it appears to be pretty well isotropic (at equal intensities no matter where you look).  It's one of the most persuasive arguments for the Big Bang model, and in fact what scientists have theorized about the conditions in the early universe added to what we know about the phenomenon of red-shifting (the stretching of wavelengths of light if the space in between the source and the detector is expanding) gives a number that is precisely what we see -- light peaking at a wavelength of around one millimeter (putting it in the microwave region of the spectrum) coming from all directions.

[Image licensed under the Creative Commons Original: Drbogdan Vector: Yinweichen, History of the Universe, CC BY-SA 3.0]

So, okay.  Olbers' paradox isn't a paradox, and its explanation led to powerful support for the Big Bang model.  But in science, one thing leads to another, and the resolution of Olbers' paradox led to another paradox -- the horizon problem.

The horizon problem hinges on Einstein's discovery that nothing, including information, can travel faster than the speed of light.  So if two objects are separated by a distance so great that there hasn't been time for light to travel from one to the other, then they are causally disconnected -- they can't have had any contact with each other, ever.

The problem is, we know lots of such pairs of objects.  There are quasars that are ten billion light years away -- and other quasars ten billion light years away in the opposite direction.  Therefore, those quasars are twenty billion light years from each other, so light hasn't had time to travel from one to the other in the 13.8 billion years since they were created.

Okay, so what?  They can't talk to each other.  But it runs deeper than that.  When the aforementioned cosmic microwave background radiation formed, on the order of 300,000 years after the Big Bang, those objects were already causally disconnected.  And the process that produced the radiation is thought to have been essentially random (it's called decoupling, and it occurred when the average temperature of the universe decreased enough to free photons from the plasma and send them streaming across space).

The key here is the word average.  Just as a microwaved cup of coffee could have an average temperature of 80 C but have spots that are cooler and spots that are hotter, the fact that the average temperature of the universe had cooled sufficiently to release photons doesn't mean it happened everywhere simultaneously, leaving everything at exactly the same temperature.  In fact, the great likelihood is that it wouldn't.  And since at that point there were already causally disconnected regions of space, there is no possible way they could interact in such a way as to smooth out the temperature distribution -- sort of like what happens when you stir a cup of coffee.

And yet one of the most striking things about the cosmic microwave background radiation is that it is very nearly isotropic.  The horizon problem points out how astronomically unlikely that is (pun intended) if our current understanding is correct.

One possible explanation is called cosmic inflation -- that a spectacularly huge expansion, in the first fraction of a second after the Big Bang, smoothed out any irregularities so much that everywhere did pretty much decouple at the same time.    The problem is, we still don't know if inflation happened, although work by Alan Guth (M.I.T.), Andrei Linde (Stanford), and Paul Steinhardt (Princeton) has certainly added a great deal to its credibility.

So as is so often the case with science, solving one question just led to several other, bigger questions.  But that's what's cool about it.  If you're interested in the way the universe works, you'll never run out of things to learn -- and ways to blow your mind.

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This week's Skeptophilia book recommendation is one of personal significance to me -- Michael Pollan's latest book, How to Change Your Mind.  Pollan's phenomenal writing in tours de force like The Omnivore's Dilemma and The Botany of Desire shines through here, where he takes on a controversial topic -- the use of psychedelic drugs to treat depression and anxiety.

Hallucinogens like DMT, LSD, ketamine, and psilocybin have long been classified as schedule-1 drugs -- chemicals which are off limits even for research except by a rigorous and time-consuming approval process that seldom results in a thumbs-up.  As a result, most researchers in mood disorders haven't even considered them, looking instead at more conventional antidepressants and anxiolytics.  It's only recently that there's been renewed interest, when it was found that one administration of drugs like ketamine, under controlled conditions, was enough to alleviate intractable depression, not just for hours or days but for months.

Pollan looks at the subject from all angles -- the history of psychedelics and why they've been taboo for so long, the psychopharmacology of the substances themselves, and the people whose lives have been changed by them.  It's a fascinating read -- and I hope it generates a sea change in our attitudes toward chemicals that could help literally millions of people deal with disorders that can rob their lives of pleasure, satisfaction, and motivation.

[If you purchase the book from Amazon using the image/link below, part of the proceeds goes to supporting Skeptophilia!]