Reversing the arrow

In my short story "Retrograde," the main character, Eli, meets a woman who makes the bizarre claim that she experiences time running backwards.

She's not like Benjamin Button, who ages in reverse; she experiences everything in reverse.  But from our perspective, nothing seems amiss.  From hers, though... she remembers future events and not past ones:

Hannah gave him a long, steady look.  "All I can say is that we see the same things.  For me, the film runs backwards, that’s all.  Other than that, there’s no difference.  There’s nothing I can do to change the way things unfold, same as with you."

"That’s why you were crying when I came in.  Because of something that for you, had already happened?  What was it?"

She shook her head.  "I shouldn’t answer that, Eli."

"It’s me, isn’t it?  For me, I was just meeting you for the first time.  For you, it was the last time you’d ever see me."  I winced, and rubbed my eyes with the heel of my hand.  "Jesus, I’m starting to believe you.  But that’s it, right?"

Hannah didn’t answer for a moment.  "The thing is—you know, you start looking at things as inevitable.  Like you’re in some sort of film.  The actors seem to have freedom.  They seem to have will, but in reality the whole thing is scrolling by and what’s going to happen is only what’s already written in the script.  You could, if you wanted to, start at the end and run the film backwards.  Same stuff, different direction.  No real difference except for the arrow of time."

Einstein's General Theory of Relativity shows that space and time are inextricably linked -- spacetime -- but doesn't answer the perplexing question of why we can move in any direction through space, but only one direction through time.  You can alter the rate of time's passage, at least relative to some other reference frame, by changing your velocity; but unlike what the characters in "Retrograde" experience, the arrow always points the same way.  

This becomes odder still when you consider that in just about all physical processes, there is no inherent arrow of time.  Look at a video clip of a pool ball bouncing off the side bumper, then run it backwards -- it'd be damn hard to tell which was the actual, forward-running clip.

Hard -- but not impossible.  The one physical law that has an inherent arrow of time is the Second Law of Thermodynamics.  If the clip was long enough, or your measurement devices sensitive enough, you could tell which was the forward clip because in that one, the pool ball would be slowing down from dissipation of its kinetic energy in the form of friction with the table surface.  Likewise, water doesn't unspill, glasses unbreak, snowbanks un-avalanche, reassembling in pristine smoothness on the mountainside.  But why this impels a universal forward-moving arrow of time -- and more personally, why it makes us remember the past and not the future -- is still an unanswered question.

"The arrow of time is only an illusion," Einstein quipped, "but it is a remarkably persistent one."

Two recent papers have shed some light on this strange conundrum.  In the first, a team led by Andrea Rocco of Surrey University looked how the equations of the Second Law work on the quantum level, and found something intriguing; introducing the Second Law into the quantum model generated two arrows of time, one pointing into the past and one pointing into the future.  But no matter which time path is taken, entropy still increases as you go down it.

"You’d still see the milk spilling on the table, but your clock would go the other way around," Rocco said.  "In this way, entropy still increases, but it increases toward the past instead of the future.  The milk doesn’t flow back into the glass, which the Second Law of Thermodynamics forbids, but it flows out of the glass in the direction of the past.  Regardless of whether time’s arrow shoots toward the future or past from a given moment, entropy will still dissipate in that given direction."

In the second, from Lorenzo Gavassino of Vanderbilt University et al., the researchers were investigating the mathematics of "closed time-like loops" -- i.e., time travel into the past, followed by a return to your starting point.  And what they found was that once again, the Second Law gets in the way of anything wibbly-wobbly.

Gavassino's model shows that on a closed time-like loop, entropy must peak somewhere along the loop -- so along some part of the loop, entropy has to decrease to return it to where it was when the voyage began.  The equations then imply that one of two things must be true.  Either:

1. Time travel into the past is fundamentally impossible, because it would require entropy to backpedal; or
2. If overall entropy can decrease somewhere along the path, it would undo everything that had happened along the entropy-increasing part of the loop, including your own memories.  So you could time travel, but you wouldn't remember anything about it (including that it had ever happened).

"Any memory that is collected along the closed time-like curve," Gavassino said, "will be erased before the end of the loop."

So that's no fun at all.  Lieutenant Commander Geordi LaForge would like to have a word with you, Dr. Gavassino.

Anyhow, that's today's excursion into one of the weirdest parts of physics.  Looks like the Second Law of Thermodynamics is still strictly enforced in all jurisdictions.  Time might be able to run backwards, but you'd never know because (1) entropy will still increase in that direction, and (2) any loop you might take will result in your remembering nothing about the trip.  So I guess we're still stuck with clocks running forwards -- and having to wait to find out what's going to happen in the future at a rate of one minute per minute.

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Non-trivial donuts

In the New Research That Sounds Crazy But Isn't department, we have: an inquiry into whether the universe is actually shaped like a donut.

[Image credit: J. Law, ESO]

The overall shape of spacetime is something that is nowhere near as obvious as it might seem to a layperson.  From the look of it, we seem to live in a completely Euclidean universe; perpendicular lines meet at a perfect ninety degree angle, parallel ones never intersect, and all of the other happy stuff you learned in high school geometry class.  But as mathematicians Leonhard Euler and Nikolai Lobachevsky showed, this isn't the only possibility.  The fabric of space could have an overall spherical shape, where there are no parallel lines (a 2-D example of a spherical geometry is the surface of the Earth).  On the other hand, in a hyperbolic space, given a line and a point not on that line, there is an infinite number of parallel lines passing through that point.  (It's harder to picture, for me at least, but a 2-D analog to a hyperbolic space is the surface of a saddle -- or a Pringle's potato chip.)

To our best measurements thus far, however, it looks like the simple solution -- that spacetime is flat and Euclidean -- is correct.  (That's on the largest scales; on small scales, anything with mass warps the geometry of spacetime.  However, it appears that those local divots and dimples are in a spacetime which is, overall, flat.)  

But according to a paper in the journal Physical Review Letters, there might be other possibilities we haven't considered -- ones even more mindblowing than a spherical or hyperbolic universe.

Theoretical physicist Glenn Starkman, of Case Western Reserve University, has proposed that the universe's geometry might have a nontrivial topology.  Euclidean spaces -- and also spheres and saddles -- have what topologists call a trivial topology; the simplest way to think about this is to consider what happens if you draw a closed loop anywhere on one of those surfaces, and then make it shrink.  On a surface with a trivial topology, no matter where you draw it, you can continue to shrink the loop all the way down to a single point.  On one with nontrivial topology, there are at least some loops that you can't do that to without deforming the shape of the surface.

Consider, for example, a donut.  A loop that goes around the donut longitudinally (i.e. through the hole and back around again) can't be shrunk indefinitely; neither can one that runs all the way around the hole.  Shapes with a single hole all the way through are called genus one tori.  A donut is a genus one torus, as is a mug with a single handle.  (Giving rise to the old joke that topologists are so smart that at breakfast, they can't tell their coffee cups from their donuts.)

This may seem like nothing more than intellectual noodling about, but if the universe has a weird non-trivial topology, it could explain ongoing mysteries like the asymmetries (and unexpected symmetries) in the cosmic microwave background radiation.  One possibility is that the geometry of the universe is some kind of multiply-connected hypertorus -- a bit like a three-dimensional version of the old game PacMan, where if you exit the screen on one side, you reappear on the opposite side.  This would mean when you look out into space in one direction, your sight line comes back at you from the other direction.  This could potentially explain another long-standing and vexing problem in physics, the horizon problem -- which is the question of why space is so homogeneous, despite the fact that there are regions of space that, if space has a trivial topology, have been causally disconnected since the time of the Big Bang.  If when you peer one direction into the night sky, your visual line travels in a gigantic loop, the horizon problem kind of goes away; you're seeing the same stuff out at the edges of the universe no matter which way you look.

Of course, even that is not as complicated as it can get.  Starkman and his colleagues have proposed a total of seventeen different possible geometries that aren't ruled out by the observational evidence.  In some, the universe twists as it loops around, so that (using our PacMan analogy) when you exit the screen and reappear on the other side, you're now upside-down.  They are currently proposing looking for similar patterns in regions of space on opposite sides of the universe, but also have to consider that the pattern on one side may be inverted with respect to the other.

As you might imagine, doing this kind of comparison work is way beyond the scope of human analysts; it's going to require some heavy-duty computational firepower.  They're planning on turning over new survey data from the JWST and ESO to rapid machine-learning software for analysis, and we might actually have some preliminary answers by the end of the year.

If they get positive results, it'll be an incredible coup -- not only proposing a whole bunch of new physics, but simultaneously making inroads into solving the long-standing flatness and horizon problems.  I'm not holding my breath -- it's all too often these odd ideas fail the test of empirical evidence -- but wouldn't it be wonderful if it holds up?

I know I'd celebrate by eating a donut.

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Flat space, Hawking radiation, and warm spots

Ever wonder if the universe is flat?

No, I haven't taken Wingnut Pills and decided that the Flat Earthers make sense.  This is an honest-to-Einstein problem in physics, one that not only raises eyebrows about the supposed "fine-tuning" of the universe but has a huge effect on its ultimate fate.

By this time most people who are reasonably scientifically literate (or at least watch Star Trek) know about curved space -- that the presence of mass warps space-time, a little like the way a heavy weight on a trampoline stretches and deforms the flexible sheet it's sitting on.  The trampoline analogy isn't a bad one; if you have a bowling ball in the middle of a trampoline, and you roll a marble on the surface, the marble's path will be deflected in such a way that it appears the bowling ball is attracting the marble.  In reality, however, there's no attraction involved; the bowling ball has warped the space around it, and the marble is only following the contours of the space it's traveling through.

Bump up the number of dimensions by one, and you've got an idea of how curved space-time works.  The trampoline is a 2-D surface warped into a third dimension; where you're sitting right now is a 3-D space warped into a fourth dimension.  (In fact, the effects of that curvature are what you are experiencing as a downward pull toward the Earth's surface right now.)

The "flatness problem" asks a seemingly simple question; okay, matter deforms space locally, but what's the shape of space as a whole?  In our trampoline analogy, you can visualize that although the bowling ball deflects the surface near it, as a whole the trampoline is flat.  Harder to picture, perhaps, is that the trampoline could be a different shape; the surface of the entire trampoline could be spherical, for example, and still have indentations on the surface corresponding to places where massive objects are located.

That, in a nutshell, is the flatness problem.  The key is the matter/energy density of the entire universe.  If the universe is flat as a whole, the matter/energy density is exactly right for the outward expansion from the Big Bang to slow down, asymptotically approaching zero, but never quite getting there (and never reversing direction).  A universe with a higher matter/energy density than the critical value would eventually halt, then fall inward again, resulting in a "Big Crunch" as all the stuff in the universe collapses back to a singularity.  (This is sometimes called a "spherical universe" because space-time would be warped into a four-dimensional hypersphere.  If you can't picture this, don't worry, neither can anyone else.)  If the matter/energy density is lower than the critical value, the universe would continue to expand forever, getting thinner and more spread out, eventually reaching the point where any particular cubic light year of space would have very little chance of having even a single atom in it somewhere.  (This is known as a "hyperbolic universe," for analogous reasons to the "spherical universe" mentioned above, but even harder to visualize.)

[Image is in the Public Domain courtesy of NASA]

So, which is it?

There doesn't seem to be a good reason, argued from first principles, that the universe has to be any particular one of the three.  When I first ran into this concept, in high school physics class, I was rooting for the spherical universe solution; ending the universe with an enormous collapse seemed (and still seems) preferable to the gradual attenuation of matter and energy that would occur with the other two.  Plus, it also raised the possibility of a rebounding second Big Bang and a new start, which was kind of hopeful-sounding even if nothing much would survive intact through the cusp.

Because there seemed to be no reason to expect the value of the matter-energy density -- known to physicists as Ω -- to be constrained, figuring out what it actually is occupied a great deal of time and effort by the astrophysicists.  It was a matter of some shock when by their best measurements, the value of Ω was:

1.00000000000000000000000000000000000000000000000000000000000000

To save you the trouble, that's exactly one, out to the 62nd decimal place.

So in other words, the universe is flat, or so close to it that we can't tell the difference.

This engenders more than a few other problems.  For one thing, why is Ω exactly 1?  Like I said earlier, nothing from the basic laws of physics seems to require it.  This brings up the issue of cosmological fine-tuning, which understandably makes us science-types a little twitchy.  Then there's the problem that the outer reaches of the universe that we can see -- so places farther away in space, and further back in time -- are moving away from us a lot faster than they should if the universe was flat.  This has given rise to a hypothesized repulsive "dark energy" to account for this, but what exactly dark energy is turns out to be even more problematic than the "dark matter" that appears to comprise over a quarter of the overall mass/energy of the universe even though we haven't been able to detect it other than by its gravitational bending of space-time.

The reason this warped topic comes up is research by the groundbreaking and often controversial Nobel laureate Roger Penrose, who published a paper in Monthly Notices of the Royal Astronomical Society that identified six "warm spots" that had been detected in the background radiation of the universe, and which Penrose believes are "Hawking points" -- places where a black hole evaporated due to its "Hawking radiation" eventually bleeding off mass (a topic I dealt with in a little more detail last year).  The problem is, the evaporation of a black hole by Hawking radiation generates theoretical lifetimes for your average black hole of many times the current age of the universe, so the presence of six of them indicates something funny must be going on.

What that funny business is, Penrose claims, is that we're seeing the ghosts of black holes that evaporated before the Big Bang that formed our universe.

In other words, in a previous universe.

"The Big Bang was not the beginning," Penrose said in an interview with Sarah Knapton in The Telegraph.  "There was something before the Big Bang and that something is what we will have in our future.  We have a universe that expands and expands, and all mass decays away, and in this crazy theory of mine, that remote future becomes the Big Bang of another aeon.  So our Big Bang began with something which was the remote future of a previous aeon."

So he's not talking about a spherical universe, collapsing in on itself; Penrose thinks that even if the universe is flat or hyperbolic, eventually random quantum fluctuations will generate an expansion that will start it all over again.  This may seem a little like the example my thermodynamics teacher used about random motion -- yes, it's possible that all the molecules in your cup of coffee will by chance jitter in the same direction at the same time, and your coffee will fountain up out of the cup.  He had us calculate the odds, though, and it turns out it's so remote that it's virtually certain it has never happened anywhere in the universe, during its entire thirteen-odd billion year existence.

But if you consider that a flat universe would have an essentially infinitely long time span, all it takes is the coffee to jitter in the right direction once, and you generate a new Big Bang.

Metaphorically speaking.

Whether Penrose is right about this remains to be seen, but it must be pointed out that he's had ideas before that have seemed "out there" and have turned out to be correct.  Martin Rees, Astronomer Royal and Fellow of Trinity College at the University of Cambridge and no faint light himself, said, "There would, I think, be a consensus that Penrose and Hawking are the two individuals who have done more than anyone else since Einstein to deepen our knowledge of gravity."

So I'm disinclined to shrug my shoulders at anything Penrose says, however odd it may sound.  And it brings me back to the hopes for an oscillating universe I first held when I was seventeen years old.  If Penrose is right, there was something that existed before our current universe, and likely something will exist afterward.  Even if those are in the impossibly remote past and future, it still seems preferable to the miserable demise of a standard flat or hyperbolic universe.

So the issue is far from settled.  Which is the way of science, after all.  Every problem you solve brings up two more new ones.  Meaning we should have enough to keep us occupied until the next Big Bang -- and maybe even beyond.

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Ripples in the cosmic pond

Springboarding off yesterday's post, about a mysterious flare-up of Sagittarius A* (the supermassive black hole at the center of the Milky Way galaxy), today we have an even more momentous discovery -- a background thrum of gravitational waves from supermassive black holes in orbit around each other.

Gravitational waves are created when massive objects accelerate through space.  They're actually pulsed fluctuations in the fabric of space-time that propagate out from the source at the speed of light.  The idea has been around for a long time; English mathematician Oliver Heaviside proposed them all the way back in 1893.  Once Einstein wrote his paradigm-overturning paper on relativity in 1915, Heaviside's proposal gained a solid theoretical underpinning.

The problem was detecting them.  They're tiny, especially at large distances from the source; and the converse difficulty is that if you were close enough to the source that they were obvious, they'd be big enough to tear you to shreds.  So observing from a distance is the only real option.

[Image licensed under the Creative Commons ESO/L. Calçada/M. Kornmesser, Artist’s impression of merging neutron stars, CC BY 4.0]

The result is that it took a hundred years to get direct evidence of their existence.  In 2015 the LIGO (Laser Interferometer Gravitational Wave Observatory) successfully detected the gravitational waves from the merger of two black holes.  The whirling cyclone of energy as they spun around their center of mass, then finally coalesced, caused the space around the detector to oscillate enough to trigger a shift in the interference pattern between two lasers.  The physicists had finally seen the fabric of space shudder for a moment -- and in 2017, the accomplishment won the Nobel Prize for Rainer Weiss, Kip Thorne, and Barry Barish.

Now, though, a new study at the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has found a whole different kind.  Instead of the sudden, violent, there-and-gone-again waves seen by LIGO, NANOGrav has found a background "hum" in the universe -- the stirring of spacetime because of the orbiting of supermassive black holes around each other.

The accomplishment is made even more astonishing when you find out how long the wavelengths of these waves are.  Frequency is inversely proportional to wavelength, so the "nanohertz" part of the name of the observatory might have given you a clue.  The gravitational waves detected by NANOGrav have wavelengths measured in light years.  So how in the hell do you detect a wave in which -- even traveling at the speed of light -- the trough of the wave doesn't hit you until a year after the crest?

The way they did it is as clever as it is amazing.  Just as you can see a pattern of waves if you look across the surface of a pond, the propagation of these gravitational waves should create a ripple in space that affects the path of any light that travels through them.  The scientists at NANOGrav measured the timing of the light from pulsars -- the spinning remnants of collapsed massive stars, that because of their immense mass and breakneck rotational speed flash on and off with clocklike precision.  And sure enough, as the waves passed, the contraction and expansion of the fabric of space in between caused the pulsars to seem to speed up and slow down, by exactly the amount predicted by the theory.

"The Earth is just bumping around on this sea of gravitational waves," said astrophysicist Maura McLaughlin, of West Virginia University, who was on the team that discovered the phenomenon.

It's a little overwhelming to think about, isn't it?  Millions of light years away, two enormous black holes are orbiting around a common center of gravity, and the ripples that creates in the cosmic pond flow outward at the speed of light, eventually getting here and jostling us.  Makes me feel very, very small.

Which, honestly, is not a bad thing.  It's always good to remember we're (very) tiny entities in a (very) large universe.  Maybe it'll help us not to take our day-to-day worries quite so seriously.

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