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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Lenses and rings

"Spacetime tells matter how to move; matter tells spacetime how to curve."

This rather mind-blowing statement by groundbreaking American physicist John Archibald Wheeler summarizes, in one sentence, Einstein's General Theory of Relativity.  The presence of matter warps the fabric of spacetime, and that curvature affects how objects are able to move through it.  In a sense, gravity isn't pulling on you right now; you're simply occupying a position in space where the mass of the Earth curves space so much that you're constrained to moving with it as it rotates on its axis.  The Earth itself traces an elliptical path around the Sun because the Sun's huge mass contorts the space around it; the Earth is following the shortest possible path through a spacetime that is itself curved.

If this is hard for you to picture, you're not alone.  It's easier if you reduce the dimensions by one, and picture a two-dimensional sheet deformed into a third spatial dimension by a heavy weight, like a bowling ball resting on a trampoline.  If you roll a marble toward it, it will follow the curvature of the surface -- not because the bowling ball is somehow attracting the marble, but because the sheet itself curves.

[Image licensed under the Creative Commons OpenStax University Physics, CNX UPhysics 13 07 spacecurve, CC BY 4.0]

So what this means is that gravity can affect even something that doesn't have mass -- like light.  Light takes the shortest possible path through the space it crosses, so the common-sense assumption is that this would be a straight line, consistent with the Euclidean geometry we all learned in high school.

The thing is, space isn't Euclidean.  Oh, it's close enough, on small scales and when you're not close to ginormously massive objects; the famed Greek mathematician did pretty well, given what information he had access to.  It's just that there are objects in the universe that are so massive that spacetime curves dramatically -- and light near them no longer travels in a straight line, but follows the curvature of the space it's passing through.  The effect is called gravitational lensing, because the light bends as if it were passing through a curved glass lens.

As you might expect, this distorts your view of whatever the light is coming from.  And the results can be nothing short of bizarre -- such as the image we just got to see this week from the Euclid Space Telescope of an "Einstein ring," where two massive astronomical objects are in perfect alignment with the Earth, so that the light from the farther one is bent as it passes around the nearer, creating a ghostly halo.

The ring is light coming from a single object which is directly behind the central bright galaxy; the mass of the galaxy has warped the space the light is passing through, stretching the background image into a circle [Image is in the Public Domain courtesy of NASA]

"An Einstein ring is an example of strong gravitational lensing," said Conor O'Riordan, of the Max Planck Institute for Astrophysics, who was lead author of the paper analyzing the ring, which was published in the journal Astronomy & Astrophysics.  "All strong lenses are special, because they're so rare, and they're incredibly useful scientifically.  This one is particularly special, because it's so close to Earth and the alignment makes it very beautiful."

"Close," of course, is a relative term.  The foreground galaxy, NGC 6505, is 590 million light years away; the background galaxy -- the one whose light has been distorted into a ring -- is 4.42 billion light years away.  But still, the fact that they've lined up so precisely that the lensing effect creates the image of a ring is pretty spectacular.

The coolest thing about this, though, is that it is a visible and tangible demonstration of a principle in physics that is kind of out there by anyone's estimation.  The results of the General Theory of Relativity -- phenomena like time dilation and Lorenz contraction -- are so bizarre that it's easy to say, "Oh, come on, that can't possibly be true."  (Never mind that even a relatively lightweight object like the Earth is massive enough that our GPS satellites have to adjust for relativistic effects -- or within a couple of days, our global positioning data would become so inaccurate as to be useless.)

But in this case, the effect is also strangely beautiful, isn't it?  It's hard to look at the photographs from Euclid and JWST and Hubble and not be overawed by how magnificent the universe is.  And the more we understand it -- like finding a glittering ring that falls right in line with Einstein's predictions -- the more astonishing it becomes.

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Bending the light

One of the coolest (and most misunderstood) parts of science is the use of models.

A model is an artificially-created system that acts like a part of nature that might be inaccessible, difficult, or prohibitively expensive to study.  A great many of the models used by scientists today are sophisticated computer simulations -- these are ubiquitous in climate science, for example -- but they can be a great deal simpler than that.  Two of my students' favorite lab activities were models.  One of them was a "build-a-plant" exercise that turned into a class-wide competition for who could create the most successful species.  The other was a striking simulation of disease transmission where we started with one person who was "sick" (each student had a test tube; all of them were half full of water, but one of them had an odorless, colorless chemical added to it).  During the exercise, the students contacted each other by combining the contents of their tubes.  In any encounter, if both started out "healthy," they stayed that way; if one was "sick," now they both were.  They were allowed to contact as many or as few people as they wanted, and were to keep a list of who they traded with, in order.  Afterwards, we did a chemical test on the contents of the tube to see whose tubes were contaminated, then used the list of trades to see if we could figure out who the index case was.

It never failed to be an eye-opener.  In only five minutes of trades, often half the class got "infected."  The model showed how fast diseases can spread -- even if people were only contacting two or three others, the contaminant spread like wildfire.

In any case, models are powerful tools in science, used to study a wide variety of natural phenomena.  And because of a friend and fellow science aficionado, I now know about a really fascinating one -- a characteristic of certain crystals that is being used as a model to study, of all things, black holes.

[Image licensed under the Creative Commons Ra'ike (de:Benutzer:Ra'ike), Chalcanthite-cured, CC BY-SA 3.0]

The research, which appeared last month in Physical Review A, hinges on the effects that a substance called a photonic crystal has on light.  (We met photonic crystals here only a few weeks ago -- in a brilliant piece of unrelated research regarding why some Roman-era glass has a metallic sheen.)  All crystals have, by definition, a regular, grid-like lattice of atoms, and as light passes through the lattice, it slows down.  This slowing effect happens with all transparent crystals; for example, it's what causes the refraction and internal reflection that make diamonds sparkle.  A researcher named Kyoko Kitamura, of Tohoku University, realized that if light could be made to slow down within a crystal, it should be possible to arrange the molecules in the lattice to force light to bend. 

Well, bending light is exactly what happens near a black hole.  So Kitamura and her team made the intuitive leap that this property could be used to study not only the crystal's interactions with light, but indirectly, to discover more about how light behaves near massive objects.

At this point, it's important to clarify that light is not gravitationally attracted to the immense mass of a black hole -- this is impossible, as photons are massless, so they are immune to the force of gravity (just as particles lacking electrical charge are immune to the electromagnetic force).  What the black hole does is warp the fabric of space, just as a bowling ball on a trampoline warps the membrane downward.  A marble rolling on the trampoline's surface is deflected toward the bowling ball not because the bowling ball is somehow magically attracting the marble, but because the marble is following the shortest path through the curved two-dimensional space it's sitting on.  Light is deflected near a black hole because it's traversing curved space -- in this case, a three-dimensional space that has been warped by the black hole's mass.

[Nota bene: it doesn't take something as massive as a black hole to curve space; you're sitting in curved space right now, warped by the mass of the Earth.  If you throw a ball, its path curves toward the ground for exactly the same reason.  That we are in warped space, subject to the laws of the General Theory of Relativity, is proven every time you use a GPS.  The measurements taken by GPS have to take into account that the ground is nearer to the center of gravity of the Earth than the satellites are, so the warp is higher down here, not only curving space but changing any time measurements (clocks run slower near large masses -- remember Interstellar?).  If GPS didn't take this into account, its estimates of positions would be inaccurate.]

In any case, the fact that photonic crystals can be engineered to interact with light the way a black hole would means we can study the effects of black holes on light without getting near one.  Which is a good thing, considering the difficulty of visiting one, as well as nastiness like event horizons and spaghettification to deal with.

So that's our cool scientific research of the day.  Studies like this always bring to mind the false perception that science is some kind of dry, pedantic exercise.  The reality is that science is one of the most deeply creative of endeavors.  The best science links up realms most of us would never have thought of connecting -- like using crystals to simulate the behavior of black holes.

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Stretching time

You know, I'm beginning to think that every time I want to write a piece about cosmology or physics, I should just write "Einstein wins again" and call it good.

One of my favorite science vloggers, theoretical physicist Sabine Hossenfelder, gives a wry nod to this every time Einstein's name comes up in her videos -- which is frequently -- giving a little sigh and a shake of the head, and saying "Yeah, that guy again."

Maybe we should just stop arguing with him.  [Image is in the Public Domain]

You may recall that a couple of weeks ago I did a post about a possible paradigm shift in cosmology that could account for the mysterious "dark energy," a property of spacetime that is causing the apparent runaway expansion of the universe.  While acknowledging that finding solid evidence for the contention is currently beyond our technical capabilities, I pointed out that it simultaneously does away with two of the most perplexing and persistent mysteries of physics -- dark energy, and the mismatch between the theoretical and experimentally-determined values of the cosmological constant.  (Calling it a "mismatch" is as ridiculous an understatement as you could get; the difference is about 120 degrees of magnitude, meaning the two values are off by a factor of 1 followed by 120 zeroes).

But this week a new study out of the University of Sydney has shown that another of Einstein's relativistic predictions about an expanding universe has been experimentally verified, so maybe -- to paraphrase Mark Twain -- rumors of the death of dark energy were great exaggerations.  A bizarre feature of the Theory of Relativity is time dilation, the fact that from the perspective of a stationary observer, the clock for a moving individual would appear to run more slowly.  This gives rise to the counterintuitive twin paradox, which I first ran into on Carl Sagan's Cosmos when I was in college.  If one of a pair of twins were to take off on a spaceship and travel for a year near the speed of light, then return to his starting point, he'd find that his twin would have aged greatly, while he only aged by a year.  To the traveler, his clocks seemed to run normally; but his stay-at-home brother would have experienced time running much faster.

As an aside -- this is the idea behind my favorite song by Queen, the poignant and heartbreaking "'39," the lyrics for which were penned by the band's lead guitarist, astrophysicist Brian May.  Give it a listen, and -- if you're like me -- have tissues handy.

In any case, the recent research looks at a weird feature of the effects of relativity on time.  The prediction is that the expansion of the universe should affect all the dimensions of spacetime -- and therefore, in the early universe, time should (from our perspective) seem to have been running more slowly.

And that's exactly what they found.  (Recall that when you're looking outward in space, you're looking backward in time.)  The trick was finding a "standard clock" -- some phenomenon whose rate is steady, predictable, and well-understood.  They used the fluctuations in emissions from quasars -- extremely distant, massive, and luminous proto-galaxies -- and found that, exactly as relativity predicts, the farther away they are (i.e. the further back in time you're looking), the more slowly these "standard clocks" are running.  The most distant ones are experiencing a flow of time that (from our perspective) is five times slower than our clocks run now.

"[E]arlier studies led people to question whether quasars are truly cosmological objects, or even if the idea of expanding space is correct," said study co-author Geraint Lewis.  "With these new data and analysis, however, we’ve been able to find the elusive tick of the quasars and they behave just as Einstein’s relativity predicts."

The bizarre thing, though, is the "from our perspective" part; just like the traveling twin, anyone back then would have thought their clocks were running just fine.  It's only when you compare different reference frames that things start getting odd.  So it's not that "our clocks are right and theirs were slow;" both of us, from our own vantage points, think time is running as usual.  Neither reference frame is right or wrong.  The passage of time is relative to your velocity with respect to another frame.

Apparently it's also relative to what the fabric of spacetime around you is doing.

I'm not well-versed enough in the intricacies of physics to know if this really is a death blow to the paradigm-shifting proposal of a flat, static universe I wrote about a couple of weeks ago, but at least to my layperson's understanding, it sure seems like it would be problematic.  So as far as the nature of dark energy and the problem of the cosmological constant mismatch, it's back to the drawing board.

Einstein wins again.

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Let's do the time warp

Dear Readers,

I will be taking a short break -- this will be my last post until Thursday, April 27.  Please keep suggesting topics, though!

See you when I return.

cheers,

Gordon

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I find it fascinating, and frequently a bit dismaying, the range that exists in what people consider "sufficient evidence."

There are us hardcore skeptics, who basically say, "Incontrovertible hard data, right in front of my face, and sometimes not even that."  It then runs the whole spectrum down to people who basically have the attitude, "if my mother's first cousin's sister-in-law's gardener's grandma says she remembers seeing it one time, that's good enough for me, especially if it confirms my preconceived beliefs."

I saw a good example of the latter a while back over at Mysterious Universe in an article by Brett Tingley entitled, "Researcher Discovers Time Warp Near Las Vegas."  Tingley, to his credit, treated the whole thing with a scornful attitude, which (when you hear the story) you'll see was fully warranted.

Turns out "noted paranormal researcher" Joshua Warren, whose name you might know from his television work (some of his finer achievements are Aliens on the Moon: The Truth Exposed!, Weird or What?, Inside the Church of Satan, Possessed Possessions, and -- I shit you not -- Inbred Rednecks), claims to have found a spot north of Vegas where he says that time is running slower than in the surrounding areas.

Okay, let me just state up front that I have a degree in physics.  I certainly wasn't God's gift to the physics department by any stretch, but I did complete my degree.  (I didn't graduate summa cum laude, or anything.  More persona non grata.  But still.)  I bring this up only to say that with all due modesty, I have more knowledge of physics than the average dude off the street.  And because of this, I know that because of Einstein's General Theory of Relativity, there are only two ways to get time to slow down locally; (1) go really really fast; or (2) get close to a powerful gravitational field, such as a black hole.  Even the Earth's gravitational field, huge as it seems to us, causes a time dilation effect so small that it took years simply for physicists to be able to measure it and confirm it exists.  (For reference; your clock here on the surface of the Earth ticks more slowly, compared to a satellite orbiting at 20,000 kilometers, by a factor of 1 in 10,000,000,000.  So being here on Earth is not exactly the answer to lengthening human lifespan.)

[Image licensed under the Creative Commons Kjordand, Treval, CC BY-SA 4.0]

So the whole story is pretty fishy right from the get-go.  But Warren thinks he's proved it.  Here's what he has to say:

At this spot, on June 18 of 2018, I actually measured for the first and only time, time itself slowing down for 20 microseconds.  The weird thing, the real holy grail here, was what we picked up with this brand-new piece of technology.  That signal is always supposed to travel at the same rate of time at any particular place.  The only way that could change is if a black hole approached Earth or something like that, which is never supposed to happen.

You could substitute "never supposed to happen" with "hasn't happened," or "almost certainly never will happen," or "we'd all be fucked sideways if it did happen."  Now, twenty microseconds may not seem like very much, but that kind of discrepancy is not only many orders of magnitude greater than any expected relativistic time dilation effect, it is also well within the range of what would be easily measurable by good scientific equipment.  (Cf. the previous example of the physicists measuring a one-part-in-ten-billion slowdown.)  In other words, if this were real, it not only would be bizarre that it hadn't already been discovered, it would be simple to confirm -- or refute.

But here's the kicker: Warren is basing his amazing, groundbreaking, "holy grail" discovery on...

... one measurement with one piece of equipment.

So my first question is: time ran slower as compared to what?

Of course, even the equipment itself sounds suspicious to me.  It's called a "DT Meter," and no, in this context, "DT" doesn't stand for "delirium tremens," although it might as well.  It's a "differential time meter," and here's how Brett Tingley describes it:

KVVU-TV in Las Vegas reports that Warren made the discovery using a gizmo called a DT Meter, or differential time rate mater.  Warren says the device was created by a Silicon Valley engineer named Ron Heath, who has no discernible presence on the internet.  The device apparently consists of a 100-foot cable with a sensor on one end.  The device sends a signal down the length of the cable and measures the time it takes to reach the other end; theoretically, the device can detect small perturbations or differences in the speed of time itself.

Now, I ask you, which is more likely: that (1) there's a spot in Nevada where time runs slowly, for no apparent reason, or (2) Warren and Heath's gizmo has a glitch?

Of course, that's not slowing down Warren one iota (as it were).  He says that the time warp he discovered is the explanation for all sorts of other things for which he also has no proof:

I think it’s really interesting when you consider that this site where we got this reading, showing this time anomaly, also happens to be one of the most popular UFO hotspots in the area.  The big question at this point is not whether or not we have these anomalies, but what’s causing them?  Is this something natural that gives us a window a gateway into another world or another level of reality?  Or is this the byproduct of some kind of weird technology, be it something secret and man-made or something that’s extraterrestrial?

So the "big question" is not whether the anomaly exists?  I think that's a pretty big question, myself.  But no, we're supposed not only to believe his time warp, but that his time warp explains UFO sightings, and is caused by gateways into another world, etc.

What's baffling is that there are lots of people who apparently find this line of... um... well, I can't call it reasoning... this line of baloney convincing.  Poking about on the interwebz for about ten minutes found lots of places this "discovery" has been posted, mostly by people claiming either that ha-ha, this proves those dumb old physicists are wrong about everything, or that there's clearly a coverup by the government to prevent us from finding out about it, and thank heaven for Joshua Warren bravely posting this online, or even that we should watch this spot closely because it's likely to be where the alien invasion of Earth starts.

All of which left me weeping quietly and smacking my forehead on the keyboard.

Anyhow.  Like I said, I'm glad Tingley scoffed at Warren's claim, because Warren is not even within hailing distance of what anyone with a background in science would find convincing.  It also made me feel marginally better that I'm not the only one scoffing.  But I'd better wrap this up, because for some odd reason I feel like I'm running short on time.

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The stubbornly persistent illusion

I was driving through Ithaca, New York a while back, and came to a stoplight, and the car in front of me had a bumper sticker that said, "Time is that without which everything would happen at once."

I laughed, but I kept thinking about it, because in one sentence it highlights one of the most persistent mysteries of physics: why we perceive a flow of time.  The problem is, just about all of the laws of physics, from quantum mechanics to the General Theory of Relativity, are time-reversible; they work equally well in forward as in reverse.  Put another way, most physical processes look the same both ways.  If I were to show you a short video clip of two billiard balls colliding on a pool table, then the same clip backwards, it would be hard to tell which was which.  The Laws of Conservation of Momentum and Conservation of Energy that describe the results of the collision work in either direction.

There are exceptions, though.  The Second Law of Thermodynamics is the most commonly-cited one: closed systems always increase in entropy.  It's why when I put sugar in my coffee in the morning and stir it, the sugar spreads through the whole cup.  If I were to give it one more stir and all the sugar molecules were to come back together as crystals and settle out on the bottom, I'd be mighty surprised.  I might even wonder if someone had spiked the sugar bowl with something other than sugar.

In fact, that's why I had to specify a "short clip" in the billiard ball example.  There is a time-irreversible aspect of such classical physics; as the balls roll across the table, they lose momentum, because a little of the kinetic energy of their motion leaks away as thermal energy due to friction with the surface.  When they collide, a little more is lost because of the sound of the balls striking each other, the (slight) physical deformation they undergo, and so on.  So if you had a sensitive enough camera, or a long enough clip, you could tell which was the forward and which the reverse clip, because the sum of the kinetic energies of the balls in the forward clip would be (slightly) greater before the collision than after it.

But I am hard-pressed to see why that creates a sense of the flow of time.  It can't be solely from our awareness of a movement toward disorder.  When there's an energy input, you can generate a decrease in entropy; it's what happens when a single-celled zygote develops into a complex embryo, for example.  There's nothing in the Second Law that prevents increasing complexity in an open system.  But we don't see those situations as somehow running in reverse; entropy increase by itself doesn't generate anything more than expected set of behaviors of certain systems.  How that could affect how time is perceived by our brains is beyond me.

The problem of time's arrow is one of long standing.  Einstein himself recognized the seeming paradox; he wrote, "The distinction between past, present, and future is only a stubbornly persistent illusion."  "Persistent" is an apt word; more than sixty years after the great man's death, there was an entire conference on the nature of time, which resolved very little but giving dozens of physicists the chance to defend their own views, and in the end convinced no one.

It was, you might say, a waste of time.  Whatever that means.

One of the most bizarre ideas about the nature of time is the one that comes out of the Special Theory of Relativity, and was the reason Einstein made the comment he did: the block universe.  I first ran into the block universe model not from Einstein but from physicist Brian Greene's phenomenal four-part documentary The Fabric of the Cosmos, and it goes something like this.  (I will append my usual caveat that despite my bachelor's degree in physics, I really am a layperson, and if any physicists read this and pick up any mistakes, I would very much appreciate it if they'd let me know so I can correct them.)

One of the most mind-bending things about the Special Theory is that it does away with simultaneity being a fixed, absolute, universal phenomenon.  If we observe two events happening at exactly the same time, our automatic assumption is that anyone else, anywhere in the universe, would also observe them as simultaneous.  Why would we not?  But the Special Theory shows conclusively that your perception of the order of events is dependent upon your frame of reference.  If two individuals are in different reference frames (i.e. moving at different velocities), and one sees the two events as simultaneous, the other will see them as sequential.  (The effect is tiny unless the difference in velocities is very large; that's why we don't experience this under ordinary circumstances.)

This means that past, present, and future depend on what frame of reference you're in.  Something that is in the future for me might be in the past for you.  This can be conceptualized by looking at space-time as being shaped like a loaf of bread; the long axis is time, the other two represent space.  (We've lost a dimension, but the analogy still works.)  The angle you are allowed to slice into the loaf is determined by your velocity; if you and two friends are moving at different velocities, your slice and theirs are cut at different angles.  Here's a picture of what happens -- to make it even more visualizable, all three spatial dimensions are reduced to one (the x axis) and the slice of time perceived moves along the other (the y axis).  A, B, and C are three events, and the question is -- what order do they occur in?

[Image licensed under the Creative Commons User:Acdx, Relativity of Simultaneity Animation, CC BY-SA 4.0]

As you can see, it depends.  If you are taking your own velocity as zero, all three seem to be simultaneous.  But change the velocity -- the velocities are shown at the bottom of the graph -- and the situation changes.  To an observer moving at a speed of thirty percent of the speed of light relative to you, the order is C -> B -> A.  At a speed of fifty percent of the speed of light in the other direction, the order is A -> B -> C.

So the tempting question -- who is right? what order did the events really occur in? -- is meaningless.

Probably unnecessarily, I'll add that this isn't just wild speculation.  The Special Theory of Relativity has been tested hundreds, probably thousands, of times, and has passed every test to a precision of as many decimal places as you want to calculate.  (A friend of mine says that the papers written about these continuing experiments should contain only one sentence: "Yay!  Einstein wins again!")  Not only has this been confirmed in the lab, the predictions of the Special Theory have a critical real-world application -- without the equations that lead directly to the block universe and the relativity of simultaneity, our GPS systems wouldn't work.  If you want accurate GPS, you have to accept that the universe has some seriously weird features.

So the fact that we remember the past and don't remember the future is still unexplained.  From the standpoint of physics, it seems like past, present, and future are all already there, fixed, trapped in the block like flies in amber.  Our sense of time flowing, however familiar, is the real mystery.

But I'd better wrap this up, because I'm running out of time.

Whatever that means.

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Tiny timepieces

One of the most mind-blowing revelations from science in the past two hundred years came out of a concept so simple that a sixth-grader could understand it.

You've all observed that the motion of objects is relative.  Picture a train with glass sides (only so you can see into it from outside).  The train is moving forward at 5 kilometers per hour, with an observer standing next to it watching it roll past.  At the same time, a guy is walking toward the back of the train, also at 5 kilometers per hour.

From the point-of-view of anyone on the train, the walking man is moving at 5 kilometers per hour.  But from the point-of-view of the stationary observer outside the train, it appears like the man on the train isn't moving -- he's just walking in place while the train slides out from under him.  This is what is meant by relative motion; the motion of an object is relative to the frame of reference you're in.  We don't observe the motion of the Earth because we're moving with it.  It, and us, appear to be motionless.  In the frame of reference of an astronaut poised above the plane of the Solar System, though, it would seem as if the Earth was a spinning ball soaring in an elliptical path around the Sun, carrying us along with it at breakneck speed.

With me so far?  Because here's the simple-to-state, crazy-hard-to-understand part:

Light doesn't do that.

No matter what reference frame you're in -- whether you're moving in the same direction as a beam of light, in the opposite direction, at whatever rate of speed you choose -- light always travels at the same speed, just shy of 300,000,000 meters per second.  (Nota bene: I'm referring to the speed of light in a vacuum.  Light does slow down when it passes through a transparent substance, and this has its own interesting consequences, but doesn't enter into our discussion here.)

It took the genius of Albert Einstein to figure out what this implied.  His conclusion was that if the speed of light isn't relative to your reference frame, something else must be.  And after cranking through some seriously challenging mathematics, he figured out that it wasn't one "something else," it was three: time, mass, and length.  If you travel near the speed of light, in the frame of reference of a motionless observer your clock would appear to run more slowly, your mass would appear greater, and your length appear shorter.  (Where it starts getting even more bizarre is that if you, the one moving near light speed, were to look at the observer, you'd think it was him whose watch was running slow, who had a greater mass, and who was flattened.  Each of you would observe what seem to be opposite, contradictory measurements... and you'd both be right.)

All of this stuff I've been described is called the Special Theory of Relativity.  But Einstein evidently decided, "Okay, that is just not weird enough," because he did another little thought experiment -- this one having to do with gravity.  Picture two people, both in sealed metal boxes.  One of them is sitting on the surface of the Earth (he, of course, doesn't know that).  The other is out in interstellar space, but is being towed along by a spacecraft at an acceleration of 9.8 meters per second (the acceleration due to gravity we experience here on the Earth's surface).  The two trapped people have a communication device allowing them to talk to each other.  They know that one is sitting on a planet's surface and the other is being pulled along by a spaceship, but neither knows which is which.  Is there anything they could do, any experiment they could perform, anything that would allow them to figure out who was on a planet and who was being accelerated mechanically?

Einstein concluded that the answer was no.  Being in a gravitational field is, for all intents and purposes, exactly the same as experiencing accelerated motion.  So his conclusion was that the relativistic effects I mentioned above -- time dilation, mass increase, and shortening of an object's length -- not only happen when you move fast, but when you're in a strong gravitational field.  If you've seen the movie Interstellar, you know all about this; the characters stuck on the planet near the powerful gravitational field of a black hole were slowed down from the standpoint of the rest of us.  They were there only a year by their own clocks, but to everyone back home on Earth, decades had passed.

Maybe you're thinking, "But isn't the Earth's gravitational field pretty strong?  Shouldn't we be experiencing this?"  The answer is that we do, but the Earth's gravity simply isn't strong enough that we notice.  If you travel fast -- say on a supersonic airline -- your clock does run slow as compared to the ones down here on Earth.  It's just that the difference is so minuscule that most clocks can't measure the difference.  Even if supersonic seems fast to us, it's nearly standing still compared to light; if you're traveling at Mach 1, the speed of sound, you're still moving at only at about one ten-thousandth of a percent of the speed of light.  The same is true for the gravitational effects; time passes more slowly for someone at the bottom of a mountain than it does for someone on top.  So on any ordinary scale, there are relativistic effects, they're just tiny.

[Image licensed under the Creative Commons Mysid, Spacetime lattice analogy, CC BY-SA 3.0]

But that's what brings the whole bizarre topic up today -- because our ability to measure those tiny, but very real, effects just took a quantum leap (*rimshot*) with the development of a technique for measuring the "clocks" experienced by a cluster of atoms only a millimeter long.  A stack of about 100,000 strontium atoms that had been cooled down to near absolute zero were tested to see what frequency of light would make their electrons jump to the next energy level -- something that has been measured to a ridiculous level of accuracy -- and it was found that the ones at the bottom of the stack (i.e. nearer to the Earth's surface) required a different frequency of light to jump than the ones at the top.  The difference was incredibly small -- about a hundredth of a quadrillionth of a percent -- but the kicker is that the discrepancy is exactly what Einstein's General Theory of Relativity predicts.

So Einstein wins again.  As always.  And if you're wondering, it means your feet are aging slightly more slowly than your head, assuming you spend as much time right-side-up as you do upside-down.  Oh, and your feet are heavier and flatter than your head is, but not enough to worry about.

All of this because of pondering whether light behaved like someone walking on a train, and if someone being towed by an accelerating spaceship could tell he wasn't just in an ordinary gravitational field.  It brings home the wonderful quote by physicist Albert Szent-Györgyi (himself a Nobel Prize winner) -- "Discovery consists of seeing what everyone has seen, and thinking what no one has thought."

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My dad once quipped about me that my two favorite kinds of food were "plenty" and "often."  He wasn't far wrong.  I not only have eclectic tastes, I love trying new things -- and surprising, considering my penchant for culinary adventure, have only rarely run across anything I truly did not like.

So the new book Gastro Obscura: A Food Adventurer's Guide by Cecily Wong and Dylan Thuras is right down my alley.  Wong and Thuras traveled to all seven continents to find the most interesting and unique foods each had to offer -- their discoveries included a Chilean beer that includes fog as an ingredient, a fish paste from Italy that is still being made the same way it was by the Romans two millennia ago, a Sardinian pasta so loved by the locals it's called "the threads of God," and a tea that is so rare it is only served in one tea house on the slopes of Mount Hua in China.

If you're a foodie -- or if, like me, you're not sophisticated enough for that appellation but just like to eat -- you should check out Gastro Obscura.  You'll gain a new appreciation for the diversity of cuisines the world has to offer, and might end up thinking differently about what you serve on your own table.

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

Loop-the-loop

Of all the bizarre and fascinating discoveries physicists have made in the last century and a half, I think the one that twists my brain the most is the effect massive objects have on the space around them.

I use the "twists" metaphor deliberately, because the concept -- commonly called "warped space" -- is that anything with mass deforms the space it's in.  You've probably heard the two-dimensional analogy, to a bowling ball sitting on a trampoline and stretching the fabric downward.  If you then roll a marble across the trampoline, it will follow a deflected path.  Not because the bowling ball is mysteriously attracting the marble; the marble is merely following the contours of the space it's traveling through.

Increase the number of dimensions by one, and you've got a basic idea of what this feature of the universe is like.  We live in a three-dimensional space warped into a fourth dimension, and something passing near a massive object (as with the trampoline analogy, the more massive the object, the greater the effect) will follow a curved path.  Possibly, if the "attractor" is big enough, curved into a closed loop -- like the Moon does around the Earth, and the Earth does around the Sun.

Where it gets even weirder is that the degree of deflection of the moving object is dependent on how fast it's going.  Again, the marble provides a good analogy; a fast-moving marble will not alter its trajectory from a straight line very much, while a slow-moving one might actually fall into the "gravity well" of the bowling ball.  The same is true here in three-dimensional space.  This is why there's such a thing as "escape velocity;" the velocity of an object has to be great enough to escape the curvature of the gravity well it's sitting in, and that velocity gets larger as the "attractor" becomes more massive.

With a black hole, the escape velocity is greater than the speed of light.  Put a different way, space around a black hole has been warped so greatly that nothing is moving fast enough to avoid falling in.  Once you get close enough to a black hole to experience that degree of space-time curvature (a point called the "event horizon"), there is no power in the universe that can stop you from falling all the way in and meeting a grim fate called (I kid you not) "spaghettification."

Which, unfortunately, is exactly what it sounds like.

Why this mind-warping topic comes up is because of a paper that appeared this week in Scientific Reports, describing research by Albert Sneppen, a student at the Niels Bohr Institute, looking at what would happen to light as it passed very near -- but not within -- the event horizon of a massive black hole.  Sneppen came up with a mathematical model showing that it creates an effect so bizarre and unmistakable that it is now being proposed as a way of detecting distant black holes.

Suppose between us and a distant galaxy is a large black hole.  The black hole (being black) is invisible; it can only be seen because of how it interacts with the matter and energy around it.  So the light from the galaxy has to pass near the black hole on its voyage to us.  The particles of light that stray too close follow the curvature of space right into the black hole, as you might expect.  The ones that get close, but not too close, are where things are interesting.

Recall that the Earth follows an elliptical path around the Sun because the Sun is warping space enough, and the Earth is moving slowly enough, that the Earth doesn't slingshot away from the Sun (fortunately for us) but remains "captured," following the shortest path through curvature of the space it's in.  So presumably there is a distance around a massive black hole that would have the same property vis-à-vis light; a distance where light speed is exactly right for it to follow the lines of the intensely curved space it's traveling through and describe a circular (or elliptical) path.

So light at that distance would become trapped, circling the black hole forever.  But what about light from the same distant galaxy that is just a leeeeeetle bit farther away?  And a leeeeetle farther than that?  What Sneppen showed is that this effect would cause the light rays from the galaxy passing progressively farther and farther away from the black hole to make a specific number of loops around the black hole before "escaping."  So of the photons of light from the galaxy that end up after that cosmic loop-the-loop heading our way, some (the ones the farthest away from the black hole to start with) would have circled the black hole only once, some twice, some three times, etc.

What this would do is create multiple images of the same galaxy, strung out in a line.

Check out the drawing by Sneppen's collaborator, Peter Laursen, showing the results of the effect:

So there you have it; this morning's reason to feel very, very small.  I don't know about you, but I think the human species can use a little humility these days,  We need to be reminded periodically that we are tiny beings in an enormous universe, one that is so bizarre that it boggles the mind.  Although I have to say it's impressive that we tiny insignificant beings have begun to understand and explain this bizarreness.  As astronomer Carl Sagan put it, "We are a way for the universe to know itself."

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I've loved Neil de Grasse Tyson's brilliant podcast StarTalk for some time.  Tyson's ability to take complex and abstruse theories from astrophysics and make them accessible to the layperson is legendary, as is his animation and sense of humor.

If you've enjoyed it as well, this week's Skeptophilia book-of-the-week is a must-read.  In Cosmic Queries: StarTalk's Guide to Who We Are, How We Got Here, and Where We're Going, Tyson teams up with science writer James Trefil to consider some of the deepest questions there are -- how life on Earth originated, whether it's likely there's life on other planets, whether any life that's out there might be expected to be intelligent, and what the study of physics tells us about the nature of matter, time, and energy.

Just released three months ago, Cosmic Queries will give you the absolute cutting edge of science -- where the questions stand right now.  In a fast-moving scientific world, where books that are five years old are often out-of-date, this fascinating analysis will catch you up to where the scientists stand today, and give you a vision into where we might be headed.  If you're a science aficionado, you need to read this book.

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

A twist in the fabric

I hope y'all will indulge me one more astronomical post, because just this week in the journal Science there was a very cool paper about an observational verification of the phenomenon of frame-dragging.

The whole thing depends on the the concept of "the fabric of space-time," something that got ripped so often on Star Trek that you'd swear the universe was made of cheap pantyhose.  To be fair, the idea isn't easy to wrap your brain around, something that becomes obvious when you hear some laypeople talking about the Big Bang.

I mean, I try to be tolerant, but if I hear one more person say, "It's a stupid idea -- that nothing exploded and became everything," I swear, I'm going to hurl a heavy object at 'em.

The problem hinges on trying to draw an analogy between the Big Bang (or in general, the expansion of the Universe) with a conventional explosion, where something blows up and spreads out into space that was already there.  With the Big Bang, it was space itself that was stretching -- if the idea of cosmic inflation turns out to be correct, at first it was at a rate that I can't even begin to comprehend -- so the matter in the Universe moved, and is still moving, not because something was physically pushing on it (as in the explosion of a stick of dynamite), but because the space it was embedded in was expanding.

(For what it's worth -- no, at this point we don't understand why this happened, what initiated it, or why the rate changed so suddenly after the "inflationary era" was over.  There is a lot still to figure out about this.  But one thing that's nearly certain is that it did happen, and the evidence still left behind of the Big Bang is incontrovertible.)

In any case, it's useful to change the comparison.  The Big Bang, and the expansion that followed, is much less like a conventional explosion than it is like blowing up a balloon.  Astronomer Edwin Hubble realized this when he first observed red shift, and found that everywhere he looked in the universe, objects seemed to be flying away from us -- the farther away, the faster they were moving.  It looked very much like we were the center of the Universe, the middle of the explosion, as if you were at the very point where a bomb exploded and were watching the bits and pieces rush away from you.

The truth, Hubble realized, was more subtle, but also way more interesting.  The fabric of space itself was stretching.  Picture a deflated balloon covered with dots.  You're a tiny person standing on one of the dots.  The balloon inflates -- and all the other dots appear to be rushing away from you.  But the weird thing is that it doesn't matter which dot you're standing on.  You could be on any dot, and still all the others would appear to be moving away, because the surface itself is expanding.  So an alien in a distant galaxy would also think everything was moving away from him, and he and Hubble would both be right.

There is no center of the Universe.  Or everywhere is the center.

Which amounts to the same thing.

So it's much more accurate, if you're trying to picture the whole thing, to think of space as being some kind of "stuff" capable of being deformed or stretched.

Which leads us to this week's mind-blowing discovery in astronomy.

One of the stranger predictions of the General Theory of Relativity -- and there's a lot of competition in that regard -- is that a massive spinning object would drag space-time along with it, twisting it out of shape in a phenomenon called Lense-Thirring frame dragging after the Austrian physicists who predicted it based on Einstein's theories, Josef Lense and Hans Thirring.  The problem is, like most of the phenomena associated with Relativity, the Lense-Thirring effect would only be observed in extreme conditions -- in this case a very high-mass object spinning really fast.

To give you an idea of what kind of extremes I'm talking about, here: with the Earth's mass and spin, the Lense-Thirring effect would cause an angular shift of about one degree every 100,000 years.

Not exactly something that jumps out at you.

[Image licensed under the Creative Commons ALMA (ESO/NAOJ/NRAO)/H. Kim et al., Celestial spiral with a twist, CC BY 4.0]

Now some scientists led by Vivek Venkatraman Krishnan of the Max Planck Institute have found a remarkable pair of stellar remnants that provide the perfect laboratory for observing frame-dragging -- a white dwarf/pulsar pair that go by the euphonious name PSR J1141-6545.  This is an ideal pairing to study because both the white dwarf and the pulsar are spinning, the white dwarf about once a minute and the pulsar 2.5 times per second.  Because the pulsar emits a lighthouse-like beam of electromagnetic radiation, this rotation makes it flicker on and off, and Conservation of Angular Momentum makes the flicker rate extremely constant -- in fact, the rotational period has been calculated to an accuracy of ten decimal places.

But the whirling of its companion star results in frame-dragging, so the pulsar's beam has developed a tilt as it got pulled through twisted space-time.  (Imagine a flexible object bending as it's dragged through water, and you have an idea of how to picture this.)  And careful observation of the pulsar's wobble has shown that the amount of tilt...

... is exactly what is predicted from the General Theory of Relativity.

So Einstein wins again.  Pretty impressive for a guy who once said to a friend struggling in a math class, "Do not worry too much about your difficulties in mathematics.  I can assure you that mine are still greater."

So that's our mindblowing science of the day.  Spinning stars, twisting space-time, and tilted pulsars.  I don't know how anyone can read about this stuff and not be both fascinated at how weird our universe is, and astonished that we've progressed to the point where we can understand at least a bit of it.  Here, several hundred quadrillion kilometers away, we've detected minuscule tilts in a whirling stellar remnant, and used it to support a theory that describes how matter and energy work throughout the Universe.

If that's not an impressive accomplishment, I don't know what is.

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The brilliant, iconoclastic physicist Richard Feynman was a larger-than-life character -- an intuitive and deep-thinking scientist, a prankster with an adolescent sense of humor, a world traveler, a wild-child with a reputation for womanizing.  His contributions to physics are too many to list, and he also made a name for himself as a suspect in the 1950s "Red Scare" despite his work the previous decade on the Manhattan Project.  In 1986 -- two years before his death at the age of 69 -- he was still shaking the world, demonstrating to the inquiry into the Challenger disaster that the whole thing could have happened because of an o-ring that shattered from cold winter temperatures.

James Gleick's Genius: The Life and Science of Richard Feynman gives a deep look at the man and the scientist, neither glossing over his faults nor denying his brilliance.  It's an excellent companion to Feynman's own autobiographical books Surely You're Joking, Mr. Feynman! and What Do You Care What Other People Think?  It's a wonderful retrospective of a fascinating person -- someone who truly lived his own words, "Nobody ever figures out what life is all about, and it doesn't matter.  Explore the world.  Nearly everything is really interesting if you go into it deeply enough."

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

Order of operations

I try not to write in Skeptophilia about topics I don't fully understand -- well, at least understand as fully as my brainpower and the available information allow.  But today I'm going to tell you about a recent paper in theoretical physics that blew my mind so completely that I had to write a post about it, even though saying "I don't completely comprehend this" is a serious understatement.

So here goes.  Just don't ask me to clarify further, because the most you'll get is the Canine Head-Tilt of Puzzlement.

The paper, which appeared last week in Nature Communications, is entitled "Bell's Theorem for Temporal Order," and was written by Magdalena Zych and Fabio Costa (of the University of Queensland), Igor Pikovski (of Harvard University), and Časlav Brukner (of the University of Vienna).  The issue the four physicists were looking at was the seeming paradox of the different way that time (specifically, temporal order) fits into general relativity and quantum theory.  In relativity, the flow of time depends on your relative speed and the distribution of mass near you; in general, the faster you're going, or the nearer you are to a massive object, the slower your clock runs.  Because reference frame is relative (thus the name of the entire theory), you don't notice this effect yourself -- to you, your clock runs just fine.  But to someone observing you at a distance, the flow of time in your frame of reference has become more sluggish.

Weird enough, but that's only the beginning.  To take the most familiar example, consider two astronauts in spacecraft zooming away from each other at a substantial fraction of the speed of light.  To astronaut A, his clock is running fine, and astronaut B's clock is slow (because he's moving away from A at a high speed).  But from B's perspective, it's A that's moving; so B thinks his own clock is accurate, and A's is the one that's running slow.

And it's not that one's right and the other is somehow being fooled.  Both of them are right -- because time is relative to your speed.

As an outcome of this (and germane to the paper I referenced), what this also means is that A and B can differ in what they perceive as the time order of two events.  Occurrences that appear simultaneous to one of the astronauts might appear sequential to the other.

With me so far?  Well, the problem that Zych et al. were investigating was that in quantum theory, there's no allowance for relativistic ordering of events.  Time's arrow is one-directional, and if event X followed Y in one reference frame, it would do so on all reference frames.

Well, that's what the physicists thought -- until this paper showed a theoretical framework that suggests otherwise.

Zych et al. proposed a thought experiment involving two spaceships, one of which is near a massive object (which, as I mentioned, warps spacetime in such a way as to slow down the passage of time).  They're engaged in a war game that requires them to fire their phasers simultaneously and immediately afterward start their engine so as to dodge the blast.  The problem is, the ship near the massive object will have a slower clock, and will not be able to fire quickly enough to escape being blasted by the other ship.

So far, weird but not that hard to understand.  What Zych et al. did was to ask a single question: what if the two ships were in a state of quantum superposition before they fired?

Superposition is one of the weirdest outcomes of quantum physics, but it's been demonstrated experimentally so many times that we have no choice but to accept that this is how the universe works.  The idea is that if a physical system could exist in two or more possible states, its actual state is an array of possibilities all existing at the same time until some measurement destroys the superposition and drops the system into one of the possible outcomes ("collapsing the wave function").  The most famous iteration of this is Schrödinger's Cat, who is both alive and dead until the box is opened.

In the case of the ships, the superposition results in quantum entanglement, where the entire system acts as a single entity (in a causal sense).  Here's how the result is described in a press release from the University of Vienna:

If a powerful agent could place a sufficiently massive object, say a planet, closer to one ship it would slow down its counting of time.  As a result, the ship farther away from the mass will fire too early for the first one to escape. 

The laws of quantum physics and gravity predict that by manipulating a quantum superposition state of the planet, the ships can end up in a superposition of either of them being destroyed...  The new work shows that the temporal order among events can exhibit superposition and entanglement – genuinely quantum features of particular importance for testing quantum theory against alternatives.

So each of the ships is in a state of both being destroyed and not being destroyed, from the standpoint of an outside observer -- until a measurement is made, which forces the system into one or the other outcome.

Note what this isn't saying; it's not implying that one of the ships was destroyed, and we simply don't know which yet.  It's implying that both ships are in an entangled state of being blasted to smithereens and not.

At the same time.

The authors write:

This entanglement enables accomplishing a task, violation of a Bell inequality, that is impossible under local classical temporal order; it means that temporal order cannot be described by any pre-defined local variables.  A classical notion of a causal structure is therefore untenable in any framework compatible with the basic principles of quantum mechanics and classical general relativity.

All of which leaves me sympathizing a great deal with Winnie-the Pooh.

So there you have it.  It turns out that the universe is a weird, weird place, where our common-sensical notions of how things work are often simply wrong.  Even though I'm far from an expert -- I run into the wall pretty fast when I try to read actual papers in physics, or (for that matter) in most scientific fields -- I find it fascinating to get a glimpse of the actual workings of the cosmos.

Even if it blows my tiny little mind.

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This week's Skeptophilia book recommendation is a must-read for anyone interested in astronomy -- Finding Our Place in the Universe by French astrophysicist Hélène Courtois.  Courtois gives us a thrilling tour of the universe on the largest scales, particularly Laniakea, the galactic supercluster to which the Milky Way belongs, and the vast and completely empty void between Laniakea and the next supercluster.  (These voids are so empty that if the Earth were at the middle of one, there would be no astronomical objects near enough or bright enough to see without a powerful telescope, and the night sky would be completely dark.)

Courtois's book is eye-opening and engaging, and (as it was just published this year) brings the reader up to date with the latest information from astronomy.  And it will give you new appreciation when you look up at night -- and realize how little of the universe you're actually seeing.

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