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Quantum Weirdness 107: Bell’s Inequality

Note:  I said in Quantum Weirdness 106 that I was done with this series for now.  There are two possibilities here.  Either my definition of “for now” is a very short time, or I have branched off into an alternate universe where the term “done for now” has no meaning.**  Then again, I could have branched off into an alternative universe where, instead of writing this post, I would be lying on a Mediterranean beach next to a super-model in a string bikini.   I wish.

**Okay, I might just have have lied.

“God does not play dice.”–Albert Einstein

“Quit telling god what to do.”–Niels Bohr

It’s complicated.  And this just about reaches the limit of my own understanding.

The whole point of Einstein’s comment is that he could not accept the random nature of the quantum world.  He could not accept that quanta of matter and energy, and all their itinerant properties, only exist as probabilities until we observe  them.  He felt that there must be hidden variables that gave them these properties whether anyone was watching or not.  “I’d like to think the moon is there whether I am looking or not,” he said.

He was wrong.  Well, I don’t know about the moon, as that invokes the infamous Schrödinger’s Cat problem and it’s obfuscation of the Copenhagen Interpretation.  But for those tiny little quantum bits of stuff, it seems as if he blew it.

It all boils down to two papers.  The first was a 1935 paper by Einstein, along with colleagues Nathan Rosen and Boris Podalsky that proposed a thought experiment to demonstrate that there are only two possible explanations for certain properties of quantum mechanics: either there are hidden variables governing the quantum world, or else, as Einstein called it “spooky action at a distance.”  This has become known as the EPR paradox.

The second was a 1964 paper by John S. Bell, proposing an equation and related experiment that could be used to determine which of the alternatives is correct.  This became known as Bell’s inequality.

The technology did not yet exist, though, to make the measurements required to determine the solution to Bell’s equation. That did not occur until Alain Aspect, et al, performed an experiment in 1981 that proved, finally, that Einstein was wrong: no hidden variables exist; it’s spooky action at a distance.  At least, that is,  until further notice.

A  fairly facile explanation of the concepts and history is available here (including a brief touching on their relationship to Schrödinger’s Cat) and some subsequent contrary opinions here.  Or for those who can’t (or prefer not to) read, see the video that follows.  Confused?  One of the greatest scientific minds of the 20th century, Richard Feynman, said that nobody understand quantum mechanics.  Boy, does that give me free rein to get crazy with conjecture #5: Quantum Solipsism.   There may actually be a universe where I finally write and post it.

Whew.

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Cosmic Quote #22

“I like physics, but I love cartoons.”–Stephen Hawking

Who knew Hawking had such a sense of humor.  No wonder he hasn’t won a Nobel Prize.  Remind me to introduce him to Stephan Pastis; they might like each other, as the strip below suggests.

This one reads like it was written for Hawking!

This one reads like it was written for Hawking! (click for full image)

(Previously published in my review of Pearls Before Swine. Cartoon ©2012 Stephan Pastis)

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Signature

@MarkSackler

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Cosmic Quote(s) #20

“The hardest thing to understand in the world is the income tax.”–Albert Einstein

“The income tax has made more liars out of Americans than golf”–Will Rogers

“Be wary of strong drink.  It can make you shoot at tax collectors…and miss.”–Robert Heinlein.

Hahaha.  I can laugh now.  It’s April 16.  It’s all over….except the crying.

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Cosmic Quote #18

“Quantum mechanics is magic.”–Daniel Greenberger.

Image credit: Matthias Giesen http://matthiasgiesen.wordpress.com/page/8/

Image credit: Matthias Giesen http://matthiasgiesen.wordpress.com

Quantum mechanics.  Niels Bohr said if you’re not shocked by it, you don’t understand it.  Richard Feynman said nobody understands it.  Albert Einstein said god does not play dice. Stephen Hawking said god does play dice and sometimes he hides the results.  I say who the hell cares, as long as they give me fodder for my blog.  Or my wife’s horse.  Or my accountant’s newt.  It all fills  space, thus proving the vacuum is not empty.  Isn’t physics fun?  [Note: vacuum is one of the few words in the English language containing “uu.”   But it’s not as cool as muumuu, duumvir or menstruum, proving that linguistics is fun, too.]

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Equations of Everyday Life#3: Media Attention Span (Part One: The Media–illogical Constant)

“It was my biggest blunder.”–Albert Einstein on his cosmological constant concept.

You have to love ‘ol Albert.  It’s not that he admitted he was wrong.  It’s that he turned out to be wrong about being wrong. In other words, the cosmological constant turned out not to be such a big blunder after all.  He thought that there must be a force in the universe that counteracts gravity and prevents a static universe from contracting on itself.  In 1917 he dubbed it the cosmological constant.  Then came Hubble’s discovery in the 1920’s that the universe is expanding, which was closely followed by the big bang theory (the actual theory, not the TV show), and out the window went Einstein’s constant.   But then, in 1998, it was discovered that the expansion of the universe is accelerating and–bingo!–the cosmological constant, now referred to as dark energy, was reborn.

So what the hell does this have to do with the current equation?  It’s also a constant, and it might turn out that it is as slippery and elusive as dark energy.  The difference though, is that this one describes contraction, not expansion; more specifically, the contraction of media attention over time as pertains to inane celebrity behavior.  I call it:

The Media-illogical Constant

If you’ve had any physics education, you’ve certainly heard of the inverse square law.  It applies to any number of physical properties, gravity, light, radio waves, sound or the attention level of undergraduates to a lecture in a large hall.  Simply stated, as one travels away from the source, the intensity of the force or signal decreases by the inverse of the distance squared.  A similar equation can describe the rate at which our tabloid-minded western media lose interest in stupid celebrity hijinks.  The equation is the same as the inverse square law with one modification:  just substitute time for distance.    Quite simply, it looks like this: 
inverse squareIn plain English:  the intensity of the media attention is proportionate to the inverse of the time since the story’s emergence to national (or international) attention, squared.  So when Lindsay Lohan gets arrested–yet again–the media attention four days after the story will be 1/16th of what it was when the story broke.  [Are you are wondering why this equation just doesn’t use an equal sign instead of a proportional to sign? It beats me.  But one immutable rule of these posts is to always use the coolest looking symbol possible.]
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There are, of course, caveats–aren’t there always?  This theoretical pronouncement exactly works, if, and only if, there is no significant obstruction or interference from other media events, whether or not they involve inane celebrities.  This is the same as applies to physical properties measured with the inverse square law.    Place a brick wall between the light source and your measuring device and all bets are off.  Likewise,  a bigger story may come along and completely drown out whatever Lady Gaga has been up to lately.   I have a name for this phenomenon and resulting calculations–pretty cheeky of me since I haven’t even invented it yet.  I call it The Big Bust Theory.   Depending on the stories involved, this may or may not be a double entendre.  Either way, part two of this post will deal with that equation.  It’s coming soon to a blogoshere near you.
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Timeout: Google This! (or, The Color of Stupidity)

“If there are no stupid questions, what questions do stupid people ask?”–Scott Adams

“We are all born ignorant, but one must work hard to remain stupid.”– Benjamin Franklin

Ben on stupidity

Good ol’ Ben knew stupidity when he saw it.

Nothing enables stupid, silly, naive, ridiculous or downright ignorant questions like internet search engines.  Judging by some of the search queries by which my blog has been found, I’m guessing that some of these people were either drunk in a bar, or reading too many ridiculous blogs.  Courtesy of WordPress.com’s excellent blog stats page, here are some of the best examples,  along with my appropriately astute responses.  (NOTE:  These are all verbatim from the aforementioned WordPress stats summary.  Somebody out there actually found my blog using these search queries.)

Where would we be if we traveled 777 billion light years?  I have no idea, but I’d hate to have to pick up the tab for the cab ride home.

Sixteen times four equals what?   Probably 42, if you are Douglas Adams

Let me explain infinity, it is a measure of a human power, which actually not compatible, .  for ex infinity is sir Albert Einstein…   I just report them; I don’t explain them.  But if you have any clue as to what planet the person who wrote this query is from, please inform us all.

Mark Sackler DVM  After 30 plus years of marriage to a veterinarian, I have apparently been awarded an honorary degree.  I certainly deserve some sort of award–or at least sympathy.

Barbayaki  Say what??!!  (According to the stats, this query has found my blog FOUR times.  As Casey Stengel said,  “you could look it up.”)

Why they add 1 millennium in 21st?  OK.  I give up.  Why?

Funny pro-conservative bumper stickers     See my post on non-existence. 

Millennium Twain NASA   You left out rutabaga.

Funny names for mark  What? “Mark” is not funny enough by itself?

Molenium conjectures  Hey, moles can have ideas, too.

Is there still a lawyer for Einstein?  I’m not sure, but I think there is a lawyer for everything–even non-existence.

Please feel free to share your responses to any of these nut-case inquiries,  and be sure to check back in a couple of months.  There are bound to be more where these came from… 😉

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“Women marry men hoping they will change. Men marry women hoping they will not. So each is inevitably disappointed.”– Albert Einstein

Copyright cartoonstock.com. Used by permission.

Hmmm.  Ol’ Albert may have known more about everyday life then he is commonly given credit for.  After 34-years, my wife still hasn’t learned this lesson.  She is still trying to change me.  I keep telling her to leave me alone as I am a finished product;  I couldn’t possibly get any worse.

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Conjecture #1: Infinity (Part 3)

I Conjecture:  The Concept of Infinity Could not Exist in a Finite Universe.

Part Three: Human Imagination

“Two things are infinite: the universe and human stupidity; and I’m not sure about the universe.”
Albert Einstein

It is certainly understandable how somebody as brilliant as Einstein could perceive the rest of us to be infinitely stupid.  Jokes about lawyers and politicians aside, I’m not sure about either.  I remain an agnostic on untestable scientific conjectures,  as well as on religion.  But my gut continues to tell me that my conjecture of infinity has merit, so I’ll proffer one final discussion before moving on to the next one.

Nothing is inherently more self-contradictory than infinity.  We can imagine it mathematically, but can’t measure it.  We can imagine–sort of–infinite time and space.  But physicists and philosophers tell us there are a finite number of possible combinations of matter and energy, at least in our observable universe with our laws of physics.  But we can imagine things beyond those laws (fantasies like Harry Potter, various science fiction scenarios,  and possibly real alternate universes with different laws of physics, to name just a few).  So our imagination does not seem to be limited by what is possible or observable in nature.  By that it would be reasonable to assume that human creativity and human stupidity are both potentially infinite.**

One of my favorite quotes about the universe is the famous J.B.S. Haldane proposition, “I suppose the universe is not only queerer (sic) then we imagine, it is queerer than we can imagine.”  This would seem to be a contradiction of the notion that human imagination is infinite.  David Deutsch says as much in The Beginning of Infinity, and he says so specifically in regard to this quote.  His point is that human imagination and creativity are potentially infinite and that Haldane is, therefore, wrong.  But where infinity is concerned, even Deutsch contradicts himself.  For as he points out elsewhere in the book,  there are mutually exclusive infinities and there are also larger and smaller infinities.  Consider the set of all even integers and the set of all odd integers.  They are mutually exclusive yet both infinite.  Now consider the set of all even integers and the set of all integers.  They are both infinite, yet the latter is twice as large as the former.  The point is: there might be both an infinity of things we can imagine, and an infinity of things we can’t imagine.   Deutsch himself indirectly alludes to this in his earlier book, The Fabric of Reality.

There is no question that the Haldane quote was true at least in the early part of the 20th century when he first espoused it.   The universe certainly turned out to be stranger than anyone could imagine at that time.  But the universe continues to surprise us, no matter what we imagine.  And if our imagination is only potentially infinite we cannot imagine, at any one time, everything that exists or the larger infinity that might exist.   To me, this is what makes the combination of human imagination with empirical knowledge so exciting.  No matter what we can test or what we can imagine, there are still surprises out there to delight and confound us.  But in my final analysis–the one that needs explanations and not just measurement–Einstein was absolutely right in another of his famous quotes:

“Imagination is more important than knowledge.”

Up next (after a few digressions and ridiculous timeouts): The conjecture of inevitability

**By potentially unlimited here, I mean no theoretical limit.  To be actually infinite, humanity would have to exist forever.

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