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Posts Tagged ‘many-worlds’

WARNING: Spoilers abound!

Do not read further if you haven’t seen the wonderful, awesome The Lego Movie!

There are two kinds of good movies.  The first kind is a movie you enjoy while watching; you appreciate the acting, the writing, the set design.  You come out of the theater thinking, that was good.  I’d recommend that.  In the past six months, I’ve seen many of these so-called Good Movies of the 1st Kind.  Examples include The Dallas Buyer’s Club, Rush, Captain Phillips, the second Hobbit movie, and the second Hunger Games movie.  I liked them all.

Emmet_Minifig

A metaphor for the everyman

But then there is a Good Movie of the 2nd Kind—a movie which leaves you jacked up on adrenaline, with a big goofy smile on your face, and ideas buzzing around the inside of your head.  A movie where you come out of the theater thinking, when am I going to go see that again?  I need to see that again.  What just happened?

Don’t get me wrong; a GM2ndK is not necessarily a happy, fun movie.  Saving Private Ryan was for me a GM2ndK; for weeks I could not get the first half hour (Omaha Beach) out of my head.  Schindler’s List was also a GM2ndK.  So was A Clockwork Orange, and Magnolia, and Paths of Glory.

So, too, The Lego Movie.

Unless you’ve seen the movie, you won’t believe it.  You won’t have the context, the conceptual framework, the raw materials from which to grasp the idea: that The Lego Movie is as profound and philosophical as any movie you’ve (probably) ever seen.

Oh sure, the movie is beautiful to look at.  The animation is unique and charmingly quantized and pixilated.  The pace is frenetic, action packed.  The worlds depicted are stunning, goofy and marvelous.  The jokes are non-stop: I laughed out loud two or three times a minute for 100 straight minutes.

So, I liked the movie.  But this post wasn’t meant to be a movie review.

My broader point is that the movie resonated with me, personally, philosophically, because it so closely matches my own world view.

SPOILERS!  PROCEED NO FURTHER, YE WHO HAVEN’T WATCHED!

The message of the movie is that there are two (seemingly) diametrically opposed ways of playing with Legos.  In the first camp are the conformists, who follow instructions to the letter, never have an original thought, and prefer a world of rigidity and order.  The head conformist is Lord Business, who wants to spray Krazy Glue on every Lego in the universe so that nothing ever changes.

To me, Lord Business represents the Abrahamic God, the God of the Old Testament.  The God of one single, rigid construction, exactly the way He designed it.  Don’t go against God’s plan (or the plan of Lord Business).  There is only one way the world (or worlds) can be, and if you oppose that plan—if you don’t follow the instructions—then you have committed heresy.  You will be melted.  There’s no place for you in such a conformist world.

Cmf_business

The God of Abraham

The other way of playing with Legos is the way children play with them: with unbridled imagination.  Sure, you can buy a Millennium Falcon Lego set and construct it as the instructions describe.  But you can ignore the instructions, too, and your play is just as valid.  Want to put Batman on the Millennium Falcon?  Sure; go for it.  Want to have Superman and Gandalf team up to battle a robot pirate?  Why not?  If you can imagine it, then you can do it, just as long as some adult doesn’t come down and spray the pieces with glue.

That’s what organized religion does: it sprays us with glue.

To me the world of organized religion is limiting, stifling.  The idea that there’s an omnipotent being that controls every aspect of everything is not comforting to me; it is horrifying.  Theologians mumble about free will and wave their hands reassuringly, but what good is free will if you’re still constricted by God’s plan?  If God has everything worked out, then you’re stuck to the world with Krazy Glue; your life is supposed to be lived in a single way and you’ll never be able to ignore the instructions.  You’ll never get to ride Unikitty into Middle Zealand and have tea with the Green Lantern.  Sorry, but you’re an average, run-of-the-mill Lego piece and that’s all you’ll ever be.

But imagine: suppose that there are an infinite number of universes, each with its own parameters, its own structure.  In such a multiverse, anything you can imagine is true.  There are still rules (each universe obeys its own laws of physics, just as Legos cannot escape their own block-like, quantized nature) but beyond those rules, anything goes.  And imagine there is no Lord Business that commands you to think in a certain way.  Imagine if you had the freedom to do as you will.

Here’s a table, to make the metaphor(s) more explicit:

In the movie… …is a metaphor for
A Lego person a human
The Lego world you’re in the universe you’re in
All of the possible Lego Worlds the multiverse
Quantized nature of Lego blocks the laws of physics
Krazy Glue God’s plan
Lord Builder (the Father) a rigid conformist deity
The Child the deity that any of us could be, using imagination
Instructions Rigid moral codes
“Everything is awesome” “Everything is awesome”

We are indeed trapped in the universe that we find ourselves in (we can’t get away from our quantized nature, alas) but we can at least imagine the other worlds, and dream, and find inspiration from them.  We can live our lives the way we like.  This isn’t anarchy; it’s freedom.  This world view doesn’t preclude morality; we shouldn’t put our hands into other people’s Lego Worlds, and mess the pieces up, and break their Lego constructions.  But we should be able to look at other people’s constructions, and value them, even love them.  If you want to have Batman marry Han Solo, and have them ride off into the Old West sunset (riding on Unikitty, no doubt) then I shouldn’t judge.  There is no Lord Business.  There is only what you can build, and what I can build, and what you can imagine, and what I can imagine.  We should not judge each other but embrace each other’s constructions.  Everyone’s trapped by the laws of physics, but no one’s trapped in their own minds; there are no laws that can ever force our imaginations to conform.

If God exists, then he’s a child, and wants us to play in all the worlds, and be free.  He wouldn’t even own a tube of Krazy Glue.

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When I was young, I once looked at a box of cereal and had an epiphany.  “Why is that cereal there?”  A universe of unfathomable complexity, with 100,000,000,000 galaxies, each with 100,000,000,000 stars, making 10,000,000,000,000,000,000,000 possible solar systems with planets around them—all that, and I’m sitting across from a box of Vanilly Crunch?

Vanilly

Since that existential crisis, I’ve always wondered why there was something instead of nothing.  Why isn’t the universe just one big empty set?  “Emptiness” and “nothingness” have always seemed so perfect to me, so symmetric, that our very existence seems at once both arbitrary and ugly.  And no theologian or philosopher ever gave me an answer I thought was satisfying.  For a while, I thought physicists were on the right track: Hawking and Mlodinow, for example, in The Grand Design, describe how universes can spontaneously appear (from nothing) according to the laws of quantum mechanics.

I have no problem with quantum mechanics: it is arguably the most successful theory devised by mankind.  And I agree that particles can spontaneously create themselves out of a vacuum.  But here’s where I think Hawking and Mlodinow are wrong: the rules of physics themselves do not constitute “nothing”.  The rules are something.  “Nothing” to me implies no space, no time, no Platonic forms, no rules, no physics, no quantum mechanics, no cereal at my breakfast table.  Why isn’t the universe like that?  And if the universe were like that, how could our current universe create itself without any rules for creation?

But wait—don’t look so smug, theologians.  Saying that an omnipotent God created the universe doesn’t help in any way.  That just passes the buck; shifts the stack by one.  For even if you could prove to me that a God existed, I would still feel a sense of existential befuddlement.  Why does God herself exist?  Nothingness still seems more plausible.

Heidegger called “why is there anything?” the fundamental question of philosophy.  Being a physicist, and consequently being full of confidence and hubris, I set out to answer the question myself.  I’d love to blog my conclusions, but the argument runs about 50,000 words…longer than The Great Gatsby.  Luckily for you, however, my book Why Is There Anything? is now available for the Kindle on Amazon.com:

rave book

You can download the book here.

You might wonder if my belief in the many-worlds interpretation (MWI) of quantum mechanics affected my thinking on this matter.  Well, the opposite is true.  In my journey to answer the question “why is there anything?” I became convinced of MWI, in part because of the ability of MWI to partially answer the ultimate question.  My book Why Is There Anything? is a sort of chronicle of my intellectual journey, one that I hope you will find entertaining, enlightening, and challenging.

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There is a principle in physics which says that, essentially, if two things are entirely indistinguishable, then you might as well call them the same thing.  There is even a branch of statistics (Bose-Einstein statistics) which is based on this principle.

Now, the meaning of the word “indistinguishable” has a very specific meaning in this context.  In physics, two things are indistinguishable if they cannot be distinguished no matter what anyone does.  That is, they cannot be told apart even in principle.  If there is a way to tell two things apart, then “regular” statistics holds; but if they truly are indistinguishable then they obey the much less intuitive Bose-Einstein statistics mentioned previously.

(As an aside, and entirely as a speculative exercise, one could argue that the existence of particles which clearly do obey Bose-Einstein statistics means that either (1) there is no God, or (2) there are things that even God cannot do—such as distinguish such particles—because if God could distinguish them then why do they obey Bose-Einstein statistics in the first place?  But that sounds like an idea for a later blog post…)

As an example, suppose a photon is absorbed by an atom, and the atom subsequently emits another photon of the exact same frequency and polarization.  One could say that a photon was absorbed and then the same photon was re-emitted; or one could say that a photon was absorbed (and destroyed) and then a completely different but identical photon was emitted.  The principle of identical particles says that these two cases are equivalent.  Neither one is right, or wrong.  Whichever you choose to believe is a matter of taste.  There is no experiment that even God could do that would tell you which was “right” and which was “wrong”, so why worry about it?  They represent the same thing.

Suppose two identical particles interact.  Initially they are traveling South and East, respectively, and interact at the origin:

collision 1

We can’t see what “actually” happens at the origin.  After the collision they are traveling South and East again.  If that’s all you know, and all you could know, then which of the following cases is correct?

Case 1.  They passed right through each other without actually interacting:

collision 2

Case 2.  They each turned 90° and switched roles, so to speak:

collision 3

A physicist would say that these are identical situations, as long as no one, not even God, is allowed to look under the veil.  And the distinction isn’t just semantic: if the particles are distinguishable, and these two cases really do represent two distinct physical possibilities, then the statistics of what we observe in such situations will be different.

Now, what in the world does this have to do with philosophy?

I’ve often felt that philosophy could stand to have a similar principle.  Well, fine, let’s just do it.  Let’s just make the following hypothesis:

If two things are indistinguishable even in principle, then they are the same.

Now I’d like to apply this principle to what I call the “Next morning” paradox but which is virtually identical to the Swampman paradox of Donald Davidson.  Suppose I go to sleep tonight and enter a deep sleep (so that I am not even dreaming).  And suppose that during this time of unconsciousness my body spontaneously disintegrates, and just happens to be replaced with an identical one: identical in every way, including the position of every molecule.  (Of course, you might try to cite Heisenberg here and say you could never make a body exactly like a previous one, because there’s always some uncertainty in position and/or momentum.  But, as in the original Swampman example, we assume that luck prevails: just by random chance the atoms are all found in the same way.)  This new version of “me” wakes up, lives his life, and no one (not even the new me) has any idea that anything has transpired.

Davidson and others contend that the new me is not “me” at all, even though no one could tell the difference.  They say that there is some intangible spark that can never be quantified that somehow still distinguishes yesterday’s me and today’s me.  That is, the difference between the two me’s is magic.  I find this ludicrous.

Any being that has all of your physical properties, and more importantly, all of your mental properties and memories, is you.  This may bother some, because it implies that more than one “me” can exist simultaneously; after all, we could make an exact replica of me and leave the old me intact.  Well, who cares?  As a many worlds adherent, I guess it’s not surprising I wouldn’t be bothered by such a scenario at all.

I find these ideas so obvious that it’s almost difficult for me to convey the ideas without screaming internally.  The principle has its beginnings in physics, but I find it applicable here: if x and y are indistinguishable even in principle, then x = y.  End of story.  I frankly have no idea why anyone takes Davidson’s ideas seriously anymore.

Think of it this way:  suppose you knew you were going to be killed, but that an exact replica of you would be put in your place, and have all your memories, and live your life.  On a visceral level, you’d probably be upset: “you” would live on, but it wouldn’t really be “you”.  This is the developmental stage that Davidson is stuck in.

My response: that scenario might have happened last night.  You might actually have died, and been replaced.  No big deal, right?  In fact, it might be true that everyone dies, every single night, and is always replaced by a perfect simulacrum.  The important point is that you could never know.  No one would know.  The universe would appear exactly the same.  We might as well take these two cases (that we are replaced, or that we are not) as being operationally identical.  For all intents and purposes, you can assume that every night you die, and that in the morning a different version of you is created with the same memories, that will act exactly as you would have acted.  Because this way of looking at things is really identical to the way we normally perceive reality, there can be no harm in thinking this way.  In fact, thinking this way may very well lead to insights and attitudes that you wouldn’t have had before.

comic2-597

I find this idea strangely liberating.  Each “me”, every day, can be thought of as a different person, related to me, and sharing some of my qualities, but separated both by time and space.  And we’ve come now to the final point of this post: how I learned to stop procrastinating.  For when you think of future selves as being entirely different people (which, in some sense, they are) then you can start thinking about doing favors for your future selves.

I don’t want to clean the kitchen now.  I could procrastinate.  However, to do so would be doing a disservice to “future me.”  Why not clean the kitchen today, and do a favor to my future self?  It’s no different than doing the dishes as a favor to your spouse, or mowing a lawn as a favor to a friend.  Your future self will appreciate it, and be grateful for your thoughtfulness.

For, if you’re a nice person, and enjoy helping others, why not put your future self in that category?  Treat your future self as a fully formed, thinking, rational person, with thoughts and feelings and aspirations and concerns.  It’s easier to do this if you actually think of a future self as a different person entirely.  Then, it will be easier to do a favor for this person, be nice to them, care for them, sacrifice for them.  When seen in this light, procrastination is just a form of selfishness.  Would you get drunk if you knew someone else, a random person somewhere, would have a terrible hangover because of your actions?  I’d hope that most people would not.  And yet, “Saturday morning you” is a person, just like “Friday night you” is.  So why be so selfish?  Why have that tequila?

I am not trained as a philosopher, although I have published works on the philosophy of quantum mechanics.  Nevertheless, I don’t think philosophy is the exclusive playground of those with philosophy PhD’s.  As this example shows, something as abstract as Bose-Einstein statistics can inform “traditional” philosophical questions such as the existence of God, the mind/brain problem, and philosophical zombies.  My intent here is to get people thinking, discussing, evaluating.  Science and philosophy are not enemies.  They’re frenemies.  Let’s hope they continue to play together in the sandbox.

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An Oulipo story

A friend of mine recently made the following challenge: can you start a story with one sentence, and logically end with another sentence?  The sentences were:

(1)   The washing machine repairman grunted.

(2)   The archbishop vowed never to eat figs again.

In the spirit of Oulipo (Ouvroir de littérature potentielle) I present my efforts here.  Don’t forget : if you’re a many-worlds adherent, then this is a true story.

bendix

The 1938 Bendix washing machine

The Foundation that Saves

The washing machine repairman grunted.  “I don’t know as you remember as much of the Bible as you think, your Excellency.”  He wiped his hands on his boilersuit.

“You may be right.  But still—can the Bendix be saved?”

“Well sir, that’s what I was referrin’ to.  Saving.  This here contraption, it wobbles a great bit, drifts, if you will.  So if’n you need it to stop walkin’ across the floor, well sir, it needs a foundation, like.”  His eyes glittered.

Lang nodded.  “I get your reference now.  You said the machine couldn’t be shaken by the steam if it were founded upon a rock.  That’s what, Luke Chapter 6?”

“Just so, your Excellency.  When the steam from the intake beats vehemently, well sir, the pantry here gets a might flooded, with all your Canterbury particulars and vestments getting wet and so forth.  ‘less of course we was to bolt the ol’ Bendix to the floor so as it didn’t walk.  And so I thought of my Sunday canon, sir, and heard my ol’ rector saying clear as a bell: ‘He is like a man which built an house, and digged deep, and laid the foundation on a rock: and when the flood arose, the stream beat vehemently upon that house, and could not shake it: for it was founded upon a rock’.”

“I am impressed.”

“As long as you ain’t impressed by no rock, sir, then we’re good, sir, if you get my meaning.”

Lang smiled.  “You have a deep knowledge of scripture, for—”

“You can say it, Excellency.  For a handyman.  My mum raised me proper, in the ecclesia anglicana if you will, sir.”

“And you were saying, I don’t remember as much of the Bible as I might think I do.”

Mr. Suttles stood up, cracking his knuckles and turning to face Archbishop Cosmo Lang.  “Well, you was talkin’ about the Lady’s feast upstairs, the bounty, how it was ‘a land of wheat, and barley, and vines, and fig trees, and pomegranates; a land of olive oil, and honey’.”

“Deuteronomy 8:8.”

“But our Lord Jesus didn’t go in for any figs, you understand, despite what the Old Testament might say.”

The archbishop smiled.  “You refer to Mark Chapter 11.  When our Lord comes across the fig tree, and finds it barren—”

“Yes, sir.  With all respect, Excellency, Jesus forbade us to eat figs ever again, and I for one don’t want to disobey.”

“Well, it was a parable, son.  The point was that—”

“Plus, them figs that grow on Dr. Speelman’s farm, well sir, they’re infested.  Wasps, you know.  They lay their eggs in the figs, and them larvae hatch inside, and eat up the seeds, sir, and get right fat and happy.  You ever bite into a fig, sir, and feel that crunchy, gritty texture?  Like them little globules that get stuck in your teeth, kinda soft yet kinda firm at the same time?  They as get stuck like that, are wasp eggs.  I kid you not, Excellency.  Jesus knew what he was talking about.  He didn’t want to eat no wasp eggs, and didn’t want his disciples eating no wasp eggs, neither.  That’s one foundation I can get behind.  So forget about no land of bounty with wheat and honey and figs.  Stay away from those larvae.”

The archbishop vowed never to eat figs again.

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2012 in review

The WordPress.com stats helper monkeys prepared a 2012 annual report for this blog.

Here’s an excerpt:

The new Boeing 787 Dreamliner can carry about 250 passengers. This blog was viewed about 1,700 times in 2012. If it were a Dreamliner, it would take about 7 trips to carry that many people.

Click here to see the complete report.

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Comix 3

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mcfly

“I am your probability density”

In an earlier post I discussed my philosophy of teaching special relativity.  My main idea was that physics professors should keep the “weird stuff” at bay, and start with non-controversial statements; once students are on board, you can push under the grass and show them the seething Lynchian bugs beneath.

Well, what about quantum mechanics?  Does the same philosophy apply?

My answer is yes, of course.  Don’t start with Schrödinger’s cat.  Don’t mention the Heisenberg uncertainty principle, or wave collapse, or the EPR experiment, or Bell’s theorem, or the double slit experiment, or quantum teleportation, or many worlds, or Einstein’s dice.  Start with the problems of physics, circa 1900, and how those problems were gradually solved.  In working out how physicists were gradually led to quantum mechanics, students will build up the same mental framework for understanding quantum mechanics.  At least, that’s how it works in theory.

Now, my perspective is from the point of view of a professor who teaches only undergraduates.  I only get to teach quantum mechanics once a year: in a course called Modern Physics, which is sort of a survey course of 20th century physics.  (If I were to teach quantum mechanics to graduate students, my approach would be different; I’d probably start with linear algebra and the eigenvalue problem, but that’s a post for another day.)  As it is, my approach is historical, and it seems to work just fine.  I talk about the evidence for quantized matter (i.e. atoms), such as Dalton’s law of multiple proportions, Faraday’s demonstration in 1833 that charge is quantized, Thomson’s experiment, Millikan’s experiment, and so on.  Then I explain the ultraviolet catastrophe, show how Planck was able to “fix” the problem by quantizing energy, and how Einstein “solved” the problematic photoelectric effect with a Planckian argument.  Next is the Compton effect, then the Bohr model and an explanation of the Balmer rule for hydrogen spectra…

We’re not doing quantum mechanics yet.  We’re just setting the stage; teaching the student all the physics that a physicist would know up until, say, 1925.  The big breakthrough from about 1825-1925 is that things are quantized.  Things come in lumps.  Matter is quantized.  Energy is quantized.

The big breakthrough of 1925-1935 is, strangely, the opposite: things are waves.  Matter is waves.  Energy is waves.  Everything is a wave.

So then, quantum mechanics.  You should explain what a wave is (something that is periodic in both space and time, simultaneously).  Here, you will need to teach a little math: partial derivatives, dispersion relations, etc.  And then comes the most important step of all: you will show what happens when two (classical!) wave functions are “averaged”:

ψ1 = cos(k1x – ω1t)

ψ2 = cos(k2x – ω2t)

Ψ(x,t) = (1/2) cos(k1x – ω1t)  + (1/2) cos(k2x – ω2t)

Ψ(x,t) = cos(Δk·x – Δω·t) · cos(k·x – ω·t)

where Δk ≡ (k1 – k2)/2, k ≡ (k1 + k2)/2, etc.

[Here I have skipped some simple algebra.]

This entirely classical result is crucial to understanding quantum mechanics. In words, I would say this: “Real-life waves are usually combinations of waves of different frequencies or wavelengths.  But such ‘combination waves’ can be written simply as the product of two wave functions: one which represents ‘large-scale’ or global oscillations (i.e. cos(Δk·x – Δω·t)) and one which represents ‘small-scale’ or local oscillations (i.e. cos(k·x – ω·t)).

This way of looking at wave functions (remember, we haven’t introduced Schrödinger’s equation yet, nor should we!) makes it much easier to introduce the concept of group velocity vs. phase velocity: group velocity is just the speed of the large-scale wave groups, whereas phase velocity is the speed of an individual wave peak.  They are not necessarily the same.

It is also easy at this point to show that if you combine more and more wave functions, you get something that looks more and more like a wave “packet”.  In the limit as the number of wave functions goes to infinity, the packet becomes localized in space.  And then it’s simple to introduce the classical uncertainty principle: Δk·Δx > ½.  It’s not simple to prove, but it’s simple to make plausible.  And that’s all we want at this point.

We’re still not doing quantum mechanics, but we’re almost there.  Instead, we’ve shown how waves behave, and how uncertainty is inherent in anything with a wave-like nature.  Of course now is the time to strike, while the iron is hot.

What if matter is really made from waves?  What would be the consequences of that?  [Enter de Broglie, stage right]  One immediately gets the Heisenberg relations (really, this is like one line of algebra at the most, starting from the de Broglie relations) and suddenly you’re doing quantum mechanics!  The advantage of this approach is that “uncertainty” seems completely natural, just a consequence of being wave-like.

And whence Schrödinger’s equation?  I make no attempt to “prove” it in any rigorous way in an undergraduate course.  Instead, I just make it imminently plausible, by performing the following trick.  First, introduce complex variables, and how to write wave functions in terms of them.  Next, make it clear that a partial derivative with respect to x or t can be “re-written” in terms of multiplication:

d ψ /dx  →  ik ψ

d ψ /dt  →  –iω ψ

Then “proving” Schrödinger’s equation in a non-rigorous way takes 4 lines of simple algebra:

E = p2/2m

E ψ = (p2/2m)ψ

Now use the de Broglie relations E = ħω and p = ħk…

ħw ψ = (ħ2k 2/2m) ψ

iħ(∂ψ/∂t) = (–ħ2/2m) ∂2ψ/∂x2

There’s time enough for weirdness later.  Right now, armed with the Schrödinger equation, the student will have their hands full doing infinite well problems, learning about superposition, arguing about probability densities.  As George McFly said, “I am your density.”  And as Schrodinger said, probably apocryphally, “Don’t mention my cat till you see the whites of their eyes.”

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