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The conventional wisdom among people who know a little bit of quantum mechanics is that quantum mechanics is weird.

The conventional wisdom is wrong.  Quantum mechanics is not weird.  Interpretations of quantum mechanics are weird.

My thinking on this has changed over the years.  In high school I read everything I could about the “weirdness” of our universe: Schrödinger’s cat, wave-particle duality, the collapse of the wave function, many-worlds theory, the Heisenberg uncertainty principle.

Then a strange thing happened: I went to college.  I studied physics.  And guess what?  None of that stuff gets more than the briefest mention in the physics classroom.  Why?

Because those things are beside the point.  Quantum mechanics works.  How you interpret quantum mechanics is your problem.

There’s a dichotomy here which is the source of most people’s confusion.  Theories are different from interpretations of theories.  A theory is a mathematical model that allows us to make predictions.  An interpretation is a philosophical construct that allows us to sleep at night; it is a squishy heuristic that helps us unimaginative humans make sense of the math before us.  Theories get things done.  Interpretations never helped anybody, not really.

sr_atlas_2b-015

An abandoned shack.

Let’s say that in an abandoned shack you discovered a notebook with the word “PHYSICS” written by hand over and over, thousands of times, apparently filling every page.  You haven’t looked at the last few pages, but your theory is that these pages will also have the word “PHYSICS” written out.  Each time you turn a page, your theory is validated: “PHYSICS” is there, as predicted.

Next to this notebook is another that looks just like it.  You open the first page, and are not surprised to see “PHYSICS PHYSICS PHYSICS” again.  What’s going on?  Did some crazy person live in this shack?  Such speculation doesn’t really matter, since you can still hypothesize that “PHYSICS” fills this notebook as well.  In fact, you have a stronger theory: every notebook in this shack is filled with “PHYSICS”.

You perform an experiment: you turn the page.  “PHYSICS PHYSICS PHYSICS”.  The experiment supports your theory.  You find more notebooks; same results.  Every notebook in the shack is filled, apparently, with “PHYSICS”.  But guess what?  There are dozens of possible interpretations.  And in the absence of further data, you can never know which one is “correct”.

Maybe the shack was once inhabited by a crazy person, who wrote “PHYSICS” precisely 250,001 times in a futile attempt at summoning Cthulhu from his ancient slumber.

Maybe a student misspelled “physics” on a test, and her cruel teacher punished her in the most depraved way possible.

Maybe Matt Damon filled the notebooks, in a method-acting attempt to get into the mindset of an OCD scientist.

Which of these interpretations is the “truth”?  Without further data you cannot really say.  Arguing about which is right and which is wrong is futile at best, and annoying at worst.

Of course, new data may turn up.  We might find out that the notebooks are 75 years old, ruling out our Matt Damon interpretation.  That interpretation is no longer a valid interpretation of the data.

Which brings me to my next point: there is no official arbiter of what constitutes a theory versus what constitutes an interpretation.  Different philosophers and scientists have used the words differently at different times.  All you can hope for is that a particular author is consistent in his/her use of the terms.  I personally use the word “interpretation” to describe competing theories that cannot currently be differentiated by any known scientific experiment.  If two different interpretations make different, testable predictions, then they are promoted to being totally different theories.  (Caveat: others use the words slightly differently.  Deal with it.)

So what does this have to do with quantum mechanics?

Quantum mechanics is an entirely mathematical theory.  Its postulates are logical, concise, and powerful.  We can use quantum mechanics to invent cell phones, computers, lasers, and iPods.  Quantum mechanics doesn’t care if you “understand what it really means”, or not.  It is arguably the most successful and powerful theory to come out of the 20th century.

Now, the mathematics of quantum mechanics are abstract and hard to visualize.  Nevertheless, people insist on trying to visualize anyway.  And the result is all kinds of weirdness: Schrödinger’s cat, wave-particle duality, the collapse of the wave function, many-worlds theory, the Heisenberg uncertainty principle.  These ideas are all mental hoops that people have jumped through to explain some unambiguous, concrete, abstract linear algebra.  The math is just math, and it works; what it means is anyone’s guess.

There’s no crying in baseball, and there’s no philosophy in quantum mechanics.

leagueoftheirown

There’s no philosophy in quantum mechanics!

Don’t like the many-worlds interpretation?  Fine.  Be a Copenhagenist.  Don’t like pilot waves?  Great.  Stick to your pet idea about superluminal communication.  Just remember that all of these competing interpretations make the exact same predictions, so for all practical purposes they are the same.  Some people go so far as to say, just shut up and calculate.  [Note added 3-19-14: there are problems with pilot wave theories that in my view rule them out as being a valid interpretations of quantum mechanics.  But there are hoops people can jump through to try and “force” pilot wave theories to be consistent with, say, Bell’s theorem.  My broader point is that there are multiple interpretations of QM and that all have followers to this day, but that none of the interpretations really have any distinct implications for our lives.]

I don’t usually go that far.  I actually think that the many-worlds interpretation is a testable theory, not an interpretation (hence the name of this blog).  I think many-worlds is falsifiable.  (If we ever observe a wave function collapsing, then many-worlds will have to be discarded.)  But I don’t think that will happen: many-worlds is too elegant, and too powerful, to not be true.

But we’ll see.

If you think it’s absurd that a cat can be alive and dead at the same time…if you think that it’s crazy to hypothesize other universes…if you think that God does not play dice with the universe…don’t blame quantum mechanics.  Blame the philosophers who try to interpret it.

Quantum mechanics works.  Otherwise, you’d be reading this on an actual piece of paper.

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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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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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I don’t think the general public is aware that, among theoretical physicists, the many-worlds interpretation (MWI) of quantum mechanics has become almost mainstream.  (See, for example, this article by Max Tegmark.)  This means, basically, that there are a large number of very, very smart people who take the idea of “other” universes seriously.

Maybe you are one of these people.  Maybe you found this blog by googling “many worlds theory” and ended up here.

So, you ask, will this blog be devoted to the “Many Worlds Theory”?  Yes and no.  Yes, in the sense that I am a theoretical physicist, who has published work (such as this) on the weirdness of quantum mechanics.  And yes, I will occasionally post on topics that relate to MWI (such as quantum interference, the philosophy of science, the existence of the universe, and whether Jet Li’s performance in The One was Oscar-worthy.)

But also, no, in the sense that I won’t always devote this blog to quantum physics.  After all, the blog is called “Many Worlds Theory”, and not the arguably more correct many-worlds interpretation or Everett’s relative state formulation or universally-valid quantum mechanics.  By “worlds” I mean not only parallel universes, but things that interest me.  Sounds self-centered, right?  Kinda personal?

Well, it is a blog.  Isn’t it supposed to be personal?

My interests include, in no particular order: recreational mathematics, classical music, philosophy, politics, games of all kinds, science fiction, history, the ouvroir de littérature potentielle movement, movies, sports…(I’ll stop before this too closely resembles an ad on a dating website.  Maybe it’s already too late for that.  Anyway, I’m very happily married, thank you very much.)

Ultimately, this blog will be devoted to examining topics using a scientific mindset.  Let’s get one thing clear from the start: I believe that it is only through science that we have learned anything about the world.  My goal is to have this theme come through in all my posts.  Sure, I might discuss the Higgs boson, the Heisenberg uncertainty principle, Berry’s geometric phase, or other physics stuff.  But even when I discuss something non-scientific like Honey Boo Boo or Deepak Chopra or the Carolina Panthers or economics, I hope to stick to facts, and what can be demonstrated through logic.  If I write a blog about how soccer is a boring sport, rest assured that I will give you reasons as to why it is boring, and cite the source(s) of my claims.

Of course, there is another universe in which this blog is devoted to how great soccer is.

Good thing we’re not in that universe.

[Note: my book Why Is There Anything? is now available for download on the Kindle!]

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