Quantum of Solace

What does quantum mean? With a new Hollywood blockbuster just out, and containing the word "quantum" in the title, it seems we'd better get to the bottom of this.

The word "quantum" was substantively introduced into atomic physics by Einstein, in his 1905 paper (PDF) on the thermodynamics of radiation. (Einstein won the 1921 Nobel Prize in physics for this work.) The meaning of "quantum" in this paper is clear: Einstein describes heat radiation as behaving thermodynamically as if it were made up of "energy quanta" -- discrete chunks of energy of exceedingly small size size hf (where f is frequency and h is Planck's constant, the latter being equal to about 0.0000000000000000000000000000000006). In other words:

    Meaning #1: quantum = very small chunk.

However, when someone refers to a "quantum theory" today, it almost always means much more than Meaning #1. As I've mentioned before, we can point to three categories of phenomena that can be tested in a laboratory, which in large part form the empirical basis of quantum theory. They are:

(1) particle diffraction;
(2) superposition; and
(3) discrete energy spectra.

Einstein's original use of the word "quantum" was an instance of item (3). But today, when one often refers to a "quantum particle," "quantum tunneling," "quantum teleportation," and the like, what is meant (broadly speaking) is:

    Meaning #2: quantum = exhibiting properties (1), (2) and (3).

Of course, this characterization is perhaps heavy on the side of the experimentalist. The theoretician might prefer to think of "quantum" as referring to the structure of a typical quantum theory. Unfortunately, it's not that easy to say precisely what that structure must be like. For example, it's certainly not a simple matter of casting one's theory in terms of bounded operators on Hilbert space, since Koopman and von Neumann showed that this is also possible for classical theories. But I think it's fair to ask that, in order for a theory to be "quantum," it must admit:

(5) a unitary representation of the Canonical Commutation Relations; or
(6) a unitary representation of the Canonical Anticommutation Relations.

Since the theories typically described as "quantum" all tend to admit at least one of these two properties, we now have available:

    Meaning #3: quantum = characterized by (5) or (6).

There's one last meaning for "quantum" that I should mention. It's a unique (and, for the moment, inescapable) feature of all our current quantum theories, but perhaps an undesirable one. Namely, quantum theories describe the world in terms of the following two kinds of processes. The first, called unitary (Schrodinger) evolution, is continuous through time. The second, called state reduction (or for von Neumann (1932), "wave function collapse"), is discontinuous. So, according to quantum theory, the typical lifetime of an entity in a particle physics lab consists in a sequence of successive evolutions and "jumps." A system evolves continuously, until a measurement interaction occurs. It then undergoes a discontinuous transition to a new point, and then begins evolving continuously again. (The nature of these jumps is a matter of debate among interpreters of quantum theory, but let's bracket that.) We thus have:

    Meaning #4: quantum = discontinuous transition.

This meaning seems most closely related to the use of the word in popular jargon. Indeed, my dear friend and fellow blogger Justin over at My Mind is Made Up thinks that the main way people use the word is in phrases like "a quantum leap." If this simply means a severe, discontinuous jump, then I'd say "the folk" have picked up on Meaning 4. Interestingly, Justin tells me that Hollywood has managed to pick up on something more like Meaning #1, which would be more historically accurate. But of course, I'm no expert on Hollywood, or the folk -- so check out what Justin has to say!

Philosophy of Physics Webcam-Debates

Sean Carroll and David Albert have had a couple of really interesting recent video-debates on BloggingHeads. If you haven't checked this phenomenon out already, I highly recommend the following:

1. Sean Carroll & David Albert I (Quantum theory, measurement problem, Everett interpretation).



2. Sean Carroll & David Albert II (Why "what the bleep" is so bad, the measurement problem, the arrow of time).

Carroll is a CalTech physicist who maintains an excellent blog over at Cosmic Variance. Albert is a philosopher of physics at Columbia.

Map of the Cosmic Acceleration Literature

Ten years ago, the physics community came to agree that the expansion of the Universe is experiencing a positive acceleration. The experts still disagree on why. Everything but the kitchen sink has been proposed (I've mentioned this twice before), but there is a paucity of experimental evidence to favor one proposal over another.

This situation strikes me as a gold-mine for philosophers physics. In particular, I would hope that we could learn something interesting about what kind of reasoning is allowed in such an empirically starved research program. In particular, what I'd like to know is:

What argumentative moves are licit in response to the cosmic acceleration problem?

As a first step toward figuring this out, I made a map of the most common arguments being made. To see my map, click the image on the left (or download the PDF). This map is inspired by a (much smaller) such diagram given by Sean Carroll (2003). Suggestions are more than welcome!

Special: What's With the Economy.

I'm a philosopher of science, not an economist. So I decided to write a story that explains what's with the economy, using small words and Disney characters. The first 5 parts explain the background. The last two parts explain what's actually going on. So here it goes.

PART 1: SECURITIES. There's a hamburger joint on your street called BurgerBee, and they do pretty good business. But they need some extra cash up front (say, to get a new grill). You have cash up front. So the two of you strike a deal: you will give BurgerBee some money (say, 1000 bucks or so). In return, BurgerBee will give you a little certificate, which says that every day, you get 1% of the money that BurgerBee makes. That sounds pretty good to you, because eventually, the money that BurgerBee gives you will add up to much more than 1000 bucks.

The certificate that BurgerBee gave you is called a security. It is a promise that you will get some money, although you will generally get it over an extended time period.

PART 2: MORTGAGES. Every month, BurgerBee (or anyone else who owns a building or a home) pays an expense called a mortgage. The reason for this goes back to when BurgerBee first became a restaurant. They wanted to buy a building to make and sell burgers in. The wealthy Scrooge McDuck had enough money to buy buildings. So they struck the following deal.

McDuck gave BurgerBee the money to buy a building for their burger joint (say, $100,000). In return, BurgerBee gave McDuck a little certificate, which says that BurgerBee will pay McDuck MUCH MORE than the original amount (say, $200,000). But the payments are made in small amounts, every month, over the course of 30 years. (Actually, the extra amount paid is interest, but let's not complicate this story.)

That payment is called a mortgage.

PART 3: PRE-PAYMENTS & FORECLOSURES. In order for the deal with McDuck to be fair, there's one exception about those mortgage payments. Imagine that, one week after McDuck gave BurgerBee the money for the restaurant building, BurgerBee came into 100,000 bucks all by themselves. (Let's say they owned another store elsewhere, and were able to sell it.) BurgerBee wants to pay back McDuck. But should they really have to pay him back the entire $200,000 dollars, after only 1 week? That doesn't seem fair! That extra money was meant to compensate for the fact that it would take 30 years to make the payment.

So BurgerBee and McDuck added the following exception to their deal: if BurgerBee pays McDuck back EARLY, then they don't have to pay as much. So after a week, they might only have to pay back $100,001 dollars. And after 15 years, they might only have to pay 150,000 dollars. And so on. (Again, what really happens is that each payment has interest added to it, but we're setting aside that complication.)

And it is exactly the same situation if the burger business goes bad, and BurgerBee can't keep making the mortgage payments to McDuck. In that situation, the two agree that McDuck takes the building away from BurgerBee as a payment. But remember, the building is only worth $100,000. So McDuck won't get his full $200,000 in that case either.

If BurgerBee completes their mortgage early, it is called a pre-payment.
If BurgerBee stops making payments and McDuck takes the building, it is called a foreclosure.

PART 4: MORTGAGE-BACKED SECURITIES. Now, McDuck is a pretty clever investor. So he decides to use his mortgage certificate to get some immediate cash. Suppose that McDuck does mortgages for a lot more people besides just BurgerBee. In total, let's say that he gave away $2 million for people to build restaurants. McDuck feels pretty good about this, because he expects to eventually get $4 million in return -- he just won't see all of it for 30 years.

But now imagine that McDuck needs some cash up front. (Let's say he wants $3 million to build a skyscraper.) The Bank has $3 million up front. So the two decide to strike a deal. The Bank will give McDuck the money for his skyscraper. In return, McDuck will give the Bank all of his mortgage certificates. These certificates are worth $4 million. But the Bank won't see all of it for 30 years.

McDuck's mortgage certificates are called mortgage-backed securities.


PART 5: RISK. The Bank just gave $3 million in cash to McDuck, and received $4 million in mortgage certificates in return. This seems like a pretty good deal: with a little patience, the Bank makes a million bucks. However, there is also a risk involved in the deal. Remember, if BurgerBee pays its mortgage back early -- or if it stops making payments -- then it won't pay back the entire $200,000 -- it might pay back much less than that. If this happens, then the Bank won't receive the full $4 million dollars.

Now, the Bank is still generally willing to take that risk. Even if BurgerBee pre-pays or forecloses on its mortgage, the Bank can still make a nice profit -- say, $900,000 instead of a million. But if EVERYONE payed back their mortgage too early -- or stopped making payments -- then the mortgage certificates could actually bring back less than $3 million total. Then the Bank will have gotten screwed: it gave McDuck $3 million, and got back less than $3 million in return. But it's pretty unlikely that EVERYONE pre-pay or foreclose. So the Bank is generally willing to take that risk, in order to make some money.

PART 6: OUR PROBLEM. The problem is, some of the most important banks and McDucks in the US got screwed in exactly this way. But not out of a million dollars -- we're talking about losing billions each, sometimes over the course of just a few months.

There were a lot of things that led to this. Here's the basic idea. Consider poor Mickey Mouse, who was struggling to make a living this decade. McDuck decided to lend him some money anyway, to buy a nice house (let's say, $100,000). This was a very risky idea. After all, poor old Mickey was struggling just to get by, let alone make regular mortgage payments. So to make up for the risk, McDuck asked Mickey to pay MUCH more than the original price of the house -- say, $500,000 over the course of 30 years. McDuck was betting that he had a chance to make a lot more money, because $500,000 is a lot more than $100,000. But it was a risky bet.

That kind of risky mortgage is called a sub-prime mortgage.

As it turned out, starting last year, millions of Mickey Mouses around the country stopped making their payments, and their houses were foreclosed. And so thousands of McDucks lost their bets.

This had a kind of domino effect. Think about the skyscraper that McDuck built. He payed the bank in mortgage certificates (mortgage-backed securities). So when all those Mickey Mouses stopped paying, the "unlikely" actually happened -- those mortgage certificates lost most of their value, and the banks got screwed.

In the news, they are calling these kind of mortgage certificates bad or toxic mortgage backed securities.

The dominos kept falling, because almost everyone was connected to those bad certificates somehow. For example, the banks also made payments using those certificates. And even worse, they themselves took out new loans ON THE BASIS of those certificates. (This kind of thing is called a derivative, and it gets very complicated.) A good analogy is a tower (i.e., US borrowing practice) with a very risky foundation (i.e., bad mortgage backed securities). So when the foundation fell out, the whole building started to wobble almost uncontrollably.

On Wallstreet, this meant that nobody knew how much anything was worth. It started with all those houses that foreclosed. Nobody's really sure how much those houses are worth. So lots of banks are invested in lots of houses of questionable value. So nobody's sure how much the banks are worth -- or all the elaborate derivatives -- all the way up. Now, when people on Wallstreet don't know how much something is worth, they often do one of two things: they do nothing, or they sell. They did both last week. And so the stock market fell dramatically.

PART 7: THE PLAN THIS WEEK. The main strategy of the US Government is now to try to restore confidence in those investors, so that the stock market doesn't fall so badly. Paulson, the Bush administration's treasury secretary, proposed a plan for the US government to buy up a lot of those bad mortgage backed securities. The idea is to take out the bad foundation, and replace it with a sturdier, cash foundation. Paulson is hoping that this will calm investors on Wallstreet, and get things on the road back to normal.

The question that nobody knows the answer to is: will this work? Or is the tower already on its way down?

Geneva Summer School in Philosophy of Physics

Read About It Here. The Geneva Summer School in Philosophy of Physics, 2008 was a 1-week intensive summer school in the middle of the Swiss alps. This year, scholars and graduate students met in Arolla's Hotel Mont-Collon for a conference on the nature of space and time. I was able to participate, thanks to a generous grant from the Wesley and Merilee Salmon Foundation. Here's my report on what happened. There is also a Google Picture Page for the event.

Next year's summer school is rumored to be about the foundations and interpretation of quantum theory. I highly recommend that any graduate student or new-Ph.D philosophers of physics consider going.

Update: 24.Sep.08, 8:45am. Justin Sytsma has posted this report, along with another summer school report by Jonathan Livengood. Justin's excellent blog is well worth checking out, for matters of phil-mind, x-phi, grad-life in Pittsburgh, and general entertainment.

What is Interesting in the Philosophy of Physics?

Philosophers of physics may have experienced this problem. You know you're interested in a particular question about physics. You come face to face with the mountain of literature on the topic. And you immediately start digging furiously. Deeper and deeper you dig, until you've finally mastered a wealth of material, and at the same time completely lost track of what the hell you were doing in the first place

To avoid this problem, John Norton suggested that Elay Shech and I make a list of really successful tactics in the philosophy of physics. The idea is to characterize a few exemplary problems in the field in terms of a very broad methodology. That way, one can more easily stay focused on the really interesting problems. Here is the list the three of us came up with.

1. Correction of a standard history. Sometimes, everyone agrees that things went one way, and they all turn out to be wrong. Examples. For years, everyone thought that the Michelson–Morley experiment lead to the discovery of Special Relativity. It turns out that this experiment had little to do with it.


2. Explication of a concept in physics. A theoretical term might allow a non-standard interpretation, or might not have an obvious interpretation at all. Examples. The concept of gauge and of the simultaneity relation.


3. Traditional philosophy illuminated by physics. A particular physical theory might imply something about more traditional problems in philosophy. Examples. Claims about substantivalism, the persistence of objects, and the passage of time have all received arguments that draw on physical theories.


4. Characterization of a a theory's foundation. Something is suggested about the most basic elements of a theory. Examples. Realism, interpretations of GR or QM, or the conventionality of geometry.


5. Analysis of 'paradoxes.' The word 'paradox' is common in physics jargon, but it almost never means a logical paradox. Analysis of what's at the bottom of the problem is often illuminating. Examples. The black hole information paradox; the paradox of cosmic acceleration.


6. Synthesis of Philosophy and Science. One often seeks to understand how big-picture philosophical views can be combined with particular physical theories. Examples. The combination of reductionism with statistical mechanics.


7. Characterization of epistemic/metaphysical limitations. Sometimes physical theories seem to place sharp limits on what can in principle exist or be known. Examples. Indeterminism. Observationally indistinguishable spacetimes.

This list is certainly not exhaustive. But I have already found it to be surprisingly useful. Comments and additional suggestions are welcome!