Archive for March, 2012

Why art matters to physics

Posted in Uncategorized on March 25, 2012 by quantummoxie

When school budgets get slashed, one of the first things to go is art.  Art is seen as superfluous and not terribly practical.  But art teaches important skills that students don’t get elsewhere, some of which are important to physics and some of which are important to life in general.  One of the most important skills that art teaches is visualization and visualization is very important to physics.  From a pedagogical standpoint, when I teach introductory physics, I find that visualization is quite possibly the single most important pre-requisite skill required to succeed.  If a student is a bit lacking in their math skills, a few extra hours of outside help usually does the trick.  But if a student can’t visualize, nothing I do seems to help.  This is particularly evident when dealing with three-dimensional problems.  Students can sometimes visualize in two-dimensions, partly because they can draw things on paper (though getting them to do so can be like pulling teeth).  But they get completely lost in three-dimensions, sometimes even with visual aids.  I’m sure there are people who will take me to task for saying so, but I believe that some exposure to three-dimensional art forms (e.g. sculpture), particularly in a tactile manner and prior to taking physics, would help with this problem.

Art, when properly taught, also teaches things like metaphor and simile.  In art, things are often representative.  Being able to see these representations for what they are, i.e. interpret them, is a tremendously important skill.  Unfortunately, I think a lot of physicists actually lack this trait.  When a pure mathematician (geometer, U. of Arkansas professor, and host of The Math Factor Chaim Goodman-Strauss) bemoans the fact that mathematics has strayed too far into the abstract, theoretical physics can’t be that far behind.  Mind you, abstraction is important.  But physics, in particular, is – or should be – grounded in reality.  When it loses that grounding it becomes metaphysics.  Of course, when working in the microscopic realm, things can get a bit murky since mathematical constructs make up the bulk of quantum mechanics.  I use analogies quite a bit (some students can’t even bridge the gap between simple analogies – x is to y as z is to [fill in the blank]), but they don’t always work in the quantum world.  Nevertheless, the visual abstraction of art can help with this in some capacity.

Finally, art also helps people see the big picture and the interconnectedness of things.  It helps teach the mind a certain type of organization that I think is very important for working through complex physical problems.  And it helps people appreciate why simple, unifying principles are important.  This latter point is something I believe we are losing in physics.  Increasingly we – physicists – are looking at different regimes as separate.  From a pedagogical standpoint, this manifests itself in the way most people teach introductory physics, emphasizing Newton’s laws from an operational standpoint first before studying conservation laws.  These same people are often (though not always) the ones who later make blithe comments like “Einstein’s relativity proved Newtonian mechanics was wrong” (forgetting the fact that you can actually derive the latter from the former).

So, in short, art matters!  Embrace it, study it, actively loathe it (at least you’re engaging with it when you do!), but don’t dismiss it.

Why decoherence and entanglement have nothing to do with Schrödinger’s cat

Posted in Uncategorized on March 10, 2012 by quantummoxie

There’s apparently an interpretation of the Schrödinger cat paradox that claims it is explained by quantum decoherence.  I ran across this on Quora where someone had asked about decoherence.  Someone from SLAC gave a mathematically correct answer, but attributed it to decoherence.  But if we use the usual quantum definition of decoherence, then it actually does not explain what happens. To understand all this let’s review coherence and decoherence.

Quantum systems have the ability to exist in superpositional states.  As a simple analogy, suppose we have a bag that contains a bunch of black and white marbles.  Now suppose that we remove a marble from the bag and hold it in our hand, but don’t look at it.  So we don’t (yet) know whether it is a black marble or a white marble.  If the marble were a quantum mechanical object, we would say that, until we open our hand, that marble exists in a ‘coherent’ superposition of black and white states.  Suppose our bag only has two marbles in it.  If we pull out the white marble, we immediately know that the other marble in the bag is black.  We say the marble in our hand is in a ‘pure’ state because when we open our hand to look at it, it is either black or white (e.g. not striped, grey, etc.), i.e. we would say that the black and white outcomes are orthogonal to one another.  So a pure state is one that allows for a coherent superposition of orthogonal states.

But sometimes the world isn’t quite so black and white (pardon the pun).  Instead of marbles, suppose we’re dealing with, say, dogs.  Pure breds would represent the orthogonal states.  So suppose I go to a (strange) shelter where I’m not allowed to see into the pens where they keep the dogs and there is one dog per pen.  Suppose this shelter has only two pure bred dogs – one dachsund and one poodle.  If I choose the first door and it turns out to be a dachsund, then the poodle must be behind the second door.  These are orthogonal states.

But what if the two dogs are mutts?  Maybe the dog behind the first door has some dachsund in him as well as other things like beagle and basset hound.  The same could be true of the dog behind the second door.  He might have some poodle in him, but he could also have some dachsund in him.  Since both dogs could have some dachsund him them, their states are not necessarily orthogonal.  We would say such a state is a ‘mixed’ state.

Another way to look at this is to consider electromagnetic (light) waves.  Imagine that we build a laser in which the light is produced by some atomic transition.  If the light waves that are produced are all perfectly ‘in step’ with one another, then we say that our beam is ‘coherent’ and represents a ‘pure’ state in that the light waves all have the same wavelength, frequency, etc.  If, however, they don’t all have the same frequency, wavelength, etc. then we have a ‘mixed’ state.

Decoherence in quantum systems, then, is the process by which a pure state becomes a mixed state.  What causes decoherence is something I will leave to another blog post.  But suffice it to say that its definition is fairly consistent throughout quantum physics.

So now what about Schrödinger’s cat?  For those unfamiliar with this gedankenexperiment, it goes something like this.  Suppose we have a cat in a box.  Inside the box is a vial of cyanide gas.  Next to this vial is a small hammer attached to a mechanism.  The mechanism is set to trigger the hammer (and thus break the glass, killing the cat) if a certain radioactive isotope decays.  So the cat’s life (or death) is governed by a purely random process.  Before we open the box, the original version of the paradox says that the cat exists in a superposition of alive and dead states.  It shouldn’t be too difficult to see that these are clearly orthogonal states.  You’re either alive or you’re dead.  Ain’t no way to be a mixture of the two.  Let’s assume it’s about a 50-50 shot that the cat is alive/dead.  The state prior to opening the box is

\frac{1}{\sqrt{2}}(|\textrm{alive}\rangle+|\textrm{dead}\rangle).

This is a coherent, pure state since it is composed of orthogonal terms (there is no dispute about this).  When we open the box the cat is either alive or dead.  Let’s be humane and assume it is alive.  Then the state after we open the box is

|\textrm{alive}\rangle.

This is clearly not a mixed state!  Therefore, decoherence does not explain what happens to Schrödinger’s cat!

Update: I forgot to mention that entanglement doesn’t describe this either.  Prior to measurement, the cat’s state is not entangled!  By definition, an entangled state is a non-factorable state.  In other words, you either need to be comparing a single observable for two objects, or two observables for a single object.  Here we have a single observable (life/death) for a single object.

Update II: Matt Leifer pointed out on Google+ that technically decoherence is not merely a transition from a pure state to a mixed state.  It is actually an irreversible transition from a pure state to a mixed state.  I should also point out that decoherence is often cited as one mechanism by which the classical world arises from the quantum world.  Matt and Thaddeus Ladd pointed out a number of other points, but for the purposes of my post (debunking a myth), I disagree with them regarding the importance of those points.

Why I don’t find quantum contextuality all that bizarre

Posted in Uncategorized on March 5, 2012 by quantummoxie

A lot of people think contextuality is one of the oddest (if not the oddest) things about quantum mechanics.  It’s certainly a little odd, but here’s why I don’t think it’s actually as odd as everyone thinks it is.  In a nutshell, contextuality is the idea that the outcomes of quantum measurements can depend on the context in which the measurement is made.  As an analogy, it might be a bit like saying that the temperature outside my house depends on how I look at the thermometer.

There are two reasons that I don’t find this all that strange.  First, we know that at the quantum level measurement is a potentially disruptive act, i.e. it’s very difficult to measure a system without disturbing it since we are working with such small systems.  I don’t find that odd.  In fact, to me, it makes intuitive sense.  The second reason I don’t think it’s odd is because it seems to me that, in a way, all physics is contextual.  One could interpret contextuality as being related to reference frames.  For example, even in classical physics one can get inconsistent results if one switches to a non-inertial reference frame.  The difference in the quantum situation is that the measurement disturbs the system (which I’ve already said doesn’t seem all that weird to me).  If you disturb a system in a different way, the result of your measurement will naturally be different.  I see no reason why that’s all that strange.

What I do find strange about quantum physics are entangled states and photons (photons are really strange if you stop to think about them).