Saturday, January 9, 2010

Uncertainty Principle: Intrinsic Property or Measurement Effect?

At last night's Saint Louis Skeptics in the Pub, the conversation came---as it always must---to physics. Saint Gasoline and unBeguiled wanted to know whether the position-momentum uncertainty principle is a real property of a quantum particle, or simply a limitation of our ability to measure both the position and momentum of quantum particles. I guess, even more strongly than "they wanted to know," they were arguing for the latter, more intuitive answer.

As an example of the kind of thinking they argued for, take this quote from the Wikipedia article on the uncertainty principle:
Heisenberg's microscope
One way in which Heisenberg originally argued for the uncertainty principle is by using an imaginary microscope as a measuring device. He imagines an experimenter trying to measure the position and momentum of an electron by shooting a photon at it.
If the photon has a short wavelength, and therefore a large momentum, the position can be measured accurately. But the photon scatters in a random direction, transferring a large and uncertain amount of momentum to the electron. If the photon has a long wavelength and low momentum, the collision doesn't disturb the electron's momentum very much, but the scattering will reveal its position only vaguely.
If a large aperture is used for the microscope, the electron's location can be well resolved (see Rayleigh criterion); but by the principle of conservation of momentum, the transverse momentum of the incoming photon and hence the new momentum of the electron resolves poorly. If a small aperture is used, the accuracy of the two resolutions is the other way around.
The trade-offs imply that no matter what photon wavelength and aperture size are used, the product of the uncertainty in measured position and measured momentum is greater than or equal to a lower bound, which is up to a small numerical factor equal to Planck's constant.

Now, I don't think this thinking is exactly wrong. I mean, if one constructed this experiment I don't doubt that it would validate the results predicted by the uncertainty principle. However, I think the model behind it is flawed. What we imagine in this gedankenexperiment is a little ball that is the electron being hit by a little ball that is the photon and the two bouncing off each other.

What this sort of explanation ignores is the fact that matter behaves as a wave.

I may need to do some argumentation to convince you (specifically Dustin) that matter waves aren't just a mathematical convenience for calculations but are, in fact, the actual nature of matter. If I need to do that, I'll do it later. Today is not the day to explain matter waves. Here, though, is a very quick argument: we know ordinary waves (water, sound, etc.) do certain things like reflection and refraction and interference and whatever. Some of those things are done only by waves and nothing else. We see quantum particles doing those same things. Here's a handy chart.

So let's simply accept for now that electrons are, in almost all circumstances, wavelike. I think we all have heard many times that quantum particles are both particulate and wavelike at times, and might take it for granted. We sort of skip over the fact that electrons are waves without really understanding what that implies, so let's investigate. This will involve a little math, but stick with me. It shouldn't be that bad.

Let us assume the electron has as its wavefunction pretty much the simplest wave you can get, a sine wave. This is a periodic function, which means that if you are at any point and you move some special distance away, everything about the function will look the same. This distance is called the wavelength, denoted by lambda. There is a relationship between wavelength and momentum called the de Broglie relation, which says momentum is equal to Planck's constant divided by wavelength.

p = \frac{h}{\lambda}

So for an electron with a sine wavefunction, we know it has a definite momentum.

What about position? To find the position of the electron, we need to square the wavefunction and integrate it over all space. (Don't worry, I won't make you sit through that.) When we do that with a sine, the result we get is meaningless. It says there is a smeared out probability to find the electron everywhere, and no place is more probable than any other. Thus there is no helpful position information we can get out of this wavefunction.

This is all summarized nicely in this picture I stole.

To make some kind of meaningful statement about position, then, the electron can't be in a state with a wavefunction that is just a sine wave. What we can do is make a "wave packet" by adding together a few different sine waves. If we pick the wavelengths and amplitudes properly, we should be able to get a decently localized position. However, by adding together different sine waves we have introduced more than one wavelength. With more than one wavelength we don't know exactly what the momentum is. Again, I stole a picture.

Now, looking over this example I gave, is this a measurement effect? Most emphatically NO. If you know the momentum exactly, it is not the case that you just can't measure the position, but the idea of position doesn't even make sense. Look back at that youtube video I posted. That is a wave with a well-defined wavelength, and therefore a well-defined momentum. I ask you: where is that wave? Is that wave in a particular place? At a particular position? No it is not. The wave is spread out over all space. If the wave had a less-precise momentum, as in perhaps there are several waves of different wavelength added together, we would see waves only in some constrained area and there would be no waves outside that area. In that case, it is meaningful to say that the wave is in a particular place, because it is localized to an area.

If we accept that matter actually has wave properties (and this is well-established both theoretically and experimentally, but perhaps that's a topic for another day), the uncertainly between position and momentum comes as an immediate consequence. By virtue of how position and momentum are defined, they are not completely compatible. This incompatibility has nothing to do with what you can measure. It has to do, as I outlined here, with what the concepts of position and momentum mean when applied to waves.

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Thursday, July 9, 2009

Jury Duty

I just had a fun jury duty experience that you might like to know about, one in which my skeptical outlook on life prevented me from being able to fairly and impartially administer justice. I was part of a jury panel, but was not selected to be a juror for the trial. Would you like to know why?

For those who have never been involved in jury duty, a brief view of the selection process from my not-well-informed perspective: a large group of potential jurors are asked broad questions by both sides in the case, who wish to bring out information about each person that would make him or her not a good juror. This is called voir dire. Once all that information is gathered, the selection is made---everyone goes home and only selected few become the jury and come back to hear the trial.

As I already said, I was not selected, because of how I answered two of the questions. First, some background. The first questions were of a type like, "Do you know anyone else on the jury panel?" or, "Do you know the judge/attorneys/defendent/etc.?" Other questions involved specific aspects of the evidence we would hear. In order to answer them accurately, we were told generalities about the case: a man was arrested in January 2008 and charged with possession of crack. So they asked, "Does anyone think that crack is not illegal?" No one raised a hand. "Does anyone think that crack should not be illegal, and for that reason could no be fair and impartial?" One guy did raise his hand, and said he agreed crack should not be illegal. They asked some followup questions, in response to which he clarified that he wouldn't convict someone for drug possession under any circumstances. So we were pretty sure he was off the list. Later questions included, "You will hear testimony from police officers. Is there anyone who would, before hearing the testimony, trust a police officer less or more than any other person?" To which several people answered, in various words, "I would never trust anything that a cop said." So they were off the list.

This went on for hours. For each question, they'd go through all the people to whom it applied, getting them to clearly say on record that whatever particular issue might be a problem for them. The "clearly" part was a problem for most, as some of the questions dealt with beliefs or opinions, which aren't always one-to-one with the legal terms they steered us towards saying. That was certainly true of the questions I had to answer.

There were two I put my hand up for, very related but not exactly the same, involving testimony. They gave some background first on the types of evidence---testimonial, circumstantial, and physical---and stressed that under the law all three are to be weighed equally. They asked, "Would you need some type of physical evidence, like a fingerprint or a videotape, to consider the state to have met its burden of evidence?" From this question I inferred that, not only would the state bring a police officer as a witness and he or she would testify that the defendant possessed drugs, but also that this would probably be the only evidence that they'd have. From what they'd told us, under the law this would be fine, and a credible witness testifying that a crime had occurred would be enough evidence to establish that element of the case. I did not agree.

So I raised my hand and responded, "If any of the elements of the case were supported only by testimony, I would not consider that element sufficiently proved." To put it into more skeptical terms, I would not accept anecdotal evidence, without any other support, as proving a claim. I could not convict one person of a crime based on another person's word. An anecdote is not enough evidence to establish that an event took place, whoever the witness or defendant is, whatever the circumstances are, and whether or not I found the witness "credible." That brings us to the second question I answered.

"Is there anyone who thinks they would not be able to determine a witness's credibility?" My interpretation of this question is, "Can you tell if a person is lying or not?" I quickly raised my hand, and I was surprised more people didn't raise theirs. If they had been honest with themselves I think they would have. When called on, I answered, "Given two people making contradictory statements [which there obviously would be, since there wouldn't be a trial if the defendant agreed that he had possessed crack] I would not be able to determine who was correct without any outside information." In the followup questions, they asked if I was unable or just unwilling, and couldn't I use body language or tone or details of the testimony to judge someone's credibility? My thought was, "Hell to the fucking no I can't! I'd just be using my biases and prejudices to come to a decision in that case. I'm not willing to send a man to prison based on my interpretation of a cop's 'body language!'" What I said was, "No."

So that's how I didn't get on the jury. A person who considers facts to be of paramount importance in all aspects of life was not considered able to fairly and impartially find facts according to the law. And I'm glad I wasn't selected. If the courts say that anecdotes have to be considered on the same level as other forms of evidence, I believe the courts are wrong, and I would have a hard time following the instruction to weigh the evidence equally. Of course, this decision came about without an investigation on my part of the history of testimony as a form of evidence, why and how it is used, how juries make their decisions and on what basis, and many other bits of information I now find I wish I had had at the time. But I was not armed with this information, only a firm---but for me empirically groundless---belief that I could not imprison a person on another person's word.

I hope I did the right thing.

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Monday, September 1, 2008

Google Chrome

Gee, Google, what are we going to do tonight?
The same thing we do every night, Flavin. Try to take over the Internet!

On tonight's episode, Google releases a browser. Will they succeed in their plan of network domination? Watch and see!

(... I'm going to try it.)

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Thursday, August 14, 2008

Madden Curse

I just read a great article on the "Madden Curse." For those who don't know, every year a new edition of the football video game Madden NFL is realeased, and for ten or so years it has featured an NFL star on the cover. Over the years, some of the players appearing on the cover have gone on to be injured or have bad seasons. A rumor has grown that the cover brings a curse to any player on it, plaguing them with injuries, bad seasons, or other maladies.

Luke Plunkett writing on Kotaku has written a great breakdown of who's been on the cover every year and exactly what did or did not happen to them during that season. My favorite paragraph is this one:

...[the curse is] all based on hearsay, selective statistic cherry-picking and misinformation. When you look at two key factors - the NFL's injury rate and the actual performance of all twelve cover stars in the year they appeared on the box - you'll see the curse is nothing but a load of baloney.
That some good skeptical thinking there, something I don't normally see crossed over from my video game sites. But, then, he's an Aussie. What else would one expect?

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Thursday, July 24, 2008

10 Most Scientifically Inaccurate Movies

I found this entertaining: Top 10 Scientifically Inaccurate Movies

My personal favorite is the Matrix: "Much in the way of physics in the Matrix -- like dodging bullets and running up walls -- gets a pass because it's all within a massive virtual world. But in reality, our supposed robot overlords are a bit dim. Humans are a remarkably inefficient energy source. Instead of turning the human race into Duracells, the machines would probably get more energy just setting those goopy people pods on fire."

I also think Alien should at least get a dishonorable mention.

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Saturday, July 12, 2008

In Support of PZ

I'm emerging from my intermittent blogtirement to ask for a bit of advice.

You probably know of PZ Myers' recent run-in with Catholic hysteria. I'll give a brief run down anyway, more for me than for you. An undergrad in Florida went to a Catholic mass and took the Eucharist home with him rather than eating it. Catholics believe that this Eucharist becomes Jesus, so they got very upset. PZ wrote about it and tried to burst the Catholic bubble on this issue. (Note: His post is entitled "It's a Frackin' Cracker!" but you can tell he tempered his words. The URL is .../its_a_goddamned_cracker.php)

PZ's post stirred up a lot of shit. The Catholic League called for his job and organized a letter writing campaign to the UMM President Robert Bruininks to demand reprimands at the least.

PZ has asked for help in a counter-campaign to write his university President in support of his job. I'd like to write something, and I have several thoughts on what it should be about, but I'd like to have a nice, clean thesis. Any thoughts? Should I stick to the First Amendment and his rights to ridicule? Obviously I don't want to respond to the comments of the rabble, but what about Catholic League president Bill Donahue? Should I reference his arguments?

Any thoughts would be appreciated. Do you think PZ was right? Do you think he was within his rights? How do you think he should handle this situation?

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Wednesday, July 9, 2008

This just in: Fools. Money. Parted.

I wish there were some details as to what people think she has done. Read here.

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Sunday, June 29, 2008


In general, I think these guys have the occasional funny comic, but this one just kind of grossed me out.

Nothing even remotely kinky should be associated with that troll.

Kudos to Robert Lancaster for handling himself perfectly when confronted by that wicked woman.

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Monday, June 23, 2008

George Carlin Dies at 71

He will be missed. There is a little story here. My favorite Carlin joke was about those psychos at Waco. It's goes something like "The government and religious people shooting at each other? I'm OK with that."

Here's a classic Carlin clip for you.

Feel free to leave your favorite Carlin moment below.

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Thursday, June 19, 2008

Guess where I'll be tomorrow?

That's right! The 999 Eyes Freakshow at Cicero's. It starts at 8:30PM. Come on down! There is a tarot card reader. We all know how fun those are!

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