Monthly Archives: April 2008

The Quantum Arena

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This post is part of the Quantum Physics Sequence.
Previously in seriesClassical Configuration Spaces

Yesterday, we looked at configuration spaces in classical physics.  In classical physics, configuration spaces are a useful, but optional, point of view.

Today we look at quantum physics, which inherently takes place inside a configuration space, and cannot be taken out.

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Classical Configuration Spaces

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This post is part of the Quantum Physics Sequence.
Previously in seriesDistinct Configurations

  Once upon a time, there was a student who went to a math lecture.  When the lecture was over, he approached one of the other students, and said, “I couldn’t follow that at all.  The professor was talking about rotating 8-dimensional objects!  How am I supposed to visualize something rotating in 8 dimensions?”
    “Easy,” replied the other student, “you visualize it rotating in N dimensions, then let N go to 8.”
            – old joke

Quantum configuration space isn’t quite like classical configuration space. But in this case, considering that 8 dimensions is peanuts in quantum physics, even I concede that you ought to start with classical configuration space first.

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How To Vs. What To

When should you seek decision advice?  One factor is decision size: the bigger the decision, the more effort you should devote, including effort to get advice.  Oddly, on our biggest decisions, other people seem to go out of their way to offer us advice that we don’t want to hear or follow.  We rarely seek out advice, and when we do it is usually on much smaller decisions. 

For example, we like HowTo books, but not WhatTo books.  How to manage your computer, not what machine to manage.  How to please your partner, not what partner to please.  How to fix your house, not where to live.  How to drive fast, not what speed to drive.  How to get promoted, not what job to work at.  How to raise your kids, not how many kids to raise.  And so on.

One reason we avoid getting advice is that it lowers our status relative to those who give advice.  Of course this is also makes asking for advice a good way to flatter and supplicate.  Not sure if this explains the puzzle though.  But all this doesn’t seem to bode well for fielding decision markets on the biggest organizational decisions. 

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Can You Prove Two Particles Are Identical?

This post is part of the Quantum Physics Sequence.
Followup toWhere Philosophy Meets Science, Joint Configurations

Behold, I present you with two electrons.  They have the same mass. They have the same charge.  In every way that we’ve tested them so far, they seem to behave the same way.

But is there any way we can know that the two electrons are really, truly, entirely indistinguishable?

The one who is wise in philosophy but not in physics will snort dismissal, saying, "Of course not.  You haven’t found an experiment yet that distinguishes these two electrons.  But who knows, you might find a new experiment tomorrow that does."

Just because your current model of reality files all observed electrons in the same mental bucket, doesn’t mean that tomorrow’s physics will do the same.  That’s mixing up the map with the territory.  Right?

It took a while to discover atomic isotopes.  Maybe someday we’ll discover electron isotopes whose masses are different in the 20th decimal place.  In fact, for all we know, the electron has a tiny little tag on it, too small for your current microscopes to see, reading ‘This is electron #7,234,982,023,348…’  So that you could in principle toss this one electron into a bathtub full of electrons, and then fish it out again later.  Maybe there’s some way to know in principle, maybe not – but for now, surely, this is one of those things that science just doesn’t know.

That’s what you would think, if you were wise in philosophy but not in physics.

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Naming Beliefs

Rolf Nelson points out that we don’t have good terminology to call “beliefs we would have had if we didn’t choose to be persuaded by the fact that everyone else believes differently”. It’s an important distinction because this kind of belief is arguably more helpful to know, for both majoritarians and others.

In classic group-decision experiments like “guess how many beans in the jar”, you get less accurate answers if people call out their guesses one after the other, because they are revealing their adjusted beliefs, that take into account the social consensus (perhaps without realizing it). If people write their answers down, we get Rolf’s kind of beliefs, uninfluenced by the consensus view, and those have been shown to be more accurate on average.

So Rolf’s point is very relevant about the lack of terminology. Devil’s Advocacy is about as close as I can come, but that doesn’t capture it. What do you suggest would be a good way to describe these kinds of beliefs? Once more people start making a conscious distinction between the two modes of believing, how should we talk about it?

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Where Philosophy Meets Science

This post is part of the Quantum Physics Sequence.
Followup toDistinct Configurations

Looking back on early quantum physics – not for purposes of admonishing the major figures, or to claim that we could have done better if we’d been born into that era; but in order to try and learn a moral, and do better next time – looking back on the dark ages of quantum physics, I say, I would nominate as the "most basic" error…

not that they tried to reverse course on the last three thousand years of science suggesting that mind was complex within physics rather than fundamental in physics.  This is Science, and we do have revolutions here.  Every now and then you’ve got to reverse a trend.  The future is always absurd and never unlawful.

I would nominate, as the basic error not to repeat next time, that the early scientists forgot that they themselves were made out of particles.

I mean, I’m sure that most of them knew it in theory.

And yet they didn’t notice that putting a sensor to detect a passing electron, or even knowing about the electron’s history, was an example of "particles in different places".  So they didn’t notice that a quantum theory of distinct configurations already explained the experimental result, without any need to invoke consciousness.

In the ancestral environment, humans were often faced with the adaptively relevant task of predicting other humans.  For which purpose you thought of your fellow humans as having thoughts, knowing things and feeling things, rather than thinking of them as being made up of particles.  In fact, many hunter-gatherer tribes may not even have known that particles existed. It’s much more intuitive – it feels simpler – to think about someone "knowing" something, than to think about their brain’s particles occupying a different state.  It’s easier to phrase your explanations in terms of what people know; it feels more natural; it leaps more readily to mind.

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Distinct Configurations

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This post is part of the Quantum Physics Sequence.
Previously in seriesJoint Configurations

Yesterday’s experiment carried two key lessons:

First, we saw that because amplitude flows can cancel out, and because our magic measure of squared modulus is not linear, the identity of configurations is nailed down – you can’t reorganize configurations the way you can regroup possible worlds.  Which configurations are the same, and which are distinct, has experimental consequences; it is an observable fact.

Second, we saw that configurations are about multiple particles.  If there are two photons entering the apparatus, that doesn’t mean there are two initial configurations.  Instead the initial configuration’s identity is “Two photons coming in.”  (Ideally, each configuration we talk about would include every particle in the experiment – including the particles making up the mirrors and detectors.  And in the real universe, every configuration is about all the particles… everywhere.)

What makes for distinct configurations is not distinct particles.  Each configuration is about every particle.  What makes configurations distinct, is particles occupying different positions – at least one particle in a different state.

To take one important demonstration…

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Conformity Questions

Follow-up to: Conformity Myths

Robin posted earlier about a NYT Magazine article on conformity. I was able to find an online copy of the scientific paper here: http://psr.sagepub.com/cgi/reprint/10/1/2.

The synopsis from the NYT is not complete. Of the 12 times that people were challenged to disagree with the social consensus, the most popular choice was to agree 0 times. 25% of the subjects did this. The second most common was to agree 3 times, done by 14%. Third most common was agreeing 8 times, 11%. Only 5% went along with the crowd all 12 times.

I think it’s quite significant that 25% of subjects never went along with the crowd and stuck to their own perceptions. In total, only 32% of the answers were wrong.

I’m not sure I follow Robin’s comments on this. It seems to me that this re-interpretation of the classic experiment suggests that people are not as conformist as generally thought. That would mean that we do more than merely give lip service to celebrating independence, that culturally we are quite effective at following the ideal of independent thinking.

The key question is, what is the right thing to do here? Should one conform when presented with 8 people denying the evidence of one’s own senses? I argue that it is the right thing to do.

Now of course, if you know you’re in a psychological experiment, maybe you can’t help but be suspicious that something fishy is going on. But in general, in real life, if 8 people come in and tell you that your perceptions are completely wrong, you should take it very seriously. I imagine that in the history of the world, in the great majority of such situations, the 8 were right and the one was wrong. As an example that some may be familiar with, if a bunch of friends come in and tell you you’re drinking too much, while your perception is that you can easily handle the alcohol, you should probably listen to them.

I would suggest that conformity is the right thing to do in these situations, and to that extent I am rather dismayed that the subjects were as non-conformist as this data shows.

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Conformity Myths

Conformity gets a bad rap.  From NYT Mag:

The psychologists Bert Hodges and Anne Geyer recently took a new look at a well-known experiment devised by Asch in the 1950s.  Asch’s subjects were asked to look at a line printed on a white card and then tell which of three similar lines was the same length. The answer was obvious, but the catch was that each volunteer was sitting in a small group whose other members were actually in on the experiment. Asch found that when those other people all agreed on the wrong answer, many of the subjects went along with the group, against the evidence of their own senses.

But the question (Which of these lines matches the one on the card?) was not posed just once. Each subject saw 18 sets of lines, and the group answer was wrong for 12 of them. Examining all the data, Hodges and Geyer found that many people were varying their answers, sometimes agreeing with the group, more often sticking up for their own view. (The average participant gave in to the group three times out of 12.)

This means that the subjects in the most famous "people are sheep" experiment were not sheep at all – they were human beings who largely stuck to their guns, but now and then went along with the group.

Our culture gives lip service to celebrating independence and dengrating conformity, but not only do we not actually discourage conformity much, it is not obvious that conformity as typically practiced is such a bad thing. 

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Joint Configurations

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This post is part of the Quantum Physics Sequence.
Previously in series:  Configurations and Amplitude

The key to understanding configurations, and hence the key to understanding quantum mechanics, is realizing on a truly gut level that configurations are about more than one particle.

Fig4_2 Continuing from yesterday, here’s an altered version of the experiment where we send in two photons toward D at the same time, from the sources B and C.

The starting configuration then is:

“A photon going from B to D, and a photon going from C to D.”

Again, let’s say the starting configuration has amplitude (-1 + 0i).

And remember, the rule of the half-silvered mirror (at D) is that a right-angle deflection multiplies by i, and a straight line multiplies by 1.

So the amplitude flows from the starting configuration, separately considering the four cases of deflection/non-deflection of each photon, are:

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