Showing posts with label Quantum Mechanics. Show all posts
Showing posts with label Quantum Mechanics. Show all posts

Tuesday, May 22, 2007

Quantum Mechanics for Dummies #2: Observation

Well, it's been a while, but an e-mail exchange not long ago prompted me to get back to this series. If you haven't yet read it (or need a refresher), I recommend you go back and read my first post, on the Wave Nature of Matter. This time, I'm going to be talking about something that can happen to waves and is a very important part of Quantum Mechanics: the collapse (which is closely tied into the concepts of a measurement and an observation).

But before that, we need to cover the concept of eigenstates. (For anyone who already knows about it, this is a vastly simplified explanation, so you're probably safe just skipping past.) Unlike particles, waves don't have discrete positions they'll be in, but rather a range of possible positions they could be found at at any time. Since waves travel, the probability distribution of where it will end up will often change with time. However, there are ways to trap waves, such as a beam of light between two mirrors. In these cases, the wave can only take on discrete stable patterns so that it doesn't end up interfering with itself. These discrete patterns are what are known as eigenstates.

But the probability distribution for a wave won't always fall perfectly into one eigenstate. Often its probability distribution will be a linear sum of multiple eigenstates. Due to interference between the waves of the different states, this pattern won't be perfectly stable and will change somewhat with time, but it will generally do so in a periodic fashion.

This also isn't limited to cases such as light waves. For instance, all particles have a property known as "spin" (if you take that exactly as it sounds, you're close enough). If you measure the spin of a particle such as an electron, you will always get one of only two values, regardless of the orientation of your measuring device: +h/(4π) and -h/(4π) (called "spin up" and "spin down." Think of it as spinning clockwise or counterclockwise).

Both spin up and spin down are eigenstates of the electrons spin, but it's not necessary for the electron to be exactly in one of these states. To generate this, say you take an electron that you just measured to be spin up, then made a second measurement at a right angle to the first. Classically, you would expect to measure a spin of zero, but this isn't one the allowable results. Instead, you'll end up with a 50% chance to measure spin up and a 50% chance to measure spin down.

And here's where things get a bit strange: After you measure it once, if you go back and measure it the same way, you'll always get the same result. It's no longer a 50/50 split. However, if you go and measure it back in the initial direction, it's a 50/50 split here. The implication here is that by measuring the spin of the electron, you somehow changed it - in this case so that it was in a spin up eigenstate with respect to your new measurement.

What's happened here is known as wavefunction collapse. After your first measurement, the electron was spin up in the first direction, which corresponded to a 50/50 split when measuring from the second direction. This 50/50 split was a combination of two eigenstates for the electron. When you then measured it in this direction, one of those states was randomly selected and the electron then became 100% in that state.

And this when the misinterpretations start to happen. The reason for the misinterpretations is the fact that quantum physicists happened to use one particular word in describing it: "observation." In the sense of what happens, an observation simply entails measuring the wavefunction of something, causing said wavefunction to collapse.

But that's not how the word "observation" sounds to the layman. When many hear it, they then think, "So, does this mean that reality is unresolved until I look at it?" People started to believe that quantum states wouldn't resolve until the information from them had filtered its way to a human mind. Even when it came to quantum physics, people wanted to put the human mind on some special pedestal in the universe.

This argument wasn't limited to laymen however. At first, the best quantum theorists couldn't decide themselves what exactly caused the wavefunction to collapse. All they knew was that if they weren't measuring particles, the wavefunction wouldn't collapse, and if you were, then it would. (They tested this by means of the double-slit experiment, which I mentioned in my previous post in this series.)

So, you have scientists not knowing the answer and using a word which heavily implies that human consciousness actually is the answer, and what do you expect happens? People pick it up and start extrapolating, saying that we then must create reality with our minds and be able to control it as we see fit. Even if we were to accept the premise (that being processed by a human mind is what caused the collapse of a wavefunction), this in no way implies that the human mind actually creates or can control reality. The results are still inherently random, whatver the processing mind may wish.

Beyond that, there's actually good reason to believe that it isn't a human mind that causes the collapse of a wavefunction. Let's go back to the case of the double slit experiment, which is our best way of determining whether or not a wavefunction has collapsed. In this case, we'll be shooting electrons from an initial source through one of two slits. One foot beyond the slits is a detector screen. We know that if the electron's wavefunction is uncollapsed at the slits, we'll end up seeing an interference pattern on the screen, while if it's collapsed, we'll see the sum of two diffraction patterns.

If we just let the experiment run, without any detectors, we end up seeing the interference pattern (nothing's causing the wavefunction to collapse). If, instead, we put in detectors at each slit that will notify us if the electron passes through (say by blinking a light on the left or right side), we see the sum of diffraction patterns on the detector screen. Now, what if you were to try this: Have the detectors at the slits and turned on, but don't look at the lights. You could simply disable the feature that has it flashing the lights on the detectors and not store data of which slit the electron passed through, so no human could ever know which way it went.

In this case, we can expect to see one of two outcomes: Either we see an interference pattern, which means that without a human observing it, the wavefunction wouldn't collapse, or we could see a sum of diffraction patterns, which would mean the interaction of the electron with the detector (or some process within the detector after the detection) caused the collapse. This has in fact been done, many times. Very frequently, scientists did experiments using a detector but didn't care which slit was detected, and so they didn't set it up to tell them this data. The result of these tests? The wavefunction collapsed anyways, so human consciousness is not necessary to cause the collapse of a wavefunction.

Why then, do we still see people claiming that it is? Mostly it's do to a poor understanding of the subject. They see words like "observation" and interpret it to mean human observation. Even some professors of quantum physics (including one I had as an undergrad) made this mistake, and then taught it as accepted fact to their students. The only way you can really know for sure on something like this is to go to the experiments themselves. Fortunately, this particular phenomenon is testable, and it has been tested.* Unfortunately, this won't stop some people; I raised this issue up with my professor at one point, and he said testing it was a waste of time because he knew that human consciousness had to be involved. Well, you can't convince everyone.

*Edit to add: Unfortunately, no one seems to have a link to the studies that actually test this, most likely because they were done so long ago that they were never published online anywhere. Actual science has moved on far past this point, while popular science is just starting to get interested in it. I've asked a few people in the know about it, and while some, like the professor mentioned above, still hold to the view that it's human consciousness that does the collapsing, the consensus is pretty clear that the collapse happens long before any human mind looks at whether the particle was detected in either slit.

In fact, even when humans are looking at this, there's so much processing that goes on in the technology that interprets the data that the particle as already traveled and hit the plate at the end before information about which slit it passed through reaches the mind of a human (the "flashing light" is just a metaphor, it's not what's actually done in these experiments). So if it was human thought that was controlling these outcomes, then this result would also have to reach back in time to collapse the particle's wavefunction at some point before it hit the plate.

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Other posts in this series:

Quantum Mechanics for Dummies #1: Wave Nature of Matter

Proceed with your information binge...

Wednesday, April 25, 2007

Why Blogism?

(Hey, it worked for Skepticism!)

Well I got tagged for this by TheBrummell (yes, it did get around to me), so here goes, a list of reasons why I blog:

  • It's something to do. Honestly, this might actually have been the biggest reason for my starting this blog. I had a ton of free time at work (what can I say? I was so good at my job they couldn't find enough for me to do), and I needed something to do. So I blogged. I still have lots of free time around school, and I'm on a short vacation right now, so I still need something to do.
  • Community. When I started this blog, I was just losing touch with all my friends from high school. I didn't plan on using this blog to make new friends online, but when it started to happen, it became a reason to keep going.
  • Interacting with "famous" people. Sure, anyone can go and post on the blog of someone moderately famous in the blogosphere, but it's an entirely different feeling when they come and post a comment on your blog. (Yes, he was correcting a minor mistake I'd made, but I've corrected him on occasion too, and I maintain that I'd prefer to be corrected than leave a mistake up.)
  • I can help grease the wheels of skepticism. I noticed early on that most of the big swaths of skepticism are already covered in various places by very good bloggers. I've found a few subjects that went unmentioned and covered them myself, but that's not my primary contribution to the cause. The most popular posts I've done have actually been what I call "Greasing" posts, where I talk more about the philosophical side of what we're doing. This includes my Why Skepticism? posts and the Distilled Wisdom series, which give explanations of why this is important and how you can argue better, respectively. While these posts aren't directly attacking woo, they serve the purpose of helping other bloggers attack it better. For instance, my second Why Skepticism? post showed how Godel's Incompleteness Theorem actually serves to help disprove faith rather than put a limit on science, as many woos are prone to claim.
  • I can teach people about science. One thing I've noticed is that many people are genuinely interested in learning about the scientific picture of the world. The problem is that they see huge barriers such as having to be great at math and studying and getting an undergraduate degree before they can even be told qualitatively what's going on. With this blog, I can create a bridge out to them to teach them roughly what's going on without having to drown them in math. It's no coincidence that my Quantum Mechanics for Dummies post is the most frequent target of Google hits (beating out Faith no More lyrics and Bible quotes by a wide margin).
  • I get to randomly reference Terry Pratchett, this note included.
I can't think of the expected five people to tag with this that haven't already been hit, but I'll send out a couple to Akusai and Tom Foss. Let's see what you've got.

Proceed with your information binge...

Wednesday, December 13, 2006

Quantum Post Tunneling

Well, I'd written up a post all about how woos misuse the term "Quantum," but apparently it's tunneled accross the internet to a more appropriate location at Rockstar's Ramblings. If you want to read it, you can find it at Doggerel 17.1: "Quantum" (Take Two),

Proceed with your information binge...

Friday, December 01, 2006

Excuse me while I spasm uncontrollably

Well, the campus newspaper has done it again. The highlighted piece of woo this week: Global Orgasm Day. In the Science section of the paper no less. Granted, it was a "Community Editorial" (which is what they call very long letters to the editor), but they still did make the decision to print it, and what section to put it in.

Now, it isn't posted online yet, so I can't give quotes (without typing the whole thing up myself, which I am not looking forward to doing) or link to it just yet. When it is, expect to see that here.

Edit: You can see the entire article here.

The article justifies the possible effects of GOD (no, not God, GOD) by bringing up Princeton's Global Consciousness Project. This was inspired by work done in PEAR (The Princeton Engineering Anomalies Research), which is about to be shut down because it's a collosal waste of money and effort. Good thing to appeal to there.

About half of the article is spent just explaining how things work over there, when it could be summed up in one sentence: They watch random numbers and see if they deviate from expected patterns during big events. Yeah, well I've got a newsflash for you: Deviations are to be expected in small time frames. The laws of probability demand it.

When the article finally gets around to an actual claim, it says:

During times such as natural disasters, wars, 9/11 or mass meditation and prayer, the numbers generated deviated from the pattern.


So, around the times of these events, the numbers didn't have a perfectly chance distribution. Maybe that would mean something, if there weren't a few huge problems with how they work:

1. There's no set time-frame for when the deviation has to be found, so it's judged subjectively. For instance, the deviation associated with the World Trade Center attacks occured a couple hours before the attacks. Opening it up like this increases the likelihood of them finding some period where the numbers deviate a little.

2. There's no set criterion for how much the numbers deviate for it to be considered significant. Again, this is all done subjectively, allowing for very weak deviations to be counted as significant.

Using guidelines as loose as these, I betcha I can find a deviation to match any given event. In fact, I'll predict right now that there'll be some slight deviation right at the time I'm typing this post.

The article goes on to claim that this is because "information, or the perception thereof, will exert an effect on the quantum energy and will change the way the numbers are produced." Odd, in my quantum mechanics classes, we never talked about how macroscopic information could effect whatever he means by "quantum energy." And the closest we ever got to talking about the effects of sex on quantum mechanics was the "Bra" in "Bra-Ket."

In fact, you know the thing about Quantum Mechanics that rules stuff like this out? Quantum Mechanics may have very weird results on small scales and with individual particles, but once you blow it up to macroscopic scale, they all get averaged out. It's only very precise experiments on very small numbers of particles that show any quantum effects. Just wait, I'm sure that one of these days "Appeal to Quantum Mechanics" is going to become a recognized logical fallacy or pseudo-fallacy. It's getting more and more popular by the day.

With this in mind, I've currently finished two of my three sample articles for getting my own column (which is apparently desperately needed). If anyone's available to look over them and comment on them, please drop me an e-mail (address in my profile) or comment here.

Proceed with your information binge...

Saturday, November 18, 2006

Quantum Mechanics for Dummies #1: Wave Nature of Matter

I got into an involved explanation of Quantum Mechanics a few days ago over at Bad Astronomy, and it reminded me of an idea for a series of posts I've had on the backburner for a while. In this series, my goal is to make Quantum Mechanics somewhat intelligible to those who haven't studied it and clear up some common misconceptions about it.

In this first post in the series, I'm going to discuss what Quantum Physicists call the wave nature of matter, and how a particle can act like both a particle and a wave. But before we go into that, I should explain by what we normally mean by "particle" and "wave."

First, in a classical sense, what is a particle? Particles are generally very small, and possibly infinitely small, being just a point in space. They can have numerous properties such as mass, electric charge, and magnetic moment, which determine how they act and interact in the universe. When they travel from place to place, they do so with a definite, linear path.

Second, what is a wave? Waves are a bit harder to explain, so I'll go with what Wikipedia says on it:

A wave is a disturbance that propagates through space or spacetime, often transferring energy. While a mechanical wave exists in a medium (which on deformation is capable of producing elastic restoring forces), waves of electromagnetic radiation (and probably gravitational radiation) can travel through vacuum, that is, without a medium. Waves travel and transfer energy from one point to another, with little or no permanent displacement of the particles of the medium (there is little or no associated mass transport); instead there are oscillations around fixed positions.


Waves also have properties associated with them, but they're generally different from particles. First, there's amplitude, which is, in a simple sense, the height of the wave. There's also frequency, which is how many oscillations a wave makes per second. Frequency and amplitude together determine the energy of the wave (with the energy being proportional to the frequency and the square of the amplitude). Classically, the amplitude and frequency of a wave are both continuous, so a wave with a given frequency can have any value of energy.

Waves also translate in space differently from particles. Instead of simply following straight lines, waves spread out. If a wave passes through a long, narrow corridor, it will spread out at wide angles when it leaves, unlike how a bunch of particles going through the corridor would act. In fact, waves act in the opposite manner to particles in this case as the thinner the corridor is, the more the wave spreads out upon leaving. This phenomenon is known as diffraction.

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Classically, light was always seen as a wave. It showed all the expected properties of waves, having a measurable frequency, diffracting, etc. But eventually a problem was found: Light of a given frequency could only have quantized energy. What this means is that essentially if you have light that's all of one frequency, there are only certain set values of its total energy that it can have. For instance, it might be allowed to have energy of 1.1 eV, 2.2 eV, 3.3 eV, and so on, but it could never have an energy of 1.5 eV or 0.5 eV unless some of it is at a different frequency.

This also meant that there was a minimum energy that light could have. If light were made out of particles (what we now call photons), this could be explained quite easily: Each particle would have energy equal to a constant times its "frequency," and they added together to form the total energy of the light. The problem was that particles classically couldn't have frequency.

So we were left with a contradiction, and had to form a new theory. Light had properties of both particles and waves. But was it particles that traveled like waves, or maybe waves that just happened to be quantized somehow? Further experiments were necessary to determine what exactly was going on.

The most famous of these experiments was the Double-Slit Experiment. In this experiment, light first diffracts out of one slit, allowing it to spread out and hit two more slits. The light that passes through each of these slits diffracts again, and the wave then hits a detector.

If a conventional wave goes through this, we see a strange interference pattern on the detector. This is cause by the waves coming from each slits being at different points along their wavefunctions. If one is at a peak and the other at a valley, the amplitudes cancel out and no light will appear at that point. If both are at peaks or valleys, then the amplitudes at together, and since we then square the amplitude to get the energy, we get four times the energy at this point as we'd get from a single wave, or twice what we'd get from two waves. Particles, on the other hand, show no interference patterns. This means that we can use a double-slit experiment to determine whether light is acting like a particle or a wave.

So, this experiment is then performed. A lot of light is shot out, and it does indeed show the interference pattern. So, if light is a bunch of particles, they can somehow interfere with each other, it would seem. We had the technology to decrease the emission rate of light low enough that only one photon was being sent out at a time, so this was the logical next step.

When we performed this experiment, the results were extremely surprising. When you plotted the frequency with which the photon would strike different points of the screen, it matched up with the interference pattern! Even single photons were acting like waves. This is something that just wasn't possible if you treated them like particles. The first problem was that particles wouldn't diffract like waves, but these photons were doing this. The second problem is that, even if particles could diffract, you would expect them to go through one of the two slits, and then diffract onto the detector. The pattern that appears should then be the some of the diffraction patterns from the two slits, but it was instead the interference pattern.

Then things got stranger. We tried firing things that we were pretty sure were particles through a double-slit experiment, such as electrons. They, too, showed a diffraction pattern. We went bigger and shot atoms through it. Same deal. Our record so far has been shooting Bucky Balls (spherical molecules of 60 carbon atoms) through it, and even they act like waves.

It was becoming cliché at this point, but there was an even stranger development still to come. We figured that if these particles were acting like particles, they had to be going through just one of the slits. We then set up detectors at both slits that would tell us if a particle was passing through it. We did so, and we got results from it: a 50/50 spread of particles between the two slits. But there was a problem. When the detector was on, the interference pattern went away! If we turned off the detector, the interference pattern appeared again. Things were seriously screwed up.

Take a few minutes to ponder this. It's taken scientists many decades, and most of them still don't have a good picture of what's actually going on that could cause this. There are a few theories out there, but none are very well accepted. I'm going to go into my personal interpretation of how this works, but remember that there are others.

When any particle is traveling, it does so as a probability wave, that is, a wave that represents the probability of the particle being at a certain point if we measure it. This isn't a theoretical wave (in my picture, at least), and the probabilities aren't simply an oversimplification like in Statistical Mechanics. Instead, the wave is an actual object, and the probability is a fundamental law of the universe.

This probability wave has properties like normal waves, even if it represents a "particle" like an electron. These properties include frequency and the value of the wavefunction at a point. Squaring the value of the wavefunction is what gives us the probability of it showing up in a certain area. Like other waves, if its path is split up, it can interfere with itself, causing an interference pattern in the probability it will show up in an area.

Now, from this description, the more statistically inclined of you might be wondering about one possible problem. Take a simplified case where a probability wave has a 50% chance of resolving into a particle in the right half of an area, and a 50% chance of resolving into a particle in the left half. Also, let's assume that the wave hits the entire area at the same instant of time. Shouldn't the probability distribution look something like the following?

Shows up in right only: 25%
Shows up in left only: 25%
Shows up in both: 25%
Shows up in neither: 25%

Well, the above distribution is only valid if the probabilities are independent. We know from experiments that this isn't the case; a particle will always resolve in exactly one spot. But the wave hits the entire surface at one instant, and Relativity tells us that the speed of light is an upper limit on data transfer. How does the left half of the wave know whether the particle has resolved in the right half, if information can't get there fast enough?

What I've described here is part of what's known as the EPR paradox. Somehow, for quantum mechanics to work the way it does, there must be some form of information transfer from one part of a probability wave to another so that particles don't randomly disappear or split into two. It would seem at first glance that this would violate Relativity, but this isn't quite so. The information you get from it resolving or not resolving in one area is no more than logical inference, and this is all the universe is doing as well. In addition to a basic law of randomness, the universe also seems to have a basic law of inference on the resolution of these waves, so that we end up with conservation of energy.

Well, that's enough for today. If there's anything in there that's still confusing, please leave a comment and ask for clarification on it; I'll be glad to explain.

Note to anyone who already knows some QM: Yes, I'm aware I came very close to talking about entanglement in the last couple of paragraphs, but I chose not to go into detail about it. This is simply because entanglement is getting its own entire post in this series.

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Other posts in this series:

Quantum Mechanics for Dummies #2: Observation

Proceed with your information binge...