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.

* * * * *

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.

* * * * *

Other posts in this series:

Quantum Mechanics for Dummies #2: Observation

43 comments:

Anonymous said...

Very helpful, a guide for dummies isnt quite true however. I've been studying physics fo the last 2 years and although i understand this, many uneducated people in the world of physics or 'dummies' would have a slight problem. However, the information is correct and the explination is well written, in simple easy to understand term.

Anonymous said...

I'm a junior in high school taking advanced physics. While your guide wasn't exactly easy for me to understand, I did find it extremely informative and helpful. Thanks for posting it.

Adam "Cody" said...

Hi,

I'd consider myself pretty much a dummy at physics. I've graduated high school, so I believe mentally I'm at a level where I can understand Physics although I've never taken a class on it because I'm not very fond of math.

I feel the article was easy to understand, until I reached this line: "Light of a given frequency could only have quantized energy." Wait, what? What does it mean when light is "quantized"? If you are writing an article that explains it to dummies you must explain the basics you're ideas and explanations are based on. I looked up the definition of when something is Quantized, but it still doesn't really make sense.

The rest of the article is alright, but starts becoming harder to understand. You should probably write a short "quantum basics" article if something you talk about starts requiring quantum terms like "quantized".

Infophile said...

Ah, sorry about that. Anyways, a brief definition of quantized: It can only have certain discrete values. For instance, the light could have an energy of 1.1 J, 2.2 J, 3.3 J, and so on, but couldn't have anything in between those. I'll try to fit something into the article about this.

JS said...

A minor nitpick:

It's something of a stretch to claim that science has 'always' seen light as a wave. IIRC, Sir Isaac Newton, for one, figured light for a particle, since it casts sharp shadows. In the version of history I heard, the wave nature of light was not firmly and finally established until the 19th century with the acceptance of the Fresnel description of wave mechanics and the Maxwell equations for electrodynamics.

- JS

Jonathan said...

Well, I really have no background in physics or science - I'm a commerce-man myself, but I always had a soft spot for Quantum mechanics, Einstein's theories of relativity, time-travel, ten dimensions... that sorta stuff.. Anyways, this article was really put nice and lucidly. However, I have two queries.
a)The basic point made here is that merely observing/measuring an event automatically collapses the wave function into one outcome, right?
So then how does the interference pattern appear even though there is somebody WATCHING it appear on the screen?
b)Has the experiment actually been physically done on the scale of a single photon or electron, or is it just a 'thought experiment'.
Really appreciate the time you've taken to post on this blog. Will look forward to any explanations!

Jonathan said...

OK, I Got the answer to the (a) part of my question from Part#2!

Anonymous said...

just stumbled across this on my random journey through the 'net and was wondering if there was more to this delightful post. Perhaps I'm not seeing the link - I'd really like to read more!

Infophile said...

Ah yes, I forgot to include a link here when I made the second entry in this series (only other one so far). I've added it to the post, or you can find it here.

Lily.Bart said...

I found your site because I hit a daisy chain of information starting with 'casimir effect' and ending with quantized--which, like that other guy, doesn't make a bit of sense to me. Does it mean it has to have particles in it? And if I don't get quantized, will I never understand casimir effect? Is there a way to have a vocabulary for dummies on this too? Something to reference while I'm reading a post that would actually explain the term in dummy words rather than giving me more physics terms that I don't understand. But I really really appreciate your even taking this on, teaching us uninformed. Thanks for trying--it does help to know that light is both wave and particle. Why has no one ever told me this before? And why did that Stephen Hawking book I read not explain it that clearly?

Infophile said...

Hmm, well, I tried to explain "quantized" earlier in the comments ("For instance, the light could have an energy of 1.1 J, 2.2 J, 3.3 J, and so on, but couldn't have anything in between those."), but I'm guessing that didn't help for you. Let's try looking at this another way.

First, the dictionary definition of "quantum": (physics) The smallest possible, and therefore indivisible, unit of a given quantity or quantifiable phenomenon. (from Wiktionary)

Think of sand at the beach. From far away, it looks pretty smooth and continuous. Up close, though, you realize that sand is made up of many little particles (the quanta (plural of quantum) of the sand), which you can't break up. If we imagine that these are all the same size, then we can describe the amount of sand simply by the number of these particles. Also to note, this number will never take fractional values.

Many things in life are really like this. The amount of water can be described by the number of H20 molecules. It will always be a whole number (1, 2, 3, and so on), and never a fraction (1.5, 4.1, etc.). More abstract things don't seem to be this way, necessarily. For instance, with light, the frequency it can have isn't quantized (any positive value is possible), but the energy light of a given frequency can have is (it must be a multiple of its frequency times Planck's constant).

Does that help you out there? Please let me know if you have any further questions.

Lily.Bart said...

oh yeah, that was great. thanks! I do wonder why light is considered more abstract than say, the ocean.

Anonymous said...

if this is QM for dummies, I must be a vegetable. I consider myself semi-intelligent, but its very hard for me to wrap my mind around this. Like, I'm still trying to figure out how, if we can barely see atoms, you can tell that just 1 electron is being emitted from some piece of equipment?

Anonymous said...

this is really a QM for dummies. Im in Middle school, and i understand it. you write this in an easy to understand format...i like it! Very helpful

Beginner said...

Hi. When the detector is turned on to measure the percentage of particles moving through the double slits, you say the interference pattern disappears. Is this a demonstration of the 'uncertainty principle' whereby position and velocity cannot be measured together and both known to be precisely accurate because when one is measured accurately you disturb the other?

Infophile said...

Like, I'm still trying to figure out how, if we can barely see atoms, you can tell that just 1 electron is being emitted from some piece of equipment?

Basically, we can measure the power output, and we know how much energy an electron generally leaves with. From this, we can calculate the average time between emissions of electrons. When this is longer than it takes an electron to cross the distance, we know that we only have one traveling at a time.

Hi. When the detector is turned on to measure the percentage of particles moving through the double slits, you say the interference pattern disappears. Is this a demonstration of the 'uncertainty principle' whereby position and velocity cannot be measured together and both known to be precisely accurate because when one is measured accurately you disturb the other?

Nope, this is a different quantum phenomenon. In fact, there isn't really any good way to demonstrate the Heisenberg uncertainty principle. When measuring particle properties using light, you can prove that it's true, but no one's actually been able to prove it's true in general cases. (Now, the Robertson uncertainty principle is quite a different beast, though it's superficially similar... but that's another post.)

Anonymous said...

I really enjoyed this guide. I believe what the author might have meant by 'dummies' is someone who has no experience in the field of quantum physics. Naturally you would assume anyone who is getting into the world of quantum mechanics would have at least a slight background in science and could understand basic scientific terms. Once again, great guide in my eyes. If you are a true dummy though and reading really 'isn't your thing' try the movie "What the Bleep Do We Know?" It's funny and informative.

Anonymous said...

Thanks for the post! Have you heard of the book, "The Secret" by Rhonda Byrnes? I finished reading it and Quantum Physics happens to be related to it.

Infophile said...

Yes, I've heard of it. Frankly, in my opinion, it's one of the worst abuses of Quantum Theory in modern times. I could go on, but I think I'll just direct you to one of Skeptico's posts on the matter.

Anonymous said...

I'm 15 and am very interested in physics and how they apply to our universe. If you are not very educated in this subject or in Einsteins theory of general reletivity, I would reccomend "A Breif History In Time" by Steven Hawking. It really helped me wrap my mind around most of these theories. remember, god doesnt play dice! =D

Cameron said...

http://www.youtube.com/watch?v=vQe0oiaBssg
this is a video it's kind of goofy but it gets allot of stuff across for us visual learners

Draycos214 said...

i am only 13 and i found this artical a little helpfull, but still there was a lot i did not understand. so you should not call this QM for dummies

Anonymous said...

The article was good. I didn't care for the language. The "we" did this and "we" did that sounds like you are taking credit for discovering these theories.

Anonymous said...

im a freshman in high school and i understood this article pretty fully, with the exeption of a couple vocabulary terms (i too had the problem with quantized, until you explained it in the comments, thanks). I've always found physics very interesting and this article was very helpful.

Anonymous said...

im a freshman in high school and i found most of this easy to understand


thanks for posting it

Samual Jacob Aumedeaus Westmoreland "Sam" said...

it was good. but I still got lost. I'm only a Sophomore sorry. I need to take a class on this. So interesting (just can't wrap my head around it) :(. oh well.:)

Anonymous said...

I am an eighth grader, and I am doing a research paper on Quantum Mechanics. This was easy for me to understand, and it will be an important resource for me.

Infophile said...

Thank you. Feel free to let me know if you have any more questions.

Anonymous said...

Well this was indeed a helpful guide. I did need to support what I read here with other sites (Im a visual heavy learner).

One thing I did not quite get was the following,

'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.'

Could you be kind enought to enlighten me a bit further on this particular point.

Cheers,

Anonymous said...

if by "dummies" you mean people who are not studying anything closely related to quantum physics, then this is a very helpful guide. Personally, i'm in eighth grade and i understood it, so i'm sure most people (especially adults) would find it easy to understand.

dwhkrm said...

I dont understand this at all..

Anonymous said...

Several things here confused me. Waves from the same "particle" cancelling each other out sounds like a violation of the coservation of energy. Just divide a photon in 2 with 2 slits and arrange the slits so a wave crest and wave valley perfectly line up on the other side. Boom you destroyed energy? What am I missing here? Also the idea that subatomic particles behave in a way which contradicts the old newtonian paradigm I understand. But atomic structure? And huge carbon 60 molecules? How is that possible without splitting apart the molecules? We are not talking about waves anymore we are talking about matter, which has a definitve location in space time. Are you saying a molecule divides in two and comes back together on the other side, because that sounds very odd at best.

Infophile said...

Waves from the same "particle" cancelling each other out sounds like a violation of the coservation of energy. Just divide a photon in 2 with 2 slits and arrange the slits so a wave crest and wave valley perfectly line up on the other side. Boom you destroyed energy? What am I missing here?

I think what you're missing is the fact that what we see when we add up the wavefunctions is a probability distribution of where the photon will hit - it will always hit somewhere. Yes, you can line up the wavefunctions so that a peak from one slit and a valley from another will line up, and this will result in a probability of zero of hitting that point. However, other points won't cancel perfectly, and some will add together. In all, the distribution will have to normalize to one so that precisely one photon will hit.

Also the idea that subatomic particles behave in a way which contradicts the old newtonian paradigm I understand. But atomic structure? And huge carbon 60 molecules? How is that possible without splitting apart the molecules? We are not talking about waves anymore we are talking about matter, which has a definitve location in space time. Are you saying a molecule divides in two and comes back together on the other side, because that sounds very odd at best.

The best way to justify this is that big molecules like C60 are solid whenever they're constantly interacting with their environment - ie. you're shining a light on them. When they're in the dark though, with nothing to force a wavefunction collapse (see my other QM for dummies post, linked at the end of the main post), they behave as waves. So, if the only two times a buckyball has a significant interaction with its environment are when it's shot out and when it hits the detector, it will behave like a wave in between. A very, very complicated wave, but a wave nonetheless.

Pam said...

Just wanted to thank you for the most comprehensive thing I've been able to find on this subject to date! You did a very good job at explaining everything, and writing in a way to help me kind of picture what was going on. Everything was really well explained, and I really appreciate it! Thanks!

odrareg said...

You were doing all right explaining to dummies, until you decided and did bring up the quotation from wikipedia to explain what is a wave.

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

You know, if you have to quote Wikipedia, why even bother to explain it to dummies, just tell people to go to Wikipedia, and save yourself the good intention of helping dummies.


Write the whole article again, now without any reference except at the end mention your choice bibliography in the web which you believe is helpful to dummies who want to read more on the dummies level.



Yrger

TheTwistedllama said...

Hi, Im a high school student who has never taken physics, (and a wikipedia surfer) but i just wanted to say how interesting your article is. I actually can get the gist of it without getting lost in strange terms and bizzare examples like "superfluidity" whatever that is. So thanks. I was curious about this kind of thing, so im glad i can indulge it without resorting to classes

Anonymous said...

Hi, I'm a 78 year old gramma having a conversation with my 'master's degree' meteorologist son-in-law. Is this a true statement" physics says that nothing exists until we observe it"? How can one observe something that doesn't exsist?

Infophile said...

In, short, no, that's not true. It's a common misinterpretation based on the use of the word "observe." First of all, when quantum physicists use the word "observe," they don't mean it has to be a human doing the observation. A human will certainly qualify, though we're not entirely sure what else will.

Secondly, it isn't that things don't exist until they're observed, it's that they're unresolved. For instance, say you flip a coin and grab it out of the air, keeping it in your enclosed hand as you lay it on the table. While your hand is still covering it, you can't tell whether it's heads or tails. In the real world, we know it's one or the other, even before you remove your hand. The coin certainly exists, as you can feel it under your hand, you just don't know what state it's in.

In the Quantum world, things are a bit different. Not only do you not know whether the coin is heads or tails, the universe itself doesn't know (if you believe in a God, feel free to invoke him here in place of the universe). It just hasn't decided, and it won't until the coin is "observed" (though remember it doesn't have to be a human to do the observing). The coin still exists, it's just that some of its properties could go either way until it's observed.

Hope this helps you out. Let me know if you need anymore clarification.

Mallika said...

"Quantized" seemed perfectly self-explanatory to me, and you even gave numerical examples; I didn't initially understand why this confused more than one person - till I figured might've sounded like a 'circular definition' to some ears. They didn't want to have to know what 'quantized' meant, whil ethey were learning what quantum meant :)

The detour suggesting the 25% probabilities for the four events and then explaining it away seemed unnecessary to me, as the 25% idea did not seem to me like a natural expectation. And I would count myself as statistically inclined, since I have a degree in the subject, albeit not one I use often. But perhaps it will be useful to others, to whom this strange idea suggests itself.

William said...

Would it sound too crazy to presume that this is evidence of a soul? I mean if one particle of our bodies is also energy at the same time, then our whole body would be a solid and energy at the same time right?

Also.. what if there was no such thing as a seperate entity? I mean, what if there was only one true entity in existance, and everything else was just a fluctuation in that existance.
Take a human or animal's body for example, It's composed of trillions upon trillions of individual "living" organisms that all work together to make "one" organism. I dunno, I know this is all kind of unorganized, and late for that matter, but I just wanted to throw those ideas out there.

eis2 said...

AHHHHHHHH SO MANY BIG WORDS
sounds smart tho

No said...

What gives scientists the right to make 'probability' a fundamental law of the universe!? Everything is based on randomness!? I mean aside from the chances of a hidden variable that humanity simply is too stupid to find, there could also be other factors such as things even smaller, messed up readings, wrong techniques and whatnot.

Kelowna Web Design & Hosting said...

So a particle can wave at you when it is going by as long as you don't look, but if you look the particle can't wave? What if it just shouted "yoo-hoo!" and left it at that?