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Normandy6644
2005-Feb-25, 05:37 AM
I'm trying to better understand how to draw the wavefunction given the potential without making any real calculations (French and Taylor call it "qualitative plots"). Let's say I had this potential:

http://img.photobucket.com/albums/v506/Normandy6644/qm.jpg

I think I understand the basics of how to draw the wave function for each eigenstate, but I'm having trouble actually doing it, i.e., I think that the amplitude is larger for regions where E-V is smaller (corresponding to a lower kinetic energy), but some of the other things are just hard to see. Anyone know much about this?

Tensor
2005-Feb-25, 05:40 AM
I'm trying to better understand how to draw the wavefunction given the potential without making any real calculations (French and Taylor call it "qualitative plots"). Let's say I had this potential:

http://img.photobucket.com/albums/v506/Normandy6644/qm.jpg

I think I understand the basics of how to draw the wave function for each eigenstate, but I'm having trouble actually doing it, i.e., I think that the amplitude is larger for regions where E-V is smaller (corresponding to a lower kinetic energy), but some of the other things are just hard to see. Anyone know much about this?

I just started a intro to QM, so you'll have to give me a few months. 8) Although I'm sure there is someone around here that can help you out a lot faster.

Normandy6644
2005-Feb-25, 05:41 AM
Didn't you tell me you're taking a class too? What book are you using?

Tensor
2005-Feb-25, 05:45 AM
Didn't you tell me you're taking a class too?

Yep.


What book are you using?

Shankar's Principles of Quantum Mechanics.

Normandy6644
2005-Feb-25, 05:46 AM
Didn't you tell me you're taking a class too?

Yep.


What book are you using?

Shankar's Principles of Quantum Mechanics.

Oh man, getting right to the good stuff! We have a two semester sequence here, and I'm in the first one now, using French and Taylor. Next year I'll take the second one and use Griffths I believe. I also just ordered Gasiorowicz (sp?), which is supposed to be good.

Normandy6644
2005-Feb-26, 01:09 AM
Should this maybe get moved to GA or something? I know it isn't exactly astronomy, but I have a feeling it might get more responses in a science forum. :wink:

jnik
2005-Feb-27, 02:16 AM
Next year I'll take the second one and use Griffths I believe.
Hmmm. I don't see any reason to not just start with Griffiths (even if you aren't supposed to just yet); his texts are very clear and easy to understand (the only complaint about them is that they could be a titch more rigorous). Feynmann's chapters on quantum are pretty good too, especially for developing intuition after you've learned the concepts (and, well, everyone should own Feynmann anyhow).

Normandy6644
2005-Feb-27, 03:40 AM
Next year I'll take the second one and use Griffths I believe.
Hmmm. I don't see any reason to not just start with Griffiths (even if you aren't supposed to just yet); his texts are very clear and easy to understand (the only complaint about them is that they could be a titch more rigorous). Feynmann's chapters on quantum are pretty good too, especially for developing intuition after you've learned the concepts (and, well, everyone should own Feynmann anyhow).

The reason we don't start with Griffiths in the physics department (engineering physics does though) is that we have a two semester sequence, and they have only one. Our first class is just an intro to QM, whereas next spring I'll take the advanced course that goes more in depth. I have the Feynman lectures, and they are really good, especially at explain concepts.

Sam5
2005-Feb-27, 03:55 AM
Yep.


Have you read Feynman’s “QED The Strange Theory of Light and Matter”?

Tensor
2005-Feb-27, 04:05 AM
Yep.


Have you read Feynman’s “QED The Strange Theory of Light and Matter”?

Of course. It's a good non-technical explanation for anyone interested in QED, even those without a science backround.

Normandy6644
2005-Feb-27, 05:08 AM
That one looked really good, but I still haven't gotten around to it. It's a good book to read on a travel day, so maybe this spring.

Sam5
2005-Feb-27, 05:54 AM
Of course. It's a good non-technical explanation for anyone interested in QED, even those without a science backround.

Why do you suppose that in the book he said that Maxwell’s wave theory had to be changed, and why did Feynman refer to light waves as “particles”? Maxwell’s theory and diagram of 1873 clearly shows them as EM wave pairs that travel as “quanta” of specific energies. They are double field waves, not “particles”, and this is still the most common model of light as shown on many university websites, such as this one:

LINK (http://micro.magnet.fsu.edu/primer/java/scienceopticsu/electromagnetic/index.html)

Sam5
2005-Feb-27, 06:01 AM
Here’s another one. This is also Maxwell theory, and these are electric and magnetic waves, issued as individual units, wave pairs, and they are waves, not particles.


LINK (http://ethel.as.arizona.edu/~collins/astro/subjects/electromag7.html)

Taibak
2005-Feb-27, 07:23 AM
Of course. It's a good non-technical explanation for anyone interested in QED, even those without a science backround.

Why do you suppose that in the book he said that Maxwell’s wave theory had to be changed, and why did Feynman refer to light waves as “particles”? Maxwell’s theory and diagram of 1873 clearly shows them as EM wave pairs that travel as “quanta” of specific energies. They are double field waves, not “particles”, and this is still the most common model of light as shown on many university websites, such as this one:

LINK (http://micro.magnet.fsu.edu/primer/java/scienceopticsu/electromagnetic/index.html)

Shorthand. You're right that 'quantum' is the most correct word for what we're talking about, but due to force of habit, most people tend to think of particles as things that exhibit a certain set of characteristics and waves as things with a different set of characteristics. Light, like everything else on quantum scales, exhibits both particle and wave properties. As such, people tend to refer to photons, particles of light, when dealing with a situation where the particle-like properties dominate. Similarly, when dealing with a situation where the wave-like properties dominate, people tend to refer to light waves. It's just easier to simplify the model in those cases.

But, the problem is that neither is a completely accurate description. Fresnel and Young proved that light, like a wave, exhibits diffraction and interference and Maxwell's equations prove that light has the properties of an electromagnetic wave (incidentally, Maxwell didn't propose that light travelled as a quantum). You can't explain any of that by modelling light as a particle. On the other hand, the wave-theory of light can explain neither the photoelectric effect nor blackbody radiation but, as Planck and Einstein showed, you can explain them once you bring in particle properties.

That's why Feynman said Maxwell's theory needed to be changed. As good as his ideas were, they were incomplete. If light is simply an electromagnetic wave, his equations should tell you all you need to know about its behavior. The theory simply can not explain the photoelectric effect. That is, if light is a classical wave, like the ones shown in the diagrams you linked to, its energy would be related to its amplitude, basically its intensity. Now, shine your light on a piece of metal and the light will dislodge electrons. For a classical wave, the electrons would travel faster (that is, with a greater kinetic energy) if you increased the amplitude (energy) of the light. Turns out it doesn't happen. Therefore, light can not be a classical wave as Maxwell argued. That's where Planck and Einstein came in. Planck showed that light's energy was proportional to its frequency - which, again, is not a typical property for a wave. Einstein took that a step further and proposed that those corresponded to the energy of particles.

It sounds strange and, in all honesty, it IS strange. Still, the only way around this is for light to be both a wave and a particle. It's the only explanation that accounts for all of its properties. Now, I'm not sure what a photon looks like - I doubt anyone can fully visualize them - but the applets you linked to aren't actually photons. They're illustrations of Maxwell's theory of light, that is, light as a classical electromagnetic wave. They make a good approximation of a photon if they're finite. If it helps, think of those waves coming in little packets. Maybe think of a laser as sort of a machinegun firing little light-wave bullets.

Taibak
2005-Feb-27, 07:33 AM
For me it was Eisberg and Resnick during my first semester of quantum and Griffiths during my second. With the latter, my prof. tried to convince us that the cat on the back cover was only sleeping.

Normandy: Anyway, my QM is more than a little rusty so take this with a grain of salt, but it sounds like you're on the right track. Unfortunately, the only other advice I can give you is to think of the potential barriers as solid walls and your waves as strings. Pluck the string as hard as you want, it can't vibrate through the wall. I realise that's a hopelessly classical analogy, but hopefully it will help some.

Tensor
2005-Feb-27, 08:13 AM
Of course. It's a good non-technical explanation for anyone interested in QED, even those without a science backround.

Why do you suppose that in the book he said that Maxwell’s wave theory had to be changed, and why did Feynman refer to light waves as “particles”? Maxwell’s theory and diagram of 1873 clearly shows them as EM wave pairs that travel as “quanta” of specific energies. They are double field waves, not “particles”, and this is still the most common model of light as shown on many university websites, such as this one:

LINK (http://micro.magnet.fsu.edu/primer/java/scienceopticsu/electromagnetic/index.html)

Note the bolding. It's a good non-technical explanation for anyone interested in QED, even those without a science backround

Maxwell died in 1879, before the discovery of the specific particle properties of EM radiation. All the way up to the development of QED, physicists had argued over whether light was particles or waves. During Maxwell's lifetime, most physicists argued for waves. Currently, EM radiation is though of as having the properties of both a wave and a particle. For instance, the photons spin of 1 has no exact classical counterpart.

Note to Normandy or anyone else whose interested: Some lecture notes on relativistic wave equations at this (http://www4.prossiga.br/lopes/prodcien/lectures/) link.

Sam5
2005-Feb-27, 01:53 PM
Shorthand. You're right that 'quantum' is the most correct word for what we're talking about, but due to force of habit, most people tend to think of particles as things that exhibit a certain set of characteristics and waves as things with a different set of characteristics.

Ok, very good. That’s what I suspected. I’m going to go over your post line by line today and comment on it. I’d like your opinions about what I say. I’ll give you mine and you give me yours. Let me know what you think about mine. I want to run some ideas past you and see what you think about them.

I’ve been studying this stuff for some time, working with light rays and photons since the 1950s. Photons break up silver halide molecules into free silver and halide gas. Both frequency and amplitude are involved in this process. There are two types of “energy” involved over a square surface area of film, one is related to the frequency and another is relate to the amplitude per second (the number of photons arriving per second per square cm). The silver halides in film require certain frequencies to break them up, and they require certain light amplitudes to break more of them up more rapidly over a large area of film.

Maxwell did talk about the energy level of a single wave of light. He recognized that light carried a certain amount of energy in each em wave pair. He spoke of amplitude in terms of fewer or greater wave pairs per area per second, as if one wave pair always had only one single standard amplitude. More amplitude required more waves to travel side by side, or back to back, or both, in the form of long “rays” of wave pairs. The wave pairs are what we call “photons” today. I’ve got his book right here and I’m looking at it. So tell me what you think of this interpretation of what he said.

Taibak
2005-Feb-27, 04:21 PM
Shorthand. You're right that 'quantum' is the most correct word for what we're talking about, but due to force of habit, most people tend to think of particles as things that exhibit a certain set of characteristics and waves as things with a different set of characteristics.

Ok, very good. That’s what I suspected. I’m going to go over your post line by line today and comment on it. I’d like your opinions about what I say. I’ll give you mine and you give me yours. Let me know what you think about mine. I want to run some ideas past you and see what you think about them.

Sure. Why not? Like I told Normandy though, my understanding of quantum mechanics isn't all that great so there may be things I'll have to defer on and I'd much rather admit my ignorance rather than try to lead you down a wrong track.


I’ve been studying this stuff for some time, working with light rays and photons since the 1950s. Photons break up silver halide molecules into free silver and halide gas. Both frequency and amplitude are involved in this process. There are two types of “energy” involved over a square surface area of film, one is related to the frequency and another is relate to the amplitude per second (the number of photons arriving per second per square cm). The silver halides in film require certain frequencies to break them up, and they require certain light amplitudes to break more of them up more rapidly over a large area of film.

A better way of thinking about it is that each photon carries a specific amount of energy and that there are two ways you can control the total amount of energy the silver halide receives: changing the number of photons (the amplitude of the light wave) and changing the energy of each photon (changing the frequency of the light wave). Your example sounds very similar to the photoelectric effect, actually. Each photon can only react with one atom, so the more photons you use (the higher the amplitude of the light wave) the more reactions you cause. But, like you say, each photon needs a certain frequency, a certain energy, to cause the reaction to happen and if the photon doesn't have enough energy, it's not going to react.


Maxwell did talk about the energy level of a single wave of light. He recognized that light carried a certain amount of energy in each em wave pair.

Understandable. All waves do that.


He spoke of amplitude in terms of fewer or greater wave pairs per area per second, as if one wave pair always had only one single standard amplitude.

Huh? That's not amplitude. That's frequency. Different concept. Do you have a citation for this?


More amplitude required more waves to travel side by side, or back to back, or both, in the form of long “rays” of wave pairs. The wave pairs are what we call “photons” today. I’ve got his book right here and I’m looking at it. So tell me what you think of this interpretation of what he said.

To be honest, it'd help if you could provide a citation here because what you're describing is most definitely not amplitude. Amplitude is the height of each wavecrest; the number of crests that go past in a second is frequency. Related, but ultimately different concepts. For light, like any other wave, you can change one of them without changing the other (it's pretty easy to get a feel for this if you have a Slinky handy).

Also, I'm not sure what you mean by 'wave pairs.' Do you mean the electric and magnetic components of the wave? If so, let's refer to that as a single wave to avoid confusion (besides, you can't have one without the other so it really is one wave with two components). Either way, that's not necessarily a photon because that model doesn't capture the photon's particle-like properties. Alternatively, do you mean one crest followed by one trough? If so, then that's not a photon. Limiting the number of crests in a wave limits the wave's frequency (again, this is easy to show if you have a guitar or, preferably, the aforementioned Slinky) and experiments have shown that photons have no constraints on their frequencies.

Sam5
2005-Feb-27, 07:23 PM
Taibak,

Ok, later I’ll make some photocopies or text copies of Maxwell’s book and post them to show you what I’m talking about. I’m getting the Maxwell stuff out of Volume 2 of “A Treatise on Electricity and Magnetism”. He also published a diagram of electric and magnetic wave pairs traveling together.

I think one reason for some of the confusion is that there are two ways of thinking and two sets of terms: classical, and QM. I think in classical terms and you tend to think in QM terms. My own experiments and observational experience over the past 45 years make sense to me in classical terms.

For example, light amplitude in photography involves more photons hitting the film per square cm all at once (ie a brighter light producing more side-by-side photons) OR more exposure time (a dim light allowed to hit a square cm of film for a longer amount of time, thus producing more back-to-back photons). I’ve never heard of any way to add amplitude to a single photon. Can you refer me to any text about how to cause a single photons to be brighter or have more amplitude?

Taibak
2005-Feb-27, 08:48 PM
Taibak,

Ok, later I’ll make some photocopies or text copies of Maxwell’s book and post them to show you what I’m talking about. I’m getting the Maxwell stuff out of Volume 2 of “A Treatise on Electricity and Magnetism”. He also published a diagram of electric and magnetic wave pairs traveling together.

Or you could just quote the relevant lines. Whatever's easier. Either way, as Tensor pointed out, Maxwell's book isn't the whole story. If you want to understand what a photon is, you have to put Maxwell aside and start looking at quantum mechanics.


I think one reason for some of the confusion is that there are two ways of thinking and two sets of terms: classical, and QM. I think in classical terms and you tend to think in QM terms. My own experiments and observational experience over the past 45 years make sense to me in classical terms.

Well, I appreciate the vote of confidence but, to be honest, I usually think in classical terms. In fact, so doesn't just about everyone else. Most of the things we'll observe throughout our lifetime can be explained perfectly well using classical physics. You only need to bring in quantum mechanics when you start dealing with ridiculously small objects, such as subatomic particles.

But just because you can usually think about things in classical terms doesn't mean that you can think about everything that way. To use a fairly mundane example, you can't explain all the properties of solder without using quantum mechanics. From a classical point of view, the two wires you soldered together are conductive but the solder itself is not. To a classical electron, the solder is an inpenetrable barrier. Quantum mechanics, on the other hand, provides a mechanism (quantum tunneling) that explains how the current manages to get through there. Granted, if you're just interested in the practical side of this (that is, if all you care about is that you can solder two wires together to make a circuit) there's no reason to bother with the quantum mechanical side of it, but to understand what's actually happening at the atomic level there's no way around the theory.


For example, light amplitude in photography involves more photons hitting the film per square cm all at once (ie a brighter light producing more side-by-side photons) OR more exposure time (a dim light allowed to hit a square cm of film for a longer amount of time, thus producing more back-to-back photons). I’ve never heard of any way to add amplitude to a single photon. Can you refer me to any text about how to cause a single photons to be brighter or have more amplitude?

Not off the top of my head, no. Really, this is something that's implicit in most any quantum mechanics textbook since the authors assume that anyone reading them already knows what a wave is. The key is that each individual photon is both a particle AND a wave. As such, each individual photon, despite acting exactly like a particle in some situations, has a wavelength, frequency, and amplitude. Also, keep in mind that photons add like waves to produce one big wave. That is, where two crests meet you get a bigger crest and where a crest meets a trough you get nothing. For the photon's particle-like properties, the peaks in that larger wave are where you find the most photons. Conversely, you won't find any photons where the wave is flat.

For better or worse, this is just one of those places where common sense and intuition break down. There is no analog for the wave-particle duality in everyday life. It's not something our brains can visualize particularly easily and we're stuck describing it with terms that, in some cases, were developed centuries before this stuff was even thought of. Sooner or later, if you want to understand this, you're going to have to learn the math. There really is no other way to fully explain quantum mechanics.

Fortis
2005-Feb-27, 10:34 PM
Another really important effect that requires QM to be quantised is blackbody radiation. You can derive the long wavelength part of the function without too much difficulty on classical grounds, but to defuse the UV catastrophe you have to start quantising. :)

Normandy6644
2005-Feb-27, 11:08 PM
Another really important effect that requires QM to be quantised is blackbody radiation. You can derive the long wavelength part of the function without too much difficulty on classical grounds, but to defuse the UV catastrophe you have to start quantising. :)

I always thought the name "Ultraviolet catastophe" was pretty cool. :D

Sam5
2005-Feb-27, 11:35 PM
Or you could just quote the relevant lines. Whatever's easier. Either way, as Tensor pointed out, Maxwell's book isn't the whole story. If you want to understand what a photon is, you have to put Maxwell aside and start looking at quantum mechanics.


Well, as long as university websites and books still show drawings and animations of the 1873 Maxwell electric and magnetic wave, I’ll continue to consider it as a good model. You might want to read a couple of Maxwell books yourself. In Volume 1, 1873, he was the first guy to suggest that the earth go on a fundamental atomic clock time standard.

And when Feynman finally has to show a drawing of a photon in his book, and he uses a little wavy line similar to the ones in the Maxwell model, rather than using a little round marble type “particle” drawing, I’ll not be too quick to give up the Maxwell model.


But just because you can usually think about things in classical terms doesn't mean that you can think about everything that way. To use a fairly mundane example, you can't explain all the properties of solder without using quantum mechanics. From a classical point of view, the two wires you soldered together are conductive but the solder itself is not. To a classical electron, the solder is an inpenetrable barrier. Quantum mechanics, on the other hand, provides a mechanism (quantum tunneling) that explains how the current manages to get through there. Granted, if you're just interested in the practical side of this (that is, if all you care about is that you can solder two wires together to make a circuit) there's no reason to bother with the quantum mechanical side of it, but to understand what's actually happening at the atomic level there's no way around the theory.

I have a roll of Radio Shack solder right here, and I find that a few-inch length of it conducts electricity just as well as a copper wire. I’ve never heard of any scientist say it blocks electricity. Is that some new idea or what?

Sam5
2005-Feb-27, 11:41 PM
For better or worse, this is just one of those places where common sense and intuition break down. There is no analog for the wave-particle duality in everyday life. It's not something our brains can visualize particularly easily and we're stuck describing it with terms that, in some cases, were developed centuries before this stuff was even thought of.

Sure there is. You can knock over a magnet without touching it, by moving another magnet near it. It’s the moving field in between the two magnets that carries the force. You don’t have to knock the one over with a “particle” when a field wave can act like a particle and knock it over. Anyway, you hear by means of field waves. No “particle” ever hits your ear drum or your cilia, only fields. That’s the way you see too.

Sam5
2005-Feb-27, 11:43 PM
I always thought the name "Ultraviolet catastophe" was pretty cool. :D

I thought that was the name of a Seattle rock band.

Normandy6644
2005-Feb-28, 12:05 AM
I always thought the name "Ultraviolet catastophe" was pretty cool. :D

I thought that was the name of a Seattle rock band.

That would be really cool! I wish I'd thought of that for my band.

Fortis
2005-Feb-28, 12:19 AM
For better or worse, this is just one of those places where common sense and intuition break down. There is no analog for the wave-particle duality in everyday life. It's not something our brains can visualize particularly easily and we're stuck describing it with terms that, in some cases, were developed centuries before this stuff was even thought of.

Sure there is. You can knock over a magnet without touching it, by moving another magnet near it. It’s the moving field in between the two magnets that carries the force. You don’t have to knock the one over with a “particle” when a field wave can act like a particle and knock it over. Anyway, you hear by means of field waves. No “particle” ever hits your ear drum or your cilia, only fields. That’s the way you see too.
How is the classical wave quantised? Quantisation of the photon energy in units of h.nu doesn't appear in the classical Maxwell's equations.

Taibak
2005-Feb-28, 02:27 AM
Or you could just quote the relevant lines. Whatever's easier. Either way, as Tensor pointed out, Maxwell's book isn't the whole story. If you want to understand what a photon is, you have to put Maxwell aside and start looking at quantum mechanics.


Well, as long as university websites and books still show drawings and animations of the 1873 Maxwell electric and magnetic wave, I’ll continue to consider it as a good model. You might want to read a couple of Maxwell books yourself. In Volume 1, 1873, he was the first guy to suggest that the earth go on a fundamental atomic clock time standard.

Maxwell's model is still taught because it does an excellent job at explaining light in the classical realm. If, for instance, you wanted to design a radio transmitter you would use Maxwell - the theory works fine for that. It's a nice, convenient, simple model when you're trying to work on, well, rather a lot. But - and this is a BIG but - Maxwell won't give you a complete understanding of what a photon is. Simply put: his theory is completely incapable of explaining the particle-like properties of light. It can't explain blackbody radiation. It can't explain the photoelectric effect. It can't explain Compton scattering.


And when Feynman finally has to show a drawing of a photon in his book, and he uses a little wavy line similar to the ones in the Maxwell model, rather than using a little round marble type “particle” drawing, I’ll not be too quick to give up the Maxwell model.

But that's the key problem: you need to incorporate BOTH the marble and the wavy line. The usual solution is to draw a football-shaped particle enclosing a wavy line (http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/compton.html#c1). It's an imperfect drawing, but it works reasonably well for most purposes.


But just because you can usually think about things in classical terms doesn't mean that you can think about everything that way. To use a fairly mundane example, you can't explain all the properties of solder without using quantum mechanics. From a classical point of view, the two wires you soldered together are conductive but the solder itself is not. To a classical electron, the solder is an inpenetrable barrier. Quantum mechanics, on the other hand, provides a mechanism (quantum tunneling) that explains how the current manages to get through there. Granted, if you're just interested in the practical side of this (that is, if all you care about is that you can solder two wires together to make a circuit) there's no reason to bother with the quantum mechanical side of it, but to understand what's actually happening at the atomic level there's no way around the theory.


I have a roll of Radio Shack solder right here, and I find that a few-inch length of it conducts electricity just as well as a copper wire. I’ve never heard of any scientist say it blocks electricity. Is that some new idea or what?

I might be misremembering the details, actually. If my memory serves me right, both the wire and solder are conductive but the interface between them acts as a potential barrier through which the electrons tunnel. Let me do some digging here, see if I can corroborate this.

Or, to switch to a better example, you can't explain how a transistor works without quantum tunneling.

Taibak
2005-Feb-28, 02:57 AM
For better or worse, this is just one of those places where common sense and intuition break down. There is no analog for the wave-particle duality in everyday life. It's not something our brains can visualize particularly easily and we're stuck describing it with terms that, in some cases, were developed centuries before this stuff was even thought of.

Sure there is. You can knock over a magnet without touching it, by moving another magnet near it. It’s the moving field in between the two magnets that carries the force. You don’t have to knock the one over with a “particle” when a field wave can act like a particle and knock it over.

Bad example. You're right, we can model magnets that way, but you've chosen an example that, in the classical realm, involves neither waves nor particles. The magnetic fields are constant, nothing's oscillating, therefore there is no wave. Similarly, in Maxwell's theory, there is no need for particles.


Anyway, you hear by means of field waves. No “particle” ever hits your ear drum or your cilia, only fields. That’s the way you see too.

Better example, but you're misunderstanding how sound works. In this case, there is no field. A sound wave, by definition, is caused by particles vibrating back and forth in the direction of the wave. As such, you don't hear anything unless those particles slam into the appropriate organs. Either way, sound is definitely a wave. There is no 'soundon' that accompanies the wave.


Regardless, I stand by what I said. There are no classical analogs of the wave-particle duality. As far as Newton and Maxwell are concerned, something is either a wave or a particle, never both. A baseball is a particle. A plucked guitar string carries a wave. There is no 'baseball wave' or 'guitarstringon' particle. Once you get into quantum mechanics, the wave-particle duality is inescapable. Classically, electrons are particles, but they also show interference patterns the same way waves do - electrons are also waves. Light exhibits interference patterns, so it's a wave, but if that's the whole story you can't explain the photoelectric effect. There's no way around this: on a quantum mechanical level things are both particles AND waves.

Sam5
2005-Feb-28, 03:20 AM
You're right, we can model magnets that way, but you've chosen an example that, in the classical realm, involves neither waves nor particles. The magnetic fields are constant, nothing's oscillating, therefore there is no wave.

Yes. I’m moving the magnet and the field. That is the field “wave”. One wave. Waves don’t necessarily have to oscillate. One wave of a strong field will knock over the other magnet. We can cause other effects by oscillating the magnetic fields at various rates.

Sam5
2005-Feb-28, 03:25 AM
Better example, but you're misunderstanding how sound works. In this case, there is no field. A sound wave, by definition, is caused by particles vibrating back and forth in the direction of the wave. As such, you don't hear anything unless those particles slam into the appropriate organs. Either way, sound is definitely a wave.

The air molecules never hit each other or any body parts. It’s the fields between the molecules that cause the molecules to move slightly. When molecules move close to one another, the fields compress and that starts the wave. The field wave continues on from the source to the eardrum and to the cilia where the various frequencies resonate the appropriate cilia. Sound is partly a mechanical process and partly an electrodynamical process. And as with light, there can be one sound wave. I use to record them and see them on optical sound tracks all the time. We can’t have half a sound wave or 1 1/2 sound waves. Sound waves come in discrete units of 1, 2, 3, etc.

Taibak
2005-Feb-28, 07:08 PM
You're right, we can model magnets that way, but you've chosen an example that, in the classical realm, involves neither waves nor particles. The magnetic fields are constant, nothing's oscillating, therefore there is no wave.

Yes. I’m moving the magnet and the field. That is the field “wave”. One wave. Waves don’t necessarily have to oscillate. One wave of a strong field will knock over the other magnet. We can cause other effects by oscillating the magnetic fields at various rates.

You have it backwards, I'm afraid. The wave is the oscillation, not the field itself. Whether or not the field is moving is irrelevant. Newton's first law tells us that anything moving with a constant velocity is identical to something at rest. In other words, a magnetic field doesn't become an electromagnetic wave just because it's moving. It doesn't matter how many crests the wave has, but you have to have an oscillation.




Better example, but you're misunderstanding how sound works. In this case, there is no field. A sound wave, by definition, is caused by particles vibrating back and forth in the direction of the wave. As such, you don't hear anything unless those particles slam into the appropriate organs. Either way, sound is definitely a wave.

The air molecules never hit each other or any body parts. It’s the fields between the molecules that cause the molecules to move slightly. When molecules move close to one another, the fields compress and that starts the wave. The field wave continues on from the source to the eardrum and to the cilia where the various frequencies resonate the appropriate cilia. Sound is partly a mechanical process and partly an electrodynamical process.

That's what a collision is, actually. The particles don't have sharply-defined edges and the only way they can interact is through the various forces.


And as with light, there can be one sound wave. I use to record them and see them on optical sound tracks all the time. We can’t have half a sound wave or 1 1/2 sound waves. Sound waves come in discrete units of 1, 2, 3, etc.

This is true, but, for the time being, irrelevant to the discussion. You can have any number of crests you want in a wave, but you have to have an oscillation to have a wave. By definition that's what a wave is.

Sam5
2005-Feb-28, 07:27 PM
That's what a collision is, actually. The particles don't have sharply-defined edges and the only way they can interact is through the various forces.

Hmm. You said in the post above, “but you're misunderstanding how sound works. In this case, there is no field. A sound wave, by definition, is caused by particles vibrating back and forth in the direction of the wave. As such, you don't hear anything unless those particles slam into the appropriate organs.”

You said specifically “there is no field” and “those particles slam into the appropriate organs”. I said there is a field involved and the compressing of the fields causes the particles to move and the wave to travel.

Now you’re saying, “The particles don't have sharply-defined edges and the only way they can interact is through the various forces.

That’s what I said in the first place. It’s the fields of the particles that compress and cause the sound waves. The particles themselves, ie the atoms and molecules of air, never directly hit the atoms and molecules of our ears or anything else.

Fortis
2005-Feb-28, 10:06 PM
And when Feynman finally has to show a drawing of a photon in his book, and he uses a little wavy line similar to the ones in the Maxwell model, rather than using a little round marble type “particle” drawing, I’ll not be too quick to give up the Maxwell model.

I've been looking for the drawing of the photon that you refer to and I don't seem to be able to find it. Are you referring to the symbol for the photon propagator? If so, then it is just a simple way to differentiate between an exchange particle propagator and other things such as electrons. :)

Taibak
2005-Feb-28, 10:20 PM
That's what a collision is, actually. The particles don't have sharply-defined edges and the only way they can interact is through the various forces.

Hmm. You said in the post above, “but you're misunderstanding how sound works. In this case, there is no field. A sound wave, by definition, is caused by particles vibrating back and forth in the direction of the wave. As such, you don't hear anything unless those particles slam into the appropriate organs.”

You said specifically “there is no field” and “those particles slam into the appropriate organs”. I said there is a field involved and the compressing of the fields causes the particles to move and the wave to travel.

Now you’re saying, “The particles don't have sharply-defined edges and the only way they can interact is through the various forces.

That’s what I said in the first place. It’s the fields of the particles that compress and cause the sound waves. The particles themselves, ie the atoms and molecules of air, never directly hit the atoms and molecules of our ears or anything else.

Okay... I think I see where we're getting confused. This is another one of those times where you model something differently depending on scale.

At macroscopic scales, a sound wave is a pulse of increased pressure propegating through a medium, usually the air. Where the wave is pressure-based, the individual air particles vibrate back and forth in the direction the wave is travelling. Since we're only looking at relatively large-scale behavior here, there's no reason why we can't model the particles as rigid, well-defined objects. As such, collisions between these particles and, well, anything else can be modelled the same way we'd model a collision between anything else on a macroscopic scale. You could, for instance, model the collision between a nitrogen molecule and your eardrum the same way you'd model the collision between a tennis ball and a brick wall. It's a simplified picture of what's 'really' going on, but it tells us all we need to know.

It's when you start looking at smaller and smaller scales that this gets messier. If you want to know more details about the collision, you will, eventually, have to zoom in to where you can see not just the atoms in the air, but also the atoms that make up your eardrum. Once you start looking at this level of detail, you can't necessarily model a particle as a rigid, well-defined object. You'll have to start looking at their wave-like behavior as well. In addition, you'll have to start looking at the collisions in terms of electromagnetic interactions, like you said, as opposed to purely mechanical terms. It's complicated, so if you can get all the information that interests you from a simpler model, there's no reason not to use that model.

Where our wires crossed is that we wound up thinking on different scales again. When I said there was no field involved, I was looking at sound from a purely macroscopic point of view. I was, essentially, saying that there is no 'sound field' in the same sense that there is, say, an electric field or a gravitational field. The individual particles may have fields associated with them, but taken as a whole, the sound wave itself does not. Either way, when you're modelling a sound wave, there isn't really any point in looking at individual particles since the wave itself is the result of collective motion. On the other hand, we'd have to bring in all the quantum mechanical stuff (such as particles not having a well-defined edge) once we start looking at the motion of individual particles but, again, where that's way more complicated, you don't want to bring that stuff in any more than you need to.

Sam5
2005-Mar-02, 03:29 AM
Ok, I think we pretty much agree basically about sound. But I don’t think we agree about this:



The individual particles may have fields associated with them, but taken as a whole, the sound wave itself does not.

There is a field that is associated directly with sound waves. An individual area of the field surrounds each air molecule. It must be present, or there would be no sound. It is not an overall continuous field spread out through a large amount of space like a gravity field, but I see it as being a lot of little round fields surrounding each of the air molecules that are located between the emitter and the observer. The “sponginess” of the fields determines the velocity of the waves.

It’s true that most people normally don’t think of these fields, because we’ve been told all our lives that sound is caused by air molecules bumping together. This is the most common simple explanation of sound that I’ve found in books and on the internet. In fact, that was what I was originally taught back sometime around ’48 or ’49.

But it’s not true.

I think it would be just as easy to tell kids what actually happens, that air molecules do move a little, but they never bump into each other and they never touch each other. The molecules have fields that surround each one, and when a molecule moves, its field repels the field of the molecule next to it (in the direction of its motion), and that causes the next molecule to move, and then its field repels the field of the next one, and so on. This causes a molecule-field repulsion wave to travel through the air, and that is what we eventually interpret as a sound wave. When the last group of air molecules reach our eardrums, their fields repel the fields of our eardrum molecules, and that causes our eardrums to vibrate. These types of field waves continue on to our cilia and eventually their resonation is turned into electrical impulses that are processed by our brains as sound. For a physical demonstration of field repulsion, a teacher could use magnets.

Normandy6644
2005-Mar-02, 03:32 AM
Ok, I think we pretty much agree basically about sound. But I don’t think we agree about this:



The individual particles may have fields associated with them, but taken as a whole, the sound wave itself does not.

There is a field that is associated directly with sound waves. An individual area of the field surrounds each air molecule. It must be present, or there would be no sound. It is not an overall continuous field spread out through a large amount of space like a gravity field, but I see it as being a lot of little round fields surrounding each of the air molecules that are located between the emitter and the observer. The “sponginess” of the fields determines the velocity of the waves.

It’s true that most people normally don’t think of these fields, because we’ve been told all our lives that sound is caused by air molecules bumping together. This is the most common simple explanation of sound that I’ve found in books and on the internet. In fact, that was what I was originally taught back sometime around ’48 or ’49.

But it’s not true.

I think it would be just as easy to tell kids what actually happens, that air molecules do move a little, but they never bump into each other and they never touch each other. The molecules have fields that surround each one, and when a molecule moves, its field repels the field of the molecule next to it (in the direction of its motion), and that causes the next molecule to move, and then its field repels the field of the next one, and so on. This causes a molecule-field repulsion wave to travel through the air, and that is what we eventually interpret as a sound wave. When the last group of air molecules reach our eardrums, their fields repel the fields of our eardrum molecules, and that causes our eardrums to vibrate. These types of field waves continue on to our cilia and eventually their resonation is turned into electrical impulses that are processed by our brains as sound. For a physical demonstration of field repulsion, a teacher could use magnets.

What is causing this "field repulsion" though? The air molecules are electrically neutral, so it can't be EM forces, not to mention that one can describe longitudinal waves in equations that have no EM terms at all.

Sam5
2005-Mar-02, 03:38 AM
What is causing this "field repulsion" though? The air molecules are electrically neutral, so it can't be EM forces, not to mention that one can describe longitudinal waves in equations that have no EM terms at all.

Well, off-hand, I’d say maybe the negative electric fields of the outer shell of electrons in the molecules? Wouldn’t they tend to repel each other if they got too close? Air molecules don’t like to be squeezed together.

Normandy6644
2005-Mar-02, 04:36 AM
What is causing this "field repulsion" though? The air molecules are electrically neutral, so it can't be EM forces, not to mention that one can describe longitudinal waves in equations that have no EM terms at all.

Well, off-hand, I’d say maybe the negative electric fields of the outer shell of electrons in the molecules? Wouldn’t they tend to repel each other if they got too close? Air molecules don’t like to be squeezed together.

I'd think they would have to get really close before the Coulomb force had any effect. Remember, the nuclear forces are much more important at the atomic level. You do have me curious now as to the mechanism of colliding molecules though. I never gave EM stuff much of a thought. I'll have to think about it a bit more.

Sam5
2005-Mar-02, 05:11 AM
I'd think they would have to get really close before the Coulomb force had any effect. Remember, the nuclear forces are much more important at the atomic level. You do have me curious now as to the mechanism of colliding molecules though. I never gave EM stuff much of a thought. I'll have to think about it a bit more.


The way I figure it, it’s like when we press on a small balloon. The air inside is already under compression. And if we squeeze the balloon, the air compresses more, but we can tell that the air doesn’t want to be compressed. Some field around the molecules are repelling each other. I assume it is the electric field.

I don’t really know what field handles the repulsion of the compression, but I just assume it is the negative charge on the outer electron shells that repel each other. It’s a field of some kind, since the molecules, atoms, and particles never touch each other. I’ve read that they don’t even touch when air is compressed and liquefied.

So, whatever that “sponginess” is that makes the air molecules want to stay a certain distance apart (and I think that is a field that is causing that), then that’s what compresses in a sound wave. The molecules move just a little, the fields are compressed, that compression moves the next set of molecules, then the original ones return to their original positions. This actually forms a compression wave that is immediately followed by a vacuum wave. This is what causes a horizontal “S” shape, a full sine wave, on an oscilloscope read-out of a single wave. A round microphone diaphragm is pushed inward by the field compression, then it springs back out, aided by the vacuum part of the wave.

By the way, I used to record and see single sound waves, back when I recorded and edited optical film sound tracks. Most people don’t know what a single sound wave sounds like. But it’s simple. It’s a “click”. Take a little metal knife and rap it quickly on a table top or a glass jar or a piece of metal, and you’ll hear a “click” sound. That is generally one sound wave and it shows up on an optical sound track as a single “blip”. And each one has wavelength and “frequency”, that is, a “pitch”. If you clunk the knife or little piece of metal on a guitar sounding box, that will usually give you a long-wavelength click. If you tap a glass with the knife that will usually give you a short-wavelength click.

Taibak
2005-Mar-02, 05:34 AM
Actually, I agree that the air particles bumping into each other is an electromagnetic effect. The molecules as a whole are electrically neutral, but it's important to remember that the charges aren't uniformly distributed: the positive charges are on the inside, the negative charges are on the outside. As such, the electron cloud surrounding a molecules generally repels the electron clouds surrounding other molecules. (For now, let's keep this simple and ignore chemical reactions). But, like Normandy said, this is only true at very small scales. There simply aren't enough electrons in your average molecule to create a very big electric field and the effect is mitigated by the protons. Unless you're looking at two molecules very close together this effect is so tiny, it's negligible.

That's really the key to the whole puzzle. A sound wave is generally much bigger than any one molecule. At those scales, the fields of the constituent particles are far, far too small to worry about. Apart from the molecules that are actually colliding, the space between molecules is just too big compared to their fields. Once you get to a macroscopic scale, the fields, essentially disappear. They're too tiny to be noticed.

Does that mean that the collisions between molecules aren't electromagnetic in nature? No, of course not. But that doesn't mean we always need to model the collisions that way. If you want to model the collision between two molecules to a high level of detail, you're going to have to bring in quantum electrodynamics. If you're interested in how only two molecules interact, that's your best (and only) option. In the case of a sound wave as a whole, however, we're interested in the collective behavior of a group of particles on a comparatively huge scale. At that scale, all the quantum mechanical effects are trivial details compared to the larger picture. Basically, if you have the choice between modelling the behavior of the particles in a sound wave - or really any other type of way gas molecules move - in all its quantum mechanical glory OR as a bunch of tiny superballs bouncing all over the place and both models give similar results, just use the second one. It's MUCH simpler and tells you exactly what's taking place on a macroscopic scale (relatively speaking) without getting you bogged down in the details.

Taibak
2005-Mar-02, 10:04 PM
Actually, I agree that the air particles bumping into each other is an electromagnetic effect. The molecules as a whole are electrically neutral, but it's important to remember that the charges aren't uniformly distributed: the positive charges are on the inside, the negative charges are on the outside. As such, the electron cloud surrounding a molecules generally repels the electron clouds surrounding other molecules.

Forgot to mention this the first time, but the other aspect of this is that the strength of the Coulomb force depends on the distance between the two charges as much as anything else and, in atomic scales, the space between the electrons and the nucleus is gargantuan. If two nitrogen molecules, for instance, get close to each other, the electrons are going to be much closer to other electrons than they are to the protons. At short distances, the repulsive force between the electrons dominates. At longer distances, the fields are essentially zero, primarily because the electrons just don't have enough of a charge to create a strong field.

Sam5
2005-Mar-02, 11:22 PM
Actually, I agree that the air particles bumping into each other is an electromagnetic effect. The molecules as a whole are electrically neutral, but it's important to remember that the charges aren't uniformly distributed: the positive charges are on the inside, the negative charges are on the outside. As such, the electron cloud surrounding a molecules generally repels the electron clouds surrounding other molecules.

Forgot to mention this the first time, but the other aspect of this is that the strength of the Coulomb force depends on the distance between the two charges as much as anything else and, in atomic scales, the space between the electrons and the nucleus is gargantuan. If two nitrogen molecules, for instance, get close to each other, the electrons are going to be much closer to other electrons than they are to the protons. At short distances, the repulsive force between the electrons dominates. At longer distances, the fields are essentially zero, primarily because the electrons just don't have enough of a charge to create a strong field.

Ok, so, let’s try to figure this thing out logically and with good old-fashioned common sense. I noticed a long time ago that when a big hi-fi speaker woofer booms out a sound, its cone will vibrate in and out as much as several millimeters. Ok, so then we know that the air molecules are being displaced by several millimeters. I think we can safely assume that the molecules are closer together than a few millimeters. Therefore, the woofer causes them to move close enough to each other (the ones nearest the speaker) for their outer electric fields to interact and repel one another. Thus, we have a sound wave moving through the air.

Taibak
2005-Mar-03, 01:48 AM
Actually, I agree that the air particles bumping into each other is an electromagnetic effect. The molecules as a whole are electrically neutral, but it's important to remember that the charges aren't uniformly distributed: the positive charges are on the inside, the negative charges are on the outside. As such, the electron cloud surrounding a molecules generally repels the electron clouds surrounding other molecules.

Forgot to mention this the first time, but the other aspect of this is that the strength of the Coulomb force depends on the distance between the two charges as much as anything else and, in atomic scales, the space between the electrons and the nucleus is gargantuan. If two nitrogen molecules, for instance, get close to each other, the electrons are going to be much closer to other electrons than they are to the protons. At short distances, the repulsive force between the electrons dominates. At longer distances, the fields are essentially zero, primarily because the electrons just don't have enough of a charge to create a strong field.

Ok, so, let’s try to figure this thing out logically and with good old-fashioned common sense.

Common sense doesn't always work in physics. Logic is good though. :-)


I noticed a long time ago that when a big hi-fi speaker woofer booms out a sound, its cone will vibrate in and out as much as several millimeters. Ok, so then we know that the air molecules are being displaced by several millimeters. I think we can safely assume that the molecules are closer together than a few millimeters.

That's an understatement. :-)


Therefore, the woofer causes them to move close enough to each other (the ones nearest the speaker) for their outer electric fields to interact and repel one another. Thus, we have a sound wave moving through the air.

Right. The cone knocks the first group of particles and they start moving. The collision is, like you said, ultimately the result of an electric repulsion but, since we're looking at a larger scale (and for the sake of brevity) we don't really need to go into the details of that. Anyway, that first group of air molecules moves away from the speaker and hits more air molecules. The first group of molecules bounce back to where they were, the second group bounces forward and hits a third group, and so on and so forth. Each group of molecules oscillates , forward and back, in the same direction that the wave is travelling and ultimately return to their original positions. They do this once for every wavecrest. The wave itself is, essentially, a ripple of increased air pressure moving away from the source (in this case, the speaker cone). Keep in mind that the wave keeps moving, even though the air particles undergo no net displacement.

Anyway, that's the basic anatomy of a sound wave - or any other longitudinal wave, for that matter. For these waves, your wavelength is the difference between pulses, your frequency is how many pulses pass any given point in one second, and your ampitude is the number of molecules that oscillate with any given pulse. At the risk of stating the obvious, for sound frequency corresponds to pitch and amplitude corresponds to volume.

Sam5
2005-Mar-03, 02:07 AM
your ampitude is the number of molecules that oscillate with any given pulse.

:) Hmm, I would say the amplitude would be the distance traveled by each molecule per time unit per frequency. The more distance, the more amplitude. For example, 2 mm travel for 20 Hz. would be “loud”, while 1/2 mm travel would be not so loud. All the molecules in front of the speaker are going to move, so it’s not the number that move that constitutes amplitude, it’s the distance they move that constitutes amplitude. A time unit of molecule swing for a 20 Hz frequency would be 1/20th of a second. If the distance moved is 2 mm per vibration, that’s loud. If it’s 1/2 mm, that’s not so loud. For higher frequency waves, the molecules can’t move that far since they’ve got to do more oscillating per second. That’s why a hi-fi tweeter doesn’t vibrate as much as 2 mm. In fact, the tweeter cone can barely be seen to move because they travel such a short distance before recoil. Ol’ Tensor should be able to rustle up some equations to verify this point of view.

What say ye?

Normandy6644
2005-Mar-04, 06:33 PM
By the way, anyone curious about the answer to the OP, it turns out I was (more or less) correct with what I turned in. So here is a - very crude - picture of the correct answers. Note that they are supposed to look smoother than I have drawn them, but the basic idea is there.

http://img.photobucket.com/albums/v506/Normandy6644/qm2.jpg

Taibak
2005-Mar-05, 04:43 AM
your ampitude is the number of molecules that oscillate with any given pulse.

:) Hmm, I would say the amplitude would be the distance traveled by each molecule per time unit per frequency. The more distance, the more amplitude. For example, 2 mm travel for 20 Hz. would be “loud”, while 1/2 mm travel would be not so loud. All the molecules in front of the speaker are going to move, so it’s not the number that move that constitutes amplitude, it’s the distance they move that constitutes amplitude. A time unit of molecule swing for a 20 Hz frequency would be 1/20th of a second. If the distance moved is 2 mm per vibration, that’s loud. If it’s 1/2 mm, that’s not so loud. For higher frequency waves, the molecules can’t move that far since they’ve got to do more oscillating per second. That’s why a hi-fi tweeter doesn’t vibrate as much as 2 mm. In fact, the tweeter cone can barely be seen to move because they travel such a short distance before recoil. Ol’ Tensor should be able to rustle up some equations to verify this point of view.

What say ye?

Not quite. The woofers vibrate the further than tweeters because they need to generate a wave with a lower frequency/longer wavelength. That doesn't effect amplitude at all. For sound, amplitude corresponds to air pressure - the higher the amplitude, the greater the pressure, the louder the sound. You increase the amplitude by packing more air molecules into any given pulse. However, they don't travel appreciably further. Instead, each wavecrest, each pulse of increased air pressure, is followed by a trough, a pulse of decreased air pressure. The extra particles come out of that trough and cram into the crest.

Taibak
2005-Mar-05, 04:45 AM
By the way, anyone curious about the answer to the OP, it turns out I was (more or less) correct with what I turned in. So here is a - very crude - picture of the correct answers. Note that they are supposed to look smoother than I have drawn them, but the basic idea is there.

http://img.photobucket.com/albums/v506/Normandy6644/qm2.jpg

Gah. Been a while since I've seen anything quite like that. :oops: Give me a good GR problem any day.

Glad you got the answer though. :)

Zachary
2005-Mar-05, 07:50 AM
That one looked really good, but I still haven't gotten around to it. It's a good book to read on a travel day, so maybe this spring.

It's also a good book to lose on a travel day :cry:

Sam5
2005-Mar-05, 03:43 PM
Not quite. The woofers vibrate the further than tweeters because they need to generate a wave with a lower frequency/longer wavelength. That doesn't effect amplitude at all. For sound, amplitude corresponds to air pressure - the higher the amplitude, the greater the pressure, the louder the sound. You increase the amplitude by packing more air molecules into any given pulse. However, they don't travel appreciably further. Instead, each wavecrest, each pulse of increased air pressure, is followed by a trough, a pulse of decreased air pressure. The extra particles come out of that trough and cram into the crest.

That’s an interesting idea, but I don’t think it is correct. The loudness (volume) alone of a hi-fi system speaker is what makes the woofer cones go out and in a large amount. The frequency determines how many times per second it goes in and out. The loudness determines the distance the woofer moves in and out.

The wavelength for a 20 Hz tone would be 55 feet. The woofers don’t have to move 55 feet out to produce that wavelength. All they have to do is move in and out 20 times in a second to produce that wavelength. The distance they move out would determine the loudness, not the wavelength.

More compression of the air would not depend on how many molecules are involved, since all of the molecules in front of the woofer are already involved. The distance they travel in 1/20th of a second determines the loudness. More distance, more compression, more loudness. It's the wave that travels 55 feet in a second, not the molecules. You can still hear the 20 Hz even if the volume is turned down low and the cones are vibrating only out as little as 1/2 mm, but they are still doing it 20 times a second. If the volume is loud, they are moving out several mm per vibration, but they are still doing it only 20 times a second.