[DewFuel]

	Originally Posted by Akzis To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	What are others? Just out of curiosity. A google search didn't give me my answers. To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

Time and Energy

Angular momentum (not total, but just component based)

It's called commutativity, or non-commuting operators.

[altoid]

Speaking of QM, I was recently reading about quantum entanglement in the context of photosynthesis. It's a very interesting topic about which I know very little. How does quantum entanglement work? How do particles become entangled? Can you force an entanglement between particles?


Very interesting thread.
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[Latro]

One application that I know of in entanglement is with superconductors. Basically what happens in a superconducting situation is two electrons will go off in two different directions but will be quantum entangled, which means that their quantum state has to change simultaneously. Then it becomes difficult if not impossible for them to both exactly simultaneously lose energy, which means they just DON'T lose energy. When this becomes generalized on a large scale (which is what happens in superconductors) you get a current that will continue flowing in a circuit indefinitely without a power supply. The implications of this are very interesting; the magnetic properties, for example, of superconductors are completely different from other materials.

[shaunmikex]

Originally Posted by altoid To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

Speaking of QM, I was recently reading about quantum entanglement in the context of photosynthesis. It's a very interesting topic about which I know very little. How does quantum entanglement work? How do particles become entangled? Can you force an entanglement between particles? Very interesting thread. To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

From what I understand, we don't understand. Einstein originally thought the notion of particles "having knowledge" of eachother's states over infinite distances was ludicrous.

In terms of photons: Certain mediums (prisms and such) can cause an incident photon to separate into two distinct photons, each having a lower frequency (energy must be conserved). These two resulting photons are entangled...insofar as if one is polarized, the other photon will polarize oppositely. Theoretically, this may happen even at infinite distances. It is almost as if the particles "know" that they were once the same and in effect act accordingly.

Extrapolating a bit (I am taking a gander here), if said photon were to split via a prism (I'm an not sure of the probability of this happening), and one of the resulting photons enters a chloroplast of a cell because it has the correct polarization, the other photon will not enter. It has "known" that its partner has been polarized in a certain manner and does the opposite counter effect.

Even more interesting is that the big bang suggests that everything in the universe originated from a tiny, immensely dense particle. Now this particle "exploded" and formed the universe as we know it. If this was one particle....is everything as we know it entangled.

It's absolutely fascinating, but I do not understand it anymore than the average scientist. Perhaps further research into elementary particles will provide us some understanding? Hadron Collider etc.
::cue X-files theme song::

To The Particle Physicists: Can someone explain quantum tunneling? I never understood it much aside from hearing of the analogy of looking in a glass window: I can see both my reflection and the outside. I understand this from a waves perspective, but I don't see the correlation with QM tunneling
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[mischachiaro]

I want to know at what time or year approximately do you estimate we'll grow meat cells in laboratories instead of farming animals.

[Architectonic]

	Originally Posted by shaunmikex To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Can someone explain quantum tunneling?

The simplest hypothetical case case is solving the eigenvalue problem (usually for energy, eg Schrödinger's equation) for a potential which contains an infinite spike barrier or well, which can be described by a Dirac delta "function". The resulting probability density still occurs on both sides of the infinite barrier!

[Latro]

Originally Posted by shaunmikex To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

To The Particle Physicists: Can someone explain quantum tunneling? I never understood it much aside from hearing of the analogy of looking in a glass window: I can see both my reflection and the outside. I understand this from a waves perspective, but I don't see the correlation with QM tunneling To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

I understand quantum tunneling this way (not sure if it's necessarily accurate). You have a particle. Its position is governed by a probability distribution. There are two regions where it has a nonzero probability of being, and a region in between where it has a zero probability of being. (This is an idealization; we essentially assume that the middle region would require the particle to have infinite energy).

In classical mechanics, we would have the particle in one region, definitely, and it would never be able to reach the region on the other side, because it could never accumulate enough energy to do so. (There are very intuitive potential energy diagrams that describe this in terms of frictionless "bowls"; my introductory mechanics professor used these.)

In quantum mechanics it doesn't have to pass through; it has a probability of being in one region and a probability of being in the other. As the wavefunction evolves the probability of it being in the other region may increase, and then we can basically say that it has "tunneled" through the region where it was forbidden to go.

[rbc]

	Originally Posted by shaunmikex To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Thankx rbc! I enjoyed the hi-jacking :D. Feel free to come in and correct/elaborate on future posts as well.

Excellent! It's good to have my geekiness properly appreciated. Just remember, you asked for it.
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	Originally Posted by shaunmikex To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Have you taken statistical thermodynamics? This discussion has piqued my interest on doing a self-study online.

Yup. In fact, the physics department where I got my undergrad doesn't have a thermo class at all -- they teach the subject only as an incidental consequence of statistical mechanics.
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Entropy is all about counting quantum states. Certain real-world phenomena are better envisioned as two-dimensional rather than three-dimensional, because the most important degrees of freedom are small changes in electron states at the surface of the Fermi sphere. Good luck with the self study; sadly, I've never found a stat mech book I actually like.

	Originally Posted by Akzis To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	What are others? Just out of curiosity. A google search didn't give me my answers. To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

One of my favorites is neutrino flavor and mass:
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. As DewFuel said, the generic term is "noncommuting observables", but searching on that only yields technical publications sadly resistant to the casual reader.

One which you can directly observe in a simple macroscopic experiment is the polarization of light. To do it, you will need three linearly-polarized filters; high-end sunglasses work OK, but it's better to use the photographic kind which don't make things darker except through polarization. If you hold one of them up to an unpolarized source of light, exactly half the incident light will make it through. If you hold a second one behind and parallel to the first, it will not filter out any additional light, because everything which made it through the first will also make it through the second. If you rotate the second slowly, the scene will get darker and darker, until at 90 degrees relative angle between the filters, nothing gets through: those photons which make it through the first filter are exactly those which cannot get through the second, and vice versa. So far, nothing surprising. The quantum weirdness appears when you have two perpendicular polarizers, and insert a third between them at a 45 degree angle. It gets brighter! Somehow, by adding more filters, you block less light! This is a purely quantum phenomenon, which occurs because linear polarizations at angles other than parallel or perpendicular are not simultaneously observable. Think of the angle of polarization as a line drawn on a compass. When the North-South light hits an East-West filter, nothing gets through. However, when N-S light hits a NW-SE filter, half of it is *changed* into NW-SE light, which does get through, and the other half is changed to NE-SW light, which doesn't. Then, when the surviving, now NW-SE, light hits the E-W filter, half of it is changed into E-W light, which does get through, and the other half is changed into N-S light, which doesn't. The light has no memory of what its polarization used to be. Observing its polarization caused its polarization to change.

	Originally Posted by DewFuel To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Angular momentum (not total, but just component based)

Angular momentum is wacky. In classical physics, angular momentum is a vector in 3D space. Its magnitude is proportional to the product of mass, speed, and distance. Its direction is perpendicular to the plane of orbit, with sign such that if your right thumb points along the vector, the fingers of your right hand curl in the direction of the orbital motion (from base toward tip).

In quantum mechanics, however, you can measure the magnitude of angular momentum but *not* its direction. You can measure the component of the angular momentum vector which happens to point along any one direction you choose to specify, but you have no idea how the rest of the rest of the magnitude is apportioned among the other two directions perpendicular to the one you chose. If you try to measure one of those, you certainly can, but as a direct and unavoidable result you will change the value along the other direction you measured first, and you won't know what its new value really is. Thinking of the vector as the triplet of numbers (x, y, z), you can know x^2+y^2+z^2, and any one of x, y, or z, but you can never know all three at once; if you already know z, and then ask about y, learning about y causes you to lose all knowledge of z.

	Originally Posted by altoid To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	How does quantum entanglement work?

Entanglement is related to partial observation. The simplest analogy I can make is with a lightbulb controlled by two different switches. If both switches are in the same position (both up or both down), the light is on. If the switches are in different positions, the light is off. The kind of entangled states physicists normally discuss are like the lightbulb when off: you know the switches are different, but you don't know which one is up and which is down until you look specifically at one of them. Once you look at one, however, you instantly know for sure which state (up or down) the other one must be in, even if you never actually look at it.

Described that way, it doesn't sound like anything special. To understand why the quantum version is so strange, you need to know something about how observation affects quantum objects. The Schroedinger equation is perfectly smooth, classical and predictable on its own: you can run the solution backward or forward in time as much as you want, with no loss of knowledge. What makes it quantum is what it describes: the distribution of probability of finding the system in a certain state, between times at which measurements are made. When a measurement is made, however, that instantly and unpredictably changes the probabilistic mixture of states describing the possible configurations of the system to coincide with exactly one, randomly determined, precise state. Schroedinger's equation then allows you to predict what is likely to happen when the next measurement is made; when that measurement is made, the dice are rolled again, and the "wave function collapses" from a probability distribution over all possible states into just the one state which corresponds to the result of the measurement. Quantum mechanics allows you to predict the *odds* with great accuracy, but it is never possible to know the actual result of the dice in advance.

What scares people about entanglement (Einstein called it "spooky") is what happens when you let the two (or more) entangled particles get separated before completing the observation. In quantum mechanics, if you only know the lightbulb is off, neither switch yet exists in a single state; each one is simultaneously both partly on and partly off, which is called a superposition of states (the sad condition of Schroedinger's infamous cat). If you then check one of them, its state changes from a superposition into one of the two definite states (either up or down), and the other switch also changes state, to the opposite of whichever you measured the first one to be -- instantaneously, even if the two particles are light-years apart. Much to Einstein's posthumous dismay, the reality of this behavior has been conclusively demonstrated by experiment:
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.

Thanks for the mention of photosynthesis; I had no idea quantum entanglement was involved in it. I haven't studied biology since high school, but now I may have to look at it again!

Originally Posted by Latro To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

One application that I know of in entanglement is with superconductors. Basically what happens in a superconducting situation is two electrons will go off in two different directions but will be quantum entangled, which means that their quantum state has to change simultaneously. Then it becomes difficult if not impossible for them to both exactly simultaneously lose energy, which means they just DON'T lose energy.

Yes! Superconductors are *fascinating*. What you describe is the traditional theory of simple (very low temperature metal) superconductors (
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); the high-temperature ceramic ones are more complicated (Nobel prize awarded 2003 vs. 1972), and I don't know much about them. This phenomenon is related to the comment in my earlier post about indistinguishable dice. In quantum mechanics, whether a particle is able to be in the same state as another of the same type is determined by its spin, which is a sort of internal angular momentum (photon polarization is an example), unrelated to any particular motion. Particles which don't go together (obey the "Pauli exclusion principle") are called fermions, and particles which do are called bosons. You can't make a fermion out of bosons, but any bound state of an even number of fermions constitutes a boson. Electrons are fermions, and they normally repel each other, so they usually don't form bound states. However, under certain conditions in certain materials, the strongly attractive interactions of each individual electron to the bulk material can act like a weak attraction between the electrons themselves. When this happens, the electrons can pair up to form bosons, and all of the pairs enter the same state, which makes them highly resistant to any further change. It is effectively the matter equivalent of how light makes lasers.

	Originally Posted by shaunmikex To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Can someone explain quantum tunneling?

Consider a ball rolling back and forth in one of the valleys between a long line of hills. For you, and others who know the math, we're doing a one-dimensional Schroedinger equation with a sine wave for V(x). Classically, if there is no friction, the ball will either go fast enough to shoot over the top of each hill and down into the next valley, and on and on through the next and the next forever; or it will be trapped forever in just one valley. Since there's no friction, the ball really slides, not rolls, but that's not important right now. In the trapped case, it will have some maximum height it reaches on the side of the hill, below the top; if that height is h, it reaches a maximum speed v=sqrt(2gh) at the bottom of the valley. The energy is being constantly converted back and forth between gravitational potential energy (mgh) and kinetic energy (1/2 mv^2). Neither speed nor height is constant, but the total energy is; it is that number which describes the quantum state of the system.

Classically, if the ball has low enough energy not to get over the hill (it stops and turns around before it gets to the top), it doesn't ever get over the hill. In quantum mechanics, sometimes the ball doesn't have enough energy to get over the hill, but nevertheless it is sometimes found in a neighboring valley anyway, without ever having been on top of any hill! This is why it's called tunneling: it's as if the particle dug a tunnel to get from one valley to the next, because it effectively got there by going *through* the hill, not over it. It's not really making a tunnel, as it does not affect the hill itself in any way (in particular, it does not make it easier for more particles to come through, or for the original one to go back), but it is an attractive metaphor. What causes this is the continuity conditions on the wave function solutions to Schroedinger's equation: you cannot drop from nonzero probability inside the box to zero probability outside it, unless the walls of the box are infinitely high.

Does that help?

[shaunmikex]

Absolutely! The hill analogy is very intuitive.


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to give everyone some visuals of solutions to the 1D Schrödinger Equation (play around with the Harmonic Oscillator). As a side note, the colors are quite trippy as you ascend to higher energy levels >.> <.<

[stasis]

We were talking about spontaneous human combustion in the chat room the other day. As far as I know, the phenomenon is a myth. While it is well known that human bodies can burn if set alight, there doesn't seem to be a way for ignition to occur without the introduction of energy from some external source, like a cigarette.

But I was thinking that if spontaneous human combustion were possible at all, it might have something to do with the cell's energy cycle. During oxidative phosphorylation, a proton gradient (H+) is created in the intermembrane space within a cell. Normally the osmotic pressures associated with this gradient power the rotation of an enzyme called the ATP synthase, which assembles the molecular unit of a cell's energy. In some organisms though, such as hibernating bears and and infants, there is an abundance of tissue called brown fat. In addition to the ATP synthase, the mitochondria in this tissue contain a pathway called
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. The proton gradient is divided between the synthase and this pathway, and the result is a lower quantity of ATP offset proportionally by a quantity of heat.

So then, if a chemical that poisoned the electron transport chain at the ATP synthase were introduced - perhaps a competitive inhibitor that blocked its intake of protons along the gradient - you'd expect a rise in osmotic pressure and therefore an increase of particle flow along the thermogenin and therefore an increase in heat. Simultaneously, you'd develop a deficit of ATP in the cell - you'd expect a tendency to increased rates of electron transport along the chain, and therefore an even greater rise in osmotic pressure, proton flow through the thermogenin, and increase in heat. This is all conveniently taking place in fatty tissue, which burns.

It seems to me that these conditions would simply cause the thermogenin (a protein) to denature, and thus cease producing heat. Presuming for the sake of silly argument that it did not denature and continued to produce heat, could this be a source of ignition? Or, in other words, can ignition occur at the molecular level when oxygen is present, or is ignition a property of larger systems?

Since this question deals more with ignition than anything else, I thought I'd ask the physical chemist instead of the biologist.

[Night Runner]

What's the meaning of life?
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[DewFuel]

Originally Posted by stasis To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

We were talking about spontaneous human combustion in the chat room the other day. As far as I know, the phenomena is a myth. While it is well known that human bodies can burn if set alight, there doesn't seem to be a way for ignition to occur without the introduction of energy from some external source, like a cigarette. But I was thinking that if spontaneous human combustion were possible at all, it might have something to do with the cell's energy cycle. During oxidative phosphorylation, a proton gradient (H+) is created in the intermembrane space within a cell. Normally the osmotic pressures associated with this gradient power the rotation of an enzyme called the ATP synthase, which assembles the molecular unit of a cell's energy. In some organisms though, such as hibernating bears and and infants, there is an abundance of tissue called brown fat. In addition to the ATP synthase, the mitochondria in this tissue contain a pathway called To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts. . The proton gradient is divided between the synthase and this pathway, and the result is a lower quantity of ATP offset proportionally by a quantity of heat. So then, if a chemical that poisoned the electron transport chain at the ATP synthase were introduced - perhaps a competitive inhibitor that blocked its intake of protons along the gradient - you'd expect a rise in osmotic pressure and therefore an increase of particle flow along the thermogenin and therefore an increase in heat. Simultaneously, you'd develop a deficit of ATP in the cell - you'd expect a tendency to increased rates of electron transport along the chain, and therefore an even greater rise in osmotic pressure, proton flow through the thermogenin, and increase in heat. This is all conveniently taking place in fatty tissue, which burns. It seems to me that these conditions would simply cause the thermogenin (a protein) to denature, and thus cease producing heat. Presuming for the sake of silly argument that it did not denature and continued to produce heat, could this be a source of ignition? Or, in other words, can ignition occur at the molecular level when oxygen is present, or is ignition a property of larger systems? Since this question deals more with ignition than anything else, I thought I'd ask the physical chemist instead of the biologist.

Interesting, except that the solvent in the human body is just water. It's a confirmed myth that humans can blow up from the inside out, aside from some unrealistic scenarios. I think if you shined a high power IR laser onto some area of the body, you could potentially cause some serious expansion of the tissue resulting in an explosion. I know this happens with eyeballs where there is a lot of fluid and not an efficient way to transfer heat out of it, basically heating the liquid to a gas and then boom. As for flames, I don't think so.

[shaunmikex]

Originally Posted by stasis To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

We were talking about spontaneous human combustion in the chat room the other day. As far as I know, the phenomena is a myth. While it is well known that human bodies can burn if set alight, there doesn't seem to be a way for ignition to occur without the introduction of energy from some external source, like a cigarette. But I was thinking that if spontaneous human combustion were possible at all, it might have something to do with the cell's energy cycle. During oxidative phosphorylation, a proton gradient (H+) is created in the intermembrane space within a cell. Normally the osmotic pressures associated with this gradient power the rotation of an enzyme called the ATP synthase, which assembles the molecular unit of a cell's energy. In some organisms though, such as hibernating bears and and infants, there is an abundance of tissue called brown fat. In addition to the ATP synthase, the mitochondria in this tissue contain a pathway called To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts. . The proton gradient is divided between the synthase and this pathway, and the result is a lower quantity of ATP offset proportionally by a quantity of heat. So then, if a chemical that poisoned the electron transport chain at the ATP synthase were introduced - perhaps a competitive inhibitor that blocked its intake of protons along the gradient - you'd expect a rise in osmotic pressure and therefore an increase of particle flow along the thermogenin and therefore an increase in heat. Simultaneously, you'd develop a deficit of ATP in the cell - you'd expect a tendency to increased rates of electron transport along the chain, and therefore an even greater rise in osmotic pressure, proton flow through the thermogenin, and increase in heat. This is all conveniently taking place in fatty tissue, which burns. It seems to me that these conditions would simply cause the thermogenin (a protein) to denature, and thus cease producing heat. Presuming for the sake of silly argument that it did not denature and continued to produce heat, could this be a source of ignition? Or, in other words, can ignition occur at the molecular level when oxygen is present, or is ignition a property of larger systems? Since this question deals more with ignition than anything else, I thought I'd ask the physical chemist instead of the biologist.

Biochemically/mechanistically - feasible
Thermodynamically - somewhat feasible
Kinetics - No

While it seems mechanically feasible, I believe kinetics, not thermodynamics alone, would preclude such an occurrence. If generated, the cells will continue to distribute heat amongst other cells and water in the tissue. The heat would have to stay confined to a particular area and continue to intensify. After this, the oxygen within the tissues would have had to be volatilized into gas (taking some of the heat as well). Yet again, this would mean the oxygen would have to stay in this area (despite the heat causing diffusion) until enough heat has been generated to cause combustion. There are just so many ways for that heat to dissipate.

This is somewhat similar to the graphite to diamond example, yet biochemical and more pathways.

Cool sci-fi idea tho

[Architectonic]

	Originally Posted by Night Runner To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	What's the meaning of life? To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

To create more of this exotic form of matter. Obviously.

[stasis]

	Originally Posted by shaunmikex To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Kinetics - No

Fuck.

	Originally Posted by shaunmikex To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	Cool sci-fi idea tho

I can scarcely imagine anything more awesome than a brown bear, having been disturbed from its hibernation by a careless passerby, emerging from its cave, rearing up, emitting a loud roar and then bursting into flames.

Thanks for the analysis.

[Nonlinear376]

bench chemists usually croak in their mid-50's. Non-Hodgkins lymphoma is usually the culprit

[envirodude]

Question:
We are often told that if we don't like the taste or odour of chlorine in our drinking water, that we should put an open pitcher of it in the fridge overnight and the chlorine will "evaporate". What is really happening? Someone told me it's going to Cl2(g) but that seems hokey. I know that UV breaks down hypochlorite, but let's assume there's no UV source in a typical refridgerator. I assume it's going to chloride, but that's intuition, not chemistry!

[Defenestration]

	Originally Posted by Akzis To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.
	What are others? Just out of curiosity. A google search didn't give me my answers. To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

Basically, if you differentiate the action (S) with respect to the variable X, i.e., Y ~ dS/dX, you will have that X and Y are conjugate variables.

For example, energy is proportional to dS/dt ---> energy and time must satisfy an uncertainty relation.

Momentum (linear) is proportional to dS/dx ---> momentum and position.

Angular momentum is proportional to dS/dw ---> angular momentum and angle (angular "position")

Etc.

---------- Post added 05-07-2012 at 09:34 PM ----------

Originally Posted by rbc To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts.

Yes! Superconductors are *fascinating*. What you describe is the traditional theory of simple (very low temperature metal) superconductors ( To view links or images in this forum your post count must be 2 or greater. You currently have 0 posts. ); the high-temperature ceramic ones are more complicated (Nobel prize awarded 2003 vs. 1972), and I don't know much about them. This phenomenon is related to the comment in my earlier post about indistinguishable dice. In quantum mechanics, whether a particle is able to be in the same state as another of the same type is determined by its spin, which is a sort of internal angular momentum (photon polarization is an example), unrelated to any particular motion. Particles which don't go together (obey the "Pauli exclusion principle") are called fermions, and particles which do are called bosons. You can't make a fermion out of bosons, but any bound state of an even number of fermions constitutes a boson. Electrons are fermions, and they normally repel each other, so they usually don't form bound states. However, under certain conditions in certain materials, the strongly attractive interactions of each individual electron to the bulk material can act like a weak attraction between the electrons themselves. When this happens, the electrons can pair up to form bosons, and all of the pairs enter the same state, which makes them highly resistant to any further change. It is effectively the matter equivalent of how light makes lasers.

It should be noted that even though Ginzburg et al got the prize in 2003, the mechanism behind the formation of Cooper pairs in (and thus the explanation of) high-T_c superconductors is still unknown.

[curiousgeorge01]

Wow, all that science talk just flew over my head. It's been over a decade since I took a chem/physics class.

You took stats right? I might have a poker question then LOL.

[MechanicalSun]

What's your stance on coarse-grained simulations?

[Dave C C]

The recipe for the powder used in the VL.22 round (.22 Cal hot air charged round).

[Reizu]

Oh HELL yeah, I really need some advice from one of you guys.

Basically, I'm getting screwed over this semester by a chemistry teacher that I am not only not learning anything from, but I'm fairly certain she's making me unlearn the stuff I already knew. I'm not a bad student; I passed the AP Chemistry exam. After this semester, though, I'm pretty sure I'm screwed up for chemistry for life. Should I take the chance for a better teacher, or pursue something else?