As mentioned earlier in another thread, this is a diversion from that thread PS Apologies for such a weird thread title Basically the idea is simple: How is a cloud (anything that is diffuse and fuzzy) different from a wavefunction? Maths detail welcome, although would be great if some explanatory comments sits next to the key expressions on what they try to physically express Prefer to have an exhaustive list of difference for future reference Motive: The cloud analogy (with the ability to interact constructively or destructively) is a key analogy in helping me to understand and visualise the quantum world particularly the wavefunction, and I just want to be more sure on whether it is sufficient in accounting for nearly 90% of the maths that describes the quantum world and its phenomenon, while also remain easy to follow given a sufficient background based on first principles Disclaimer: The knowledge gained in the thread is NOT a substitute in doing math when tackling quantum problems
In lots of ways. But we need to backtrack a little. Take a look at wavefunction on wiki and note this: "In one important interpretation of quantum mechanics called the Copenhagen interpretation, the modulus squared of the wavefunction, |ψ|², is a real number interpreted as the probability density of finding a particle in a given place at a given time". But now look at Aephraim Steinberg's web page and at Jeff Lundeen's piece here where he says this: "With weak measurements, it’s possible to learn something about the wavefunction without completely destroying it. As the measurement becomes very weak, you learn very little about the wavefunction, but leave it largely unchanged. This is the technique that we’ve used in our experiment. We have developed a methodology for measuring the wavefunction directly, by repeating many weak measurements on a group of systems that have been prepared with identical wavefunctions. By repeating the measurements, the knowledge of the wavefunction accumulates to the point where high precision can be restored. So what does this mean? We hope that the scientific community can now improve upon the Copenhagen Interpretation, and redefine the wavefunction so that it is no longer just a mathematical tool, but rather something that can be directly measured in the laboratory". This says wavefunction isn't something to do with probability after all, but is something that's actually there. Something real, that exists. Something wavelike, propagating through space. Something like a seismic wave, but in space rather than in the ground. Now try comparing such a wave with a cloud. They are very very different.
If you multiply the value of the state function or wavefunction at a coordinate by its complex conjugate (a complex number equivalent of squaring it), you get the probability density at that location. So if you integrate this over a volume of space, you get the probability of finding the particle there, or in other words the proportion of its time that is spent in that volume of space. So when people speak of "clouds" they mean clouds of probability, derived from working out these probability densities at a series of points and then plotting them in 3D. I find the most helpful approach is to think of waves (and especially, in the context of the atom, of resonant standing waves that allow a series of spherical harmonics, corresponding to stable electronic states) and then to picture the associated probability densities as clouds. The thing in QM, as you may already know, is that a whole range of physical attributes of a system is derived from the state function by operating on it with the appropriate QM operator. So the state function (wave function) carries all the information about the system. It does not itself correspond directly to anything physical, but underlies everything that can be said about it. So I think of the wave first and then of the resultant physical properties emerging from it.
Sorry to interrupt, but: Sounds good to me. What probability densities? What clouds? You know how I referred to the wiki atomic orbitals article re standing waves? See this from the selfsame article: "This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus". We've got photons and electrons. E=hf applies to photons, because they are singleton electromagnetic waves. And we made the electrons (and positrons) out of photons in pair production. And we can diffract electrons. So they have a wave nature too. So we don't have any point particles. So the probability of finding a particle at a particular location just doesn't make sense. It makes as much sense as detecting one seismic wave with another, and then putting an X on the map and saying the seismic wave is exactly here and nowhere else. Have I mentioned the Optical Fourier Transform?
OK Farsight, now you are starting to inject your own eccentric views into the thread. I HEREBY WARN THE OPENING POSTER (and other readers) that Comrade Farsight is not always to be relied on for a good explanation of conventional theory - he or she has idiosyncratic ideas in some areas. These things are all wave-particles. For understanding atomic structure and spectra, it is true that it is often most helpful to think of the wave first and then only subsequently to keep in mind that what we call "electrons" are the quantised units (of mass, energy, charge, spin, etc) that these waves seem to come in. BUT, since they do only come in these units, we do actually call them electrons and much of physics and chemistry does not require us to consider their wave aspect at all. AND FURTHER, it is worth bearing in mind that the wave representation of electrons comes from the form of the eigenfunctions of Schrodinger's equation. And this equation contains expressions for the potential and kinetic energy of a pointlike PARTICLE with a pointlike mass and charge. So in a very real sense, you cannot construct the wave concept without postulating a particle first! So I stick to my guns and say the square modulus of the wave is the probability density of a pointlike PARTICLE, in undefined motion about the nucleus. Although the wave certainly feels more fundamental than the particle, in the situations we have been discussing, the irony is that the wave can only be modelled by reference to a particle postulate.
I doubt it. AND THERE YOU GO AGAIN, Pretty sure the we above did not include you. The question is who does it include? You still have not provided any reference that experimentally supports the statement. You continue to CONFUSE a theoretical gamma-gamma pair production with what has been experimentally confirmed. Experimental pair production involves an interaction between a high energy gamma ray and a nucleus, not a gamma-gamma interaction. Exchemist is correct in his caution re entertaining any illusion that Farsight's interpretation of most of what he spews out is even remotely similar to any accepted scientific consensus.
They aren't eccentric. You can diffract electrons. They aren't little billiard ball things. In atomic orbitals electrons "exist as standing waves". There's nothing idiosyncratic about that. It's a wave equation. See wikipedia and note that E=hf and E=mc². The presence of the m does not indicate a pointlike particle because a standing wave trapped in a mirror-box adds mass to that system. When you open the box it's a radiating body that loses mass. See Light is Heavy by van der Mark and 't Hooft (not the Nobel 't Hooft). Go and read the weak measurement material re Aephraim Steinberg and Jeff Lundeen. In particular read the physicsworld article In praise of weakness. Probability is passé.
I'm not confused. See two photon physics on Wikipedia. We know that electron-positron annihilation results in gamma photons, and those of us who understand the physics know that such processes can go the other way too. I merely know more physics than you do. Here, let me quote something for you: "Two-photon physics, also called gamma–gamma physics, is a branch of particle physics that describes the interactions between two photons. If the energy at the center of mass system of the two photons is large enough, matter can be created". Have a read of the tutorial. And do not angrily dismiss the physics that you are ignorant of.
Most of those who really understand physics, know that you are confused. Now you are confusing what you believe with what you know.., and then projecting that misguided knowledge, as representing some sort of consensus. To know gamma-gamma interactions result in pair production, it is first necessisary to experimentally confirm the process. You have yet to provide any experimental evidence that in reality any photon-photon interaction occurs, let alone a gamma-gamma interaction. So now you not only have a problem associated with misinterpretation, you also have a problem distinguishing belief and imagination from fact and reality. It seems you have repeated bad interpretation so often you have come to believe it... That does not make it true.
Farsight, the link you provide shows no direct experimental results involving gamma-gamma interaction. At best it implies a gamma-gamma interaction based on the results of e+/e- interactions... As long as it remains implied it also remains theoretical. Besides there is a great deal of difference between electrons and gamma rays and even more between comparring electron/positron interactions where there is a charge difference and photon-photon interactions where there is no charge, let alone any charge difference. Cite a peer reviewed experimental gamma-gamma interaction. Do you seriously believe that photons interact directly with eachother?
Actually Schrodinger's equation is a diffusion equation, as it has only a first derivative of time. "Diffusion of what?", one might ask. The time-independent version, which is the special case used in resonant (standing wave) states such as atomic orbitals, is a wave equation, but for standing waves only, obviously. So indeed, there is nothing wrong with you describing atomic orbitals as standing waves, and I did not suggest there was. But there IS something wrong with you asserting that electrons always have an associated STANDING wave. In the case of electron diffraction for example, I would not expect them to. As for your rather obvious remarks about that (electron diffraction), nobody is arguing with you. They are wave-particles, which means they have aspects of behaviour that requires BOTH wave AND particle descriptions. If you think electron diffraction precludes the possibility of electrons being particles, it rather looks as if you cannot get your head round wave-particle duality. Look I'm sorry Farsight, but what you are saying is bound to cause confusion to the person who originally started this thread. But now at least there have been enough warning flags, raised by both myself and OnlyMe, to prevent anyone spending too much time worrying about your bizarre attempts to deny, apparently, the well-attested particulate aspects of the electron.
The wavefunction still involves probability when dealing with measurements and collapse, even in the experiment described by your quote from Aephraim Steinberg. I think you're reading too much into that quote; they're arguing that through weak measurements, particles (or multiple copies of them prepared in the same quantum state) can be directly detected as waves even before they hit the screen. With only the interference pattern at the screen, all you can do is make an indirect inference and leave what happens at the slits open to interpreation.
I'm not trying to help promote any of Farsight's views, but I think gamma-gamma pair annihilation has been experimentally observed now. According to Wikipedia that seems to be the case, and I've heard the claim many times before, but if you want me to go digging for a peer-reviewed source, I could have a look around.
From a link cited within the Wiki link above, Two-photon physics, which Farsight has also referenced, Every experimental refrence I have seen begins with a particle beam. The gamma-gamma interactions are interpreted results. Which means they fit the prediction. Not that they prove photon-photon interaction. I am not saying that it does not happen, just that it has not been directly observed. Mostly this is part of a current rant of mine. With the forum moderators on an extended break, there has been a significant increase in fringe interpretations and confussion between theory and proven reality. And yes even accepted authorities often reference gamma-gamma pair production as if it were proven, but if you look close that is mostly in a lay oriented context. Experimental results always include error rates and statements qualifying conclussions as within the range of prediction or as consistent with an expected theoretical result. It really isn't a big deal to me, other than I have been repeatedly asking Farsight, for a credible reference. So far all he returns with is Wiki or I think on one occasion a paper than specifically dealt with a gamma-nucleous collision that resulted in e+/e- pair production. Just because a electron/positron collision can produce two gamma rays does not mean two colliding gamma rays will produce an electron/positron pair. I would not want you to go to too much trouble, but if you do run across a definitive case of any photon-photon interaction I would find it interesting... And I expect it would open many other possibilities for discussion.
I checked the link, and I'm not sure whether it's describing indirect measurements of photon-photon interaction through the usual electron-positron scattering, or whether it's talking about high energy electrons and positrons being used to generate photons when they're deflected, with the photons' existence being inferred from the electron-positron scattering, and products of the photon-photon annihilation being subsequently identified. Not a huge deal to me either, and like you I'm confident that it's real whether or not modern experiments are powerful and precise enough to detect it, but the sources I've looked at do seem to imply that it's been directly observed; I won't push that viewpoint until I've found a good peer-reviewed source explicitly stating it. Yeah, I too lament what people like Farsight, Quantum Quack and Reiku have been doing to this place for years. It used to be really cool when guys like Southstar were posing interesting, challenging math problems and guys like BenTheMan and Alphanumeric were laying down the hard facts on demand, but lately there's been an abnormal surge in patrons wearing dunce caps.
Here's the Jeff Lundeen quote again, this time with some bolding: "With weak measurements, it’s possible to learn something about the wavefunction without completely destroying it. As the measurement becomes very weak, you learn very little about the wavefunction, but leave it largely unchanged. This is the technique that we’ve used in our experiment. We have developed a methodology for measuring the wavefunction directly, by repeating many weak measurements on a group of systems that have been prepared with identical wavefunctions. By repeating the measurements, the knowledge of the wavefunction accumulates to the point where high precision can be restored. So what does this mean? We hope that the scientific community can now improve upon the Copenhagen Interpretation, and redefine the wavefunction so that it is no longer just a mathematical tool, but rather something that can be directly measured in the laboratory". I know more physics than you. A lot more. What I tell you about isn't "my theory". It's physics you've never heard about because you slavishly follow your textbook and the popscience media. You are like OnlyMe in your dogged ignorance, but not as bad. Now pay attention, use what I tell you to do your own research, and you will learn something for a change.
Why the answer to that must certainly be cheese. Because as we all know the Moon is made out of cheese, and since electrons and other particles make up the moon, they too are made of cheese. It looks like this. Take one hydrogen atom. The electron is in a 1s orbital. It exists as a standing wave. Now remove the proton. Does the electron magically morph into a point particle? No. Now add one positron. The result is two 511keV gamma photons. How did that happen? Magic? No. And note that E=hf applies to those photons. And E=hc/λ. Because they aren't point particles either. They are waves. You can make electrons and positrons out of them, and then you can diffract those electrons and positrons, because they're waves too. I can. I'm the one who understands it. A particle like the electron is a "Dirac spinor", it is wavefunction, or light if you prefer, in a Dirac's belt configuration. Your answers are non-answers. They are not satisfactory. Step aside, exchemist.
Farsight, this is delusional. Stop trying to patronise people with a proven track record of posting good science.
It no delusion. CptBork and I had a recent exchange. He knows full well that I'm the guy who quotes Einstein and Minkowski and Maxwell and gives the references to bona-fide papers and the hard scientific evidence. He knows I'm no my-theory guy. He knows that it was he who dismissed Einstein. He knows full well that I'm not like Quantum Quack or Reiku. Do you know what I am like? Here, chew on this: As you are to Quantum Quack, so am I to you.
Two-photon physics - Wikipedia links to Two photon physics at CESR. If photons collide with enough energy, they can indeed make other particles. However, that does not vindicate the circling-photon theory of the electron. When one calculates the rates of high-energy electron-photon processes and compares them to observations, they are most consistent with what the Standard Model states: the electron field is a 4-component Dirac spinor field, not a circling photon.
