juanrga Posted April 28, 2012 Share Posted April 28, 2012 (edited) I am not an expert in quantum mechanics, so please feel free to educate me here. I thought there are two basic ways to model in quantum mechanics. In the first way, quantum field theory, a wave function travels from place to place. When an interaction occurs, the wave function collapses to a local wave packet of energy we can refer to as a particle. The wave function gives the probability of detecting this particle at a certain place and time. The second method, Quantum Electrodynamics (QED), models particles as single points. The sum of all paths method is used to determine the probability that the particle is detected at a given place at a certain time. The probability amplitudes for each possible path the particle could take are summed, then squared to compute this probability. There is no wave in QED. (Summing amplitudes from Feynman diagrams of interaction events and squaring is also a way to determine probability.) The first method uses waves and wave mechanics. The second uses particles and the sum of all paths. I think they both give equivalent results. Quantum electrodynamics is a quantum field theory and quantum field theory does not use wave-functions. No I'm pretty sure it's exactly related to what you said, that's why I quoted you, you said wave mechanics in quantum mechanics is a flat out wrong and a "myth", which I don't see how it could be a myth seeing as how it's documented that scientists to this day use to to achieve values of some things because of how well certain aspects of atoms can be described by it, like predicting molecular bonding. Also, aren't wave functions used with Dirac equations? And don't Dirac equations have problems too? http://en.wikipedia....i/Klein_paradox You grossly misinterpret me, misquote me, ignore what I have said and repeated... For instance, I wrote that Nikolic emphasizes that "wave-particle duality" is a myth [*]. In no other part of the post that you quoted I used the word "myth". But you now pretend that I said that "wave mechanics in quantum mechanics is a myth", when in the post that you quoted I wrote: "The wave-function approach is still given in introductory courses to QM, which only deal with simplest problems". If you cannot read my posts and/or understand what I am really saying, maybe you would stop from reading them. [*] Indeed the corresponding section of his paper is titled "Wave-particle duality as a myth" ) Edited April 28, 2012 by juanrga Link to comment Share on other sites More sharing options...
questionposter Posted April 28, 2012 Share Posted April 28, 2012 (edited) OR, you could just accept that a lot of quantum wave mechanics isn't wrong and outdated. Also, you seemed to be in support of his paper, so it is only logical that you would think a similar thing. There's even a chemist I know who still uses quantum wave mechanics to create accurate models of molecules in a computer, and that's today, not 50 years ago. Furthermore I don't see how you could say everything else is right when all the other systems to describe quantum particles also have their own problems and are also mostly approximations. The Heisenberg Uncertainty principal can even be derived by looking at the patterns of applying quantum wave mechanics to particles. Edited April 28, 2012 by questionposter Link to comment Share on other sites More sharing options...
juanrga Posted April 28, 2012 Share Posted April 28, 2012 OR, you could just accept that a lot of quantum wave mechanics isn't Also, you seemed to be in support of his paper, so it is only logical that you would think a similar thing. There's even a chemist I know who still uses quantum wave mechanics to create accurate models of molecules in a computer, and that's today, not 50 years ago. Furthermore I don't see how you could say everything else is right when all the other systems to describe quantum particles also have their own problems and are also mostly approximations. Based on the fact that there are so many different interpretations of the original data gathered, I don't know if there is a good way to answer the original question. You grossly misinterpret me, misquote me, and ignore what I have said and repeated. Link to comment Share on other sites More sharing options...
questionposter Posted April 28, 2012 Share Posted April 28, 2012 (edited) You grossly misinterpret me, misquote me, and ignore what I have said and repeated. No I'm pretty sure you repeatedly said the wave mechanics used for describing particles isn't something that's used now or is wrong, which I'm pretty sure is an assumption that is in of itself wrong. Maybe CERN does use quantum wave mechanics by using wave-packets to describe free-particles. The belief that electrons are waves or behave as waves (electrons behave as quantum particles always) is a typical misconception that one finds in non-rigorous literature (science news, popular books...). There exists a well-known article published in FOP that devotes an entire section to explain why wave-particle duality is a myth and would be abandoned. Which, why bring it up in your argument if your not in support of it in at least some way? I am also not citing (and still less discussing) here recent works as [1] where it is shown that wavefunctions, or even Dirac kets |Psi>, cannot describe a large kind of quantum systems. If you want study the dissipative behaviour of an electron in an electron transfer reaction you cannot use wavefunctions neither Dirac kets. No 'wavelike' property is used to define what an electron is. Therefore an electron is a particle, not a wave. [*] Traced back to Dirac! Some of Dirac's equations ARE wave equations! How many different ways are there to interpret "an electron is not a wave"? Edited April 28, 2012 by questionposter Link to comment Share on other sites More sharing options...
juanrga Posted April 28, 2012 Share Posted April 28, 2012 No I'm pretty sure you repeatedly said the wave mechanics used for describing particles isn't something that's used now or is wrong, which I'm pretty sure is an assumption that is in of itself wrong. Maybe CERN does use quantum wave mechanics by using wave-packets to describe free-particles. Which, why bring it up in your argument if your not in support of it in at least some way? Some of Dirac's equations ARE wave equations! How many different ways are there to interpret "an electron is not a wave"? It is good that now you give quotations of entire phrases and paragraphs that I wrote. Link to comment Share on other sites More sharing options...
questionposter Posted April 28, 2012 Share Posted April 28, 2012 (edited) It is good that now you give quotations of entire phrases and paragraphs that I wrote. Please address the issue of what you actually mean if you do not mean to say that electrons are not anything like a wave at all, even though today many parts of industrial sciences use quantum wave mechanics to describe particles and alternative quantum theories still use some quantum wave mechanics. Edited April 28, 2012 by questionposter Link to comment Share on other sites More sharing options...
juanrga Posted April 28, 2012 Share Posted April 28, 2012 (edited) Please address the issue of what you actually mean if you do not mean to say that electrons are not anything like a wave at all, even though today many parts of industrial sciences use quantum wave mechanics to describe particles and alternative quantum theories still use some quantum wave mechanics. I already stated, explained, and supported my point in many occasions. And you have already quoted me explaining what is an electron and what is not. Edited April 28, 2012 by juanrga Link to comment Share on other sites More sharing options...
questionposter Posted April 28, 2012 Share Posted April 28, 2012 (edited) I already stated, explained, and supported my point in many occasions. And you have already quoted me explaining what is an electron and what is not. You said there are many contemporary operators professional scientists always use over quantum wave mechanics because quantum wave mechanics is outdated. This is false, yet you said I was wrong in assuming you that's what you meant, so please explain what you really mean clearly. I quoted you 4 times with you not supporting the use of quantum wave mechanics, and you seemed to be fine with those quotes. Edited April 28, 2012 by questionposter Link to comment Share on other sites More sharing options...
juanrga Posted April 29, 2012 Share Posted April 29, 2012 You said there are many contemporary operators professional scientists always use over quantum wave mechanics because quantum wave mechanics is outdated. This is false, yet you said I was wrong in assuming you that's what you meant, so please explain what you really mean clearly. I quoted you 4 times with you not supporting the use of quantum wave mechanics, and you seemed to be fine with those quotes. Maybe I could use other words but I would say the same that I said in the quotes. Link to comment Share on other sites More sharing options...
questionposter Posted April 29, 2012 Share Posted April 29, 2012 (edited) Maybe I could use other words but I would say the same that I said in the quotes. Well not only are some of the modern operators and equations such as Dirac's equations (which you seem to like) based off of and use wave mechanics and also have ways to show equivalence to other operators and properties of quantum wave mechanics, but quantum wave mechanics is still used by scientists today in an industrial capacity. I know both a chemist and hydrologist and in the past both of then have brought up using quantum wave mechanics when I asked them about things they do on their job, and there isn't much of a reason to not use them. Virtually any "model" is just an approximation of particles anyway, because math isn't the universe, the universe is the universe, and all of the alternative models you had said either have their own problems and places where they fail, use quantum wave mechanics, or both. And as I had already said before, I'm fine with quantum wave mechanics not being the "only" aspect of a quantum particle, but with current experimental evidence there's no reason to throw it away. At can easily see a sort of Bohr situation, but that would only suggest that at the very least that newer models of quantum particles are built off of the data of quantum wave mechanics and in many cases can be shown to have equivalent results, not that quantum wave mechanics is completely wrong. Not even the Bohr model is completely wrong, there ARE quantized energy levels and the electron orbitals can accurately describe the approximate average distances of many electron states away from the nucleus. Edited April 29, 2012 by questionposter Link to comment Share on other sites More sharing options...
juanrga Posted April 29, 2012 Share Posted April 29, 2012 (edited) Well not only are some of the modern operators and equations such as Dirac's equations (which you seem to like) based off of and use wave mechanics and also have ways to show equivalence to other operators and properties of quantum wave mechanics, but quantum wave mechanics is still used by scientists today in an industrial capacity. I know both a chemist and hydrologist and in the past both of then have brought up using quantum wave mechanics when I asked them about things they do on their job, and there isn't much of a reason to not use them. Virtually any "model" is just an approximation of particles anyway, because math isn't the universe, the universe is the universe, and all of the alternative models you had said either have their own problems and places where they fail, use quantum wave mechanics, or both. And as I had already said before, I'm fine with quantum wave mechanics not being the "only" aspect of a quantum particle, but with current experimental evidence there's no reason to throw it away. Well as explained before the solutions to the Dirac equation cannot be interpreted as wavefunctions, although outdated and non-rigorous literature still consider the Dirac equation as if it was a wave equation. You allude to a chemist and a hydrologist. Well, I know several recent textbooks written by chemists where it is still said that the Dirac equation is a wave equation. This same people is unaware of the proofs demonstrating why their claim makes no sense and if you were to say them that the Dirac equation is now reinterpreted as an identity for a field operator, they would look you as this . Modern and rigorous formulation of quantum mechanics does not use the old wave mechanics formulation by reasons stated before. The "wave-particle duality" is a myth that would be eliminated from the literature. Finally the term "wave mechanics" has a historical origin in the initial work by Schrödinger, but it would be best abandoned today because is the source of much confusion [*]. [*] Even for the own Schrödinger. Edited April 29, 2012 by juanrga Link to comment Share on other sites More sharing options...
questionposter Posted April 29, 2012 Share Posted April 29, 2012 (edited) Well as explained before the solutions to the Dirac equation cannot be interpreted as wavefunctions, although outdated and non-rigorous literature still consider the Dirac equation as if it was a wave equation. You allude to a chemist and a hydrologist. Well, I know several recent textbooks written by chemists where it is still said that the Dirac equation is a wave equation. This same people is unaware of the proofs demonstrating why their claim makes no sense and if you were to say them that the Dirac equation is now reinterpreted as an identity for a field operator, they would look you as this . Modern and rigorous formulation of quantum mechanics does not use the old wave mechanics formulation by reasons stated before. The "wave-particle duality" is a myth that would be eliminated from the literature. Finally the term "wave mechanics" has a historical origin in the initial work by Schrödinger, but it would be best abandoned today because is the source of much confusion [*]. [*] Even for the own Schrödinger. Why would multiple scientists get such an obviously simple understanding wrong? Makes no sense, unless...it's not completely wrong. Also, the Dirac equations or matrices used in modern field operators can be shown to have equivalent results as the former Dirac wave mechanics. There's also the issue of what physically exists, because if a quantum particle is to comprise physical objects, it has to itself be physical. For as many questions that your "modern" operators answer, they ask deeper questions, and in modern computation the "field" version of Dirac's equations can be interpreted as relativistic versions of Schrodinger equations. When you say Dirac's equations have been revised to fit into field theory, I assume your talking about a fermion field, which can be described as plane-wave solutions. Furthermore, quantum field theory does not address what a particle "is", so you cannot say a particle as not a wave in any way just because wave mechanics is not used in quantum field theory, it is meant to show how forces interact and are mediated, and this is probably why you don't see wave mechanics mentioned a lot in QTF. Edited April 29, 2012 by questionposter Link to comment Share on other sites More sharing options...
juanrga Posted April 29, 2012 Share Posted April 29, 2012 (edited) Why would multiple scientists get such an obviously simple understanding wrong? Makes no sense, unless...it's not completely wrong. Also, the Dirac equations or matrices used in modern field operators can be shown to have equivalent results as the former Dirac wave mechanics. There's also the issue of what physically exists, because if a quantum particle is to comprise physical objects, it has to itself be physical. For as many questions that your "modern" operators answer, they ask deeper questions, and in modern computation the "field" version of Dirac's equations can be interpreted as relativistic versions of Schrodinger equations. When you say Dirac's equations have been revised to fit into field theory, I assume your talking about a fermion field, which can be described as plane-wave solutions. Furthermore, quantum field theory does not address what a particle "is", so you cannot say a particle as not a wave in any way just because wave mechanics is not used in quantum field theory, it is meant to show how forces interact and are mediated, and this is probably why you don't see wave mechanics mentioned a lot in QTF. And again you ignore the technical details given, the quotes from standard textbooks claiming the contrary, and so on... In that well-known branch of physics known as particle physics, we have a precise definition of what is a particle, and using this precise definition of what is a particle we can know when, or when not, particles are detected in some accelerator experiment and if some of the particles detected has a set of properties that no other known particle has, then scientists claim that they have discovered a new particle. We also have beautiful tables with all the known elementary particles and its properties Yes, contrary to what you believe, the electron is a particle, not... a wave Edited April 29, 2012 by juanrga Link to comment Share on other sites More sharing options...
questionposter Posted April 29, 2012 Share Posted April 29, 2012 (edited) And again you ignore the technical details given, the quotes from standard textbooks claiming the contrary, and so on... In that well-known branch of physics known as particle physics, we have a precise definition of what is a particle, and using this precise definition of what is a particle we can know when, or when not, particles are detected in some accelerator experiment and if some of the particles detected has a set of properties that no other known particle has, then scientists claim that they have discovered a new particle. We also have beautiful tables with all the known elementary particles and its properties Yes, contrary to what you believe, the electron is a particle, not... a wave The only evidence you've had that electrons are in no way shape or form related to a wave is modern operators which use or are built from quantum wave mechanics and have planar wave solutions, quantum field theory which does not address what a particle is, but more of how forces act, a book that you yourself said had some things wrong in it, and then this table which is merely information we can confirm with certainty and contains no equations to describe the particles whatsoever, spin is used in quantum wave mechanics, and so is mass, and all of the families of particles. As for CERN, I'm sure they can easily use Gaussian wave packets to describe free particles. Edited April 29, 2012 by questionposter Link to comment Share on other sites More sharing options...
juanrga Posted April 29, 2012 Share Posted April 29, 2012 (edited) The only evidence you've had that electrons are in no way shape or form related to a wave is modern operators which use or are built from quantum wave mechanics and have planar wave solutions, quantum field theory which does not address what a particle is, but more of how forces act, a book that you yourself said had some things wrong in it, and then this table which is merely information we can confirm with certainty and contains no equations to describe the particles whatsoever, spin is used in quantum wave mechanics, and so is mass, and all of the families of particles. Your 'evidence' is different from everyone else, what you say about quantum field theory is nonsense... As for CERN, I'm sure they can easily use Gaussian wave packets to describe free particles. You have alluded to the CERN guys before, but you would stop because they do not support your wrong point of view about electrons being... waves! Go to this page at the CERN, how many times you find the word "wave" or the word "wavefunction"? Yes, zero times. You only can find the word particle in that page by CERN. Yes, guys at CERN think that an electron is a particle (not a wave) and they even go beyond and write: Everything around us is made of matter particles. They are completely right and I already explained why. People at CERN are not repeating the mistakes that your friend the 'chemist' and your friend the 'hydrologist' are doing. You can also go to this glosary from CERN and search the word particle or the word electron and check by yourself that CERN considers that the electron is a particle. You can also search the terms "wave" or "wavefunction" in the glosary and again you will not find them . And yes they consider themselves the world's leading laboratory for particle physics. Since those guys at CERN are very consistent, they consider that the LHC is an particle accelerator and that they are an international laboratory for particle physicists, and they now are searching a new particle named the Higgs. The conclusion is pretty simple: An electron is a particle Edited April 29, 2012 by juanrga Link to comment Share on other sites More sharing options...
questionposter Posted April 29, 2012 Share Posted April 29, 2012 (edited) Your 'evidence' is different from everyone else, what you say about quantum field theory is nonsense... You have alluded to the CERN guys before, but you would stop because they do not support your wrong point of view about electrons being... waves! Go to this page at the CERN, how many times you find the word "wave" or the word "wavefunction"? Yes, zero times. You only can find the word particle in that page by CERN. Yes, guys at CERN think that an electron is a particle (not a wave) and they even go beyond and write: They are completely right and I already explained why. People at CERN are not repeating the mistakes that your friend the 'chemist' and your friend the 'hydrologist' are doing. You can also go to this glosary from CERN and search the word particle or the word electron and check by yourself that CERN considers that the electron is a particle. You can also search the terms "wave" or "wavefunction" in the glosary and again you will not find them . And yes they consider themselves Since those guys at CERN are very consistent, they consider that the LHC is an particle accelerator and that they are an international laboratory for particle physicists, and they now are searching a new particle named the Higgs. The conclusion is pretty simple: An electron is a particle Bolding or coloring the word "particle" doesn't make an electron a little sphere. Furthermore, the definition of a quantum particle can be something that follows quantum wave mechanics. As I already said multiple times now, I'm fine with an electron or proton or w/e not only being only a wave, but you need more than "oh, well, they happened to not use it for every single sentence to describe every single property of a particle" to conclusively say an electron is not in any way shape or form related to a wave. Quantum field theory does not define what a particle "is", therefore you cannot say an electron does not follow any wave mechanics because of the absence of wave mechanics in QTF. QTF is more to describe how forces interact. In fact, http://dictionary.re...se/particle?s=t All it says is that a particle is a constituent of matter, nothing more. Edited April 30, 2012 by questionposter Link to comment Share on other sites More sharing options...
derek w Posted April 30, 2012 Share Posted April 30, 2012 juanrga the word "particle" is a misleading word and should not be taken as a literal description. Link to comment Share on other sites More sharing options...
juanrga Posted April 30, 2012 Share Posted April 30, 2012 (edited) Bolding or coloring the word "particle" doesn't make an electron a little sphere. Furthermore, the definition of a quantum particle can be something that follows quantum wave mechanics. As I already said multiple times now, I'm fine with an electron or proton or w/e not only being only a wave, but you need more than "oh, well, they happened to not use it for every single sentence to describe every single property of a particle" to conclusively say an electron is not in any way shape or form related to a wave. Quantum field theory does not define what a particle "is", therefore you cannot say an electron does not follow any wave mechanics because of the absence of wave mechanics in QTF. QTF is more to describe how forces interact. In fact, http://dictionary.re...se/particle?s=t All it says is that a particle is a constituent of matter, nothing more. Evidently bolding or colouring the word "particle" had a different goal . The goal was to show how CERN guys do not support your claims (although you said us the contrary, they affirm that an electron is a particle not a a wave). The concept of quantum particle applies to situations where quantum wave mechanics do not apply. This automatically invalidates your point about electrons being waves. You insist on that "QTF is more to describe how forces interact". This is nonsense. There is little that I can do here . juanrga the word "particle" is a misleading word and should not be taken as a literal description. There is nothing misleading in a word. Although it happens that some people incorrectly believes that "particle" is a synonym for "little sphere". Edited April 30, 2012 by juanrga Link to comment Share on other sites More sharing options...
questionposter Posted April 30, 2012 Share Posted April 30, 2012 (edited) Evidently bolding or colouring the word "particle" had a different goal . The goal was to show how CERN guys do not support your claims (although you said us the contrary, they affirm that an electron is a particle not a a wave). The concept of quantum particle applies to situations where quantum wave mechanics do not apply. This automatically invalidates your point about electrons being waves. You insist on that "QTF is more to describe how forces interact". This is nonsense. There is little that I can do here . There is nothing misleading in a word. Although it happens that some people incorrectly believes that "particle" is a synonym for "little sphere". In many aspects of quantum mechanics, "wave" is/can be part of the definition of a quantum particle, or at the very least "something that has both point like and wave-like properties". I don't know why you are incapable of seeing this. The use of the word "particle" is used over "wave" means nothing because of this. It's like arguing "No, electro-magnetisms isn't the attraction and repulsion between two bodies, it's a force. See, right there in the definition, it says force, not something that causes things to attract and repel based on their charge", even though if you just researched or kept on reading, you would see it say that it is a force that causes attraction and repulsion based on charge. Your arguments are next to meaningless at this point. You have failed to acknowledge that wave mechanics can be included in the definition of a quantum particle and have a lot of math to support it, including mathematics you have mentioned. Edited April 30, 2012 by questionposter Link to comment Share on other sites More sharing options...
juanrga Posted April 30, 2012 Share Posted April 30, 2012 In many aspects of quantum mechanics, "wave" is/can be part of the definition of a quantum particle, or at the very least "something that has both point like and wave-like properties". Nowhere in the definition of a quantum particle, "wave" is used. Link to comment Share on other sites More sharing options...
questionposter Posted April 30, 2012 Share Posted April 30, 2012 Nowhere in the definition of a quantum particle, "wave" is used. Well I'm sorry to say that's not what quantum mechanics and experimental evidence suggests. Link to comment Share on other sites More sharing options...
juanrga Posted May 1, 2012 Share Posted May 1, 2012 (edited) Well I'm sorry to say that's not what quantum mechanics and experimental evidence suggests. No apologize is needed, because both quantum mechanics and experimental evidence support the idea of that a quantum particle is not a wave but... a particle. Edited May 1, 2012 by juanrga Link to comment Share on other sites More sharing options...
questionposter Posted May 1, 2012 Share Posted May 1, 2012 (edited) No apologize is needed, because both quantum mechanics and experimental evidence support the idea of that a quantum particle is not a wave but... a particle. I don't think you really understand what the word "particle" means. Particle is just used to describe anything in very small realm. In a strict sense, the actual definition of "quantum particle" is something like "a fermion with a radiant energy equal to Planck's constant times the associated radiation". However, there are different variations of quantum mechanics for which this principal will hold true. Some of those variations are Schrodinger's wave equations and things built off of that like Dirac's equations, and then there's more simplified operators like with what Heisenberg made. But, because all the multiple variations of quantum mechanics generally get the same results, which includes Schrodinger's quantum wave mechanics, an electron or any sub-atomic mass is better described as "something that has both point-like and wave-like properties". Because in the end, matter isn't actually a classical "particle" or a "wave", matter is its own thing. In order to say matter doesn't have wave-like properties though, you need to come up with a theory for why the double-slit experiment results happen and have the equations for it achieve the same results that will somehow disprove wave mechanics. QTF as far as I know does not directly address this. http://en.wikipedia....um_field_theory Electrons and protons and other fermoins have similar probability properties to photons, and photons are described as waves or wave-like particles or "ripples in a field" (http://en.wikipedia....um_field_theory). In the same sense, an electron can merely be a ripple in a matter-field rather than an electro-magnetic field. It actually even emphasizes that things can "look like" particles. Edited May 1, 2012 by questionposter Link to comment Share on other sites More sharing options...
juanrga Posted May 1, 2012 Share Posted May 1, 2012 (edited) I don't think you really understand what the word "particle" means. Particle is just used to describe anything in very small realm. In a strict sense, the actual definition of "quantum particle" is something like "a fermion with a radiant energy equal to Planck's constant times the associated radiation". That is not the definition of particle, not even close. QTF as far as I know does not directly address this. http://en.wikipedia....um_field_theory Electrons and protons and other fermoins have similar probability properties to photons, and photons are described as waves or wave-like particles or "ripples in a field" (http://en.wikipedia....um_field_theory). In the same sense, an electron can merely be a ripple in a matter-field rather than an electro-magnetic field. It actually even emphasizes that things can "look like" particles. Wikipedia is not usually a good place for looking for academic stuff. The first phrase in that wiki-page already needs technical corrections, for instance. But the page says "it is impossible (for various reasons) to define a wavefunction for a single photon." That is correct. I already pointed to the limits of the wavefunction formulation. It makes no sense to say that "photons are described as waves" when the old wave formulation of QM does not apply to particles as photons. Edited May 1, 2012 by juanrga Link to comment Share on other sites More sharing options...
questionposter Posted May 1, 2012 Share Posted May 1, 2012 (edited) That is not the definition of particle, not even close. Well it's what quantum means anyway, and then we substitute "particle" for "fermoin" because there are non-fermion pieces of matter with their own rules. But the page says "it is impossible (for various reasons) to define a wavefunction for a single photon." That is correct. I already pointed to the limits of the wavefunction formulation. It makes no sense to say that "photons are described as waves" when the old wave formulation of QM does not apply to particles as photons. That's because a photon isn't a single wave function, it's two: it's an electric oscillation perpendicular to an electro-magnetic oscillation http://www.astronomy...om/light/s3.htm Besides, whether you want to believe it or not, multiple views and aspects of quantum mechanics can account for experimental results in things such as the double slit experiment, and this includes Schrodinger and Dirac mechanics. So far every aspect of QM has some place where it fails, and this includes what you claim to be contemporary operators. Edited May 1, 2012 by questionposter Link to comment Share on other sites More sharing options...
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