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The author of Quantum Mechanics Eugen Merzbacher hs a page online about the Copenhagen Interpretation. He concludes the artilce by saying Case closed!

He's not confused. They refer to exactly the same thing. I.e. http://en.wikipedia.org/wiki/Copenhagen_interpretation immortal: Please take note that juanrga has never provided nor recognized the definition for the terms that he's using. In this way he keeps his straw argument alive and kicking. I recommend ignoring him unless and until he states the definitions of wave-particle duality and Copenhagen interpretation. Also, did you notice that juanrga never provided a reason why the 'Copenhagen interpretation' is supposed to be wrong?

I doubt that there are any textbooks on that subject. It's too trivial tomake a text out of it. What you might want to do is to pick up a chemistry text and go over the section of dimensional analysis. There are no theoretical barriers to finding the positin of an electron so there's nothing to laugh about. Even quantum mechanics doesn't give a limit of the precision on measuringthe position of an electron.

I'm going to bed right now. Tommorow when I wake up I'll go cash my check and buy an ink cartridge for my printer so that I can print that out and read it. At that time I'll get back to you on this. Severian - Do you believe that there is a wave-particle duality? If so then can you please post a definition of it? Thanks.

Here's the way I see it. From Principles of Quantum Mechanics - 2nd Ed. by R. Shankar, page 116. The autrhor writes To my thinking this is the Copenhagen interpretation. Without it we'd be without this postulate and not know what the wavefunction means. I.e. we'd have the prediction but we wouldn't know what it meant or what to do with it. We can't make a prediction without this interpretation to tell us what it is we're looking to measure. Taking away the Copenhagen interpretation takes away our understaning of the meaning of the wavefunction. In that sense I disagree with you. I was referring to quantum mechanics, not quantum field theory. I don't understand. What are you saying that its problems are? There is the concept that the observer making the measurements are a quantum system. Is this what you're referring to?

I want to get some ideas and oponions from my the people I've grown to admire here. Please check the paper I wrote called On the Concept of Mass in Relativity at http://arxiv.org/abs/0709.0687 Please take a glance throught it and let me know what you think. Let's start with the abstract. I changed my mind on what I want the purpose of this article should be about. I want it to address all the errors used in counter arguments used against the concept of relativity and to give counter examples where needed. Here's the abstract as it reads now. Mind you that I don;t wamt people to get the idea that I'm pushing the conecept of relativistic mass since people who know about it have already made up their minds for the most part. The goal here is to present arguments used against the concept of rel-mass which are erroneos, such as the claim that its just another term for energy. I give a counter example on that point whereby I present a worked out example where the relativistic mass is not equal to the energy/c2 as is often claimed. I eagerly await your result. This is not an excuse for those who oppose the idea to try to prove that nobody uses it. That would be hijacking this thread.

A test? Don't I get a chance to study for it? The periodic table is a list of the known elements arranged according to their properties Nothing, becase I never talk about the periodic table. I forgot what those zones are. Its been decade since I've studied it. Your definition does not conform to the standard definition which is as follows: the definition of a periodic function means that f(x) = f(x + L) where L is the period of the function. What you have doesn't define a periodic function. E.g. your function could meet that meaning "f(a) is a solution then f(2a) is" but have arbitrary values inbetween a and 2a and etc. and it'd still be periodic by your account. What do you mean by "solitary"?

Thank you. Yes. That's what I've been doing. I have to admit that being human means having to restrain myself when what I really want to do is say that they're breaking forum rules. Is it okay to say that their argument is outside mainstream physics and therefore belongs in the speculation forum? If not then I appologize for having done that.

I prefer Pete, even in open forum. You wrote [math]\Psi(x, t) = Ae^{i(kx - \omega t)}[/math] We need to put this in a similar form so we write [math]\Psi(x, t) = Ae^{ik[x - (\omega/k)t]}[/math] Let [math]v = \omega/k[/math]. This is the phase velocity of the wave. We now have [math]\Psi(x, t) = Ae^{ik(x - vt)}[/math] which is now in the form [math]\Psi(x, t) = F(x - vt)[/math] Numbers aren't periodic. n is an integer which labels the wave-parameter andenergy eigenvalues. The wave function is periodic in the temporl sense but not in the spatial sense. Note that the wave function goes to zero outside the walls of the potential. This is not a spatially perriodic function though. I disagee. Quantizing a variable does not make it periodic whatsoever. Bound particles do not have a spatially periodic wavefunction.

That comment flies in the face of mainstream quantum mechanics. The Copenhagen interpretation is one of the postulates of quantum mechanics. To claim otherwise is personal conjecture and as such it doesn't belong in the ordinary physics forums but belongs in the speculation forum.

Yeah. That's true. It was just easier describing waves in general. Note on jargon: The typical way to refer to that is to say that is that its periodic in time. By the way, I only meant to imply that waves aren't periodic by definition. And not all waves in quantum mechanics are periodic. The expression you just gave is the solution for a free particle with a well defined momentum. It isn't a general solution. There really isn't a geneal solution to Schrodinger's equation since the equation has the potential as a variable in it. Let's take a look at the situation of an infinite step potential well where V(0) = + infinitity and V(L) = infinity and V(x) = 0 for 0 < x < L . The solution is of the form [math]\psi(x) = C_1e^{ikx} + C_1e^{-ikx}[/math] where C1 and C2 are constants. Putting [math]\psi(0) = 0[/math] we get [math]\psi(x) = C_1(e^{ikx} - e^{-ikx})[/math] or [math]\psi(x) = A sin kx[/math] Applying [math]\psi(L) = 0[/math] requires sin kL = 0 or [math]kL = n\pi[/math] This means that k is restricted to the following values [math]k_n = \frac{n\pi}{L}[/math] The energy eigenvalues are [math]E_n = \frac{n^2h^2}{8mL^2}[/math] The complete solution has then the following eigenfunctions [math]\Psi_n(x, t) = A_n sin \frac{n\pi x}{L} e^{-i(E_n/\hbar)t}[/math] 0 < x < L [math]\Psi_n(x, t) = 0[/math] (x < 0 and x > L) These are standing waves of course. The most general solution is a sumation of these eigenfunctions. When that is done the result no longer specifies a particle with well defined momentum. A wave packet is locaized in space. To create one you have to have a superposition of a continuum of wave numbers to form a Fourier integral. Wave packets aren't always periodic either.

That's the way most people percieve it to be, including myself. That's called personal time which is seperate and distinct than objective time, which is the time that we all agree on.

A classical wave is defined as any function that satisfies the classical wave equation [math]\nabla^2\Psi = \frac{1}{a^2}\frac{\partial^2\Psi}{\partial t^2}[/math] The general solution is of the form [math]f(x, t) = F(x - at) + G(x + at)[/math] There is no requirement for the wave to be periodic. A wave-packet is a good example of wave which isn't periodic. See details at http://en.wikipedia.org/wiki/Wave_packet The wavefunction in a potential well isn't periodic either.

How so? Can you elaborate? I.e. what would you like to add on to it? It's not intended to address anything except for particles. Sure, there are other things besides particles such as fields. But that doesn't pertain to the wave-particle duality. Each particle has a wave function to it and that wavefunction is interpreted according to its probability density. The definition was never intended to speak about all fundamental entities in quantum theory, only particles and their associate wave property. As a general rule, I disagree. This is a forum which has several purposes, one of which is to help people learn physics and/or particular aspects of physics. In this case qft123 started a thread to learn about the wave-particle duality, i.e. to learn what the definition is. He couldn't very well have come here to state what something is when his purpose was to learn all about it. For the sake of argument, how would you define the wave-particle duality? How would you have me change the definition that I gave? If I disagree with other people's definitions then that's perfectly fine. I'll just refer to this as my definition. I think it'd be hard to get a definition which we'd all agree on. studiot - Thank you very much for your input.

When I talk about particles scattering off step potentials I can't use photons as an example because they don't interact with step potentials. When I talk about the double slit experiment I use photons since that's what I'm most familiar with in that experiment. That's all. The problem is that he's not acknowledging the associated wavelength of a particle with the particlelike aspects of quantum particles. You'll never get him to acknowledge that fact since he's employing a straw argument which doesn't allow for it. We have already pointed out to you that this is not what the wave-particle duality is about. We know all too well that an individual particle is not wave. If it had been then there'd be no wave-particle duality. Please stop arguing a mistake that nobody here has made. I also explained to you that when you use the argument you have, rather then an argument actually pertaining to the wave-particl duality, you commit the logical fallacy known as the straw argument which is defind as follows This is precisely what you do when you claim that an individual particle does not act like a wave. Nobody in this thread has disagreed with that all too simple point. We know that quite well and the fact that you refuse to aknowledge this is quote irritating to all of us as their posts have demonstrated. For the purpose of this thread I propose that we define the wave-particle duality as follows. 1) An particle with a well defined momentum has the following associated wavefunction [math]\Psi(x, t) = Ae^{i(kx - \omega t)}[/math] where the wave number k is related to the momentum p through the de Broglie relation [math]p = \hbar k[/math] An arbitrar wave function for a particle is made by summing individual wave functions either by a Forier sers or a Fourier integral. 2) From Principles of Quantum mechanics - 2nd Ed. by R. Shankar (graduate level quantum mechanics text), page 113 All this has been explained to you already and you ignored it and keep repeating yopur straw argumen. Note: To the members of the forum who are participating in this thread, please review the definition I gave for the wave-particle duality and let me know if you object to using it as the definition for the wave-particle duality. Thank you.

I don't understand. Are you trying to say that it we report someone whom we believe is breaking the rules that its frowned upon? I've gotten feeback from people who have said that they were not happy about being mislead in certain cases/topics. That happens when I send then a part of a text that explains the relevant details. We need to take that kind of thing seriously. And I'm not saying that they need to be silenced. I'm saying that their argument should be moved to the speculation forum where people can read about it when they care to and not being confused about it in a normal discussion of bread and butter physics. I find it incredibly irritating when someone uses the logical fallacy of the straw argument and the moderators do nothing about it when they are informed of it. Also when the opponent refuses to acknowledge and respond to your counter arguments its also very irritating. That happens quote a lot. Isn't there a rule against that?

That is a not uncommon misconception. An free electron with a well defined momentum has the following associated wavefunction [math]\Psi(x, t) = Ae^{i(kx - \omega t)}[/math] where the wave number k is related to the momentum p through the de Broglie relation [math]p = \hbar k[/math] This is what it means to say that an elecron has wavelike aspects. The wavefunction can scatter off a step potential like a wave can. When a single photon impinges on a double slit its location is localized like that of a particle. But when this reslt is compared to the results of a large ensemble of identical experimental setups the interference pattern appearns but it can't be said that the electrons interact with each other. It is for these reasons, not for the single particle nature of electrons/photons, that there is said to be a wave-particle duality. You have set up a straw arguement whereby you keep repeating what we all klnow very well and purport it to mean that it proves that thre is no wave-particle duality. The error in your straw argument is that nobody is saying that an individual partilce is physically behaving like a wave all by itself. That's not what the wave-particle duality is all about. Its exactly what I just said it was about, i.e. that to every particle there is an associated wavelenth and wavefunction. Straw arguments are logical fallacies and as such are not allowed in the forum.

That's a good idea studiot. swansont said that they enforce the rules. Let's take a look at the rules. From http://www.scienceforums.net/index.php?app=forums&module=extras&section=boardrules I found this very interesting. It's nice to know that using logical fallacies is mpt allowed. And that's what's being used. In this case its a straw arguement that we've been concerned about, i.e. an I'm sure we have all recognize examples of this kind of thing in the past. Well now you know how to report it and since its a logical fallacy it can't be used. And when someone presents an argument which contradicts stanard textbook physics that's an example of personal conjecture and should be moved to the appropriate forum as stated in the rules.

You can also check out http://home.comcast.net/~peter.m.brown/sr/mmx.htm

Okey dokey. It so east to get side tracked, isn't it? Actually that's another good reason to neg rep them. Not a strong one though so its not one that I'd use.

Yes. I have seven quantum mechanics/modern physics texts. Most, but certaintly not all, of them has a section on the wave-particle duality but all of then employ the wave-particle duality equation which is de Broglies equation [math]\lambda = \frac{h}{p}[/math] which connects the wave aspect of a particle to its particle properties. I.e. every particle with momentum p has a wavelength [math]\lambda[/math]. The wave-particle duality concept isn't always defined explicitly. Sometimes its just buried in there. But whenever you have a particle with an associated wave equiation tied to it then, in essense anyway, you have the wave-partuicle duality. If you looked up where it defines the de Broglie expression connecting the wave and particle aspects of a particle then you'll see the wave-particle duality being touched on. This relationship is embedded in all aspects of quantum mechanics. Its used to define the wave function of the particle snd is used to write Forier Integrals and transforms. My point is that every QM text uses the wave-particle duality properties of matter through the De Broglie equation. It's true that many texts have a section on the wave-particle duality but not all of them I tried to be very careful so that I didb't claim that they all had a section on that. I appologize if I wasn't clear on that point. Let me give you an example: I have the text Modern Quantum Mechanics by J.J. Sakurai in front of me. The index does't mention "wave-particle duality" at all but its wrong to assume it doesn't engulf the concept in it. On page 47 the author writes That is the wave-particle duality in its essense. The graduate QM text I was going to use a few years ago at UMass Lowell is Principles of Quantum Mechanics - 3nd Ed. by R. Shankar. On page 113 the autor writes The list goes on and on. But I'm certain that no matter what QM text that you'd pick up it would talk about or use de Broglies equation and employ the concept of the wave-particle duality whereby a particle has an associated wave and has a wave-function which describes it. All these things are the heart of quantum mechanics, can be found in all QM texts and has at their root the wave-particle duality as Shankar's text defines the concept. Again, I appologize for writing something which you found misleading. My bad. Did you read the Wikipedia article on this topic? It's at http://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality I underlined the statement of the wave-particle duality. Do you see where the author says that its a central concept of qauntum mechanics? I agree with the author on that point.

Not in all cases. E.g. the wave behaviour of quantumn particles is statistical in nature. That means that if we have an experiment which we keep repeating on a single particle and record measurements then the wave nature of the particle will appear when the ensemble is looked at. E.g. No individual particle will exhibit wave bahavioru in this case but the collection of expeiments shows the interference effects by the statistical properties, i.e. particles will have a high probability of gathering near the amplitude of the wave is high. That in no way is classical wave behaviour. I believe that juan has done is to construct a strawman whereby the he created is own interpretation of what the term wave-particle duality means and has argued that his version is a myth. Straw arguments are logical fallacys. In reality it has a particular meaning, found in most QM texts, which is quite correct and is what quantum mechanics is based on. I've sent the real meaning to my fellow posters here so they're well educated on the subject and its true meaning. CERN has a web site about the wave-particle duality http://choruswww.cern.ch/Public/textes/english/node4.html

Yeah, but how can it be enforced? Its nice in theort but impossible in practice. For example: the wave-partiucled duality is the main staple in quantum mechanics as I'm sure that we all know. Yet it only takes one poster to disturb the discussion with a non-truth, i.e. in this case trying to convince people that its a all just a myth. It's next to impossible to find a QM text which doesn't explain it and its relationship and importance to QM. That really cofuses people as StringJunky told us. Yet the moderators leave it alone.

You got me my friend. I have no idea about all that Higgs stuff. I hope to learn about it someday.

The wave-paricle duality is no myth. So long as there is a waveklength associated with a particle by [math]\lambda = \frac{h}{p}[/math] the wave-particle duality will have meaning and exist since that's precisly what it means. The term crackpot refers to someone who is crazy or strange. I'd hazard to guess that immortal believes that you're strange for rejecting the heart of quantum mechanics, i.e. the wave nature of particles. Also, when you post quotations without stating the source it doesn't look good.