Pete

That's what I was talking about. All such magnets have already been manufactured and thus any aligning of the crystaline structure has already been established. Melting and resolidifying is merely repeating the process its already gone through. While magnetic domains may realign due to various reasons I don't see how the crystaline structure could have changed. Domains can be realigned even when the crystaline structure is out of line. Pete

I'd still like to read more about what you're saying. Do you have a textbook reference for me? Have you ever worked with a metal lathe? I did in High School (one of those things I actually remember from those days. ) and from that experience I can't see any reason to assume that machining a magnetized magnet is any more difficult than maching an unmagnetized one.

Why would manufactures do it this way if they can obtain a stronger field otherwise?

Yes. That is correct. Thanks. Pete

I imagine that was already done when the magnet was created in the first place. insane_alien - What kind of temperatures are you talking about? What is the melting temperature of the material that a neodium magnet is made of? I can't see how you'd magnetize the magnet to a particular field strength unless you have a magnetic field that is at least that strong (usually stronger is required). Pete

I never assumed that heating it would present a problem (depending on what temperature it melts at that is). Its the melting that can be difficult since it'd have to be melted and poured into a mold, each of which would have to be able to withstand the heat. As far as how to remagnetize then one can do so using a a very strong electromagnet. That's how they are magnetized in the first place, i.e. after the magnets are created/formed they are then magnetized. What advantage to do think there is in melting it first?? But it'd be much much easier to simply buy a new one. Pete

From the OP's comments it doesn't appear that it was heated to an extent that would alter it to a significant extent. Seems to me that melting and solidifying a magnet in that way is just as unpractical. Pete

Why is that? If it was placed inside a a very strong magnetic field, e.g. inside a coil which when a current is applied, then the it should be possible to magnitize the magnet again. Then again that depends on the hysteresis curve of the material. I imagine that would be very hard to do though given the strength of the field that needs to be applied. This web site - http://www.duramag.com/neodymium.html - states Pete

That would be akin to a man who weighs 200lbs carrying around 800 lbs of weights constantly. I get the feeling that if it were me that either my arms or legs would break of my knees would snap! In any case that would make your legs strong (increasing mass of slow twitch muslces). What you need to do is to make them fast as well (increase mass of fast twitch muscles). Pete

The laws are in fact different. Each law is based on observation and that is the reason for the difference, i.e. it is what we observe. I.e. for two point charges Coulomb's Law - [math]F_{12} = kq_1 q_2/r^2[/math] while for two masses Newton's Law of Gravitation - [math]F_{12} = -Gm_1 m_2/r^2[/math] Notice the negative sign in the later. It is that negative sign which gives gravitational repulsion (when both masses are postive that is). Pete

In the rest frame of the wire it is assumed the wire is uncharged. That doesn't mean you won't get zapped when you touch a wire. In order to be zapped you have to form a ciruit with your body. I.e. one finger reaches inside a light socket while your foot touches the ground. A current is then set up your body due to the difference in potential of the wires. Sorry. That is a typo in the web page. The "-" is supposed to be a subscript to indicate the distance between negative charges. I should also have pointed out that this is an ideal case. In the real world there is actually a non-zero charge density on the surface of the wire which is non-uniform. This surface charge distribution creates an electric field inside the wire and it is that field that pushes the current along. That charge density is extremely small though. I doubt that the electrostatic attraction due to this charged can be measured in practice since it is that small.

The force on one conductor is due to the charges in that conductor moving through the magnetic field generated by the other conductor. The motion of the charge in wire which is parallel to the other wire is that of charge moving perpendicular to the magnetic field generated by the other wire. In such case the charges experience a force which ends up causing the wire itself to experience a force on it. You might also want to learn about the 4-current 4-vector. It is used to determine the charge and current densities in other frames when they are specified in one frame.

But you're right. It could very well be the Yukawa potential. In fact that is a common example that is used in QM for a potential energy function. Pete ps - I never mentioned gravitational potential in my post so I don't know where booker got that idea from.

Correcting a formula is not nit-picking, its simply pointing out a mistake. I already did. Yipes! Where did you get that idea from??? Note - I was using your notation. Normally the potential function is labeled with "V" and not [math]\Phi[/math]. The potential that appears in Schrodingers equation is not " potential," its potential energy. I.e. the quantity whose -grad gives force is potential energy and has units of energy. Potential is something different. In the case of an electric field it has the value of potential energy per unit charge. In a gravitational field it has units of potential energy per unit mass. This is confused a bit in QM since they use the term "potential" to refer to "potential energy." Its a very unfortunate convention. Notice that Energy is given by E = K + V where K = kinetic energy and V = potential energy. The operator corresponding to this value is the Hamiltonian operator and given by H = p^2/2m + V V must have units of energy in order to be able to add it to kinetic energy to get the value of H which also has units of energy. Pete

Something like a rock can be considerd to be a huge quantum mechanical system. Quantum mechanics applies here as well. The properties of quantum mechanical systems hold for rocks in this sense. E.g. the uncertainty in position is so small as to be beyond human senses can detect and the human imagination can picture (i.e. we have no experience in variations in position of rocks which are of atom dimensions). In non-relativistic mechanics particles not disappear either. Pete

Physicists always argue about what is really "conclusive" or not. Experiment is the true test. I look forward to when you have the time. Pete

Please elaborate. What is this missunderstanding of which you speak? Researchers who write such articles are not as naive as that statement seems to make them out to be. In the mean time you might want to consider reading the following articles. I haven't read more than the abstracts to date (been too busy on other projects) so if you believe you've found an error in one or more of them please post it. Thank you. Can EPR-correlations be used for the transmission of superluminal signals? P. Mittelstaedt, Ann. Phys (Leipzig) 7 (1998), 7-8, 710-715 Superluminal signal velocity, G. Nimtz, Ann. Phys (Leipzig) 7 (1988), 7-8, 618-624 Faster than Light?, Raymond Y. Chiao, Paul G. Kwiat and Aephraim M. Steinberg, Scientific American, August 1993 Pete

Mind you, I don't know relativistic quantum mechanics so take what I say on this with a large grain of salt. However from what I understand there doesn't seem to be any problem in this respect, hence the graviton is still lurking around. Its common for people to say that there is no such thing as a gravitational force in GR etc. The truth is that there are two classes of forces. One is known as inertial forces (like the gravitational force) while the other is sometimes referred to as poderomotive forces (like the Lorentz force). Just because has a frame dependant existance and the other doesn't doesn't mean that one should be considered "real" and the other shouldn't. Thinking otherwise can make one question whether gravitons exist or not. What one should really be asking is whether the observation of gravitons is dependant on the observer. A similar question comes up when one considers the fact that wether a charged particle is observer to radiate or not depends on the obsever's frame of reference. Why? Since when?? QM does not violate quantum entanglement, it is actually consistent with it. And there have been reports of FTL signals and there are several articles on FTL using quantum entanglement that are in the physics literature. Pete

The only point I was making with that comment was F = -grad [math]\Phi[/math]. Nothing more and nothing less. If I don't comment on something else it doesn't mean that I didn't/don't understand it, okay? Pete

Thanks. That in itself is helpful. Pete

Actually a path integral contains all paths, not just a subset of them hence the term explore all paths was coined/. I understand what your opinion on this ajb, I just disagree with it. A classical trajedctory gives the position (i.e. location of point) as a function of time. Lets drop that example for herein because it will only serve as a distraction. I started this thread seeking examples of those classical concepts which are meaningless in quantum mechanics, not those which have a qm counterpart. Can you think of any? I myself am not interested in such things. It was a mistake for me to use that word in the first place. Please note: I'm sure all of you have your own opinions of the corresponding quantum mechanical concept of a given classical concept. Lets stick to those examples of concepts which are well defined classically but not quantum mechanically. I would appreciate it. Thanks. Pete

Note that I chose not to consider anything containing the term "lost" since it has an ill-defined meaning in this context. Correct me if I'm wronge by [math]\delta S =0[/math] refers specifically to geodesics, not worldlines in general. I was speaking about general trajectories of particles. This is, which is different than that used in path intergrals. This is a case of something that was perhaps changed/redefined. I.e. the classical trajectory was replaced with path integrals. Mind you, these two quantities are not the same thing. No. I was talking about trajectories (i.e. worldlines in spacetime) in general. For example; a classical charged partilce moving in nn EM field would move on a trajectory/worldline (not simply geodesics). Such a trajectory is defined by the set of points for which X(t) = [t, x(t), y(t), z(t)]. That is quite different than a path integral and has quite a different meaning. In relativity a particle can be considered to be observed at each point on the trajectory (i.e. is located at different point spacetime for all t). That is quite different than the notion of a path integral. A theory is limited by its axioms. I didn't say that an experiment didn't hold. The two are not the same thing. It is well known that nothing can be said about a quantum mechanical system unless an observation has taken place. That is a fundamental part of QM. Force is not the integral of the potential energy function, its the gradient of that function, i.e. F = -grad [math]\Phi[/math]. Pete

and that lost is the notion of a worldline. I know of plenty of things that are unchanged when going to QM. Those things aren't why I created this thread. Its those things which become meaningless that I'm interested in. Also, if something needs to redefined in QM then that in itself a strong indication that it might be meaningless in QM, hence the need for redefinition. The newly defined concept then becomes meaningful. But is not the same definition. Perhaps I need to clarify more. Forget "lost" since it seems that term is either vauge or misleading. Instead consider the example I gave of the fact that classical physics uses trajectories (continuous position of particle with respect to time) is a well definend and meaningful concept in relativity while in its meaningles in QM. These serve as an illustrative examples of what I'm looking for. Seems that just asking the question has led me to think of answers I could't think of before. Determinisim is another example of something that does not hold in QM. Force is another example in that force cannot be defined as the time rate of change in momentum, at least not in the Schrodinger picture. Momentum is an operator and in the Schrodinger picture operators are not functions of time so taking the derivatives of them is meaningless. Another concepts is that of reality, e.g. to talk of the "actual" state of an object without reference to an observer in meaningless, e.g., "Cat is alive/Cat is dead" has no meaning unless an observation is made, unobserved position is also meaningless in quantum theory. Pete

In a discussion I got into off the forum there was an objection about a concept that finds use in relativity. The person (who shall remain nameless) who objected based his objection, in part, on the notion that the concept, supposedely, has no meaning in relativistic quantum mechanics. This is clearly a very poor arguement since there is absolutely no reason to expect that all useful ideas in classical mechanics will still be useful in quantum mechanics. For example, the concept of a classical trajectory/worldline looses its meaning when one transitions to quantum mechanics. But one cannot argue that this is a reason to abandon the very useful idea of worldlines in classical relativity. Infact its a very important concept. I believe that force is another concept that gets lost in the transition? I wanted to ask for help in finding more examples of this, i.e. what concepts get lost in the classical --> quantum transition? I'd greatly appreciate your help folks. Thank you in advance. Pete

Yes. That is quite true. This is not merely my personal opinion but is the definition found in textbooks on quantum mechanics such as Sakurai's or the one I used in graduate school, i.e. that by Cohen-Tannoudji et al Sorry for the confusion. I was having difficulties with my computer earlier which prevented me from posting correctly. What I meant was that I disagree with the following - ..while now you are saying it's only a property of a measurement?. If that is how my post was interpreted then I want to state that it was not how I meant it to be interpreted. I had asked you several questions in this thread which had gone unanswered. The most important of them had to do with providing me with a precise mathematical definition of undertainty as it is used in phrasing the uncertainty principle as it is found in quantum mechanics text books, preferably at the graduate level since undergraduate level texts are sometimes vauge on this point. I also suggested that we find a derivation of the uncertainty principle that we both agree with. When both of these tasks are accompished I believe our differences will be resolved in the process. Here is one that I took a brief look at - http://en.wikipedia.org/wiki/Uncertainty_principle In my brief review of it, it appeared to be correct. It also mentions another synonym for uncertainty that I had forgotten, i.e. uncertainty = root-mean-square (RMS) deviation of the position from its mean. Doesn't it seem reasonable to you that a wave function which has a pronounced peak at x = x0 is interpreted to mean that there is a high probability that the particle will be found in a region centered at x = x0? The smaller the region the higher the probability that it will be found near there. Thus if the wave function is spread out the region in which it is likely to be found is also spread out. According to your own interpretation of "uncertainty" (as refering to how likely the particle is to be found in a region) this also makes sense. I'm also curious as to what you think about the Copenhagen Interpretation? To your knowledge what does it say and what does it mean? Since the above web site is saying what I've said all aloing I recommend that you find a definition of [math]\Delta X[/math] and/or a derivation of the uncertainty principle. Preferably from a QM text that you have and respect, i.e. perhaps you have a QM text that you learned QM from or you know of/can find onlinelecture notes from a university graduate course on QM or an e-book on QM that is online that we both have access to. If you prefer I can scan the relevant pages from the text I have and then upload them to my web site so you can download them and read them. Then we'd be working from the same source(s). Notice that I used an upper case X here. I've been loosey-goosey about the case until now. From now on I will use upper case letters to refer to the operator corresponding to an observable and lower case letters to refer to the corresponding eigenvalues. Some authors will use a caret over the letter to indicate that is the "observable" rather than the corresponding eigenvalue (note that in QM observables are operators). Does this sound like a reasonable next step in our discussion to you? If so then I found an E-book online about quantum mechanics which is located under the physics department web site of San San Francisco State University. See http://www.physics.sfsu.edu/~greensit/book.pdf See section 4.4 Eq. (4.75). Note where the author writes This, of course, implies that given a different state [math]\Psi[/math], the uncertainty will be different as a result. See also http://www.lsr.ph.ic.ac.uk/~plenio/lecture.pdf There is a set of graduate level quantum mechanics lecture notes at http://farside.ph.utexas.edu/teaching/qm/389.pdf http://quantummechanics.ucsd.edu/ph130a/130_notes/node188.html See section 2.14. The author provides a derivation of Heisenberg's Uncertainty Relationship. Edit - I just finished scanning and uploading the relavent portions of Quantum Mechanics, by by Claude Cohen-Tannoudji, Bernard Diu and Frank Laloe. You can download it from http://www.geocities.com/pmb_phy/uncertainty.pdf I'd like to delte that file as soon as possible so as to avoid copyright infringement problems. Best wishes Pete