tag:blogger.com,1999:blog-8666091.post5219884164071350850..comments2019-09-16T06:47:32.608+02:00Comments on The Reference Frame: Fifteen questions CV readers wouldn't be afraid to askLuboš Motlhttp://www.blogger.com/profile/17487263983247488359noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-8666091.post-70769499108243240362010-11-24T06:33:40.383+01:002010-11-24T06:33:40.383+01:00Dear Andrew,
every object that is a part of physi...Dear Andrew,<br /><br />every object that is a part of physics responds to every other object or event in its sufficient neighborhood, by the definition of physics. That's true whether the object that reacts is fundamental or not. <br /><br />If it couldn't react to the external processes, it wouldn't prove that it's "fundamental". Instead, it would prove that the object that doesn't react is unphysical nonsense.<br /><br />Magnetic field is created in the vicinity of moving charges and current because one of Maxwell's equations is Ampere's circuital law with Maxwell's correction,<br /><br />curl(H) = J + dD/dt<br /><br />Whenever the currents J are nonzero, or whenever the electric field (D) changes, it must be true that the magnetic field (H) is nonzero.<br /><br />The equation above, like other Maxwell's equations, is fundamental. They're the fundamental answers to all your questions and other similar questions about electromagnetism.<br /><br />2. You're mixing spin and isospin. It's not the same thing. Spin is a motion in the real 3D space - or whatever space one considers. Isospin is a "motion" in an abstract space of internal charges that are not linked to spatial geometry. It's called "isospin" because its mathematical properties are isomorphic to those of the spin. But the physical interpretation - the interactions of isospin with other things - are not identical to the spin.<br /><br />Cheers<br />LMLuboš Motlhttps://www.blogger.com/profile/17487263983247488359noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-5148331859769613322010-11-24T04:14:03.289+01:002010-11-24T04:14:03.289+01:00Hi Lubos,
1. The question about magnetic field wa...Hi Lubos,<br /><br />1. The question about magnetic field was because I didn't see how a magnetic field can be fundamental yet created by a moving charged particle. Well, if X is fundamental then it should be the origin of Y, not vise versa - that's what I thought. I did some further reading and ok I agree that magnetic field always exists everywhere (in vacuum its strength is mu_0 = vacuum permability), and is just "amplified" by a moving charged particle - but then my original question gets rephrased (and probably still confusing): <br /><br />1.1. Why this fundamental magnetic field reacts to the particles' movements at all? And why its strength decreases with distance? <br /><br />2. The question about spin was because I wanted to confirm (and you seem to have confirmed) that all we have is just probabilities about spins, and for a magnet there's a higher probability that all its electrons would have the same spin. As for visualization of spin, what I got is that it's some feature which manifests itself <i>also</i> as if the particle was rotating (although it wasn't). And then I found notion of "isospin dimension" which now makes me think that spin is a movement in some unobservable dimension, which - the movement - looks to us <i>also</i> like the particle was rotating. I'm not sure whether it's correct - but now I can draw an analogy with 3D movement of, say, a coin which is projected on a 2D wall as like the coin was changing its size (although it wasn't). <br /><br /><br />Thanks,<br />AndrewAndrew Kazyrevichhttps://www.blogger.com/profile/04046561837342984580noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-3336367078445430502010-11-23T09:08:58.600+01:002010-11-23T09:08:58.600+01:00Dear Andrew, thanks for your kind words:
0) Yes, ...Dear Andrew, thanks for your kind words:<br /><br />0) Yes, ferromagnets become weaker as the temperature goes up because the thermal noise tries to disrupt the desire of the spins to align. It becomes brutal near the Curie temperature: above this temperature, characteristic for each magnetic material, the material can't be a ferromagnet at all! The Curie temperature is the point of a second-order phase transition.<br /><br />In principle, you may go to 0 K and if the basic structure of the material survives, the magnetic field will indeed be the strongest one. But even if the iron is a ferromagnet at 0K, and it may be, you won't gain much. There are many more interesting effects at extremely low temperature - such as superconductivity that can allow you to make even more powerful magnets (such as those at the LHC which is cooled down to 1.9 K).<br /><br />On the other hand, the drop of the magnetic field just below the Curie temperature is very dramatic - it goes to zero at the critical temperature.<br /><br />1) I probably don't understand this question. The magnetic field spreads in the same way across short distances as well as arbitrarily long distances - the field is just everywhere and obeys Maxwell's equations. Matter has lots of preferred distance scales - e.g. the radius of the atom - but the electromagnetic field itself doesn't. Its laws are scale-invariant, in the classical limit. So the same phenomena may be scaled up in arbitrarily ways and they apply to all distance scales.<br /><br />The important thing to keep in mind is that the magnetic field is fundamental and it exists at each point of space and time. There is an arrow remembering the magnetic (and another for electric) field at each point. In quantum field theory, these arrows become operators.<br /><br />2) The spin is the quantum mechanical version of the angular momentum of an elementary particle. So when you collect lots of spin, they will have exactly the same effect as if you catch a spinning gyroscope: it is the angular momentum, after all.<br /><br />However, the nature of the elementary quanta of the angular momentum is totally different than in classical physics. There's no way to "visualize" it using classical concepts because at the microscopic level, the world works like nothing we know from the everyday life. The desire for visualization is just misguided.<br /><br />Around any axis, the electron may be spinning either up, or down. There are always two choices only. So if you prove that the two electrons have spin "up" with respect to the same axis, they will have absolutely the same "state of their spin".<br /><br />There is no contradiction between rotational symmetry and the fact that spin can only be "up" or "down". That's because the question whether it is "up" or "down" is probabilistic - both up and down are associated with a complex probability amplitude. By combining these amplitudes properly, you may also get the complex probability amplitudes for "up" and "down" with respect to any other axis in space. For each axis, there will always be only two choices but the probability amplitudes (and the probabilities that follow from them) will be different. This is what it means for spin to obey the laws of quantum mechanics. The possible values of j_z, j_x, j_y, or j_anyaxis are quantized - just +1/2 or -1/2 (that's where the word "quantum" comes from) - but for each choice, one can always determine the probabilities only. However, there are really just 2 possibilities for a chosen system of coordinates, so there are only 2 complex numbers in the wave function that remember the spin.<br /><br />Best wishes<br />LubosLuboš Motlhttps://www.blogger.com/profile/17487263983247488359noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-81181550017279640432010-11-23T00:00:31.355+01:002010-11-23T00:00:31.355+01:00Hi Lubos,
Thanks for this post, lots of things to...Hi Lubos,<br /><br />Thanks for this post, lots of things to ponder. My life had definitely changed for the better, after I found your blog :)<br /><br />Now I'm thinking about magnets - apparently, as magnetic force comes from atoms and electrons being "properly aligned", so if we cool a magnet then its magnetic power would increase (!) because the lower the temperature, the fewer random oscillations will happen to those atoms and electrons, thus they will become "even better aligned" in the magnet.<br /><br />Is this reasoning correct? Would the biggest value of a magnetic field appear exactly at zero K?<br /><br /><br />And two more general questions.<br /><br />1. Say we have an electron moving in a vacuum, creating a magnetic field around.. I still don't quite get, how does this magnetic field spread on the small distances? Is it, say, because some type of quantum fluctuations are more probable than others, and it's those fluctuations that create the magnetic field?<br /><br />2. How can I visualize the spin? What does it physically mean, "electron A are spinning in the same direction as electron B"? Shouldn't they be spinning in unpredictable directions accordingly to the laws of quantum mechanics?<br /><br /><br />Thanks,<br />AndrewAndrew Kazyrevichhttps://www.blogger.com/profile/04046561837342984580noreply@blogger.com