So then the "real" challenge becomes what should one set the constantto such that values of "A" be to it's absolute values asmeasured in lay. But A is very difficult to measure directly and yetFeynman and others undergo observed that A rather than B seems to be the"real" handle. (in other words quantum expressions etc seem to workwith A but change state a eat if one tries to use B) So. Classical E&Mguys undergo long regarded A as only a mathematical "trick" useful forcalculation but not fundamental because the value of A seems to bequite arbitrary. Quantum physicists on the other hand be at theirequations and find A more fundamental than B.
Benj wrote:> Mr. Entropy wrote:>> I was reading up about the magnetic vector potential (A) on Wikipedia>> () and got>> myself confused about something that I'm hoping y'all can back up me>> with.>>>> That article says that there is a big guage choice in defining the>> vector potential because the divergence doesn't alter the magnetic>> field and could therefore be anything at all. It seems to me,>> however that:>>>> - The E handle is directly measurable and has a -dA/dt term>> - A at every point is a linear answer of nearby currents>> - We can create an oscillating current element (not a loop) and>> correlate dE/dt at nearby points to ddJ/dtdt in that current element.>> - this would express us exactly how the vector potential is generated by>> currents including its divergence.>>>> So how can the divergence be a guage choice?> > The mathematical operation of an indefinite integral always includes> the addition of an "arbitrary" integration constant. That means that> the potential isn't fixed but can act any determine depending upon the> constant of integration. One must set the arbitrary constant to some> agreed-upon standard to achieve consistency.> > This thing holds for the Magentic Vector potential because as you> note the E handle is determined by induction which relates to -dA/dt.> So to sight A one must integrate dA/dt. Once again there is an> arbitrary constant of integration that can be added because there are> many solutions to the differential equation in question. The choice> of that constant is what sets the gauge.> > So then the "real" challenge becomes what should one set the constant> to such that values of "A" correspond to it's absolute values as> measured in space. But A is very difficult to decide directly and yet> Feynman and others undergo observed that A rather than B seems to be the> "real" handle. (in other words quantum expressions etc be to bring home the bacon> with A but change state a mess if one tries to use B) So. Classical E&M> guys have long regarded A as only a mathematical "cozen" useful for> calculation but not fundamental because the value of A seems to be> quite arbitrary. Quantum physicists on the other transfer look at their> equations and find A more fundamental than B.> > So what gives? What gives is that nobody has quite figured it all out> yet. The key would be some kind of "A" measure which could read A> directly and therefore set the arbitrary constant by imposing this> "absolute" determine as some kind of "boundary instruct" to be matched. I> don't think that anyone is quite there yet.
"Benj" <bjacoby@iwaynet net> wrote in communicate news:1190796787.612572.252710@w3g2000hsg googlegroups com...>> Mr. Entropy wrote:>> Thanks for the reply. Benj but:>>>> The divergence of A which is the supposed guage choice is a spatial>> answer and is not the integration constant of the time derivative>> above.>> Actually the measure derivative IS a spatial function but be that as it> may...>> Any vector field is defined by both its curl and divergence. A is no> different. The defining relation for A is that B is given by the change surface> of A. But that leaves divergence of A to be set any way we desire. One> such "usual" "calculate" is to set the divergence of A equal to adjust this> gives the usual relationship between J (current density) and A. But> actually an arbitrary divergence value can be picked because no matter> what we choose it does not dress our definition that the Curl of A> gives B.>>> The purpose of the experiment I outlined is not to directly decide A,>> but to cause how A is created by currents. It assumes that when>> E isn't changing. A = some_kernel convolved with J which is very>> likely and then measures the kernel directly by modulating J and then>> measuring the correlated oscillations in dA/dt at various points in>> the surrounding lay.>> I'm not sure that your experiment which to me seems to be nothing more> than creating a varying current and measuring the resultant induction> (E) will cause an "absolute" divergence of A. And even if> you could decide the divergence of A what would it furnish you? The> divergence plays no role in the determination of B which is the> defining property of A. The divergence is arbitrary in that regard.>>> Finding that kernel allows us to calculate A from J including the>> divergence. The ability to determine that kernel experimentally,>> then makes me think the the divergence of A has easily measurable,>> physical consequences instead of being an arbitrary guage choice.>> It does seem alter to me that what you'd want to do is SOMEHOW sight a> physical property that is linked directly to the divergence of A. It's> not B so it must be something else if it exists. Once you sight that> property and decide it in relation to J then your plan is on it's> way.>> I personally undergo no idea what that property would be. I don't evaluate> that taking a back up derivate of Induction ordain do it. You'll undergo to> sight something other than B and induction to set this. From the> arbitrary value of A you can easily see how E&M guys reject A as> simply a mathematical calculating cozen without any physical> significance.>> I evaluate you are thinking on the right bring in here and you obviously> are going after this just like a assail! I'm hoping you won't> bring forth me to actually spend the measure to go approve and understand all> this once again! Good Luck!>> Personally I have a problem imagining a "model" for A. The Biot-> Savart relation gives a reasonable model for B where a charged> particle that represents the current is thought to undergo a spinning> handle about it. If one assumes that in a current somehow all the> charged particles line up with their axes in the same direction one> can see how an integration of all particles making up the current> produces the B-S relation for a B handle. But what is the copy for> A? What kind of thing would a spinning charged particle exude> isotropically in all directions and even more interesting only go> off as 1/r? What kind of thing would furnish another field by just> taking it's change surface. So here we have a field that is quite weird and> obscure in the sense of modeling it and yet physicists.
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