|
Propeller Head Plaza Technical and scientific discussion of amps, cables and other topics. |
|
|
|
Propeller Head Plaza Technical and scientific discussion of amps, cables and other topics. |
|
In Reply to: Distinction between theorem and law posted by andy_c on June 7, 2003 at 23:53:19:
"But Maxwell's equations, which are routinely used to predict all aspects of electromagnetic field behavior, are laws."This is not exactly true, but I understand your main point. Maxwell's equations are actually derived from other laws, and hence is another theorem (theory, whatever), but they are so fundamental as to appear to be a pure set of laws, and they prove to work empirically. The same is true of Einstein's work, and the empirical data would suggest to us that they are laws, too, but technically they may be considered more than a law, a theorem from laws such as the speed of light is the limiting speed in the universe. Gauss' law and Ampere's law are a couple of the laws that Maxwell used to derive his point form of those equations, as I understand it. He shrunk down the line integrals and surface integrals of E&M fields to points through mathematics from other laws to arrive at a unified electromagnetic theory. But the displacement current was added as a needed postulate, or a new law was added. That I can see.
So, okay, in essence Einstein's work is not technically a law, even though it sure looks like one being it's so fundamental to us today. It is a theorem from a new law, though, the new law about the speed of light. Closely related, and it gets easily confused what technically is what.
For whatever it's worth, the term "law" is a poor one, IMO, because it is a rather arrogant view of a postulate, or an assumption that we think is true, and empirically found to work. It seems to say in effect it must be true, it's the law. That right away spells trouble to me in what impression it gives people about them, even scientists. The law of motion needed the addition for effects near the speed of light, just like displacement current was needed in Maxwell's equations. They get new terms added when the model falls apart in certain cases. To think such a model is complete for all time is very presumptuous.
Also, regarding Maxwell's equations, which can solve anything seemingly, really only works today as a solution finder for linear systems. That means the permeability and permittivity have to be assumed to be linear for a high powered computer to solve reasonable problems. Real world dielectrics and magnetic materials are not linear unless you keep to the very linear materials, like air and copper. Plastic insulation, for example, is not all that linear to electric fields and iron is not linear to magnetic fields. Maxwell's equations still apply in the nonlinearity if you account for it with complex equations and keep track of amplitudes, but it's just that no arbitrary field simulator like HFSS can account for it and solve for it. Linearity is assumed in those simulators. Nonlinear solutions using Maxwell's equations is not here today as far as I know. But most audio problems seem to come from nonlinearities. So if we're looking for answers to some of these problems, or real computations for why something might not sound right in cables and you think you can solve it with computers and fundamental equations then we aren't there yet, and it might be awhile. And so no, there's still poor understanding for why cables might sound different, and poor predictability for designing good ones. Marketing crapola is all we got to read about them. And it all seems to measure as if there's no appreciable difference.
My cables sound great to me, at about $10 per interconnect and $10 for the speaker wire, but it's a DIY thing and I did A/B them to the pricy stuff and the standard junk and it actually sounded best in my application. Go figure. Money and hype aren't the answer to me, but there are differences in materials and designs.
I think some solutions are hard to solve by conventional methods, and we can't solve some of the seemingly simplest problems using fundamental equations like Maxwell's to this day, despite the supercomputers and all the measurement tools. It still eludes us, even if we can spot some empirical effects.
This post is made possible by the generous support of people like you and our sponsors:
Follow Ups
- Re: Distinction between theorem and law - kurt s 20:34:10 06/08/03 (1)
- Glad you brought up the point about nonlinearity... - Leisure7 14:06:30 06/09/03 (0)
Top of Page ]
[ Contact Us ]
[ Support/Wish List ]
[ Copyright © 2025, Audio Asylum, all rights reserved ]
