On Apr 28, 8:12 pm, Clay <phys...@bellsouth.net> wrote:> > Bohr with his theory of the atom gave a theoretical basis for Balmer's > formula. But spectroscopists soon discovered a slight flaw in that > some of the energy levels had finely spaced details. A spectral "line" > under close observation turned out to be 2 or more lines very close > together.i remember studying this in 3rd semester physics. from the NIST site, they were saying that the very first occurance of alpha that Sommerfeld had as that it came out to be the ratio of the speed of the electron in the lowest shell of the Bohr atom to the speed of light in vacuo.> Alpha, as the constant is usually denoted, was discovered to be a > dimensionless number which may be expressed as (e*e)/(2*epsilon_0 * > h*c) and "e" is the charge of the electron, h is Planck's constant, c > is the speed of light in a vacuum, and epsilon_0 is the permititivity > of free space. We know alpha to be basically = 1/(137.0359895...).check NIST, there are new 2006 CODATA: 1/alpha = 137.03599956 +/- something 2002 CODATA had it at 137.03599911. this mathematician, James Gilson (i had an email convrsation with him, too) says he has some theory that calculates alpha to be alpha = cos(pi/137)/137 * tan(pi/(29*137))/(pi/(29*137)) . it comes out almost within one stadard uncertainty to the latest accepted value. it might be just numerology. i dunno. it turns out that sqrt(alpha) is the ratio of the elementary charge to the Planck charge and that's how i like to look at it. i like to think that alpha takes on th value it does because of the amount of charge, measured in Natural units, that nature has bestowed upon the electron, proton, and positron. (what are the other charged particles?) because i think that it would be more natural to normalized 4*pi*G and epsilon_0 (instead of what Planck did normalizing G and 4*pi*epsilon_0), then the elementary charged measured in these more natural Planck units would be sqrt(4*pi*alpha) = 0.30282212 and THAT is the number i think that theoretical physicists should be putting up on their walls. that dimensionless number is the charge of the electron measured in the most natural units that are defined soley normalizing the parameters of free space, without any use of a prototype object, particle, or "thing". and alpha results from that. at least this is my armchair physics opinion.> It shows up in many places such as in the interaction of E-M fields > with electrons and in nuclear and particle physics.sure, given a geometry or constellation of charges, all made up from some given integer number of fundamental charged particles, the force between any pair of charges, measured in natural units, is proportional to e^2 which is proportional to alpha. increase alpha by 5% and the EM force has also increased by 5% (relative to the other fundamental forces).> p.s. A book you may find interesting is "Universal Constants in > Physics" by Gilles Cohen-Tannoudji, 1993 McGraw-Hill. The parts on "h" > & "k" are interesting with "h" being the quantum of action and "k" > being the quantum of information.sounds like a real physics text since it is McGraw-Hill. i have the Barrow book for "light" reading. r b-j
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In Praise of Dimensional Analysis
Started by ●April 24, 2007
Reply by ●April 28, 20072007-04-28
Reply by ●April 29, 20072007-04-29
robert bristow-johnson wrote:> i'm getting less tolerant in my middle age. (Jerry, does it get worse > or better as we get older?)It sounds like you failed at life. Success at life is to observe it, and become deeply cynical. Its hard not to tolerate anything when you are sufficiently cynical. :-) Steve
Reply by ●April 29, 20072007-04-29
Robert Adsett wrote:> In article <vrKdnQpuRMllhK7bnZ2dnUVZ_u6rnZ2d@comcast.com>, glen > herrmannsfeldt says...>>The problem with the way I called the physics way is that it can >>result in unusual or inconsistent units. One might end up with >>an acceleration in meters/second/hour, for example, or worse.> I can imagine circumstances in which that would quite a useful unit for > acceleration.I suppose so, but my first thought is to convert to meters/minute**2 -- glen
Reply by ●April 29, 20072007-04-29
robert bristow-johnson wrote:> On Apr 28, 6:57 am, glen herrmannsfeldt <g...@ugcs.caltech.edu> wrote: >>robert bristow-johnson wrote:>>>i disagree, i guess. when i was teaching EE classes (circuits) and as >>>a grad student in EE, i would be pretty hard on any engineering >>>student that did it the latter way. i think Jerry's little proverb >>>said it best: "Mathematicians routinely ignore units, but engineers do >>>so at their peril.">>It isn't ignoring units, but more like tunneling then.> dunno what that means. A large calculation can be made up of many small steps. If one computes intermediate results on a calculator, one can attach the appropriate units onto the intermediate result from the calculator. The numbers go through the calculator, the units go around and are attached appropriately onto the result. Usually the steps will be small enough not to lose track of the units. (snip)> sure. as noted by sombuddy else, you can program computers > (especially with C++ or some other OOP) to attach a unit from a known > list to the numerical quantity. that way we conceptually have a > dimensionful quantity in the computer.I used to know of a computer based physics teaching system using PLATO: http://en.wikipedia.org/wiki/PLATO For physics problems the user was expected to enter an answer with units. As I understand it, each unit was given a numerical value, and the resulting expression was evaluated and expected to be close to the correct answer. As an example, m (for meter) might be 123.45, cm would then be 1.2345, in (inch) 3.13563, etc. Once for a problem expecting velocity units entered erg**0.5 g**-0.5 (I forget the actual exponential operator), and the answer was judged correct.>>The problem with the way I called the physics way is that it can >>result in unusual or inconsistent units. One might end up with >>an acceleration in meters/second/hour, for example, or worse.> this is what conversion factors are for. these conversion factors, > like (0.3048 m/ft) are dimensionless (even though they have units > inside the expression), in fact should be the dimensionless 1 so that > multiplying or dividing by it changes nothing.>>For the engineer way, one converts all given units to those >>specified, does the algebra keeping the units (except when >>entering them into a calculator), and then converts the result >>to the desired unit.> but the requirement is that all units chosen must be consistent. the > so-called "physics" way you can actually accelerate a pound mass by > (mi/hr)/s and have a meaningful equation (and an unusual unit of > force) naturally pop out.It is ChE that uses pound for mass, and adds another constant into the equations to make them consistent. I used to work in a lab with ChE people, with many experiments related to absorption or emission spectra. I once did an emission spectrum in BTU/pound mole, a unit that only ChE would use. (A pound mole, similar to the more common gram mole, is the amount of some substance such that its mass in pounds equals its molecular weight in Daltons.) -- glen
Reply by ●April 29, 20072007-04-29
glen herrmannsfeldt wrote:> Robert Adsett wrote: >> In article <vrKdnQpuRMllhK7bnZ2dnUVZ_u6rnZ2d@comcast.com>, glen >> herrmannsfeldt says... > >>> The problem with the way I called the physics way is that it can >>> result in unusual or inconsistent units. One might end up with >>> an acceleration in meters/second/hour, for example, or worse. > >> I can imagine circumstances in which that would quite a useful unit >> for acceleration. > > I suppose so, but my first thought is to convert to meters/minute**2 > > -- glen >Nah, furlong-seconds per cubic fortnight. Cheers, Phil Hobbs
Reply by ●April 29, 20072007-04-29
glen herrmannsfeldt wrote:> Robert Adsett wrote: >> In article <vrKdnQpuRMllhK7bnZ2dnUVZ_u6rnZ2d@comcast.com>, glen >> herrmannsfeldt says... > >>> The problem with the way I called the physics way is that it can >>> result in unusual or inconsistent units. One might end up with >>> an acceleration in meters/second/hour, for example, or worse. > >> I can imagine circumstances in which that would quite a useful unit >> for acceleration. > > I suppose so, but my first thought is to convert to meters/minute**2Miles/hour/second is a pretty common unit. Of course, an hour-second equals a square minute. :-) Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●April 29, 20072007-04-29
Phil Hobbs wrote:> glen herrmannsfeldt wrote: >> Robert Adsett wrote: >>> In article <vrKdnQpuRMllhK7bnZ2dnUVZ_u6rnZ2d@comcast.com>, glen >>> herrmannsfeldt says... >> >>>> The problem with the way I called the physics way is that it can >>>> result in unusual or inconsistent units. One might end up with >>>> an acceleration in meters/second/hour, for example, or worse. >> >>> I can imagine circumstances in which that would quite a useful unit >>> for acceleration. >> >> I suppose so, but my first thought is to convert to meters/minute**2 >> >> -- glen >> > > Nah, furlong-seconds per cubic fortnight.A furlong per fortnight is a velocity. That leaves second per square fortnight (a frequency) if we factor it out. Frequency of what? Microlightyear per century is another interesting speed. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●April 29, 20072007-04-29
On 27 Apr 2007 15:10:19 -0700, Clay <physics@bellsouth.net> wrote:>> Our educators should make more of a big deal of this than they do. >> Thanks, Tim. >> >> Jerry >> -- >> Engineering is the art of making what you want from things you can get. >> ����������������������������������������������������������������������� > >Hello Jerry et al, >I can assure you that my students are forced to show units all of the >way through their physics calculations. I also show the utility of >expressing things as ratios, so the units cancel out. Such as given a >pendulum clock that runs normally on Earth, how much faster/slower >will it be on the Moon? (g_moon approx 1/6 that of the Earth's)A venerable approach. Galileo used it, in fact. Algebra, at the time, he felt was not yet rigorously founded while ratios had been for quite some time. Jon
Reply by ●April 29, 20072007-04-29
Jonathan Kirwan wrote: (snip)> A venerable approach. Galileo used it, in fact. Algebra, at the > time, he felt was not yet rigorously founded while ratios had been for > quite some time.I had known that Galileo's first experiments with rolling balls were an attempt to slow down the fall of gravity, and allow him to understand the effect. I hadn't known why he decided to do it that way, without the algebra to show what the result would mean. -- glen
Reply by ●April 29, 20072007-04-29
Jerry Avins wrote: (snip)> Miles/hour/second is a pretty common unit. Of course, an hour-second > equals a square minute. :-)One of my least favorite units is the one power companies like to use to describe usage: Kilowatt hours/day. Kilowatt seems like a fine power unit, without an extra factor of 24. -- glen
