Here is an elegant way to define human-scale natural units. You merely say:

time unit = 54 milliseconds
speed unit = one billionth of c
action unit = one nonillion hbar.

These equalities are exact and define the units. The value of G in the system turns out to be 1.00 billionth. You can give whatever names you like to the units. BTW a physical quantity which is the product of energy and time is called an action and it has become fashionable to call hbar "the natural unit of action"---there is no competition for the title.

Have to have some names: suppose we call the time unit trice and the distance unit centipace (since it works out to a hundredth of the traditional sort of pace---a thousand paces to a mile and so on). And since the SI metric system HAS NO ROOM IN IT FOR erg, we can take that name for the energy unit. So these are exact by definition:

time unit = trice = 54 milliseconds
speed unit = centipace per trice = one billionth of c
action unit = erg trice = one nonillion hbar.

It determines the sizes of the units and it's easy on the eyes: no need to use exponents and powers of ten or any math symbols.

It's conventional to make the mass unit equal the unit of energy divided by square speed---and in this system it comes out to a roughly ounce-sized 22 grams:

mass unit = ounce = erg (sqtrice/sqcentipace) = about 22 grams
force unit = dyne = erg/centipace = about one eighth of an SI newton.
power unit = erg/trice = about 36 milliwatts

Dyne is another expatriate metric term we can recycle. It used to be the metric unit of force but now that job has been taken over by the newton. One ounce of mass weighs 1.76 dynes in standard sealevel gravity, which is 1.76 cp/t^2. Standard sealevel airpressure is 219 dynes per square cp. The solar constant is approximately 10 erg/trice on a square centipace.

Metric units can be defined using this same time, speed, action approach but it is messy. Mess notwithstanding, this could even be how the SI is redefined later in this decade as the system gets away from dependence on artifacts.

First of all, Leonard, i am unable to login here. Apparently i have either lost my password or my browser is set at too high a security level in the interest of stinginess with cookies.

Second, i liked what you said about "redefining" metric so as to be independent of artifacts. By "artifacts", would i be correct in assuming you to mean the monstrous numerical profligacies of coefficients? Such has by now become a monument to those very impractical complex irregularities which SI owes its design to avoid. Unfortunately such a "monument" is guaranteed to be a "stumbling block". The time has come to do something tangible about it. I have been absent for a while due to other pressing matters on the East Coast (which i hope to resolve by moving there).

As you know, "we who are the world" are steeped in SI to the point that "we who move and shake the world" do not have the political capital to summarily dismiss metric in one fell swoop. But we can certainly change the point of view from one of "intractibly grotesque coefficients" to one that is broadly based on "rationally defined physical constants". There are two sources of rest inertiae which are proving incredibly massive: (a) the entrenchment of SI itself and (b) establishmentarian knotheads who have so long knocked themselves senseless by incessantly beating their heads against the walls of the box inside the which they are damned to esconce themselves.

Hello pint drinker, a pleasure to hear from you! I gather you've been on East Coast of late, but actually don't know your homebase---thought perhaps somewhere in Canada, but don't remember why I thought that.
I'll attempt to reply to your letter first, using CAPS to indicate pockets of response:

[First of all, Leonard, i am unable to login here. Apparently i have either lost my password or my browser is set at too high a security level in the interest of stinginess with cookies.]

BAD NEWS, perhaps this network54 board structure is cranky. Fortunately we do not have to log in and I usually do not unless I want to peek at the "views to date" tally. I was urging one of the doodah people to register at metrictusks ONLY because in that bedlam people readily take each others names. Here I do not see any reason to register or log in. But I wish that network54 would make it easier for you to do it anyway.

[Second, i liked what you said about "redefining" metric so as to be independent of artifacts. By "artifacts", would i be correct in assuming you to mean the monstrous numerical profligacies of coefficients?]

ACTUALLY NOT. I do hate the numerical profligacies with a passion but "independence from artifacts" means something else. It is even a buzzword among NIST bureaucrats and metrologists. they recognize that they are embarked shifting the (metric) units so they are based on the constants of nature and not on OBJECTS (artifacts) contrived and manufactured by humans. I was recently reading this buzz in an NIST document
about electrical standards. Interesting. A cost-benefit analysis meant for internal consumption by high level bureaucrats or congressional oversight. Justifying the cost to taxpayers of the Josephson junction volt standard by pointing to the economic benefits to NASA, arms industry, other hightech industry etc. Anyway, everybody believes in "independence from artifacts" now because it works better. And the centerpiece of the program is to get rid of the metal kilogram. This will probably mean
defining mass by declaring an exact value of Planck's constant.

BUT THE HIDEOUS NUMBERS WILL probably REMAIN. They will just do more stuff analogous to throwing out the artifacts once used to define meter and using the exact number 299792458 and a natural constant (c) instead.

[Such has by now become a monument to those very impractical complex irregularities which SI owes its design to avoid. Unfortunately such a "monument" is guaranteed to be a "stumbling block". The time has come to do something tangible about it.

As you know, "we who are the world" are steeped in SI to the point that "we who move and shake the world" do not have the political capital to summarily dismiss metric in one fell swoop. But we can certainly change the point of view from one of "intractibly grotesque coefficients" to one that is broadly based on "rationally defined physical constants". There are two sources of rest inertiae which are proving incredibly massive: (a) the entrenchment of SI itself and (b) establishmentarian knotheads who have so long knocked themselves senseless by incessantly beating their heads against the walls of the box inside the which they are damned to esconce themselves.]

You are quite right the inertia is stupendous and I cannot blame those (a majority of practical people) who are entrenched in using SI! Occasionally a kind of arrogant assumption of SI superiority galls me, or a thoughtless complacency. But these are not big sins!
Everybody is allowed a little of that.

I agree with you that it is time to do something---stir things up, I suppose, create some dissatisfaction. Otherwise humanity will be stuck with this boring antique system with its disconnect from nature, with less and less chance of escaping from it. But I think of this as a very long term project.

I have been doing some hunting on the web for highschool and college physics text-like material and have in the past couple of days found a bunch more. I wonder if the web will gradually change how physics is taught. I have been helping a young person in Hong Kong with a physics project. (Of course metric units only!!!! One must be bilingual.)

I wonder what the effect would be of making text material like this available on web but translated into cp-oz units. the vulernable point is not the world of everyday affairs, I think, but at the freshman physics level. It is part and parcel of physics to adapt and modify systems of units and choose units suitable to the problem etc. Whereas in the practical world one finds rather more resistance (for some very good reasons).

BTW you made a good point about shiptonnage being volume (displacement).

I am currently delighted by the elegance of this, and the freedom from math notation:

------------------------------------------

time unit = 54 milliseconds
speed unit = one billionth of c
action unit = one nonillion hbar.

It is needs some mental prep. One must know that
billion is E9 and that nonillion is E30. Even more
important one must know that there is a meaningful
type of physical quantity called "action" which is the product of energy multiplied by time. the unit of action is the same as the unit of angular momentum
it just kind of sounds better to say "joule second"
rather than "kilogram square meter per second". They mean the same but one is the action format of energy x time and the other is the angular momentum format of momentum (kg m/s) multiplied by radius of rotation.

----------------------------------------
YOU SHOULD CONSIDER posting a brief, dry summary of
your trimmed metric units. If the proposal looks good
(say for highschool or college students) it will help to create satisfaction---all to the good.

I would advise you to tolerate as much as 25 percent shift in size of the metric units. If it is a sandbox system for educational use only this is not going to cause commercial catastrophes etc. Only some optional mental efficiciency for a few struggling students. So 25 percent is not prohibitive IMO.

Cheers, hope post not too long

[...hope post is not too long]
Gads Leonard!! Of course the post is not too long! Do you think i have the attention span of a gnat?

no, but it actually is too long.
If I had extra time to spend I could
condense and organize.
some famous person said he didn't have
time to write a short letter so would
have to write a long one. forget who

this is a great online article by
frank wilczek of MIT
he has the most comprehensive vision
of current state of physics theory
that I know

I return and read it over or parts of it
again and again. something to assimilate gradually

http://www.aip.org/web2/aiphome/pt/vol-55/iss-8/p10.shtml

it was published august 2002.

when they finally closed down CERN's enormously successful venerable electron positron collider "LEP"
they got Wilczek to give the valedictory address
surveying all that had been found out during the
years that the accelerator had been run for research
and projecting forward to what might come from the
next generation of accelerator replacing it.
the big picture. the man has class
this online article derives from his validictory address.

Did you ever see online pictures of the waveshapes
of a hydrogen atom? Pretty

http://micro.magnet.fsu.edu/electromag/java/atomicorbitals/

select p (or higher) and turn px, py, pz on one by one or together

BTW a caltech student wrote a very informal history
of quantum mechanics that is a bit irreverent and
has quotes of the different founding fathers badmouthing each other's ideas and saying such and such is sh--t and quotes of einstein saying duh I dont understand. It makes the history of the 1920 discovery of QM live in a way that essays by professors rarely do.
It is very short. Maybe I will bring a copy here or find the link. the guy's name is Ali Something (arabic).
He likes David Rees' insulting online antiwar comic strips. May possibly be cool.
(Get Your War On, etc)

http://www.physlink.com/Community/Forums/viewmessages.cfm?Forum=17&Topic=876

This is just a sample of Ali S. you can get more
by and about him by following the link. He posted this exerpt of a student paper he wrote on QM. I like the informality (sometimes attitude makes things more understandable). Ali writes:

[[I dug up this old paper I wrote on the history of QM, and figured some here might find it interesting. Feel free to correct and critique. It's a little preachy and disorganized, sorry; I'm not a particularly good writer. Criticism/corrections/additions are welcome! I adapted and shorted it slightly to answer a question mmly asked.
----

OK, so right now we are the stage quantum mechanics was in the 1920's. Waves, particles.... it looks like we have these two totally different ways of looking at stuff:
quote:

--------------------------------------------------------------------------------
There are therefore now two theories of light, both indispensable, and - as one must admit today despite twenty years of tremendous effort on the part of theoretical physicists - without any logical connection. -Einstein, 1924
--------------------------------------------------------------------------------

So let's try and get a model of the atom, using particles; after all, light was originally thought to be a wave, but back then making electrons wave-like was a sketchy idea. First, the big problem: Rutherford and others had shown that atoms had a big positive nucleus in the center, with relatively light electrons surrounding them; the modern-day picture. Presumably the EM force kept the atoms together, and so the electrons had to be in little Keplerian orbits. But clasically, accelerating charges emit radiation, and orbits imply centripetal acceleration. The classical formulae were well-known, and it was found orbiting electrons would emit light (EM radiation) and fall into the nucleus; hydrogen should collapse in about a nanosecond. Big Problem #1.

Also, observation of the radiation from excited atoms(atomic spectroscopy) found that only certain frequencies of light were emitted or absorbed; these corresponded to certain allowed energy levels. Clasically, bodies can orbit at any radius and hence all energies should be allowed. Big Problem #2.

Well, in 1924, Bohr came up with his famous model of the atom, with electrons still as particles. Bohr found if you required angular momentum to be an integer multiple of hbar, only certain orbits were allowed. He got the observed levels of hydrogen right, and also explained why the electrons didn't fall in to the nucleus -- they were stopped at the smallest allowed orbit. Won a Nobel for it.

But this had big issues, as you prob know: 1) it didn't seem to work for anything but hydrogen. 2) there was no explanation for how, when, or why at all electrons should "jump" from one orbit to the other and emit radiation, even though there were definite rates observed for each jump. 3) fine structure of the emission lines was beginning to be seen: what had seemed one line was revealed to be several close together. 4) QM was looking like a bunch of ad hoc rules, with no systematic way decide when or how to apply them. When was something a particle, when a wave, and how the hell did it decide which one it wanted to be? People were unsatisfied.
quote:

--------------------------------------------------------------------------------
You surely must understand, Bohr, that the whole idea of quantum jumps necessarily leads to nonsence... If we are going to have to put up with these damn quantum jumps, I am sorry that I ever had anything to do with quantum theory. -Schrödinger

If [quantum theory] is correct, it signifies the end of physics as a science. -Einstein

The art of guessing correct formulas [we] brought to considerable perfection. -Born

Physics is very muddled again at the moment; it is much too hard for me anyway, and I wish I were a movie comedian or something like that and had never heard anything about physics! -Pauli, 1925
--------------------------------------------------------------------------------

The next year, though, the two basic forms of modern QM were developed: Heisenberg decided to forget about particles, waves, mechanisms, and try and formulate a theory "solely in terms of observable quantities." He (with others) started working with detailed tables of experimental measurements, and tried to find some simple way to generalize them. In '25, he realized that not only did he have a consistent method, but it unexpectedly conserved energy:
quote:

--------------------------------------------------------------------------------
One evening I reached the point where I was ready to determine the individual terms in the energy table... When the first terms seemed to accord with the energy principle, I became rather excited, and I began to make countless arithmetical errors. As a result, it was almost three o'clock in the morning before the final result of my computations lay before me. The energy principle had held for all the terms, and I could no longer doubt the mathematical consistency and coherence of the kind of quantum mechanics to which my calculations pointed. At first, I was deeply alarmed. I had the feeling that, through the surface of atomic phenomena, I was looking at a strangely beautiful interior, and felt almost giddy at the thought that I now had to probe this wealth of mathematical structures nature had so generously spread out before me.
--------------------------------------------------------------------------------

At the same time, Schrodinger was trying to use the idea that all particles were actually waves to completely reformulate mechanics. Late in '25 -- while spending Christmas away from his wife, at a Swiss resort with "an old girlfriend from Vienna" -- he fit everything together. Particles were wavepackets, in his view; waves of probability... when you looked, you always found a whole particle or not, but with a probabiltity given by its wavefunction. His theory gave the same energy levels, and transition probabilites, as Heisenberg's.

Now there were two seemingly successful quantum theories, where a year before there had been none! As might be expected from the vastly different approaches: visualization in terms of waves on the one hand, and matrix manipulations on the other. When Pauli criticised his theory for being too 'formal', Heisenberg responded
quote:

--------------------------------------------------------------------------------
You will have to allow that, in any case, we are not seeking to ruin physics out of malicious intent. When you reproach us that we are such big donkeys that we have never produced anything new in physics, it may well be true. But then, you are also an equally big jackass because you have not accomplished it either! (1925)
--------------------------------------------------------------------------------

Schrodinger wrote that Heisenberg's theory was "repellant," and Heisenberg's view of Schrodinger's was equally colorful:
quote:

--------------------------------------------------------------------------------
The more I think of the physical part of the Schrödinger theory, the more detestable I find it. What Schrödinger writes about visualization makes scarcely any sense, in other words I think it is sh*t.
--------------------------------------------------------------------------------



Luckily, some semblance of tranquility was restored the next year, when the two theories were proven equivalent, by Schrodinger, Pauli, and Eckert. Physicists rushed to apply the new theory to all sorts of situations, and consistently succeeded. QM was born. Wave/matrix mechanics, taught in QM classes today, is essentially unchanged from its 1926 form, though the specific methods of calculation, terminology, and exposition are quite different.

---

To summarize the rest: QM was reformulated and axiomatized shortly afterward by Dirac and von Neumann. In this formulation (which makes the most sense to me) the state of a particle, or a system, is given by a ray in a type of vector space called Hilbert space. Interactions/measurements are functions of these states; physical consistency requires them to be Hermitian. Basically, the components of the vector representing a particle give the chance it has to have the property represented by that component, and measurements are just geometric projections in this Hilbert space.

A final note: QM conflicts with special relativity, possibly one of the reasons Einstein disliked it so much. Experiments found SR won (mostly). Schrodinger, Dirac and others fixed up a relativistic quantum theory, but it had serious flaws. This eventually led to the development of QFT, which solved them. At the same time, Einstein came up with General Relativity.

Now, in a historical replay, QFT and GR conflict... the big theoretical challenge (in high-energy at least) is to figure out how to fix the problem.

Cheers,
Ali]]

Am just now getting the chance to chk those URLs. TNX.
--p.d.

http://www.cco.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html

Wilcek's articles are mostly incomprehensible. It is the general drift and a few paragraphs.
I may have been mistaken. do not let the incomprehensibility cause grief.

But THIS url is infallibly beautiful.

It has no words, only the moving picture of the electric field from a pointcharge.
You get to select various motions. Like circle and spiral and bobbing up and down.

EM radiation comes from acceleration in the motion of charge. Circular motion has this constant acceleration which radiates beautifully.

Caltech Moving Charge animation. Love it.

Cant remember if I posted the url earlier or not.

http://www.cco.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html