Ahhh, Statistical Mechanics- entropy, partition functions (and integrals- yikes!), macro vs. micro, canonical ensembles, etc., etc.... Those were the days... :Vomit:
My understanding of the Virial Thorem is that it is mostly a "steady state" time averaged beast of highest utility in classical mechanical models. Considerable information can be lost when taking "averages" in various ways, depending upon one's mathematical model. Thermodynamics is
full of
idealized models as I recall. Consider
any sinusoidal function- it time averages to zero [ad infinitum]. Yet 50 and 60 Hz alternating current is used to do work (of questionable efficiency) worldwide.
I have alluded to the "common" or "earth" reference point [usually in a voltage context] here before. I can arbitrarily define dangerously high and unstable electrical potentials [voltages for the layperson] as "zero volts" simply by moving the "common" lead on my reference meter. I wouldn't rush right in there and start touching conductors (especially capacitors) however...
YCD's statements above are certainly consistent with those of mainstream academia (from my experience). I suspect there are some missing terms in the "potential energy" portion of the Virial Thorem formulations [and that is mostly where AuGgie and I have semi-accidentally driven this particular thread, I think]. I don't have my reference books with me at my internet connection point and I don't really like Wikipedia, but the following appears to be mostly correct:
http://en.wikipedia.org/wiki/Virial_theorem
Waaaay down at the bottom of the page, the author(s) pull in the electromagnetic fields (as G_sub_k, W_superE, W_superM, p_sub_ik, and T_sub_ik). Of interesting note is
"T is the kinetic energy of the 'fluid', U is the random "thermal" energy of the particles." Could that be an "aetheric" fluid hidden inside there perhaps? Unfortunately, we have now moved into the realm of Magnetohydrodynamics (MHD), and I'm no expert there, yet.
I and several other scientists and researchers will contend here that mainstream electrodynamics AS TAUGHT has been rather broken for the last 150 years or so. The definition of "system" AS TAUGHT in mainstream thermodynamics is also highly flawed IMHO. Causality also depends heavily upon our definition of "system" and our models, reference points, and terminology.
On to the Equipartition Theorem...
http://www.plmsc.psu.edu/~www/matsc597c-1997/systems/Lecture4/node1.html
I note the examples are
IDEAL gases- hmmm.... Also see the last section there.
I also remember the "memory" effect being more true of chemical batteries [and also inadequately explained], not so much of capacitors per se.
I often find myself going back to square one (or zero
) and verifying my reference point(s).
http://www.merriam-webster.com/dictionary/theorem
I find definitions 2 and 3 to be the most interesting here.
"2
: an
idea accepted or
proposed as a demonstrable truth often as a part of a general
theory : proposition <the
theorem that the best defense is offense>
3
: stencil"
Now the "stencil" description is an interesting paradigm- a device that "cookie cutters" negative images of itself in a pre-formulated manner. No individuality, no deviations, no variation- absolute conformity. Some people consider this consistent conformity as beautiful or "elegant" [Ed: many of those people decide our Anglo-American academic "curricula" by the way, but that's another thread]. My experience indicates that pure science usually lies very far in the other direction, however (the non-linearity and [finite?] anharmonicity YCD mentioned above).
Going back to the original meaning, "from Greek
theōrēma, from
theōrein to look at, from
theōros spectator, from
thea act of seeing [see also theater]". Hmmm,
objective observation, not
proposed or
accepted pre-conceived notions... wouldn't Aristotle be proud? How far exactly has the meaning of "theorem" evolved in the last 2500 years? :thinkingcap:
Classical models don't lend themselves well to [post-]Modern Physics in fields of electrostatics, electrodynamics, MHD, etc. Enter Quantum Mechanics (QM) and Heisenberg's Uncertainty Principle [and its untidy corrolaries/implications].
http://en.wikipedia.org/wiki/Uncertainty_principle
Ummm, let's see... we can't
explicitly or
exactly describe position, or momentum, or frequency, or ENERGY, or TIME, or... In the words of Eeyore, "Oh dear..."
Enter Paul M. Dirac, with all those untidy little implications like anti-matter, anti-time, dark matter, and negative energy.
http://www.physics.fsu.edu/DiracSymposium/Talks/Bagger.pdf
------
Ok, so back to Virial and Equipartition Theorems- besides
real gases and solid heat capacity, what else can't they explain? Stochastic "ratchets", thermal diode arrays, and Brownian motors.
http://www.uoregon.edu/~linke/papers/Reimann02_ApplPhysA.pdf
http://physicsmathforums.com/showthread.php?t=1376
http://space.newscientist.com/article/mg16121685.100-glorious-noise.html
We have come a long way since Clausius' work back in 1870. Einstein's special relativity
theory and "thought experiments" have been disproven- faster than light (FTL) effects are very real- photons have been sped up, slowed down, and even stopped (at Harvard). Einstein's general relativity leaves much to be desired as well.
http://science.nasa.gov/headlines/y2002/27mar_stoplight.htm
Quantum tunneling and Terahertz radiation don't really jive with special relativity's V_max~= 3.0E08 m/sec either. To paraphrase Einstein and Sammy Hagar, "God can't drive 55!"
Also see Gisin's 1997 work in Geneva, Switzerland:
http://dustbunny.physics.indiana.edu/~dzierba/HonorsF97/Week1/NYTJuly22.html
While we're on the subject, how does an algebraically-derived quantity speed of light 'c' with dimensions of [length/time] stay constant while [length] contracts and [time] dilates exactly? Oh yes, then there's that infinite mass problem too- do the math.
Does E
really equal m*c^2? I've seen another energy formulation that throws 'c' and special relativity right out the window along with the associated problems above, but I don't have permission from the NASA scientist who came up with it to disclose it publicly, so I won't here. Now his work is simple AND elegant, and I saw him BRIEFLY disprove the 1st/2nd "Laws" of Thermodynamics at least twice with
macroscopic mechanical gyroscopes. Again, we've got either spin, capacitance, spark gaps, magnets, curl, higher-dimensional "fields" or "potentials" involved with ZPE effects. I question the "foundations" of any science when they need to go back and put a "zeroth" law underneath the "first." AuGgie, how well would a house stand if built that way? Newton didn't seem to have that problem with his Laws of Motion, but I do prefer the calculus terminology of Leibnitz myself.
ZPE, entropy, and "free energy" are pretty loosely [and carelessly] defined from what I've seen. In my research, I've found ZPE defined as the energy inherent in space at 0 Kelvin (when there is theoretically NO thermal energy or vibration left). I saw no references to QM, SHO's or vibration specifically. Opinions seem to vary on whether matter is needed or this is a "universal" "vacuum" "radiant" effect with no matter needed. ZPE is claimed to be on the order of 10E35 Joules (or higher) as I recall- see the work of Nikola Tesla, T. Henry Moray, Edwin Gray, Bruce DePalma, Thomas Valone, Eric Dollard, Dr. Peter Lindemann and others here.
http://www.free-energy.ws/index.html
http://www.nasa.gov/centers/glenn/research/warp/possible.html
Now are we talking about Gibbs Free Energy, environmental energy, universal "aetheric" "vacuum" radiant energy, or what? The 3rd "Law" of Thermodynamics gives us yet another
defective definition of entropy [problematic in that ARE there ANY PURE crystals in existence and in that 0 Kelvin is unattainable as far as I've seen, even in the "vacuum" of deep space, due to the universal microwave background radiation (growing ever-increasingly near 3K as I recall)]. Liquid [and solid??] helium is fairly close to 0K though. I believe that the University of Helsinki reported 100 picoKelvin and MIT reported 500 picoKelvin, but I don't recall hearing of any ZPE measurements in those experiments.
http://library.thinkquest.org/3659/thermodyn/third_law.html
As to "no free rides"- ever been surfing? Ever seen the North Shore of Oahu in the wintertime? It's downright
scary to me, and I'm no stranger to "adventure." Again, what AuGgie and I are talking about is tapping "off-grid," non-CORPORATE, [often environmental] energy sources, if he will allow me the bold presumption of speaking for him. Again, a re-definition of "system" and change of paradigm may be needed here. If one disagrees with my research (and that of others), very well, back "in the box", "move along, there's nothing to see here..."
-----
Some other things not adequately explained by "establishment" science:
Ahranov-Bohm Effect
Coanda Effect
Thomas Townsend Brown's electrogravitics work
[quantum] tunneling/Zener diodes
cosmic rays
neutron stars
"spontaneous" capacitor charging
electrets
diamagnetism, paramagnetism, and ferromagnetism
an actual
definition of electrical charge- not 'q', NOT a description of its behavior, but a statement of WHAT IT IS and WHAT CAUSES IT- I haven't seen a satisfactory definition yet in 20+ years of studying mainstream physics...
-----
Here's an interesting quote:
" Other characteristics of this time in science [1960s] were intolerance, arrogance, and rigidity. Scientists preened and postured, became intensely political, and delegated the 'doing' of science to students. Science was becoming big science - a big governmental and corporate enterprise - demanding more resources and becoming less accountable. We now have an expensive standing army in American science, marching in place, with little creative, definable mission. Most of what passes for science is merely chauvinism - who has the largest accelerator, etc.
Now along comes Randell Mills. Without expending billions or even millions or even hundreds of thousands of US taxpayers' dollars, Dr. Mills has apparently completed Einstein's quest for a unified field theory. Dr. Mills' theory is presented in his book, The Grand Unified Theory of Classical Quantum Mechanics (July 2002). This is a huge achievement for three reasons. First, the Mills Theory tidies up theoretical physics by stitching together quantum mechanics and relativity. That in itself is a major triumph. Second, and more important, the Mills Theory explains several major empirical anomalies that have vexed physicists for decades: the sun's energy balance deficit; the dark matter in space phenomena; and mountains of atomic-electron spectral data that is inconsistent with prevailing theory. Third, the Mills Theory gives rise to the possibility of an inexhaustible energy source based on phenomenology not yet recognized and accepted by the scientific community.
Remarkably, Dr. Mills has developed his theory and its energy generation application as an entrepreneur -- without largesse from the US Government, and without the benediction of the US scientific priesthood. Because his enterprise does not suffer these two impediments, it just might succeed. If so, Mills will be the next Thomas Edison. " Shelby T. Brewer, former Assistant Secretary of Energy
(top nuclear official in the Reagan Administration)
-----
-----BEGIN MALLOVE QUOTES
Here are some more, courtesy of the late Eugene Mallove's "Open Letter":
"
TO ALL PEOPLE OF THE WORLD who have open-minded curiosity, good will, good judgment, and imagination. To Scientists and Engineers, Philanthropists, Environmentalists, Energy Developers, High Technology Investors, Healthcare Professionals, Journalists, Artists, Writers, Business People, Entertainers, and Political Leaders. Whether you are Conservative, Liberal, Democrat, Republican, Libertarian, or Anarchist, and whether you may be Agnostic, Buddhist, Christian, Jewish, Hindu, Muslim, Atheist, or some other category of spirituality, this message is directed to all people of good will like you …"
“The exception tests the rule.” Or, put another way. “
The exception proves that the rule is wrong.” That is the principle of science. If there is
an exception to any rule, and if it can be
proved by observation, that rule is wrong.
Richard P. Feynman (1963), Nobel Laureate in Physics (1965)
The progress of physics is unsystematic…The result is that
physics sometimes passes on to new territory before sufficiently consolidating territory already entered; it assumes sometimes too easily that results are secure and bases further advance on them, thereby laying itself open to further possible retreat. This is easy to understand in a subject in which development of the great fundamental concepts is often slow;
a new generation appears before the concept has been really salted down, and assumes in the
uncritical enthusiasm of youth that everything taught in school is gospel truth and forgets the doubts and tentative gropings of the great founders in its eagerness to make applications of the concepts and pass on to the next triumph…But each new young physicist…is in danger of forgetting all the past rumination and present uncertainty, and of starting with an uncritical acceptance of the concepts in the stage of development in which he finds them.
Percy W. Bridgman (1961), Nobel Laureate in Physics (1946)
American Nobel Laureate in Physics (1988) Leon M. Lederman is no proponent of research into
radical forms of new energy; one might accurately call him a “pathological skeptic” based on at least one opinion he has voiced (see
The God Particle, 1993, p.122). Nonetheless, he somehow senses that a physics revolution may be upon us. He said recently, “You can smell discovery in the air…The sense of imminent revolution is very strong.” (
New York Times, November 11, 2003, p.D12). He is much more accurate than he can imagine, but not at all for reasons that he would readily accept! Perhaps he may be thinking of esoteric academic physics subjects such “string theory” or “cosmic dark energy,” but certainly not practical technologies based on radical new physics. Having the intellectual problems identified by physics Nobel Laureate P. W. Bridgman in the quotation above, Lederman has not been looking at a large body of research that will indeed revolutionize the foundations of physics and give us command of fantastic new forms of energy. Too bad for Lederman; and too bad for us all that he has not been paying attention. We could use the support of people like Lederman…if they would only come to their senses, that is, examine open-mindedly the validity of
experimental data that challenges their
cherished theories.
In an article in Science, November 1, 2002, eighteen experts reported that they examined all the
conventionally understood alternatives to fossil fuels and found them all to have “severe deficiencies” in their ability to deal with environmental problems while also being adequate to growing planetary energy needs. Physics Professor Martin Hoffert, leader of that research group, told the press that the United States would have to undertake an urgent energy research crash program, like the Manhattan atomic bomb project or the Apollo lunar missions. According to the
New York Times (November 4, 2003, D1), Hoffert stated that we would need “Maybe six or seven of them [massive projects] operating simultaneously…We should be prepared to invest several hundred billion dollars in the next 10 to 15 years.”
Well, I have news for these experts: The solutions to our energy problems are very close at hand, and they do require initial research and funding, but not the billions of dollars that such Establishment “experts” are accustomed to from government largesse. Rather, all that is needed perhaps are only several tens of millions of dollars to create robust prototype electric power generators based on new energy physics discoveries
that have already been made. That is what this Appeal for Support is all about: to
raise consciousness and funding for these
radical alternative new energy sources.
Question: Do you believe that it is possible that modern science has overlooked or ignored major scientific discoveries, which—if developed into technologies— would revolutionize almost every aspect of civilization?
It has!
[...]
The basic scientific direction of the path forward has already been mapped out. We need your support to go further on the path and reach our common destination: A world of abundant, clean, and safe energy from sources that have no centralized geopolitical control.
[...]
Who am I to ask
anything of you on behalf of others, whether your attention for these brief moments, or for your financial and moral support? I am a scientist and an engineer with two engineering degrees from MIT (1969, 1970) and a doctorate from the Harvard University School of Public Health (1975). I have worked all my adult life as a dedicated scientist, despite my engineer’s stripes.
I have always sought to learn how the cosmos really works, and I find this process to be an exciting, difficult, and unending adventure, despite those who so erroneously claim that we are approaching “The End of Science” or a “Final Theory of Everything.” Apart from my work in government-funded research at MIT and Harvard and later in corporate settings, I have also broadened my horizons by writing about science as an author and a journalist. Articles by me and about me have appeared in such venues as
MIT Technology Review,
The Washington Post Sunday “Outlook” section, the
New York Times,
Popular Science,
Analog,
TWA Ambassador in-flight magazine,
Wired, and
New Hampshire Magazine. I have appeared on many national radio programs, and for a time in the mid-1980s I was proud to have been a regular science and technology broadcaster for The Voice of America.
I am telling you something about me, not to elevate myself, but to convey to you something of my experience, sincerity, and integrity. I have written three acclaimed science books for the general public:
The Quickening Universe: Cosmic Evolution and Human Destiny (1987, St. Martin’s Press),
The Starflight Handbook: A Pioneer’s Guide to Interstellar Travel (1989, John Wiley & Sons, with co-author Dr. Gregory Matloff), and
Fire from Ice: Searching for the Truth Behind the Cold Fusion Furor (1991, John Wiley & Sons). The late Nobel Laureate in physics (1965) Julian Schwinger endorsed my book
Fire from Ice with these words: “Eugene Mallove has produced a sorely needed, accessible overview of the cold fusion muddle. By sweeping away stubbornly held preconceptions, he bares the truth implicit in a provocative variety of experiments.” (He shared the 1965 Nobel Prize with Richard P. Feynman and Sin Itiro Tomanaga.) I am most proud of this latter book, because it began a jarring quest that led to finding out not only dramatic new truths about
new accessible forms of energy in nature, but more important for me and you, the following
most astonishing truth about modern “official” science: Official science is not really intent on truly expanding scientific knowledge, in particular when some very, very fundamental scientific dogmas and theories are put at risk.
Here is how one famous nuclear science professor at my alma mater MIT reacted to my request to him in 1991 to study the summary reports from two pioneering Ph.D. scientists, who had compiled seminal reviews about frontier experiments in low-energy nuclear reactions (a.k.a. “cold fusion”). One of the reviewing scientists was 34-year veteran researcher at our Los Alamos National Laboratory (LANL) and the other was a leader of research at India’s Bhabha Atomic Research Center (BARC):
“I have had fifty years of experience in nuclear physics and I know what’s possible and what’s not!…I will not look at any more evidence! It’s all junk!” —MIT Prof. Herman Feshbach, May 1991, on the telephone to Dr. Mallove
I hope you recognize that the late Professor Feshbach’s most unfortunate and ill-considered reaction was
fundamentally unscientific. It reminds me of the Church leaders at the time of Galileo, who refused to look through Galileo’s telescope at the Moon or at Jupiter, because they “knew” that nothing new could be seen! Yes, many modern scientists are filled with catastrophic hubris; they have become in many ways
mere “technicians of science,” and guardians of what amounts to a pernicious “Holy Writ.” Don’t bother me with the experimental evidence, my theory can tell me what is possible and what is not!
I
f by chance you are one of those who believe that “all is well in the house of science” and that “official science” can be counted on to behave itself and always seek the truth—even in matters of central, overarching importance to the well-being of humankind—you are sorely mistaken, and I could prove that to you with compendious documentation. (If you want to read what happened at just one institution, MIT, when a paradigm shift threatened established hot fusion research programs and “vested intellectual interests” such as those Prof. Feshbach so vehemently defended, read my 55-page report about this monumental tragedy at
www.infinite-energy.com.) But as a first step, you should reflect on
the broader history of science, which is so fraught with revolutionary leaps and paradigm shifts. These have often been made against great opposition—with
revolutionary data staring an older, unaccepting generation of scientists right in the face! Read this Appeal carefully and then
reconsider your opinion about who is telling the truth and who is defending falsehood about revolutionary new prospects for science and civilization.
From:
http://www.pureenergysystems.com/obituaries/2004/EugeneMallove/LastMessage040513/
-----END MALLOVE QUOTES
P.S. Bonus points will be awarded to anyone who can CORRECTLY tell me how many "Maxwell's Equations" that Mr. James Clerk M. wrote back in the 1860's and in how many unknowns. There is a "special" branch of mathematics that is needed here too. Can anyone even provide me with the correct title of Mr. Maxwell's thin little book for that matter?
Also, who can tell me what Thomas Edison and Guglielmo Marconi REALLY did in which time frames?
For working models, you might want to look for 120V alternators and inverters. Battery and/or capacitor storage is always a good idea, too (windmills and [low-efficiency] photovoltaic [PV] solar usually go the 12VDC storage/inverter way as I recall).