Free Republic
Browse · Search
News/Activism
Topics · Post Article

Skip to comments.

UC Riverside Researchers' Discovery Of Electrostatic Spin Topples Century-old Theory
Science Daily ^ | 4-3-2003 | Editorial Staff

Posted on 04/03/2003 4:14:50 PM PST by vannrox

RIVERSIDE, Calif. -- April 2, 2003 -- In a discovery that is likely to impact fields as diverse as atomic physics, chemistry and nanotechnology, researchers have identified a new physical phenomenon, electrostatic rotation, that, in the absence of friction, leads to spin. Because the electric force is one of the fundamental forces of nature, this leap forward in understanding may help reveal how the smallest building blocks in nature react to form solids, liquids and gases that constitute the material world around us.

Scientists Anders Wistrom and Armik Khachatourian of University of California, Riverside first observed the electrostatic rotation in static experiments that consisted of three metal spheres suspended by thin metal wires, and published their observations in Applied Physics Letters. When a DC voltage was applied to the spheres they began to rotate until the stiffness of the suspending wires prevented further rotation. The observed electrostatic rotation was not expected and could not be explained by available theory.

Wistrom and Khachatourian designed the study with concepts they had developed earlier. "Experimental and theoretical work from our laboratory suggested that the cumulative effect of electric charges would be an asymmetric force if the charges sitting on the surface of spheres were asymmetrically distributed," said Wistrom. "In the experiments, we could control the charge distribution by controlling the relative position of the three spheres."

Yet, for more than 200 years, researchers have known only about the push and pull of electric forces between objects with like or unlike charges. Since as early as 1854, when Thomson, later to become Lord Kelvin, theorized about an electric potential surrounding charged objects, scientists have concentrated on understanding how electric and magnetic phenomena are related.

"While Thomson's hypothesis of electric potential has brought enormous benefits when it comes to modern electromagnetic technologies, we now realize that his definition of electric potential was not exact," said Wistrom. "The effects are particularly noticeable when the spheres are very close to one another." (Electric potential is the ratio of the work done by an external force in moving a charge from one point to another divided by the magnitude of the charge.)

Indeed, the general applicability of Thomson's theory has not been tested experimentally or theoretically until now. In the Journal of Mathematical Physics, Wistrom and Khachatourian recently published the breakthrough that provides the theoretical underpinnings for electrostatic rotation. "It is very satisfying to learn that electrostatic rotation can be predicted by the simple laws of voltage and force that date back at least 200 years," Wistrom said.

He added, "This is curiosity driven research that starts with a simple question and ultimately leads to findings that will likely have impacts across many fields of science and engineering. Because electrostatic rotation without friction leads to spin, we can only speculate how this discovery will provide new approaches to aid the investigation of fundamental properties of matter."

Spin is used in quantum mechanics to explain phenomena at the nuclear, atomic, and molecular domains for which there is no concrete physical picture. "So the discovery of electrostatic rotation and the identification of electrostatic spin as a natural phenomenon opens up an entirely new field of inquiry with the potential for significant advances," Wistrom said.

Editor's Note: The original news release can be found here.

Note: This story has been adapted from a news release issued for journalists and other members of the public. If you wish to quote any part of this story, please credit University Of California - Riverside as the original source. You may also wish to include the following link in any citation:

http://www.sciencedaily.com/releases/2003/04/030403072949.htm


TOPICS: Business/Economy; Culture/Society; Extended News; Foreign Affairs; Government; Japan; News/Current Events; United Kingdom
KEYWORDS: application; atom; atomic; chemical; chemistry; electron; electrostatic; news; radio; science; spin; stringtheory; technology; theory
Cool. And shocking!
1 posted on 04/03/2003 4:14:51 PM PST by vannrox
[ Post Reply | Private Reply | View Replies]

To: vannrox
Anyone want to put that in layman's terms for those of us who are not electrically inclined?
2 posted on 04/03/2003 4:17:42 PM PST by El Sordo
[ Post Reply | Private Reply | To 1 | View Replies]

To: vannrox
BUMP!
3 posted on 04/03/2003 4:18:32 PM PST by HighRoadToChina (Never Again!)
[ Post Reply | Private Reply | To 1 | View Replies]

To: vannrox
Now the Greens are going to want to ban Static-Guard....
4 posted on 04/03/2003 4:19:20 PM PST by EternalVigilance
[ Post Reply | Private Reply | To 1 | View Replies]

To: vannrox

5 posted on 04/03/2003 4:19:27 PM PST by Slyfox
[ Post Reply | Private Reply | To 1 | View Replies]

To: vannrox
But What Does It Mean?

I'm still working on that perpetual motion machine, just a few kinks yet....
6 posted on 04/03/2003 4:19:35 PM PST by homeagain balkansvet
[ Post Reply | Private Reply | To 1 | View Replies]

To: vannrox; Physicist

In my classes, this old "effect" was called the right-hand rule. Hardly new...

7 posted on 04/03/2003 4:20:15 PM PST by Southack (Media bias means that Castro won't be punished for Cuban war crimes against Black Angolans in Africa)
[ Post Reply | Private Reply | To 1 | View Replies]

To: vannrox
Now we know the physics behind media spin.
8 posted on 04/03/2003 4:21:59 PM PST by remitrom
[ Post Reply | Private Reply | To 1 | View Replies]

To: vannrox
As a rather ignorant but moderately read layman,

bells are going off that this is somehow related to zero point energy.

OK, scream tinfoil hat all you wish.

Tnen perhaps someone with a fair minded perspective and some significant reading on the topic will tell me whether my notion is totally far fetched or not.
9 posted on 04/03/2003 4:22:07 PM PST by Quix (QUALITY RESRCH STDY BTWN BK WAR N PEACE VS BIBLE RE BIBLE CODES AT MAR BIBLECODESDIGEST.COM)
[ Post Reply | Private Reply | To 1 | View Replies]

To: EternalVigilance

10 posted on 04/03/2003 4:22:49 PM PST by Slyfox
[ Post Reply | Private Reply | To 4 | View Replies]

To: Southack
This is just the point I've been trying to make for years....
11 posted on 04/03/2003 4:23:55 PM PST by JusPasenThru (Eliminate the ninnies and the twits...)
[ Post Reply | Private Reply | To 7 | View Replies]

To: El Sordo
Run a current through some spheres and they start to rotate. Not enough detail in the story to say why - could be the old right-hand rule; could be some interaction with the Earth's magnetic field. One thing for sure - nobody is creating angular momentum out of thin air.

Not particularly new - Toshiro Higuchi at the University of Tokyo has been working on applications of electrostatic rotation for several years now. And I don't see what is so exciting - the idea that macroscopic "rotation" has anything to do with quantum mechanical "spin" seems totally off the wall.

12 posted on 04/03/2003 4:28:06 PM PST by John Locke
[ Post Reply | Private Reply | To 2 | View Replies]

To: Slyfox
The dreaded red x....
13 posted on 04/03/2003 4:30:13 PM PST by EternalVigilance
[ Post Reply | Private Reply | To 10 | View Replies]

To: Gary Boldwater
The observed electrostatic rotation was not expected and could not be explained by available theory.

PINK MATTER ALERT
14 posted on 04/03/2003 4:36:17 PM PST by aruanan
[ Post Reply | Private Reply | To 1 | View Replies]

To: El Sordo
On a quick read:

Basic understanding of the Electric force says that it simply has a radial component - no angular dependence. (It only pushes or pulls along the line separating the two charges.)

This result would seem to indictate that there is a (as yet unknown) component of electricity which causes things to want to rotate around some axis as well.

My gut feeling is to be pretty sceptical. My first objection is a symetry objection - how would the charge be able to decide which axis to rotate around? There would have to be some prefered directionality in space-time for this to be true, and that's not observed in other places.

On the other hand, we have no idea why electron's exhibit magnetic moments and have an associated "spin". If there is some effect like this - then the electron (and proton) spin might necessarily follow.

(Interesting side note - neutrons have spin and yet are electrically neutral. I've seen this attributed to the magnetic moments of the constituent quarks - I wonder if there's a way to test the new model via this mechanism?)

Ah well - I think I'll wait for other verification. If true this is certainly unexpected.
15 posted on 04/03/2003 4:37:41 PM PST by waspguy
[ Post Reply | Private Reply | To 2 | View Replies]

To: waspguy
There would have to be some prefered directionality in space-time for this to be true, and that's not observed in other places.

What, exactly, would a preferred direction in space-time consist of, and how would it be measured?

16 posted on 04/03/2003 4:46:19 PM PST by templar
[ Post Reply | Private Reply | To 15 | View Replies]

To: vannrox
Simply put: "Electrostatic spin is cold fusion without the cold or the fusion."
17 posted on 04/03/2003 4:46:45 PM PST by Born to Conserve
[ Post Reply | Private Reply | To 1 | View Replies]

To: Southack
In my classes, this old "effect" was called the right-hand rule. Hardly new...

The right-hand rule deals with an electric current. The news above deals with an electrostatic charge.
The right-hand rule for force on a conductor can be used to determine the direction of the force experienced on the conductor. If the right thumb points in the direction of the current in the conductor and the fingers of the right hand point in the direction of the external magnetic field, then the force on the conductor is directed outward from the palm of the right hand.

18 posted on 04/03/2003 4:47:15 PM PST by aruanan
[ Post Reply | Private Reply | To 7 | View Replies]

To: templar
Re: a preferred direction in spacetime...

That's the problem. According to Relativity, there can be no preferred frame of reference. My "up" is no more valid than your "up". If electrostatic charges were to setup some sort of spin - then that would have to be spin around an axis. But given the spherical symmetry of the situation, how would the charge be able to pick an axis out all the possible choices?

My argument is similar to a question once posed to me by my thesis advisor - "Why is it that the Laplace operator shows up so often in physics?" A: Because it's the simplest rotationaly invariant operator - the simplest way to ensure there's no prefered direction in the Universe.

For this result to be true (and it might be for all I know) we'll have to toss out most of our understanding of classical physics - but then replace it with something that gives exactly the same results in most cases, but now includes this unexpected result. You'd have to toss out most of classical physics (and Quantum mechanics as well since it has the Laplace operator in the Schroedinger equation as well.)

I guess it just seems to me that there's too much beauty in the symmetry arguments of classical physics to do such a thing.

(Of course I'll bet Ptolomey felt the same way about the geo-centric universe. Grin.)
19 posted on 04/03/2003 4:58:17 PM PST by waspguy
[ Post Reply | Private Reply | To 16 | View Replies]

To: aruanan
"When a DC voltage was applied to the spheres they began to rotate until the stiffness of the suspending wires prevented further rotation."
20 posted on 04/03/2003 5:18:28 PM PST by Southack (Media bias means that Castro won't be punished for Cuban war crimes against Black Angolans in Africa)
[ Post Reply | Private Reply | To 18 | View Replies]

To: aruanan
"The right-hand rule deals with an electric current. The news above deals with an electrostatic charge."

Silly me, I always thought that DC (as in the "DC Voltage" applied to the spheres in this experiment) stood for Direct Current...

< /SARCASM >

21 posted on 04/03/2003 5:20:48 PM PST by Southack (Media bias means that Castro won't be punished for Cuban war crimes against Black Angolans in Africa)
[ Post Reply | Private Reply | To 18 | View Replies]

To: vannrox
Already posted.
22 posted on 04/03/2003 5:34:21 PM PST by Physicist
[ Post Reply | Private Reply | To 1 | View Replies]

To: Southack
When things like this come out, it is sometimes hard to tell whether the "scientists" are really that stupid, or if they are just bold frauds, playing to the ignorant in hopes of notoriety and grant money.
23 posted on 04/03/2003 5:38:19 PM PST by Yeti
[ Post Reply | Private Reply | To 7 | View Replies]

To: John Locke
Run a current through some spheres and they start to rotate...

Not a current. An electrostatic charge. There is no electromagnetic effect if there is not current.

Hank

24 posted on 04/03/2003 5:58:51 PM PST by Hank Kerchief
[ Post Reply | Private Reply | To 12 | View Replies]

To: waspguy
"I guess it just seems to me that there's too much beauty in the symmetry arguments of classical physics to do such a thing."

From my reading, the effect is very small. And for a very small effect, I suspect that very small asymmetries in the experimental setup might be the cause.

Still, this is interesting. Zero-point energy should be a scalar value, not a vector. This would be something else.

25 posted on 04/03/2003 5:59:29 PM PST by MainFrame65
[ Post Reply | Private Reply | To 19 | View Replies]

To: Southack
Silly me, I always thought that DC (as in the "DC Voltage" applied to the spheres in this experiment) stood for Direct Current...

They used DC to charge the spheres. After they were charged, their charge was static. A static charge has no flow of current. The right-hand rule applies to a current flowing along a conductor.
26 posted on 04/03/2003 6:06:12 PM PST by aruanan
[ Post Reply | Private Reply | To 21 | View Replies]

To: Hank Kerchief
Maybe. But the story said they applied "a DC charge" to the spheres. That implies an electric current, at least for a short while. But hey, the story sure confuses me, so I could be wrong.
27 posted on 04/03/2003 6:20:50 PM PST by John Locke
[ Post Reply | Private Reply | To 24 | View Replies]

To: waspguy
There would have to be some prefered directionality in space-time for this to be true, and that's not observed in other places.

My feeling also. Of course, there is a preferred directionality in a terrestrial laboratory, thanks to the Earth's rotation and magnetic field. That would be my first suspect if things start mysteriously to spin.

28 posted on 04/03/2003 6:23:33 PM PST by John Locke
[ Post Reply | Private Reply | To 15 | View Replies]

To: John Locke
Maybe. But the story said they applied "a DC charge" to the spheres. That implies an electric current, at least for a short while. But hey, the story sure confuses me, so I could be wrong.

I agree the article did lack a certain lucidity, well, actually, it was damn confusing. You are absolutely right, DC is current, not a charge, and a charge is "electorstatic," not current. There is also the fact that the spin had something to do with the relationship of the charged spheres to each other, which think is the most interesting aspect (but apparently most neglected) of the story.

Hank

29 posted on 04/03/2003 6:44:26 PM PST by Hank Kerchief
[ Post Reply | Private Reply | To 27 | View Replies]

To: aruanan
It can be explained by current knowledge (forgive the pun). The field of an isolated charged conducting sphere is circularly symettric and the charge is on the surface. It experiences no torque.
In the presence of the other spheres the field is no longer circularly symettric. Forces are experienced by the sphere, causing rotation and probably pendular displacement.
The simplest example of this is an electron above a flat metal plate. The field of the electron is no longer circularly symettric. Because of this, it tends to move toward the plate (by induction of "positive" charge density on the surface of the plate, "positive" meaning less electrons in the vicinity).
If the net lines of force on a charged object are not symettric, the object will go into motion to try and make the field lines symettric through the motion. This is more apparent with materials that have less charge mobility.
The rotation rate is inversely proportional to the conductivity. The greater the conductivity, the faster the relaxation time of the material (the quicker charge can redistribute on the surface)and the less torque it experiences.

The rotating spheres do create a magnetic field.
30 posted on 04/03/2003 7:32:17 PM PST by Gary Boldwater
[ Post Reply | Private Reply | To 14 | View Replies]

To: aruanan
While "a [Direct Current] DC voltage was applied to the spheres they began to rotate until the stiffness of the suspending wires prevented further rotation."
31 posted on 04/03/2003 7:41:21 PM PST by Southack (Media bias means that Castro won't be punished for Cuban war crimes against Black Angolans in Africa)
[ Post Reply | Private Reply | To 26 | View Replies]

To: vannrox
Call us when you get linear propulsion a la 'The Dean Drive.'

Knight's Quest: Or How I learned to stop worrying and love the Crack of Doom

32 posted on 04/03/2003 7:44:45 PM PST by JoeSchem
[ Post Reply | Private Reply | To 1 | View Replies]

To: vannrox
Spin is used in quantum mechanics to explain phenomena at the nuclear, atomic, and molecular domains for which there is no concrete physical picture.

Spin is used in other areas too. Sigh. I wish I understood stuff like this but I'm too lazy or busy or both to study it. It sounds cool, though.

33 posted on 04/03/2003 7:46:00 PM PST by TenthAmendmentChampion (The Coalition forces are in BadGhag!!)
[ Post Reply | Private Reply | To 1 | View Replies]

To: Slyfox
AHHH!!! Check out the spin out of these two metal spheres???


34 posted on 04/03/2003 7:59:13 PM PST by bonesmccoy (Defeat the terrorists... Vaccinate!)
[ Post Reply | Private Reply | To 5 | View Replies]

To: Southack
While "a [Direct Current] DC voltage was applied to the spheres they began to rotate until the stiffness of the suspending wires prevented further rotation."

You altered the quote:

When a DC voltage was applied to the spheres they began to rotate until the stiffness of the suspending wires prevented further rotation.

The sentence in question does not say "while" but "when". You're assuming that it means "throughout the time that the current was being applied, the spheres rotated". This is not what it says. It does not say that a continuous current supplied the motive force for the rotation. This sentence is somewhat ambiguous. It could just as easily be saying that an applied DC current imparted a static charge which then drove the motion of the spheres in a manner hitherto unexpected. Since the whole point of the article is that the motion is unlike that of a typical motor, the latter is the more likely interpretation of the sentence.
35 posted on 04/03/2003 7:59:58 PM PST by aruanan
[ Post Reply | Private Reply | To 31 | View Replies]

To: aruanan

I'm just saying that from the article, it appears to me as though these two "geniuses" have re-discovered the Right Hand rule.

Apply direct current [DC]. Get magnetic field effect.

Now, can I have my grant money for this "breakthrough"?!

36 posted on 04/03/2003 8:11:52 PM PST by Southack (Media bias means that Castro won't be punished for Cuban war crimes against Black Angolans in Africa)
[ Post Reply | Private Reply | To 35 | View Replies]

To: vannrox
Gee wizz, I knew about this years ago. Didn't think it meant much. Still don't
37 posted on 04/03/2003 8:38:07 PM PST by wcbtinman (Not from 'my cold dead hands', but from your's.)
[ Post Reply | Private Reply | To 1 | View Replies]

To: vannrox
Anybone here understand the principle upon which a 'circulator' (three port RF device) or 'isolator' (two port RF device) operates on (electron precession)?
38 posted on 04/03/2003 8:38:35 PM PST by _Jim ( // NASA has a better safety record than NASCAR \\)
[ Post Reply | Private Reply | To 1 | View Replies]

Comment #39 Removed by Moderator

To: vannrox
Ayn Rand's electrostatic engine?

All government shills (arch enemies of personal freedom) now chime in.

40 posted on 04/03/2003 11:32:03 PM PST by Enduring Freedom (To smash the ugly face of Socialism is our mission)
[ Post Reply | Private Reply | To 1 | View Replies]

To: Southack; Gary Boldwater
I'm just saying that from the article, it appears to me as though these two "geniuses" have re-discovered the Right Hand rule.

Apply direct current [DC]. Get magnetic field effect.

Now, can I have my grant money for this "breakthrough"?!


Well, the operative words are "appear" and "to me". You're talking about a Lorentz force as observed with an electric current running along a wire, which produces a magnetic effect. They're talking about a Coulomb force as observed in a charged piece of amber--it has an electric charge, but since there is no movement of this charge, there no magnetic effect. The right-hand rule applies to the former, not to the latter.

As I said, the wording was not completely straightforward but that it supported my rather than your interpretation. I said that the right-hand rule pertained to the effect produced by an electrical current
Ampère showed that two parallel wires carrying electric currents attract and repel each other like magnets. If the currents flow in the same direction, the wires attract each other; if they flow in opposite directions, the wires repel each other. From this experiment, Ampère was able to express the right-hand rule for the direction of the force on a current in a magnetic field. He also established experimentally and quantitatively the laws of magnetic force between electric currents.
and that in this particular case the DC voltage was applied to produce an electrostatic field not to maintain an electric current. I read the actual paper and found that my interpretation of the slightly ambiguous sentence in question was, indeed, the correct one:
In all experiments, the surface-to-surface separation distance between spheres exceeded that for sparking in dry air by at least one order of magnitude. Surface-to-surface separation distances were typically larger than 5 mm. Also, the experiments were conducted in isolation from the surroundings by carefully insulating all fasteners and connectors, by utilizing a large open space, or by installing the experimental assembly in a Faraday box. Hence, current flow was negligible. We have found that our experimental model offers a particularly powerful approach to investigating electrostatic phenomena, and we have previously used similar setups to successfully calibrate the electrostatic force.1,2 The absence of electrical current and magnetic materials, natural or induced, leads us to conclude that the experimental assembly was electrostatic.
--Appl. Phys. Lett. 80, 2800 (2002), pp.2800-2801.

41 posted on 04/04/2003 8:02:22 AM PST by aruanan
[ Post Reply | Private Reply | To 36 | View Replies]

To: Gary Boldwater
Here's more of the paper:
The spheres are stationary in both configurations, held in place by a combination of electrostatic, gravitational, and tension forces. Evidence for moment of force is based on experimental observations after 10, 20, and 200 h after voltage is applied to the center sphere at which times the spheres were deemed to be in static equilibrium. The experimental evidence for an electrostatic moment of force was as follows: 1. translational movement is not observed, 2. rotation about the vertical axis of the sphere proceeds until standstill where the induced moment of force is offset by the restoring torque of the suspending wire ~only after the external power supply is disconnected does the sphere return to its starting position, 3.the direction of the rotation remains invariant between replicate experiments, and 4. the magnitude of the net angular displacement increases with the length of the suspending wire.

We propose that rotation is the result of the continuum of static charges residing on the surface of the metal spheres. Theoretical evidence for rotation about the geometrical center of each sphere is obtained from the classical definition of the static moment of force, which, in the spirit of Cavendish and Coulomb, is determined from an action-at-a-distance perspective.

The correspondence between the theoretical prediction and the experimental observations lends considerable support to the notion that the rotation is an electrostatic entity. It is important to note that the direction of the rotation is explicit in the equation for moment of force. Rotation is either up or down, taken perpendicular to a plane passing through the sphere centers.

We have demonstrated a Coulomb motor where the moment of force is induced by an assembly of three spherical conductors held at constant potential. The rotation of the spheres about the axis perpendicular to the plane passing through the center of the spheres is shown to be a natural consequence of the electrostatic force. We find that when the charged spheres are stationary the only degree of motion that remains is rotation. Hence, the electrostatic coupling between the three charged spheres is converted to a net rotation beyond the observation that the rotation is likely to be general. The Coulomb motor appears to be feasible in systems ranging in size from molecular to macroscopic, and would be a useful device in situations that require angular motion.

42 posted on 04/04/2003 9:39:17 AM PST by aruanan
[ Post Reply | Private Reply | To 30 | View Replies]

To: El Sordo
Anyone want to put that in layman's terms

This is already in layman's terms.

43 posted on 04/04/2003 9:41:45 AM PST by RightWhale (Theorems link concepts: Proofs establish links)
[ Post Reply | Private Reply | To 2 | View Replies]

To: RightWhale
How about layman's layman's terms?
44 posted on 04/04/2003 11:10:23 AM PST by El Sordo
[ Post Reply | Private Reply | To 43 | View Replies]

To: vannrox
Ok, just a little background: I am a senior physics major at Hillsdale College, and have been working on this exact problem for my senior thesis. Results have been mildly conclusive, however, a few things worth mentioning:

The paper which this article refers to contains very few details which are sketchy at best. It contains precious little data about the magnitude of the rotation observed or the factors which determine it. While this does not prove them wrong by any means, this should invoke extreme skepticism already. Hence one of the reasons I have chosen this for my thesis.

Now, I have not completed analysis of my data yet. However, I have come to one very important conclusion: The orientation of a sphere effects the amount of rotation. I do NOT mean that the orientation of a sphere -with regard to the other two- influences the rotation. If you remove one of the spheres and then proceed to reattatch it to the same position in space but rotated from its initial orientation (Say, 1/4 a turn or so), the amount of rotation of that sphere is effected.

What does this mean? If I had more time to work on this, I'd love to dig deeper into it, but the most obvious conclusion is that the rotation is not fundamental to a perfect sphere, but rather is due to small imperfections on real spheres. You cannot make a sphere which is perfectly smooth. There is always some error, however small. With large voltages being applied (in my case, 3-12 kV... in their's, I believe it went as high as 20 kV, although I am not positive), even small surface imperfections could cause small forces. Given that the magnitude of rotation is very small (About 1/16 of a full rotation, at most. On the order of 1/400 of a rotation at least. Given the hair-thin Tungsten wire used, this is a tiny force), this seems quite plausible.

However... I should really be working on writing my thesis instead of talking about it... so... away I go!
45 posted on 04/28/2004 7:03:02 PM PDT by AdranGarrison
[ Post Reply | Private Reply | To 1 | View Replies]

To: AdranGarrison
Hum...I wonder if the surface geometry and texture would have a large effect on the outcome. Your studies seem to indicate position is the key factor, and not really geometry. However, if this is caused by imperfections on a real sphere, as opposed to an ideal sphere, then it would appear that surface geometric considerations are of major consequence. Hum...
46 posted on 04/30/2004 6:52:59 PM PDT by vannrox (The Preamble to the Bill of Rights - without it, our Bill of Rights is meaningless!)
[ Post Reply | Private Reply | To 45 | View Replies]

...this leap forward in understanding may help reveal how the smallest building blocks in nature react to form solids, liquids and gases that constitute the material world around us.
However, this topic is from 2003.

47 posted on 03/16/2007 11:23:15 PM PDT by SunkenCiv (I last updated my profile on Sunday, March 11, 2007. https://secure.freerepublic.com/donate/)
[ Post Reply | Private Reply | To 1 | View Replies]

Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.

Free Republic
Browse · Search
News/Activism
Topics · Post Article

FreeRepublic, LLC, PO BOX 9771, FRESNO, CA 93794
FreeRepublic.com is powered by software copyright 2000-2008 John Robinson