User talk:PeR

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For old messages on my talk page, see user_talk:PeR/Archive_1 --PeR 16:56, 25 May 2005 (UTC)

[edit] Akkari, Sorry

Sorry about reverting your previous edit... I was too quick to respond to it and due to lack of formatting it seemed that you were saying the Prophet peace be upon him. Now that you've restored your previous edit, I've just cleaned it up a touch. Netscott 13:33, 9 March 2006 (UTC)

[edit] Thanks

We've discussed Omegatron's suggestions and are implementing some of them, some we've explained why we made the decision we did a (mostly on the edit summaries, if we did reasons we'd be giving away our ruleset that powers the bot) Again, thanks for the praise, we really appreciate it! -- Tawker 10:28, 10 March 2006 (UTC)

I turned angry mode off when I went to sleep, we had just had some repeat vandals going on and its almost cleaner to have the bot do it so it can keep track of the number of vandalism if/and a warning is necessary. -- Tawker 17:33, 10 March 2006 (UTC)

[edit] Tawkerbot2

It does ignore users who are on the CVU's whitelist. joshbuddy^talk 18:01, 27 March 2006 (UTC)

[edit] The coriolis effect as taken in to account in meteorology

Hi PeR,

I noticed you have taken an interest in the coriolis effect article. My particular interest is the coriolis effect as taken into account in meteorology. I have a website of my own, with several articles that deal with aspects of (the Earth's) rotation. In my articles, I use animations to illustrate the physics. There is a wikipedia article about the Eötvös effect, which was written by me, and that article is also on my own website. Some of my articles are only on my own website. Will you please have look at my site and tell me whether you would support adding more of my material to wikipedia. --Cleonis | Talk 10:59, 9 November 2006 (UTC)

Hi Cleonis, In general, I think you should go with the WP:BOLD principle, and add whatever you think is appropriate. However, keep in mind that Wikipedia, as an encyclopedia, is not a place to publish mathematical deductions. Hence the derivations of formulas should in general be left out, and references given to physics text-books. In general, I think most of the coriolis-related wikipedia aricles need less - not more - material in order to be accessible to the general public. (Focus should be on making the texts easy to read, and providing concise examples.)

By-the-way. The article on the Eötvös could use a new introduction. The original article by Anders Persson first mentions the Coriolis effect, and then the Eöstvös effect as the special case of the vertical component of the coriolis force on earth. The current wikipedia article starts from the middle of Perssons article, and doesn't reference the coriolis force until very late in the text. --PeR 12:57, 9 November 2006 (UTC)

Well, the wikipedia article about the Eötvös effect is not meant to be about the Coriolis effect, it's about the Eötvös effect. The overall article by Anders Persson is about the Coriolis effect as taken into account in meteorology. In passing, Persson notices how the Coriolis effect as taken into account in meteorology is related to the Eötvös effect. Likewise, in the article about the Eötvös effect is is appropriate to notice towards the end the relation to the Coriolis effect as taken into account in meteorology. I think the current introduction of the Eötvös effect article is what it should be.

In order to achieve clarity the following distinction must be made: the Coriolis effect as taken into account in ballistics and the Coriolis effect as taken into account in meteorology. While the two have the same name, the physics is distinct. Specifically, this distinction is recognizable in motion from east to west. If a cannon is fired in east-to-west direction then the subsequent motion of the projectile is along a great circle (more precisely, the groundtrack of the projectile is a great circle). So if a cannon is fired the projectile proceeds towards the equator. Precisely how it proceeds with respect to the Earth depends on the projectile's velocity with respect to the Earth, but no matter what the velocity of the projectile is, if fired east-to-west it does not move north of the latitude it was fired from.

Schematic representation of flow around a low-pressure area in the Northern hemisphere. The pressure gradient force is represented by blue arrows, the Coriolis acceleration (always perpendicular to the velocity) by red arrows

On the other hand, in meterology, what is taken into account is that air mass that is moving east-to-west will tend to move closer to the nearest pole, which is opposite to what an object on a ballistic trajectory does. In oceanography, the phenomenon of inertial oscillation is recognized, which is the purest example of the coriolis effect (as taken into account in oceanography and meteorology). In the schematic image of cyclonic flow on the northern hemisphere, the pressure gradient is stronger than the coriolis effect, but the tendency is there.

On my website I have devoted an article to illustrating the distinction between what is taken into account in meteorology and what is taken into account in ballistics. Another way of seeing the distinction: in ballistics there is no counterpart of the Eötvös effect. --Cleonis | Talk 15:28, 9 November 2006 (UTC)

Actually, the phenomenon that Eötvös observed is directly related to the Coriolis effect. The first term of the formula is in fact the vertical component of the Coriolis effect. Persson mentions this in the referenced article, and I've included a mention of this in the Wikipedia article now. The reason why meteorologists often only consider the horizontal component of the Coriolis effect is that the length scale in the vertical direction is so short.

Besides the approximation that meteorologists often neglect the vertical component, there is no difference between the Coriolis force in ballistics and in meteorology. An object in the northern hemisphere, whether it be a ballistic missile or an air molecule, is deflected to the right. (Hence the missile in your example will move towards the pole.) This is why the inertial circles turn clockwise (to the right) in the northern hemisphere. What may be confusing you is the fact that cyclones in the northern hemisphere turn counterclockwise (to the left). The force pulling to the left is caused by the pressure gradient. (See the picture above.)

The Eötvös effect is definitely accounted for in ballistics. It is the reason why satellites are almost always launched toward the east. (On the other hand it can usually safely be neglected in meteorology, as stated above.) --PeR 16:14, 9 November 2006 (UTC)

It just occurred to me what you mean by "great circle". When you plot the shortest path between two points on a typical map (Mercator projection), then the path appears to be turning towards the equator (i.e. to the left in your ballistic missile example). This has nothing to do with the Coriolis effect. The path is in fact neither turning left nor right, but slightly downwards, as can be seen if it is plotted on a sphere. This is the path that a ballistic missile would follow if the earth were not rotating. The Coriolis force makes the projectile deviate (to the right on the northern hemisphere) from this path. --PeR 17:00, 9 November 2006 (UTC)

In the case of ballistics: if a projectile is fired in east-to-west direction then it proceeds towards the equator. Of course, since the earth is rotating underneath the projectile, the course of the projectile with respect to the Earth is shifted to the right as compared to what the course would be if the Earth would be non-rotating. However, either with a rotating planet uniderneath the projectile or with a non-rotating planet underneath the projectile, if a projectile is fired parallel to the latitude line, it will never hit the ground north of the latitude it was fired from. Generally, a projectile that is fired parellel to the latitude line will proceed towards the equator. --Cleonis | Talk 19:56, 9 November 2006 (UTC)

When you write "since the earth is rotating underneath the projectile, the course of the projectile with respect to the Earth is shifted to the right" that is the Coriolis effect! (Well, not exactly - it is rather the fact that the speed becomes higher when the missile comes closer to the equator. Since the cannon was already moving along with the earth, this does not happen at the original latitude.) Note that the deflection is indeed to the right, same as the meteorological phenomenon. However, the speed of a ballistic missile very high compared to that of an oceanic current, so the radius of curvature is large. The missile does travel a small distance north of its original latitude, because the surface of the earth is not perpendicular to the true vertical (see the pictures from Persson's article that have been copied into the Eötvös article), what the canon operator perceives as "up" is indeed a bit to the north. In order for the Coriolis force to take an object significantly north of the original latitude, the speed must be much slower. In this case the object must also be affected by the normal force from the earth's surface, which exactly compensates for gravity and the centrifugal force. (See Persson's article.) --PeR 20:46, 9 November 2006 (UTC)

(reset indent)
First, to simplify the discussion I take air resistance to be negligable. Theorem of Newtonian dynamics: The trajectory of any object in ballistic motion is a keplerian orbit, regardless of its velocity

A keplerian orbit is planar, with the center of gravity of the Earth at one focus of the ellipse. In the case of an object being flung away at very low velocity, the keplerian orbit is very shortlived of course, in a matter of seconds the object impacts the ground again. But for the duration of the flight the motion is keplerian orbit! If an object is flung almost straight up then the component of its velocity parallel to the ground is very small. You can make that velocity-component as small as you like.

The (shortlived) keplerian orbit has one focus at the center of gravity of the Earth. The line of intersection of the orbital plane and the surface of the Earth is a great circle. In the case of a non-rotating planet, the groundtrack of any ballistically moving object, no matter how slow it moves, is a great circle.

For an object flung away in east-to-west direction, it is inherently impossible to proceed towards the nearest pole. This can also be shown as follows. Take a stable satellite orbit, with an inclination of 60 degrees away from the Earth's Equator. No matter how fast or how slow you turn the Earth underneath that 60 degrees tilted orbit, the groundtrack of that 60 degrees tilted orbit will always be between 60 degrees southern latitude and 60 degrees northen latitude.

The fact that the Earth is an oblate spheroid instead of a perfect sphere is negligable in the case of ballistics. Interestingly, for the highest performance technology (GPS), the oblatenes of the Earth does need to be taken into account. In the case of an equatorial bulge, satellites in a tilted orbit are gradually drawn towards alignment with the plane of the Equator (For example, it is no coincidence that Saturn's rings lie in the plane of Saturn's equator). While totally negligable for terrestrial ballistics, if you would calculate the effect you find a net force towards the plane of the equator) -Cleonis | Talk 22:57, 9 November 2006 (UTC)

Whether or not the Coriolis effect is strong enough to make a ballistic missile follow a latitude (which is not a straight line, or even a great circle (in general)) is beside the point. You seem to agree with me now, that the Coriolis effect is to the right in this case, and hence there is no difference between the Coriolis effect in ballistics and the Coriolis effect in meteorology. That's really all I wanted to discuss.

By the way; You can't use the word "negligible" in conjunction with an absolute like "inherently impossible ... no matter how fast or or how fast you turn the Earth". I've already conceded that the Coriolis effect is small on Earth. Imagine a very fast spinning planet, such that the spheroid shape is streched out into a disc. Then imagine a missile being fired at exactly the local speed of rotation, but in the oposite direction (i.e. "east-to-west" in the above example). In an inertial frame of reference the velocity of the missile is zero. Hence, its Keplerian orbit will take it straight towards the center of the planet, i.e. towards the pole. --PeR 08:55, 10 November 2006 (UTC)

Well, here's my point: ballistics and what is depicted in the animation Image:Corioliskraftanimation.gif have the following in common: absense of a force(-component) in a direction parallel to the surface.

In the animation Image:Corioliskraftanimation.gif the object is resting on a flat surface, and there is no force in a direction parallel to that surface. The object is in inertial motion, it moves along a straight line. As seen from a rotating point of view, there is an apparent deflection. This apparent deflection away from inertial motion is an artifact of looking at the motion from a non-inertial perspective.

In the case of ballistics (and satellite orbits) the objects are in inertial motion. The only force acting upon them is gravity, which is spherically symmetrical. For an object following a ballistic trajectory, there is negligable force(-component) that acts in a direction parallel to the Earth's surface. The actual motion of a projectile is a keplerian orbit; as seen from a rotating point of view there is an apparent deflection, an artifact of using a non-inertial perspective.

The force of gravity and the normal force. The resultant force acts as the required centripetal force. This resultant force is referred to as the poleward force.

In the case of the physics that is taken into account in meteorology, the dominant factor is the resultant force of gravity and the normal force. (When the motion is mapped with respect to a rotating coordinate system the term representing that resultant force is several times larger than the coriolis term.)

In the absence of any pressure gradient, air mass (and water mass) that is moving east-to-west with respect to the Earth is pulled towards the nearest pole, because a force parallel to the Earth's surface is being exerted upon the water mass: the poleward force. The deflection is real; it is due to an actual force.

By contrast: in the case of an object on a ballistic trajectory there is negligable force(-component) parallel to the Earth's surface, there is just no force to pull it to the nearest pole. Any "deflection" is just apparent deflection.

(By the way, in the case of an equatorial bulge the center of gravity does not coincide with the geometrical center. In the case of the Earth: the equatorial radius is about 20 kilometers more than the polar radius. For an object located on the equator, if all the Earth's mass would be concentrated in a single point, where would that point be in order to exert the same gravitational force? That point is not the Earth's geometrical center, but 10 kilometers above that. This is why over time satellite orbits tend to become aligned with the plane of the equator.) --Cleonis | Talk 11:32, 10 November 2006 (UTC)

OK. I see what you mean. However, the argument applies to the centrifugal force, not the Coriolis force. The poleward force has the property of always exactly canceling the centrifugal force that is due to the rotation of the Earth. (Same as a parabolic turntable.) For an object sliding along the surface (such as an air or water mass) the centrifugal force is canceled by gravity and the normal force, and the only thing left to worry about is the Coriolis force. For an object in flight, on the other hand, the centrifugal force must also be accounted for, and it will always be directed towards the equator. (All of this seen from a rotating frame of reference, of course.) Agreed? --PeR 16:20, 10 November 2006 (UTC)

(reset indent)
I think it is essential to keep clear that what is referred to as "centrifugal force" and "coriolis force" is not a force, but a bookkeeping device, as is emphasized in the entry does centrifugal force hold the moon up? of the Usenet Physics FAQ. There is no such thing as a bookkeeping device counteracting an actual force. I think it is essential to discuss the physics and the coordinate transformation separately. In the case of ballistics, there are two operative factors: gravity and the everpresent inertia. That accounts for the actual motion. The centrifugal term and the coriolis term take care of the coordinate transformation, there's no physics content in them. In the case of meteorology and oceanography, there are three operative factors: gravity, normal force, and the everpresent inertia. The purpose of physics is to identify the actual forces that cause the effects that occur. For mass that can slide around (almost) frictionless over the surface of the Earth, a centripetal force is required, without it the mass would slide to the equator. The poleward force provides that centripetal force. The presence of the poleward force explains the phenomenon of inertial oscillations

Of course, in the case of meteorology the fastest calculation strategy is the one with the motion mapped with respect to a rotating coordinate system. But to understand the physics only the actual forces matter. So what I am arguing is that in the case of coriolis the quickest calculation strategy doesn't coincide with the actual physics taking place. (This is reminiscent of the calculation strategy for electrical circuits where at some stage in the calculation imaginary numbers are used. That is the fastest way of doing the math, but there is no physical counterpart to those imaginary numbers. Likewise, the "centrifugal force" and "coriolis force" are excellent calculational devices, it's just that they shouldn't be confused with physics.) --Cleonis | Talk 13:14, 12 November 2006 (UTC)

Yes, the Coriolis force is a fictitious force. So is gravity. This does not mean that we shouldn't use them whenever it suits us. They are part of physics. Imagine if the weatherman tried to explain everything from an inertial frame of reference. "This low pressure area is moving east at a thousand kilometers per hour, slowly accelerating northwards and downwards, and we are moving beneath it at almost the same speed..."

Imaginary numbers are unfortunately named, because they are not less connected to reality than, for example, negative numbers. Without them, quantum physics would be nearly impossible. --PeR 14:14, 28 December 2006 (UTC)

[edit] The relevant factors in physics analysis

Objects circling each other as seen from non-rotating perspective

The animation on the right shows two objects, connected by a spring, circling each other. (Effects due to friction are ignored). As the spring contracts, potential energy is converted to kinetic energy. At some point the objects do not increase in kinetic energy any further, their velocity has increased so much that they swing wide again, stretching the connecting spring, converting kinetic energy to potential energy.

Objects circling each other as seen from a point of view that rotates at constant velocity

The second animation shows the same objects, but with the motion mapped with respect to a coordinate system that is rotating at a constant angular velocity. This makes the oscillation in angular velocity of the objects clearly recognizable. From a physics point of view, the analysis of the motion as depicted in the second animation must be identical to the analysis of the motion as depicted in the first animation. The only difference between the two animations is a shift of perspective, which is irrelevant.

What is happening is that there is a back and forth oscillation between potential energy and kinetic energy. The key to understanding why the system moves as it does is in knowing the properties of springs, what force a spring exerts and how springs can store and release potential energy.

From a physics point of view, anything that is frame-dependent is not relevant for the physical analysis. If the motion is mapped with respect to a rotating coordinate system, as is the case in the second animation, then there is a centrifugal term and a coriolis term in the equation of motion. Since the presence of those terms is frame-dependent, they are irrelevant for the physical analysis. The two physics operative factors that matter are the spring and of course the ever present phenomenon of inertia. --Cleonis | Talk 12:05, 10 November 2006 (UTC)

Nice animations. They could be useful in the Coriolis effect article. Maybe adding a stationary frame of reference in the background (which would be rotating in the second picture) would make it even clearer. --PeR 12:24, 10 November 2006 (UTC)

They are GIF-animations, which is an inefficient format. Adding a background frame would blow up the animation to 200 KB or so.

This animation displays a parabolic dish with markings on the rim. --Cleonis | Talk 13:21, 12 November 2006 (UTC)

[edit] Know your crackpots: "Free energy suppression"

Umm... removing huge chunks of text without any discussion? That's very close to vandalism. Apparently you're not familiar with that particular conspiracy theory, since the text you removed is central to the crackpot claims being described. They're not talking about wind/solar devices being suppressed, they're talking about the suppression of purported energy sources currently unknown to physics... the critical issue being that the basement inventors claiming to have discovered direct-conversion nuclear power are distinct from the basement inventors claiming to have built perpetual motion machines. "Free energy suppression" is a longrunning piece of inventor lore, while "perpetual motion suppression" is not. I've restored the removed text, but changed the labels from "over-unity devices" to the more common version: "free energy devices." --Wjbeaty 03:26, 27 December 2006 (UTC)

This question was crossposted under Talk:Free energy suppression. See my response there. --PeR 09:33, 27 December 2006 (UTC)

[edit] Xkcd centrifugal-force comic

[edit] Possibly unfree Image:Centrifugal force comic strip.png

My mistake. I don't object to removing the image. --PeR 08:21, 4 January 2007 (UTC)

[edit] In GR, description of inertia and description of gravitation are unified

I copy and paste from above:

Yes, the Coriolis force is a fictitious force. So is gravity. [...] --PeR 14:14, 28 December 2006 (UTC)

The suggestion that gravity is a fictitious force is quite a widespread misconception. Here is the proof that it is in fact a misconception. In physics, four fundamental interactions are recognized: gravitational interaction, electromagnetic interaction, weak nuclear interaction and strong nuclear interaction. The four fundamental interactions of nature are the very rockbottom of physics.

Now, if fictitious force were to be given the same status as gravitational interaction, then the physics community would have to expand the list of four fundamental forces of nature to the 6 fundamental forces: gravitational force, electromagnetic force, weak nuclear force, strong nuclear force, centrifugal force and coriolis force. Obviously, no physicist offers such a list of 6 fundamental forces, that would be silly.

The name 'fictitious force' is a really bad misnomer. Whenever the expression 'fictitious force' is used in a context like:"the observer on the merry-go-round notices a fictitious force", then what is being referred to is inertia, and inertia - by general agreement - is not to be categorized as a force. Secondly, inertia is not fictitious, inertia is just as real as gravitation. Whenever the expression 'fictitious force' is used, it refers to something that is (1) real and (2) not a force.

In Einstein's general theory of relativity the description of inertia and the description of gravitation are unified at a fundamental level. To express this a John Stachel professor of physics and director of the Center for Einstein studies has introduced the expression 'inertio-gravitational field'. I can recommend this article by Michel Janssen who teaches history of the development of ideas in relativistic physics at the University of Minnesota. Michel Jansen explains how it can be seen that the general theory of relativity is in fact a theory of the inertio-gravitational field.

This helps to understand how things can get garbled. In GR, inertia and gravitation are interrelated. When inertia has somehow been mislabeled as "fictitious", sometimes even gravity gets labeled as "fictitious".

The coriolis effect as taken into account in meteorology involves inertia. There is nothing fictitious about the coriolis effect as taken into account in meteorology. That which is affecting the motion of air mass in meteorological events is not fictitious.
(By contrast: take the example of a satellite that circumnavitates the Earth in a polar orbit. Then the groundtrack of that satellite is a complicated curve, because the Earth is rotating underneath the orbit. The actual orbit is planar in shape; celestial bodies orbit along planar trajectories. This planar orbit results in a curved groundtrack because the Earth is rotating underneath the satellite.) --Cleonis | Talk 17:11, 5 January 2007 (UTC)

I know that gravity is more complicated than the Coriolis force, and don't really plan to ever go deep enough into theoretical physics to understand it all. In special relativity gravity is a fictitious force. Of course physics have moved on since then, but it's still a pretty good approximation of reality, and Einstein was able to make some remarkable predictions from this metaphor.

However, most of the time Newtonian physics will do just as well.

In fact, my point is that (not just in physics) it is a good idea to use the model that is best suited to the situation. Somebody who reads an article about the Coriolis, Eötvös, or any other fictitious force is probably interested in how to work with it (because it is a suitable metaphor in his/her situation). Then it makes no sense to write the entire article from the perspective of an inertial frame of reference. --PeR 22:10, 5 January 2007 (UTC)

The science of physics finds itself in a unique position among the sciences: both newtonian dynamics and relativistic dynamics are acknowledged as valid theories of physics. Relativistic physics has superseded newtonian dynamics, but newtonian dynamics is so good that it is fully retained as a way of looking at the world. It's not just that almost all calculations are in terms of newtonian dynamics; schools start with teaching newtonian dynamics. Newtonian thinking is suited best for stimulating and nurturing physics thinking in students.

But this luxury of two thinking modes, newtonian and relativistic, can become a problematic when concepts from newtonian thinking and relativistic thinking are intermixed with no regard for selfconsistency. Things can get badly garbled.

Ideally, a physics teacher should be proficient in both newtonian thinking and relativistic thinking, but the two modes of thinking should not be mixed inappropriately.

For matters of meteorology (and the foucault pendulum), newtonian thinking is best suited to the purpose.

When the general theory of relativity was introduced in 1915, it was recognized that it is inherently impossible for special relativity to accommodate a theory of gravity. So the statement "In special relativity gravity is a fictitious force" is ill defined. Special relativity and theory of gravitation have no overlap.

My assessment is that someone who looks up an encyclopedic article will be keen to gain physical insight. I think only few people prefer superficial information. For comparison: the encyclopedia brittannica uses an explicit subdivision. For every entrance there is a 'ready reference' section and there is a 'knowledge in depth' section. Wikipedia articles do not have such an explicit subdivision, but generally the opening section of a wikipedia article gives a rough overview, and subsequent section provide elaboration, thus catering to a range of visitors.

I think it unlikely in the extreme that someone who trains for the profession of meteorology will consult wikipedia to find how meterorological calculations should be set up. There are textbooks for that. I think that wikipedia visitors are keen on acquiring insight in the underlying physical principles. The only clear view on motion and the forces that are involved is to consider the motion with respect to the inertial frame of reference. --Cleonis | Talk 00:03, 6 January 2007 (UTC)

So you say that while it is OK to disregard the "real" relativistic physics and use the provably wrong Newtonian physics to simplify calculations, using a non-inertial reference frame (a mere coordinate transformation, which does not affect the result) is wrong and should not be done even in an article about a fictitious force? --PeR 00:47, 6 January 2007 (UTC)

The adjectives "right" and "wrong" do not apply. Indeed the very concepts "right" and "wrong" do not apply. At present the two cutting edge theories of physics are relativistic physics and quantum physics and the two are known to be incompatible. This is not seen as a problem, physicist confidently apply both relativistic physics and quantum physics. The hope and expectation in the physics community is that a successor to the two theories will be developed, and this successor will do to relativistic physics what relativistic physics did to newtonian physics.

Any philosophy that physics theories are to be categorized as either "right" or "wrong" is out of date. An example of the modern view is the following quote from Stephen Hawking: "I don't demand that a theory correspond to reality because I do not know what it is. Reality is not a quality you can test with litmus paper. All I am concerned with is that the theory should predict the results of measurements. Quantum theory does this very successfully." Stephen Hawking wikiquote entry

What is not doubted is the following: if a successor to relativistic physics is found, relativistic physics will be a limiting case of the successor, just as newtonian physcis is a limiting case of relativistic physics. Like newtonian physics has been superseded, relativistic physics is expected to be superseded one day (but it will never be discarded).

The coriolis effect as taken into account in meteorology does not involve any fictitious elements; it is physics taking place, air mass gets redirected by an actual force. That said, calculations by meteorologists are always with the motion mapped in a rotating coordinate system. That involves a centrifugal term and a coriolis term in the equations. The centrifugal term and the coriolis term do not represent forces, they are bookkeeping devices.

A complete explanation of the coriolis effect as taken into account in meteorology starts with explaining the physics. The next step - quite a straightforward step - is to explain why the calculation with the centrifugal term and the coriolis term yields the correct result.

I want to emphasize the primary aim of the science of physics: to explain the physics taking place in terms of forces. Here, the concept of force is defined as follows: an interaction between two particles (or two objects) where the two particles either attract or repel each other. This definition of 'force' slots in naturally both in newtonian dynamics and relativistic dynamics; it's a generic, theory-independent definition. The four fundamental interactions of Nature are covered by this definition. --Cleonis | Talk 03:00, 6 January 2007 (UTC)