Talk:Fictitious force/Archive 3

Centrifugal force: 2 citations

1- 'A great deal of confusion has arisen regarding the term 'centrifugal force'. This force is not a real force, at least in classical mechanics, and is not present if we refer to a fixed coordinate system in space. We can, however, treat a rotating coordinate system as if it were fixed by introducing the centrifugal and coriolis forces. Thus a particle moving in a circle has no centrifugal force acting on it, but only a force toward the center which produces its centripetal acceleration. However, if we consider a coordinate system rotating with the particle, in this system the particle is at rest, and the force toward the center is balanced by the centrifugal force.'

Source: Mechanics, by Keith R. Symon, University of Wisconsin, Addison-Wesley publishing company, inc.

2- 'Centrifugal force is the inertial (or fictitious) force radially outward on objects when they are view from a rotating frame of reference. The force arises solely from choosing an accelerated frame, and 'disappears' when the problem is viewed from a stationnary frame. ... Remember: 'In a non-rotating frame of reference, there is no such thing as centrifugal force.' '

Source: Physics - A new introductory course, Particles and Newtonian Mechanics, by A. P. French and A. M. Hudson, by the Science Teaching Center at the Massachusetts Institute of Technology. --24.202.163.194 01:38, 4 January 2006 (UTC)

Euler force

Does anyone have a citation for the term Euler force? Salsb 19:20, 27 January 2006 (UTC)

added to article GangofOne 19:42, 27 January 2006 (UTC)

Physlets by Brian Fiedler

I have added the following two links to the external links section: Motion over a flat surface Java physlet by Brian Fiedler Motion over a parabolic surface Java physlet by Brian Fiedler

The following GIF-animations illustrate the same thing as the 'motion over a flat surface' physlet:
Inertial motion as seen from non-rotating perspective
Inertial motion as seen from rotating perspective
6 images with vectors depicting centrifugal term and coriolis term.
--Cleonis | Talk 11:53, 23 February 2006 (UTC)

Object dropped a equator example: isn't Coriolis zero at the equator?

This article has an example: "Neglecting air resistance, an object dropped from a 50 m high tower at the equator will fall 7.7 mm eastward of the spot below where it was dropped because of the Coriolis force.[1]" Whereas Coriolis effect states: "...in the equatorial region the coriolis parameter is small, and exactly zero on the equator." subasd 07:25, 22 April 2006 (UTC)

I now removed that example, because the fall eastward doesn't have to do with Coriolis, which is indeed zero at the equator.[1]subasd 07:43, 22 April 2006 (UTC)

Um, did you notice that that fact was cited from a well-known physics textbook? I'll double-check on monday (the book is in my office) if it makes you feel better. -- SCZenz 08:28, 22 April 2006 (UTC)

Your reference doesn't say the coriolis force is zero at the equator, as far as I can tell. -- SCZenz 08:31, 22 April 2006 (UTC)

In the CE article, that bit is talking about the CE in the plane tangent to the surface as a result of motion in that plane. So, that excludes things falling vertically. At the equator, since CE is perp to the motion and the rot axis, any CE will be perp to the plane and therefore the Coriolis parameter for Met equations (but not the CE) is zero William M. Connolley 08:42, 22 April 2006 (UTC)

Very well, maybe that should be clarified in the CE article then. And SCZenz, my reference (pretty much the first google result) does say "The Coriolis force is zero right at the equator." subasd 08:51, 22 April 2006 (UTC)

You're absolutely right, it does say so and I missed it (likely because I was tired). However, I do think you should be a bit careful removing explicitly cited facts because the first google result contradicts them. -- SCZenz 17:38, 22 April 2006 (UTC)

William is correct. If the distance to the rotational axis isn't stationary, then you have a corriolis force. This is all very elementary stuff, no need to look up anything, just use your brains! If the motion is along the surface of the Earth, then the corriolis force is zero at the equator. Count Iblis 12:31, 22 April 2006 (UTC)

No, not quite! If the motion is along the sfc, but not || to the rot axis, the CF isn't zero, but it is perp to the sfc (and hence disappears from the 2D equs) William M. Connolley 14:13, 22 April 2006 (UTC)

Yes, of course! I guess my brains weren't working properly :). An extreme case of this is mentioned in the article: A star viewed from the rotating spacecraft which I put in some time ago, so I should have known! Count Iblis 16:09, 22 April 2006 (UTC)

this article is misleading

Problem point: it claims that " There are two ways of analyzing the problem", and next it forces the choice between the use of real forces in an inertial frame, and pseudo forces in a more handy frame - thus denying the way it's analyzed in classical mechanics. Probably that author doesn't know better; but as it stands, this article is making propaganda for the use of pseudo forces, and is thus not conform to Wikipedia standards. Harald88 10:37, 22 April 2006 (UTC)

I disagree. First of all this article is about fictitious force. So, most of the article is about how to make use of this technique. Second, the fictitious force method is part of the curriculum for first year students when they learn classical mechanics. In high school, teachers will usually avoid the concept of fictitious force. However, high school physics education is so low in standard, especially in the US, that we shouldn't pay attention to that here. Count Iblis 12:22, 22 April 2006 (UTC)

Your point one is a faulty argument: an article about a technique should be focussed on it, but not make faulty claims about competing techniques. That's definitely a NPOV violation (your point two didn't address the subject matter). Harald88 10:33, 23 April 2006 (UTC)

In the introduction it is clearly mentioned that sometimes it is useful to use this technique. And it is also clear from the very defefinition of fictitious force that it is just a mathematical technique. So, you don't need to use it, but then you need to work in an inertial reference frame. This is all such elementary stuff that it is hard to see how anyone could be misled.

It's elementary stuff that your claim is erroneous. That approach may sometimes come handy, but working in an inertial reference frame if one doesn't use fictitious forces isn't the only alternative. Instead, the standard alternative is to simply map to a rotating frame, based on an inertial frame - without exchanging potential and kinetic energies. Harald88 13:59, 23 April 2006 (UTC)

B.t.w., perhaps you should take a look at maths articles here. The article on differentiation suggests that to find the N-th derivative you must differentiate a function N-times. It fails to explain that you only need Log[N]/Log[2] steps. That makes a huge difference if you want to compute the billion-th derivative of some function. Is this misleading, POV? Count Iblis 12:42, 23 April 2006 (UTC)

Nice article! But I don't see the claim that you must use that method to find the answer. And exactly that is the issue here; if that article would similarly deny the existance of other methods, it would indeed be misleading (false claims are worse than just "POV"). Harald88 13:59, 23 April 2006 (UTC)

This article doesn't deny alternative methods either. In fact, it is completely trivial to see that you can do without fictitious forces. Count Iblis 17:27, 23 April 2006 (UTC)

I now changed the sentence in order to make your above claim true. Remains that next the statement that Neither viewpoint is more "correct" in any sense recognized by physicists isn't encyclopedic: has an opinion poll about this been published? Idf so, where? Almost certainly the majority of physicists has a contrary opinion. Harald88 17:52, 23 April 2006 (UTC)

Physicists generally recognize the difference between calculational tools and truth claims. One could cite a wealth of physics textbooks that use both methods, and exhort the student (as long as he is careful) to use the one most convenient to the problem at hand. This is not controversial. -- SCZenz 03:45, 24 April 2006 (UTC)

In order to keep such a claim in wikipedia, it must be possible to corroborate it with citations. Harald88 18:04, 24 April 2006 (UTC)

Uncontroversial statements that appear in an overwhelming number of sources usually don't need to be cited. — Laura Scudder ☎ 18:25, 24 April 2006 (UTC)

This one certainly is controversial, as the whole subject is controversial: looking at on the web published comments by academics, apparently many physicists are opposed to the use of fictitious forces. With Google you can readily find sites such as http://regentsprep.org/Regents/physics/phys06/bcentrif/centrif.htm. Some go to extremes in their aversion against that concept wanting to ban it (http://www.physicsclassroom.com/Class/circles/U6L1d.html and http://www.antonine-education.co.uk/Physics_GCSE/Unit_3/Topic_2/topic_2.htm), while others go to extremes in their defense of it, claiming that it's a "real" force. Thus the claim as appears in this article needs at least corroboration, and most probably it needs correction. Harald88 20:17, 24 April 2006 (UTC)

These are all web sites, and they are all designed for teaching; they certainly oversimplify. I see no reason to conclude, for example, that someone who tells a high school student that "there is no such thing as centrifugal force" actually means that centrifugal forces aren't useful for solving problems if you know how to handle them. You are only presenting evidence that people like to teach about fictitious forces in different ways. That's reasonable, since fictitious forces can be philisophically troublesome in certain ways; that's why physicsts don't go in for philosophy much. ;) -- SCZenz 20:48, 24 April 2006 (UTC)

No problem. Now please provide a reference that backs up the claim about physicists in general, or we must change it to make it encyclopedic (no OR). Harald88 20:54, 24 April 2006 (UTC)

Kleppner and Kollenkow, page 340: "By introducing non-inertial systems we can simplify many problems; from this point of view, the use of noninertial systems represents one more computational tool." Now your turn: provide evidence that this statement is controversial among physicists (i.e. not among people who make websites). -- SCZenz 20:58, 24 April 2006 (UTC)

Thanks; note that no-one challenges that it can be used as a tool. Please back up that "Neither viewpoint is more "correct" in any sense recognized by physicists", or modify it such that it corresponds to your source. And do I correctly hear you claim that those web courses are not given by physicists? Harald88 21:23, 24 April 2006 (UTC)

I can find many sources of physicists suggesting different frames be used interchangably; you have yet to present any of physicists claiming that one frame is more correct than another. None of the webpages you cited were created by physicists as far as I can tell; they are high-school-level or corporate created sites. -- SCZenz 21:30, 24 April 2006 (UTC)

See Twin paradox for the claim that inertial frames are special. And so far you have provided nothing that backs up your above counter claim. If it can't be backed up by decent sources, it is unsuited for Wikipdia. Harald88 11:40, 25 April 2006 (UTC)

I'll thank you to stop lecturing me on WP:NOR; we've been disputing whether a statement was original research, not what OR is or whether it's bad. Your understanding of the claim in twin paradox is incorrect: special relativity, like Newtonian mechanics, must have modifications made to make calculations in a non-inertial frame; the paradox arises because calculations are made in a non-inertial frame as if it were inertial. (Of course inertial frames are unique in that they have no fictitious forces, but that doesn't support your claim that people don't use them or don't think of them as equally correct.) -- SCZenz 23:00, 25 April 2006 (UTC)

As far as I know there was no dispute nor any "lecturing"; of course, a dispute will arise if someone here insists on including his/her unsupported POV as fact in this article. And you will have a hard time to find even one ~single physicist who agrees that a frame in which all stars have superluminal velocities is "equally correct" as frames in which they all move at less than c. In general we don't agree with that. Harald88 20:28, 26 April 2006 (UTC)

I don't think I really follow exactly what you dislike about that statement. I mean, the discussion above that is merely comparing the experience of two observers. How can anyone say that one observer is more correct than another? It seems to me like the very experimental nature of science itself forces physicists to accept both observers' experiences on equal footing. — Laura Scudder ☎ 22:53, 24 April 2006 (UTC)

See above. Harald88 11:40, 25 April 2006 (UTC)

I think that Harald's point has more to do with the fact that fictitious forces are not due to any "real" interactions of the physical system and merely an artifact of the choice of coordinates. We discussed this here some time ago. But in this article this isn't very relevant, because we focus on the use of the fictitious force technique. You could say the same thing about virtual particles being an artifact of perturbation theory.... Count Iblis 01:17, 25 April 2006 (UTC)

Yes indeed; and that makes unfounded statements about physicist's opinions of what point of view is or is not equally correct off-topic and thus soapbox, apart of being unencyclopedic. I'll now simply "be bold" and correct it, as too much time is wasted for a minor correction. Harald88 11:40, 25 April 2006 (UTC)

Your minor correction, aside from reflecting your POV, is rather misleading. Physicists commonly use the inertial frame for certain problems, and commonly use other frames for other problems. I'll see if I can't change it to something that's both accurate and won't annoy you, but it's frankly beyond me why people have so many philisophical issues with this article. -- SCZenz 22:50, 25 April 2006 (UTC).

That's fine of course. Note that your remark that "so many people" have issues with this article" is a real surprise of me for I understood from earlier in this conversation that all this was "non-controversial". In any case, we all agree that when presented as a calculation tool, it's indeed non-controversial. Regards, Harald88 20:28, 26 April 2006 (UTC)

If you like, I can refer you to some introductory university-level texts that discuss this technique in some detail. You did remind me to restore the emphasis that fictitious forces are a tool or technique—as such, there's really no such thing as propaganda for them since people can either use them or not and they'll get the same answer. Fictitious forces are used a lot in climatology, because a reference frame fixed to the surface of the earth is rotating once every 24 hours, as we discuss above. -- SCZenz 17:50, 22 April 2006 (UTC)

Thanks but I don't need to be instructed about that technique, it's pretty straightforward. And there is no need to introduce fictituous forces when mapping to a rotating frame; I can refer you to an introductory university mechanics book by Alonso&Finn on that. Harald88 10:33, 23 April 2006 (UTC)

Perhaps you can state clearly for us which sentences in the article are wrong or misleading, or write down what information we should add? -- SCZenz 17:23, 23 April 2006 (UTC)

I did at the start, and corrected it; but I haven't checked the whole article yet. Harald88 17:52, 23 April 2006 (UTC)

What's in a Name?

We observe an aircraft looping the loop and infer that 'real' forces are present, and can quantify them from the trajectory curvature, etc.. On board the aircraft, we can measure the acceleration directly. Contrary to the fundamentals of empirical science, we view the inference as 'real' and the measurement as 'fictitious'. Maybe the barf bag is fictitious also, and we are left with a not so fictitious mess to clean up.

If we combine the forces acting on bodies within the aircraft with those acting on the aircraft itself, and resolve them into inertial axes, divide by the mass, integrate twice, taking account of the change in direction of the forces over the integration period, and then resolve back, we get the correct motion within the moving frame of reference. But this is an extremely tedious process. It is far simpler to work in the non-inertial frame and introduce the additional terms. In so doing, force no longer equals rate of change of momentum, so we must introduce additional terms, derived from the known motion of the frame of reference, basically to recover Newton's Second Law in its simplest form.

In fact, all we are saying in introducing 'fictitous forces' is that the body moving in an accelerating frame of reference, itself has the acceleration of the frame of reference. The two accelerations must be added vectorially, and resolved to the moving frame for the motion to be predicted correctly. Resolving the acceleration of the moving frame from inertial axes into itself gives rise to the so-called 'fictitious' forces.

In short 'fictitious forces' are 'real' forces acting on a moving frame of reference which are resolved into the moving frame. Somewhere in the process of resolution they apparently left 'reality' behind.

Gordon Vigurs 09:56, 9 July 2006 (UTC)

You wrote "In fact, all we are saying in introducing 'fictitous forces' is that the body moving in an accelerating frame of reference, itself has the acceleration of the frame of reference."

That however is (indeed!) not fictitious at all! There is no necessity when doing that to introduce fictitious forces, and consequently most(?) textbooks don't do that. For the distinction, see the article centrifugal force. Harald88 20:59, 10 November 2006 (UTC)

All I am saying is 'fictitious forces' furnish a simple means of dealing with motions within accelerating frames of reference, nothing more. They are every bit as 'real' as their resolutions into inertial axes, indeed they are the same forces.

For example, circular motion may be interpreted as two orthogonal harmonically-varying motions (with respect to an inertial frame) in quadrature with each other, but it is far easier to deal with an apparently constant 'centrifugal acceleration' if we are interested in finding out if the main spar will break or not. By using the 'fictitous' centrifugal force, we reduce a rather cumbersome dynamics problem to one of simple statics. Gordon Vigurs 20:27, 25 November 2006 (UTC)

still misleading statements

Checking the situtaion now, I immediately hit on an erroneous statement: "fictious forces could be felt easily by humans, as they are on a spinning carousel."

No fictitious forces can be felt; only true forces can be felt. Fictitious forces are calculation aids for rotating frames. One can't feel what doesn't exist!

What one feels in a spinning carousel is the contact force from the carousel which pushes against the body as it deviates the person from an inertial trajectory. Harald88 20:55, 10 November 2006 (UTC)

But a person's perception is that they are being pushed outward for some reason, and they have to hold on to avoid flying off. -- SCZenz 21:45, 10 November 2006 (UTC)

Sure. According to mechanics theory, that perception of a mystical distant force without a source is erroneous: instead of being pushed outward they are being accelerated inward by the caroussel, as already the second sentence of this article points out. Due to that acceleration, they themselves are pushing back against the caroussel with a real local (and centrifugal) contact force. Claiming that the fictitious force is "real" implies denying the acceleration, thus contradicting the intro and mechanics theory -- one can't have it both ways. Harald88 09:16, 11 November 2006 (UTC)

I claim that the intention of the sentence is that what people "feel" is what they "perceive themselves to feel"... perhaps the sentence needs to be clarified. In fact it is in some cases impossible in principle to distinguish (without outside reference points) whether one is perceiving a fictitious force or a real force. -- SCZenz 09:23, 11 November 2006 (UTC)

There is no disagreement that the contact force that people feel is real, and that is now also emphasized in the Centrifugal force article. People may perceive the real cause as what it is according to science ("absolute" acceleration), or what it looks like from a near-sighted perception (a mysterious force from an unknown source).

Anyway, according to both classical mechanics and modern science the acceleration is "real" -- so that fictitious forces can be imagined but not be felt. Harald88 15:59, 11 November 2006 (UTC)

Actually, true forces can't be felt either, see e.g. here. What you feel are always deformations in your body. If your body doesn't deform, then there is nothing you can notice. If you are accelerated in a homogeneous gravitational field at a million g's you will still be weightless. You need to have non homegeneous forces acting on your body, such as a normal force that acts on the boundary of an object. Then that body will deform, stresses will build up in that body until the normal force is transferred through the body. So, on a closer examination, all forces are fictitious. Indeed you can formulate classical mechanics entirely without introducing forces at all. Count Iblis 23:00, 12 November 2006 (UTC)

In case of the spinning carousel, if the contact force is replaced by a long rang force, e.g. a strong magnetic field (in an experiment scientists have succeeded in letting frogs float in strong magnetic fields), you wouldn't feel anything, even if accelerated by a million g's. Count Iblis 23:06, 12 November 2006 (UTC)

the chain from cause to effect as the criterium

I copy and paste from above:

I claim that the intention of the sentence is that what people "feel" is what they "perceive themselves to feel"... perhaps the sentence needs to be clarified. In fact it is in some cases impossible in principle to distinguish (without outside reference points) whether one is perceiving a fictitious force or a real force. -- SCZenz 09:23, 11 November 2006 (UTC)

I think a distinction must be maintained between what is felt and what supposition one is tempted to make. Sitting in a soft seat in a car that is accelerating hard, the tempting supposition is that one is being pushed into the seat. From a physics point of view, the seat is doing the pushing. The tempting supposition is one in which cause and effect are reversed. Likewise, in the case of the carroussel, the tempting supposition is to reverse cause and effect.

Then there is the thought experiment of a very large carroussel, with a capsule on it with no outside view. Let the carroussel be pulling 1 G. The passenger in the capsule feels the floor of the capsule pushing against him, and because of inertia his own weight exerts a force upon the floor of the capsule. By general agreement, inertia is not referred to as a force. Adding a vector for inertia in a diagram does not add information to the diagram, for inertia is omnipresent anyway.

The reason that "centrifugal force" and "coriolis force" are referred to as fictitious forces does not amount to a claim that inertia is fictitious. Inertia is real of course!
The reason for the label 'fictitious' is the direction of cause and effect that is attributed. The reactive force (the contact force) in the case of acceleration is due to inertia. Inertial reactive force is always a reaction to acceleration due to a force. That is the chain from cause to effect. --Cleonis | Talk 15:34, 12 November 2006 (UTC)

Thanks for the comment, I agree. The inertial reaction force in a carousel is determined by the carousel's acceleration. The way I see it, causally we have:

carousel rotation -> acceleration of body -> body resists with counter force F=-ma -> carousel pushes with F=ma

Harald88 17:37, 12 November 2006 (UTC)

Huh? The only reason the body accelerates in the first place is that the carroussel pushes it. If you make the push an (indirect) effect of the acceleration, you've got yourself a cyclic causal chain, which is generally frowned upon. Henning Makholm 23:45, 12 November 2006 (UTC)

I think this chain is non-cyclic:
carousel rotation -> carousel pushes with F=ma -> acceleration of body -> body resists with counter force F=-ma

Jeepien remarked the following: as a physics teacher, he would ask the biggest guy in the class to come forward and try to push hard against Jeepien. At first, Jeepien didn't put up any resistance. As a consequence, the big guy could not push hard; if something doesn't resist your push, then you can only exert a faint push on it. The more resistence Jeepien put up, the more force could be exerted upon Jeepien. I'd say something like that was on Harald's mind as he formulated his cause-to-effect chain. --Cleonis | Talk 00:32, 13 November 2006 (UTC)

Exactly, and I must confess that I only achieved a sharp perception of this thanks to discussions in Wikipdia. The caroussel pushes with F= m_body * a because the body is resisting with -F=-m_body*a. It's the body that determines how much the push force must be at given carousel acceleration. Without undergoing the body's inertial resistance the caroussel can't push it with F. However, for this discussion one may also summarize it as follows:

carousel rotation -> acceleration of body -> body resists resulting in a force/counter-force pair of F=ma.

These forces are real; they should not be confused with fictitious forces. Harald88 22:24, 13 November 2006 (UTC)

I would agree with your chain, if forced to write one down. In general, however, I am not convinced that such explicit accounting for causality is particularly helpful when discussing action and reaction. The Third Law of Newton is not a causal relation. It merely asserts the empirical fact that (non-fictitious) forces somehow always manage to occur in balanced pairs, and using it causally has an uncomfortably teleological feel to me. The conceptual status of "the reaction force" seems to get more confused the deeper you dive into the quantum origin of contact forces. If I understand correctly, modern physics prefers to speak instead of conservation of momentum, which is equivalent as far as Newtonian dynamics is concerned and appears in the modern physicist's worldview to be more fundamental than action-reaction pairs. Henning Makholm 01:19, 13 November 2006 (UTC)

A statement about inertia does not necessarily involve Newton's third law. One can also opt to take Newton's third law as a statement about the concept of physical interaction: for example stating that electrostatic force is an interaction precisely because it involves two particles interactng with each other. One can then assert that inertia falls outside the scope of Newton's third law, because it involves just one particle.

Inertia is one of the enigma's of physics. So, yeah, asserting a particular sequential order is on the edge. However, there can be no doubt that the existence of inertia must be assumed in order to formulate a theory of motion. Newton's first and second law are statements about inertia. --Cleonis | Talk 07:52, 13 November 2006 (UTC)

With my above causal chain I did not mean to suggest sequential order, as such implies delay times. A macroscopic description of a local inter-reaction doesn't have any, to my knowledge. Harald88 22:37, 13 November 2006 (UTC)

The original question was about the passenger of the carousel. The passenger of the carousel is correct in feeling that he is exerting a force upon the floor of the carousel; the reality of inertia. Since the carousel is much heavier than the passenger we opt to say that the floor started pushing; size matters. By contrast: let the carousel be a lightweight one, about as heavy as the passenger. Then the situation is more symmetrical. The carousel can push the passenger around, because of the carousel's inertia, the passenger can exert a force upon the carousel because of his own inertia. The carousel's leverage for altering the passengers momentum arises from its own inertia, and vice versa. For Newton's third law to hold good, interactions must be reciprocal (such as with electrostatic force) and inertia must be uniform throughout space. The law of conservation of momentum holds good only if inertia is uniform throughout space. Hence, asserting conservation of momentum is a statement about inertia. --Cleonis | Talk 15:53, 13 November 2006 (UTC)

The question which observer is preferred

I copy and paste from above:

How can anyone say that one observer is more correct than another? It seems to me like the very experimental nature of science itself forces physicists to accept both observers' experiences on equal footing. — Laura Scudder ? 22:53, 24 April 2006 (UTC)

I think that Harald's point has more to do with the fact that fictitious forces are not due to any "real" interactions of the physical system and merely an artifact of the choice of coordinates. [...] Count Iblis 01:17, 25 April 2006 (UTC)

I take it as generally agreed that the observer who has more information at his disposal (and puts it to use) is preferred. In the case of the Earth's motion around the Sun, we have the geocentric model of the Solar system and the heliocentric model. For several centuries now, we have the knowledge to see that the heliocentric model is superior. Anyone who adopts the geocentric model is disregarding a wealth of knowledge.

If motion is mapped with respect to an inertial frame of reference then there are no artifacts. The evergreen among the examples: a carousel with a passenger. The carousel is exerting a force upon the passenger, causing the passenter to move along a circular trajectory, and the passenger is exerting a force upon the carousel. (Generally the carousel is much heavier than the passenger, and then the motion of the carousel due to the force exerted by the passenger is imperceptible.)

For any object, the leverage enabling that object to exert a force upon another object comes from inertia. Important as inertia is, inertia is never specified in any diagram. Inertia never being specified is not a problem: inertia is always present, hence adding a vector for inertial reactive force in a diagram would not add information to the diagram.
When motion is mapped with respect to a non-inertial frame of reference, then vectors for the acceleration with respect to the inertial coordinate system are added. In the case of motion along a circular trajectory, the vector for the centrifugal force coincides with the vector for the inertial reactive force. As is emphasized in the centrifugal force article, what is referred to as the 'fictitious centrifugal force' is quite distinct from what is referred to as the 'inertial reaction force'.

The point of view that recognizes that the passenger and the carousel are exerting a force upon each other, and that the carousel and the passenger are both circling around their common center of mass, is the point of view that has the highest information content. That point of view is preferred.
The very information accumulating, deductive nature of science forces physicists to recognize that not all observer's experiences are on equal footing.

Inertia is still an enigma, but there are theories that seek to describe properties of inertia. The general theory of relativity asserts that inertia must be seen as a property of spacetime. According to general relativity, spacetime itself acts like a field, in the sense that spacetime itself is opposing change of velocity (with respect to space) of inertial mass. This assertion of general relativity can retroactively be taken as a corresponding axiom of newtonian dynamics. (This shows in what respect there is a continuity from newtonian dynamics to relativistic physics.)

Finding out which frames are inertial frames and which frames aren't is a process of gathering information. Observers who have gathered that information and put it to use are preferred. --Cleonis | Talk 23:09, 15 November 2006 (UTC)

"Preferring" one observer over another is, it seems to me, essentially POV. What an encyclopedia should do is explain how one the different observer's frames differ from each other, and how to do mechanics in each of them, without adding any artificial (and essentially non-scientific) value judgements between them. Henning Makholm 01:13, 16 November 2006 (UTC)

Making assessments is part of the endeavour of science. For example, in the period of the Copernican revolution, individual scientists had to make up their mind which research programme to follow, the ptolemaic programme or the copernican/keplerian/newtonian programme. Long after the scientific revolution has taken place, evidence has mounted, and the choice is obvious. However, during the actual transition, the evidence was inconclusive, and which research programme to follow was a judgement call. There can be no doubt that the scientists who made that judgement call were scientists indeed.

Making assessments as to what avenues are worthwile to explore is part and parcel of science. An academic who would be so foolish as to avoid judgement calls altogether has little opportunity to be scientifically productive.

Generally, ranking points of view on the basis of their information content is part of science. --Cleonis | Talk 05:54, 16 November 2006 (UTC)

In physics, we write down theories to determine measurable quantities. How can the superiority of one reference frame over another be determined if calculations in both give all the same measurements? It's philosophy that assigns value judgements like that; physics just seeks to answer concrete questions correctly. -- SCZenz 08:00, 16 November 2006 (UTC)

At the same time, there are certain very clear conveniences to setting up a basic theory in inertial reference frames. For example, when I jump up and down the entire universe moves from my perspective—it's clear that it's far saner to work in a frame where I'm not jumping than to try to treat the motion of the universe as arising from a physical mechanism. -- SCZenz 08:05, 16 November 2006 (UTC)

The use of fictitious forces goes even further than that. According to the Force article, "In physics, force is an influence that may cause a body to accelerate". An influence is an effect that results from something that causes it, and a fictitious force lacks one -- a fictitious force is an influence without a cause, or more precisely, the cause is first admitted but next denied to exist: the "pulling" is caused by no other physical entity. BTW, that is not the case with gravity, so that the article's statement that gravity is also a fictitous force is (I think) contested. Harald88 07:35, 17 November 2006 (UTC)

I don't really agree with the causality argument. Causality is very hard to define rigorously, because of invariance under time reversal. Causality is not something that is present in Newton's Laws, but it has to be put in by hand in the form of low entropy initial conditions.

All that you can say is that whenever there is an acceleration, there is a force such that F = m A. There is no cause and effect here at all. The problem is that when we write about this in English, words like "cause" etc. slip in. Language is not a very suitable way to describe the physical world and there is usually no alternative than to tolerate inaccuracies to prevent readers being confronted with an unreadably convulated piece of text. Physicists do this all the time when they write.

As I wrote in the previous section above, ordinary force is just as fictitious as "fictitious force". You can't measure a real force directly either (we can measure deformations, deformations etc.). What you can say, however, that a force in an inertial system is more directly related to observable effects like deformation of an object, than fictitious force. Count Iblis 13:33, 17 November 2006 (UTC)

First of all, this page is not meant to express our agreement or disagreement. Causality is certainly included in Newton's theory and classical mechanics. But if you can show that the Force article is erroneously sourced, please don't hesitate to correct it. Harald88 20:13, 17 November 2006 (UTC)

The purpose of theories is that the raw perceptions are ordered into overseeable structures. A point of view along the lines of "physics just seeks to answer concrete questions correctly" is very naive. I recommend reading the following two works by the historian of science Thomas Kuhn: 'The copernican Revolution' and 'The structure of scientific revolutions'. Thomas Kuhn adresses naive suppositions and describes what scientists actually do. (It is necessary to read the actual books, to my knowledge, the majority of reviews and commentaries misrepresent the work of Thomas Kuhn. I am pleased to see that the Synopsis section of the wikipedia article about Thomas Kuhn's work is pretty good.) --Cleonis | Talk 01:03, 17 November 2006 (UTC)

Removing derivations of equations

I would like to remove the derivations of the equations in the last two sections, and just keep the final result plus a few references to textbooks, preferably available on-line. (For example section 3.4 of this textbook on celestial mechanics for the rotating frame of reference.)

There main reason why I want to do this is that I think the mass of equations (even though they are near the end of the article) might scare some non-mathematical readers into thinking they will not understand the article, even though the rest of it in written in a way that should be accessible to most. For those readers who are interested in the deductions of the equations, I still think references are better than including the deductions, because a textbook can give much better context to the equations than Wikipedia can.

Anybody opposed?

--PeR 11:17, 11 February 2007 (UTC)

I am. I don't think your stated reason is a good one for removing useful information from Wikipedia. -- Matthew Woodcraft 14:07, 11 February 2007 (UTC)

OK. How about moving the derivations to articles entitled "Derivations of ..." (or similar) and linking to those? That way the information isn't removed from Wikipedia. --PeR 15:39, 11 February 2007 (UTC)

I'd have no objection to that. --Matthew Woodcraft 16:23, 11 February 2007 (UTC)

PeR, you mentioned section 3.4 of the celestial mechanics textbook in connection with rotating frames of reference. From what I can see, section 3.4 is about the derivation of general acceleration components for polar coordinate systems. You seem to be confusing the two topics. I can't actually find anything to do with rotating reference frames and fictitious forces in the entire book. There would be no reason for having a rotating reference frames chapter in a celestial mechanics book because it is not remotely relevant.

This seems to be at least part of the reason why you don't believe that the linear expansion of a radial vector can be real when the vector is rotating. You associate rotating frames of reference with fictitious forces, and hence you are wrongly associating polar coordinates with fictitious effects. David Tombe 11th February 2007 (203.87.176.3 16:48, 11 February 2007 (UTC))

Opposed

The derivations are at the end of the article, so I don't see the nonmathmatical being scared off - by the time they have read that far, they have got all they are going to get from the article. On the other hand, the mathematically or physically inclined reader needs the derivation to get a good grip on the topic. For that reader, the math makes more sense than the chatter. More than that, one of the advantages of Wiki is that you don't need a book - that is the point of the free encyclopedia and a big part of its convenience and value. And to add a minor point - the math is useful on discussion pages when issues come up. Brews ohare (talk) 23:13, 7 May 2008 (UTC)

Opposed, I agree with Brews ohare. Also, people who are scared of mathematical equations should seek psychiatric treatment for their "mathaphobia"  :) Count Iblis (talk) 00:27, 8 May 2008 (UTC)

Yes, I would agree with Brews ohare too. The maths equations in this particular case are extremely revealing. David Tombe (talk) 14:05, 16 May 2008 (UTC)

Real Centrifugal Force

Mr. Connolley, are you sure that your reversion wasn't simply a knee jerk reaction in relation to the edit war on the 'Centrifugal Force' page? The edits to the centrifugal force page that were the source of controversy were much more extensive than the small article that I inserted in this topic. I had already stopped reverting in the centrifugal force page as a reasonable discussion had opened up on the talk pages.

The essence of what I was saying was that in meteorology, the Coriolis force is always fictitious. Nobody is disputing this fact. I was merely pointing out that by its very nature, a rotating frame of reference will impose a circular motion artifact on all objects in the inertial frame. This artificial circular and tangential motion is catered for by the Coriolis force equation.

The situation regarding centrifugal force is not so simple. A rotating frame of reference cannot create a real radial effect. If a real radial effect occurs in the rotating frame of reference, then it must exist as a reality in any frame of reference.

Fictitious centrifugal force is said to act radially outwards on objects that are stationary in the rotating frame of reference. But these objects possess tangential motion in the inertial frame and the radial expansion is already real.

If this kind of centrifugal force is really an artifact, how can it throw somebody against the inside of the door of a car? In the centrifugal force article, this real centrifugal force is actually acknowledged under the title of 'Reactive Centrifugal Force'.

Was there really any reason for you to delete my insertion, or were you merely jumping on the bandwagon which began when Racecarr deleted my insertions in the Coriolis force article?

Rracecarr deleted my insertions in the Coriolis Force article for his own selfish reasons. He obviously sees himself as a guardian of Einstein's theories of relativity. I finally acknowledged that my insertions about real Coriolis force were original research and so I stopped the edit war. But that is no reason why you should have to delete a simple insertion pointing out that centrifugal force is often real. David Tombe 11th February 2007 (203.87.176.3 14:03, 11 February 2007 (UTC))

David, there is long discussion about this insertion on Talk:Centrifugal force. You are the only one in favor, while a number of editors have spoken against it. Repeatedly inserting the text serves no purpose, and causes annoyance to others. Please stop. --PeR 18:55, 11 February 2007 (UTC)

Mr. Connolley, the long discussion in the centrifugal force section is about a different insertion. But at any rate, the essence of that discussion comes down to a denial on their part, of the reality of two objects having a mutual radial acceleration, if they have a mutual tangential velocity. It is an undeniable fact, yet they seem to think that it can be screened out by viewing the situation from cartesian coordinates.

It was cheap of you to ask me to please stop making the insertion when you have already blocked me from doing so, and when I wrote to you asking you why. You have totally ducked the issue. It's a bit like somebody getting sacked from a job. When they ask why they were sacked, they receive the reply 'Please don't come back'.

You failed to address the question, 'how can a rotating frame of reference cause a radial outward acceleration as an artifact?' If you think about that question, you will see that my insertion into this article was valid. Instead you chose to play the numbers game and point out that I am outnumbered by a group of zealous people who keep a 24 hour vigil on the article. David Tombe 12th february 2007 (222.126.33.122 19:32, 11 February 2007 (UTC))

Mr. Connolley, I must apologize for my reply to you above. I have just noticed that it was actually Mr. PeR who wrote the letter that I was responding to. The position of his letter made me assume that it was your reply to my letter to you directly above it. The fact that it was Mr PeR who told me to stop making the insertion now makes it all the worse because he already knows fine well that I have stopped reverting on the Centrifugal force article, and he would have seen my letter to you querying the reversion on this article. David Tombe 12th February 2007 (222.126.33.122 20:10, 11 February 2007 (UTC))

David, I know that you have stopped making the insertion to Centrifugal force, but the text was inserted twice today into this (Fictitious force) article. If it wasn't you I apologize, but it was natural to assume since you have inserted that text into different articles at least a dozen times before from various IPs. In order to avoid further confusion, perhaps you could consider creating an account? --PeR 20:45, 11 February 2007 (UTC)

Are you replying as proxy for Mr. Connolley? The offending text in question points out that a rotating frame of reference can induce circular and tangential effects as artifacts (Coriolis Force), but that it cannot, by its very nature, produce radial effects. The underlying tangential velocity in the inertial frame causes the radial effects in a centrifuge.

I'm fascinated as to how this basic realization has managed to cause so much upset. I'd like to hear Mr. Connolley's views directly as to why he blocked me from making this insertion. David Tombe 12th February 2007 (222.126.33.122 10:09, 12 February 2007 (UTC))

I edit as myself, not via proxies. Please get yourself an account. Who is Mr Connolley? You were blocked, as I recall, for breaking 3RR. Please don't William M. Connolley 11:02, 12 February 2007 (UTC)

I assumed from your user name William M. Connolley that you are Mr. Connolley. I'm sure you don't edit via proxies, but clearly Mr. PeR presumed to be your proxy by replying to my original letter to you. Are you not going to reply to it yourself? We know the reasons why I was blocked. That doesn't need to be restated. My letter to you was asking you to reconsider the issues in the blocked insertion. You can read it at the beginning of this section. Are you willing to consider the fact that if a centrifuge causes radial acceleration, that this cannot be a fictitious artifact? Whereby Coriolis force is fictitious in all officially recognized situations, centrifugal force is often not fictitious at all. David Tombe 12th February 2007 (222.126.33.122 12:03, 12 February 2007 (UTC))

If you know you've been blocked for 3RR, why did you write I'd like to hear Mr. Connolley's views directly as to why he blocked me from making this insertion? Please get yourself an account, if you want to avoid irritating people. You might also avoid the meningless officially recognized situations terminology, unless there is some institute for certifying physics I'm unaware of William M. Connolley 12:31, 12 February 2007 (UTC)

Mr. Connolley, the officially recognized situations are such as in meteorology and oceanography, as opposed to in magnetism where it is not officially recognized. On the other point, I wasn't asking to hear your views as to why I was blocked. You twisted that one completely. Here's the quote from a few paragraphs up "My letter to you was asking you to reconsider the issues in the blocked insertion."

Are you willing to face up to the fact that centrifugal force in a centrifuge is not fictitious? And if so, can the insertion be reinstated? I don't see why this issue has to be irritating people. David Tombe 12th February 2007 (222.126.33.122 13:45, 12 February 2007 (UTC))

William - In talk:centrifugal force#Inertia, David cites the geodesic equation for radial motion in polar coordinates ${\frac {\mathrm {d} ^{2}r}{\mathrm {d} t^{2}}}-r\left({\frac {\mathrm {d} \theta }{\mathrm {d} t}}\right)^{2}=0$, and says that

I don't adopt the Newtonian concept that this motion is explained by inertia.

This makes David's claim complete and total original research. It is kindly requested that you semiprotect this article and centrifugal force if David should try to edit either one again. --EMS | Talk 14:46, 12 February 2007 (UTC)

ems57fcva, that is a downright lie. I have never quoted that equation as being equal to zero. Check the two citations once again. The equation that I referenced contains the left hand side of the one that you have just quoted, but equates it to radial aceleration, and not to zero as you have alleged. One of these two terms is the centrifugal acceleration. If we equate the other term to Newton's inverse square law of gravity, then we have got the planetary orbital equation that leads to ellipses, hyperbolae, or parabolae. If the kinematical approach upsets you, then multiply it through by inertial mass and convert it into force.

My quote about inertia has got absolutely nothing to do with this basic textbook kinematics. Once again, you are twisting the facts in order to try to get my arguments excluded on the grounds of being contrary to wikipedia policy.

You basically haven't got a clue what you are talking about. David Tombe 12th February 2007 (202.69.162.228 16:16, 12 February 2007 (UTC))

To anon/David: I trust EMS on this. And please... get yourself an account if you intend to contribute seriously William M. Connolley 15:00, 12 February 2007 (UTC)

Mr. Connolley, that is one of the weakest arguments that I have ever heard. You trust EMS? EMS is a person who misrepresents the truth. EMS said that I used that equation above. EMS knows that I equated the terms to radial acceleration and not to zero.

If you trust EMS, then I can only conclude that either you haven't got a clue about fictitious forces, despite being an editor for this topic, or that you are merely closing ranks with a little clique.

What has having an account got to do with whether a contribution is serious or not? You are trying to insinuate that I am not serious about my arguments. Is that self delusion on your part to avoid you having to face up to the fact that rotational motion cannot create a radial artifact? David Tombe 12th February 2007 (202.69.162.228 16:25, 12 February 2007 (UTC))

ems57fcva, I have seen right through you now. Here is your profile [2]

You are hoping that some day your own original research will appear in wikipedia.

"I hope to see an article on Flat Background General Relativity here eventually, but in order to play it safe I will not be the one who starts it."

What I have been advocating is basic textbook applied mathematics but it contradicts your own original research. That is the grounds upon which you are trying to make the editors believe that what I am saying is original research. You want it excluded on that false premises because it contradicts your own original research. David Tombe 12th February 2007 (202.69.162.228 16:39, 12 February 2007 (UTC))

David - You would do well do read the No personal attacks policy. If this keeps up, I will ask William to protect these talk pages too! You have chosen not to accept that a radial coordinate acceleration in polar coordinates is an effect of inertial motion. That is where everyone else disagrees with you. I know that you cannot see what you have done, but I honestly assure you that this is a novel application of the geodesic equation given above and Newton's second law. Try getting this past a physics professor and see what he or she has to say. In the meantime please stop bugging us, or at least please learn how to be civil. --EMS | Talk 17:31, 12 February 2007 (UTC)

EMS, you say

"You have chosen not to accept that a radial coordinate acceleration in polar coordinates is an effect of inertial motion. That is where everyone else disagrees with you."

First of all, the radial acceleration is a reality irrespective of what coordinate system we use. Secondly, if the acceleration occurs due to the tangential velocity, then there is absolutely no need to bring the subject of inertia into the discussion. The only factor that gives rise to this centrifugal acceleration is the mutual tangential velocity, and we can solve the orbital equation without even bothering to multiply through by inertial mass. It's no good saying "Try getting this past a physics professor". Which particular physics professors are you talking about? What about an applied maths professor? David Tombe 13th February 2007 (124.217.34.54 01:17, 13 February 2007 (UTC))

Detection of non-inertial reference frame

I am unhappy with the "Detection of non-inertial reference frame" section. Its general disposition of setting up a strawman argument, attributed to some unidentified "philosophers", only to knock it down smugly seems to me to be unsalvageably non-encyclopedic. While such rhetoric is not uncommon in textbooks that aim for a informal touch here and there, an encyclopedia article deserves a rather more detached tone.

I tried briefly to trim the section down to make it less polemic and more matter-of-fact – but ended up with nothing, or at least no definite points that clearly deserve to be made early in an article about the fictitious force concept. If I understand the intent of the section correctly, its basic point is that one can know that one is in a non-inertial frame by observing that bodies move in ways that appear to require fictitious forces to explain. But even to make this point properly for readers who learned Newtonian gravity in school would seem to lead into a discussion of GR or at least the Equivalence Principle, and I don't think we want to go there as early in the article as this section. GR should not come before we have exhausted most of what there is to say about the subject in a Newtonian context.

I'm not quite bold enough to just delete the section unilaterally and wait for the outcry, so if somebody thinks this section has redeeming qualities, could they please speak up? –Henning Makholm 02:38, 4 March 2007 (UTC)

Agreed, what do you think of it now? Zedall 05:54, 13 August 2007 (UTC)

Are fictitious forces Newtonian?

Correct me if I am wrong, but my understanding is that in Newtonian Dynamics there is no such thing as fictitious forces. If we believe in an Absolute Space, as Newton did, we have frames of reference absolutely at rest or absolutely in motion (and also absolutely accelerating). When a body experiences a centrifugal force it is clear that there is a rotating frame of reference whose motion needs to be taken into account when transforming coordinates from a different frame of reference. But Newton wouldn't call this fictitious force; he would simply say that the frame of reference is moving (or rotating) with respect to absolute space.

The example of the passenger inside an accelerating car shows this very clearly: the first way of analyzing the problem says that the car is accelerating wrt absolute space and it pushes the passenger. This is Newton's view. The second interpretation using fictitious forces is post-newtonian.

The concept of fictitious force arises only when we reject absolute space and, as far as I know, Newton never used this term.

If the above is correct, then the heading "Newtonian examples of fictitious forces" in this article should be changed, because it is contradictory. I would suggest simply "Examples of fictitious forces". —The preceding unsigned comment was added by Dukeofalba (talk • contribs) 09:09, 4 May 2007 (UTC).

• The Coriolis force is a ficticious force that appears in Newtonian dynamics. Newtonian in this example probably refers to Newtonian physics, not the old virgin who worked at the mint. But I recall Newton doing the spinning bucket experiment (at least in thought). Which involves a ficticious centrifugal force.WilyD 12:36, 4 May 2007 (UTC)

Sure, Newton mentioned these and similar experiments. But the point is, however, that his interpretation of these experiments did not include the concept of fictitious force. Therefore, the word "Newtonian" should not be used in this case. It is not a physical, but a historical remark.

It is a fact that the term Newtonian, as commonly used today, does not imply a restriction to ideas formulated (or believed) by Isaac Newton himself. It refers more generally to the physical worldview that reigned in physics from the time of Galileo and Newton until it was superseded by (special and general) relativity. Your contention that the word should only be used to refer to what Newton himself thought, is not supported by modern usage. –Henning Makholm 08:31, 5 May 2007 (UTC)

Sorry, but that is not the point I am trying to make. As you correctly say, Newtonian means pre-relativitistic physics, not only what Sir Isaac thought -- although if you look up "Newtonian" in this Wikipedia, it reads: "Newtonian refers to the scientific work of Isaac Newton". The point I am trying to get across is that the Classical, Newtonian or pre-Relativistic view did not include fictitious forces. Fictitious forces correspond to the modern view. (It is not strictly post-Relativistic either, because some authors like Mach and Bishop Berkeley hinted at it, but these were not mainstream philosophers at that time.) Therefore, fictitious forces and Newtonian (or Classical) mechanics ARE MUTUALLY EXCLUSIVE. I believe that this point should be made clear in this article, so deleting the word "Newtonian" from the above mentioned heading is but one step, the next one should be to add an explanatory paragraph.

You are wrong. There is no conflict between fictitious forces and classical mechanics. They are not "mutually exclusive" in any sense. Sorry, and thanks for playing. –Henning Makholm 22:50, 5 May 2007 (UTC)

In a scientific discussion it is essential to provide evidence, or at least, to show your logical process of deduction. Therefore, I would like to ask you to substantiate any of your categorical assertions. For example, it would be appreciated if you could provide one single reference of an author speaking of "fictitious forces" before 1905 - the date of publication of the theory of relativity. Lacking that, I would kindly ask you to stop interfering in this serious debate.

"Before 1905" is not relevant. The relevant point is that the fictitious forces arise within the Newtonian model of time and space, which continues to be a useful model also after the publication of the theory of relativity. –Henning Makholm 12:12, 6 May 2007 (UTC)

Indeed "before 1905" is not relevant in itself. What is relevant, is that in Newtonian theory any fictitious cause is rejected for a physical description of mechanics. And of course, in Newtonian mechanics gravity is not fictitious. It's a hallmark of Newtonian mechanics to ascribe physical causes to physical phenomena. The introduction of a rotating frame of reference as being in rest with the resulting unphysical description of nature is not just "post-Newtonian", it is pertinently anti-Newtonian. Suggesting that anti-Newtonian concepts belong to Newtonian theory is misguided and readers should be spared such a misrepresentation. Harald88 13:04, 6 May 2007 (UTC)

That is just nonsense. The examples in the article are Newtonian, because they are about forces that arise in accelerating frames that live inside ordinary Newtonian spacetime. Since they are completely deductive consequences of inertial-frame Newtonian mechanics (no new physics at all is involved, it's just a purely mathematical re-framing of the same theory), it makes no sense to refer to them as "anti-Newtonian". –Henning Makholm 13:18, 6 May 2007 (UTC)

I agree. I think that this sort of discussion also happened when people first started to use negative numbers, imaginary and complex numbers, etc. etc.... Count Iblis 15:16, 6 May 2007 (UTC)

I agree with Harald88: the concept is anti-Newtonian. Speaking of "Newtonian fictitious forces" is just like speaking of "Relativistic aether"; it's an oxymoron. So is the "Newtonian spacetime", that someone has mentioned in this discussion, since in Classical Mechanics space and time are two completely separate concepts. In Newtonian mechanics time has the property of being absolute and the need for the idea of fictitious force arises only when we reject absolute space. Therefore this idea is fundamentally anti-Newtonian. It seems that some people confuse the physical system with the interpretation we make of it. A system can behave within Classical limits if there are no close-to-speed-of-light velocities, and yet our interpretation can be completely non-classical. Of course Nature does not change one bit its behavior, what changes is our interpretation of the phenomena.

Far from being "anti-Newtonian", the concept of fictitious forces is at its core a Newtonian one; it does not work well except within Newtonian mechanics. In Newtonian mechanics, fictitious forces give a complete and exact answer to the problem of describing motion relative to non-intertial space coordinates. On the other hand, within relativity they can only be approximate, and they are only helpful at all in precisely those low-speed cases where the Newtonian theory is also a useful approximation. For example, according to special relativity an observer that rides on the outside edge of a spinning centrifuge experiences less time than an observer that rides the centrifuge closer to its center. There is no way to fix up a rotating Lorentzian space to do that simply by adding extra fictitious force; time cannot be influenced by forces in SR. In Newtonian mechanics, on the other hand, fictitious forces provide a complete and exact explanation of all the ways in which observations in a rotating coordinate system differ from observations in an inertial system. Fictitious forces are, if possible, even farther removed from general relativity which embraces the use of non-uniform coordinates as its basic substrate; a non-uniform coordinate system does not need any special correction in GR, because the core theory is born to deal with it.

Also, Newtonian mechanics does reject the concept of absolute space; this rejection is not particular to Einstein's theories. Sir Isaac himself may have believed in absolute space, but the theory that modern physicists apply his name to does not. –Henning Makholm 20:17, 6 May 2007 (UTC)