Talk:Fictitious force/Archive 1

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Archive 1

Archive 2

Archive 3

It looks OK to me

Dear William,

thanks for your message. I've read the article and this particular text looks fine to me. The examples - Coriolis and centrifugal - are right, and the reason why the're fictitious is described correctly, too. I don't know whether you will find exactly this wording anywhere; nevertheless I believe that most other physicists would agree with the definition, too. Concerning GR: GR was a real intellectual breakthrough, and it is based on the idea that all frames - both inertial as well as non-inertial frames - are equally good to describe reality. From this viewpoint, you can describe gravity as a "fictitious" force, or you can also classify the centrifugal force as a "real" force, a form of gravity. In principle, it's a matter of convention. In reality, we still use the Newtonian approximation that allows us, in most cases, to distinguish the "real" and "fictitious" forces, and that allows us to distinguish - which is related - the inertial and non-inertial frames. This apparent contradiction is not a real contradiction in physics: physics is about making predictions, not about deciding whether an obviously observable effect should be called "real" or "fictitious".

I agree that it is not easy to find an explicit "definition" of the fictitious force somewhere. It's because the words "fictitious force" are not quite a scientific term - the use of the adjective "fictitious" is kind of informal. They're still two separated words, but it's good that someone tried to define this frequent combination of the words as a single term.

All the best, Lubos

I personally think that the much longer version of the article right now is less meaningful than the previous shorter one, but don't get discouraged. --Lumidek 23:57, 22 Jan 2005 (UTC)

Well, you know, in special relativity for example, the following is valid: expressions that are invariant under Lorentz transformation are the most important expressions, they express the true 'nuts and bolts' of special relativity. The spacetime interval: c²(dt)²-(dx)²-(dy)²-(dz)², is invariant under Lorentz transformation; therefore it is considered to be more informative than spatial distance or time difference separately. To describe a force as arising "because of a change of reference frame" is just about as far away from relativistic physics as you can get.

So from my point of view, I do find it discouraging to see that the idea of "because of a change of reference frame" is considered to have meaning. Cleon Teunissen 01:33, 23 Jan 2005 (UTC)

Disagree

(William M. Connolley 20:10, 3 Nov 2004 (UTC)) I disagree with this page. For two reasons:

The defn (doing no work) is plausible (though it needs to be qualified by "in principle" to make any sense) but its not at all clear that this defn is accepted by the physics community (I don't assert its not: but when I have discussed this with colleagues, on the question of the fictitiousness of coriolis, they reacted badly to this defn. Is there evidence that this defn is used?).
Para 2, about GR, then fatally conflicts with the defn in para 1.

Well, feel free to edit away :) I simply created this article because the term is used, although finding a definition is actually quite difficult. -- ALoan (Talk) 11:13, 4 Nov 2004 (UTC)

(William M. Connolley 18:24, 4 Nov 2004 (UTC)) OK. I think that the difficulty of finding a defn may have been a clue; and you shouldn't invent one.

I said difficult, not impossible. Look at some of the external links. There is no problem in finding people who use the expression, and they must intend it to mean something. The context often allows you to work out what they seem to mean by it, but I certainly did not "invent" a definition. -- ALoan (Talk) 18:54, 4 Nov 2004 (UTC)

(William M. Connolley 23:20, 4 Nov 2004 (UTC)) I admit I hadn't looked before, but I have now, and they don't help. None of them define fictitious force. The mathworld is blank: just some see-alsos. The other two talk about centrifugal.

No, none of them define the term, but they all use it, and some of them explain what they mean (if only tangentially, in how they use it). If you click through from mathworld to centrifugal force and Coriolis force, you can see the sense in which they are using the term. -- ALoan (Talk) 10:14, 5 Nov 2004 (UTC)

(William M. Connolley 12:57, 5 Nov 2004 (UTC)) OK, but nonetheless I stick to my point above and clarify it: it is dangerous/wrong to explicitly define a term in wikipedia if that definition isn't to be found in the outside world. A discussion of the concept is fine, but the current hard definition is misleading (as well as in disagreement with para 2, still). I will actually edit the text somewhat to reflect this.

Please do - I invited you to do so above - feel free to edit away. -- ALoan (Talk) 13:01, 5 Nov 2004 (UTC)

The Sagnac Effect

Choice of frame of reference
It is sometimes suggested that the principles of relativistic physics imply that there is no choice of frame of reference that reflects the actual dynamics more than other choices of frame of reference. To explain the physics involved, any choice of frame of reference would then be equivalent. This is valid for uniform motion, but it is not valid in the case of rotation; relativistic physics implies that rotation can be measured absolutely.

Measuring absolute rotation is possible, for example, with the experimental setup called ring interferometry. You can split a beam of light, have the light go around a circuit in both opposite directions, and then you allow this light to create an interference pattern. For example, you can make the light take a square path by setting up mirrors on the corners of a square. This setup measures absolute rotation. One of the first experimentors to conduct this type of experiment was called Sagnac, he conducted his experiment in 1913, and the effect is now called the Sagnac effect.

Fiber optic laser ring interferometers are widely used as navigational devices in ships and aeorplanes, replacing the mechanically operating gyroscopes that were used for navigation. Fiber optic laser ring interferometers are called optical gyroscopes.

External link: Reflections on Relativity, by Jonathan Vos Post section 2.7 The Sagnac effect.

External link: Ring interferometry experiment. University of Canterbury, New Zealand

(William M. Connolley 21:39, 21 Jan 2005 (UTC)) Right, as promised, comments. In the interests of brevity, I've been blunt, rather than add polite caveats throughout. Disclaimer: I've thought about this, or tried to, but I'm not a physicist. At base, I think your interpretation of relativity is wrong. In GR, all (local) coordinate systems are equivalent for describing physics (of course if you switch you may end up with more or less of things that look like forces). I don't think you are correct in your description of the Sagnac effect: I am just about sure that the INS systems using that are measuring changes, not absolutes. This is supported by the 2nd link you provide: Ring laser gyroscope development, to measure local variations in Earth rotation, is expanding rapidly (I've bolded variations; its the crucial point). Being able to measure absolute rotation, locally, would destroy the underpinning of GR. I'm less able to explain the first of your links, to the math pages. These appear to be respectable, but are unsigned: who is the author? I am not convinced by it, as yet. There is no wiki page on the Sagnac effect. Err, well, those are my views at the moment. William M. Connolley 21:39, 21 Jan 2005 (UTC)

Exactly what is making you assume that the equivalence of all inertial reference frames extends to include equivalence of accelerating reference frames?

(William M. Connolley 12:50, 22 Jan 2005 (UTC)) This is exactly the diff between SR and GR.

I would say the difference between SR and GR is: SR's space-time geometry is Minkowski space-time geometry. GR's space-time geometry is a type of Riemann geometry, more specifically referred to as a semi-riemannian 4-dimensional manifold. Cleon Teunissen 11:41, 23 Jan 2005 (UTC)

I am just about sure that the INS systems using that are measuring changes, not absolutes. (William M. Connolley 21:39, 21 Jan 2005 (UTC))

Astronomers have proposed using a set of well chosen Pulsars as the fundamental source of the scientific standard of timekeeping. According to measurements, the Pulsar frequency fluctuates less then Earthbased atomic clocks. Of course, without the Pulsars, the fluctuations in atomic clock time-keeping would be beyond measurement. Radio-astronomy and optical astronomy measure fluctuations in Earth rotation. Ring interferometry measures fluctuations in Earth rotation too, confirming and exceeding astronomical measurement. In order to measure fluctuations, you need a steady background. What can the steady background of ring interferometry be? Cleon Teunissen 01:16, 22 Jan 2005 (UTC)

[...] the first of your links, to the math pages. These appear to be respectable, but are unsigned: who is the author? (William M. Connolley 21:39, 21 Jan 2005 (UTC))

Reflections on relativity is written by Johathan Vos Post as a relativity textbook for undergraduate students. As far as I can find, in performing google searches, it is a standard, completely non-controversial textbook.

External link: Jonathan Vos Post is a Professor of Mathematics at Woodbury University in Burbank, California. His first degree in Mathematics was from Caltech in 1973. He is also, or has been also, a Professor of Astronomy at Cypress College in Orange County, California; Professor of Computer Science at California State University, Los Angeles [...]

His Erdos Number is 5.

One of the external links of the wikipedia article on general relativity links to Reflections on Relativity. Cleon Teunissen 09:59, 22 Jan 2005 (UTC)

(William M. Connolley 12:50, 22 Jan 2005 (UTC)) This is getting somewhat above my head. I shall invite Lumidek to comment, he know these things better than me.

Reference frames and translations

Cleon Teunissen 08:22, 22 Jan 2005 (UTC)
(In the following, I mean by 'newtonian dynamics' the modern way it is used and interpreted in, say, the 19th, 20th and 21st century. I do not mean it to refer to any of the opinions of Isaac Newton.)

In newtonian dynamics, Galilean relativity is one of the basic assumptions. In newtonian dynamics space is assumed to be Euclidian, and in Euclidian space transforming between inertial frames of reference is straightforward and trivial: just addition of the vectors of the velocities.

A word that is quite suitable to express this property of inertial frames of reference is 'symmetry'. Alle inertial frames of reference are perfectly symmetrical with respect to each other. Physicists have a very strong intuition that this symmetry simply must be a property of Nature, and as far as known, it is.

In the nineteenth century, a dilemma arose. The Maxwell equations of Electrical and Magnetic fields were introduced, and if you assume that the Maxwell equations are correct, and you assume that space is Euclidian, than you must deduce that measuring absolute velocity is possible. Reluctantly, physicist resigned themselves to the conclusion that Galilean Relativity was not a property of Nature after all. Then, in 1905, Einstein showed that it is possible, by assuming that the Lorentz transformations are the fundamental transformations between inertial frames of reference, to have both the Maxwell equations, and full symmetry of all inertial frames of reference. Etc, etc.

In Newtonian dynamics, transformation between two reference frames that are not inertial with respect to each other is performed by linear addition of the vectors. For example: in order to transform between a non-rotating frame of reference, and a rotating frame of reference, the acceleration vector is expressed as a function of time, and/or spatial coordinates. As long as you can represent the acceleration vector mathematically, you can express the transformation of the acceleration as a function of time and/or spatial coordinates.

In newtonian dynamics, if you are sufficiently mathematically able, you can transform between all reference frames. According to newtonian dynamics, the transformations between inertial frames of reference represent a fundamental property of Nature. The other transformations are seen als calculation tricks, not representing a property of Nature

In order to have a fully equipped toolbox, Einsteinian Relativity had to be extended to also provide transformations involving a non-inertial reference frame. In the following years, Einstein pursued two goals, assuming correctly the two goals were interconnected. Einstein sought to formulate general transformations, and he sought to formulate a law of gravity in which the mediator of gravitational influence would propagate through space-time at lightspeed. (Newton had shown mathematically that with an inverse-square law of gravitation there is conservation of angular momentum only if gravity propagates at infinite speed. Newton argued that only a dynamics with conservation of angular momentum has scientific crediblility.)

In 1915, the two goals were reached in the formulation of General Relativity.. Now there was a full set of transformations, just as in newtonian dynamics. According to general relativity, when an object is being accelerated, all of space-time appears to be distorted; with gravity, local space-time is distorted.

I argue that the principle of equivalence can be understood to be an assumption concerning the way matter interacts with space-time. It seems to me that there is no logical necessity to assume that the principle of equivalence is fundamentally about reference frames. (General relativity does predict frame dragging. Possibly, frame dragging is a significant astrodynamical factor close to rapidly rotating neutron stars and rapidly rotating black holes. It seems to me that on the surface of the planet Earth, frame dragging is not a significantly contributing factor. ) Cleon Teunissen 08:22, 22 Jan 2005 (UTC)

Definition

The introduction should be more clear and simple. [1] Duk 03:51, 29 Nov 2004 (UTC)

(William M. Connolley 11:21, 29 Jan 2005 (UTC)) I agree with that, it seems quite convoluted and is hard to read. Within the dynamics section, the stuff about how-you-detect accelration seems wrong within the context of GR, since it fails the equivalence of acceleration/gravity test.

Relativistic dynamics is backwards compatible with newtonian dynamics

Mathematically, newtonian dynamics is a limiting case of relativistic dynamics. At non-relativistic speeds, the higher order terms in the formula's become negligable, and the formulas become identical to the newtonian formulas. To use a computer metaphor: to everyone's surprise (and delight) relativistic mathematics is backwards compatible with newtonian mathematics. For the first time in the history of physics a completely novel mathematical formulation was backwards compatible.

Therefore I was keen to find an interpretation of relativistic dynamics that mirrors that mathematical backwards compatiblity. I think I found that in the concept of geodesic motion. At non-relativistic speeds, and non-relativistic volumes of space, relativistic space is indistinguishable from euclidian space. Newtonian mathematics describes a straight line as the shortest distance between to points: that is the newtonian geodesic. Newtonian dynamics says that a force is required to make an object deviate from moving along the geodesic. Newtonian dynamics categorizes anything that causes deviation from moving along the newtonian geodesic as a force, hence gravity is categorized as a force.

According to general relativity, when you are standing on the surface of a planet there is only one force. The surface of the planet is pushing you, accelerating you in a direction away from the center of gravity.
(Anything else going on is space-time geometry related.)
So yeah, gravity is fictitious, but the fact that your distance to the center of the planet remains constant is not fictitious. Cleon Teunissen 10:18, 30 Jan 2005 (UTC)

The Jan 29 version of the article

Hi William,
It is not clear to me whether your comment was archived, but I caught a fleeting glimpse of it. Please check out the wikipedia article on the gyrocompass. In 1915, Einstein was consulted as an expert witness in a patent infringement law suit concerning a highly succesfull gyrocompass design.
To my knowledge, in this article I present textbook general relativity. At an earlier stage, I used the expression: absolute rotation. That was in error, I replaced that with: measuring rotation with respect to the local inertial reference frame. Cleon Teunissen 12:13, 29 Jan 2005 (UTC)

Here is my line of thinking.
According to theoretical physicists, if general relativity is correct, then the phenomenon called frame dragging must occur. To verify that, Gravity Probe B was build and launched. The mechanical gyroscopes inside Gravity Probe B are suspended as frictionless as is possible with current technology (cooled to superconducting temperature, etc.) The theoretical physicists expect that the gyroscopes will follow a rotation of space-time that is induced by the presence of the rotating mass of Earth. This phenomenon is sometimes called gravitomagnetism. In their local inertial frame of reference the gyroscopes will retain alignment. The designers of Gravity Probe B have gone though extreme measures to provide the maximum amount of shielding from electromagnetic influences. The mediator that causes the gyroscopes to deviate must be the very fabric of space-time itself. Only if space-time itself has intrinsic orientation it is possible to influence the orientation of the mechanical gyroscopes inside Gravity probe B. The physicists are very keen to see the results, only general relativity predicts frame dragging. Cleon Teunissen 13:24, 29 Jan 2005 (UTC)

Hi Duk,
my apologies for deleting the Britannica.com definition on the previous disscussion page.
I agree that the definition I give doesn't look particularly clear. It looks clear to me, having immersed myself in the subject, but that doesn't count.
I have been puzzling to find a definition that is compatible with both newtonian dynamics and relativistic dynamics. I think the present one is. And I don't think it is possible to find a definition that is instantly clear to most people, it's all very counter-intuitive. Cleon Teunissen 12:13, 29 Jan 2005 (UTC)

(William M. Connolley 11:21, 29 Jan 2005 (UTC)) I agree with that, it seems quite convoluted and is hard to read. Within the dynamics section, the stuff about how-you-detect accelration seems wrong within the context of GR, since it fails the equivalence of acceleration/gravity test. (William M. Connolley 11:21, 29 Jan 2005 (UTC))

Hi William, in the article it is explicitly announced that the first section will discuss the subject in terms of newtonian dynamics. Basically, you are complaining that newtonian dynamics is different from relativistic dynamics.

According to general relativity, there are two fundamentally distinct kinds of acceleration.

Deviation from moving along the geodesic. This can always be measured locally with the proper equipment, because a mechanical force is being exerted.
Moving along the geodesic in curved space-time. When an object is moving along the geodesic in curved space-time, then it is stationary with respect to its local inertial frame of reference. Then, all equipment measuring locally will measure zero linear acceleration. Seen from a sufficient distance the object is seen to be accelerating with respect to a general background.

So the word acceleration is ambiguous, and that ambiguity needs to be resolved.
Further on in the article, I do resolve that ambiguity, by emphasizing the difference between geodesic motion and non-geodesic motion.
But at the start of the article, the subject is discussed in newtonian terms. I need the reader to read the start of the article as a newtonian discussion. Cleon Teunissen 17:47, 29 Jan 2005 (UTC)

(William M. Connolley 21:40, 29 Jan 2005 (UTC)) Well, I'm in danger of being out of my depth here - you probably want to try to persuade Lumidek to have a closer look perhaps if you want a more expert opinion. But I don't see how starting with Newtonian, then switching to GR, is going to help avoid confusion, because it means that a whole pile of the article becomes wrong by the time you get to the end. And since GR is correct - as far as we know - I think the whole thing should be done from a GR prespective. Within dynamics it says "When there is accelerated motion..." with respect to what? Within GR, there is no (local) way the man-in-the-lift can tell is he is in a gravity well or being pulled by the rope.

Hi William, its not being out of depth that is the issue, I feel.
The problem of how to avoid confusion seems insurmountable.
Newtonian dynamics is a selfconsistent dynamics, and so is relativistic dynamics. But the words, the languages, have fundamentally different meanings in the two paradigms.
I have trained myself to switch back and forth between the paradigms, maintaining consistency in each context.
Please read the new article I wrote on centrifugal force. I had also written a dutch version of the article, and I was given valuable advice.

What a legacy Einstein left us!
In every school physics is first introduced by teaching newtonian physics, and they should. Learning newtonian physics is such a good entry to physics, it teaches thinking physics, without overwhelming, you can't teach basic physics any other way. It's the only way to pave the way for relativistic dynamics. Schools should never skip newtonian dynamics. You work as a climate modeler, the air currents are calculated with newtonian dynamics, only particle accelerator physicists and cosmologists use relativistic calculations, that's like point zero zero one percent of the physics community.
So there we are: a science with two current paradigms simultaneously.

Err, don't get me wrong; if particle accelerator physicists wouldn't use relativistic calculations the machines wouldn't work, that proves beyond doubt that Einstein was right.Cleon Teunissen 07:50, 30 Jan 2005 (UTC)

I feel the article should start with discussing in newtonian terms and that it should subsequently move on to relativistic dynamics.
the reader doesn't have to plough through the relativistic stuff, the newtonian discussion is sufficient. The only purpose of the general relativity section is to show that as far as the fictitiousness is concerned general relativity agrees with newtonian dynamics. Cleon Teunissen 07:37, 30 Jan 2005 (UTC)

Passing the equivalence of acceleration/gravity test

Introduction

I realized that it is also possible to write the article with a deeper level of interpretion of general relativity, in the jan 29 version of the article I stay relatively close to the mathematics.
I call this version of the article the 'passing the equivalence of acceleration/gravity test' version, since is is specifically aimed at passing that test.

The first section tries to stay as close as possible to everyday experience, close to everyday language, close to intuitive notions.
Then a very short section on how gravity is categorized in newtonian dynamics.
Then a substantial section on general relativity, showing that general relativity agrees with newtonian dynamics as far as fictitious forces are concerned. That is, general relativity does agree, but on different grounds.

proposal for new article jan 31

There is the intuitive notion that if two forces that are acting on an object are balanced then the object remains stationary. If an observer mistakenly assumes an object is stationary while in fact it is being accelerated, he will automatically assume the presence of a force. This assumed force is called a fictitious force (also known as an apparent force, fictional force, imaginary force, or pseudo force)

Natural motion If a car is turning a sharp corner, the tyres of the car need to have enough grip to provide the necessary force directed towards the inside of the curve. If they have no grip at all the car will continue to move in a straight line.

Natural motion is motion in a straight line, with constant velocity. This is called uniform motion. To make an object deviate from unifom motion, a force must be exerted.

An observer on a rotating disk is in motion, but it is not natural motion, it is circular motion and in order to maintain a circular motion a centripetal force must be provided. If the observer is unaware the disk is rotating (or if he chooses to ignore that possibility), he finds that in order to maintain his position he needs to provide some force directed towards the middle of the disk. Since he chooses to assume he is maintaining a stationary positon, he assumes he is opposing a force that is pulling him away from the middle of the disk. The force that is supposedly pulling him away from the middle of the disk is the fictitious force called centrifugal force.

This centrifugal force is very different from its opposite counterpart. A centripetal force that maintains the circular motion is transmitted by contact. The observer on the rotating disk who is standing up needs grip, his shoes must have enough grip, otherwise he cannot maintain position on the disk. (If the rotating disk is in space, the observer would need a space-suit with magnetic boots.) If the centrifugal force would actually exist it would be a force that is the same for all particles in the body, so you cannot feel it and there is no instrument that can measure it, you can only measure the effort to oppose it.

Newtonian dynamics In newtonian dynamics anything that makes an object deviate from uniform motion is categorized as a force. Therefore gravity is categorized as a force, but it is recognized as a very odd force, compared to all the other forces. For if gravity is a force it is equal for all particles, no exceptions whatshowever.

Relativistic dynamics
In general relativity, gravity is seen as something unique, uncomparable to anything else.

The way the mathematics of general relativity describes the alteration of space-time by gravitational influence can to some extent be modeled with the concept of accelerating flow. Around a gravitating body, for example a planet, there is . When an observer is standing on the surface of a planet, the surface of the planet is pushing the observer, accelerating the observer with respect to local space-time.
That is why accelerometers give the reading that anything on the surface of the Earth is being accelerated away from the center of the Earth.

If on the other hand nothing is stopping the observer, then he will "go along with the flow" towards the center of the Earth. As long as the observer is going along with the flow the accelerometers he is carrying with him will not measure anything.
According to general relativity, planets in orbit around a sun stay in their orbit because they are going along with the space-time acceleration of the space-time they are moving through. An accelerometer onboard a space station orbiting a planet does not measure anything, because the spacecraft is not accelerating with respect to the local space-time it is moving through. Space-time is transparant to velocity, it will leave any relative velocity untouched, but accelerating space-time can and does impart acceleration to objects moving through it.

So in general relativity the word 'stationary' does not mean the same thing as in daily life. If you - understandibly - assume that an observer on the surface of a planet is stationary, then you will automatically assume there is a gravitational force, to accomodate your intuitive sense that two forces must be balancing each other. According to general relativity, it makes a difference whether you just look at the space-time close by, or whether you consider a larger volume of space.

In summary:

If you are in a space capsule, and the thrust of the rocket-engine is accelerating you with respect to space-time; the accelerometers will register acceleration.
If you are in a space capsule, and the space capsule is in circular motion at the end of a cable, the capsule is accelerating with respect to space-time; the accelerometers will register acceleration.
If you are in a space capsule, on the surface of a planet, the surface of the planet is accelerating you with respect to the accelerating space-time; the accelerometers will register acceleration.

The nature of gravity
To an extent, gravity too fits the description of a fictitious force:

Unless you are in fysical contact with something that opposes it, you don't feel anything.
If you do not oppose it or fight it in any way, you will move in natural motion.

However, there is also a big difference between gravity and the fictitious forces:
With the fictitious forces, once the observer releases his grip (for example by switching off his electromagnetic boots) his motion will from that moment on remain unaccelerated motion, seen from all perspectives, from local to universal.
If the observer is in a region of space-time where space-time is accelerating, then if the observer releases his grip, he may be unaccelerating in a very local perspective, but in all larger perspectives he is accelerating, towards something that is much heavier than he is.

Limitations of the model
The flow model is linear, it doesn't reflect the property of relativistic gravitation that the gravitational potential energy is itself a source of gravity, and it is exactly this non-linearity that makes the predictions of general relativity slightly different from the predictions of newtonian dynamics. However, in this context the purpose of the model is to illustrate that an observer on the surface of a planet is not stationary with respect to local space-time.

Discussion of the Jan 31 proposal

(William M. Connolley 18:11, 31 Jan 2005 (UTC)) OK, starting from the above. In the Newtonian section it now says: In newtonian dynamics anything that makes an object deviate from uniform motion is categorized as a force. This offers no guidance for judging if a force is fictitious or not. Left like that, the concept "fictitious" becomes meaningless (which I think is my POV anyway).

Within the GR section, it says: constant acceleration of space-time towards the center of the planet. This makes it sound like some real physical thing is moving, which it isn't.

This version starts: If an observer mistakenly assumes an object is stationary while in fact it is being accelerated, he will automatically assume the presence of a force. This assumed force is called a fictitious force. I don't think you can say that in the intro. "stationary" and "accelerated" don't mean much.

Cleon Teunissen 22:51, 31 Jan 2005 (UTC) Ah well, I guess that's it. I gave it my best shot.
I suggest you and I do not continue discussing the subject of fictitious force, for it is clear to me now that I am unsuccesfull in reaching you.

In writing an article on fictitious force I'm setting my aim very high. I want the first part to be helpfull and comprehensible for someone without a physics background, and then I want to move on to an almost exhaustive discussion of the subject. I've written three versions now, and I'm not sure I am getting nearer to my goal. It is a fascinating journey though, I have no regrets.

In every field of human endeavour, words from daily life get a novel meaning, a context related meaning. In mathematics, imaginary numbers are as real as real numbers, and trancedental numbers are not necessarily esoteric numbers, etc etc. In physics the multitude of meanings is larger than anywhere else I suppose, because it has such a long history, and its theories have gone through profound conceptual revolutions. So in physics writing and reading it is especially important that people are sentitive to context: everyday life, newtonian thinking, relativistic thinking. Without that sensitivity to context, communication falls apart.

William, judging from what you say about general relativity, I think you are way underestimating its beauty and scope. A physicist who is experienced in dealing with relativity will confirm that what I write is consistent with general relativity, though he will probably say I use a rather unusual angle to present general relativity. Cleon Teunissen 22:51, 31 Jan 2005 (UTC)

General relativity isn't newtonian

Within the GR section, it says: constant acceleration of space-time towards the center of the planet. This makes it sound like some real physical thing is moving, which it isn't. William M. Connolley 18:11, 31 Jan 2005 (UTC))

I have made sure not to write that the space-time is moving, I only wrote the space-time is accelerating. In physics, if you cannot measure something, nor any consequences of it, it is pointless to make statements about it. Space-time is transparent to motion, so I think the concept of a velocity of space-time is meaningless. The consequences of the acceleration of space-time are measurable: masses gravitate towards each other. I agree that in good old newtonian dynamics and good old euclidian space acceleration implies motion. However, general relativity isn't newtonian, and it isn't euclidian. Cleon Teunissen 09:15, 1 Feb 2005 (UTC)

Cleon Teunissen 11:15, 1 Feb 2005 (UTC) I certainly don't mean to imply that "since it's not euclid, anything goes". The criterium must be whether the axioms of the theory are followed through consistently. According to general relativity, when an object is in free fall, towards the center of a planet, then at every point that object is not accelerating with respect to its local space-time. According to general relativity, being in free fall towards the center of a planet is locally indistinguishable from uniform motion in zero-curvature space. The logical conseqence of the axioms of general relativity is that there is acceleration of space-time towards the center of a gravitating mass. Cleon Teunissen 11:15, 1 Feb 2005 (UTC)

General relativity isn't newtonian #2

Within the GR section, it says: constant acceleration of space-time towards the center of the planet. This makes it sound like some real physical thing is moving, which it isn't. William M. Connolley 18:11, 31 Jan 2005 (UTC))

According to general relativity, when two masses are orbiting each other they lose angular momentum due to radiation of gravitational waves. So what is carrying away that energy? In general relativity, space-time is categorized as being a part of the realm of real, energy-carrying physical things. Cleon Teunissen 14:41, 1 Feb 2005 (UTC)

Symmetry, special relativity and general relativity

According to general relativity, the reference frame that is co-moving with an observer who at some stage in her yourney is being accelerated by a mechanical force, can without ambiguity be distinguished from the reference frame that is co-moving with an observer who at no stage in his yourney is being accelerated by a mechanical force.

When calculations are performed, both the observers, performing the calculation in their own co-moving reference frame only, agree that the observer that at some stage in her yourney was being accelerated by a mechanical force has incurred more time dilation. (More time dilation means: less time has elapsed in the comoving reference frame.)
External link: The story of non-symmetric journeys, also known als 'the twin paradox'
Cleon Teunissen 10:22, 1 Feb 2005 (UTC)

GR - gravity not equivalent to acceleration + Why not "reaction force" versus "fictitious force"? + "non-contact" forces

GR - gravity, acceleration

With GR, the intensity of a gravitational field results in fixed time dialation, while acceleration results in a constantly changing time dialation, so there is a difference, but it requires an "outside" observer. For example, a person on earth could observe a clock in a non-orbiting rocket that is rising vertically (along earth's orbital path around the sun is good enough for "vertical") at a constant speed As the rocket increases it's distance from the earth, the intensity of the gravitational field is reduced, and the rocket's clock appears to speed up. In the second phase of the experiement, the rocket starts to accelerate holding it's altitude (following a path orbiting the earth), and the rocket's clock will steadily slow down as the speed of the rocket increases.

"reaction force"

For forces that are the result of inerital resistance to an applied force, why not call these reaction forces? Centrifugal force would be an exampleof a reaction force. Using the accelerating car example, the seat applies a force to the person in the car accelerating the person, and the person's body applies an equal and opposing "reactive" force against the seat, increasing the pressure and causing deformation at the point of contact.

"non-contact forces"

Other forces don't require physical contact. Gravity is one of these and is relative to mass. Electrical forces are relative to charge. Should electrical forces be considered "fictitious"? What about the nuclear strong and weak forces?

Jeffareid 21:18, 12 September 2007 (UTC)

1. You appear to be making the common mistake of thinking that coordinates have physical significance. If I understand you correctly, by "time dilation" you mean the ratio between coordinate time and proper time. However, this ratio is not a physical thing, but purely results from your choice of coordinate time - GR allows you to use any smooth and monotonic coordinate time you care to. If you have a metric where you and your neighbors have each have constant dilation, you can transform it to one in which everybody's time dilation change simply by applying a nonlinear substitution to the time coordinate. And it is a fundamental tenet of GR that descriptions that are related by (metric-preserving) coordinate transformation are physically identical. Your "outside observer" would have to observe not only phenomena in the physical world, but also differences in expression that (thus claims GR) have no physical reality.

2. The best reason not to call fictitious forces reaction forces is that "reaction force" already has a different meaning, namely the opposite end of an action-reaction pair according to Newton's third law. Sometimes people do call fictitious forces "reaction forces", which often results in confusion and misunderstanding - see the archives of Talk:centrifugal force for plenty of examples.

3. I don't get your point. Physical contact or the lack of it is not a defining feature for fictitious forces - in fact the very question of whether a force acts locally or at a distance makes sense only for real forces (which obey Newton's third law and always occur in pairs, such that you can ask whether the two sides of the pair are at the same place). A fictitious force involves only a single object and its relation to your coordinate system, so there is neither anything that can "contact" nor anything that can be "at a distance". The observation that hints (*) that gravity may be thought of as a fictitious force is not that it acts at a distance, but that the acceleration it causes a body to have (in the absence of other forces) does not depend on the mass (or any other intrinsic properties) of the body. Electromagnetic or nuclear forces do not have this property.

(*). This hint is of course not sufficient to deduce that gravity must be a fictitious force. A much stronger argument is the fact that the idea happens to work and agree with observation when worked out in detail, namely GR. –Henning Makholm 21:09, 13 September 2007 (UTC)

Removal of addendum

I've deleted the addendum by 97.66.28.156 (Talk) about fictitious force. It appears to contradict the discussion that precedes it, which is entirely accurate. In my view, "fictitious force" is a technical term, as defined in the article, and clearly present in the noninertial frame of the accelerating car. The addendum confuses it with a "feeling" by the car passenger. That is not a correct interpretation. Brews ohare (talk) 15:31, 14 May 2008 (UTC)

New category

I've now created a new category, Category:Fictitious forces, to include all articles about fictitious forces. Question: should gravity be in this category? -- The Anome (talk) 11:54, 15 May 2008 (UTC)

I would say yes. Because it occurs as a fictitious force in a prominent scientific theory. Taemyr (talk) 12:12, 15 May 2008 (UTC)

I've posted a link to here from Talk:Gravitation. Personally I wouldn't include it in the category. I don't know general relativity well enough to make a definitive statement, but graivty is certainly very different from the other current members of the category. Perhaps the category description could include a link to Introduction to general relativity? --PeR (talk) 13:18, 15 May 2008 (UTC)

I agree with Per. Gravity is not a fictitious force as you cannot transform it away globally using a coordinate transformation. This fact actually led Einstein to the idea that gravity generated by mass is a curvature in space-time which you cannot get rid off by coordinate transformations. Count Iblis (talk) 15:28, 15 May 2008 (UTC)

Curved spacetime is a coordinate transformation. You might want to say that you can not transform it away with a coordinate transformation that is independent of the objects that the force act on. Taemyr (talk) 16:02, 15 May 2008 (UTC)

Gravity is described by the Riemann tensor. If some of its components are nonzero in one frame then no matter what coordinate transformations you perform, you cannot get all the components of that tensor to become zero. Physically this corresponds to the fact that an observer in a free-falling box can still detect the effects of the gravitational field via tidal effects.

It seems to me that fictitious force must be defined as those forces that are purely an artifact of the chosen coordinate system. But that's equivalent to saying that a fictitious force field can be globally transformed away using a single coordinate transformation. Count Iblis (talk) 16:18, 15 May 2008 (UTC)

Some questions, what do the above argument look like if we assume a uniform gravity field? And do we always take tidal forces into account when constructing our models? Taemyr (talk) 16:48, 15 May 2008 (UTC)

I do not think adding gravity to Category:Fictitious forces will enhance understanding, nor will anyone look for it there. As for whether gravity is a fictitious force in the context of general relativity, the treatment of that question on Wikipedia will be defined by what the sources say, not by discussions like the one above. -- SCZenz (talk) 17:13, 15 May 2008 (UTC)

I agree: it looks like gravity definitely shouldn't be in the category, based on the discussion above. -- The Anome (talk) 20:56, 15 May 2008 (UTC)

Gravity (along with general relativity and the equivalence principle) NEEDS to be mentioned as something that blurs the distinction between fictitious and non-fictitious forces. I modified the "Gravity as a fictitious force" section to not be so apologetic about it. The section needs to be expanded in my opinion. It is fundamental.

108.7.244.101 (talk) 05:44, 27 July 2011 (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Fictitious force/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

The article presents the general mathematical derivation and then presents the rotating coordinate systems case. The latter is not a special case of the former and so it's confusing, absent further information. How is x_rot defined from x_in? How is the angular velocity vector omega determined from this change of coordinates? Without this information, the reader can't reproduce the calculations; calculations which should be only marginally more complcated than those presented in the general mathematical derivation section.

Last edited at 15:53, 17 October 2006 (UTC). Substituted at 20:33, 2 May 2016 (UTC)

Merge and redirect from Rotating reference frame

On 10 July, user:Brews ohare tagged the Rotating reference frame page with an RfD tag and asserted that "This article is a poorly described version of what is done better in the Fictitious force article". I've converted that to a {{mergeto}} tag since this appears to be a request to merge and redirect (or possibly just redirect) content here, not a nomination to delete a redirect.

I have no opinion yet on the proposal to merge/redirect. Rossami (talk) 21:17, 10 July 2008 (UTC)

I have revised Rotating reference frame to remove its obscurities. It now is an application of Fictitious force to the case of a rotating reference frame. I think that the article has value as a simple example that is more accessible than the general treatment in Fictitious force so I am removing the merger template. Brews ohare (talk) 16:57, 29 September 2008 (UTC)

Sounds like the afterimage effect

If it happens that there´s a fast change one can realize that he doesn´t just appercept but is superposed with imagination. If the change going on is to small this will not be realized. Only if the change is going on too fast or no change at all is going on for a long time.

91.19.40.170 (talk) 11:28, 1 March 2009 (UTC)

Changes in perception of centrifugal force

if a person lets out a tethered force on a rotating platform, he should soon note that the farther out on the platform the greater force in the tether is required. This should give him some indication that he is in a physical system that involves more than just the length of the tether. And if somebody told him that the force in the tether was related to the kinetic energy of motion of the tethered object, he might be able to deduce that he was on a rotating platform. But he wouldn't regard the force in the tether to be fictitious, Because it's a real measurable force and has the same reality as the force of gravity even if he doesn't have an explanation for it.WFPM (talk) 00:57, 28 February 2012 (UTC)

Is anything here actually in the B reference frame?

As I understand the point of this math, we are trying to reformulate the laws of motion in another reference frame. Obviously A is inertial, B is not. We have an object that can then be modeled in either frame. Because of this, I have a very hard time with parts like this:

${\frac {d\mathbf {v} _{\mathrm {B} }}{dt}}=\sum _{j=1}^{3}{\frac {dv_{j}}{dt}}\mathbf {u} _{j}+\sum _{j=1}^{3}v_{j}{\frac {d\mathbf {u} _{j}}{dt}}=\mathbf {a} _{\mathrm {B} }+\sum _{j=1}^{3}v_{j}{\frac {d\mathbf {u} _{j}}{dt}}.$

This equation implies the following. As far as I can tell, this is the only definition of this variable in the article.

$\mathbf {a} _{\mathrm {B} }=\sum _{j=1}^{3}{\frac {dv_{j}}{dt}}\mathbf {u} _{j}$

Am I just missing something? This acceleration is useless for modeling things in the B reference frame because it's converted (by means of the B unit vectors) into the A reference frame orientation. If you were going to model the motion of something in the B reference frame you would need $a_{j}=d^{2}x_{j}/dt^{2}$ , and nothing here provides that. There's not even an easy way to get it. Alan (talk) 18:22, 13 November 2012 (UTC)

Fictitious forces and illusions

I think one of the greatest problems in physics, especially today, is for people to mistake the difference between a real force and an apparent force, or a real parameter and a derived parameter. The concept of space-time curvature is fraught with the ability of the human mind to create illusions that contradict reality.

The mistake that is made with so-called fictitious forces seems to be substituting acceleration for force. An acceleration 'seems' to be observed and a force is implied. Basic engineering analyses will quickly reveal the cause of such distortions. With centrifugal forces, it becomes immediately apparent, with a little analysis, that in the case of someone swinging a bucket of water around his head, there is only one force, besides gravity, and that is an inward force along the rope toward the swinger, called centripetal force. There is no centrifugal force traveling outwardly along the rope.

The implication is that acceleration is causing a force rather than the other way around. In Newton's F = ma, the equation can be expressed mathematically as a = F/m, which makes sense mathematically but not in reality. An acceleration requires a force but a force is not dependent on an acceleration. Forces and masses are real but acceleration is a phenomenon observed by the human mind that has little meaning in reality.

We need to be clear about the difference between the reality that is there without humans and the quasi-reality the human mind introduces. Humans introduced the concept of time by observing the rotational period of the Earth and subdividing it into hours, minutes and seconds. That fabricated reality was introduced to F = ma as acceleration, a changing phenomenon that can be observed by the human mind but measured only by introducing the human invention of time.

When we observe motion using mathematics, we begin to introduce qualities to nature that are not there. For example, time cannot dilate in reality simply because there is no such phenomenon as time. Something is dilating, and if we look closer, without the math, it becomes obvious that the dilation is an illusion produced by the human mind. By transposing equations so that time becomes an independent parameter, the equation can be worked out so that time seems to dilate. In reality, that cannot happen.

I have no doubt that an explanation exists for what is worked out mathematically as time dilation and I think it needs serious investigation. I have the same lack of doubt that the answer will involve real forces and masses and their properties, not something worked out mathematically that is implausible.

In the same way, fictional forces are fictitious because they are distortions of the human mind. Objects in flight involving the Coriolis effect don't curve due to a force on them, they curve because the human mind is deluded into seeing the curvature and presuming a force is causing the curvature.

Space-time curvature is equally a distortion of the human mind. We have created 3-dimensional coordinate systems to measure space, and time to keep tract of events and moving objects. None of that exists in reality, but when we plot it mathematically, we build a case in our minds for time dilation and space-time curvature. — Preceding unsigned comment added by Gordoxyz (talk • contribs) 18:21, 12 July 2013 (UTC)

Focault pendulum doesn't prove rotation of the Earth

In the end of the "Detection of non-inertial reference frame" section, the article incorrectly says that the focault pendulum proves the rotation of the Earth. Suppose the Earth is not rotating and that the pendulum is going along a really thin elliptical path that is slow slightly elliptical that we can't tell with the naked eye that that it's not passing through the bottom position, then the fact that acceleration varies as the sin of the angle from the bottom rather than linearly combined with the noneuclidian geometry of a sphere making the circumference of any circle on a sphere be less than π times its diameter means the pendulum will still precess anyway if it's swings aren't perfectly linear. An observed rotational period of 24 hours or more is probably so long that that distance away from the bottom position the pendulum must pass in order to have that rate of precession is so slight that we can't tell with the naked eye that it's not passing through the bottom position.Blackbombchu (talk) 18:26, 25 September 2013 (UTC)

Name

Pseudo force is a much better name for this, and the page should be moved. Bumblebritches57 (talk) 17:51, 25 February 2015 (UTC)

Agree. "Pseudo", "inertial", "d'Alembert", etc. are all as equally technically correct as "fictitious", but "fictitious" too easily leads laity into thinking there's something not real about it all, which does them a disservice. 72.74.19.224 (talk) 14:02, 29 March 2015 (UTC)

Wrong information about fictitous forces

In § Detection of non-inertial reference frame, the article says an observer can tell whether or not they're in an accelerating frame of reference but that's not true. They would be unable to distinguish a rectilinear fictitious force from a gravitational field or a combination thereof. Since the gravitational constant is so small, any gravitational field the same strength as that at the surface of Earth would vary at an ever so slow rate with respect to position, to tiny a difference to distinguish it from a rectilinear fictitious force which would have a uniform force field according to Newtonian physics. Blackbombchu (talk) 15:54, 23 June 2015 (UTC)

Please change this entry to "apparent force"

Wouldn't it be better to encourage the use of the term "apparent force", which is well-used in literature, has the same definition, and is more apt?

"Fictitious" implies "doesn't exist" or "made-up". "Apparent" means "what you detect" without implying it's what's actually there.

"Apparent wind" is commonly used in sailing, and is perfectly apt. No sailer would ever talk about "pseudo-wind" or "fictitious wind" as he sets his sails to the apparent wind. Shouldn't physicists be at least as clear in use of terms as sailors? — Preceding unsigned comment added by Learjeff (talk • contribs) 17:46, 17 June 2014 (UTC)

Yes, I have been told many times that the forces I feel when I accelerate or break or turn when driving are fictitious - as in illusory - they are not, they are real. We have equivocation over the meaning of the word "fictitious" - in normal parlance it means illusory, not really there, a perceptual mistake... whereas in physics it means that the origin of a force is the accelerating inertial frame as opposed to mechanical interaction. People are thus misled by the word to believe that science tells us these forces are illusory. The use of "apparent" is less likely to mislead (as pointed out above) since it is (more) neutral with respect to ontology.Richwil (talk) 10:27, 17 August 2015 (UTC)

Rotating coordinate systems

The result of the derivation in 'Rotating coordinate systems' currently reads:

\mathbf {F} _{\mathrm {fict} }=-2m{\boldsymbol {\Omega }}\times \mathbf {v} _{\mathrm {B} }-m{\boldsymbol {\Omega }}\times ({\boldsymbol {\Omega }}\times \mathbf {x} _{\mathrm {B} })-m{\frac {d{\boldsymbol {\Omega }}}{dt}}\times \mathbf {x} _{\mathrm {B} }.

in which $\mathbf {x} _{\mathrm {B} }$ is the position vector for the particle/object in the rotating reference frame B (not A!). It is stated that the first term is the Coriolis force, the second term is the centrifugal force, and the third term is the Euler force.
Contrast the formulæ in this article with those on 'Rotating reference frame':

the Coriolis force: $\mathbf {F} _{\mathrm {Coriolis} }=-2m{\boldsymbol {\Omega }}\times \mathbf {v} _{\mathrm {r} }$

the centrifugal force: $\mathbf {F} _{\mathrm {centrifugal} }=-m{\boldsymbol {\Omega }}\times ({\boldsymbol {\Omega }}\times \mathbf {r} )$

and the Euler force: $\mathbf {F} _{\mathrm {Euler} }=-m{\frac {\mathrm {d} {\boldsymbol {\Omega }}}{\mathrm {d} t}}\times \mathbf {r}$

in which $\mathbf {r}$ is the position vector of the particle/object in the inertial reference frame A (not B!).
Although $\mathbf {r}$ and $\mathbf {x} _{\mathrm {B} }$ could be equal for some specific choices of the rotating reference frame B, it does not appear that they are generally equal, and I didn't see a clear restriction defined in this article.
—DIV (120.19.160.192 (talk) 14:23, 6 September 2016 (UTC))