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Rotation and fallacy of composition

Scientific discovery and discussion
GoSeigen
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Rotation and fallacy of composition

#278672

Postby GoSeigen » January 20th, 2020, 8:32 am

I've been reading a bit about rotation -- Newton's Bucket, centrifugal force, absolute rotation, etc -- and I am stunned by the apparent weakness of discussion around this topic. I am no expert, but to me centrifugal force is a completely unnecessary distraction, Neston's bucket seems to fill people with awe whereas I can't see what the fuss is about, and my view having done this small amount of reading is that a lot of what is written about rotation is classic fallacy of composition. What I mean is, rotation is intrinsically a property of a collection of things, it does not exist in the context of a single object (if such a thing exists).

Even the greats from Newton to Mach seem to gloss over certain aspects and miss the crux of the matter, which to me is this: if an observer is to observe an object which is rotating, there is already a collection of objects with relations to each other. At a very minimum there is the object rotating, which we could philosophically argue is an indivisible point of zero size, but secondly there is the so-called observer who is stated to also be rotating or at rest (as the case may be) -- and sure, we can assume that the observer is also an indivisible point of zero size -- but then thirdly, there must be the means of making the observation: how is that supposed to happen??

To my mind even in the simplest cases rotation always involves at least two objects and as such it is a collective property of a group of objects which has no meaning otherwise. Now probably one would have to prove that the property of the collection does not extend to the individual but I really don't have a problem with the hypothesis. The thing that surprises me is that this aspect is not even touched upon in what I have seen written.

The treatment of Neston's bucket in particular seems ludicrous to me. The water's curvature appears to have little to do with detection of rotation per se and a lot to do with gravity, fluids and the fact that the bucket forms a solid barrier to its liquid contents. A much nicer illustration of the effect of rotation would seem to be our galaxy itself, which is rotating under its own gravitational forces with little obvious external interference (forces). Do we see the stars piling up at the edge of the galaxy? No: the "piling up" of the water has to do with matters other than the water's rotation.

Finally I am amazed at how often reference is made to centrifugal force to explain these things when there is no centrifugal force at work. In rotating (and harmonic) systems the net forces are always centripetal: that seems blindingly obvious to me but there are many articles on Wikipedia, for example which talk about Centrifugal Force almost as if it is a real phenomenon! It's almost like we are in a medieval period where, just because we are on a steadily rotating planet, we think we should arrange our maths to work most easily from a rotating frames perspective! Why do maths from two different frames of reference: one of them: rotation at constant speed is a vanishingly rare case anyway so it seems to me to just be an unnecessary complication and distraction.

Sorry for the ramble, but just thought I should write my impressions down somewhere.

EDIT -- some links:

https://en.wikipedia.org/wiki/Absolute_rotation
https://en.wikipedia.org/wiki/Bucket_argument
https://en.wikipedia.org/wiki/Fallacy_of_composition


GS

GoSeigen
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Re: Rotation and fallacy of composition

#278699

Postby GoSeigen » January 20th, 2020, 10:28 am

In arguably the most useful location of all for making use of the so-called centrifugal force, i.e. on earth, it turns out the force is so small in most practical cases that it can simply be ignored. What a waste of time! The wikipedia article on centrifugal force which explains the above is so bad that I can only shake my head:

https://en.wikipedia.org/wiki/Centrifugal_force

For starters, why does it give such prominence to a "fictitious force"? In reality this is a mere abstract, mathematical simplification available only in extremely rare circumstances, generally hypothetical ones! Yet this bizarre concept of centrifugal force seems to dominate people's thinking about rotation...

GS

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Re: Rotation and fallacy of composition

#278721

Postby SalvorHardin » January 20th, 2020, 11:59 am

GoSeigen wrote:Finally I am amazed at how often reference is made to centrifugal force to explain these things when there is no centrifugal force at work. In rotating (and harmonic) systems the net forces are always centripetal: that seems blindingly obvious to me but there are many articles on Wikipedia, for example which talk about Centrifugal Force almost as if it is a real phenomenon! It's almost like we are in a medieval period where, just because we are on a steadily rotating planet, we think we should arrange our maths to work most easily from a rotating frames perspective! Why do maths from two different frames of reference: one of them: rotation at constant speed is a vanishingly rare case anyway so it seems to me to just be an unnecessary complication and distraction.

Sorry for the ramble, but just thought I should write my impressions down somewhere.

Centrifugal force is a real phenomenon. It exists because the laws of physics differ somewhat for an observer who accelerating when compared to a second observer who is not accelerating. It's tricky because you're moving away from Newtonian physics and entering the realm of Einstein's physics :D

The "real" force exerted in a rotating system is Centripetal Force, which is constantly exerted towards the centre of rotation in order to force the object to move in a circle (or other form of closed curve such as an ellipse) otherwise it will revert to moving in a straight line due to "inertia" aka Newton's First Law of Motion; "an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force".

https://en.wikipedia.org/wiki/Centripetal_force

Consider an object on a piece of string being rotated about a fixed point. Centrifugal Force is "fictional" to the typical external observer because if you remove the Centripetal Force the object does not move away from the centre of rotation along the line of the string. Instead it moves away at a tangent to the circle formed by its rotation (i.e. at right angles to the string). The problem is that the external observer sees things differently to anyone who is on the rotating object (or on the string). To an observer who is in the rotating system, centrifugal force is real.

We're now leaving Newtonian mechanics. The key term here is "reference frame"; a system of co-ordinates with reference points so that you can make measurements (e.g. X, Y and Z-axis plus time measurements). Newton thought that there was only one type of reference frame ("absolute space"). The problem is that there are two types of reference frame (Einstein's "spacetime" is the other one) and the laws of physics change if you are measuring from an accelerating reference frame. This article gives a good explanation:

""Centripetal force and centrifugal force are really the exact same force, just in opposite directions because they're experienced from different frames of reference. If you are observing a rotating system from the outside, you see an inward centripetal force acting to constrain the rotating body to a circular path. However, if you are part of the rotating system, you experience an apparent centrifugal force pushing you away from the center of the circle, even though what you are actually feeling is the inward centripetal force that is keeping you from literally going off on a tangent."

https://www.livescience.com/52488-centr ... orces.html

Edit: This link is a pretty good video explaining the difference between reference frames

https://www.youtube.com/watch?v=wD7C4V9smG4

Rotating and oscillating motions take place in "non inertial reference frames" (frames which are accelerating), but the typical observer in Newtonian mechanics is in an inertial reference frame (not accelerating). The difference between the two frames is trivial in the everyday world, but becomes quite noticeable once the effects of special relativity and general relativity come into play. The Newtonian laws of physics apply to inertial reference frames; in non-inertial reference frames we move into Einstein's Special and General Relativity. These differences are so small in everyday life that they are not noticeable.

For example, in Newtonian physics all observers agree as to the order in which a series of events take place at different times. But an observer in an accelerating reference frame (e.g. on a rotating object, in an accelerating spaceship) can disagree as to the order in which these events take place.

https://en.wikipedia.org/wiki/Non-inert ... ence_frame

https://en.wikipedia.org/wiki/Spacetime

Hope this helps. It's been great revision for me, digging out physics I haven't used for some years :D

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Re: Rotation and fallacy of composition

#278767

Postby GoSeigen » January 20th, 2020, 3:52 pm

SalvorHardin wrote:Hope this helps. It's been great revision for me, digging out physics I haven't used for some years :D


Sadly doesn't help at all, largely quoting or referencing the nonsense I was referring to in the OP! A couple of points:

1. "Centrifugal force" as I referred to it long predates Einstein and relativity as a concept. What I am referring to is its widespread use as an explanation of Newtonian physics, not Einsteinian, e.g. cars turning corners, stones on strings etc. Einstein is a red herring. C.F. has IMO no place in a sensible discussion of Newtonian physics (save in some extremely limited contexts with rather artificial constraints).

2. Rotating and oscillating motions do NOT take place in "non inertial reference frames" [as asserted by SH]. They simply take place. The observation may be thought to be made within such a reference frame. But the actual rotation or oscillation is occurring in exactly the same frame as everything else in the universe.



Seems SH is a believer in centrifugal force as a useful concept. I'd invite him or anyone else interested to state exactly what use it serves and what they perceive as its limitations. I refer to the use of "centrifugal force" as claimed to exist in a rotating frame of reference and exactly equalling the centripetal force causing the circular motion. Maybe address this proposition: "Centrifugal Force is not a (Newtonian) force at all but something else entirely."



IMV the problem is the word force in the phrase "centrifugal force". People don't really mean force. They mean something woolly like "movement" or "instability".


GS

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Re: Rotation and fallacy of composition

#278775

Postby SalvorHardin » January 20th, 2020, 4:31 pm

GoSeigen wrote:Seems SH is a believer in centrifugal force as a useful concept. I'd invite him or anyone else interested to state exactly what use it serves and what they perceive as its limitations. I refer to the use of "centrifugal force" as claimed to exist in a rotating frame of reference and exactly equalling the centripetal force causing the circular motion. Maybe address this proposition: "Centrifugal Force is not a (Newtonian) force at all but something else entirely."

Physics has progressed a bit beyond Newton (and Galileo which is where relativity started).

The whole inertial vs. non-inertial frame of reference stuff is a major building block of relativity. Observers in a non-inertial reference frame can see the same event happen quite differently from that seen by observers in an inertial reference frame.

Centrifugal force is a consequence of being in a non-inertial frame of reference. People in a car that takes a corner at speed feel a centrifugal force pushing them away from the corner. It's the same force viewed as happening in a different direction because of the observers having different frames of reference.

If you don't want to consider reference frames, think of Newton's third law. The centripetal force creates an equal but opposite centrifugal force as a reaction. It's close enough (but not quite right).

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Re: Rotation and fallacy of composition

#278794

Postby TheMotorcycleBoy » January 20th, 2020, 5:28 pm

FWIW I don't find either centripetal or centrifugal force at all useful. They are arbitary ideas - to my mind.

The only *real* forces in this debate are either gravity (planets, satellite), tension* (pendulum) or the "normal" force (people in cars taking corners*).

[*] The normal force ultimately comes from the friction between one's tyres and the road tyres. Which on further decomposition is electro-static in nature, I think. i.e. repulsive forces between electrons between the rubber and the tarmac. But that's probably a good point to park my extensive knowledge of quantum mechanics.

:lol:

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Re: Rotation and fallacy of composition

#278856

Postby 9873210 » January 21st, 2020, 3:00 am

The difference between a non-rotating and rotating frame of reference is simply a change in coordinate systems. In cylindrical coordinates it is a change from (t,r,θ,z) to (t,r,θ-ωt,z). If you have any mathematical expression of a physical law in one coordinate system you can express exactly the same thing in the other by substituting (baring certain unfortunate mathematical events, such as divide by zero, which don't occur here). In this case simply set θ = θ'-ωt .

Since the transformed equations are mathematically equivalent you cannot tell them apart experimentally, any observation will either agree with both representation or disagree with both. The choice between them is arbitrary. There is no physical basis to say one is "real" and the other isn't.

You could use a philosophical principle like Occam's Razor and choose the simpler one. But which is simpler? In everyday life the rotating (and moving in other directions as well) reference frame of the Earth's surface is hugely simpler. In most cases the centrifugal force is negligible, but not in all cases. Certain people, like long range artillery layers and meteorologist, need to take account of centrifugal force, which is just as real in the rotating frame as inertia is in a non-rotating frame.

Notice that gun laying and meteorology can be done in a non-rotating frame, but they are hugely more difficult in that frame because more of the coordinates are changing, and the magnitudes of the changes are large (The Earth's equator rotates at about 1666 km/h, London is moving at 1040 km/h).

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Re: Rotation and fallacy of composition

#278884

Postby GoSeigen » January 21st, 2020, 9:04 am

TheMotorcycleBoy wrote:FWIW I don't find either centripetal or centrifugal force at all useful. They are arbitary ideas - to my mind.


Perhaps it's another of those British vs American things? Americans seem to accept centrifugal force uncritically; British on the whole reject it?

GS

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Re: Rotation and fallacy of composition

#278890

Postby GoSeigen » January 21st, 2020, 9:19 am

9873210 wrote:You could use a philosophical principle like Occam's Razor and choose the simpler one. But which is simpler? In everyday life the rotating (and moving in other directions as well) reference frame of the Earth's surface is hugely simpler.


This is simply untrue. It is only simpler because in most cases we simply ignore the "centrifugal force". The cases where it is not ignored are so trivial as to be laughable. Perhaps someone can show how the following is more simple in from the rotating reference frame:

-There is a large level rotating plane platform. 30m from the axis a car is standing. In the rotating frame it is stationary because the friction of the wheels equals the "centifugal force", but where is the observer in this rotating frame situated?

-An occupant of the car places a marble on the platform (with negligible friction between the marble and platform) beside the car and releases it. In this rotating frame what is the equation of the path of the marble to the observer in the rotating frame? (The car continues to be stationary presumably.)



( Note that in the more complex, non-rotating frame, the marble moves in a straight line tangential to the car's movement when released. The car continues in a neat circle. Really tricky stuff! )


GS

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Re: Rotation and fallacy of composition

#279066

Postby 9873210 » January 21st, 2020, 11:04 pm

GoSeigen wrote:
9873210 wrote:You could use a philosophical principle like Occam's Razor and choose the simpler one. But which is simpler? In everyday life the rotating (and moving in other directions as well) reference frame of the Earth's surface is hugely simpler.


This is simply untrue. It is only simpler because in most cases we simply ignore the "centrifugal force". The cases where it is not ignored are so trivial as to be laughable. Perhaps someone can show how the following is more simple in from the rotating reference frame:


I am referring specifically to the rotating frame of the Earth's surface. This frame is simpler because in this frame most things we care about are stationary or moving slowly. As an added bonus the centrifugal force is often negligible. But even when centrifugal force is non-negligible it's still simpler.

We use frames of reference for all sorts of things that are not conservation of momentum physics experiments. In the non-inertial frame of Earth's surface you can locate your house with a fixed latitude, longitude and (implicit or explicit) altitude, or some equivalent such as a grid reference or street address. In any inertial frame your house's location is a function of time, and it is moving quite fast most of the time.

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Re: Rotation and fallacy of composition

#279106

Postby XFool » January 22nd, 2020, 8:52 am

TheMotorcycleBoy wrote:FWIW I don't find either centripetal or centrifugal force at all useful. They are arbitary ideas - to my mind.

Uh?

You don't think "centripetal force" at all useful? Does that mean you don't believe the Earth orbits the Sun and the Moon orbits the Earth? If you do (I assume you do) then how do you explain the observed facts? Newton explained it by the 'force of gravity' - acting centripetally.

As for the troublesome "centrifugal force", I too was told it was a "fictitious force". It feels real enough if you experience it, but it is a 'force' only experienced by those who are in a rotating frame, observers outside that frame have a different take on it.

Mind you, ISTM that Einstein went on to take a similar approach to the 'force of gravity' but that's another story.

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Re: Rotation and fallacy of composition

#279235

Postby TheMotorcycleBoy » January 22nd, 2020, 5:09 pm

XFool wrote:
TheMotorcycleBoy wrote:FWIW I don't find either centripetal or centrifugal force at all useful. They are arbitary ideas - to my mind.

Uh?

You don't think "centripetal force" at all useful? Does that mean you don't believe the Earth orbits the Sun and the Moon orbits the Earth? If you do (I assume you do) then how do you explain the observed facts? Newton explained it by the 'force of gravity' - acting centripetally.

As for the troublesome "centrifugal force", I too was told it was a "fictitious force". It feels real enough if you experience it, but it is a 'force' only experienced by those who are in a rotating frame, observers outside that frame have a different take on it.

Mind you, ISTM that Einstein went on to take a similar approach to the 'force of gravity' but that's another story.

Sorry, yes of course centripetal force is conceptual term for the force to the centre. By arbitary I just meant it's not a primary force in the same as gravity, or electro-magnetic/static, weak/strong force.

GoSeigen wrote:
TheMotorcycleBoy wrote:FWIW I don't find either centripetal or centrifugal force at all useful. They are arbitary ideas - to my mind.


Perhaps it's another of those British vs American things? Americans seem to accept centrifugal force uncritically; British on the whole reject it?

GS

Dunno. Generally centrifugal force is a crock. In centrifuge there aint no force pushing the particles *away* from the centre in a radial direction. The particles are acted on by a normal force from the vessel's walls (electromagnetic - i.e. electrostatic repulsion stops the particles smashing their way through the vessel wall), and they (the particles) have an instantaneous velocity whose vector forms a tangent to the point of the vessels circumference where the particle resides.

The particle goes around in a circle while this state is maintained (i.e. velocity of the particle) and there is normal (yes centripetal) force *towards* the centre. Yo, of course the particle is accelerating toward the centre.

(Strictly speaking there are other forces acting on the particle in centrifuge explaining it's motion, i.e. that tangential velocity I mentioned earlier. Those are explained, typically by fluid mechanics - shear/viscosity. Imagine how a centrifuge, starts spinning. All the fluid is at rest, but the vessel is spinning, the frictional forces tween the vessel wall act on the neighbouring particles gradually effecting those ones moving closer and closer to the centre etc. etc. No magical centrifugal force.)

Matt


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