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Centrifugal force from GR perspective

  1. Nov 15, 2004 #1

    Chi Meson

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    I got this from Wikipedia (under the definition of centrifugal force):
    I need some clarification here. I had understood that the "ficticious forces" of centrifugal and coriolis were "inertial effects," and that with GR the gravitational force was also an inertial effect. The Wikipedia definition contradicts this. This messes with my head.

    So, before I start digging through my old Spacetime Physics text again, is Wikipedia correct here: does Centrifugal become real while gravity becomes ficticious? [smiley:puking:]
     
  2. jcsd
  3. Nov 15, 2004 #2

    NateTG

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    This isn't my strong suit, so don't take this as gospel truth. Moreover, as far as I can recall, the coriolis

    That said, from a GR perspective gravity bends space-time rather than directly acting as a force on objects, as a consequence, what would be considered an intertial reference with a gravitational field in Newtonian mechanics is considered an accelerated frame of reference in GR.

    In that sense, both gravity in GR and the centrifugal force are 'ficticious' forces that are the result of an accelerated reference frame rather than some sort of 'force interaction'.

    It's important to realize that describing forces as 'real' or 'ficticious' is primarily an interpretation issue, and is usually not an important distinction in physics. Since GR does not treat accelerated reference frames as 'unnatural' in the same way that Newtonian mechanics does, and there is no 'preferred' frame of reference GR, AFAIK, does not make a distinction between so-called real or ficticious forces.
     
  4. Nov 15, 2004 #3

    DW

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    You are correct. Wikipedia is wrong. It wouldn't be the first time. In general relativity a real force i.e. four-vector force can not be transformed away. The force of gravity can be locally transformed away simply by going transforming to a free fall frame so you can tell right away that it is not a real force. The gravitational force is the same thing as an inertial force and in relativity is given by affine connections, the Cristoffel symbols of the second kind. Those connections vanish according to local free fall frames. To better understand how fictitious forces such as Centrifugal etc are gravitational consider the metric of special relativity as there is no gravitational sources for that metric. Simply transform coordinates to that of a frame with spin so that the metric becomes equation 6.3.23 at
    http://www.geocities.com/zcphysicsms/chap6.htm
    An exact calculation of geodesic motion for a test particle according to these coordinates results in the coordinate acceleration of equation 6.3.31. From that one can immediately read off the Coriolis, Centrifugal, and transverse forces 6.3.33. Now since the test particle is in free fall in a spacetime that has NO gravitational sources, you must realise that the forces reckoned to be acting on the particle according to the spinning frame observer absolutely must be fictitious. There is nothing in the spacetime to put a force on it at all. However, these fictitious forces are a result of geodesic motion according to the spin frame observer so he considers them to be the result of a gravitational force. You see, the gravitational force and the inertial or fictitious forces acting on a particle are completely equivalent in general relativity. They are the forces of affine connection.
     
    Last edited by a moderator: Nov 18, 2004
  5. Nov 15, 2004 #4

    jcsd

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    To be honest this article isn't that great. Newytonian physics is invaraint under a Galilean transformation and as such assumes no universal reference frame, only a special set of reference frames where Newton's laws of motion apply and it givese us no way of deteriming such a frame. The theory of special relativty keeps this asusmption, but extends it so that the equations of Maxwell are also invaraint in inertial frames. The gernarl theory formulate sphysics in a frame invaraint manner.

    Gravitaional and inertial forces are treated with equality in GR, so you either say they are both 'real' or both 'ficticious'.
     
  6. Nov 16, 2004 #5

    Chi Meson

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    This is how I understood it (not that I really understand it). Thank you all. Who should tell Wikepedia about their error?
     
  7. Nov 16, 2004 #6
    Wikipedia is a user made encyclopedia, anyone can make or edit articles. If you think an article is incorrect or incomplete you can edit it yourself. So go ahead!
     
  8. Nov 16, 2004 #7
    That article doesn't make a lot of sense.
    You are correct. It is best to refer to the Coriolis force and the centrifugal force as an "inertial force" since it is misleading to think of them otherwise, especially in GR. To Einstein inertial forces were "real". Einstein argued that a uniform gravitational field cannot be distinguished from a uniformly accelerating frame of reference. A similar thing holds for all non-inertial frames. One is therefore in no position to claim that the Coriolis force is real and fictitious fake or gravity reak and Coriolis fictitious. It is best to simply call them "inertial forces."

    Einstein showed that it was possible to generate coriolis and centripetal forces using finite distributions of matter. In particular he used a hollow spherical shell which was rotating. An observer at rest outside and far away in free-fall is in an inertial frame of reference. An observer inside the shell, where the spacetime is flat, who is in free-fall is also in an inertial frame. However the inside observer is rotating with respect to the outside observer. If he wants to be at rest relative to the outside observer then he must choose a non-inertial frame. In particular he must choose one that is rotating with respect to his inertial frame. Hence the Coriolis force can be thought of as a gravitational force.

    Einstein commented on the Coriolis force in the February 17, 1921 issue of Nature
    Other people have commented on inertial forces too. E.g. A.P. French did in his mechanics text, i.e. from Newtonian Mechanics, A.P. French, The M.I.T. Introductory Physics Series, W.W. Norton Pub. , (1971) , page 499.
    It would be incorrect to think of inertial forces as "fictitious" and 4-forces as "real". It would go against the idea of GR in fact. It would imply that there are special frames of reference and there are no special frames of reference in GR.

    Pete
    [/quote]
     
  9. Nov 17, 2004 #8
    I have a question unrelated to the above discussion:-how can an 'inertial' force have a quantum?What does it really mean?
     
  10. Nov 17, 2004 #9

    selfAdjoint

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    David, calm down. You have an excellent site, and I admire your work. But nobody likes flame wars here. Roll with the punches and help us out.

    BTW, I am not the guy who deletes your posts, but I value your contributions here too much too see you banned for behavior.
     
  11. Nov 17, 2004 #10

    Tom Mattson

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    And DW has, in fact, racked up warning points for his recent outbursts. I think that he is perhaps not aware of it because he has elected not to receive private messages (which is why we are in the unfortunate situation of having to deal with this in a science thread). If he keeps it up, he most certainly will find himself banned temporarily, because there is a limit to the number of warning points a member is allowed to have.

    DW, why do you carry on like this?

    His name is Tom Mattson.
     
  12. Nov 18, 2004 #11

    Garth

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    Being wary of jumping into a "flame fight" nevertheless I would like to point out that actually this question is right on the subject of this thread.

    There are different ways of dealing with 'objects' in four dimensions, as MTW very clearly spell out in the box 3.2, page 76, in 'Gravitation'.
    1. "Geometric language" favoured by MTW
    2. “Coordinate language” favoured by Weinberg (G&C); and it is possible also to use
    3. “Coordinate-Based Geometric Language”.

    After reading these and other earlier posts, am I not correct in concluding that DW will only allow the first and Pete the second?

    Geometric language is the fully 4 dimensional “spacetime” perspective that is not frame dependent. In this language the equation of four-momentum is fundamental, complete with mass and not rest mass, fictitious inertial forces and real four-forces.

    Coordinate language requires a frame of reference, the observer’s, a basis tetrad, or axes, relative to which measurements are made. The mass of a body increases with its relative velocity, as it acquires ‘kinetic energy’, and therefore it may be said to have “relativistic mass”. Inertial forces can do work (fall off a cliff and you will hurt yourself!) and therefore may be thought of as real.

    It might be thought more ‘pure’ to use geometric language, however as observers looking out onto the universe we are undoubtedly in a ‘preferred’ frame of reference – our own (!) – and so coordinate language is also perfectly appropriate.

    It is a shame that these different perspectives are not equally recognised as being equally valid in their own right allowing a decent discussion to ensue.

    Returning to gptejms question – The problem with the fully geometric language in relating GR to QM in the pursuit of a Quantum Gravity is that the most significant “fictitious” inertial force is of course gravity itself. If gravity is truly fictitious then there will be no graviton to carry it.

    As the electro-magnetic, the weak and the strong forces are united in the GUT, so perhaps the situation is that all the existing 'real' forces are already united and nobody has recognised the fact!!

    Garth
     
    Last edited: Nov 18, 2004
  13. Nov 18, 2004 #12

    Chi Meson

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    OK. I teach HS physics, and so I only barely get into SR and GR with my AP class. Bringing up tensors, transformations, and distributions is way beyond the scope of what I need to teach, and sadly also beyond what I remember from long ago.

    But I want to not say anything "wrong" as I simplify the initial steps into physics for my students:

    I take the adamant potsition that, from a Newtonian point of view, the centripetal force is not a force but the effect of inertia and the lack of a centripetal force (no argumants there).

    I admit to my students that, when they get to GR, then they will see that gravity is also an inertial effect, so therefore if you call centrifugal a ficticious force, then gravity must also be ficticious.

    What I pick up from this thread, is that ficticious vs. real is a matter of semantics, and therefore if gravity is real then centrifugal is a real force. But the point made by pmb is to refer to this group as "inertial forces" which are different from (what to call them?) "4-forces."

    This still leaves the problem that when living in a Newtonian world, the inertial forces do not satisfy the definition of "force" according to Newton's Laws. For the time being, I'm going to continue calleing them "inertial effects" with the asterisk that, when the student gets to advanced physics, there will be changes in definitions, noting that the problem lies more with the language than with the physics.

    I would be interested to know if anyone sees a glaring problem with this treatment of the "problem." Remember, I teach high-school, and only a tiny fraction of my students will become engineers or physicists.
     
  14. Nov 18, 2004 #13

    Garth

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    Keep up the good work Chi Meson! High School is where the vision is either caught or lost; behind every genius there's a teacher who inspired them.

    My post about the different "languages" used in SR/GR, basically geometric or coordinate language, is rather more than just semantics. I believe it is all to do with the perspective one can adopt in order to conceptually model physical reality.

    The 4-force, geometric language, is coordinate free. Therefore the 3D of space and 1D of time become a 'block' 4D spacetime. Past present and future lose their different meanings and everything seems set in 'concrete'. There are no absolute membranes of simultaneity of 'the present moment' dividing past from future; rather simultaneity is relative to each observer. The invariants of this world are the spacetime interval between two events, the mass (the norm or length of the energy-momentum vector) of a particle and the speed of light. It is the world introduced to us by Special Relativity and developed by General Relativity. In GR the inertial forces may be transformed away and are seen to be fictitious, including as we have said, gravity. Real 4-forces, such as that produced by an external force accelerating a spacecraft have the interesting property that they do not increase the norm of the 4-momentum vector but rather rotate it in energy-momentum space. Actually the total energy of the spacecraft increases, as does its normal 3-momentum, but when combined in the energy-momentum vector the effect of the signature of the metric is that one is subtracted from the other and the resultant 4-energy-momentum vector is constant in length.

    However it is a world that has defied unification with QM in a Quantum Gravity. It is also a world that we manifestly do not experience, for we are set in a particular frame of reference and observe the world from it. We experience inertial forces, be it the ground supporting us against gravity or the centripetal force keeping us on the roundabout. They are real to us.

    The understandings of SR and GR are useful in that they allow us to transform from one observer to another and predict the effects of gravitational fields, but their perspective may have no reality beyond this.

    Personally I like to think both languages describe real viewpoints of view and it is a matter of perspective as to which one you find most convenient to use.

    I hope this helps and not confuses!

    Garth
     
  15. Nov 18, 2004 #14
    I'm sure you're resting easy Tom since there is nothing that you can be sued. As everyone knows, as fact, this is a private forum with a moderator. A moderator is not defined as a person who deletes posts that dw does not like.

    Pete
     
  16. Nov 18, 2004 #15

    pervect

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    I also got it strongly hammered into me in High School that centrifugal forces weren't real. So you are doing the standard thing there. Though as I look back on the issue, I'm not sure why this concept was stressed so much and so strongly.

    I've come to view a centrifugal force as a "generalized force". I'm not sure if giving that idea to HS students would be a good idea, though. The basis of this statement is the Lagrangian formulation of mechanics. (You could probably also do this with the principle of least action). Without Lagrangian mechanics, it's not clear that the students would understand the terminology.

    I think the best thing to do, on the overall, is to stress that centrifugal force is not a force in Newtonian mechanics. By making the statement specific to Newtonian mechanics, you leave the door open for them being called forces in other versions of mechanics. But you don't have to go in to details, in fact doing so would be outside the scope of your course.
     
  17. Nov 21, 2004 #16

    Andrew Mason

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    This is quite an interesting discussion.

    It seems to me that there is a real centrifugal force that is the 'reaction' to centripetal force. This is illustrated by a cord with a weight attached to the end through a piece of pipe and another weight at the top that is whipped around in a circle. The first (down) weight provides the centripetal force that keeps the circling mass from flying away. The force that keeps that mass from falling down through the pipe is the centrifugal force - resulting from the inertia of the circling mass. (It is not responsible for the circling mass flying away when the cord is cut. That is due to the cessation of the centripetal force).

    With gravity, the centrifugal force seems to disappear for an orbiting body. While the astronaut on the training centrifuge feels a gut crushing feeling, the orbiting astronaut experiences no such feeling. Unlike the roller coaster, the orbiting object cannot flee its orbital path without adding energy: the orbiting mass does not have a natural tendency to flee the center of rotation.

    At least I thought this was the case. Astro-physicist Marek Abramowicz from Sweden seems to think otherwise. See:
    http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1990MNRAS.245..733A

    Parts of this paper are very readable and provide several thought experiments to provide examples. I must confess, however, that I don't really understand his concept of centrifugal force in a gravitational field.

    AM
     
    Last edited: Nov 21, 2004
  18. Nov 22, 2004 #17

    krab

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    Kudos from me too.
    Unfortunately there are HS teachers who know just enough physics to be dangerous.
    Technically, this is correct. But keeping in mind that people already live in a "world" (not "Newtonian"), and have developed an understanding for the word "force", I find it kind of presumptuous to tell them that what they think of as a real force is in fact fictitious. That might not be clear, so let me give an example. A student says that he was cornering in a car and centrifugal effect caused his head to hit the side window. The HS physics teacher (not you, Chi Meson) says "No, this is wrong wrong wrong. There is no such thing as centrifugal force; you must observe from an inertial frame and then you will see that the car window came up and hit you on the side of the head." Do you think that the student will be impressed with the wonderful world of physics? I think not. So I think "inertial" is vastly preferable to "fictitious"; everyone knows that "fictitious" means "not real", but "inertial" would be a new adjective that a student can get a feeling for by studying physics further.
     
  19. Nov 22, 2004 #18

    Chi Meson

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    I, uhh, I actually do say that. I do avoid the word "ficticious" though. I am adamant about this because the notion of centrifugal force confuses the idea of Newtonian force. Too many are already confused. The simple fact that there is NO object that pulls outward on a revolving object means that the 3rd law (which has just been learned) is violated.
    Actually, most of my students are most fascinated by this part of my lecture. It's the presentation that makes it good.
    And I agree with you there. I think this is the "way out" of the conundrum.
     
  20. Nov 22, 2004 #19

    Chi Meson

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    I personally get annoyed with it because it is the one thing that most people "know" about physics before they take the class, and it's wrong. even though it may be considered a force from a GR perspective, that is still not where the students are coming from. Centrifugal force, as it is misunderstood by the general public, does not satisfy any definition of force. Then they refuse to correct it. Ask any mentor how annoying that is! (See TD forum).

    Understanding the centrifugal effect is one of the more satisfying moments of conceptual synthesis in HS physics. Allowing a watered down GR version of centrifugal as a force does impede the understanding of Newtionan force.

    I I again agree with you all that those few who continue with physics should not have any doors closed. NEarly every day I say at one point "anyone who goes into advanced physics will find that...etc.etc." But I feel very strongly that students must learn Newtonian correctly before moving on.
     
  21. Nov 22, 2004 #20

    Chi Meson

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    Here is another wrinkle. The reaction force is actually another centripetal force. No object (from Newtonian perspective) can be the "center" of a circle while pulling on an other object that revolves around it (think earth-moon). The "central" object also moves in a smaller epi-circle. Even if the object is much larger, there will still be a theoretical radius of revolution (sort of like the earth's theoretical acceleration toward a dropped ball).

    Thanks again to everyone. I am enjoying this thread; it has been very helpful to me.
     
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