The title of this thread is taken from the 1952 paper by Professor D.W.Sciama. Having just spent the lunch-hour reading it, I have a question. (I accept that I should go and do some more reading to find the answer myself, but life is short and my desire to know is strong.) To what degree of accuracy are we sure that the inertia of a body is always the same with respect to a force coming from any direction? Given that the Cosmic Microwave Background hints at areas of slightly lower mass density in the early universe, and the recent identification of large voids within which no galaxies exist might it be possible to detect a slightly different value of inertia with respect to those directions? Obviously such an effect must be extremely small otherwise all sorts of dynamic measurements would have revealed it long ago.
This is a bit of a trick question. We can safely say mass and inertia are interchangeable units of measure, and all observations indicate they behave consistent with their predicted gravitational interactions [also proportionate to mass]. No observations suggest any variance between these relationships,
That's a great paper. The ideas are so neat that I find it quite disturbing that GR does not reduce to it as an approximation. I think we know that the effects of inertia, both with respect to linear acceleration and rotation, are isotropic to very high accuracy, mainly from tests primarily designed to test the equivalence principle. I get various interesting hits from a search on keywords such as "inertia isotropy", especially associated with name "Drever", but so far I can't find anything I can read in full without a subscription. You can of course have coordinate systems in which lots of things such as the speed of light are NOT isotropic, but the overall effect when the coordinate mass, distance and so on are all taken into account cancels out to make the result isotropic in any local frame. It is of course theoretically possible (as in the Sciama model) that if you choose an arbitrary coordinate system but calculate the inertia in that system by some Mach's principle scheme, you will find that the inertia appears to be isotropic in the local frame simply because the relevant factors about the distribution of matter and ruler sizes etc. all balance out or remain scalar in a free-falling frame. I think Brans Dicke theory may work like that. However, the standard theory of space and time at the moment is General Relativity, which does not work in this way.
If inertia is anisotropic, so is the propagation of light. It is not difficult to show that there exists a relation between the convention of a simultaneity definition and the isotropic and anisotropic propagation of light. Only the Einstein simultaneity definition leads to an isotropic propagation of light, whereas other alternative simultaneity definitions ([itex]\epsilon[/itex]-simultaneity, [itex]\epsilon \neq 1/2[/itex]) lead to anisotropic propagation of light. So, isn't an isotropic inertia a consequence of the conventional choice of a definition of simultaneity in special relativity? (I have no access to that paper, but it would be great if someone could send it to me per email)
A translation of Einstein's 1905 paper "Does the inertia of a body depend upon its energy content" ends with the sentence "If the theory corresponds to the facts, radiation conveys inertia between the emitting and absorbing bodies." Now I shall introduce a hand-waving argument of some magnitude. Taking what Einstein says at face value, it is not surprising that inertia today is isotropic given the long history of the Universe and the massive amount of radiation it contains. However, would this have been true early on in that history? When the universe was considerably smaller than today might the effects of inertia been anisotropic? Might this explain inflation?
Inflation itself is what caused the universe to become so incredibly smooth. So that seems unlikely. But what do you mean by an inertia being anisotropic anyway?
Chalnoth I'm afraid I have more questions than answers. Was inertia present in the universe right from the very first moment? a) it was just part of the unified field of the time b) it was present because of the Wheeler "absorber" theory waves moving backwards in time from the future universe c) it developed at some later moment e.g. right after the postulated inflationary period d) any other idea You say that inflation did the job of smoothing out the Universe. Presumably then it is not unreasonable to suppose that prior to that episode it may well have been quite lumpy. If inertia today is so isotropic it may be because of inflation and the subsequent development of the Universe. Could not inertia have been anisotropic before inflation? I think this question is very deep and I lack the intellectual horsepower necessary to get anywhere with it. Nonetheless if it sparks any kind of useful reflection I'll be satisfied.
The very idea of anisotropic inertia makes no sense to me. It would seem that any apparent anisotropic inertia would simply be the result of a bad choice of coordinates, and by just changing your coordinates, the inertia will come out to be isotropic.
A force trying to accelerate a body will encounter an inertial resistance which is the same in whichever direction the force is applied. This is not a problem of choosing a coordinate system as far as I can see. It's more a question of why should this be so and what would happen if this were not the case. I honestly don't expect to get very far with this reflection but until someone can really explain the origin of the inertial force then I think all possible conceptual ideas deserve their Warholian 15 minutes in the spotlight of scrutiny.
Well, if there were an anisotropy of this in any one direction, then it would also effect the structure of matter. If I were to take an object that would be a perfect cube if inertia were isotropic, for instance, the anisotropy would cause said cube to stretch or compress in some direction, as the effects of the forces that hold it together would change as I rotate it. So it might make more sense to just consider that I had misinterpreted the length scale of a particular spatial direction than I actually had a cube that was changing shape through simple rotation. There is no such thing as an "inertial force". Or rather, an inertial force is another name for a pseudo force: a force that only appears as a consequence of looking in a particular reference frame. Perhaps you meant to say something else?
If inertia was anisotropic we would have to establish a new and more detailed S.I.unit for mass a new definition of force and so on.Oh what fun that would be.
Chalnoth That was very loose expression on my part. Thanks for the correction. Well, this seems like a pretty convincing dismissal of any inertial anisotropy. I did suggest that this may not exist now but might have existed in the early Universe, but this is speculation on my part. The great physicists attribute inertia preponderantly to the most distant matter in the Universe. What happened when the most distant matter in the Universe was not very far away at all? Obviously we don't know. I'd really like to know whether the question has any merit or not. I think you've already told me that it doesn't make much sense as a question so perhaps we'll leave it there. Thanks for your help.
Section 4.3 of Ciufolini and Wheeler's text "Gravitation and Inertia" is devoted to the origin of inertia. In particular there is a very nice table on pages 250 and 251 that compares classical mechanics, Einstein's Geometrodynamics (General Relativity in Wheeler-ese), and Einstein's Geometrodynamics with additional requirements. You may find this section of the book interesting. (Actually, the whole book is interesting). Also there is a book of essays: "Gravitation and Relativity" edited by H.Y. Chiu and W.F. Hoffman that has two relevant chapters: Chapter 6, "Mach's Princile and Experiments on Mass Anisotropy" by V.W. Hughes and Chapter 7 "The Many Faces of Mach" by R.H. Dicke.
I had argued above with a somewhat obscure argument that anisotropic inertia might be a matter of convetion, but your argument is great, very clear and convincing.
Since you put it that way ... If the expansion of the universe is a continuing transfer of mechanical energy, then the expansion is the force underlying all motion, and the physical basis for resistance to acceleration.
In 1920 (Leyden Address) and 1924 (Essay On the Ether) Einstein rejected the Machian idea that inertia arises from matter's spooky action-at-a-distance interaction with all the matter in the universe. It's only been a bit less than 100 years, so it's unsurprising that word has not gotten out. Einstein thought that gravitational and inertial effects resulted from matter's interaction with the local space in which it is embedded, and not from any action-at-a-distance. He was not able to extend GR to encompass this concept before his death, but that doesn't mean that he was wrong.
I will take the view that Inertia is anisotropic - by virtue of the equivalence principle - there is no difference between a gravitational field and an acceleration - the force required to accelerate a 10 lb mass at 35 ft/sec^2 near the earth in the direction of the earth, is less than the force required to accelerate the same mass at 35 ft/sec^2 parallel to the earth. If you were in a closed container and had no knowledge of the presence of the earth - you would conclude inertia is different in different directions
Chalnoth - I can hide the fact that the mass would move by itself e.g., by imposing an isotropic frictional restraint of 10.001 lbs. Equivalence obscures any difference between a local G field and any other acceleration -