G is usually measured with mechanical apparatus similar to that invented by Cavendish (sort of torsional pendulum). Oscillating test masses are made from metal, say stainless steel, thus they are good conductors. The numerical value of G is inferred from the period of their oscillations. But this period is certainly influenced by damping! My idea is that the damping is created, among other, by eddy currents generated in conductive bodies moving in Earth's magnetic field (or located nearby the moving magnetized objects). Thus the remedy would be to perform the measurement inside a magnetically shielded chamber and using only non-(ferro)magnetic materials. If this is not possible (test masses have to be dense in order to be easily placed close to each other) then at least the construction of the remaining parts of apparatus should be made from poor conductors, certainly not from brass or alumina. Do you think my idea makes sense?
P.S. I have found only one mention of possibly disturbing magnetic effects, in Phys. Rev. Lett. 85 (2000) 2869-2872, see below. This description, however, indirectly implies that extra magnetic field was certainly non-uniform, so the net forces generated by (disordered) eddy currents might be indeed negligible.
The lab-fixed horizontal magnetic field at the apparatus was measured to be \approx 100 mG. We ran tests by exaggerating the field at the center of the apparatus to \approx 5 G and at the location of the spheres to \approx 100 G. The observed acceleration difference due to the exaggerated fields was (6 \pm 8) x 10^{-12} rad/s^2 . Therefore, a 0.6 ppm error was attributed to magnetic accelerations.
I am not an expert on the subject, but what does not help is the fact that g is not a constant but depends on the global position you measure it. It may even be time dependent if the influence of the tides and moon positions are taken into account as well.
This makes it hard/impossible to determine its value with a high accuracy (as it varies even during a measurement).
Dear Marek,
If you take into account that the frequency is not very high and the magnetic field is around 0.5 gauss, it is easy to see that the eddy currents induced in metallic sphere are almost negligable with respect to the oscillatory damping motion due to Coriolis or other mechanical effects as the tidal due to the Moon position.
In any case perhaps I am wrong and my suggestion is to repit the experiments that you refer, change metal by non metal (eddy currents are higher for ferromagnetic metals) and to compare with other measurements as in
P. J: Mohr and B.N. Taylor, Rev. Mod. Phys.77,1 (2005)
Phys.Rev.Lett.89,161 (2002)
It might be interesting for some to compare current and future experimental results against the exact-per-definition prediction of iSpace theory. In this framework the originally identified relation for the Newtonian gravitational constant G (as presented in my IMS-2015 conference paper in Prag, please see "iSpace - Deriving G from α, e, R∞, μ0 and Quantum of Gravitational Force Fg") showed a structure indicating a 10-dimensional relation to finestructure-constant, a 4-dimensional to Rydberg-constant R∞ and electron-charge e, a 2-dimensional to the magnetic-constant which was finally multiplied with the proposed quantum of gravitation Fg as identified by iSpace theory.
Now my recent work instead reveals a much more *simple* and natural relation involving only the exact same Fg multiplied with the Bohr-radius a0 times the classical electron-radius re and divided by the square of the electron-mass me, just using very well-known relation of Newtonian gravity. This new (to the best of my knowledge) and stunningly simple relation also maps directly to the preferred units of G by dimensional analysis: force*length^2/mass^2.
A detailed paper on that and other consequences following from this discovery like *unification* of electromagnetic and gravitational force by the unique unusual geometrical methods of iSpace (representing a partially discretized spacetime using a changed distance definition, small prime numbers and Golden-Ratio) is currently in preparation. While I have typically no time to discuss this here in the groups, I am happy to answer specific questions (please allow for some time for my reply).
Code iSpace - The possibly biggest Surprise calculated - ever ......
Conference Paper iSpace - Deriving G from α, e, R∞, μ0 and Quantum of Gravita...
Conference Paper iSpace - Exact Symbolic Equations for Important Physical Con...
Given the date I'd like to add - my above post is not at all an April fools joke ...
@Erik Carton: g (free fall acceleration) and G (universal gravity constant) are two different things. Let's not mix them up.
@Remi Cornwall: The natural extension of your kind of thinking would be to measure G using neutrons. Very good idea, but do you have any knowledge how to perform such an experiment?
@Daniel Baldomir: first I would like to correct the reference you presented. It is Phys.Rev.Lett. 89,161102 (2002). I will have to study it soon as this article describes something different than Cavendish balance. As it comes to eddy currents: I was impressed by recent article in Am. J. Phys. 84 (2016) 181 "A slowly rotating hollow sphere in magnetic field: First steps to de-spin a space object". It is not (directly) the frequency but rather time derivative of magnetic flux what is responsible for current generation. The corresponding formula produces current density. Given sufficiently large cross section quite a strong (eddy) currents can be produced, thus certainly not always negligible. You can also find on You Tube a short presentation(s) showing large permanent magnet falling onto thick (1 inch or so) aluminum plate. Its free fall is considerably slowed. If you don't believe (presentation may be a fake) - think about magnetic breaks installed in training bikes (those to be ridden at home).
@Christian G. Wolf: perhaps my wording was not precise enough (as it often happens to me). My question is not related to any sophisticated theory but rather to the quality of relevant experiments/measurements.
Finally to all interested in this thread: when measuring anything, we tend to eliminate any possible source of disturbances, be it a wind, static electricity, humidity, etc. My impression is that not enough care was taken until now to remove sources of magnetic forces. They are certainly comparable with forces generated by static electricity, thus orders of magnitude stronger than the gravity itself. But, maybe, you have still other ideas what could be wrong/neglected during G measurements?
Dear Marek,
I don't understand you very well. If you have:
It is not (directly) the frequency but rather time derivative of magnetic flux what is responsible for current generation.
Obviously you can apply Faraday's law and you obtain a current, but this needs to be ridícula if the Earths magnetic field is the source. The power of eddy currents are always proportional to the square of the frequency and the frequencies that you have mentioned are negligable. It is a very simple calculation.
Dear Daniel,
Concerning frequency: the excitation (change of magnetic flux) need not to be periodic, hence the notion of frequency may be simply inapplicable. In the experiment you recommended two big tanks (~1 cubic meter of volume) filled with mercury are moved and then stopped. I can imagine that the flux (Earth's) is no longer changing but induced currents are still present. They will decay thanks to Joule heat they generate - isn't it? But the currents are small and so is the resistivity of mercury. In this situation I wouldn't be surprised to observe presence of the said currents for minutes. This is more or less based on my experience with big classical laboratory electromagnet: after slight disturbance with small permanent magnet I was able to see slow restoration of the original field between magnet poles lasting up to 20 minutes(!). Such a small curiosity spotted during completely different experiments, so not investigated further. Of course, at least part of this effect could be attributed to magnetic relaxation (magnetic viscosity) of the poles but I haven't noted such a effect in smaller electromagnets. On the other hand, the tanks containing mercury are made of steel (a material with pretty high magnetic susceptibility), which may be magnetized by eddy current pulse and then relax by slow (viscous) mechanism (maybe months at low enough temperature).
In summary, I think magnetic effects (in sense of force) well override eventual influence of changing Moon position. Anyway - eliminating possible influences of magnetism won't do any harm to the G measurement but rather might improve (i.e. decrease) its uncertainties.
Dear Marek,
You write in your question:
The numerical value of G is inferred from the period of their oscillations. But this period is certainly influenced by damping!
Thus I have assumed that you had frequency and you followed this kind of experiment trying to take into account the damping. And you added more:
Thus the remedy would be to perform the measurement inside a magnetically shielded chamber and using only non-(ferro)magnetic materials.
Why do not employ one insulator where the Earth magnetic field doesn't do any effect?
If this is not possible (test masses have to be dense in order to be easily placed close to each other) then at least the construction of the remaining parts of apparatus should be made from poor conductors, certainly not from brass or alumina. Do you think my idea makes sense?
Frankly I don't see the sense of your question. G doesn't have relation with the electromagnetic changes and only the application of the Earth magnetic field can induce currents which could change the oscillation by damping, as you said, but in a very negligable form.
Let me to give you one suggestion because I see that you are an expert in electromagnetism, why do not use the Einstein-de Haas effect leaving to follow a ferrmagnetic metal and measuring the angles adding an extra magnetic field to the Earth's one?
Dear Daniel,
Similarly to you I am not inclined to the so called gravitomagnetism surfacing from time to time in literature, including shielding of gravity by superconductors (--> Podkletnov). Yet in G measurements some kind of relocation seems unavoidable. Consequently either the presence of magnetic field (Earth's or arising from remanent magnetization of some part(s) of apparatus) or magnetic/conductive movable bodies will create some forces of electromagnetic and not gravitational origin. It is unavoidable and thus the question arises whether those forces are indeed negligible. I admit, I am unable to estimate them reliably but I'm quite sure they do exist and have the potential to distort experimental results to more extent than we think. That's why I suggest to make them simply absent in future G measurements.
I'm sorry, I don't see the connection with Einstein-de Haas effect. Would you be so kind to add a few words of explanation?
Dear Marek,
The idea that I have is very simple and for making good experiment obviously it needs to solve many problems. If the eddy currents are important ( or significative) they are going to change the angular momentum of the sample. Thus measures it under the conditions of G measurement for taking it into account in the mechanical experiment.
The idea may be checked using any high-precision Cavendish-type experimental setup. This setup should be placed on turn base. One experimental seria: test mass moves along magnetic meridian, other seria- in perpendicular direction.
Dear Alexander,
At first sight your idea is quite obvious. But there is a small trouble: almost everywhere you will have both mentioned components of Earth's magnetic field present in the horizontal plane (I understand that test mass in Cavendish-type experimental setup moves in horizontal plane). Therefore your idea might be indeed successful only somewhere near the equator. Anyway, certainly worthwhile hint. Thank you!
Dear Marek Wojciech,
I know only one component of Earth`s magnetic field in the horizontal plane- from south to north. What is the second one? Test mass doesn`t move in vertical direction, so the vertical component is negliglible.
Negligible vertical component of Earth's magnetic field? Also in the neighborhood of poles?
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