What Does Anisotropic Effective Mass Mean?

[inflector]

What Does "Anisotropic Effective Mass" Mean?

I'm reading "The definition of Mach's Principle" by Julian Barbour:

http://arxiv.org/abs/1007.3368

from July of this year, and it contains a paragraph (Section 9 bottom of page 23) I do not understand, the beginning of which says:

Even with the strong Poincaré sharpening of causality and the relativity principle that suggested the formulation of the previous section, there are many different possible theories that implement the above Mach’s principles for particle models. However, nearly all of them predict an anisotropic effective mass. That this could lead to a conflict with observation was already foreseen by the first creators of such theories: Hofmann, Reissner and Schr ̈odinger (their papers are translated in [6]). Since then, the extraordinarily accurate Hughes–Drever null experiments [33, 34] have completely ruled out such theories.

I have bolded the part that I don't understand. I tried googling the phrase but couldn't find a good definition.

What does "anisotropic effective mass" mean? I understand the individual words but they clearly have a meaning when combined that has specific meaning in physics.

Thanks in advance.

 

[PAllen]

I assume you could find out by looking at the following reference in this paper:

[34] R W P Drever. A search for anisotropy of inertial mass using a free
precession technique. Philosophical Magazine, 6:683–687, 1961.

However, it is not available on arxiv. You can buy it from here:

http://www.informaworld.com/smpp/155130749-86406572/content

for the exorbitant price of $37 (for one paper!). Wait, I found a scanned in version of it:

http://virgo.lal.in2p3.fr/NPAC/relativite_fichiers/Drever.pdf

The other reference on this can also be purchesed:

http://prl.aps.org/abstract/PRL/v4/i7/p342_1

Hope this helps.

 

[bcrowell]

Thanks, PAllen, for posting that. There is something deeply wrong with our copyright laws when a paper from half a century ago is still inaccessible without breaking the law or paying $37.

I hadn't realized before that typically, a Machian theory would predict anisotropic behavior of inertia. The fact that Drever limits the effect to no more than 5x10^-23 help to rule out Mach-flavored theories, such as relational mechanics, that predict such an anisotropy. On the other hand, Brans-Dicke gravity involves a scalar field, so I guess it predicts no anisotropy.

 

[inflector]

Okay, so it looks like I'm reading more into this than is meant. It really does mean just that mass would be measured differently from different directions. No special meaning other than the words themselves, as bcrowell says: "anisotropic behavior of inertia."

From the reference by Barbour it seemed like a term/effect that had been discussed widely but I suppose it must have been among Machian theorists so that in that context the expression does have a richer meaning because Machian's would be aware that a) Machian theories predicted anisotropy for inertial mass measurement and b) the null result of the Hughes-Drever attempts to measure anisotropy with respect to the galaxy.

Thank you PAllen!