What Does Anisotropic Effective Mass Mean?

In summary, the author is reading about a concept called "anisotropic effective mass" and doesn't understand what it means. The author mentions that nearly all Machian theories predict this anisotropic behavior, but it has been disproven by Hughes-Drever null experiments. The author also found a scanned-in version of a paper that discusses the concept in more detail.
  • #1
inflector
344
2
What Does "Anisotropic Effective Mass" Mean?

I'm reading "The Defintion 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.
 
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  • #2


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.
 
  • #3


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.
 
  • #4


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!
 
Last edited:

Related to What Does Anisotropic Effective Mass Mean?

What is an anisotropic effective mass?

An anisotropic effective mass refers to the effective mass of a particle that varies in different directions. This means that the particle's mass is not the same in all directions, and can change based on external factors such as electric and magnetic fields.

How is anisotropic effective mass measured?

Anisotropic effective mass can be measured using various experimental techniques, such as cyclotron resonance, Hall effect, and magnetoresistance. These techniques involve applying external fields and measuring the resulting changes in the particle's motion or conductivity.

What factors can affect anisotropic effective mass?

Several factors can affect anisotropic effective mass, including the crystal structure and symmetry of the material, the presence of impurities or defects, and external influences such as temperature, pressure, and electric or magnetic fields.

What are the applications of anisotropic effective mass?

Anisotropic effective mass plays a crucial role in understanding the electronic and optical properties of materials. It is particularly relevant in fields such as condensed matter physics, materials science, and semiconductor technology, where the behavior of particles in different directions is essential for designing and optimizing devices.

How does anisotropic effective mass differ from isotropic effective mass?

The main difference between anisotropic and isotropic effective mass is that the latter assumes a constant mass in all directions, while the former considers the directional dependence of the particle's mass. This means that anisotropic effective mass provides a more accurate description of the particle's behavior in materials with varying crystal structures and external influences.

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