# Torque direction rule and metamaterials

1. Apr 11, 2008

### metalore

Hi, I´m new. I actually found this board with the message about speculative theory about the density of space and its relation to time but I see that post is two years old.

Anyway I have another simple question that I just can´t find the answer to.

What determines the direction of torque!!!?

Is this just an unexplained phenomenon of the universe? I understand that the torque direction of all natural materials can be determined by using the right-hand rule. However, the left hand rule is also used but only for certain man-made left-handed or negative index materials.

I also understand this is related to "metamaterials" which have a negative refractive index and are not natural but man-made. Are there any natural occuring materials that use the left-hand rule for torque but are not metamaterials (i.e. have a normal refractive index but still use the left-hand rule for torque)?

What is determining this direction, and why do all natural materials use the right hand rule?

2. Apr 11, 2008

### Ben Niehoff

Refractive index has nothing to do with torque. Can you give an example of a material that uses the left-hand rule for calculating torque?

Really, you can use the left-hand rule instead of the right-hand rule if you want, as long as you are consistent, and as long as you distinguish between polar vectors (ordinary vectors) and axial vectors (vectors that are calculated from the cross product of two polar vectors).

Right-hand vs. left-hand is merely a sign convention. We could also, for example, choose all of our velocities to be negative. It wouldn't affect the physical results (but it might be more cumbersome to calculate with).

Also, left-handed torque would be used in left-handed coordinate systems (which could be what you're referring to). But this has no bearing on the actual physics; it's just a bookkeeping device.

Last edited: Apr 11, 2008
3. Apr 11, 2008

### metalore

Okay, I haven´t really read about anything that uses the left hand rule for torque. But I have read about materials that use the left hand rule for opposite wave propagation and a negative refractive index (are those two related)?

I wonder if these are really torque-like properties being expressed on a microscopic level? In any case, my original question still stands: Why do naturally occuring materials use the right-hand rule and not the left (Whether it be torque, wave propagation, or refractive index)? What determines this direction? All I read is that using the right hand is a "convention", but it does not explain why everything goes in that direction in the first place. The fact that materials which use the left-hand rule are "unique", begs the question what is determining this direction in the first place?

I do know that artificially creatd metamaterials are able to produce the negative refractive index because of man-made changes in the structure of the material (as opposed to composition). But what was in the composition of all natural materials in the first place that makes them all use the right-hand rule.

Admittedly I should have titled this thread "Right-hand rule vs left-hand rule" since this is not just about torque.