Defining left and right independent of a human body?

Is it possible to define right and left independent of the asymmetric human body? I am unable to think of such a definition without circular reasoning.

Example:
If you are facing east, your left hand side is the one pointing to North. (But did we not define North as being on the left hand side while facing East?)

Another example: Your heart is on the left side or is the left side defined by the position of heart.

• This question appears to be off-topic because it is about terminology/definitions and not physics. – Kyle Kanos Jan 27 '14 at 16:52
• This question appears to be off-topic because it is about possible options for redefining directions. There is no physics content to this question. – Brandon Enright Jan 27 '14 at 16:52
• As some laws/rules in physics refer to left/right hand - like direction of force on a current carrying conductor in a magnetic field. This may have some relevance in this forum? – juvva Jan 27 '14 at 17:11
• I think this should be kept open (assuming it is not a duplicate). Whether or not parity is a true symmetry of the universe is a huge question that was answered last century. Feynman gave a great lecture about it shortly after the discovery, centered on whether or not left/right-ness could be communicated to an alien species. – user10851 Jan 27 '14 at 17:16
• This is an interesting question related to every formula which involves cross product. But I doubt someone will give a better answer than Feynman. – jinawee Jan 27 '14 at 18:58

Indeed most examples of unambiguously labeling chiral states fall back on having another pre-labeled chiral object on hand. For a long time it seemed as though "left" and "right" were entirely interchangeable labels. This symmetry is known as parity.

However it turns out there is a way to distinguish left from right in a fundamental way; parity is not respected in certain circumstances. A very good talk on this topic was given by Richard Feynman. (See also the corresponding text.)

Summarizing what he says, consider the beta decay of a neutron: $$n \to p + e^- + \bar{\nu}.$$ Experimentally it was observed that the electron always comes out with left-helical spin. That is, if you measure the projection of its intrinsic quantum mechanical spin onto the axis defined by its direction of motion (with the positive direction pointing forward), then you will always get $-\hbar/2$ and never $+\hbar/2$. This parity violation, discovered in 1957, is in some sense maximal when the weak force is involved, even though other interactions (e.g. electromagnetism and gravity) show no sign of it.

With this violation, you can define your right hand as "the one that, when the thumb is pointed backward along the path of an electron emitted in beta decay, has fingers curling in the direction of the angular momentum of the electron."

After it was discovered that parity is not a true, universal symmetry of the universe, physicists began to wonder if maybe one could both take the mirror image of an actual scenario and flip the charges on all the particles (i.e. interchange matter and antimatter) and end up with another physically valid scenario. This is known as CP-symmetry. Shortly before Feynman gave that lecture, it was discovered that the weak force also violated CP-symmetry. This leaves CPT as the inviolable symmetry: If you flip all the charges, look at a mirror image, and run the movie backward, you get an equally plausible physical scenario in every case.

• Excellent answer - and I hope the question gets a few up votes from those that were unaware of parity violation and have learnt something here! – Keith Jan 28 '14 at 2:15
• On further search: "The left hand of the electron" a book by Isac Asimov explains parity violation ( hence a way of defining left and right.) – juvva Jan 28 '14 at 10:29

Chirality assignment was arbitrary as electric charge assignment by Ben Franklin was arbitrary (and unfortunate versus current). As a vector cross-product in a 3-D Cartesian grid, X×Y = Z defines a right-handed coordinate system; X×Y = -Z is left-handed. Consider Lorentz force and railguns (extra credit: where is the recoil?)

One can design a molecule that is "perfectly" geometrically chiral (J. Math. Phys. 40, 4587 (1999), Symmetry: Culture and Science 19(4), 307 (2008)) but cannot be named left- or right-handed. Do equations generating a Möbius band show a chiral twist? Parity violations, symmetry breakings, chiral anomalies, Chern-Simons repair of Einstein-Hilbert action suggest physics may still be defective toward chirality. Phys. Rev. 104(1) 254 (1956), Phys. Rev. 105(4) 1413 (1957), and a Nobel Prize in 1957. The same parity violation was observed - and denied - in 1928, PNAS 14(7) 544 (1928).

(Clockwise as as sense of rotation in the northern hemisphere might be traceable to sundials and deosil versus widdershins.)

"Left" and "Right" depend on what is forwards and what is up. Let $\vec f$ be a vector pointing forwards, and $\vec u$ be a vector pointing upwards. Then "left" is the direction that $\vec u \times \vec f$ points in. This is a cross product, and in elementary math / physics students are often taught how to evaluate it using the "right-hand-rule," which might seem like it introduces circularity because of the reference to the right-hand (rather than left-hand). However, the cross product has a perfectly natural mathematical definition that makes no reference to human anatomy. Letting $\vec v = \sum_i _i \hat i$ for any vector,

$$\vec u \times \vec f = \left| \begin{array}{ccc} \hat 1 & \hat 2 & \hat 3 \\ u_1 & u_2 & u_3 \\ f_1 & f_2 & f_3 \end{array} \right|$$

• This is not valid, because you definition assumes that $\hat i \hat j \hat z = 1$, but it could be $-1$. – jinawee Jan 29 '14 at 16:45
• It could have been, but its not. I think I've interpreted the question differently from others. Specifically, I think the other answers are reading subtlety into the question that isn't there. It wasn't the old "How would I tell an alien what direction is left if we don't have the same language/math?" for which the parity violation of the weak force provides a good illustration. It was much simpler - just asking how to define left/right independent of a human body. The cross product does that. – jwimberley Jan 29 '14 at 18:49
• The reference coordinate system 1^ 2^ 3^ would be defined as right handed, hence circularity? – juvva Jan 30 '14 at 5:49
• Ahh now I get it. – jwimberley Jan 30 '14 at 15:41