# Explaining "Left" and "Right" to an Alien using Chirality and Helicity

my professor told us that we could hypothetically explain the concept of "Left" and "Right" to a Martian (an alien, etc.) using the fact that Helicity is invariant under parity.

Now, I understand this last statement, if we flip our axes the helicity is invariant, this is because helicity is the projection of the spin onto the direction of the momentum, and parity would flip both what we would call positive or negative spin and also the sign of momentum.

Moreover in the limit of zero mass we have that Helicity and Chirality become the same thing, this means that also Positive or Negative Chirality, i.e. Right and Left respectively, became invariant under parity.

Given all of this I can't still connect the dots and use all of this to be able to explain to "an alien" what left and right is.

Edit: Thinking about this I have another question, is "Left" and "Right" really invariant under parity? At first I would say yes from what I said before (helicity = chirality for $$m \rightarrow 0$$), but on the other hand (pun intended) the left and right projections for spinors are respectively $$P_{L}=\frac{1 - \gamma_{5}}{2}$$ and $$P_{R}=\frac{1 + \gamma_{5}}{2}$$, but under parity we have that $$\gamma_{5} \rightarrow - \gamma_{5}$$ and so $$P_{R} \leftrightarrow P_{L}$$.

• Do you mean explain just the idea of leftness and rightness, or also communicate to the aliens what our "left" is? PS don't you mean "helicity" in the title? Commented Oct 3, 2022 at 19:43
• @myorbs yes I meant Helicity, sorry I messed and "H". Mmmh, I think also communicate which is the left and which is the right Commented Oct 3, 2022 at 19:51
• See here.
– J.G.
Commented Oct 3, 2022 at 20:05
• Near duplicate. Commented Oct 3, 2022 at 21:14

First check that your alien is made of matter not antimatter. To check this you might have to have them send some particles somewhere, and you do the same, and you watch to see if the particles annihilate each other.

Ok now get your alien to set up an experiment with cobalt-60 nuclei. They will need to be able to determine the angular momentum of the nuclei, and to detect electrons. Find out which way most of the emitted electrons go in beta decay. Also put a little turntable near your experiment, and have the turntable rotate so that its angular momentum has the same direction as that of the nuclei. OK, now make two shapes like human hands, of opposite handedness. Hold each shape above the turntable, with the fingers curled around in the direction the turntable is rotating in. One of the two shapes will then have its thumb pointing in the direction the beta-decay electrons are mostly emitted, the other will have its thumb pointing in the opposite direction. The first one (where the thumb points in the preferred emission direction) is the one we call right-handed.

(And by the way, momentum flips but spin does not under parity, so helicity changes sign under parity).

• This is the example Feynman gave. “If the alien now travels to Earth to meet you and extends his left hand, RUN!” - see feynmanlectures.caltech.edu/I_52.html : I found it by Googling “Feynman nucleus hairs “ (isn’t the internet a wondrous thing). Commented Oct 3, 2022 at 23:12

the fact that Helicity is invariant under parity.

No such fact. Momentum is a vector, so odd under parity, but spin is an axial (like angular momentum) so even under parity (who made you think it flips?), so

• Helicity is odd under parity. Chirality is also odd under parity (L is sent to R). The fact/limit that detectable neutrinos are L but not R is living proof our world breaks parity, and, presumably, so would the alien's world, since we are sharing the same universe with the same weak interactions.

So you get to agree with the three-handed alien what left helicity for their neutrinos is, drawing the suitable arrows, etc... and you have gotten the concept of a left-handed screw across...