## Degrees of Freedom

The boundless dimensions of math and physics

# Galactic Challenge Part III: The "Easy" Solutions

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Which hand is this?

Scores of readers responded to my Galactic Challenge (proposed in Part I of this series), with lots of cool ideas. The challenge was to explain our concept of left and right to far away aliens; or to explain it to Martians over the phone, as Richard Feynman put it and as I describe in Part II.

Here I will review the solutions that came up and I will discuss how one could implement them in practice. I will focus on the "easy" solutions, meaning the ones that appeal to the shared experience of a physical object, be it observing configurations of galaxies or interacting with the same electromagnetic waves. In a follow-up post I will talk about the tougher problem of explaining our concepts of left and right spiral motion to aliens with whom we share no such experience. All we can do, then, is refer to the laws of physics, which for all we know hold the same everywhere in our universe, throughout space and time.

Kimballk and others suggested using galaxies as reference points. To assign an orientation of space, we would need three galaxies in addition to our Milky Way. Together, the four galaxies should not lie on the same plane (which implies in particular that no three of them should be aligned). Given all these assumptions, we could define the center of our galaxy to be the origin, and the lines connecting it to the three galaxies to be our x, y and z axes. Once we have such a labeled reference system, it is easy to talk about left and right corkscrew motion, for example.

A variation on that theme was the one proposed by _jeremy, who said that an advanced civilization should be able to leave radio beacons scattered troughout the galaxy. By referring to those beacons, one could construct axes for an oriented system of coordinates.

In fact, it should not even be necessary to place the beacons too far apart from one another--just far enough that a good radio telescope such as Arecibo would be able to tell them apart.

Unfortunately the power required to broadcast signals in all directions throughout the galaxy would be enormous, so as @therealtinasky and others suggested, it might be cheaper for everyone to refer to beacons offered by nature free of charge: pulsars. The rotational frequency of pulsars can be measured with great accuracy and precision from enormous distances.

jtdwyer pointed out that our alien friends probably would be aware of the fact that our galaxy, the Milky Way, is rotating. Its rotation by itself does not define an orientation of 3-D space, but it does if paired with a notion of “up” and “down”: for that, we could choose the direction of another galaxy, for example we could say that the Andromeda Galaxy is “up.” (The Andromeda Constellation, or any other constellation for that matter, would not be very helpful because constellations are just arbitrary groupings of stars as seen from our vantage point: the aliens might not know what we are talking about.)

Another way to distinguish an “up” direction could be to point to the galaxy’s motion with respect to the cosmic microwave background, which could even be detected from other galaxies. (It was by detecting the relative motion of galaxies with respect to the CMB that astronomers discovered the strange and unexplained phenomenon called dark flow (story I wrote for Science News magazine).

Now comes one of my favorite solutions, which had been suggested to me by my friend David Harris and which several readers, beginning with KWillets, quickly thought of as well: the aliens could impose a circular polarization on the radio signal. Here’s how that works.

As the name suggests, electromagnetic waves propagating in space consist of oscillating electric and magnetic fields. Those oscillations are at 90 degrees to each other, and each of them is at 90 degrees from the direction of propagation of the wave. If the direction of the electric and magnetic oscillation is always the same instead of turning randomly--for example, if the electric fields always oscillate vertically--the wave is called linearly polarized.

Linearly polarized light

In a circularly polarized wave, the fields’ direction rotates continuously as the wave moves on, in a corkscrew motion. As I mentioned in Part I of this series, a corkscrew defines an orientation of 3-D space.

Circularly polarized light

Typically, radio antennas emit linearly polarized waves, but it is not difficult to build a circularly polarized radio antenna. So we could send right-handed corkscrew waves to our aliens and tell them, “this is what we mean by right-handed.”

To pick up the orientation of our radio waves in the correct way, the aliens would have to build a receiving antenna that discriminates between left and right circular polarization. An easy way to do so could be to place antenna rods at 90 degrees from each other but also on different planes, separated by one-fourth of the wavelength of the signal. When the wave’s electric field aligns with the first rod, the aliens' apparatus would record a maximum electric field there, say, going “up.”

At the same instant, one-fourth of a wavelength ahead, the electric field would be rotated by 90 degrees either to the left or to the right. If it went right, the apparatus would record a maximum electric field going in that direction, and the aliens would know that we have transmitted waves with a right-handed spiral motion. If instead the electric field on that plane were going left, the motion would be in a left-handed spiral.

A skeptic might ask, How do the aliens know what we mean by electric field? On Earth, our convention is that the electric field points in the direction going from positive to negative charges; electrons are by convention called negative and they accelerate in the opposite direction to the electric field. An engineer on Earth would know which way the electric field points by measuring small electric currents induced on the antenna. So it’s easy! Just tell the aliens which way the electrons in their antennas are supposed to move.

There is one subtlety though, the skeptic says. What's an electron? We could explain our notion of electrons to the aliens by saying that electrons are the things that orbit atoms, and they are about 2,000 times lighter than their positively charged counterparts, the protons. But what if the aliens were made entirely of antimatter? It is not entirely impossible that there could be antimatter galaxies far, far away. In an antimatter world, the small things that orbit atoms would be anti-electrons, also known as positrons, and they would accelerate in the direction of the electric field, not the opposite.

Fortunately, though, our instructions for building the antenna would give exactly the same result whether the aliens are made of matter or of antimatter. In the latter case, the aliens would have a notion of electric field that points in the direction opposite to ours. But while our electric field rotates to the right by 90 degrees, its evil antimatter twin also rotates the same way!

Read the next installment in this series: Why There's No Such Thng as North and South

 This post is part of a series on handedness. Here are the all the posts in the series:  Galactic Challenge, Part II: The Richard Feynman Files Galactic Challenge Part III: The “Easy” SolutionsWhy There’s No Such Thing as North and South

The New Ambidextrous Universe: Symmetry and Asymmetry from Mirror Reflections to Superstrings: Third Revised Edition. By Martin Gardner​. 2005.

The Handedness of the Universe. Roger A. Hegstrom and Dilip K. Kondepudi in Scientific American, Vol. 262, pages 108-115; January 1990.

Alien Pizza, Anyone? On other worlds, biochemistry could have taken a different turn. Davide Castelvecchi in Science News, Vol. 172, No. 7, pages 107-; August 18, 2007

Alien courtesy of lauren/Open Clip Art

The views expressed are those of the author and are not necessarily those of Scientific American.