Wishing Upon a Star


Alpha Centauri (Wikimedia Commons)

By The Metric Maven

Bulldog Edition

A wish can be a supernatural request which is granted by a supernatural talisman. The song, When You Wish Upon a Star, when modulated onto an electromagnetic (radio/light) wave, that is traveling in a vacuum, moves at 300 Megameters per second. This is only true if the light is traveling in a vacuum (we’ll get back to that), and space is a pretty good vacuum. Einstein was rather clear about the fact that information cannot be propagated faster than the speed of light. This means that any receiving star (other than the Sun) would have to wait years to know that a wish was requested of it.

The Alpha Centauri star system is the closest and it would take light a little over four years for a supernatural request to arrive, so your wish would be delayed by at least that amount of time. Alpha Centauri is also only seen in the U.S. for very short periods of time, and only at latitudes which are south of Houston Texas and is practically invisible. Assuming Alpha Centauri is the ineffective talisman that I expect it is, one would have to wait about eight-years for a non-reply. If you wish on a star that takes light over 75 years or so to arrive, well, then you will not be alive to receive the non-reply. Unless you plan to live to 150 years of age. The odds of that happening are not good.

Astronomers like to conflate time and distance into a strange and exotic sounding description called a light-year. Each of the multitude of stars we view at night has light that emanated at a different time, and so when a star is farther and farther away in distance, we witness how it looked longer and longer ago. Every star has a unique time delay associated with it. The further we look out into the Universe, the farther back in time we see.

When you look at any object or person, you do not see them instantaneously. If a person is 500 mm from you, the light you see has taken about 1.67 nanoseconds to impact your retina. The person is therefore 1.67 light-nanoseconds away from you. If you see an erupting volcano that is 1000 meters distant, the image seen by your eyes has a “distance” of 3.33 light-microseconds. Standing in Denver Colorado, Pike’s Peak (which is visible from Denver), is about 160 Km distant or 533 light-microseconds. Which has more meaning in terms of distance?—160 Kilometers or 533 light-microseconds? This is not really fair one might argue. As far as a person is concerned, this amount of time is instantaneous, and so it makes perfect sense to use distance and forget about the propagation speed of light.

When does a product of the speed of light and time begin to be a distance that makes some sense? There are a lot of choices:

Light-Second 300 Mm (Megameters)

Light-minute 18 Gm (Gigameters)

Light-hour 1.08 Tm (Terameters)

Light-day 25.92 Tm (Terameters)

Light-week 181.44 Tm (Terameters)

Light-month 725.76 Tm (Terameters)

Light-year 9.46 Pm (Petameters)

Light-Century 946 Pm (Petameters)

When the New Horizons probe was near Pluto, it took about four hours for the radio signal to propagate from the Earth to the spacecraft. It was not typically said that the probe was 4 light-hours from the Earth. Why not use light-hours if the conflation of light-speed and distance is so useful? A light second is a 3000 hour long (100 Km/hr) drive, or 3000 car-hours. It is also 7.5 times around the Earth. A light-minute is not enough distance to traverse from one planet to the next in our solar system. The light hour is  a distance from the  Sun to a point between Jupiter and Saturn. The light-day, light week and light month are all well short of our nearest star system, Alpha Centauri. A light century (which no one generally uses) is 100 light years. Betelgeuse is over six times this far, and it can be called a nearby star. The length across the Milky Way galaxy is about 100 000 to 180 000 light-years. Our closest galaxy is Andromeda and it is 2 500 000 light-years distant. The observable universe is about 91 000 000 000 light-years. It is hard to see that this single “unit,” the light-year, is really descriptive over the large dynamic range of the Universe. Enormous numbers cannot be visualized, but they can be categorized, which gives them more intrinsic relative meaning. The metric system is quite useful for accomplishing exactly that.

Furthermore, the light-year has a built-in assumption about what year is used. According to Wikipedia: “As defined by the International Astronomical Union (IAU), a light-year is the distance that light travels in vacuum in one Julian year.” My favorite engineering reference for unit definition has this entry:

Buzzed-Light-YearThe options given for a light year length are:

Anomalistic Light Year: 9.460 980 Petameters

Julian Light Year: 9.460 730 Petameters

Siderial Light Year: 9.460 895 Petameters

Tropical Light Year: 9.460 528 Petameters

There are two questions that in my view are rather separate: 1) How far away is an object based on a linear measurement? 2) How long does it take an electromagnetic wave to get from there to here (or vice-versa)? Astronomers might argue that the light-year is really the best description in their view, but when one looks at a star there is no way to really grasp the amount of time or distance. They all look very similar. The first question one probably wants to know is: “how far is that star?” rather than “how long does an electromagnetic wave take to arrive?”

ShimmerThere is another apparent problem. Suppose I were to ask: what is the radius of the Sun? One might immediately say it is 696 000 Kilometers, but I could also argue that it’s about 100 000 light-years, or 1000 light-centuries in extent! Light does not always travel at 300 000 meters/second, it can travel slower than this value when a dielectric medium is present, such as plastic, glass or gas. It takes a photon about 100 000 years to make its way from the Sun’s center to its surface. The photon also loses energy (changes frequency) as it works its way through stellar plasma, but light is a general term for an electromagnetic wave, and its frequency is not specified by astronomers. They just say “light,” so if a photon is just one millimeter inside of the event horizon of a black hole, would its distance to any other body in the universe, in light years, be infinite?—or even possess an imaginary distance?  Is this a legitimate use of a light-year as a “measurement unit?” Well, no, it is not. Astronomers define a light-year in a vacuum, but Wikipedia also calls it an informal unit and claims it is a length, and should not be confused with time—even though time is in the name of the “unit.” The light-year reminds me of Saturday Night Live’s Shimmer Floor Wax, it’s both a floor wax and a dessert topping. Some astronomers have been less than enthusiastic about the light-year as a “unit.” According to Wikipedia:

The light-year unit appeared, however, in 1851 in a German popular astronomical article by Otto Ule.[18] The paradox of a distance unit name ending on year was explained by Ule by comparing it to a hiking road hour (Wegstunde). A contemporary German popular astronomical book also noticed that light-year is an odd name.[19] In 1868 an English journal labelled the light-year as a unit used by the Germans.[20] Eddington called the light-year an inconvenient and irrelevant unit, which had sometimes crept from popular use into technical investigations.[21]

Astronomers define a light year as the distance light travels in a year in a vacuum; but there is another unit which is defined as the distance light travels in a given amount of time in a vacuum. It is the meter, and it’s the base linear measurement value of the metric system. The meter does not have any unit of time in its name, and so it would alleviate the time confusion immediately. Astronomers who might not be familiar with this unit can convert it to 3.33564 light-nanoseconds for clarity. The metric system also has a unique unit of time, the second. One can use metric prefixes with it to describe intervals of time. It’s about time, it’s about space, but only one at a time, unless it’s a relative place.

Postscript: And Then There Were Two? I have been informed that Myanmar has quietly continued to pursue metrication:

5 thoughts on “Wishing Upon a Star

  1. BTW, the rather curious beva- prefix in “bevameter” (see above) probably comes from “billions of electronvolts” (as in the Bevatron); anyway, it’s the same as today’s giga- (10^9) SI prefix: 1 Bm = 1Gm…

  2. Not directly related to this article… but rather interesting TV documentaries like “Extreme Engineering” and others should really begin to systematically use metric units, instead of USC (even if metric units are of course used when the show is translated into other languages – but in the US…): thus, they could contribute towards an informal – i.e., the most effettive one, in everyday life – metric education in your country…

  3. I found “Wishing Upon a Star” to be another excellent essay by the Maven, a start-to-finish one of both “renumeracy” and humor.

    However, it would have been even better if he would spare us of a couple of now-common sickening words replacing natural ones. Here are two sentences from the essay:

    “If a person is 500 mm from you, the light you see has taken about 1.67 nanoseconds to impact your retina.”
    “The metric system is quite useful for accomplishing exactly that.”

    What about, more naturally, replacing those sickening words. Thus:

    If a person is 500 mm from you, the light you see has taken about 1.67 nanoseconds to affect your retina.
    The metric system is quite useful for accomplishing just that.

    Ah! Gibberish gone! Isn’t such better?!

    • Neither “just” nor “exactly” is necessary in that sentence. However, photons do “impact” your retina and transfer their energy, by kicking an electron loose, creating a small electric current. It will then take some milliseconds for nerves to carry that signal to the brain for interpretation.

      • Anyway, despite my English-driven response, good SI-related reply, JS!

Comments are closed.