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Planck units

Max Planck and the Aliens

Max Planck is one of the biggest names in physics. Most famously, he was the first person to realize that electromagnetic radiation can only be emitted in discrete chunks in accordance with the fundamental parameter now known as Planck’s constant. This groundbreaking discovery paved the way to quantum theory, and earned him the Nobel Prize for Physics in 1918. What is less well known, however, is that Planck was one of the first people to speculate on the practicalities of communicating with extraterrestrials.

The basic problem is to come up with some kind of “universal language”. It’s often said that certain forms of mathematics, such as binary arithmetic, are fundamental enough to be considered a natural language suitable for conversing with aliens. But there’s a problem. When people use numbers, they’re almost always referred to physical units of some sort. “Thirty miles per hour”. “Two liters”. “Twelve ounces”. “Sixty seconds”. Such phrases are easy enough for us to understand, but they would be meaningless to a entity from another planet. The units we use in everyday speech are essentially “anthropic” – human centered.

Scientists use rigorously defined SI (“Système International”) units such as meters, seconds and kilograms. But even these units have their origins in the human world. The meter was originally defined as a certain fraction of the circumference of the Earth, and the second as a certain fraction of the Earth’s rotational period. A kilogram was originally the mass of a certain volume of water – the volume being specified in cubic meters. So an alien culture that was unfamiliar with the planet Earth wouldn’t be able to make head or tail of measurements specified in SI units.

Old units in London

Standard units of measurement in Trafalgar Square, London (courtesy of Paul Jackson)

It’s possible to envisage “non-anthropic” units, based for example on the frequency or wavelength of certain types of radiation, or the mass of certain fundamental particles. But there are dozens of equally valid options to choose from. We could never be sure the aliens would choose the same frequencies, wavelengths or masses that we did.

Planck approached the problem from a different angle. His proposal for “natural measurement units” is tucked away at the end of a long paper on irreversible radiative processes that he presented to the Prussian Academy of Sciences in 1899. Despite the early date – the last year of the 19th century – the application to extraterrestrial communication is made explicitly in the following quote from the paper: “Units for length, mass, time and temperature which, being independent of specific bodies or substances, retain their meaning for all times and all cultures, even non-terrestrial and non-human ones.”

So how did Planck do it? The key lies in that strange quantity called Planck’s constant. Usually represented by the symbol ħ, this has the value (in scientific notation) of 1.05E-34 kgm2s-1. That looks horribly obscure, but it’s a fundamental property of the universe. It’s so fundamental, Planck argued, that it really ought to be given the value 1. So he defined his units in such a way that ħ = 1.

But that’s not the end of the story. In order to pin down units of mass, length and time, we need to set three quantities to 1, not just ħ. The other two constants that Planck chose were the speed of light c, and the gravitational constant G. Like ħ, these are fundamental properties of the universe that any scientifically literate civilization would be aware of. In his original paper, Planck also added a fourth quantity – Boltzmann’s constant k – in order to add temperature to the mix as well as mass, length and time.

In Planck’s system, the fundamental units are called the Planck length, the Planck time and the Planck mass (he didn’t give them these names, but that’s how they’re known today). They’re not totally unambiguous – for example some people might argue for 2πħ instead of ħ, or 4πG instead of G. But the number of meaningful variations is still much smaller than with any other system of units.

So what are the Planck units? The Planck length and Planck time are both incredibly small quantities – much smaller than anything encountered in the “real world”. That’s not true of the Planck mass, however, which is about 22 micrograms – not much less than the mass of a flea. All the known subatomic particles are just a tiny fraction of the Planck mass. For quantum physicists the Planck mass is just as extreme as the Planck length or the Planck time… except that (by the standards of quantum systems) it’s extremely large, not extremely small.

Although Planck’s original motivation was simply to come up with a “universal” set of units, it’s possible the Planck units have a deeper physical significance. Because they combine both quantum effects (ħ) and gravity (G), some scientists believe they may point the way to quantum gravity – the long-sought “theory of everything”.

Quantum gravity

Quantum gravity may involve structures on a Planck scale

Andrew May

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