In 1874, the little heard of physicist George Johnstone Stoney dreamed of devising a new universal measuring system based on Nature itself. A century later his system, with a minor modification from Max Planck, would perfectly describe some of the most basic properties of the smallest possible black hole. Moreover, there’s a mysterious, compelling relationship between Stoney’s unit of length and the fundamental unit of information – the binary digit, better known as the bit.

Stoney’s dream fits a scientific pattern: as knowledge has increased, scientists have tended to take a less Earth-centered view of the universe. For Stoney, this included ditching the familiar Earth-centered measuring units:

- a kilogram – the mass of a liter of water
- a meter – one ten-millionth of the distance from the North Pole to the Equator
- a second –
^{1}⁄_{86400}of an Earth day

Presumably alien civilizations – if any exist – will use entirely different everyday units for mass/length/time.

George Johnstone Stoney asked if universal units existed – and he found they did.

Stoney discussed his findings at the British Association for the Advancement of Science in 1874 and published them in 1881. He based his new units on three indispensable universal physical constants:

- the speed of light
- the unit of electric charge derived from Faraday’s law
- the gravitational constant

### The Planck Scale

Following in Stoney’s footsteps, Max Planck produced his own universal constants in 1899, identical to Stoney’s except Planck used his own Planck constant in place of electric charge. The effect of this was relatively small – Stoney’s units and Planck’s differ by a factor of √137.

In Planck’s natural units the speed of light, the Planck constant, and the gravitational constant all have a value of 1. Here’s how his units compare to our everyday units:

**The Planck Mass**

One unit of Planck mass is small – about 10 micrograms – the weight of an eyelash.

**The Planck Length**

One unit of Planck length is about 10^{-33} cm. You can get some idea of this size by considering that the same number of Planck lengths would fit inside a proton’s diameter as Earth diameters would fit inside the observable universe. The Planck length measures an almost shockingly small scale, but as we’ll soon see, it’s a scale that seems to have real physical meaning.

**The Planck Time**

If the Planck length seems shockingly small, the Planck time takes the cake. One unit of Planck time is about 5 x 10^{-44} s – it’s the time light takes to travel the Planck length.

### Planck’s Units and Black Holes

In 1971, Stephen Hawking proposed that tiny black holes could exist, revealing one incredible property of the Planck scale – it determines the properties of the smallest possible black hole – a quantum black hole:

- Black hole mass = 1 Planck mass ∼ 10 micrograms
- Event horizon radius = 1 Planck length ∼ 10
^{-33}cm - Black hole half-life = 1 Planck time ∼ 5 x 10
^{-44}s

A quantum black hole is strange thing – a halfway house between the world of elementary particles and collapsed stars, governed by unresolved rules and possessing properties that nobody can predict with any certainty.

### Measuring a Black Hole

The mass inside any black hole, no matter how massive, takes up even less space than the Planck length. It has no size at all. A black hole’s entire mass is crushed utterly by gravity so that it occupies a volume of precisely zero. It becomes a geometrical point with infinite density known as a singularity.

We can’t see a singularity because the enormously powerful gravitational field it creates around it traps light in its vicinity as far out as a boundary known as the event horizon – hence the ‘blackness’ of the black hole. No light within the horizon can escape, so we can never look inside it.

If Earth were crushed to form a black hole, the distance from the singularity to the event horizon – the Schwarzschild radius – would be just under one centimeter. If the sun’s mass were crushed the radius would be about 3.0 km. The supermassive black hole believed to lurk at the center of our galaxy is about 4 million times the mass of our sun. It’s Schwarzschild radius is about 3 billion km – similar to the Sun-Uranus distance in our solar system.

### A Remarkable Discovery

In 1972, Jacob Bekenstein published a paper whose findings are now mainstream science. Bekenstein calculated the effect of adding 1 bit of information to a black hole – **any** black hole of **any** size. His calculation revealed something truly remarkable.

Bekenstein found that when a black hole takes in a single elementary particle containing 1 bit of information the area of the event horizon increases by 10^{-66} cm^{2} – in other words, 1 square Planck length. Don’t worry too much about how a photon could be described as a bit of information – we see things only because photons carry information to our eyes.

### The Universe Creates Complexity from Information

A century after Stoney produced the first universal scale, Bekenstein showed that a natural unit scale really does measure something rather profound. His discovery that the Planck area is the smallest area that can accommodate one bit of information suggests a deep link between the structure of the universe and information, which physicists are now busily exploring.

Some, such as Seth Lloyd, believe the universe itself acts as a quantum computer processing information to produce the complexity we see around us.

**Further Reading**

Stephen Hawking

Gravitationally collapsed objects of very low mass

Monthly Notices of the Royal Astronomical Society, Vol. 152, p. 75. 1971

John D. Barrow and Frank J. Tipler

The Anthropic Cosmological Principle

Oxford University Press. March 1986

Seth Lloyd

Programming the Universe

Alfred A. Knopf, 2006

Leonard Susskind

The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics

Little, Brown and Company. July 2008

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