Infinitesimal to Gargantuan
The Story of the Universe in Powers of Ten
From Plato’s Cave into the Wide Open
In the ‘Allegory of the Cave’ Plato describes how prisoners are chained together at the back of a dark cave. They thus believe the world is all darkness with fleeting shadows. It is only when one prisoner becomes free and escapes outside the cave that the prisoner realizes the world’s enormity and beauty.
The story of human knowledge is like Plato’s story of the prisoner. For most of our history, we have not been aware of the universe’s incredible scale from the smallest to the largest. It is our five senses through which we gain information about the world that are also the cause of our limited understanding. It was only after the invention of instruments such as telescopes and microscopes that we were able to “improve” our eyesight and “see” more of the universe.
Edward Wilson, the great biologist and humanist, writes, “With instrumental science, humanity has escaped confinement and prodigiously extended its grasp of physical reality. [Using instruments we can] peer downward to the trajectories of subatomic particles and outward to star birth in distant galaxies whose incoming light dates back to the near beginning of the universe. [Instruments allow us to measure and visualize] matter across thirty-seven orders of magnitude.”
“Science,” admits Wilson, “is much more than just the haphazard expansion of sensory capacity by instruments,” however, without instrumentation, we cannot collect the required data, classify phenomena or experiment. Without instruments we would be ignorant of the vastness of space-time.
Powers of Ten
Three books I have greatly enjoyed reading and that form important parts of my library are:
- ‘Powers of Ten — About the Relative Size of Things in the Universe’ by Philip Morrison & Phylis Morrison
- “The Measure of the Universe” by Isaac Asimov
- “Time in Powers of Ten — Natural Phenomena and Their Timescales” by Gerard ‘t Hooft and Stefan Vandoren
All three books describe the range of space-time in the universe using powers of ten. Starting from what we perceive in our daily lives, the books take steps up and down, from large to small. The books complement each other. The Morrisons’ book deals with distances and the Hooft and Vandoren book with time. Asimov takes a broader view and discusses the range of lengths, times, masses, densities, pressures, speeds, and temperatures observed in the universe.
If the reader has not yet started on this journey, my recommendation would be to start with the Morrisons’ ‘Power of Ten.’ Read the book from the middle, at 10⁰ meters (m) = 1 m, close to the height of an adult person. Go upwards in steps of a factor of ten, reaching 10²⁵ m at the largest scale and delve downwards to 10⁻¹⁶ m at the smallest.
Up the Scales
The mean height of an adult man on earth is 1.71 m and that of an adult woman at 1.59 m. Let us approximate a human’s height as close to 1 m =10⁰ m.
A Blue whale, one of the largest animals, is ~10 times our size, so 10¹ m. If we multiply this by 10 again, we reach 100 m =10² m. This is the distance Usain Bolt ran in 9.58 seconds (s) (~10 s). While 10² m is already larger than our human size, 10² s is only 1 minute 40 seconds and still a fraction of the time we spend each day (awake or asleep!).
We need to go to 10⁵ s (27.78 hours) to arrive at a time that is a little over 1 day. 10⁵ m is approximately the distance between Paris and London (344 km). Asimov tells us that the heaviest dinosaurs approached 10⁵ kilograms (kg) in mass. But in terms of speed 10⁵ m/s is, as Asimov says, “beyond our orbital planetary speeds.” Mercury has the fastest orbital speed of any planet and, when it is closest to the Sun, is moving at 0.56 x 10⁵ m/s.
As humans began to use telescopes, they realized that cosmic distances were truly immense. The distance between the earth and the Sun is 10¹¹ m. This is still a tiny distance in terms of the universe’s size, but by our human scales, it is almost unimaginably large. However, it takes light (electromagnetic radiation) from the Sun to reach our earth in just 500 s (8 minutes and 20 seconds).
The distance to the next set of stars, Alpha Centauri A and B, is 10¹⁶ m. It takes light 4.24 years to reach us from these stars. As humans continued their discovery of galaxies, they found that, like humans, stars also have a lifecycle. Stars are born, and they die. Scientists also discovered the incredible fact that most of the atoms of which we are made, other than hydrogen) are made in giant explosions called Supernovas. Supernovas occur when certain types of stars end their lives with an explosion, giving off an amazing electromagnetic show. As Carl Sagan wrote:
“The nitrogen in our DNA, the calcium in our teeth, the iron in our blood, the carbon in our apple pies were made in the interiors of collapsing stars. We are made of star stuff.”
Hooft and Vandoren explain that a star such as our Sun ends its life after around 10¹⁷s (10 billion years) as a white or brown dwarf consisting of only carbon and oxygen atoms. Heavier stars live for much shorter times (~ 10¹⁴ s) and, in their last phase, often become black holes, still mysterious objects where time seems to standstill. 10¹⁷s is also of the order of magnitude for the present age of the universe which is 4.354 x 10¹⁷s (13.8 billion years).
The Morrisons’ book was published in 1982, and the furthest distance he explored was 10²⁵ m. However, in December 2020, a team led by the astronomer Nobunari Kashikawa announced that “GN-z11 seems to be the farthest detectable galaxy from us, at 13.4 billion light-years, or 134 nonillion kilometers” (134 x 10³⁰ km, approximately 10³⁵ m).
Hooft and Vandoren end their exploration up the scales at 10⁹⁰s (~10⁸³ years). By this time, through the action of the second law of thermodynamics, “the universe will have practically ceased to exist.” How amazing, though, that over the average life span of a human being (2.3 x 10⁹ s = 72.6 years), we can contemplate the universe at 10⁹⁰ s.
Through our explorations of the cosmos and the use of our incredible telescopes, we have discovered that there are other planets that go around stars as the earth goes around the Sun. How tremendously exciting that some of these exo-planets have an atmosphere and water and could also harbor life. It is no longer science fiction to imagine that one day we might receive a message from an alien civilization in the skies. Are we ready?
Down the Scales
Just as telescopes gave us super-human eyesight to see the distant stars, microscopes gave us the magnified capability to see the very small. Once again, starting our journey with our human size, 10⁰ m, let’s first divide by 10. This is written as 10⁻¹ m. This is 10 centimeters and is around the size of your palm. This is also the length of your mobile phone. Divide again by 10, and you reach 10⁻² m. This is 1 centimeter. This is the size of one key on your laptop. Dividing this by 10,000 we reach 10⁻⁶ m. This is the size of a human cell.
Cells are the building blocks of life on earth. They are like mini-cities, with a “power station” that converts food into fuel, “roads” along which molecules travel, and a nucleus, inside of which the cell contains information about making new copies of the cell. Dividing the size of a cell by 100, we reach 10⁻⁸ m. This is the size of our DNA (Deoxyribonucleic acid). The Morrisons’ book has a beautiful close-up photograph of DNA. We see it as a long molecule whose atoms twist around each other in a double helix shape. It contains all the information and instructions to make us.
Dividing again by 100 and we arrive at the surface of atoms (10⁻¹⁰ m). The existence of atoms was once only speculation. It was Einstein who provided a theoretical basis for the existence of atoms, and today, we can “see” pictures of atoms using special electron microscopes.
To investigate particles even smaller than an atom, we use the Large Hadron Collider (“LHC”). This is a high-energy particle collider. It smashes small particles together to create even smaller particles. The LHC was built by the European Organization for Nuclear Research (CERN) and is housed in a tunnel 27 kilometers (2.7 x 10⁴ m) long and located on the France-Switzerland border near Geneva.
Using the LHC we have discovered particles that are astonishingly small. An atom is made up of electrons, protons, and neutrons. The proton and neutron are themselves made up of smaller particles called quarks. 10⁻¹⁵ m is around the smallest the LHC can “see.” Here the rules of quantum mechanics apply. Objects behave as if they were particles and waves!
Hooft and Vandoren describe how in 2008, an extremely short laser pulse was created that lasted 80 attoseconds = 8 x 10⁻¹⁷ s. These short pulses match the movement of electrons within an atom. In October 2020, scientists in Germany from the Goethe University in Frankfurt, the Fritz Haber Institute of the Max Planck Society in Berlin, and DESY measured the time it took for a photon to cross a hydrogen molecule. This was 247 zeptoseconds ~ 10⁻¹⁹ s.
It takes 0.5 ms = 5 x 10⁻⁴ s for a signal to go from one neurotransmitter molecule in our brain to another, and the wonder is that in that time frame, we can contemplate an even smaller fleeting moment such as a zeptosecond.
Still so much to discover
There is still so much to discover. It is perhaps best to keep in mind what the great physicist and mathematician Isaac Newton said:
“I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.”
