by Caleb Scharf
Your head may be spinning, so here is the bottom line: those things that we call particles are best thought of as the quanta of various relativistic quantum fields—the lowest-frequency ripples that can form. They are the excitations of these fields—whether they’re electrons, photons, quarks, gluons, or anything else, from neutrinos to Higgs bosons.
So really, when we talk about the physics of the subatomic we are talking about all the repercussions that come from fields. When you hear scientists get excited about the detection of a Higgs particle, it’s not so much the particle that’s got them excited—it’s the fact that it reveals the existence of the Higgs field.
That’s one way to think about the subatomic universe. We’re brushing up against the very real limits of human knowledge and the constraints of our tools of investigation. Fields, waves, and quanta are just a part of our quest for insight into the underpinnings of the world. They also happen to provide us with some of the most accurate theoretical predictions about the properties of nature ever made in science.
ALL THE WAY
Our current understanding of the uncertainty principle tells us that somewhere around a scale of 10−35 meters the universe runs out of any semblance of acceptable behavior—at least by the rules as we know them.
We know that it takes light about 5 × 10−44 seconds to traverse this distance—yielding the Planck length and the Planck time (two physical constants based on the properties of empty space). We derive these numbers from combinations of other constants of nature—the speed of light, the strength of gravity, the Planck constant (related to the quanta of light and matter), and π. In that sense, these Planck units might at first glance seem to be just amusing number play.
Except we suspect that something important is going on at this scale.
It appears to be the scale where there is no possibility of making genuine measurements anymore; the entire concept of location and time is disrupted by uncertainty. Theoretical physicists have proposed that at this level the very fabric of space-time stops being smooth. Instead, space-time may be “discretized,” actually quantized into indivisible bits. At this scale we really need a theory of quantum gravity in order to grapple with reality. We don’t have that complete theory yet.
It is also a scale where virtual black holes could appear and disappear, behaving as if they too are the quanta of a field. For the much-discussed idea of string theory, this would also be the smallest meaningful scale: the approximate size of the oscillating strings that make up all elementary particles (yes, strings, fields, quantum gravity, and all of that conflated).
Another appealing proposal for these tiny scales is that space-time itself becomes a quantum foam. If this is correct, the simple geometry of space that we’re familiar with can no longer hold at such small distances. Instead space-time warps and oscillates, bubbles and jitters with the fury of uncertainty. The idea of quantum foam extends the notion of virtual particles (quanta) appearing and disappearing all the time in empty space. That same virtual “sea” of the vacuum might possibly be related to the dark energy that we saw pushing the universe apart at the largest scales. In the case of quantum foam, it’s the very fabric of space-time that is writhing with virtual twists and turns.
Can we ever hope to confirm the existence of this foam? Perhaps one day. On scales of 10−19 meters (small, but still a long way from 10−35 meters), we have been able to tell that space-time still appears to be smooth and regular. But what lurks at the bottom of the ladder of size is for now still out of our reach.
END TO END
Here, after passing through more than sixty orders of magnitude in scale, we come to what I’ll call “the end for now.” Of course, we could also have started here, at the Planck scale, and inflated ourselves upward until we gazed at the observable universe filled with its glinting motes and structures—itself not unlike a composite particle, a place sprinkled with energy and activity.
That journey would have taken us from deep inside a single proton, inside a single carbon atom, inside a twist of deoxyribonucleic acid, perhaps within a single cell of a bacterium, on the surface of one cell of a louse, captured in the beak of a bird, perched on the leathery hide of an elephant, on a patch of scrub in the Rift Valley on one corner of a great continent on a floating crust of a rocky planet, deep in the gravity well of a single star in lonely interstellar space within a swirling galaxy of gas, dust, and dark matter, part of a group and supercluster of other galaxies, strewn across a swath of a 13.8-billion-year-old void of expanding mostly empty space-time.
Our cosmic circumstances influence the way we see reality.
All scales of the zoomable universe. In powers of ten, humans exist almost halfway between the inconceivably big and the unimaginably tiny, and the final plunge from 10−19 meters to 10−34 meters is as deep as the descent from the human scale to the interior of a proton.
Those choices of direction and focus are interesting because they must reflect something about us, our species, but also about the particular circumstances we find ourselves in. What would this book look like if written in a hundred or a thousand years’ time? What would it look like if written by another intelligence living a billion light-years from here?
The precise trajectory followed by those hypothetical writers, artists, and designers (or their alien equivalents) would surely be different in its details. Another continent on Earth would be zoomed in on, a different tableau of rock, water, and life. Or perhaps it would be an entirely different type of galaxy: a new stellar host, another planetary home.
Yet that pathway is likely to be familiar in its scope. There are underlying principles at play in nature, from the fields, quanta, and forces of the universe to the ebb and flow of complexity, emergence, and organization. Those principles form a language rich enough to transcend any separation in time or space—we just have to learn how to translate it all.
The odds are good that we’ll manage to do more of that translation. Anatomically modern humans have existed for around a hundred thousand years. That’s only seven-millionths (or 0.0007 percent) of the present age of the universe. We’ve been around for the tiniest sliver of cosmic time, yet our science can already take us across sixty orders of magnitude in scale.
To put that in perspective, if the age of the universe were a human lifetime, it would have taken the cosmos about five hours to attain its present understanding of itself in the form of us.
Endpoint: The Planck scale, deep in the finest texture of space-time
We are accelerating and extending our minds through our computers and algorithms, through our medical prowess and our accumulated knowledge. These minds of ours are the most precious things; we need to cherish all seven-plus billion of them. Walking this rocky globe somewhere today may be a human who will take us to the next level of insight. This person could be anywhere—from Africa to Asia, Oceania to Europe, or in the Americas. This person could even be you.
And that next journey will be at least as extraordinary as this one.
Another place, another story of scale
FROM NEARLY NOTHING TO ALMOST EVERYTHING
What is known to exist at any scale? A very incomplete list.
0.001 fm or less (a femtometer is 10−15 meters): Approximate mirror displacement sensitivity of the Advanced LIGO gravitational wave detector at a frequency of 40 hertz
0.84 fm: Effective diameter of a proton
0.1 nm (a nanometer is 10−9 meters): Effective diameter of a hydrogen atom
0.14 nm: Effective diameter of a carbon atom
0.8 nm: Average amino acid size
2 nm: Diameter of a DNA alpha helix
4 nm: Globular protein
6 nm: Diameter of actin filaments—part of cellular cytoskeletons
7 nm: Approximate thickness of cell membranes
20 nm: Size of the ribosome
25 nm: Typical outer diameter of a microtubule—tubular structure forming part of a cell’s cytoskeleton or structural support
30 nm: Smallest known viruses—porcine circovirus, single DNA loop of only 1,768 base pairs
30 nm: Rhinoviruses (common cold)
50 nm: Nuclear pore
100 nm: a retrovirus like HIV
120 nm: Large virus (orthomyxoviruses, includes the influenza virus)
150–250 nm: Very large virus (rhabdoviruses, paramyxoviruses)
150–250 nm: Smallest known bacteria, such as Mycoplasma
200 nm: Centriole—cylindrical organelle in animal cells
200 nm (200 to 500 nm): Lysosomes—organelles in eukaryotic cells involved in producing enzymes that break down proteins, carbohydrates, and more
200 nm (200 to 500 nm): Peroxisomes—organelles in eukaryotic cells that help break down long-chain fatty acids
750 nm: Approximate size of a giant mimivirus
1–10 µm (a micrometer is 10−6 meters): The general size range for prokaryotes (bacteria and archaea)
1.4 µm: Maximum length of filamentous Ebola virus (about 80 nm wide)
2 µm: Escherichia coli—a bacterium
3 µm: Size of a large mitochondrion inside a eukaryotic cell
4 µm: Size of a small neuron
5 µm: Length of a chloroplast in plant cells
6 µm (3–10 µm): cell nucleus
9 µm: Human red blood cell
10 µm (range 10–30 µm): Most eukaryotic animal cells
10 µm (range 10–100 µm): Most eukaryotic plant cells
90 µm: Small amoeba
120 µm: Size of human egg
160 µm: Largest size megakaryocyte
500 µm: Largest size giant bacterium Thiomargarita
800 µm: Large amoeba
1 mm: Diameter of a squid giant nerve cell
40 mm: Largest diameter of the giant amoeba Gromia sphaerica
5.8 cm (a centimeter is 10−2 meters): Size of Etruscan shrew
12 cm: Diameter of an ostrich egg
1 m: Typical height of a newborn elephant
3 m: Length of longest nerve cells in a giraffe’s neck
13 m: Length of (female) giant squid
15 m: Length of adult humpback whale
32 m: Length of adult blue whale
39.7 m: Estimated length of titanosaur Argentinosaurus huinculensis
3 km: Approximate size of largest known honey fungus, Armillaria solidipes
8.848 km: Height above sea level of Mount Everest
10.994 km: Depth of Challenger Deep—deepest region of Mariana Trench in north Pacific Ocean
16 km: Approximate size of smallest sunspots on the Sun
21 km: Height of Olympus Mons on Mars, measured above global datum
300 km: Diameter of Vredefort asteroid impact crater in South Africa
504 km: Diameter of Saturn’s moon Enceladus
950 km: Diameter of Ceres, closest dwarf planet to the Sun
6,000 km: Length of the Great Rift Valley
6,000 km: Approximate length of longest path across Antarctica
6,779 km: Diameter of Mars
92,000–117,580 km: Radii of inner and outer edge of Saturn’s B ring
160,000 km: Approximate size of largest sunspots on the Sun
384,400 km: Average distance of the Moon from Earth
149.6 million km: Average distance of Earth from the Sun
1.643 billion km: Diameter of red supergiant star Betelgeuse
4.28 billion km: Distance at closest approach between Pluto and Earth
8.6 billion km: Diameter of event horizon of a 1-billion-solar-mass black hole
74 billion km (2.86 light-days): Approximate length of all the DNA contained in one human stretched out end to end
40.14 trillion km: Distance to Proxima Centauri
2.35 quadrillion km (24,100 light-years) to 2.69 quadrillion km: Estimated distance to the center of the Milky Way galaxy
2.1 quintillion km (220,000 light-years): Diameter of the Andromeda galaxy (M31)
3.1 quintillion km (326,000 light-years): Total length of Cygnus A radio jets from central supermassive black hole
525 quintillion km (55.5 million light-years): Approximate length of all human DNA stretched out end to end (from 7.4 billion currently living people)
13 sextillion km (1.38 billion light-years): Length of the Sloan Great Wall cosmic structure (galaxy filament), about one-sixtieth the size of the observable universe
295 sextillion km (31.217 billion light-years): Co-moving radial distance of farthest cosmic object yet detected—a proto-galaxy seen as it was 400 million years after the Big Bang
880 sextillion km (93 billion light-years): Diameter of the observable universe (co-moving distance)
NOTES
1. Almost Everything
This first chapter is both a scene-setter, a journey plan, and an effort to start conveying the enormity of, well, everything. The room full of dust motes came along after an earlier version in which I tried to give a friendly (perhaps rather epistemological) crash course on what we really mean by terms like universe, existence, and so on. Thanks to Amanda Moon for suggesting otherwise.
The facts and figures come from a wide range of sources. Many, like the number of stars in our galaxy or the number of humans who ever lived, are “common knowledge,” which scientists soon learn is a way of saying “gross approximation.” For example, estimates of the number of stars in the Milky Way are still actively debated, ranging from the 200 billion I quote to as many as 400 billion. New results on the number of galaxies in the observable universe now suggest ten times more than previously thought—bumping us from around 200 billion to over a trillion. See Christopher J. Conselice et al., “The Evolution of Galaxy Number Density at z < 8 and Its Implications,” The Astrophysical Journal 830, no. 2 (2016): 83.
Discrepancies arise because no one is actually counting stars or galaxies one by one. Instead, for stars in the Milky Way, they’re extrapolating from how much light we see from the galaxy, the estimated mass of the galaxy, and how much mass and light we expect each star to contribute. A couple of interesting sources on galactic mass and contents are: Jorge Peñarrubia et al., “A Dynamical Model of the Local Cosmic Expansion,” Monthly Notices of the Royal Astronomical Society 433, no. 3 (2014): 2204–22; and Timothy C. Licquia and Jeffrey A. Newman, “Improved Estimates of the Milky Way’s Stellar Mass and Star Formation Rate from Hierarchical Bayesian Meta-Analysis,” The Astrophysical Journal 806, no. 1 (2015): 96.
There are many great popular accounts of our current understanding of cosmology. Older but still excellent ones include Steven Weinberg’s short The First Three Minutes: A Modern View of the Origin of the Universe (updated edition, New York: Basic Books, 1993), and John Gribbin’s classic In Search of the Big Bang: The Life and Death of the Universe (new edition, New York: Penguin, 1998). More recent reads include Lawrence Krauss’s pugnacious but excellent A Universe from Nothing: Why There Is Something Rather Than Nothing (New York: Free Press / Simon and Schuster, 2012), and the relevant parts of Sean Carroll’s The Big Picture: On the Origins of Life, Meaning, and the Universe Itself (New York: Dutton, 2016).
I mention the idea that our universe might be at least 250 times larger than the present cosmic horizon. That comes from Mihran Vardanyan et al., “Applications of Bayesian Model Averaging to the Curvature and Size of the Universe,” Monthly Notices of the Royal Astronomical Society 413, no. 1 (2011): L91–L95. As for estimates that the “full” universe is much, much bigger—well, all bets are really off. Cosmic inflation in the early universe can give you almost any size you can stomach—right up to 10-to-the-10-to-the-10-to-the-122. That’s from Don N. Page, “Susskind’s Challenge to the Hartle-Hawking No-Boundary Proposal and Possible Resolutions,” Journal of Cosmology and Astroparticle Physics 2007, no. 1 (2007): 004. Really, no wonder many physicists end up in finance.
I find multiverse ideas equal parts fascinating, logical, and “you must be kidding.” It’s hard not to admit that from a physics point of view there are a lot of
theoretical ideas pointing in this direction. But, to use the old adage: extraordinary claims require extraordinary evidence—and that evidence has not yet made itself known to us.
The “foaminess” of the cosmos, sometimes referred to as the “cosmic web,” is a remarkable aspect of the universe. This large-scale texture is mainly driven by the way gravity pulls together the primordial distribution of matter, and that matter’s primordial velocity field. Two projects that give insight into the cosmic matter distribution are the Sloan Digital Sky Survey (www.sdss.org) and the 6dF Galaxy Survey (www.6dfgs.net).
2. Darkness and Light
The general emptiness of the universe (across all scales) is a very hard thing to appreciate without some extreme thought experiments. To make the back-of-the-envelope calculations here, I’ve assumed all stars are the same physical size, which they’re not—most stars are less than about 70 percent of the radius of the Sun, while rare giant stars can be a thousand times larger. Taking the Sun’s radius as an average is a rough-and-ready approximation. I debated discussing black holes here, but feel that it’s important to point out what physics does and doesn’t allow. It is also nicely counterintuitive that the physical size of a black hole (defined by the event horizon) doesn’t scale with mass the way it does with “normal” matter.
The numbers for the density of matter in interstellar and intergalactic space are typical, average values. There are lots of variations. These data are sourced from a century of astronomical observations.
Intergalactic voids are a fascinating manifestation of the primordial variations in matter density on very large scales in the cosmos. They tend to “self-clean,” because low-density cosmic regions (of about 10 million to over 100 million light-years across) experience slightly greater cosmic expansion rates. Galaxies in voids also show signs of somewhat different histories and properties. A review can be found in P.J.E. Peebles, “The Void Phenomenon,” The Astrophysical Journal 557, no. 2 (2001): 495–504.
