The universe as a giant harpstring, oscillating in and out of existence! What note does it play, by the way? Passages from the Numerical Harmonies, I supposed?

—Ursula K. Le Guin, The Dispossessed

Chapters 1 and 2 described the twin pillars of twentieth-century physics: quantum mechanics and Einstein's theories of relativity. Both pillars have been proven valid through experimentation and observation. Any discrepancies come from extreme cases, such as when subatomic particles encounter the crushing gravity of a black hole.

These discrepancies, mostly due to that rascal gravity, have pressed scientists to search for a grand unified theory that will reconcile relativity with quantum mechanics. Superstring theory (aka string theory) is one candidate for the theory of everything (ToE). It proposes that tiny strings vibrate everything into existence. These strings are so small that atoms seem really, really huge in comparison.

As the Doctor (from the television series Doctor Who) might say, string theory is intuitively “wibbly-wobbly timey wimey”¹ and possibly more allegory than science. And yet, it might theoretically explain phenomena that can't be explained using the more conventional models described in the first two chapters. When stretched to its limits, string theory is compatible with many more forms of nature than are observed or predicted by conventional models.

There is no evidence for the existence of strings; however, it is based on solid (albeit complicated) math. This is a touchy topic among scientists because, yes, this math is able to describe the structure of nature, but it is also compatible with describing the natural world. This means that, according to math, all of these worlds must exist even though we cannot see them.

Now, if these universes somehow do exist, there is no causal contact between them and our universe. This is not science. So as long as strings are not observable and no direct experiments can test the theory, it must dwell more in the realm of philosophy than science.

EXTRA DIMENSIONS

String theory relies on the existence of dimensions that we cannot see or conceptually imagine, and, as I suggested before, math does the heavy lifting. Don't worry, you won't see any equations in this chapter!

As mentioned in the first interlude, the Standard Model explains most of what we observe in the universe but not everything (i.e., gravity). So the Standard Model is not quite a theory of everything; rather, it is a theory of most things. Some physicists believe we can go deeper than quarks (the constituent parts of protons) and electrons. To do this, we must depart the known and head for the speculative.

This is where string theory comes in. Instead of thinking of quarks and electrons as single-dimension particles, string theory suggests they might really have two or more dimensions. These dimensions might be tiny, curled-up ones, or so large that our three-dimensional universe can comfortably dwell within it.

Imagine the four strings of a violin. Each string is tuned (stretched) differently so that when they are bowed (an excitation), a different musical note is produced. This isn't too much different in string theory where the elementary particles (quarks, electrons, and their antimatter equivalent siblings) are the musical notes of strings. However, unlike our violin, which anchors the strings so they can stretch in different ways, the strings in the theory float in spacetime. They are tied to nothing, and yet they have tension.

Something to ponder: if they exist, where do the strings come from?

A violin's music comes from its strings vibrating in three dimensions. When we draw these vibrations on a two-dimensional sheet of paper, it looks like a sine or cosine wave (math terms for wavy lines drawn across a flat screen or paper). The strings in string theory are strumming their music in ten, eleven, or twenty-six dimensions.2 The fundamental particles in the Standard Model arise from these vibrations.

Chapter 1 described four of these dimensions: three spatial (length, width, and height) and one of time. The other six or seven or more, if they exist, must be hidden. Otherwise we would be able to experimentally detect them. A good hiding place would be to compact them to a size that is so small that they become Planck-length small—a millionth of a billionth of a billionth of a billionth of a centimeter. Named for Max Planck who defined the base units (length for example) used to define quantum mechanics, Planck-length is so small that classical ideas about physics are no longer valid. Quantum mechanics dominates.

I know this is hard to imagine, so let me help. Consider the edge of a piece of paper that is one millimeter thick. Now imagine a character named Ralph. He is insecure because of his size. He stands one-tenth the height of the paper's edge (0.1 mm). If his size were to represent the size of the entire observable universe, then Planck size would equal 0.1 mm relative to him.

In the early 1990s, physicists realized that string theory faced an uncomfortable dilemma: there was no single string theory. Five unique versions each successfully describe phenomena under certain conditions, and each theory requires an additional dimension or two to describe a particle in the Standard Model, but each breaks down while explaining other particles. If only the five could be united into a single theory then almost everything could be described.

This is where M-theory comes in. M-theory gives us an explanation for why so many dimensions are necessary. It treats each of the five string theories as subsets and serves as a road map to connect them. Of course, another dimension had to be added for M-theory to work. But who's counting? Don't ask me what the M stands for. It is a mystery in physics. I have heard many suggestions but nothing conclusive.

If there are fewer dimensions than quantum events then negative probabilities must be included. Trust me, if this is true then things get ugly. Scientists do not like ugly. So it is better to add them in than subtract them out. If extra dimensions do exist, they might be really small and rolled up into their space. Or possibly the extra dimensions might be very large and contain all of matter and gravity within them.

These large ones are called membrane dimensions, sometimes called branes by physicists. In brane theory, our three-dimensional universe might be a stretched brane floating through a four-dimensional background called the bulk. Imagine a two-dimensional sheet of paper riding the winds of our three-dimensional world. Add a dimension to both (along with a few other considerations), and you get a brane floating in the bulk.

Within the M-theory framework, a brane is required as an attachment point for all of the strings. The tiny dimensions are squashed down into a particular dimensional shape called Calabi-Yau space, from which they are able (mathematically) to produce all of the physics we are able to see. An atom's fundamental qualities depend on this geometry.

Science fiction has plenty of room for these extra dimensions. In Liu Cixin's novel The Three-Body Problem, Earth is invaded by technology hidden in curled dimensions.3 China Meiville's The City & the City deals with a conflict between overlapping dimensions.⁴ Sunborn by Jeffrey A. Carver uses a lot of the science ideas in this book. He has ancient AIs living in compact dimensions inside a black hole.⁵ Now that you know all about hidden dimensions, all you need to do is read the chapters about black holes and AIs.

MEET THE COMPETITION

Loop quantum gravity (LQG) theory is the chief competitor in the search for a grand unified theory. Where string theory attempts to explain everything in the Standard Model and bring gravity into the family of universal forces, LQG is much more modest. It seeks only to reconcile quantum gravity with spacetime.

General relativity treats gravity as a property of the geometry of spacetime, while quantum mechanics treats gravity as a quantum force. LQG theory holds that spacetime itself might be quantized, meaning it treats space as granular rather than continuous as Einstein believed.

So, if you kept zooming in on an area of space, say the distance between you and this book, with an impossibly powerful microscope, you would begin to see space itself pixilate and appear granular. The theory holds that these grains are woven together by finite loops of gravity. This is profound because it means space might be discrete (individual grains) and not continuous.

Unlike string theory, there might be a way to test for loop quantum gravity. All you need to do is study the radiation a black hole evaporates. Researchers believe that if quantum gravity exists, measurable discrepancies will appear in the types of radiation evaporating from a black hole.6

One of the biggest challenges for researchers is to find an evaporating black hole. So far, no one has detected one. The same technique might also be used to find evidence of quantum gravity in background radiation left behind after the beginning of the universe. Don't worry if you have no idea what black hole evaporation means. The topic is absorbed into chapter 6. For now, just know that this theory is testable.

CAN QUANTIZED SPACE SOLVE A PARADOX AND HURT A VILLAIN?

Loop quantum gravity theory might answer the paradox of infinite distance. Allow me to unjustly turn you into a criminal mastermind having a bad day. You, the criminal, spot the Green Arrow, a hero of DC Comics, just in time to see the arrow launching toward your head. Greeny is in a take-no-prisoners state of mind.

If we believe Zeno of Elea (who lived during the 400s BCE), you are safe.⁷ The arrow passes halfway across the warehouse you call a lair, then half the remaining distance, then half again, and so on. I've divided its journey into infinite numbers of shorter and shorter segments. A half, then a half of the half, then half of the half of the half, and so on. The arrow never hits you because it must pass through an infinite number of points that make you infinitely far away. The arrow always gets closer but never strikes. Math has saved you!

Only it won't. Not really. According to physics, you are about to feel a sharp pain and then probably nothing ever again. I will tell you why. There are a few philosophical and mathematical explanations I could provide, but let's go with the quantum one. At any given time after the shot is taken, only a finite number of quantized grains of space are between you and the arrow. Sorry, infinity is not going to help a criminal.

PARTING COMMENTS

The idea behind all the different versions of string theory is that strings are the most fundamental unit of nature. They strum their music in dimensions of the universe we cannot perceive, and yet they create all that we can see. To us, these dimensions might only exist as mathematical constructs. The tiniest of them might be curled into the tiniest of scales, which is Planck length. This size is so small that length might not matter anymore. The largest dimension might be a brane that contains our entire universe.

The five string theories are internally consistent, but separately they fail as an explanation of everything. M-theory is an umbrella theory that unites them. It is a road map for which theory is best at explaining which type of phenomenon.

Loop quantum gravity theory takes the more modest approach of not attempting to explain all particles. Instead it focuses only on gravity. If it can connect gravity to quantized spacetime, then it will have unified relativity and quantum mechanics.

FOR THE RECORD

My favorite intersection of Murphy's Law and string theory: anything in string theory that theoretically can go wrong will go wrong, but if nothing does go theoretically wrong, then experimentally, it is ruled out.