$$\require{cancel}$$

# 17.28: String Theory and Cosmology

How ambitious should scientists be in their hunger for explanation? Is it really possible to explain the universe and everything it contains? In the earliest age of science, Archimedes tried to identify a few axioms or principles from which he could deduce anything, and the Atomistic believed that the diversity of all observed phenomena were caused by the collision of atoms. Much later, the power of Newton’s universal law of gravitation led the French mathematician Pierre-Simon Laplace to suggest that a sufficiently powerful intellect (we might say a computer) that knew the positions and motions of all particles at one time, could calculate their motions and positions at any time in the future.

The determinism implied by Newtonian mechanics and gravity was abhorrent to many humanists and philosophers because we humans are collections of particles, so perhaps our choices and free will are illusory. The 20th century reshaped these grand expectations with a dose of uncertainty. Determinism is in practice thwarted by the probabilistic nature of quantum theory, by the unpredictable and emergent properties of complex systems, and by extreme sensitivity to initial conditions that leads to mathematical chaos. Since a "theory of everything" must also be a self-consistent, mathematical theory, notable physicists like Freeman Dyson and Stephen Hawking concluded that the search for an ultimate theory with a small number of principles might be fruitless. Even if we find a set of equations that describes everything in the universe, we’re still left with unanswered questions about origin and meaning. As Stephen Hawking has asked: "What is it that breathes fire into the equations and makes a universe for them to describe "

Most scientists accept that no single theory can be used to understand and predict the behavior of every physical system. Rather, they hope that they can continue the march towards the unification of the four fundamental forces, where those forces that are each distinct in our current low-energy universe are melded into a single super force at a sufficiently high energy. Grand unified theories try to unite the electromagnetic force with the weak and strong nuclear forces. The most promising theories are based on super symmetry, where known particles have a "shadow" partner and there’s no distinction between the particles that make up matter and the particles that carry forces.

The final step on this road is the unification of grand unified theories of elementary particles with general relativity, our best theory of gravity. Einstein beat his head against this brick wall for thirty years, until he was on his death bed. The problem’s hard because particles are grainy and discrete while gravity is smooth and supple. They’re as distinct as wood and marble. Particle theory only works when gravity is so weak we can pretend it doesn’t exist and general relativity only works when the graininess and uncertainty of quantum theory is ignored. Quantum gravity has been the "Holy Grail" of physics since Einstein’s death yet there’s no chance of any lab experiment creating the conditions where the four fundamental forces are unified. Instead, all roads point back to the big bang, and something called the Planck time.

Projecting the expanding universe back towards a singularity — a state of infinite temperature and density — the limit of physical understanding is reached at the Planck time. The Planck time is an infinitesimal 10-43 seconds after the big bang. It’s the smallest interval where time has any meaning. At that very early epoch, the universe was a mere 10-35 meter across, or one hundred billion billionth of the size of a proton. That distance is called the Planck scale. At that tiny size, space and distance measurement don’t have any meaning. Space-time might be foamy rather than smooth and continuous as general relativity would predict. The temperature back then was a staggering 1032 Kelvin, hot enough that the puny force of gravity was equal to the other forces that are far stronger in the current, cold universe. These benchmarks define the limits of both measurement and understanding. Here’s another way to think of the Planck time and the Planck scale, independent of whether or not we are describing the early universe. Heisenberg’s uncertainty principle says evanescent or virtual particles come and go all the time, and they can be massive if their lifetime is very short. Einstein’s general relativity says enough mass in a small enough space can create a black hole: a region with gravity so strong its escape velocity is the speed of light. Combining these ideas, there is a scale small enough for virtual black holes to exist. It’s the Planck scale. In first instant of time after the big bang, space was curved on the scale of particles, particles had the attributes of black holes, and space-time distortions were governed by quantum uncertainty. Think of a pot of water on a hard boil and that’s a very crude approximation for the seething space-time foam of the very early universe.

Physicists think they have found a way forward by making an audacious leap beyond the Standard Model. Think of a guitar string. It’s under tension, and depending on the amount of tension and how it’s plucked, it gives off different sounds. Different harmonics or excitation modes of the string make different musical notes. Now imagine the string is freed from the guitar but it still has tension so it can oscillate and vibrate. Some of these floating guitar strings remain open, with both ends free, and others are closed, forming a loop. Now imagine that these strings are invisibly small and far smaller than any particle — they are one-dimensional objects on the Planck scale, about 10-35 meters. That, in a very small nutshell, is what physicists came up with for unifying gravity and quantum mechanics. In string theory, each different particle is a mode of vibration or "note" of an invisibly small string. The open and closed strings can interact and combine. As a string moves through time, it traces out a sheet or a tube, depending on whether it’s open or closed. The vibration modes of the string generate the mass, spin, and charge that a conventional particle would have. By adding super symmetry to the mix, strings can describe both particles and forces, so an electron is a vibrating string, but so too is a graviton, which carries the gravity force. The theory, renamed super string theory, naturally includes gravity as well as all the interactions of particles in the Standard Model.

The promise of the new theory was so great that many smart young physicists were willing to learn the gruelingly complex and abstract mathematics needed for a quantum theory of interacting strings. But there were two problems and one big surprise. The first problem was that the size and the energy scale of strings is many trillions of times beyond what can be probed by lab experiments or accelerators, so there seemed to be no way to test the theory. Second, detailed work in the 1980’s showed there were five different types of string theory, each fiendishly difficult to work on, with no apparent way to decide between them. And the surprise? All of the supersymmetric string theories involved ten space-time dimensions! The next breakthrough was achieved in the 1990’s by theoretical physicists at several universities, most notably Edward Witten at Princeton. What they thought were five completely different string theories were actually different ways of looking at the same theory. Imagine each theory was like a large planet where we only knew of a small island somewhere on the planet. It’s so difficult to explore the theory mathematically that we don’t know what else might be found on the planet. As techniques improve, we’re able to travel around the seas on each planet and find new islands. Only then is it realized that those five string theories are islands on the same planet, not different ones! This world has been called M-theory, where the M stands for membrane. Many theorists think that a formulation using membranes will be the most productive way forward. The fundamental object is a membrane or sheet rather than a string. The general object, called a "brane," can range in dimension from zero to nine. A point is a zero-brane, a line is a one-brane, a surface or membrane is a two-brane, and so on up to dimensions that have no name to describe them. M-theory is a beast to work with because the number of different types of membranes in different dimensions increases exponentially. The number of distinct physical states in a theory with ten or eleven dimensions is essentially infinite. However, the number of states that correspond to a universe roughly like ours, with just four dimensions of space and time, is a more tractable number, "only" 10500! Each of these states has hidden dimensions on the Planck scale and a unique and different set of forces and particles on the macroscopic scale. This situation is called the string theory "landscape." The question arises: What if our universe represents one of these states, while the others represent other possible universes, radically different from each other and from ours?

String theory notched up an important success in 1996 when it was used to explain the surprisingly large entropy of black holes. For the first time, a result derived from classical physics had been derived using string theory, demonstrating the explicit connection between strings and gravity. However, string theory has been subject to a substantial backlash as its enormous promise seems unfulfilled. In the past decade, several hundred exceptionally talented theoretical physicists have written thousands of papers on string theory, yet it’s not been tested so it can’t be confirmed or refuted. Some argue that the complexity and non-uniqueness of the theory means that it can’t be tested and therefore isn’t truly science.

Is string theory a Theory of Everything or a Theory of Nothing? As usual in these heated academic debates, the truth is likely to be somewhere in between. String theory has provided real insights into the unification of quantum mechanics and gravity, and although the conditions where hidden dimensions can’t be created in the lab, the hypothesis makes predictions of effects at lower energies. The Large Hadron Collider will test super symmetry, for example, which is a key component of string theories. Edward Witten, the string theory guru who was made a full professor at age 29, has said: " String theory is a part of 21st century physics that fell by chance into the 20th century." He noted that the technical tools required to create the theory were still being invented. We’re exploring a vast undiscovered country and are still building the vehicles that we need for the journey. It will take time, and patience is required.