What is the singularity theory? Why did Hawking come to question his theory of Big Bang singularity?

Hawking’s mathematical proof that space and time had a beginning, according to general relativity, was what first propelled him to fame within the physics community. Later, reflecting on his own theoretical proof about the big bang singularity, Hawking came to believe that they imply the theory of general relativity is incomplete, not that the universe actually did begin at a singularity.

Read more to learn about the singularity theory and why Hawking came to believe that it indicates a problem.

## A Quantum Theory of Gravity

Although the inflationary big bang theory explained why some of the initial conditions of the universe were just right, Hawking felt that further theoretical development was needed to scientifically (that is, without invoking a divine creator who could arbitrarily fine-tune the universe for the benefit of humankind) explain how the universe came to be the way it is.

This led Hawking to suggest that a quantum theory of gravity might provide a better solution, for two reasons: First, it would eliminate the “singularity” (which we’ll discuss in a moment). Second, it would address the fine-tuning problem more comprehensively. However, before we discuss these two benefits, let’s take a step back and discuss what the “singularity” is.

### The Big-Bang Singularity

By the time Hawking was in graduate school, the expansion of the universe was widely accepted, and much of Hawking’s early work in physics focused on using general relativity to model the early universe.

So, what is the singularity theory? Hawking (along with George Ellis and Roger Penrose) was able to show that, based on general relativity, the universe began at a “singularity,” that is, a point where the entire universe was compressed into an infinitely small point, with infinite density and infinite curvature of space-time. Hawking points out that, at a singularity, all the laws of physics break down, because space-time itself ceases to exist. After all, if you confine space into an infinitely small space, then you don’t have any space left.

Since time is relative to the curvature of space (or, equivalently, to gravity), this means that time also ceases to exist at a singularity. Thus, Hawking’s work showed that according to general relativity, time itself began at a finite point in the past.

Hawking’s mathematical proof that space and time had a beginning, according to general relativity, was what first propelled Hawking to fame within the physics community.

#### Eliminating the Singularity

Later, reflecting on his own theoretical proofs about the big bang singularity, Hawking came to believe that they imply the theory of general relativity is incomplete, not that the universe actually did begin at a singularity.

Hawking points out that the infinite density and temperature of the universe at the singularity are red flags, indicating a problem with the theory, because quantities are never infinite in real life. Just as quantum mechanics was developed to solve the problem that classical theories predicted infinite radiation from a hot body, a quantum theory of gravity would eliminate the singularities (and infinite quantities) that general relativity predicts.

Furthermore, according to Hawking, in quantum gravity, spacetime could take the shape of a closed four-dimensional surface (like a sphere, except that the surface of a sphere is just two-dimensional instead of four-dimensional) with no beginning or ending point. Thus, he refers to this concept as the “no-boundary model.”

Hawking explains that the “no-boundary model” makes sense because, to model gravity in quantum mechanics, you have to use “imaginary numbers” for the time variable. (In mathematics, an “imaginary number” is the square root of a negative number.) According to Hawking, if you allow the time variable in a quantum model to have an “imaginary” value, then there is no longer any difference between the time dimension and the spatial dimensions of the model. This means that …

### Eliminating the Fine-Tuning Problem

Recall from the previous Question that quantum mechanics doesn’t give you an exact path for a particle that you’re modeling—rather, it gives you a probability map showing where the particle is most likely to be. You find this probability map by adding up all the possible paths that the particle could take.

Hawking conjectures that if you could model the big bang with a quantum theory of gravity, this would completely eliminate the need to fine-tune the initial conditions of the universe, because the universe wouldn’t have just one set of initial conditions, but every possible set of initial conditions. Therefore, the conditions we observe will have to show up somewhere on the probability map.

This has a similar effect to postulating an infinite number of universes, as the strong anthropic principle does, but without contradicting the scientific method as the SAP does.

### Recap

According to the theory of general relativity, the universe began at a “singularity” where all matter, energy, space, and time came into existence at an infinitely small point and expanded outward from there.

What Is the Singularity Theory in Physics?

### ———End of Preview———

#### Like what you just read? Read the rest of the world's best book summary and analysis of Stephen Hawking's "A Brief History of Time" at Shortform .

Here's what you'll find in our full A Brief History of Time summary :

• The search for a theory that explains the history and evolution of our universe
• Stephen Hawking's discussions about time, space, dimensions, and quantum theory
• How time travel would theoretically work

#### Elizabeth Whitworth

Elizabeth has a lifelong love of books. She devours nonfiction, especially in the areas of history, theology, and philosophy. A switch to audiobooks has kindled her enjoyment of well-narrated fiction, particularly Victorian and early 20th-century works. She appreciates idea-driven books—and a classic murder mystery now and then. Elizabeth has a blog and is writing a book about the beginning and the end of suffering.