Can There Be a Successful Theory of Quantum Gravity?


By Don LincolnFermilab

Why do scientists think that we’ll one day discover a theory of quantum gravity? I suppose one answer is that all of the other forces all have a quantum formulation, so surely gravity must, right? After all, if one does it, everyone must, right? Somehow, and I don’t quite know why, I have a mental image of how Mother Nature would answer this.

A 3D rendering of gravitational waves around a black hole
It may seem that there should be something called quantum gravity. (Image: Varuna/Shutterstock)

Mother Nature and Gravity

Let’s imagine Mother Nature lecturing her son, whose name is gravity by the way. She’s saying, “Gravity Nature! Why did you become all quantum-y?” Gravity, being a typical kid says, “But, Mom, all the other forces were doing it.” To which Mother Nature replied, “I don’t care! If all the other forces jumped off a bridge…” 

Well, I think you get the drift of how the rest of that conversation would go. The answer, “That’s how the other forces turned out,” really isn’t all that great of an answer. Yet the idea of quantum gravity is a popular one. Why is that?

So, to answer that question and to understand why physicists think that there must be a quantum nature of gravity, we need to first turn to why they thought that there must be a theory of quantum mechanics governing the orbits of atoms. So, we’re talking about a time well over a century ago.

Rutherford’s Discovery

It was in 1911 that physics legend Ernest Rutherford discovered that an atom had a nucleus at its center, surrounded by electrons. He didn’t know exactly what the electrons did, but he knew of a paper written by Japanese physicist Hantaro Nagaoka that imagined that electrons orbited a small nucleus. 

Nagaoka devised his model in 1904, so his thinking predated Rutherford’s experimental evidence of the structure of an atom. Rutherford was aware of Nagaoka’s work and cited it in his discovery paper.

There was a problem, and the problem is simple to understand. According to the theory of electromagnetism first worked out in the 1870s by James Clerk Maxwell, any electrical charge will emit radiation when it is accelerated. Any object that moves in a circular path does so because it is accelerated. Otherwise, it would move in a straight line. Like Newton said, an object in motion tends to stay in motion, unless acted on by a force.

This article comes directly from content in the video series The Evidence for Modern Physics: How We Know What We KnowWatch it now, on Wondrium.

Why Should There Be Fixed Orbits around Atoms?

An electron moving in circular orbits both has a charge and it experiences acceleration, so it would have to emit radiation, which means it would lose energy. If it lost energy, it would move more slowly and, eventually, the electron would spiral down into the nucleus. You can even calculate how long it would take. It would take 16 trillionths of a second. Yet that doesn’t happen. Atoms don’t implode in a fraction of a second. 

Portrait of Niels Bohr circa 1910
According to Niels Bohr, atomic orbits are quantized. (Image: Unknown/Public domain)

So, why is that? Well, it’s quantum mechanics. In 1913, Niels Bohr proposed the Bohr model of the atom. It said that, for reasons that he didn’t understand at the time, there were a series of fixed orbits around the atom, each with an increasing unit of spin. The lowest possible orbit had a spin of one unit.

And that, as they say, was that. Atomic orbits were proposed to be quantized. Quantum mechanics moved on, of course. It all started to save the atom. An electron orbiting an atomic nucleus and experiencing classical electromagnetism couldn’t exist.

The Problem of Quantum Gravity

So, what does that have to do with quantum gravity? Well, to begin with, according to general relativity, a massive body emits gravitational radiation when it experiences acceleration. And, as we have established, an electron orbiting a nucleus is accelerating. 

Thus, the same motivation that required the creation of ordinary quantum mechanics also means that there must a solution of some sort to answer the problems of gravitational radiation in general relativity.

Now, does that mean that quantum gravity must be similar to ordinary quantum mechanics? Well, no, it doesn’t. In fact, technically, I guess you don’t even need to call it quantum gravity, but there are two things that are true. 

The first is that there needs to be a solution to the problem of the stability of atoms to gravitational radiation. And the second is that general relativity falls apart when it is applied to the world of the very small. At a minimum, there needs to be a new and improved theory that works in the microcosm. So, calling it quantum gravity is pretty apt, but it doesn’t mean that a successful theory of quantum gravity will look anything like quantum mechanics.

Common Questions about a Successful Theory of Quantum Gravity

Q: What was the problem regarding the Nagaoka model and Rutherford’s work?

According to James Clerk Maxwell, electrical charges emit radiation when accelerated. Also, objects moving in a circular path emit radiation since they are accelerated, or they move in a straight line. And since, electrons moving in circular orbits have a charge and experience acceleration at the same time, they would have to emit radiation, meaning they would lose their energy, move more slowly, and eventually spiral down into the nucleus by the force of gravity in 16 trillionths of a second. But that never happens.

Q: What is the Bohr model of the atom?

According to this model, there are a series of orbits around the atom, each with an increasing unit of spin, and atomic orbits were quantized. Bohr’s model also proposes that electrons could not orbit an atomic nucleus while experiencing classical electromagnetism.

Q: Why a successful theory of quantum gravity will not necessarily look like quantum mechanics?

Since there needs to be a solution to the problem of the stability of atoms to gravitational radiation. Furthermore, general relativity doesn’t work when it comes to very small scales. So there has to be a new, improved theory about microcosms.

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