Do Black Holes Unify Quantum Theory and General Relativity?

Actual radio image of a black hole (Source: here)

This blog post is a brief layman's review of Quantum Theory, the Theory of General Relativity, and the reasons for the perceived incompatibility of the two theories. I place particular emphasis on black holes, which have played a key role in efforts to reconcile the two theories. None of this stuff is cutting edge. I am not even a physicist. My objective is solely to improve my own understanding of this fascinating subject. In future notes, I may explore more recent developments in Quantum Theory and General Relativity.

Theoretical physicists have dreamed of unifying Quantum Theory and the Theory of General Relativity for more than a hundred years. Both theories are absolutely pivotal in modern physics and both have contributed significantly to our understanding of the universe. Both theories are also strongly supported by empirical evidence.

It is therefore quite remarkable that Quantum Theory and General Relativity appear fundamentally incompatible. Is one theory is right and the other wrong? Or are both theories right, at least in part, but somehow subordinated to a larger over-arching and yet-to-be discovered 'Theory of Everything' that reconciles them?

Of all the observable phenomena in the universe, black holes incorporate both the macro world of General Relativity and the micro world of Quantum Theory, making black holes uniquely suited for the study of unification of Quantum Theory and General Relativity.

Let us kick off with a review of theory.

Quantum Theory explains the behaviour of the tiniest fundamental particles in the universe and the forces that guide them. The quantum world is a micro environment, at and below atomic level. At the other end of the scale, General Relativity explains the behaviour of huge objects in the macro world of planets, stars, galaxies, black holes, and the universe itself.

No other theories have achieved the depth and scope of Quantum Theory and General Relativity.

Both theories focus on the interactions between matter within their respective realms. Interactions are the acceleration, deformations, or other changes that occur when matter comes into proximity with other matter.

Quantum Theory fully explains three of the four known fundamental interactions in the universe, namely electro-magnetism, the strong force that binds together sub-atomic particles in the atom, and the weak force, which accounts for radiation. Together, the three forces are known as the Standard Model. General Relativity only focuses on one interaction, namely how large objects bend spacetime. Gravity is often called a fundamental force, but gravity is actually not a force.

General Relativity and Quantum Theory both perform spectacularly well in experiments. Predictions based on Quantum Theory are astonishingly accurate in repeated experiments and the theory has been applied with great success to the real world in the development of transistors, electron microscopes, lasers, medical imaging, light-emitting diodes, even mobile phones.

You can thank Quantum Theory for your modern day dog and bone (Source: here)

General Relativity has a similarly impressive track record. The theory accurately determines the location and speed of objects in space ranging from light particles emitted from distant stars to entire galaxies, and beyond, including black holes. All space travel, including numerous successful journeys to the Moon and Mars, is based on the predictions of the Theory of General Relativity.

Yet, despite their phenomenal successes, Quantum Theory and General Relativity are to all intents and purposes incompatible. Let me try to illustrate the nature of this incompatibility.

In Quantum Theory, time is absolute, meaning everyone experiences time the same way, whereas General Relativity regards time as subjective, meaning that time varies (is ‘relative to’) the position and momentum of the observer. Quantum Theory treats time and space as different and unrelated concepts, while General Relativity regards time and space as an integral entity (spacetime).

The two theories also have very different prescriptions for how we should view the world. Quantum Theory says the speed and position of particles can never be pinpointed with accuracy, because entities are so small that by merely observing them, we change them or move them, or in other ways alter them. This is known as the Heisenberg Uncertainty Principle.

Brian Kiefer, my inspirational high school chemistry teacher, likened the challenge of observing sub-atomic entities to trying to discern the contours of a mosquito by bouncing a bowling ball off the mosquito!

The Heisenberg Uncertainty Principle plays no part in General Relativity. At macro level, it makes no sense to say the location and momentum of objects can only be determined with non-zero probability. Take the example of yourself! Do you know where you are in this moment in time? Do you know if you are moving? Yes, of course you do!

Given these rather fundamental differences between Quantum Theory and General Relativity, much of the research undertaken to reconcile the two theories has focused on black holes in which both General Relativity and Quantum Theory ought, in principle, to co-exist.

At the surface of a blck hole, the bending of spacetime increases sharply. We call this bending of spacetime gravity. It is the only fundamental ‘force’, which does not have a known particle base (although such a particle has already been given a name, graviton). By contrast, the three fundamental forces in the Standard Model each have a particle base; photons and electrons are the particles in magnetic and electrical fields, while gluons and W and Z bosons are particles in the strong and weak force fields, respectively.

It not clear if the force is with gravity (Source: here)

Actually, the word ‘particle’ is misleading, because what we call particles are actually waves, which have been put into a state of excitation; they only appear as particles when we look at them, because by looking at them we distort them (a manifestation of the Heisenberg Uncertainty Principle).

While no one has yet discovered a graviton, no one has disproven their existence either. Gravity waves were discovered in 2015, so it may well be that gravitons exist as well. If they do, the unification of General Relativity and Quantum Theory will have taken a huge leap forward as gravity will then clearly belong alongside the three forces in the Standard Model and Theory of General Relativity will then have to be adapted accordingly.

Unfortunately, in practice it may not be easy to find gravitons, because they have absolutely tiny energies. If the force of gravity even exists, it will be among the weakest forces in the universe. To fully appreciate the weakness of gravity, consider how easily you pick up, say, an apple. The gravity of the entire Planet Earth acts on the apple, trying to pull it to the ground, yet you hardly expend any energy lifting it. If the gravitational pull of Planet Earth is that weak, imagine how weak must be the gravitational pull of a graviton, which is hypothesised to have a diameter of 10^-37 meters (a zero point thirty-six zeros and then a one).

Graviton diameter:

0.0000000000000000000000000000000000001m

General Relativity does not concern itself with gravitons. It is a macro theory and defines gravity as curvature in spacetime. Spacetime has four dimensions: three directions plus time. Any object with a non-zero mass creates a curvature in the fabric of spacetime. Additionally, when an object moves it produces waves in spacetime, just like ripples on water. The greater the mass of an object the steeper its associated curvature in spacetime and the greater the gravity waves that are created as it moves. Interestingly, the gravity wave discovered in 2015 originated from a collision of two black holes 1.3 billion light years away. What the universe does genuinely echoes in (near) eternity.

Planet mass depresses spacetime: two-dimensional representation (Source: here)

According to General Relativity, when a small object enters the vicinity of a large object in space, it will ‘fall’ into the depression in spacetime created by the larger object. The small object does not actually change direction. Rather, it continues on its merry way in a straight line, albeit at a higher speed due to the steeper gradient of spacetime around the large object. The flight path of the small object only appears to be curved because we tend to represent the journey in two-dimensional space.

Geodesic flight path (Source: here)

Trajectories through curved space are called geodesics. They are exactly like the flight paths of jetliners. Jetliners fly in perfectly straight lines across the world even though their trajectories appear to be curved. General Relativity says that when a small object is 'drawn' to a larger object, it is not actually pulled in by a 'force' emanating from the larger object, but accelerates as spacetime curves more sharply in the proximity of the larger object. General Relativists do not believe the force of gravity exists.

Satellite traveling in a straight line on a geodesic in three dimensions, including time (Source: here)

Having discussed the basics of gravity, we can now turn our attention to black holes and their role in the quest to unify Quantum Theory and General Relativity. As mentioned previously, they contain within themselves both the micro world of Quantum Theory near the singularity at the heart of the black hole as well as the macro world of General Relativity with bending of spacetime at the rim and just outside the black hole.

Because of this duality, it should be possible, in principle at least, to observe empirically how an object that enters a black hole transitions from obeying the laws of General Relativity at the rim to obeying the laws of Quantum Theory at the singularity.

As an aside, black holes should also have the potential to explain how the universe began, since the conditions in the singularity are believed to closely resemble the conditions that once existed in the Big Bang.

Imagine an object entering a black hole. The object starts its journey outside the event horizon, which is a distinctly General Relativity macro world. General Relativity perfectly describes the object as it crosses the event horizon and drops towards the singularity due to bending of spacetime. When the object reaches the singularity, it now exists in a distinctly quantum world due to the unfathomably small dimensions of the singularity.

Unfortunately, black holes have not proven easy to study and efforts to reconcile General Relativity and Quantum Theory using black holes have been disappointing. For starters, physicists have not been able to observe what goes on inside black holes, because the bending of spacetime is so strong near the singularity that observation never leave the black hole. Black holes are black precisely because not even light can escape.

Physicists have therefore been forced to study black holes using mathematics. And herein lies the second problem. Using the language of mathematics, General Relativity says that gravity (the curvature of spacetime) reaches infinity in the singularity of the black hole. The singularity also has infinite mass – or energy – and zero volume.

The bottom of the black hole stretches to infinity (Source: here)

Infinity, as in the singularity, presents major conceptual and practical problems. After all, infinity is generally not found in nature and it is impossible to do calculations with infinity. General Relativity is therefore rendered useless by its own prediction of infinity, at least as far as describing reality in the singularity is concerned. In other words, at the very point where the two theories are supposed to reconcile one of the theories (General Relativity) breaks down.

So where does that leave physics and the reconciliation of Quantum Theory and General Relativity? While black holes have unified the theories all is not lost. In 1974, physicist Stephen Hawking discovered so-called Hawking Radiation, which is a kind of evaporation emitted by black holes. The existence of Hawking Radiation suggests that General Relativity’s prediction of infinite mass/energy in the singularity cannot be true and that black holes must have finite lives. As such, they are not the end of time and space, but rather stages in enormously long life-cycles of stars.

But if black holes are indeed finite events that can be fully described by the macro Theory of General Relativity then we lose the link to the micro world of Quantum Theory.

So, its back to basics. Meaning forming hypothesises, designing experiments, collecting data, and testing the hypothesis. Basic fundamental science. Black holes may yet offer a way to reconcile Quantum Theory and General Relativity, but for now we are back at Square One.

The End