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 are fundamentally incompatible. Does that mean one theory is right and the other is wrong? Or does it mean both theories may be right, at least in part, but they are 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 uniquely incorporate the worlds of both General Relativity and Quantum Theory. Black holes are also characterised by extreme gravity. As we shall see, these particular characteristics make black holes especially 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 forces that govern behaviour of matter within their respective realms. Forces are influences that, when applied to matter, cause matter to accelerate or deform or undergo other changes.
Quantum Theory fully explains three of the four known fundamental forces in the universe, which are 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 force: gravity. Gravity is often called the fourth fundamental force, but as we shall see gravity may or may not be a force.
General Relativity and Quantum Theory both perform spectacularly well. 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 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 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 entirely different and unrelated concepts, while General Relativity regards time and space as an integral entity called 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 merely by 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 problem of observing sub-atomic entities to bouncing a bowling ball off a mosquito to discern its contours!
While the Heisenberg Uncertainty Principle is hugely important in Quantum Theory, it plays no part in General Relativity. At macro level, it makes no sense to say that the location and momentum of objects can only be determined with non-zero probability. Take yourself! Do you know where you are in this moment? Do you know if you are moving? Yes, of course you do!
Given the large differences between Quantum Theory and General Relativity, much of the research undertaken to reconcile the two theories has focused on gravity, particularly in the context of black holes. Gravity is special, because it is the only fundamental force, which does not (yet) have a known base particle (although such a particle has already been given a name, graviton). By contrast, the three fundamental forces in the Standard Model each have one; 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 they are distorted by our observations (a manifestation of the Heisenberg Uncertainty Principle).
While no one has yet discovered a graviton, it is equally true that no one has disproved their existence either. Gravity waves were discovered in 2015, so it may well be that gravitons do exist. 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 General Relativity will have to adapt accordingly.
Unfortunately, it will not be easy to find a graviton, because gravitons have absolutely tiny energies. Gravity is the weakest force in the universe. To fully appreciate its weakness, consider how easily you are able to pick up, say, an apple. The gravity of the whole of Planet Earth is acting on that apple, trying to pull it to the ground, but you hardly spend 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 after all. It 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 the object moves, it produces waves in spacetime, just like ripples on water. The greater the mass of the object, the steeper its associated curvature in spacetime and the greater its gravity waves when it moves. The gravity wave discovered in 2015 originated in a collision of two black holes 1.3 billion light years away. What the universe does echoes in 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 as the gradient of spacetime around the large object increases. The flight path of the small object only appears 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 due to a 'force', but simply an acceleration that occurs due to the curvature of the spacetime through which it travels. In fact, to General Relativists, the force of gravity does not exist.
Satellite traveling in a straight line on a geodesic in three dimensions, including time (Source: here)
Having discussed the basics of gravity, we are now turn our attention to black holes and their role in the quest to unify Quantum Theory and General Relativity. Black holes are characterised by extreme gravity. They also contain within themselves both the micro world of Quantum Theory in the singularity at the heart of the black hole as well as the macro world of General Relativity at the rim and just inside the black hole.
Because of these features of black holes, it should therefore be possible, in principle at least, to observe empirically how an object entering a black hole transitions from obeying the laws of General Relativity at the rim to obeying the laws of Quantum Theory in the singularity.
Imagine an object entering a black hole. The object starts its journey from outside the event horizon, which is a distinctly General Relativity macro world. General Relativity also perfectly describes the object as it crosses the event horizon and drops towards the singularity. Once it reaches the singularity, however, the object enters a distinctly quantum world due to the unfathomably small dimensions of the singularity.
In addition to potentially reconciling General Relativity and Quantum Theory, black holes also have the potential to explain how the universe began, because the conditions in the singularity are believed to closely resemble the conditions that existed in the Big Bang.
Unfortunately, despite their promise, black holes have not proven easy to study and the results have been disappointing.
For starters, physicists have not been able to actually observe what goes on inside black holes, because the gravitational pull is so strong that any observation, we might wish to make can never leave the black hole. Indeed, black holes are black because not even light escapes.
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)
The prediction of infinity at 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 basically rendered useless by its own prediction of infinity, at least as far as describing reality in the singularity is concerned.
So where does that leave physics and the reconciliation of Quantum Theory and General Relativity? Black holes may have not brought physicists much closer to their elusive goal of unifying theory, but 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 means that General Relativity’s prediction of infinite mass/energy in the singularity simply cannot be true. Hawking Radiation also means that black holes must have finite lives. Black holes are therefore not the end of time and space as was once believed, but rather a stage in the enormously long life-cycles of stars.
The great source of hope arising from Hawking's discovery is that Hawking Radiation is consistent with Quantum Theory and it exists in the macro world of General Relativity. Hence, it would seem there may yet be new avenues for physics to find a unification of Quantum Theory and General Relativity.
The End
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