We can summarize electricity, magnetism and gravity into equations one inch long, and that’s the power of field theory. And so I said to myself: I will create a field theory of strings. And when I did it one day, it was incredible, realizing that on a sheet of paper I can write down an equation which summarized almost all physical knowledge.”
There are many unsolved problems in fundamental physics that are routinely examined yet to this day have yielded no solutions. Perhaps one of the most perplexing problems on the forefront of physics is the fact that the four fundamental forces of nature don’t seem to warrant unification. The strong and weak nuclear forces along with the electromagnetic force are unified into the theory of the small, which is quantum mechanics. However, the fourth fundamental force, gravity, is a bit more stubborn. General relativity, the theory of the large and massive, describes how gravity works; but when one tries to use the equations of each theory together, to predict gravitational effects on the quantum scale, the basic principles begin to break down. The math is no longer conclusive and the equations begin to fall apart. It seems the theory of the small and the theory of the large are forever separated. However, some mathematicians and physicists have come up with ways to get the mathematics to behave properly, and their hypotheses (such as string theory) have profound implications; but there is currently no way for their innovative ideas to be tested. This lack of conformity between the two theories has been one of the most perplexing problems in physics for most of the last century, and still is today.
General relativity, developed by Albert Einstein in the early twentieth century, describes the effects of gravity in terms of the curvature of space-time due to the presence of mass. One could imagine a bed sheet held flat in the air, and a bowling ball being placed in the middle of it. The bowling ball could represent the Sun, and a golf ball on the edge could represent the planet Earth. When the golf ball is released, it falls along the curvature of the sheet, in toward the bowling ball. Raise this example from a two-dimensional sheet to three-dimensional space, and you have a basic understanding of general relativity. Gravity is also a long range force, meaning that every object in the universe that has mass is gravitationally attracted to you, and you to it. Right now, the bending of space around the planet Earth is keeping you secured to your chair, and that same bending of space extends throughout the entirety of the universe. General relativity is also critical to cosmology, as it describes the behavior of space-time on the largest of scales.
Unlike general relativity, quantum mechanics describes the nature of reality on extremely small scales. Once one is in the realm of subatomic particles, such as the electrons, protons and neutrons that constitute atoms, the quantum laws become prevalent. Quantum mechanics is not very well understood, as at its heart is the quantum measurement problem, which is another discrepancy in physics that I will not go into but you can read more here. Quantum mechanics deals with uncertainty, utilizing the Heisenberg Uncertainty Principle which describes the most basic of quantum phenomena. The principle says that the position of an electron cannot be known with total certainty if the velocity is known with total certainty, and vice versa. If you know the position of something with certainty, it has no velocity to measure; if you know the velocity with certainty, the position is constantly changing, so it cannot be known with certainty. Since the quantum deals with uncertainty, it can only make predictions in terms of probability.
For example, before observing an electron and hence knowing its position with almost complete certainty, the wave function of the electron (which can also be called the probability wave) is spread throughout all of space and time. What this means is that before the position of the electron is known (before the particle is observed), it could be anywhere throughout space and time, and it could even be in two places at once. I know this all sounds fantastical and counter intuitive, and it is; but the probabilities produced on this small scale have been verified again and again by experimentation over the last century. It only seems strange and counter intuitive because we are much too large to observe these quantum phenomena in our daily lives. They are still present, but too miniscule to be noticed. If we lived on the quantum scale, the collapse of the wave function describing a quantum system (the probability that the electron could be anywhere) down to one quantum state (the electron being in one place) due to measurement would be a very normal occurrence.
The two theories described above may not work together mathematically, but they seem to be working together in nature. There are places where it seems they are one, two of which are black holes and the primordial universe. A black hole is a region of space so distorted and warped by the presence of a large amount of mass squeezed in a very small volume that light can’t even escape the gravitational field. The primordial universe (the universe as we know it in its most early known state) is an incomprehensible amount of energy (equivalent to the presence of an incomprehensible amount of mass) squeezed into a very small volume, smaller than a single atom. Both of these scenarios involve huge amounts of mass which would fall under the realm of general relativity, but they are squeezed in such small volumes that they fall under the realm of quantum mechanics as well.
At the heart of a black hole, a certain amount of mass is squeezed down to an infinitely small point. At the very beginning of the universe, an infinite amount of energy was squeezed into an infinitely small volume. In both cases, these infinitely small spaces are known as singularities. A singularity in physics is a place where our understanding of how the physics works is non-existent. Our knowledge of how physical laws work in both of these cases is non-existent because general relativity and quantum mechanics are not compatible with our current mathematical models and understanding. When we use the equations of general relativity with quantum mechanics to describe black holes or the primordial universe, the equations break down and mathematical anomalies occur that just don’t make any real sense, yet. But it is the knowledge that the two theories seem to be working together in nature that drives humanity forward always searching for the solution.
This is arguably the biggest problem in fundamental physics. There are candidates for the Grand Unified Field Theory (the theory that would bring general relativity and quantum mechanics together) such as string theory (which isn’t actually a theory, but rather a hypothesis) and loop quantum gravity. However, both of these currently have no way of being tested, so they will remain hypotheses until they can be experimentally verified or dismissed. So it seems for the time being that the theory of general relativity and the theory of quantum mechanics will remain separate. But, you or I could be the ones that figure this out! This is one of my favorite aspects of science and reality, that everything is not known, and that there are problems that need to be solved.
So go forth and learn!