1.2 Contradictions in Physics Review

summary

The scientific quest to understand the fundamental laws of nature has been ongoing for centuries.

In this lecture, you will learn about our ongoing confusion, progress, and excitement about the edge of our knowledge.
Interestingly, the edge of our knowledge—the frontier of what we currently understand—coincides with the edge of the physical universe; horizons that surround things like black holes.
We understand an amazing amount about the universe that we live in. We can launch a rocket from the surface of Earth and precisely predict its trajectory through space.
But at the same time, there are very basic questions we can ask whose answers are still completely unknown. Why are there three spatial dimensions? How did our universe begin?

There have been many famous contradictions throughout the history of physics.

The interesting questions left are the ones that we are beginning to have a clue of how to answer. But how do we figure out which questions we want to think about. If we want to learn about the physical universe around us, the best thing we can hope for is a contradiction.
One famous discovery came from a thought experiment by Einstein. He imagined holding a mirror and running faster and faster until he reached or exceeded the speed of light. What would he see in the mirror? Would his image vanish?
At the time, there were two ways of thinking about this problem: one given by the Maxwell equations (the image should disappear) and the other given by Galileo & Newton (all inertial reference frames are the same, so nothing abnormal should happen). But these are not consistent, and this contradiction bothered Einstein.
Just from this small contradiction, Einstein came up with a shocking conclusion: Nothing can travel faster than light. He detailed his discovery with the special theory of relativity. This transformed our view of space & time, and changed the world.

All such revolutions in physics are seeded by similar contradictions.

For instance, in the 19th century, the laws of thermodynamics had been extensively studied. We knew, for example, how much energy we had to give to a pot of water to bring it to a boil.
At the end of the 19th century, electromagnetism was discovered. The electric and magnetic forces were found to be the same phenomenon. And so, one could try to apply thermodynamic reasoning to electromagnetism.
But this led to a conclusion that at certain wavelengths, an object could emit an infinite amount of energy—something that was obviously not observed in the laboratory. To resolve this contradiction, the electromagnetic field had to be discrete. Thus began the formulation of quantum mechanics.
Another contradiction: Einstein’s special theory of relativity said that nothing could move faster than the speed of light. But in Newton’s law of gravity, the gravitational force is instantly transmitted. If the Sun moves an inch, the gravitational field at Pluto changes instantaneously (according to Newton). This contradiction ultimately led to Einstein’s general theory of relativity.

There are still unresolved contradictions.

The previously mentioned discoveries culminated in the 20th century with two great bodies of knowledge—quantum field theory (the synthesis of quantum mechanics and special relativity) and general relativity. These two fields are incompatible.
Physicists believe that when we understand how to reconcile general relativity with quantum mechanics, the new theory that emerges will have implications for the way we think about the universe that are at least as revolutionary as the implications from quantum theory and general relativity individually.
It’s a very exciting problem, but it’s a problem so big that active work has been ongoing for over 30 years. This problem sits at the interesting edge of our knowledge.
String theory, and the related web of ideas, is the leading candidate for how these pillars might come together, but it’s far from confirmed.