2.2 Quantum Gravity Review

summary

General relativity reshaped how we think about space and time.

- According to Einstein’s general theory of relativity, space is curved, not flat. A mass that sits in the fabric of spacetime will warp and curve it, much like a bowling ball in the center of a trampoline.
- An object moving through spacetime will want to move in a straight line, but it will appear to move in a curve due to warping caused by other massive objects.
- The Earth moves in a straight line in a spacetime which is curved by the Sun. This is one of the principal tenets of general relativity.

The essence of quantum mechanics is captured by the uncertainty principle.

- Introduced by German physicist Werner Heisenberg, the
*uncertainty principle*states that there is inherent uncertainty in the nature of things. - The position and momentum of a particle cannot simultaneously be measured with arbitrarily high accuracy.
*Planck’s constant*, $h$, governs how big the uncertainties of these measurements are. - These two tenets alone are enough to understand why it is problematic to put together with general relativity and quantum mechanics. Before Einstein, spacetime was viewed as the platform on which all other physical processes happened. But now we understand that the platform itself is not a fixed reference point. The uncertainty principle says that everything must be uncertain, and that must somehow include space and time.
- But making precise sense of those words is difficult both conceptually and experimentally. This translates into mathematical inconsistencies and paradoxes.

Quantum field theory brings us closer to an answer.

- Quantum field theory governed much of 20th-century physics. You can think of it as a machine that adapts classical theories to quantum theories.
- Quantum electrodynamics, which is a quantum field theory of the electromagnetic force, is the most accurately tested theory in the history of human thought. In fact, quantum field theories work spectacularly for describing the strong, weak, and electrodynamic forces in the language of quantum physics.
- However, when trying to reconcile gravity with quantum mechanics, quantum field theory fails miserably.
- What we need is a new “attachment” for the QFT machine. In the 1970s, a new attachment was discovered, called string theory.
- If we modify the machine, we can actually make sense of gravity with quantum physics. But we don’t know if this attachment was ordered by nature.