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There are various theories that provide good approximations to nature at different scales. Newtonian mechanics describes the behaviour of macroscopic objects reasonable well, while quantum field theory is the best theory of elementary particles that we currently have. On the other hand, we have general relativity which works perfectly at astronomical scales. It is commonly believed that to describe nature at even tinier scales than we can currently probe, a new theory is needed that merges general relativity with the principle of quantum field theory. This hypothetical theory, which has not been found so far is called quantum gravity. There are several proposed theories of quantum gravity, but none of them has been experimentally confirmed so far.

Field Theories vs. Particle Theories

In a particle theory, the solutions describe particle trajectories:

while in a field theory the solutions describe sequences of field configurations:

Relationship Between the Theories

The image above shows a cube with the most important fundamental theories at each edge. Each axis here depicts one the three fundamental constants $G$, $\hbar$ and $1/c$, where $G$ is the gravitational constant, $\hbar$ the reduced Planck constant and $c$ the speed of light.

Although these quantities are constants, as far as we know, we can theoretically vary them in our theories. What we end up when we do this is different limits of the various theories. For example, if we start with special relativity, but note that everything in our system moves much slower than the speed of light $c$, this upper speed limit play no role hence we end up with classical mechanics. Mathematically this corresponds to sending $c$ to infinity, which means $1/c$ goes to $0$.

Analogously, if we start with quantum mechanics, but only consider systems with an action much larger than $\hbar$, i.e. $\hbar \to 0$, quantum effects play no role and we once more end up with classical mechanics.

For more on the cube of theoretical physics, see chapter 1 in Sleeping Beauties in Theoretical Physics by Thanu Padmanabhan

Image by GYassineMrabet published under a CC BY-SA 3.0 (], via Wikimedia Commons

Contributing authors:

Jakob Schwichtenberg
theories.txt · Last modified: 2018/03/13 14:01 by jakobadmin