Introduction
What we know about our Universe is encapsulated into three major theories:
- Quantum mechanics, which is the general theoretical framework for describing dynamics.
- The standard model of particle physics, which describes all matter we have so far observed directly, with its non-gravitational interactions.
- General relativity, which describes gravity, space and time. Anything beyond these theories is speculative. But these theories are not the final story about the elementary world, of course. Among the open problems, three stand out: Dark matter - Unification - Quantum gravity.
The Open Problems
The first problem is due to converging elements of empirical evidence indicating that about 85% of the galactic and cosmological matter is not described by the standard model. The second is the old hope of reducing the number of free parameters in our elementary description of Nature. The third, quantum gravity, is the problem we discuss here, and it's not necessarily related to the first two. This problem is simply the fact that the current theories are not capable of describing the quantum behaviour of the gravitational field. Because of this, we lack a predictive theory capable of describing phenomena where both gravity and quantum theory play a role.
Quantum Gravity
Elaborate a theory of quantum gravity is incredibly difficult because general relativity is not just a theory of gravity. It's a modification of our understanding of the nature of space and time. Einstein's discovery is that spacetime and the gravitational field are the same physical entity, spacetime is a manifestation of a physical field. All fields we know exhibit quantum properties at some scale, therefore we believe space and time to have quantum properties as well. So, we have to understand what quantum space and what quantum time are. This is the difficult side of quantum gravity, but also the source of its beauty.
The Starting Point of LQG
The quantum nature of a physical quantity is manifest in three forms:
- In the possible discretization (or "quantization") of the quantity itself.
- In the short-scale "fuzziness" implied by the uncertainty relations.
- In the probabilistic nature of its evolution.
But physical regions cannot be always arbitrarily small in the case of general relativity. So, the starting point of LQG theory is that space and time are quantized (analogously to the way quantities like energy and momentum are quantized in quantum mechanics). The theory gives a physical picture of spacetime where space and time are granular and discrete.
The Plank Length
The first implication of a quantized space is that a minimum distance exists so, smaller distances are meaningless. LQG postulates that the structure of space is composed of finite loops woven into an extremely fine fabric or network. These networks of loops are called: spin networks. The evolution of a spin network, has a scale on the order of a Planck length, approximately 10⁻³⁵ metres. Consequently, not just matter, but space itself, prefers an atomic structure. Moreover, a manifestation of the innate uncertainty of these quantum levels are quantum fluctuations, but we talk about this topic in the net post.
Pros & Cons
It's a bit restricting not being able to enter into technical and mathematical details, because they would really explain the potential of this theory, but it requires too many complex requirements. However, the strength of the theory is its compelling capacity to describe quantum spacetime and its genuine attempt to synthesize the conceptual novelties introduced by quantum mechanics with the ones introduced by general relativity. On the other hand, loop quantum gravity is not yet a complete theory, it's not even clear whether it can reproduce all the phenomena already described by Einstein's theory.
LQG vs String Theory
The other large research program for a quantum theory of gravity, is string theory, which is a tentative theory as well. But string theory is more ambitious than loop gravity, since it also aims at unifying all known fundamental physics into a single theory. It also has a lot of theoretical evidence indicating that it's interesting, more than LQG. So, many people prefer string theory instead of LQG. But the interesting thing about LQG is that it starts with general relativity, then following this formulation to its logical conclusion, one finds that there is an ultimate unit of volume which cannot be further divided. So unlike general relativity, which allows for the possibility of a singularity (infinite density), LQG states that there's ultimately a density you can't go beyond.
Loop Quantum Cosmology
Another interesting consequence of loop quantum gravity is LOOP QUANTUM COSMOLOGY (LQC). It's the most well-developed theory that has been advanced as a direct result of loop quantum gravity. LQC advances the study of the early universe, incorporating the concept of the Big Bang into the broader theory of the Big Bounce, which envisions the Big Bang as the beginning of a period of expansion that follows a period of contraction, which one could talk of as the Big Crunch. So, even if there are theories that seem to be more comforting in terms of results, it has a relevant importance to continue developing this theory like the others.
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