Unifying General Relativity and the Standard Model

Albert Einstein proposed a revolutionary geometrical theory of gravity called general relativity. Prior to Einstein’s proposition in 1915 most physicists were party to a combination of special relativity (which Einstein had already proposed) and Newton’s law of universal gravitation. Einstein proposed that gravity was not some sort of abstract force but actually a manifestation of a new cosmological model. Einstein proposed that the fabric of space was actually like a blanket being held between two people with certain mass-bearing entities upon its surface, creating a series of curvatures known as spacetime. Since the surface (spacetime) is “sunk in” at certain spots in the universe (around heavy objects such as a planet or star) this creates a funnel effect on adjacent entities which causes them to be drawn toward the depression created by their mass, sort of like the effect a whirlpool has on passing by ships.

This model of gravitation created a new paradigm in the scientific community of the era because it replaced the concept of a gravitational “force” which somehow created and fostered attraction between objects with a new model dependant on geometrical considerations and consequences. Instead of a force of gravity pulling us to the ground as we would find in classical mechanics, in general relativity we have inertial motion against curved spacetime geometry. The ‘force of gravity’ for Einstein is a continuous physical acceleration caused by resistance against a surface.

At the core of both special and general relativity were the mathematics of differential geometry and more specifically the theory of relativity. Before Einstein could even conceive that general relativity was possible, he first had to unify Newton’s notions of space and time with Maxwell’s electromagnetism. He accomplished this in 1905 by publishing “On the Electrodynamics of Moving Bodies” which succeeded in the unification, creating the special theory of relativity (special relativity). The famous theory proved the the speed of light was constant and also predicted the famous e=mc2, two concepts which would later prove critical in the formulation of general relativity. Special relativity also began to hint more explicitly at the existence of a “theory of everything” – a theory that would explain all the mechanics of the universe. Now that Einstein had unified electromagnetism and Newton to create the concept of spacetime it now sought to unify special relativity with Newton’s law of universal gravitation to finally create general relativity, which in succeeded in.

Although general relatively is very effective at explaining the universe on a large scale (planets, stars, even down to humans and grains of sand) it runs into some serious problems when attempting to explain subatomic mechanics.

At the subatomic level we use quantum mechanics (which had unified Newtonian mechanics and classical electromagnetism earlier) to explain the chaotic (and sometimes random) environment and happenings within the individual atom and beyond that, individual subatomic particles. Here the effect of gravity is so insignificant that it is outweighed by radiation and other forces. While general relativity suggests an orderly and predictable universe at the large level (Einstein was known to say “God does not play dice”) it is unable to explain the unpredictable subatomic environment that quantum physics so accurately describes. Conversely quantum mechanics has trouble explaining the mechanics behind large objects. Both sciences seem perfectly suited for their particular purposes. If both general relativity and quantum mechanics could ever be reconciled it would theoretically conclude with a “theory of everything” – a single set of equations that could explain all mechanics of the universe. After Einstein formulated general relativity he spent the rest of his life looking for such a theory, one which he never succeeded in finding.

String theory was eventually proposed to bridge the gap between general relativity and quantum mechanics. The theory states that the fundamental building blocks of matter are not zero-dimensional points as would be proposed in the Standard Model (of quantum mechanics) objects which are often called strings. Because string theory utilizes the string (a vibrating, supersymmetric, one dimensional object) it avoids problems caused by point particles in physical theory. Since the smallest particle is proposed to be the string at Planck length (10-35 m) singularities (a zero point) would be impossible and with them also the theory of big crunch. In other words the universe could never be compressed smaller than the length of a string, which although incredibly small, does have a length longer than 0. In string theory the frequency of the vibration of the string determines what type of particle it is. Although string theory has lead to leaps in algebraic geometry and other mathematics developed to prove it, it has not yet produced a theory of everything nor has it been proven at a fundamental level.

String theory has promising solutions for the quantum gravity problem (the contradiction between quantum mechanics and general relativity) and could lead to unification, and perhaps a theory of everything.

String theory cannot be proved (at least not now) because the string unit is not yet measurable. Even if we did have a device advanced enough to measure a string, other elements of string theory (such as its proposed 11 dimensional cosmology) would also need to be verified empirically. If this hurdle could be jumped it would literally mean a theory of everything, which would practically reveal to human beings the most fundamental workings of the universe, the mathematics that formed our existence.