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Fundamental Concepts & Controversies of Relativity


Fundamental Principles of Relativity

  • General principle of relativity: The laws of physics must be identical for all observers, regardless of whether or not they are accelerated.

  • Principle of general covariance: The laws of physics must take the same form in all coordinate systems.

  • Inertial motion is geodesic motion: The world lines of particles unaffected by forces (i.e. inertial motion) are timelike or null geodesic of spacetime. (This means the tangent vector is either negative or zero.)

  • Local Lorentz invariance: The rules of special relativity apply locally for all inertial observers.

  • Spacetime curvature: As described by Einstein's field equations, the curvature of spacetime in response to mass, energy, and momentum results in gravitational influences being viewed as a form of inertial motion.
The equivalence principle, which Albert Einstein used as a starting point for general relativity, proves to be a consequence of these principles.

General Relativity & the Cosmological Constant

In 1922, scientists discovered that application of Einstein's field equations to cosmology resulted in an expansion of the universe. Einstein, believing in a static universe (and therefore thinking his equations were in error), added a cosmological constant to the field equations, which allowed for static solutions.

Edwin Hubble, in 1929, discovered that there was redshift from distant stars, which implied they were moving with respect to the Earth. The universe, it seemed, was expanding. Einstein removed the cosmological constant from his equations, calling it the biggest blunder of his career.

In the 1990s, interest in the cosmological constant returned in the form of dark energy. Solutions to quantum field theories have resulted in a huge amount of energy in the quantum vacuum of space, resulting in an accelerated expansion of the universe.

General Relativity & Quantum Mechanics

When physicists attempt to apply quantum field theory to the gravitational field, things get very messy. In mathematical terms, the physical quantities involve diverge, or result in infinity. Gravitational fields under general relativity require an infinite number of correction, or "renormalization," constants to adapt them into solvable equations.

Attempts to solve this "renormalization problem" lie at the heart of the theories of quantum gravity. Quantum gravity theories typically work backward, predicting a theory and then testing it rather than actually attempting to determine the infinite constants needed. It's an old trick in physics, but so far none of the theories have been adequately proven.

Assorted Other Controversies

The major problem with general relativity, which has been otherwise highly successful, is its overall incompatibility with quantum mechanics. A large chunk of theoretical physics is devoted toward trying to reconcile the two concepts: one which predicts macroscopic phenomena across space and one which predicts microscopic phenomena, often within spaces smaller than an atom.

In addition, there is some concern with Einstein's very notion of spacetime. What is spacetime? Does it physically exist? Some have predicted a "quantum foam" that spreads throughout the universe. Recent attempts at string theory (and its subsidiaries) use this or other quantum depictions of spacetime. A recent article in New Scientist magazine predicts that spactime may be a quantum superfluid and that the entire universe may rotate on an axis.

Some people have pointed out that if spacetime exists as a physical substance, it would act as a universal frame of reference, just as the ether had. Anti-relativists are thrilled at this prospect, while others see it as an unscientific attempt to discredit Einstein by resurrecting a century-dead concept.

Certain issues with black hole singularities, where the spacetime curvature approaches infinity, have also cast doubts on whether general relativity accurately depicts the universe. It is hard to know for sure, however, since black holes can only be studied from afar at present.

As it stands now, general relativity is so successful that it's hard to imagine it will be harmed much by these inconsistencies & controversies until a phenomena comes up which actually contradicts the very predictions of the theory.

Quotes about Relativity

"Spacetime grips mass, telling it how to move, and mass grips spacetime, telling it how to curve" — John Archibald Wheeler.

"The theory appeared to me then, and still does, the greatest feat of human thinking about nature, the most amazing combination of philosophical penetration, physical intuition, and mathematical skill. But its connections with experience were slender. It appealed to me like a great work of art, to be enjoyed and admired from a distance." — Max Born

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