 | Equivalence principle: Encyclopedia II - Equivalence principle - History
Equivalence principle - History
The origins of the equivalence principle begin with Galileo demonstrating in the late 16th century that all objects are accelerated towards the center of the Earth at the same rate. This was codified by Newton with his gravitational theory in which it was postulated that inertial and gravitational masses are one and the same.
The equivalence principle proper was introduced by Albert Einstein in 1907. At that time, he made the observation that the acceleration of bodies towards the center of the Earth with acceleration 1g (g=9.81 m/s2 is the acceleration of gravity at the Earth's surface) is equivalent to the acceleration of inertially moving bodies that one would observe if one was on a rocket in free space being accelerated at a rate of 1g. Einstein stated it thus:
we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system. (Einstein, 1907)
That is, remaining at rest in a uniform gravitational field is physically equivalent to experiencing an acceleration (e.g. being at rest with respect to the Earth, while under the influence of its gravitational field, is an accelerated state of motion). From this principle, Einstein deduced that free-fall is actually inertial motion. By contrast, in Newtonian mechanics, gravity is assumed to be a force. This force draws objects towards the center of a massive body. At the Earth's surface, the force of gravity is counter-balanced by the mechanical resistance of the Earth's surface. So in Newtonian physics, a person at rest on the surface of a (non-rotating) massive object is in an inertial frame of reference. While this picture works very well for most calculations, it was a mystery why the inertial mass in Newton's second law, F = ma, is equal to the gravitational mass in Newton's law of universal gravitation. Under the equivalence principle, this mystery is solved by virtue of gravity being an acceleration from inertial motion caused by the mechanical resistance of the Earth's surface. So a corollary of the equivalence principle is that
Whenever an observer detects the local presence of a force that acts on all objects in direct proportion to the inertial mass of each object, that observer is in an accelerated frame of reference.
This equivalence principle was precisely formulated by Einstein in 1911, referring to two reference frames K and K'. The frame K is in a uniform gravitational field, whereas K' has no gravitational field but is uniformly accelerated such that objects in two frames experience identical forces:
We arrive at a very satisfactory interpretation of this law of experience, if we assume that the systems K and K' are physically exactly equivalent, that is, if we assume that we may just as well regard the system K as being in a space free from gravitational fields, if we then regard K as uniformly accelerated. This assumption of exact physical equivalence makes it impossible for us to speak of the absolute acceleration of the system of reference, just as the usual theory of relativity forbids us to talk of the absolute velocity of a system; and it makes the equal falling of all bodies in a gravitational field seem a matter of course. (Einstein, 1911)
This observation was the start of a process that led to the development of general relativity. Einstein suggested that it should be elevated to the status of a general principle when constructing his theory of relativity:
As long as we restrict ourselves to purely mechanical processes in the realm where Newton's mechanics holds sway, we are certain of the equivalence of the systems K and K'. But this view of ours will not have any deeper significance unless the systems K and K' are equivalent with respect to all physical processes, that is, unless the laws of nature with respect to K are in entire agreement with those with respect to K'. By assuming this to be so, we arrive at a principle which, if it is really true, has great heuristic importance. For by theoretical consideration of processes which take place relatively to a system of reference with uniform acceleration, we obtain information as to the career of processes in a homogeneous gravitational field. (Einstein, 1911)
He used this principle, together with special relativity, to predict that clocks run at different rates in a gravitational potential and the bending of light-rays in a gravitational field, even before he developed the concept of curved spacetime.
So the original equivalence principle, as described by Einstein, was one of the physical equivalence of free fall and inertial motion.
Although the equivalence principle helped to guide the development of general relativity, it is not a founding principle, but rather is a simple consequence of the geometrical nature of the theory. In general relativity, objects follow geodesics of spacetime, and what we perceive as the force of gravity is instead a result of our being unable to follow those geodesics of spacetime due to the mechanical resistance of matter keeping us from doing so.
Interest in the modern extensions of the equivalence principle was catalyzed in 1937 when Paul Dirac formulated his large numbers hypothesis which asserts that large, dimensionless numbers should not arise as fundamental quantities in physics: there should only be one fundamental energy scale in physics. He supported this by pointing out a coincidence: the dimensionless ratio of electric to gravitational forces in a hydrogen atom is about the same as the age of the universe, measured by the time it takes light to cross the hydrogen atom. Both are about 1040. To explain this surprising coincidence, Dirac postulated that Newton's constant varied as the inverse of the age of the universe, and the feebleness of gravity was due to the great age of the universe. While he turned out to be wrong, he led people to consider that the laws of physics may be different at different points in space and time, and the values of the physical constants, rather than being fundamental, may be set dynamically. These ideas, together with Mach's principle – roughly, the idea that inertia of a mass should be induced by the other masses in the universe – led physicists to develop scalar-tensor theories, in particular Brans-Dicke theory, in which the value of the gravitational constant is determined dynamically.
Other related archives1907, Albert Einstein, Albert Einstein's, Astrophysics, Birkhoff's theorem, Black hole, Brans-Dicke theory, Cassini, Cavendish experiments, Compton wavelengths, Copernican, Cosmology, Earth, Einstein equations, Event horizon, Exact solutions, FLRW metric, Galileo, General relativity, Gravitational lens, Gravitational radiation, History, Kerr metric, Lorentz invariant, Loránd Eötvös, Lunar Laser Ranging Experiment, Mach's principle, Mathematics, Newton's constant, Newton's second law, Newtonian mechanics, Nordtvedt effect, Oklo, Overview of GR, Paul Dirac, Pioneer anomaly, Pound-Rebka experiment, Quantum gravity, Resources, Riemannian geometry, Robert Dicke, STEP (Satellite Test of the Equivalence Principle), Schwarzschild metric, Singularity, Special relativity, String theory, Tests, University of Washington, Yukawa forces, acceleration, bending of light-rays, big bang nucleosynthesis, black hole, constants and mass ratios, cosmological constant, dark matter, dimensionless, dynamically, electron, elegant, energy scale, fifth force, fifth forces, fine-structure constant, force, frames of reference, free-fall, galactic center, general relativity, gravitational constant, gravitational potential, gravitational redshift, gravity, hydrogen, inertial, inertial motion, inverse-square law, large numbers hypothesis, law of universal gravitation, metric, natural nuclear fission reactor, principle of relativity, proton, quantum theory of gravity, quasars, quintessence, radio sources, relativity, scalar fields, special relativity, strong interaction, sun, supergravity, tidal forces, very long baseline interferometry
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