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In relativity the term equivalence principle has come to be applied to multiple concepts dealing with accelerated frames of reference and the unformity of physical measurements in inertial frames of reference.
The original equivalence principle was introduced by Einstein in 1907, and is not known as the weak equivalence principle. It may be summarized by the following statement:
- Whenever an observer detects the local presence of a force that acts on all objects in direct proportion to the inertial mass of the object, that observer is in an accelerated frame of reference.
The weak equivalence principle is therefore a rule for determining if one is in an accelerated frame of reference.
Another form is the Einstein equivalence principle which states that the results of an experiment in an inertially moving frame of reference are independent of the velocity of the experiment. (This is an extension of the postulates of special relativity, with the "laws of physics" mentioned in the special principle of relativity including the constancy of physical values such as Plank's constant, the mass and charge of an electron, etc. as well as the speed of light)
Finally, there is the strong equivalence principle, which states that the results of an experiment in an inertial frame of reference are independent of where and when in the universe they are conducted. This form extends the EEP's assumption of the constancy of fundamental physics values to everywhere and everywhen in the universe and also assumes that gravitational mass is always equivalent to inertial mass.
History
The origins of the Equivalence Principle begin with Galileo demonstrating in the lat 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 was introduced by Albert Einstein in 1907. An that time, he made the observation that the acceleration of bodies towards the center of the Earth at 1g 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. (It is from this equivalence that the equivalence principle was named.) From this principle, Einstein deduced that freefall is actually inertial motion , while being at rest with respect to the Earth (while under the influence of its gravitational field) is really an accelerated state of motion. This observation is now known as the weak equivalence principle. This observation was the start of a process that eventually led to the development of general relativity.
Although the equivalence principle helped to guide the development of general relativity, it actually is in that theory a consequence instead of being a foundation principle. Once Einstein was able to explain why inertial motion is really freefall instead of being at rest with respect to the Earth, it was no longer necessary to demonstrate that this must be the case. However, the equivalence principle continues to be cited to this day because it is an excellent pedagogical tool, helping people to bridge the conceptual gap between Newtonian mechanics and the geometrical world of general relativity.
Since the development of general relativity, the equivalence principle has come to be extended. The extension is call the strong equivalence principle.
Comparison with Newtonian mechanics
In Newtonian mechanics, gravity is assumed to be a force drawing objects towards the center of a massive body (such as the Earth). At its surface, this force is counter-balanced by the mechanical resistance of the surface to being penetrated. So a person on the surface of a non-rotating massive object is at rest in an inertial frame of reference due to the force of gravity being counter-balanced by the upward force of the surface on that person.
In general relativity and according to the equivalence principle, the situation is quite different. Since inertial mass is the same as gravitational mass in the gravitational fields of massive bodies, the equivalence principle indicates that free-fall is actually inertial motion. In that case, there is only one force acting on a person standing on the surface of a massive object, and that is the upward force of the surface on that person.
The strong equivalence principle
One of the consequences of the weak equivalence principle is that experiements that are not sensitive to curvature will produce the same results in either an accelerating spaceship or on the surface of a planet, given that the constants of physics are unaltered between the reference frames. In special relativity, Einstein assumed this kind of invariance for the speed of light, and extended that principle to hold locally in general relativity. Over time, some researchers have chosen to assume to that all phyical constants, such as the gravitational constant, Plank's constant, and the rest masses of subatomic particles are also independent of the state of motion on the experimenter and where and when in the universe the experimenter is. This is called the stong equivalence principle.
Another variation of the strong equivalence principle involves the equivalence of inertial mass and gravitational mass. Various alternate theories such as Brans-Dicke theory have scalar fields that can manifest themselves as variations between the effect of gravity of compact bodies (such as a bowling ball) and extended bodies (such as planets). Therefore any dicrepancy between the effect of gravitation on different bodies is a violation of this strong equivalence principle, and raises the possibility that general relativity will need to be modified.
A misunderstanding of the strong equivalence principle is that is states that
- The (local) effects of a gravitational field are identical in all respects to the effect of uniform acceleration.
This is not the strong equivalence principle and is not true. The gravitational fields for massive bodies such as the Earth are not uniform nor do such fields behave as if they were uniform. There are variations in both strength and direction between neighboring positions in the gravitational fields for massive objects. These variations create measurable tidal effects. On an accelerating rocket far from any gravitating object, the gravitational field is uniform, and no tidal effects will be observed.
Validation
Tests of the validity of the equivalence principle are those that verify the equivalence of gravitational mass and inertial mass. This is evidenced by all objects falling at the same rate when the effect of air resistance is either eliminated or negligible. Notable test are:
| Researcher
| Year
| Method
| Result
|
| Galileo Galilei
| ~1610
| Dropping metal balls of different mass from the Tower of Pisa
| no detectable difference
|
| Isaac Newton
| ~1680
| measure the period of pendulums of different mass but identical length
| no measurable difference
|
| Friedrich Wilhelm Bessel
| 1832
| measure the period of pendulums of different mass but identical length
| no measurable difference
|
| Roland Eötvös
| 1908
| measure the torsion on a wire, suspending a balance beam, between two nearly identical masses under the acceleration of gravity and the rotation of the Earth
| difference is less than 1 part in a billion
|
| Neil Armstrong
| 1969
| Dropped an eagle feather and a hammer at the same time on the Moon
| no detectable difference (Not a very good experiment, but it was the first lunar one.)
|
| Branginsky and Panov
| 1971
| torsion balance with effects of the Sun's gravitation accounted for
| difference is less than 1 part in a trillion (most accurate to date)
|
See also
References
- Hans Ohanian and Remo Ruffini Gravitation and Spacetime 2nd edition ISBN 0-393-96501-5, Chapter 1.
- Albert Einstein On the influence of gravitation on the propagation of light, Annalen der Physik, 35 (1911), as translated in The Principle of Relativity ISBN 0-486-60081-5, pp 99-108.
External links
