In relativity the Principle of Equivalence, introduced in 1907, was used extensively by Albert Einstein in his succesful attempt to find a unification of the description of the physics of special relativity and the physics of gravitation
In non-technical terms the principle can be represented as follows:
- Inside a space-capsule situated on the surface of a gravitating body the same physics is taking place as inside a space-capsule that is uniformly accelerating due to a force being exerted. Locally, all measurable aspects of physics are affected in the same way in both situations.
- When a space-capsule is being accelerated by gravitation, then the effects due to the acceleration cancel the effects due to the gravitation. This cancelation extends to all measurable aspects of physics. Thus, being in free fall in a gravitational field and free floating in gravitationfree space are fundamentally indistinguishable.
There is a severe restriction on the validity of the principle of equivalence: sufficiently sensitive devices will detect whether there are tidal forces, wich are second order effects of gravitation. Inside the space-ship being accelerated in gravitationfree space, there will be only first order effects, no tidal effects. The principle of Equivalence only holds in the limit of going to infinitisimally small intervals of space-time. Mathematics provides the tools to bridge that restricton. It must at all times be kept in mind that the principle of equivalence only holds in the limit of infinitisimally small intervals of space-time. By reasonable approximation it also holds for human scale intervals of space-time. On astronomical scales the principle of Equivalence does not apply.
Unification
In itself the Principle of Equivalence is not helpful in elucidating physics, but in conjunction with special relativity it is. To show this the space-time physics of acceleration must be discussed first.
The physics of acceleration
An observer can set up a latticework of measuring rods and clocks, and this serves as his local frame of reference. As long as this frame of reference is moving inertially all clocks are counting time at the same rate. Timing signals transmitted at one second intervals by one clock will be recieved with one second intervals by other clocks.
On the other hand, if the latticework of rods and clocks is being accelerated by a force, then the clocks will not be running at the same rate. When the latticework is being accelerated, then timing signals transmitted at one second intervals by the clocks "in the front" will be received with shorter intervals by clocks "in the back". If, after a journey, a clock is retrieved from the "front end" and it is compared to a clock from the "rear end" then the front clock is seen to have counted more time. When there is acceleration, then over the length of the latticework there will be an incline, a slope in the rate of time. More generally: over the length of the latticework of rods and clocks, there will be an incline in the 4-dimensional space-time geometry.
The physics of gravitation
Gravitation alters the rate of time, gravitation alters the 4-dimensional space-time geometry, and thus physics is affected in fundamentally the same way in the two contexts.
In the case of the latticework of rods and clocks being accelerated by a force, the incline in space-time geometry is actual physics for that latticework only. In the case of gravitational alteration of space-time geometry the alteration is pervasive. Objects like planets and suns are so large that they contract to a spherical shape, and subsequently the shape of the gravitational alteration of the rate of time around that planet or sun is spherically symmetrical. The further away from the center of gravitation, the weaker the alteration away from the normal, straight geometry of space-time.
Acceleration and Inertia
In the situation of a space-capsule in gravition-free space, being acccelerated by a force, all objects inside the ship are being co-accelerated. There is the force of acceleration, pointing in the direction of acceleration, and there is manifestation of inertia, pointing in the opposite direction. The manifestation of inertia opposes the acceleration, but does not prevent it. It is worth mentioning the manifestation of inertia separately, because without the existence of inertia, all objects would be instantly accelerated to lightspeed. It is because of the existence of inertia that acceleration is proportional to mass. The expression 'inertial mass' refers to exactly the same as the word 'mass'.
The mass of an object is measured by measuring its inertia, that is the only measure of mass.
An elevator cabin inside a space-ship that is accelerating requires an extra force to climb from the "tail" of the space-ship to the "nose", because during the ascent it must accelerate somewhat harder than the ship. When the elevator cabin goes down again the energy that was spent to climb to the nose can be regained by regenerative braking. When the elevator cabin is in controlled descent from the nose of the ship to the tail less force is required to accelerate the elevator cabin. The difference is the regnerable energy.
Gravitation and inertia
Following the equivalence principle: in the situation of the space-capsule standing on the surface of a planet, there is the upward force that the surface of the planet is exerting, keeping the capsule at a constant distance from the center of gravitation. There is a downwards manifestation of inertia, that opposes the upwards force, but does not prevent the upwards force from maintaining the same situation.
When an elevator cabin is in controlled descent, the energy that is released can be "harvested". Closer to the center of gravity of a gravitating body the rate of time is slower. If the descent would not be a controlled one but free-fall instead, then the energy difference corresponding to the difference in the rate of time would be relaesed in the form of kinetic energy, the elevator would accelerate.
Dependency on the perspective
The way gravitational interaction is mediated is unlike that of any other interaction. Gravitation alters space-time geometry itself and as a consequence what you see is highly dependent on how close you "zoom in", or how widely you "zoom out". When in the case of free-falling objects in a gravitational field an observer zooms in to the smallest perspective, then he detects no acceleration with respect to the local inertial frame, hence no force. On the other hand, when the observer zooms out and takes a wider look, collecting more information about the physics taking place in the system as a whole, gravitation is seen to accelerate objects.
Spectrum from weak to strong Principle of Equivalence
In its weakest form the equivalence is only assumed to hold voor laws of motion of material objects. The Principle of Equivalence that Einstein stated was that it holds for all aspects of physics. No violations of the Einstein Principle of Equivalence are known.
Testing an implication of the Principle of Equivalence
Asserting the Principle of Equivalence implies asserting that inertial mass and graviational mass must always be equal. Equality of inertial mass and gravitatonal mass is a necessary condition for the Principle of Equivalence to hold, but not a sufficient one, since equality of inertial and gravitational mass does not exclude the possibility that gravity simply couples to to all matter equally.
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
|
| David Scott
| 1971
| 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.
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