The equivalence principle - and it all began with a simple thought experiment *
Header:https://www.sciencealert.com/these-5-crazy-thought-experiments-show-how-einstein-created-his-amazing-hypothesises
Sitting in his room in the Bern patent office, Einstein had a happy thought, which he would later describe as the happiest thought in his life: "If a person falls freely, he will not feel his own weight" [0]. In the fullness of time, he refined this thought to a situation where the falling man was in an enclosed chamber such as an elevator in free fall. Perhaps these days he would have used the example of a spaceship. As Walter Isaacson describes the situation[1]: in the chamber he would feel weightless, and any objects he dropped would float alongside him. There would be no way he could tell and no experiment he could devise, to determine if the chamber was falling at an accelerated rate or floating in a gravity-free region of outer space.
This is the kind of weightlessness experienced by astronauts on the International Space Station (ISS). It is not as though the space station and crew have escaped the earth's gravitational field. In the ISS’s altitude and orbit, the pull of the gravitational force is still 90 per cent as strong as on the earth's surface. However, the astronauts do not feel the force of gravity. Their weightlessness is due to the fact that, along with their station, they are in free fall. Not in the kind of free fall that takes them directly towards the earth, but in free fall that takes them around the earth - in earth’s orbit [2].
In his thought experiment, Einstein then imagined that the man was in the same chamber way out in space far away from all gravitational influences, far away from all stars, planets and other massive bodies, accelerating upward with an acceleration equal to that of Earth’s gravity (32 feet (9.8 meters) per second squared) and compared this to a man in an elevator at rest in the earth's gravitational field. There would be no way to make any distinction between the effects of gravity and those of being accelerated upwards at the same rate. If the man in the elevator on earth dropped an object. it would be impossible to know whether the ball is falling towards the earth, or the cabin floor accelerating towards the ball, and the same for the man in the upward accelerating elevator far out in space - the ball will also accelerate toward the floor at the same rate.
This was the key insight galvanising Einstein’s "grand epiphany" [3] from gravity being considered as a force (as it was in Newtonian terms) to a warper of space-time. The almost total similarity between the two situations led Einstein to jettison the idea of gravity as a force. In other words, Einstein was equating gravitational mass with inertial mass, the consequence being that in a reference frame that is in free fall, the laws of physics are the same as if there were no gravity at all - the laws of physics become those of special relativity! The equivalence principle therefore states that gravity and accelerated motion are but different sides of the same coin, and that the principles of spacetime curvature are as equally relevant in all instances of accelerated motion to those where a gravitational field is in play.
Einstein’s idea of the curvature of space in the presence of mass stemmed from his realisation that ordinary Euclidean geometry based on lines drawn on flat surfaces does not apply when say a circle is drawn on a sphere. For spheres with the same radius, a circle drawn on a sphere has a shorter circumference than one drawn on a flat sheet of paper. (Aircraft utilise this principle every day in their journeys across the globe, the shortest distance between two cities being the curved route.) This led Einstein to the realisation that the warping of space, and indeed of time, holds in all instances of accelerated motion[4] So, gravity pulling in one direction is effectively the same as acceleration in the opposite direction, and since there is no difference between an accelerated vantage point without a gravitational field and a non-accelerated vantage point with a gravitational field, by the inclusion of gravity general relativity ensures that all possible observational vantage points are on an equal footing[5].
Because gravity is equivalent to acceleration, and motion affects measurements of time and space as demonstrated by special relativity, it necessarily follows that gravity does so as well. So, the benchmarks for all motion, and accelerated motion in particular, are freely falling observers who are fully giving in to gravity and are being acted upon by no other forces[6].
Another of Einstein's thought experiments in this area centred around the question "What happens if light travels in the presence of a gravitational field?"[7] Imagine that the chamber is being accelerated upwards and a light beam comes in through a pinhole in one wall. By the time it reaches the opposite wall, the light is a little closer to the floor because the chamber has moved upwards. If you could plot the trajectory across the chamber, it would be curved because of the upwards acceleration. "The equivalence principle says that this effect should be the same whether the chamber is accelerating upward or is resting still in a gravitational field. In other words, light should bend when passing through a gravitational field."[8]
The first practical proof of this aspect of Einstein's theory would come in 1919 with the observation of light deflection by the Sun when an expedition led by Arthur Eddington headed to the Principe Island off the coast of Equatorial Guinea in West Africa to observe a total eclipse of the sun and was able to observe, during the eclipse, the effect of the Sun on the light coming from a far away star[9].
In the fullness of time other practical illustrations of this principle would come to include [10]:
..... and to think that it all started with a basic thought experiment - or two!
* See "Inside Einstein’s Mind – The Enigma of Space and Time", NOVA/WGBH, BBC4 (2015) at https://www.youtube.com/watch?v=lgeB4b1WR0Y, a precis of which appears on the Special Relativity page.
[0] For a depiction of this thought experiment and how it occurred to Einstein, see channel.nationalgeographic.com/genius/videos/elevator-thought-experiment/ from the excellent National Geographic series on Einstein, entitled simply "Genius".
[1] In "How Einstein invented reality", Scientific American, Special Issue - 100 years of General Relativity, September 2015, 28,30. See also Carlos I Calle, Einstein for Dummies, Kindle Locations 2810-2811, Wiley 2005. Kindle Edition.
[2] http://www.einstein-online.info/spotlights/equivalence_principle. See also Dana Mackenzie, op cit, 161.
[3] https://www.physicsforums.com/threads/a-baffling-quote-from-einstein-badly-requiring-explanation.300849/
[4] For more detail as to the steps of Einstein’s reasoning process, see Greene (2000), 62-67.
[5] Greene (2000), 61.
[6] Green (2000), 73.
[7] http://www.light2015.org/Home/CosmicLight/Einstein-Centenary.html - website by Lightsources.org,
[8] Walter Isaacson, op cit, 30.
[9] http://www.light2015.org/Home/CosmicLight/Einstein-Centenary.html - website provided by Lightsources.org. As the author points out, two expeditions were organised to observe the eclipse (on May 29). The other was directed to Sobral, north of Brasil, led by Charles A. Davidson and Andrew C. P. Crommelin.
[10] Ibid. These phenomena are all discussed elsewhere on this webpage.
[11] George Musser, "Where is here?"", Scientific American, November 2015, 60 at 63, a resume of his forthcoming book Spooky action at a distance.
Sitting in his room in the Bern patent office, Einstein had a happy thought, which he would later describe as the happiest thought in his life: "If a person falls freely, he will not feel his own weight" [0]. In the fullness of time, he refined this thought to a situation where the falling man was in an enclosed chamber such as an elevator in free fall. Perhaps these days he would have used the example of a spaceship. As Walter Isaacson describes the situation[1]: in the chamber he would feel weightless, and any objects he dropped would float alongside him. There would be no way he could tell and no experiment he could devise, to determine if the chamber was falling at an accelerated rate or floating in a gravity-free region of outer space.
This is the kind of weightlessness experienced by astronauts on the International Space Station (ISS). It is not as though the space station and crew have escaped the earth's gravitational field. In the ISS’s altitude and orbit, the pull of the gravitational force is still 90 per cent as strong as on the earth's surface. However, the astronauts do not feel the force of gravity. Their weightlessness is due to the fact that, along with their station, they are in free fall. Not in the kind of free fall that takes them directly towards the earth, but in free fall that takes them around the earth - in earth’s orbit [2].
In his thought experiment, Einstein then imagined that the man was in the same chamber way out in space far away from all gravitational influences, far away from all stars, planets and other massive bodies, accelerating upward with an acceleration equal to that of Earth’s gravity (32 feet (9.8 meters) per second squared) and compared this to a man in an elevator at rest in the earth's gravitational field. There would be no way to make any distinction between the effects of gravity and those of being accelerated upwards at the same rate. If the man in the elevator on earth dropped an object. it would be impossible to know whether the ball is falling towards the earth, or the cabin floor accelerating towards the ball, and the same for the man in the upward accelerating elevator far out in space - the ball will also accelerate toward the floor at the same rate.
This was the key insight galvanising Einstein’s "grand epiphany" [3] from gravity being considered as a force (as it was in Newtonian terms) to a warper of space-time. The almost total similarity between the two situations led Einstein to jettison the idea of gravity as a force. In other words, Einstein was equating gravitational mass with inertial mass, the consequence being that in a reference frame that is in free fall, the laws of physics are the same as if there were no gravity at all - the laws of physics become those of special relativity! The equivalence principle therefore states that gravity and accelerated motion are but different sides of the same coin, and that the principles of spacetime curvature are as equally relevant in all instances of accelerated motion to those where a gravitational field is in play.
Einstein’s idea of the curvature of space in the presence of mass stemmed from his realisation that ordinary Euclidean geometry based on lines drawn on flat surfaces does not apply when say a circle is drawn on a sphere. For spheres with the same radius, a circle drawn on a sphere has a shorter circumference than one drawn on a flat sheet of paper. (Aircraft utilise this principle every day in their journeys across the globe, the shortest distance between two cities being the curved route.) This led Einstein to the realisation that the warping of space, and indeed of time, holds in all instances of accelerated motion[4] So, gravity pulling in one direction is effectively the same as acceleration in the opposite direction, and since there is no difference between an accelerated vantage point without a gravitational field and a non-accelerated vantage point with a gravitational field, by the inclusion of gravity general relativity ensures that all possible observational vantage points are on an equal footing[5].
Because gravity is equivalent to acceleration, and motion affects measurements of time and space as demonstrated by special relativity, it necessarily follows that gravity does so as well. So, the benchmarks for all motion, and accelerated motion in particular, are freely falling observers who are fully giving in to gravity and are being acted upon by no other forces[6].
Another of Einstein's thought experiments in this area centred around the question "What happens if light travels in the presence of a gravitational field?"[7] Imagine that the chamber is being accelerated upwards and a light beam comes in through a pinhole in one wall. By the time it reaches the opposite wall, the light is a little closer to the floor because the chamber has moved upwards. If you could plot the trajectory across the chamber, it would be curved because of the upwards acceleration. "The equivalence principle says that this effect should be the same whether the chamber is accelerating upward or is resting still in a gravitational field. In other words, light should bend when passing through a gravitational field."[8]
The first practical proof of this aspect of Einstein's theory would come in 1919 with the observation of light deflection by the Sun when an expedition led by Arthur Eddington headed to the Principe Island off the coast of Equatorial Guinea in West Africa to observe a total eclipse of the sun and was able to observe, during the eclipse, the effect of the Sun on the light coming from a far away star[9].
In the fullness of time other practical illustrations of this principle would come to include [10]:
- the phenomenon of gravitational lensing;
- the bending of light around galaxies and clusters of galaxies producing a lensing effect, leading to a distortion of the images of these galaxies and enabling the observation of clumpiness of other celestial objects closer at hand;
- gravitational redshift (light changing frequency when it moves in a gravitational field);
- and, as a practical illustration of the latter, the gravitational redshift of light from galaxies and exploding stars (supernovae) as the basic tool that allows us to "map" the Universe and study its "geometry", giving rise to the realisation that the Universe is expanding (all galaxies are moving away from each other) and even accelerating);
- black holes (the inability of even light to escape their strong gravitational field);
- the realisation that our universe originally sprang from a very energetic state, the Big Bang, imprinted on the cosmic microwave background radiation (CMBR); and
- gravitational waves: ripples in the spacetime fabric producing peculiar polarisations in the CMBR light;
- the fact that interlinked points in the gravitational field tend to flop around, although collectively, still maintaining the same internal relationship with one other, resulting in the impossibility of pinpointing any particular location in a malleable dynamic: spacetime[11]. To get a feel for this, have a look at Brian Greene's mesh depiction of spacetime towards the end of the Youtube video on the Einstein and Newton page.
..... and to think that it all started with a basic thought experiment - or two!
* See "Inside Einstein’s Mind – The Enigma of Space and Time", NOVA/WGBH, BBC4 (2015) at https://www.youtube.com/watch?v=lgeB4b1WR0Y, a precis of which appears on the Special Relativity page.
[0] For a depiction of this thought experiment and how it occurred to Einstein, see channel.nationalgeographic.com/genius/videos/elevator-thought-experiment/ from the excellent National Geographic series on Einstein, entitled simply "Genius".
[1] In "How Einstein invented reality", Scientific American, Special Issue - 100 years of General Relativity, September 2015, 28,30. See also Carlos I Calle, Einstein for Dummies, Kindle Locations 2810-2811, Wiley 2005. Kindle Edition.
[2] http://www.einstein-online.info/spotlights/equivalence_principle. See also Dana Mackenzie, op cit, 161.
[3] https://www.physicsforums.com/threads/a-baffling-quote-from-einstein-badly-requiring-explanation.300849/
[4] For more detail as to the steps of Einstein’s reasoning process, see Greene (2000), 62-67.
[5] Greene (2000), 61.
[6] Green (2000), 73.
[7] http://www.light2015.org/Home/CosmicLight/Einstein-Centenary.html - website by Lightsources.org,
[8] Walter Isaacson, op cit, 30.
[9] http://www.light2015.org/Home/CosmicLight/Einstein-Centenary.html - website provided by Lightsources.org. As the author points out, two expeditions were organised to observe the eclipse (on May 29). The other was directed to Sobral, north of Brasil, led by Charles A. Davidson and Andrew C. P. Crommelin.
[10] Ibid. These phenomena are all discussed elsewhere on this webpage.
[11] George Musser, "Where is here?"", Scientific American, November 2015, 60 at 63, a resume of his forthcoming book Spooky action at a distance.