How does Einstein's perception of gravity differ from Newton's?
The warping of spacetime is the geometric (left hand side of the EFE) equivalent of a gravitational field (the right hand side). “Matter here causes space to warp over there, which causes matter over there to move, which causes space way over there to warp even more, and so on. General relativity provides the choreography for an entwined dance of space, time, matter and energy….The earth, the moon, the distant planets, stars, gas clouds, quasars and galaxies all contribute to the gravitational field, spacetime curvature, right where you’re now sitting. Things that are more massive and less distant exert a greater gravitational influence, but the gravitational field you feel represents the combined influence of all the matter that’s out there”.[1]
In an empty unchanging universe – no stars, no planets, no matter or energy, no anything at all – there is no gravity (at least no attractive gravity) and without gravity, spacetime like a smooth wooden floor has no warps or curves. It’s flat. Under this scenario, general relativity reduces to special relativity. But the presence of matter or energy has an effect on space much like the warps and curves on the same wooden floor after it has sustained water damage. Matter and energy, like the sun, causes space (spacetime) to warp and curve, and anything moving through warped space, such as the earth moving in the vicinity of the sun, although travelling in straight lines or geodesics, will travel along a curved trajectory. “It’s as if matter and energy imprint a network of chutes and valleys along which objects are guided by the insatiable hand of the spacetime fabric”[2]. Space and time are dynamic in general relativity; they are mutable, and they respond to the presence of mass and energy. They are not absolute.[3].
Stephen Hawking gives the nice analogy that what we see is like the curved motion of a shadow on the ground from a plane flying in a straight line over hilly terrain[4]. So is it also with the ellipse you see in pictures of planetary orbits, which projects the path of a planet on a slice of space at different points of the ellipse at different times. That is not what the planet really traverses in space-time. It is only the shadow of the true path of the planet, and seems much more curved than the true path really is[5].
George Musser provides an even nicer analogy[6]. Objects that are moving freely through space, he says, are like raindrops streaking across a car windshield, revealing the curve of the glass; they trace out the shape of space. The problem in understanding this is one of abstraction. We can’t see spacetime, let alone discern its shape. So we have to rely on indirect glimpses, such as Hawking’s hilly terrain and Musser’s windshield to obtain an inkling of what is involved. Musser goes on: “astronomers routinely observe rays of starlight that begin as parallel, pass near a giant lump of mass such as the sun, then afterward intersect. Textbooks and articles describing this effect often say that the sun’s gravity has bent the light rays, but that’s not quite right. The rays are as straight as straight can be. What the sun has really done is to alter the rules of geometry – that is, to warp space –such that parallel lines can meet”.
The novelty of Einstein’s idea is that gravity is a geometrical concept constituted by the “bending” of time and space. Newton had demonstrated the existence of gravity – the celebrated and probably apocryphal apple falling from the tree – but not what actually caused it.
According to Newton’s analysis, gravity is always an attractive force: all objects with mass attract all other objects with mass, and the strength of the force involved is proportional to the product of the 2 masses acting upon one another and inversely proportional to the square of the distance between them – the inverse square law once more. Masses experiencing that force respond by accelerating toward its source. Different masses are accelerated at the same rate, because the force pulls them in proportion to their mass: a small mass experiences a small pull, a greater mass a greater pull. Why this was so, Newton was unable to say. This was his "spooky action at a gravitational distance".
Newton’s equations, by the way, remain good enough for most purposes when dealing with massive objects where comparatively weak gravity is involved, and men have been able to travel to the moon and space probes to distant parts of our solar system using them. However, upon his analysis, light is exempt from any form of gravitational attraction because it (or rather, as we now know) its individual photons are without mass.
On the other hand, Einstein’s theory of general relativity sewed space and time into a unified entity called space-time, which can stretch and wrinkle in the presence of matter or energy, like a malleable rubber sheet, producing the space-time curvature we feel as the force of gravity[7].
It is not the mass of an object, let’s say a star, which is determinative. Instead, it is the curvature of spacetime created by the star’s mass which creates gravity. Thus, gravity is the curvature of space around mass concentrations: the bigger the mass and the smaller the volume, the more space is bent around it, and the stronger the gravitational pull toward it. Matter can bend space and thus deform its geometry away from flatness[8].
In other words,"(s)pacetime is a kind of substance that can be squeezed or stretched like a giant sheet or rubber. A massive object like a star deforms this fabric, causing everything in its vicinity to feel the pull towards it”[9]. All objects with mass alter the curvature of spacetime, and other objects moving thereabout such as light simply follow the curves that have been created, the paths of least resistance. If light traverses the same curvature - as it does - it also necessarily follows the curvature of space already created by the other heavenly body, and the amount of apparent "bending" (understand: curvature) increases as the mass of the object it is passing increases.
To sum up then, Newton’s instantaneous and miraculous gravitational force operating at a distance is replaced by the curvature of spacetime. Moving a mass causes ripples to form in this curvature, and these ripples travel with the same speed as light. A distant mass would not feel any instantaneous change in the gravitational force, and special relativity is not violated. All objects with mass alter the curvature of spacetime, and other objects moving thereabout simply follow the paths that are open to them - the curves that have been created, the paths of least resistance[10].
Einstein's theory also explains why objects fall independently of their mass: they all follow the same straightest possible line in curved space-time. In fact, it is not the mass of an object, let’s say a star, which is determinative, but the curvature of spacetime created by the star’s mass which creates gravity. In this sense, gravity is the curvature of space around mass concentrations, and the bigger the mass and the smaller the volume, the more space is bent around it. “In this new world, there is no absolute time or space, and gravitation is not a force – not a tug between one object and another – but a property of space and time”.[11]
Brian Greene succinctly explains these principles involving spacetime curvature as the central tenet of General Relativity in this clip from "The Elegant Universe":
As he would later describe the situation some years later, "instead of Earth grabbing hold of a tea cup that slips from your hand and pulling it to an untimely demise on the floor, general relativity says that the planet dents the surrounding environment, causing the cup to slide along a spacetime chute that directs it on to the floor. Gravity, Einstein declared, is imprinted in the geometry of the universe”[12].
Other heavenly consequences
Einstein’s theory of the warping of space is confirmed every time there is a solar eclipse and the observer sees light rays from stars behind the sun, which would not normally be seen, curve around its mass causing them to change trajectory and appear displaced towards the red end of the spectrum. [12.1] This is because the light from the stars behind the sun are bent toward the sun and toward the earth[13]. The light appears to come from a direction that is different to where the star really is. Einstein’s theory of special relativity also predicted light deflection, but since general relativity says that time is also stretched the deflection is twice the magnitude[14].
Another consequence is that the orbital ellipse of a planet undergoes a slow rotation, as in the case of the hitherto unexplained perihelion of Mercury’s orbit[15]. The following illustration demonstrates how the curvature of space near the sun appears to cause light to bend around it and, further down, how this same curvature causes the orbit of Mercury to precess, that is, change in the direction of its rotation.
Other heavenly consequences
Einstein’s theory of the warping of space is confirmed every time there is a solar eclipse and the observer sees light rays from stars behind the sun, which would not normally be seen, curve around its mass causing them to change trajectory and appear displaced towards the red end of the spectrum. [12.1] This is because the light from the stars behind the sun are bent toward the sun and toward the earth[13]. The light appears to come from a direction that is different to where the star really is. Einstein’s theory of special relativity also predicted light deflection, but since general relativity says that time is also stretched the deflection is twice the magnitude[14].
Another consequence is that the orbital ellipse of a planet undergoes a slow rotation, as in the case of the hitherto unexplained perihelion of Mercury’s orbit[15]. The following illustration demonstrates how the curvature of space near the sun appears to cause light to bend around it and, further down, how this same curvature causes the orbit of Mercury to precess, that is, change in the direction of its rotation.
Source: Lewis Carroll Epstein, “Relativity Visualized”, cited in http://physics.stackexchange.com/questions/3009/how-exactly-does-curved-space-time-describe-the-force-of-gravity, also in http://www.physics.ucla.edu/demoweb/demomanual/modern_physics/principal_of_equivalence_and_general_relativity/curved_spacetime.html
Newton’s theory gave the wrong prediction for the precession of the perihelion of Mercury's orbit. Mercury's orbit is elliptical, as predicted by Newton's theory of gravity, but the ellipse doesn't stay in precisely the same place all the time. It precesses, which is to say that as Mercury orbits the sun, the entire ellipse rotates about the focal point (i.e. the sun) as shown in the illustration below:
Newton’s theory gave the wrong prediction for the precession of the perihelion of Mercury's orbit. Mercury's orbit is elliptical, as predicted by Newton's theory of gravity, but the ellipse doesn't stay in precisely the same place all the time. It precesses, which is to say that as Mercury orbits the sun, the entire ellipse rotates about the focal point (i.e. the sun) as shown in the illustration below:
Literally, there’s a little more space near the Sun than there “should” be, and as a result the direction in which Mercury’s orbit is elliptical, moves.
Source for foregoing and illustration: “Gravity as Curved Space: Einstein's Theory of General Relativity”:http://theory.uwinnipeg.ca/mod_tech/node60.html
Source for foregoing and illustration: “Gravity as Curved Space: Einstein's Theory of General Relativity”:http://theory.uwinnipeg.ca/mod_tech/node60.html
The precession is very small; only 570 seconds of arc per century. (It takes a little over 3 million years for it to go full circle). A second of arc is 1/360 of a degree. Most of it could be understood in the context of Newton's theory of gravity by taking into account perturbations of the orbit due to the presence of other planets. However, once this was done, there still remained a discrepancy of about 40 seconds of arc per century between the prediction, and the observed value. This discrepancy was a complete mystery to scientists at the turn of the century, and they even went as far as postulating the existence of an unseen planet (Vulcan) on the far side of the Sun in order to explain it. It was not until Einstein published his work on the general theory of relativity that the perihelion shift of Mercury was truly understood. Einstein said the discovery was so exciting that it gave him heart palpitations.
[1] Greene (2005), 72, 73.
[2] Greene (2000), 69.
[3] Ibid, 74, 75.
[4] http://www.astronomynotes.com/relativity/s3.htm
[5] Source: http://physics.stackexchange.com/questions/3009/how-exactly-does-curved-space-time-describe-the-force-of-gravity
[6] "Where is here?", Scientific American", November 2015, 60 at 62. A preview from his forthcoming book "Spooky action at a distance".
[7] “About time: Countdown to the Theory of Everything”, Amanda Gefter, New Scientist, 10 October 2011.
[8] Marcelo Gleiser, Imperfect Creation, 67.
[9] Justin Mullins, “The quantum time machine”, New Scientist, 20 November 2010, pp 35-37.
[10] Ibid.
[11] Robert P. Crease, op cit, 199.
[12] Brian Greene, “Why he matters – The fruits of one mind shaped the civilization more than seems possible”, Scientific American, September 2015, Special Issue – 100 years of General Relativity, 24 at 26. Actually, falling objects like this are a time rather than a space thing: see George Musser, op cit (footnote [6] above at 62).
[12.1] Here see the excellent article by Dennis Overbye, "The eclipse that revealed the universe", describing Arthur Eddington's 1919 observation of the 1919 eclipse which confirmed Einstein's theory: https://www.nytimes.com/2017/07/31/science/eclipse-einstein-general-relativity.html
[13] This is graphically illustrated on the Nick Strobel’s astronomy notes website at http://www.astronomynotes.com/relativity/s4.htm
[14] 1.7 seconds of arc instead of 0.85 seconds of arc, the old Newtonian value
[15] See Crease’s resume of Einstein’s March 1916 paper published in the Annalen der Physik in The Great Equations, op cit, 199-200.