In the previous article, Einstein’s Thought Experiments 1, we looked at Einstein’s basic insight into the nature of gravity which he called the Principle of Equivalence. This idea established that gravity was essentially the same as a force of acceleration. You can feel this identity for yourself when you get into an elevator and it starts to rise — the upward acceleration feels just like weight — or descend, in which case you feel nearly weightless for a moment. This fact eventually became memorialized in the term for the acceleration pilots feel when pulling out of a dive, “g-force.”
There were two other factors shaping the development of his theory.
It had been known since the time of Galileo that a falling body accelerates at a rate which is independent of the mass of the object. The legendary experiment Galileo used to demonstrate this was to drop a canonball and a small stone off the top of the Leaning Tower of Pisa (which was in Pisa, Italy, and has nothing to do with Pizza, which is in New York). In fact, Galileo performed several experiments with gravity, but it’s not likely he used the Tower of Pisa for this study. One needs a more careful observation of the time of impact than naked eye impressions. In any case, this principle was verified repeatedly and exhaustively until Newton gave a more mathematical description of the principle. Objects accelerate with a constant force a such that, in time t, they will cover a distance s = ½at². The speed of a falling body, after time t, will be v = at. Notice that in neither case does the value depend on the object’s mass, m.
Lastly, Einstein had long disagreed with the Newtonian strategy of describing gravity as a force acting at a distance. Instead, he had formed the principle of local action, i.e., that a particle can only respond to forces and causes in its immediate vicinity. The classic type of interaction is collision, which can alter the particle’s kinetic energy and momentum vector. If not collision, the only other kind of interaction available to mediate gravity would be some kind of slope or gradient, which alters paths by affecting the amount of work the particle must do to traverse the path. Particles (objects of any kind) do not like to do more work than they have to. This principle of least action is a well-known and long-recognized quality of physical motion which eventually became vested in a concept of entropy. But for Einstein, these ideas of local action and least action pointed strongly toward an application of geometry. Just as a river will choose the path of least energy across terrain, so too, any particle moving in a gravitational region must travel by the shortest path. Otherwise it would be going “uphill.” And this concept of path led to the idea of a geometric interpretation of gravity.
We’ve all seen the illustration of gravity that uses a taut rubber sheet with a dimple or well in it. A marble or steel ball rolled across the sheet will travel a straight path, until it comes into the vicinity of the well. Then it curves from its path, following the local curvature of the sheet in a trajectory that swerves around the well. If it gets too close to the well, instead of swinging past and coming out on a new heading, it will spiral around the well until it reaches the bottom. It can go no farther, then, because any additional movement would require it to move uphill, which it can’t do on its own.
I always wondered, as a youngster, why this rubber sheet example was supposed to be meaningful, because anyone could see that it needed gravity to work, and in an explanation of gravity, you can’t use the idea of gravity to explain the motion. What was not so obvious to me at the time is that nothing needs to hold the marble onto the rubber sheet or pull it down into the well. The geometry of the situation does this automatically. All you need to assume is that the marble is constrained to stay on the sheet, and of course, any particle of matter is always constrained to move in the three-dimensional region of space it lies within. In other words, it can’t jump off the “rubber sheet.”
This geometrical approach has a happy consequence. The geometrical path of least energy on a surface or in a region of space is a matter of pure geometry. You just have to do like a golfer does, and discover the “lie” of the green, the angle of its slope, in order to figure the putt. It has nothing to do with how heavy the particle is or how much mass it has. Indeed, a beam of light would be forced by the geometry of the space it’s moving through to follow the same bending path as anything else moving near a star or planet, and so we get Galileo’s first result, that mass is irrelevant, as a direct implication.
This insight of Einstein’s, that gravity must affect the path of a light beam in exactly the same way as a particle of matter, led to the first experiment ever conducted to confirm his theory. According to his theory, any light beam passing close to a star would be bent away from its normal path by the star’s gravity well. Sir Arthur Eddington, an English astronomer and astrophysicist, led an expedition to observe a total solar eclipse expected in that year.
This event is described in a Wikipedia article here, which I quote:
After the war, Eddington travelled to the island of Príncipe near Africa to watch the solar eclipse of May 29, 1919. During the eclipse, he took pictures of the stars in the region around the Sun. According to the theory of general relativity, stars near the Sun would appear to have been slightly shifted because their light had been curved by its gravitational field. This effect is noticeable only during an eclipse, since otherwise the Sun’s brightness obscures the stars. Eddington showed that Newtonian gravitation could also be interpreted to predict half that predicted by Einstein.
In summary, by reasoning from a few basic principles, Einstein developed his entire theory of gravitation, which would have been significant even if it only improved on the predictive accuracy of Newton’s theory. Einstein’s not only explained the confusing precession of Mecury’s orbit around the sun, it also provided a better value for the observed displacement of starlight passing close to the sun. But beyond this predictive improvement, Einstein’s theory finally gave a rationale to the phenomenon of gravity itself. Newton’s theory only described its behavior without explaining why it exists at all, but with Einstein’s work, at last we can see how it comes about: matter alters the local geometry of space-time, and that alters the motions of everything near it. In fact, because it is only the geometry of space that creates the effects of gravity, we see, in the end, that gravity is not a force at all; it is nothing more than the consequences of inertia and accelerated motion. It’s just like centrifugal forces, which certainly do influence the behavior of an object, but nobody today believes there is a centrifugal force field. And after Einstein’s work, gravity is exposed as the same kind of thing.
The form of Einstein’s theory had a significant impact on the science of Physics and future research, for it provided an intuitive confirmation that the Universe follows certain logical principles. And so, you could say Einstein was devoted to a belief in the Logos, or ordering principle that governs the real world. This idea of Logos, or the regulation of the material universe by intangible logic, runs throughout this blog, and Einstein’s work is another example of it.
