It’s About Time

The Theory of General Relativity: A Guide for the Perplexed

Why did Einstein develop the theory? What is its actual significance? And what does all this have to do with black holes? Profs. Zohar Komargodski and Ofer Aharony explain Einstein’s theory.

Albert Einstein writes out an equation for the density of the Milky Way on the blackboard at the Carnegie Institute in Pasadena, California, on January 14, 1931.
AP

Albert Einstein labored for about 10 years on the formulation of a theory of physics that makes it possible to explain and predict the way in which bodies with mass affect their surroundings. His road to the “Theory of General Relativity” was paved with potholes, errors and corrections, and rife with stormy disagreement and correspondence with the greatest mathematicians and physicians of his time. However, 100 years ago, in November 1915, Einstein publicized the theory that changed the way physics describes the relationship between different bodies in space and to their movement on earth and in outer space.

In the century that has passed since then, the Theory of General Relativity has become (even if it is not devoid of deficiencies) the most significant theory for understanding the universe, encompassing the entire spectrum of physical phenomena occurring in it: from the existence of the event in which the universe was created – the “Big Bang – through the continuous expansion of the universe to the phenomenon of black holes, and less familiar phenomena such as “gravitational lensing.”

The Theory of General Relativity goes well beyond theoretical physics. Among other things, it is at the core of attempts to develop tools for the observation and study of the universe. It laid the foundations for precision measurement and observation of satellites and their locations, and subsequently for the development of navigation systems like GPS.

The attempt to understand, and to explain in simple language, the meaning of the Theory of General Relativity – how it came to be, on which principles it is based, what are its byproducts and what is its status today – is a tall order. To that end, we enlisted the help of Prof. Zohar Komargodski and Prof. Ofer Aharony, two experts on particle physics and astrophysics at the Faculty of Physics of the Weizmann Institute of Science in Rehovot.

What is the background to the development of the Theory of General Relativity?

Einstein’s Theory of General Relativity was conceived as an attempt to settle a contradiction between two prior theories of physics: the first is the Law of Universal Gravitation, developed by the English physicist and mathematician Isaac Newton in the 17th century, and the second is the Special Theory of Relativity, formulated by Einstein himself, which he published in 1905.

The Special Theory of Relativity argued that there is no body capable of moving faster than the speed of light, and it is impossible to transmit any information at any speed higher than this. However, this argument was at odds with Newton’s Law of Universal Gravitation. According to the latter, every body attracts every other body in the universe in an immediate manner, and in a manner that is dependent upon the distance between them. Moreover, the transmission of information in space is unlimited and is possible even at speeds higher than the speed of light, essentially at infinite velocity.

The contradiction between these two ideas was more than theoretical. It was backed up by physics equations, mathematical calculations, observations and findings on the movement of bodies in space. Therefore, Einstein devoted the years that followed publication of his Special Theory of Relativity to the attempt to reconcile this contradiction.

What was he actually looking for?

Einstein sought a new theory that would resolve Newton’s Law of Universal Gravitation with his own Special Theory of Relativity. After 10 years of this quest, he succeeded in formulating the equations that enabled him to unravel the tangle and resolve the conflict: On one hand, they support the claim that there is no body or information that moves at a speed higher than the speed of light, on the other, they successfully predict the movement of heavenly bodies no less well than does Newton’s Law of Universal Gravitation (and even better, as we will describe below).

In the course of this arduous campaign, Einstein rediscovered major portions of an entire field of mathematics (differential geometry) with which he was not familiar. He formulated several fascinating principles of physics, but also committed more than a few errors along the way.

As opposed to Newton’s Law of Universal Gravitation, which can be explained in a high school classroom, Einstein’s new equations are a great deal more complicated, both mathematically and theoretically. It can be assumed that if Einstein had not invested 10 years of his life in this fascinating quest, it would have taken many more decades until some other scientist would have discovered the Theory of General Relativity.

What are the basic principles of the Theory of General Relativity?

The Theory of General Relativity is founded upon several important principles. In order to understand the key principle, we must go back to 17th-century Italy and the astronomer and physicist Galileo Galilei. Galileo proposed as a basic principle of nature the following: If two people carry out the same exact experiment (for example, measuring the time of a pendulum’s cycle, or measuring the quantity of radiation emitted by any radioactive material) while they are moving, one in relation to the other, at a constant speed, then the two experiments will produce the same exact results. For example, an individual measuring the periodic movement of a pendulum within an automobile moving at constant speed will receive the same exact result as another individual conducting the same measurement on the ground and without movement.

This principle remains valid to this day, and no violation of it has ever been observed. However, it does not relate to instances in which the speed varies – meaning that it either slowed or accelerated. Therefore, for purposes of the demonstration, if we place a pendulum within an accelerating automobile it will execute a movement that differs from that of a similar pendulum found in the hands of an individual standing on the ground.  

Essentially, the most important principle in the Theory of General Relativity is an expansion of the principle set down by Galileo. Einstein argued that during freefall (imagine, for example, an elevator falling out of control from a high floor), gravitational force completely disappears. In other words, every experiment conducted in space, far from any source of gravity, would produce the same exact results as an experiment conducted in a plummeting elevator on earth. This principle is called the “equivalence principle,” and it enabled Einstein to cancel out the force of gravity in certain conditions. In these conditions, he could have used equations of the Special Theory of Relativity, which does not include gravitational force, in order to solve specific problems such as light bending (when a ray of light is bent as it passes near bodies with mass).

What does the Theory of General Relativity say?

The Theory of General Relativity says that every body possessing mass also possesses gravitational force, and accordingly also affects the space in which it is situated and other objects in its surroundings. The fact that it has mass essentially creates a distortion in space and causes bodies moving in its environs to move in a way that seems like a diversion from its straight path.

Another way to look at the Theory of General Relativity is as a framework (or theory) that corrects Newton’s Law of Universal Gravitation. So long as the engagement in these corrections is carried out within the solar system, they are very difficult to identify or measure. Essentially, at that time only one example had been observed that supported Einstein’s corrections to Newton’s law. This was when movements of the planet Mercury slightly deviated from the predictions of Newton’s law. Were it not for that, it is reasonable to assume that the Law of Universal Gravitation would have been found to be erroneous many years before Einstein came into the picture.

However, in the time that has passed since then, the Theory of General Relativity has succeeded in explaining and forecasting several physical phenomena that do not arise in classic physics (that which predates the Theory of General Relativity). There are at least two prominent and relatively well-known examples of this: One is the ability to predict the existence of black holes, and the second is the manner in which the theory supports an idea according to which our universe is in a state of expansion, such that distant galaxies seem to be accelerating further away from us.

Why only “seem to be”? The galaxies are not really growing more distant from one another. What is happening is that the universe is adding to itself increasingly more space. To illustrate this point, imagine a balloon on which two points are marked. Once the balloon is inflated, the points may not have moved, but the space between them has grown along with the volume of the balloon.

What are black holes and how are they related to the Theory of General Relativity?

According to the Theory of General Relativity, black holes are bodies from which it is not possible to extract information (anything that possesses energy or mass), because their gravitational force is so immense that it does not enable even emitting particles of light. These bodies can be heavy and very large.

Today, many people believe that nearly every galaxy in the universe contains at least one large and massive black hole. The massive black hole found in our galaxy is called Sagittarius A, and its mass, according to estimates, is one million times that of the sun. According to the Theory of General Relativity, black holes grow by absorption of stars, dust and gas that simply fall into the black hole in a one-way path that rules out any possibility of their restoration.

An interesting historical fact is that after Einstein discovered the equations of the Theory of General Relativity, he believed that they were so complicated that no one would ever find a solution for them. To his delight, he was mistaken, and shortly after the publication of the Theory of General Relativity, the German-Jewish physicist and astronomer Karl Schwarzschild found the connection between the theoretical equations and the phenomenon itself, thereby confirming the Theory of General Relativity on black holes.

What is the theoretical revolution that the Theory of General Relativity brought about?

The Theory of General Relativity made it possible to pose real scientific questions about the universe. It made it possible to relate in a scientific and analytical manner to its processes as a whole, and to specific phenomena that take place within it. For example, it made it possible to describe and explain the expansion of the universe. In 1929, the American astronomer Edwin Hubble discovered that we indeed live in such a universe – in which distant galaxies continually draw further away from us at expanding speed.

At the most fundamental level, one of the important things that the Theory of General Relativity contributed to physics itself, as it relates to the study of space and time, is the fact that massive bodies distort the space around them. To illustrate the point, if a tennis ball is placed on a taut sheet, a sort of dimple will form around it. If a basketball is placed there, the dimple will be larger – the same is true in space.

What can the Theory of General Relativity tell us about the universe’s past?

The fact that the universe is expanding enables the Theory of General Relativity to conclude that at some point the universe began with a Big Bang, in other words that the universe began from a certain point (what is also called “singularity”).

What existed before that point that began the universe?

Concepts of “before” or “after” are dependent upon the existence of a time continuum, and the Theory of General Relativity maintains that the time continuum itself also began to take on significance only after the onset of singularity.

And what about the future? Where will the process of the universe’s expansion end?

According to the process described by the Theory of General Relativity, the universe will increasingly cool off, and the hundreds of billions of galaxies in it will grow immeasurably distant from one another. In the end, the Theory of Relativity predicts a future of frozenness and emptiness – the increasing separation of galaxies from one another.

What is the status of the Theory of General Relativity today?

The Theory of General Relativity offers numerous predictions of astronomical observations related to the movement of planets, satellites and spaceships, observations of stars and distant galaxies and the evolution of the entire universe. All the observations conducted to date corroborate these predictions, such that it seems that the Theory of General Relativity is describing gravitational force in the universe with great precision.

However, like every other theory of physics, it can be assumed that this theory is not absolutely precise, and that the day will come when experiments and observations will be carried out that will necessitate the replacement of the Theory of Relativity with another theory.

For example, at present scientists do not know how to reconcile the Theory of General Relativity with Quantum theory, and it is very possible that a new theory of physics is therefore required. Any such alternate theory would have to provide an explanation for results that have been proven by means of the Theory of General Relativity, but it is possible that this alternate theory would have different predictions vis-à-vis future experiments and observations.