With special relativity, Einstein resolved the apparent conflict between Newton’s laws of motion and the constancy of light speed as Maxwell proposed in his electromagnetism framework. Einstein proved that intuition was simply wrong but realized that the idea that nothing can move faster than light speed was fundamentally incompatible with Newton’s theory of universal gravitation. So, in resolving the first major conflict of physics, Einstein created the second. Einstein resolved this conflict through his theory of general relativity, published in 1915.

Greene considers gravity. In 1687, Newton proposed “that the strength of the gravitational attraction between two bodies depends on precisely two things: the amount of stuff [mass] composing each of the bodies and the distance between them” (54). Newton’s theory of gravity states that a larger mass results in stronger attraction and a smaller mass results in weaker attraction but that this force also depends on distance. Newton’s law of universal gravitation accurately predicts and describes the motion of the planets, comets, and the moon. The agreement between Newton’s math and observed reality is so accurate that it was the accepted science for centuries, until special relativity.

According to Newton’s theory of gravity, the force of attraction between any two objects is felt instantaneously, and any change to that force is also felt instantaneously, regardless of the distance between the objects. If the sun exploded, the earth would instantly feel the loss of that gravitational pull and fly out of orbit. However, according to special relativity, absolutely nothing (no object, no force, no influence of any kind) moves faster than light speed. Due to the distance between the sun and the earth, light from the sun takes approximately eight minutes to reach the earth. Gravity would have to be faster than light speed for that influence to be instantaneous, which Einstein proved impossible.

Einstein’s efforts to resolve this contradiction led him to general relativity. Special relativity emphasizes a focus on constant-velocity motion, putting aside the question of accelerated motion. However, Einstein then wondered how one might bring accelerated motion into line with relativity. He realized that gravity and accelerated motion are “profoundly interwoven” (60).

Greene uses an analogy to explain. Imagine you are in a tiny windowless compartment. You can feel the pull of gravity at your feet. If that compartment began moving forward at a steady rate, you would be pressed backward against the wall. Lacking any way to see that you are moving, you could reasonably deduce that the compartment has flipped onto its back, and you are feeling the pull of gravity (rather than motion). This is what Einstein called the equivalence principle. Under the right conditions, the force one feels “from a gravitational field or from accelerated motion are indistinguishable” (60). Einstein showed that because no discernible difference exists between a viewpoint that is accelerating without a gravitational field and a viewpoint that is not accelerating but has a gravitational field, all viewpoints are fundamentally equal.

Einstein then showed that accelerated motion leads to a warping of space and time, so that flat (Euclidean) geometry no longer functions, and he combined this with gravity. Special relativity had already laid the groundwork by demonstrating that space and time were inextricably linked, leading to the “unified structure of spacetime” (66). Einstein had also already shown that gravity and accelerated motion were indistinguishable. After he demonstrated that accelerated motion leads to a warping of space and time, he was able to argue that gravity is the warping of space and time.

This is best understood with the analogy of a thin rubber membrane stretched flat. This is spacetime. The introduction of any object, especially one with a large mass like a bowling ball, dropped into the middle of the rubber membrane warps that membrane into a curved space. A smaller object like a ball bearing pushed into motion on that curved membrane will “fall” toward the bowling ball, following a curved path. Ignoring friction, if you set the ball bearing into motion at the right speed and direction, it will continue to move along that curved path indefinitely, just as the mass of the sun warps the fabric of space and the earth moves along the curve created by the warping. This is gravity.

This new concept resolves the conflict with special relativity. To understand why, think again of the rubber membrane. Absent any mass, the membrane will remain flat. A ball bearing travels at a constant velocity in a straight line across the membrane. Now drop the bowling ball into the center, thus warping the space around it. The ball bearing will be affected, but not instantaneously, as Newton’s theory would predict. The disturbance of the bowling ball travels as ripples through the membrane at a set speed, determined by the properties of the rubber material, before reaching the ball bearing and influencing its motion. The same is true for space, where light speed determines the ripples. Thus, if the sun exploded, Earth’s inhabitants would not feel change in gravity instantly but rather eight minutes later.

Einstein’s theory was confirmed in a 1919 experiment by astronomer Arthur Eddington, which proved that light from stars bent around the massive warping from the sun, exactly as Einstein’s theory predicted. The equations of general relativity even accurately predicted the observable fact that the universe is expanding, a thought so radical at the time that Einstein did not even believe his own results. General relativity has been accepted as an accurate description of spacetime and gravity. However, it is “fundamentally incompatible with another extremely well-tested theory: quantum mechanics” (84)

Quantum mechanics is a “conceptual framework for understanding the microscopic properties of the universe” (86). Whereas relativity upended the prevalent worldview regarding things that are massive or fast, quantum mechanics changed the knowledge of the subatomic. Even many theoretical physicists have difficulty understanding the esoteric realm of quantum mechanics. Theoretical physicist Richard Feynman once famously stated, “I think I can safely say that nobody understands quantum mechanics” (87). Nevertheless, physicists know that the most basic concepts of accepted physics “fail to have any meaning when our focus narrows to the microscopic realm” (87), necessitating quantum mechanics.

Quantum mechanics begins with a puzzle in electromagnetism: In the early 1900s, physicists tried to calculate the total energy carried by all electromagnetic waves in an oven set to a particular temperature. Physicists use three elements to describe a wave: wavelength (the distance between peaks or troughs), frequency (the number of up-and-down oscillations a wave completes in one second), and amplitude (the maximum height or depth of the wave). When physicists used thermodynamics to determine how much energy the heat of the oven could pump into electromagnetic waves of each allowed wavelength, they determined that “each of the allowed waves—regardless of its wavelength—carries the same amount of energy” (90). Because an infinite number of wave patterns are possible and each wave pattern carries the same amount of energy, the result is an infinite amount of energy. An infinite answer, particularly when disproved by measurable observations, indicates a flaw in the theory.

In 1900, physicist Max Planck proposed a solution so inspired it earned him the 1918 Nobel Prize in Physics. Planck argued that the energy carried by electromagnetic waves comes in lumps and that these lumps occur only in whole numbers (no fractions). Furthermore, he suggested that the “energy denomination of a wave—the minimal lump of energy that it can have—is determined by its frequency” (92). Specifically, larger frequency results in larger minimum energy, and smaller frequency results in smaller minimum energy. Planck’s calculations showed that this “lumpiness of the allowed energy” of each wave removed the previous results of infinite total energy.

Planck further showed that adjusting a single parameter in his calculations allowed him to accurately predict the measured energy of an oven for any chosen temperature. This parameter is Planck’s constant: the proportionality factor between the frequency and minimal energy of a wave, which is measured at “about a billionth of a billionth of a billionth in everyday units” (93). The tiny value of this constant is important: It keeps most energy lump values miniscule and keeps the inherent weirdness of quantum mechanics contained to the microscopic realm. Planck had no “justification for his pivotal introduction of lumpy energy” (94). He did not know what these lumps were and had no proof that they existed beyond the fact that the math worked. Einstein proved the existence of these lumps with his work on the photoelectric effect.

The photoelectric effect describes the reactions when light strikes a metallic surface, ejecting electrons from the surface. Intuition suggested that the more intense (brighter) the light, the more electrons would be ejected from the surface, but instead it was the wavelength of light (its color) that caused more electrons to break loose. Einstein applied Planck’s concept of lumpy energy to light to propose that light is composed of tiny packets or particles. The energy of these particles was determined by the proportionality to its frequency (Planck’s constant). Thus, Einstein proved that Planck’s guess about lumpy energy was a “fundamental feature of electromagnetic waves” (97): All electromagnetic waves are composed of particles. These particles are now called photons.

This leads to two questions. The first is whether they are particles or waves. The answer is both. An experiment devised by English physicist Thomas Young in the early 1800s, called the double-slit experiment, examines the behavior of light as it passes through one or two slits cut into a metal plate. Scientists expected the light to behave a certain way if it was composed of waves. Despite proof in other experiments that light is composed of photons, it still behaved like a wave in double-slit experiments. This led scientists to determine that “light has both wave-like and particle-like properties” (103).

Scientist Louis de Broglie proposed in 1923 that this wave-particle duality might be applied to matter particles as well. Similar experiments with electrons showed that they also behave like waves under certain conditions, forcing scientists to “conclude that each electron embodies a wave-like character” (104) while also being a particle. In addition, the wavelength of matter particles is proportional to Planck’s constant, and the resulting waves are so tiny that they do not affect the everyday world.

The second question is what are these waves. Physicist Erwin Schrodinger proposed that “electron waves must be interpreted from the standpoint of probability” (105). The magnitude of the wave indicates the higher or lower probability of where an electron is likely to be found at any given moment. Thus, quantum mechanics “implies that matter itself must be described fundamentally in a probabilistic manner” (106). This conclusion was so unacceptable to Einstein that he famously objected: “God does not play dice with the Universe” (107).

Feynman refined wave-particle duality further when he proposed two things. First, by attempting to observe and measure the behavior of electrons in experimentation, scientists fundamentally influence the result. Second, each electron goes through both slits at the same time. Moreover, he argued that “each individual electron traverses every possible trajectory simultaneously” (110) and the probability of that electron wave is determined by the “combined effect of every possible” path (111). This seems to defy the observable rules of reality. However, as with most things in quantum mechanics, this is noticeable only on miniscule scales, becoming negligible in the realm of everyday objects. Feynman showed that “all paths but one cancel each other [...]. In effect, only one of the infinity of paths matters as far as the motion of the object is concerned” (111)—ensuring that in all but the smallest scales, objects still behave as one intuitively expects them to.

From this arises the “hallmark feature that fundamentally differentiates quantum mechanics” from classical physics: the uncertainty principle. Proposed by physicist Werner Heisenberg in 1927, this states that at a microscopic level one cannot know both a particle’s location and its velocity at the same time, and “moreover, the more precisely you know one, the less precisely you know the other” (114). The uncertainty principle shows that the features of reality one considers “so basic as to be beyond question” are only so because Planck’s constant and its resultant “microscopic weirdness” (85) are so small that no one notices them. However, applying these new concepts to the realm of spacetime reveals the third conflict of modern physics.

Despite advancements in physics, Greene posits that physicists will not be content until they have reached the deepest and most complete understanding of the universe. Theoretical physicist Stephen Hawking once alluded to this as “a first step toward knowing ‘the mind of God’” (117). Unfortunately, evidence shows that general relativity and quantum mechanics do not provide this deepest understanding; their mutual incompatibility demonstrates that something is wrong.

First, the uncertainty principle implies that the universe is a “frenetic place” (118) when observed at smaller distances and shorter time scales. Moreover, the uncertainty principle suggests a “frantic shifting back and forth of energy and momentum” (119) that occurs constantly at the microscopic level, even in empty space. The extreme fluctuations possible between energy and mass mean that (as one example) an electron and its antimatter partner can spontaneously burst into existence and then wink out again. An empty region of space looks calm only at levels larger than the microscopic because these fluctuations cancel each other out. However, “this frenzy is the obstacle to merging general relativity and quantum mechanics” (120).

In the 1930s-40s, physicists successfully combined quantum mechanical uncertainty with the forcefield theories of electromagnetism, the weak force and the strong force, while also accounting for certain aspects of special relativity. This combination was based on two concepts. The first was the supposition that if electromagnetic force is transferred by a particle (the photon), it stands to reason that other forces also have a corresponding “messenger particle” (124). The weak force particle is a weak gauge boson; the strong force particle is a gluon. This also suggests that the gravitational force likewise has a messenger particle, the graviton. The second concept was the discovery that just as gravity relies on symmetry (ensuring that all viewpoints are equally valid), a subtle kind of symmetry governs the other forces: Quarks and other particles have identical interactions if the symmetries are maintained. Successfully combining quantum mechanics with the three nongravitational forces suggests that a similar combination should be possible with gravity. However, this does not work.

General relativity and Einstein’s concept of gravity require that the fabric of spacetime, absent of any mass, be flat and calm. However, quantum mechanics shows that at small enough scales, the fabric of spacetime becomes a chaotic undulating substance called “quantum foam,” within which the equations of general relativity fail. The equations of general relativity and quantum mechanics allow physicists to approximate the scale at which general relativity fails. The smallness of this scale corresponds with Planck’s constant, yielding a result called the Planck length, “which is small almost beyond imagination: a millionth of a billionth of a billionth of a billionth of a centimeter” (130). Therefore, general relativity and quantum mechanics become incompatible at shockingly small scales, leading one to wonder why it is worth worrying about. However, any level of conflict suggests that these theories are flawed. Physicists believe that “a logically sound theory” (130) must exist that encompasses everything. Attempts to find this theory failed until the discovery of string theory.