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Kindle Notes & Highlights
by
Brian Greene
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June 7, 2005 - November 1, 2018
General relativity is a classical theory: it does not incorporate any of the probabilistic concepts of quantum theory. A primary goal of the modern unification program is therefore to combine general relativity and quantum mechanics, and to describe all four forces within the same quantum mechanical framework.
Quantum Jitters and Empty Space
Remember, in the seventeenth and eighteenth centuries, scientists believed that a complete description of physical reality amounted to specifying the positions and velocities of every constituent of matter making up the cosmos. And with the advent of the field concept in the nineteenth century, and its subsequent application to the electromagnetic and gravitational forces, this view was augmented to include the value of each field—the strength of each field, that is—and the rate of change of each field’s value, at every location in space. But by the 1930s, the uncertainty principle dismantled
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The electromagnetic field, the strong and weak nuclear force fields, and the gravitational field are all subject to frenzied quantum jitters on microscopic scales. In fact, these field jitters exist even in space you’d normally think of as empty, space that would seem to contain no matter and no fields.
A field’s value can jitter around the value zero but it can’t be uniformly zero throughout a region for more than a brief moment.3 In technical language, physicists say that fields undergo vacuum fluctuations.
Jitters and Their Discontent
By the highest level in the figure, which shows the fabric of space on scales smaller than the Planck length—a millionth of a billionth of a billionth of a billionth (10−33) of a centimeter—space becomes a seething, boiling cauldron of frenzied fluctuations. As the illustration makes clear, the usual notions of left/right, back/forth, and up/down become so jumbled by the ultramicroscopic tumult that they lose all meaning. Even the usual notion of before/after, which we’ve been illustrating by sequential slices in the spacetime loaf, is rendered meaningless by quantum fluctuations on time
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Does It Matter?
If you use the combined equations of general relativity and quantum mechanics, they almost always yield one answer: infinity. And that’s a problem. It’s nonsense. Experimenters never measure an infinite amount of anything.
If we ever hope to understand the origin of the universe—one of the deepest questions in all of science—the conflict between general relativity and quantum mechanics must be resolved.
The Unlikely Road to a Solution31
Broad knowledge, technical facility, flexibility of thought, openness to unanticipated connections, immersion in the free flow of ideas worldwide, hard work, and significant luck are all critical parts of scientific discovery.
The quantum mechanical equations of string theory predicted that a particular, rather unusual, particle should be copiously produced in the high-energy collisions taking place in atom smashers. The particle would have zero mass, like a photon, but string theory predicted it would have spin-two, meaning, roughly speaking, that it would spin twice as fast as a photon. None of the experiments had ever found such a particle, so this appeared to be among the erroneous predictions made by string theory.
Although gravitons have yet to be detected experimentally, the theoretical analyses all agreed that gravitons must have two properties: they must be massless and have spin-two.
To be viable, a theory must be free of all anomalies.
One stormy night, while working late at the Aspen Center for Physics in Colorado, they completed one of the field’s most important calculations—a calculation proving that all of the potential anomalies, in a way that seemed almost miraculous, did cancel each other out. String theory, they revealed, was free of anomalies and hence suffered from no mathematical inconsistencies. String theory, they demonstrated convincingly, was quantum mechanically viable.
The First Revolution
String Theory and Unification
A string vibrating in one particular pattern might have the properties of an electron, while a string vibrating in a different pattern might have the properties of an up-quark, a down-quark, or any of the other particle species in Table 12.1. It is not that an “electron string” makes up an electron, or an “up-quark string” makes up an up-quark, or a “down-quark string” makes up a down-quark. Instead, the single species of string can account for a great variety of particles because the string can execute a great variety of vibrational patterns.
Why Does String Theory Work?
The main new feature of string theory is that its basic ingredient is not a point particle—a dot of no size—but instead is an object that has spatial extent. This difference is the key to string theory’s success in merging gravity and quantum mechanics.
Just as resolution on your TV screen is limited by the size of individual pixels, resolution of the gravitational field in string theory is limited by the size of gravitons. Thus, the nonzero size of gravitons (and everything else) in string theory sets a limit, at roughly the Planck scale, to how finely a gravitational field can be resolved.
Thus, by limiting how small you can get, string theory limits how violent the jitters of the gravitational field become—and the limit is just big enough to avoid the catastrophic clash between quantum mechanics and general relativity. In this way, string theory quells the antagonism between the two frameworks and is able, for the first time, to join them.
Cosmic Fabric in the Realm of the Small
Instead, when you get down to the Planck length (the length of a string) and Planck time (the time it would take light to travel the length of a string) and try to partition space and time more finely, you find you can’t. The concept of “going smaller” ceases to have meaning once you reach the size of the smallest constituent of the cosmos.
The Finer Points
Some scientists argue vociferously that a theory so removed from direct empirical testing lies in the realm of philosophy or theology, but not physics.
Amen, brothers and sisters!
The standard model takes the particles in Tables 12.1 and 12.2 (again, ignoring the graviton) as input, then makes impressively accurate predictions for how the particles will interact and influence each other. But the standard model can’t explain the input—the particles and their properties—any more than your calculator can explain the numbers you input the last time you used it.
Why do the elementary particles have just the right properties to allow nuclear processes to happen, stars to light up, planets to form around stars, and on at least one such planet, life to exist?
The standard model can’t offer any insight into this question since the particle properties are part of its required input.
But string theory is different. In string theory, particle properties are determinedby string vibrational patterns and so the theory holds the promise of providing an explanation.
Particle Properties in String Theory
The mass of a particle in string theory is nothing but the energy of its vibrating string.
Faster and more furious vibration means higher energy, and higher energy translates, via Einstein’s equation, into greater mass. Conversely, the lighter a particle is, the slower and less frenetic is the corresponding string vibration; a massless particle like a photon or a graviton corresponds to a string executing the most placid and gentle vibrational pattern that it possibly can.
Other properties of a particle, such as its electric charge and its spin, are encoded through more subtle features of the string’s vibrations.
For every vibrational pattern with spin-½ there was an associated vibrational pattern with spin-0. For every vibrational pattern of spin-1, there was an associated vibrational pattern of spin-½, and so on.
In short, for string theory to be viable, its vibrational patterns must yield and explain the particles of the standard model.
If the properties of these vibrational patterns match the particle properties in Tables 12.1 and 12.2, I think that would convince even the diehard skeptics of string theory’s veracity, whether or not anyone had directly seen the extended structure of a string itself.
Too Many Vibrations
The masses of the permissible string vibrational patterns bear no resemblance to the experimentally measured particle masses recorded in Tables 12.1 and 12.2.
Thus, all but the simplest string vibrational patterns are highly energetic and hence, via E = mc2, correspond to particles with huge masses.
Thus, the possible masses of string vibrations are 0 times the Planck mass, 1 times the Planck mass, 2 times the Planck mass, 3 times the Planck mass, and so on, showing that the masses of all but the 0-mass string vibrations are gargantuan.15
Thus, we see clearly that the known particle masses do not fit the pattern advanced by string theory.
This led the skeptics to proclaim that superstring theory, despite all its potential for unification, was merely a mathematical structure with no direct relevance for the physical universe.
Superstring theory requires the existence of six dimensions of space that no one has ever seen. That’s not a fine point—that’s a problem.
Unification in Higher Dimensions
Kaluza proposed that in addition to left/right, back/forth, and up/down, the universe actually has one more spatial dimension that, for some reason, no one has ever seen. If correct, this would mean that there is another independent direction in which things can move, and therefore that we need to give four pieces of information to specify a precise location in space, and a total of five pieces of information if we also specify a time.
Kaluza had found a framework that combined Einstein’s original equations of general relativity with those of Maxwell’s equations of electromagnetism.
Of course, there was still a problem. Although the mathematics worked, there was—and still is—no evidence of a spatial dimension beyond the three we all know about.
The Hidden Dimensions
