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According to their work and subsequent studies, every electron in the universe, always and forever, spins at one fixed and never changing rate.
If an electron were not spinning, it would not be an electron.
All of the matter particles (and their antimatter partners as well) have spin equal to that of the electron. In the language of the trade, physicists say that matter particles all have "spin-1/2," where the value 1/2 is, roughly speaking, a quantum-mechanical measure of how quickly the particles rotate.
Moreover, physicists have shown that the nongravitational force carriers—photons, weak gauge bosons, and gluons—also possess an intrinsic spinning characteristic that turns out to be twice that of the matter particles. They all have "spin-1."
Well, even before string theory, physicists were able to determine what spin the hypothesized graviton must have to be the transmitter of the gravitational force. The answer: twice the spin of p...
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Supersymmetry and Superpartners
Supersymmetry cannot be associated with a simple and intuitive change in observational vantage point; shifts in time, in spatial location, in angular orientation, and in velocity of motion exhaust these possibilities. But just as spin is "like rotational motion, with a quantum-mechanical twist," supersymmetry can be associated with a change in observational vantage point in a "quantum-mechanical extension of space and time." These quotes are especially important, as the last sentence is only meant to give a rough sense of where supersymmetry fits into the larger framework of symmetry
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Instead, detailed theoretical analysis showed that if the universe incorporates supersymmetry, then every known particle must have an as-yet-undiscovered superpartner particle, whose spin is half a unit less than its known counterpart.
The Case for Supersymmetry: Prior to String Theory
Physicists distinguish this quantum-mechanical increase in strength as we get closer to the electron from that known in classical physics by saying that the intrinsic strength of the electromagnetic force increases on shorter distance scales. This reflects that the strength increases not merely because we are closer to the electron but also because more of the electron's intrinsic electric field becomes visible. In fact, although we have focused on the electron, this discussion applies equally well to all electrically charged particles and is summarized by saying that quantum effects drive the
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In 1973, Gross and Frank Wilczek at Princeton, and, independently, David Politzer at Harvard, studied this question and found a surprising answer: The quantum cloud of particle eruptions and annihilations amplifies the strengths of the strong and weak forces. This implies that as we examine them on shorter distances, we penetrate more of this seething cloud and hence are subject to less of its amplification. And so, the strengths of these forces get weaker when they are probed on shorter distances.
Their calculations showed that if this haze is penetrated by examining the forces not on everyday scales but as they act on distances of about a hundredth of a billionth of a billionth of a billionth (10-29) of a centimeter (a mere factor of ten thousand larger than the Planck length), the three nongravitational force strengths appear to become equal.
A refinement of the calculation of force strengths reveals that without supersymmetry they almost, but not quite, meet.
Why haven't we discovered any of the superpartner particles? The calculations that lead to the convergence of the force strengths, as well as other considerations studied by a number of physicists, indicate that the superpartner particles must be a good deal heavier than the known particles.
We have described how supersymmetry elevates our theories to their most symmetric form—but you might suggest that the universe does not care about attaining the most symmetric form that is mathematically possible. We have noted the important technical point that supersymmetry relieves us from the delicate task of tuning numerical parameters in the standard model to avoid subtle quantum problems—but you might argue that the true theory describing nature may very well walk the fine edge between self-consistency and self-destruction. We have discussed how supersymmetry modifies the intrinsic
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Supersymmetry in String Theory
If string theory is right, physicists expect that so is supersymmetry.
A Super-Embarrassment of Riches
In the arena of fundamental explanations, more is definitely less.
by 1985 physicists realized that supersymmetry, by then a central element in the structure of string theory, could actually be incorporated into string theory in not one but five different ways.
We live in one universe; we expect one explanation.
In the wry words of Witten, "If one of the five theories describes our universe, who lives in the other four worlds?"
Chapter 8
More Dimensions Than Meet the Eye
String theory so thoroughly shakes the foundations of modern physics that even the generally accepted number of dimensions in our universe—something so basic that you might think it beyond questioning—is dramatically and convincingly overthrown.
The Illusion of the Familiar
In 1919, however, a little-known Polish mathematician named Theodor Kaluza from the University of Königsberg had the temerity to challenge the obvious—he suggested that the universe might not actually have three spatial dimensions; it might have more.
Kaluza's Idea and Klein's Refinement
The answer, implicit in Kaluza's work and subsequently made explicit and refined by the Swedish mathematician Oskar Klein in 1926, is that the spatial fabric of our universe may have both extended and curled-up dimensions.
Comings and Goings on a Garden Hose
Unification in Higher Dimensions
Modern Kaluza-Klein Theory
The essential requirement, again, is that all of these dimensions have a spatial extent smaller than the smallest length scales we can probe, since no experiment has yet revealed their existence.
More Dimensions and String Theory
when expressed as percentages, probabilities are numbers between 0 and 100. Physicists have found that a key signal that a quantum-mechanical theory has gone haywire is that particular calculations yield "probabilities" that are not within this acceptable range.
In the early days of string theory physicists found that certain calculations yielded negative probabilities, which are also outside of the acceptable range.
The negative probabilities arose from a mismatch between what the theory required and what reality seemed to impose: The calculations showed that if strings could vibrate in nine independent spatial directions, all of the negative probabilities would cancel out.
Moreover, rather than just postulating the existence of extra dimensions, as had been done by Kaluza, Klein, and their followers, string theory requires them.
Some Questions
In our discussion of string theory, we will stick to the more "conventional" approach in which all of the curled-up dimensions are space dimensions, but the intriguing possibility of new time dimensions could well play a role in future developments.
The Physical Implications of Extra Dimensions
According to string theory, the universe is made up of tiny strings whose resonant patterns of vibration are the microscopic origin of particle masses and force charges. String theory also requires extra space dimensions that must be curled up to a very small size to be consistent with our never having seen them. But a tiny string can probe a tiny space. As a string moves about, oscillating as it travels, the geometrical form of the extra dimensions plays a critical role in determining resonant patterns of vibration. Because the patterns of string vibrations appear to us as the masses and
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What Do the Curled-Up Dimensions Look Like?
Now that we have a better sense of what the extra dimensions look like, what are the physical properties that emerge from strings that vibrate through them, and how do these properties compare with experimental observations?
Chapter 9
The Smoking Gun: Experimental Signatures
Certainly, there is no way to establish that any theory describes our world without subjecting its predictions to experimental verification. And no matter how compelling a picture string theory paints, if it does not accurately describe our universe, it will be no more relevant than an elaborate game of Dungeons and Dragons.
As Witten has said, "the fact that gravity is a consequence of string theory is one of the greatest theoretical insights ever."
Most physicists would be far happier with one of two things: a bona fide prediction from string theory that experimentalists could confirm, or a postdiction of some property of the world (like the mass of the electron or the existence of three families of particles) for which there is currently no explanation.
And with a good deal more luck, indirect fingerprints of the theory could be confirmed at any moment.
And we're still waiting.
