**THE FABRIC of the COSMOS,****Brian Greene,**2004

```(annotated and with added

**bold highlights by Epsilon=One**)

**Chapter 12 - The World on a String**

**Quantum Jitters and Empty Space**

If I had to select the single most evocative feature of quantum mechanics, I'd choose the uncertainty principle. Probabilities and wavefunctions certainly provide a radically new framework, but it's the uncertainty principle that encapsulates the break from classical physics. 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 this conception of reality by showing that you can't ever know both the position and the velocity of a particle; you can't ever know both the value of a field at some location in space and how quickly the field value is changing. Quantum uncertainty forbids it.

As we discussed in the last chapter, this quantum uncertainty ensures that the microworld is a turbulent and jittery realm. Earlier, we focused on uncertainty-induced quantum jitters for the inflation field, but quantum uncertainty applies to all fields. 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. This is an idea of critical importance, but if you haven't encountered it previously, it's natural to be puzzled. If a region of space contains nothing — if it's a vacuum — doesn't that mean there's nothing to jitter? Well, we've already learned that the concept of nothingness is subtle. Just think of the Higgs ocean that modern theory claims to permeate empty space. The quantum jitters I'm now referring to serve only to make the notion of "nothing" subtler still. Here's what I mean.

In prequantum (and pre-Higgs) physics, we'd declare a region of space completely empty if it contained no particles and the value of every field was uniformly zero.

The random nature of vacuum field fluctuations ensures that in all but the most microscopic of regions, there are as many "up" jitters as "down" and hence they average out to zero, much as a marble surface appears perfectly smooth to the naked eye even though an electron microscope reveals that it's jagged on minuscule scales. Nevertheless, even though we can't see them directly, more than half a century ago the reality of quantum field jitters, even in empty space, was conclusively established through a simple yet profound discovery.

In 1948, the Dutch physicist

Think about how thoroughly odd this is. You place two plain, ordinary, uncharged metal plates into an

When Casimir first announced these theoretical results, equipment sensitive enough to test his predictions didn't exist. Yet, within about a decade, another Dutch physicist, Marcus Spaarnay, was able to initiate the first rudimentary tests of this Casimir force, and increasingly precise experiments have been carried out ever since. In 1997, for example, Steve Lamoreaux, then at the University of Washington, confirmed Casimir's predictions to an accuracy of 5 percent.

It took scientists the better part of the twentieth century to fully develop the mathematics for describing such quantum activity of the electromagnetic, and strong and weak nuclear forces. The effort was well spent: calculations using this mathematical framework agree with experimental findings to an unparalleled precision (e.g., calculations of the effect of vacuum fluctuations on the magnetic properties of electrons agree with experimental results to one part in a billion).

Yet despite all this success, for many decades physicists have been aware that quantum jitters have been fomenting discontent within the laws of physics.

As we discussed in the last chapter, this quantum uncertainty ensures that the microworld is a turbulent and jittery realm. Earlier, we focused on uncertainty-induced quantum jitters for the inflation field, but quantum uncertainty applies to all fields. 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. This is an idea of critical importance, but if you haven't encountered it previously, it's natural to be puzzled. If a region of space contains nothing — if it's a vacuum — doesn't that mean there's nothing to jitter? Well, we've already learned that the concept of nothingness is subtle. Just think of the Higgs ocean that modern theory claims to permeate empty space. The quantum jitters I'm now referring to serve only to make the notion of "nothing" subtler still. Here's what I mean.

In prequantum (and pre-Higgs) physics, we'd declare a region of space completely empty if it contained no particles and the value of every field was uniformly zero.

*****Let's now think about this classical notion of emptiness in light of the quantum uncertainty principle. If a field were to have and maintain a vanishing value, we would know its value — zero — and also the rate of change of its value — zero, too. But according to the uncertainty principle, it's impossible for both these properties to be definite. Instead, if a field has a definite value at some moment, zero in the case at hand, the uncertainty principle tells us that its rate of change is completely random. And a random rate of change means that in subsequent moments the field's value will randomly jitter up and down, even in what we normally think of as completely empty space. So the intuitive notion of emptiness, one in which all fields have and maintain the value zero, is incompatible with quantum mechanics.*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.***In technical language, physicists say that fields undergo***3**vacuum fluctuations.*The random nature of vacuum field fluctuations ensures that in all but the most microscopic of regions, there are as many "up" jitters as "down" and hence they average out to zero, much as a marble surface appears perfectly smooth to the naked eye even though an electron microscope reveals that it's jagged on minuscule scales. Nevertheless, even though we can't see them directly, more than half a century ago the reality of quantum field jitters, even in empty space, was conclusively established through a simple yet profound discovery.

**Figure 12.1**

(a)Vacuum fluctuations of the electromagnetic field.

(a)

**(b)**Vacuum fluctuations between two metal plates and those outside the plates.

In 1948, the Dutch physicist

**Hendrik Casimir figured out how vacuum fluctuations of the electromagnetic field could be experimentally detected.**Quantum theory says that the jitters of the electromagnetic field in empty space will take on a variety of shapes, as illustrated in Figure 12.1a. Casimir's breakthrough was to realize that by placing two ordinary metal plates in an otherwise empty region, as in Figure 12.1b, he could induce a subtle modification to these vacuum field jitters. Namely, the quantum equations show that in the region between the plates there will be fewer fluctuations (only those electromagnetic field fluctuations whose values vanish at the location of each plate are allowed). Casimir analyzed the implications of this reduction in field jitters and found something extraordinary. Much as a reduction in the amount of air in a region creates a pressure imbalance (for example, at high altitude you can feel the thinner air exerting less pressure on the outside of your eardrums), the reduction in quantum field jitters between the plates also yields a pressure imbalance: the quantum field jitters between the plates become a bit weaker than those outside the plates, and this imbalance*drives*the plates toward each other.Think about how thoroughly odd this is. You place two plain, ordinary, uncharged metal plates into an

*empty*region of space, facing one another. As their masses are tiny, the gravitational attraction between them is so small that it can be completely ignored. Since there is nothing else around, you naturally conclude that the plates will stay put. But this is*not*what Casimir's calculations predicted would happen. He concluded that the plates would be gently guided by the ghostly grip of quantum vacuum fluctuations to move toward one another.When Casimir first announced these theoretical results, equipment sensitive enough to test his predictions didn't exist. Yet, within about a decade, another Dutch physicist, Marcus Spaarnay, was able to initiate the first rudimentary tests of this Casimir force, and increasingly precise experiments have been carried out ever since. In 1997, for example, Steve Lamoreaux, then at the University of Washington, confirmed Casimir's predictions to an accuracy of 5 percent.

**(For plates roughly the size of playing cards and placed one ten-thousandth of a centimeter apart, the force between them is about equal to the weight of a single teardrop; this shows how challenging it is to measure the Casimir force.) There is now little doubt that the intuitive notion of empty space as a static, calm, eventless arena is thoroughly off base. Because of quantum uncertainty, empty space is teeming with quantum activity.***4*It took scientists the better part of the twentieth century to fully develop the mathematics for describing such quantum activity of the electromagnetic, and strong and weak nuclear forces. The effort was well spent: calculations using this mathematical framework agree with experimental findings to an unparalleled precision (e.g., calculations of the effect of vacuum fluctuations on the magnetic properties of electrons agree with experimental results to one part in a billion).

*5*Yet despite all this success, for many decades physicists have been aware that quantum jitters have been fomenting discontent within the laws of physics.

*****For ease of writing, we'll consider only fields that reach their lowest energy when their values are zero. The discussion for other fields—Higgs fields—is identical, except the jitters fluctuate about the field's

*nonzero,*lowest-energy value. If you are tempted to say that a region of space is empty only if there is no matter present and all fields are

*absent,*not just that they have the value zero, see notes section.

*2*