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

```(annotated and with added

**bold highlights by Epsilon=One**)

**Chapter 16 - The Future of an Allusion**

Quantum Averaging

In Chapter 12 we discussed how the fabric of space, much like everything else in our quantum universe, is subject to the jitters of quantum uncertainty. It is these fluctuations, you'll recall, that run roughshod over point-particle theories, preventing them from providing a sensible quantum theory of gravity. By replacing point particles with loops and snippets, string theory spreads out the fluctuations—substantially reducing their magnitude—and this is how it yields a successful unification of quantum mechanics and general relativity. Nevertheless, the diminished spacetime fluctuations certainly still exist (as illustrated in the next-to-last level of magnification in Figure 12.2), and within them we can find important clues regarding the fate of spacetime.

First, we learn that the familiar space and time that suffuse our thoughts and support our equations emerge from a kind of averaging process. Think of the pixelated image you see when your face is a few inches from a television screen. This image is very different from what you see at a more comfortable distance, because once you can no longer resolve individual pixels, your eyes combine them into an average that looks smooth. But notice that it's only through the averaging process that the pixels produce a familiar, continuous image. In a similar vein, the microscopic structure of spacetime is riddled with random undulations, but we aren't directly aware of them because we lack the ability to resolve spacetime on such minute scales. Instead, our eyes, and even our most powerful equipment, combine the undulations into an average, much like what happens with television pixels. Because the undulations are random, there are typically as many "up" undulations in a small region as there are "down," so when averaged they tend to cancel out, yielding a placid spacetime. But, as in the television analogy,

Quantum averaging provides a down-to-earth interpretation of the assertion that familiar spacetime may be illusory. Averages are useful for many purposes but, by design, they do not provide a sharp picture of underlying details. Although the average family in the U.S. has 2.2 children, you'd be in a bind were Ito ask to visit such a family. And although the national average price for a gallon of milk is $2.783, you're unlikely to find a store selling it for exactly this price. So, too, familiar spacetime, itself the result of an averaging process, may not describe the details of something we'd want to call fundamental. Space and time may only be approximate, collective conceptions, extremely useful in analyzing the universe on all but ultramicroscopic scales, yet as illusory as a family with 2.2 children.

A second and related insight is that the increasingly intense quantum jitters that arise on decreasing scales suggest that the notion of being able to divide distances or durations into ever smaller units likely comes to an end at around the Planck length (10^-33 centimeters) and Planck time (10^-43 seconds). We encountered this idea in Chapter 12, where we emphasized that, although the notion is thoroughly at odds with our usual experiences of space and time, it is not particularly surprising that a property relevant to the everyday fails to survive when pushed into the micro-realm. And since the arbitrary divisibility of space and time is one of their most familiar everyday properties, the inapplicability of this concept on ultrasmall scales gives another hint that there is something else lurking in the microdepths — something that might be called the bare-bones substrate of spacetime—the entity to which the familiar notion of spacetime alludes. We expect that this

Thus, looking for familiar spacetime in the deepest laws of nature may be like trying to take in Beethoven's Ninth Symphony solely note by single note or one of Monet's haystack paintings solely brushstroke by single brushstroke. Like these masterworks of human expression, nature's spacetime whole may be so different from its parts that nothing resembling it exists at the most fundamental level.

First, we learn that the familiar space and time that suffuse our thoughts and support our equations emerge from a kind of averaging process. Think of the pixelated image you see when your face is a few inches from a television screen. This image is very different from what you see at a more comfortable distance, because once you can no longer resolve individual pixels, your eyes combine them into an average that looks smooth. But notice that it's only through the averaging process that the pixels produce a familiar, continuous image. In a similar vein, the microscopic structure of spacetime is riddled with random undulations, but we aren't directly aware of them because we lack the ability to resolve spacetime on such minute scales. Instead, our eyes, and even our most powerful equipment, combine the undulations into an average, much like what happens with television pixels. Because the undulations are random, there are typically as many "up" undulations in a small region as there are "down," so when averaged they tend to cancel out, yielding a placid spacetime. But, as in the television analogy,

*it's only because of the averaging process that a smooth and tranquil form for spacetime emerges.*Quantum averaging provides a down-to-earth interpretation of the assertion that familiar spacetime may be illusory. Averages are useful for many purposes but, by design, they do not provide a sharp picture of underlying details. Although the average family in the U.S. has 2.2 children, you'd be in a bind were Ito ask to visit such a family. And although the national average price for a gallon of milk is $2.783, you're unlikely to find a store selling it for exactly this price. So, too, familiar spacetime, itself the result of an averaging process, may not describe the details of something we'd want to call fundamental. Space and time may only be approximate, collective conceptions, extremely useful in analyzing the universe on all but ultramicroscopic scales, yet as illusory as a family with 2.2 children.

A second and related insight is that the increasingly intense quantum jitters that arise on decreasing scales suggest that the notion of being able to divide distances or durations into ever smaller units likely comes to an end at around the Planck length (10^-33 centimeters) and Planck time (10^-43 seconds). We encountered this idea in Chapter 12, where we emphasized that, although the notion is thoroughly at odds with our usual experiences of space and time, it is not particularly surprising that a property relevant to the everyday fails to survive when pushed into the micro-realm. And since the arbitrary divisibility of space and time is one of their most familiar everyday properties, the inapplicability of this concept on ultrasmall scales gives another hint that there is something else lurking in the microdepths — something that might be called the bare-bones substrate of spacetime—the entity to which the familiar notion of spacetime alludes. We expect that this

*ur*-ingredient, this most elemental spacetime stuff, does not allow dissection into ever smaller pieces because of the violent fluctuations that would ultimately be encountered, and hence is quite unlike the large-scale spacetime we directly experience. It seems likely, therefore, that the appearance of the fundamental spacetime constituents— whatever they may be—is altered significantly through the averaging process by which they yield the spacetime of common experience.Thus, looking for familiar spacetime in the deepest laws of nature may be like trying to take in Beethoven's Ninth Symphony solely note by single note or one of Monet's haystack paintings solely brushstroke by single brushstroke. Like these masterworks of human expression, nature's spacetime whole may be so different from its parts that nothing resembling it exists at the most fundamental level.