The Fabric of the Cosmos: Space, Time, and the Texture of Reality (69 page)

8. Bohm actually rediscovered and further developed an approach that goes back to Prince Louis de Broglie, so this approach is sometimes called the de Broglie-Bohm approach.

9. For the mathematically inclined reader, Bohm's approach is local in
configuration
space but certainly
nonlocal
in real space. Changes to the wavefunction in one location in real space immediately exert an influence on particles located in other, distant locations.

10. For an exceptionally clear treatment of the Ghirardi-Rimini-Weber approach and its relevance to understanding quantum entanglement, see J. S. Bell, "Are There Quantum Jumps?" in
Speakable and Unspeakable in Quantum Mechanics
(Cambridge, Eng.: Cambridge University Press, 1993).

11. Some physicists consider the questions on this list to be irrelevant by-products of earlier confusions regarding quantum mechanics. The wavefunction, this view professes, is merely a theoretical tool for making (probabilistic) predictions and should not be accorded any but mathematical reality (a view sometimes called the "Shut up and calculate" approach, since it encourages one to use quantum mechanics and wavefunctions to make predictions, without thinking hard about what the wavefunctions actually mean and do). A variation on this theme argues that wavefunctions never actually collapse, but that interactions with the environment make it
seem
as if they do. (We will discuss a version of this approach shortly.) I am sympathetic to these ideas and, in fact, strongly believe that the notion of wavefunction collapse will ultimately be dispensed with. But I don't find the former approach satisfying, as I am not ready to give up on understanding what happens in the world when we are "not looking," and the latter—while, in my view, the right direction—needs further mathematical development. The bottom line is that measurement causes something that
is
or is
akin to
or
masquerades as
wavefunction collapse. Either through a better understanding of environmental influence or through some other approach yet to be suggested, this apparent effect needs to be addressed, not simply dismissed.

12. There are other controversial issues associated with the Many Worlds interpretation that go beyond its obvious extravagance. For example, there are technical challenges to define a notion of probability in a context that involves an infinite number of copies of each of the observers whose measurements are supposed to be subject to those probabilities. If a given observer is really one of many copies, in what sense can we say that he or she has a particular probability to measure this or that outcome? Who really is "he" or "she"? Each copy of the observer will measure—with probability 1—whatever outcome is slated for the particular copy of the universe in which he or she resides, so the whole probabilistic framework requires (and has been given, and continues to be given) careful scrutiny in the Many Worlds framework. Moreover, on a more technical note, the mathematically inclined reader will realize that, depending on how one precisely defines the Many Worlds, a preferred eigenbasis may need to be selected. But how should that eigenbasis be chosen? There has been a great deal of discussion and much written on all these questions, but to date there are no universally accepted resolutions. The approach based on decoherence, discussed shortly, has shed much light on these issues, and has offered particular insight into the issue of eigenbasis selection.

13. The Bohm or de Broglie-Bohm approach has never received wide attention. Perhaps one reason for this, as pointed out by John Bell in his article "The Impossible Pilot Wave," collected in
Speakable and Unspeakable in Quantum Mechanics,
is that neither de Broglie nor Bohm was particularly fond of what he himself had developed. But, again as Bell points out, the de Broglie-Bohm approach does away with much of the vagueness and subjectivity of the more standard approach. If for no other reason, even if the approach is wrong, it is worth knowing that particles can have definite positions and definite velocities at all times (ones beyond our ability, even in principle, to measure), and still conform fully to the predictions of standard quantum mechanics—uncertainty and all. Another argument against Bohm's approach is that the nonlocality in this framework is more "severe" than that of standard quantum mechanics. By this it is meant that Bohm's approach has nonlocal interactions (between the wavefunction and particles) as a central element of the theory from the outset, while in quantum mechanics the nonlocality is more deeply buried and arises only through nonlocal correlations between widely separated measurements. But, as supporters of this approach have argued, because something is hidden does not make it any less present, and, moreover, as the standard approach is vague regarding the quantum measurement problem—the very place where nonlocality makes itself apparent—once that issue is fully resolved, the nonlocality may not be so hidden after all. Others have argued that there are obstacles to making a relativistic version of the Bohm approach, although progress has been made on this front as well (see, for example, John Bell Beables
for Quantum Field Theory,
in the collected volume indicated above). And so, it is definitely worth keeping this alternative approach in mind, even if only as a foil against rash conclusions about what quantum mechanics unavoidably implies. For the mathematically inclined reader, a very nice treatment of Bohm's theory and issues of quantum entanglement can be found in Tim Maudlin,
Quantum Nonlocalityand Relativity
(Malden, Mass.: Blackwell, 2002)
.

14. For an in-depth, though technical, discussion of time's arrow in general, and the role of decoherence in particular, see H. D. Zeh,
The Physical Basis of the Direction of
Time
(Heidelberg: Springer, 2001).

15. Just to give you a sense of how quickly decoherence takes place—how quickly environmental influence suppresses quantum interference and thereby turns quantum probabilities into familiar classical ones—here are a few examples. The numbers are approximate, but the point they convey is clear. The wavefunction of a grain of dust floating in your living room, bombarded by jittering air molecules, will decohere in about a billionth of a billionth of a billionth of a billionth (10
^-36
) of a second. If the grain of dust is kept in a perfect vacuum chamber and subject only to interactions with sunlight, its wavefunction will decohere a bit more slowly, taking a thousandth of a billionth of a billionth (10
^-21
) of a second. And if the grain of dust is floating in the darkest depths of empty space and subject only to interactions with the relic microwave photons from the big bang, its wavefunction will decohere in about a millionth of a second. These numbers are extremely small, which shows that decoherence for something even as tiny as a grain of dust happens very quickly. For larger objects, decoherence happens faster still. It is no wonder that, even though ours is a quantum universe, the world around us looks like it does. (See, for example, E. Joos, "Elements of Environmental Decoherence," in
Decoherence:Theoretical, Experimental, and Conceptual Problems,
Ph. Blanchard, D. Giulini, E. Joos, C. Kiefer, I.-O. Stamatescu, eds. [Berlin: Springer, 2000]).

Chapter 8

1. To be more precise, the symmetry between the laws in Connecticut and the laws in New York makes use of both translational symmetry
and
rotational symmetry. When you perform in New York, not only will you have changed location from Connecticut, but more than likely you will undertake your routines while facing in a somewhat different direction (east versus north, perhaps) than during practice.

2. Newton's laws of motion are usually described as being relevant for "inertial observers," but when one looks closely at how such observers are specified, it sounds circular: inertial observers are those observers for whom Newton's laws hold. A good way to think about what's really going on is that Newton's laws draw our attention to a large and particularly useful class of observers: those whose description of motion fits completely and quantitatively within Newton's framework. By definition, these are inertial observers. Operationally, inertial observers are those on whom no forces of any kind are acting— observers, that is, who experience no accelerations. Einstein's general relativity, by contrast, applies to all observers, regardless of their state of motion.

3. If we lived in an era during which
all
change stopped, we'd experience no passage of time (all body and brain functions would be frozen as well). But whether this would mean that the spacetime block in Figure 5.1 came to an end, or, instead, carried on with no change along the time axis—that is, whether time would come to an end or would still exist in some kind of formal, overarching sense—is a hypothetical question that's both difficult to answer and largely irrelevant for anything we might measure or experience. Note that this hypothetical situation is different from a state of maximal disorder in which entropy can't further increase, but microscopic change, like gas molecules going this way and that, still takes place.

4. The cosmic microwave radiation was discovered in 1964 by the Bell Laboratory scientists Arno Penzias and Robert Wilson, while testing a large antenna intended for use in satellite communications. Penzias and Wilson encountered background noise that proved impossible to remove (even after they scraped bird droppings—"white noise"— from the inside of the antenna) and, with the key insights of Robert Dicke at Princeton and his students Peter Roll and David Wilkinson, together with Jim Peebles, it was ultimately realized that the antenna was picking up microwave radiation that originated with the big bang. (Important work in cosmology that set the stage for this discovery was carried out earlier by George Gamow, Ralph Alpher, and Robert Herman.) As we discuss further in later chapters, the radiation gives us an unadulterated picture of the universe when it was about 300,000 years old. That's when electrically charged particles like electrons and protons, which disrupt the motion of light beams, combined to form electrically neutral atoms, which, by and large, allow light to travel freely. Ever since, such ancient light—produced in the early stages of the universe—has traveled unimpeded, and today, suffuses all of space with microwave photons.

5. The physical phenomenon involved here, as discussed in Chapter 11, is known as
redshift.
Common atoms such as hydrogen and oxygen emit light at wavelengths that have been well documented through laboratory experiments. When such substances are constituents of galaxies that are rushing away, the light they emit is elongated, much as the siren of a police car that's racing away is also elongated, making the pitch drop. Because red is the longest wavelength of light that can be seen with the unaided eye, this stretching of light is called the redshift effect. The amount of redshift grows with increasing recessional speed, and hence by measuring the received wavelengths of light and comparing with laboratory results, the speed of distant objects can be determined. (This is actually one kind of redshift, akin to the Doppler effect. Redshifting can also be caused by gravity: photons elongate as they climb out of a gravitational field.)

6. More precisely, the mathematically inclined reader will note that a particle of mass
m,
sitting on the surface of a ball of radius R and mass density, experiences an acceleration, d
²
R/dt
²
given by (4 /3)R
³
G /R
²
, and so (1/R) d
²
R/dt
²
= (4 /3)G. If we formally identify
R
with the radius of the universe, and with the mass density of the universe, this is Einstein's equation for how the size of the universe evolves (assuming the absence of pressure).

7. See P.J.E. Peebles, Principles of Physical Cosmology (Princeton: Princeton University Press, 1993), p. 81.

The caption reads: "But who is really blowing up this ball? What makes it so that the universe expands or inflates? A Lambda does the job! Another answer cannot be given." (Translation by Koenraad Schalm.) Lambda refers to something known as the cosmological constant, an idea we will encounter in Chapter 10.

8. To avoid confusion, let me note that one drawback of the penny model is that every penny is essentially identical to every other, while that is certainly not true of galaxies. But the point is that on the largest of scales—scales on the order of 100 million light-years—the individual differences between galaxies are believed to average out so that, when one analyzes huge volumes of space, the overall properties of each such volume are extremely similar to the properties of any other such volume.