The Fabric of the Cosmos: Space, Time, and the Texture of Reality (65 page)

15. For a more detailed, yet general-level, explanation of the warping of space and time according to general relativity, see, for example, Chapter 3 of
The Elegant Universe.

16. For the mathematically trained reader, Einstein's equations are G
= (8 G/c
⁴
) T
, where the left-hand side describes the curvature of spacetime using the Einstein tensor and the right-hand side describes the distribution of matter and energy in the universe using the energy-momentum tensor.

17. Charles Misner, Kip Thorne, and John Archibald Wheeler,
Gravitation
(San Francisco: W. H. Freeman and Co., 1973), pp. 544-45.

18. In 1954, Einstein wrote to a colleague: "As a matter of fact, one should no longer speak of Mach's principle at all" (as quoted in Abraham Pais,
Subtle Is the Lord,
p. 288).

19. As mentioned earlier, successive generations have attributed the following ideas to Mach even though his own writings do not phrase things explicitly in this manner.

20. One qualification here is that objects which are so distant that there hasn't been enough time since the beginning of the universe for their light—or gravitational influence—to yet reach us have no impact on the gravity we feel.

21. The expert reader will recognize that this statement is, technically speaking, too strong, as there are nontrivial (that is, non-Minkowski space) empty space solutions to general relativity. Here I am simply using the fact that special relativity can be thought of as a special case of general relativity in which gravity is ignored.

22. For balance, let me note that there are physicists and philosophers who do not agree with this conclusion. Even though Einstein gave up on Mach's principle, during the last thirty years it has taken on a life of its own. Various versions and interpretations of Mach's idea have been put forward, and, for example, some physicists have suggested that general relativity
does
fundamentally embrace Mach's ideas; it's just that some particular shapes that spacetime can have—such as the infinite flat spacetime of an empty universe—don't. Perhaps, they suggest, any spacetime that is remotely realistic—populated by stars and galaxies, and so forth—does satisfy Mach's principle. Others have offered reformulations of Mach's principle in which the issue is no longer how objects, such as rocks tied by a string or buckets filled with water, behave in an otherwise empty universe, but rather how the various time slicings—the various three-dimensional spatial geometries—relate to one another through time. An enlightening reference on modern thinking about these ideas is
Mach's Principle: From Newton's Bucket to Quantum Gravity,
Julian Barbour and Herbert Pfister, eds. (Berlin: Birkhäuser, 1995), which is a collection of essays on the subject. As an interesting aside, this reference contains a poll of roughly forty physicists and philosophers regarding their view on Mach's principle. Most (more than 90 percent) agreed that general relativity does not fully conform to Mach's ideas. Another excellent and extremely interesting discussion of these ideas, from a distinctly pro-Machian perspective and at a level suited to general readers, is Julian Barbour's book
The
End of Time: The Next Revolution in Physics
(Oxford: Oxford University Press, 1999).

23. The mathematically inclined reader might find it enlightening to learn that Einstein believed that spacetime had no existence independent of its metric (the mathematical device that gives distance relations in spacetime), so that if one were to remove everything—including the metric—spacetime would
not
be a something. By "spacetime" I always mean a manifold together with a metric that solves the Einstein equations, and so the conclusion we've reached, in mathematical language, is that metrical spacetime is a something.

24. Max Jammer,
Concepts of Space,
p. xvii.

Chapter 4

1. More accurately, this appears to be a medieval conception with historical roots that go back to Aristotle.

2. As we will discuss later in the book, there are realms (such as the big bang and black holes) that still present many mysteries, at least in part owing to extremes of small size and huge densities that cause even Einstein's more refined theory to break down. So, the statement here applies to all but the extreme contexts in which the known laws themselves become suspect.

3. An early reader of this text, and one who, surprisingly, has a particular expertise in voodoo, has informed me that something
is
imagined to go from place to place to carry out the voodoo practitioner's intentions—namely, a spirit. So my example of a fanciful nonlocal process may, depending on your take on voodoo, be flawed. Nevertheless, the idea is clear.

4. To avoid any confusion, let me reemphasize at the outset that when I say, "The universe is not local," or "Something we do over here can be entwined with something over there," I am not referring to the ability to exert an instantaneous intentioned control over something distant. Instead, as will become clear, the effect I am referring to manifests itself as
correlations
between events taking place—usually, in the form of correlations between results of measurements—at distant locations (locations for which there would not be sufficient time for even light to travel from one to the other). Thus, I am referring to what physicists call
nonlocal correlations.
At first blush, such correlations may not strike you as particularly surprising. If someone sends you a box containing one member of a pair of gloves, and sends the other member of the pair to your friend thousands of miles away, there will be a correlation between the handedness of the glove each of you sees upon opening your respective box: if you see left, your friend will see right; if you see right, your friend will see left. And, clearly, nothing in these correlations is at all mysterious. But, as we will gradually describe, the correlations apparent in the quantum world seem to be of a very different character. It's as if you have a pair of "quantum gloves" in which each member can be either left-handed or right-handed, and commits to a definite handedness only when appropriately observed or interacted with. The weirdness arises because, although each glove seems to choose its handedness randomly when observed, the gloves work in tandem, even if widely separated: if one chooses left, the other chooses right, and vice versa.

5. Quantum mechanics makes predictions about the microworld that agree fantastically well with experimental observations. On this, there is universal agreement. Nevertheless, because the detailed features of quantum mechanics, as discussed in this chapter, differ significantly from those of common experience, and, relatedly, as there are different mathematical formulations of the theory (and different formulations of how the theory spans the gap between the microworld of phenomena and the macroworld of measured results), there isn't consensus on how to
interpret
various features of the theory (and various puzzling data which the theory, nevertheless, is able to explain mathematically), including issues of nonlocality. In this chapter, I have taken a particular point of view, the one I find most convincing based on current theoretical understanding and experimental results. But, I stress here that not everyone agrees with this view, and in a later endnote, after explaining this perspective more fully, I will briefly note some of the other perspectives and indicate where you can read more about them. Let me also stress, as we will discuss later, that the experiments contradict Einstein's belief that the data could be explained solely on the basis of particles always possessing definite, albeit hidden, properties
without any use or mention of nonlocal entanglement.
However, the failure of this perspective only rules out a local universe. It does not rule out the possibility that particles have such definite hidden features.

6. For the mathematically inclined reader, let me note one potentially misleading aspect of this description. For multiparticle systems, the probability wave (the wavefunction, in standard terminology) has essentially the same interpretation as just described, but is defined as a function on the
configuration space
of the particles (for a single particle, the configuration space is isomorphic to real space, but for an N-particle system it has 3N dimensions). This is important to bear in mind when thinking about the question of whether the wavefunction is a real physical entity or merely a mathematical device, since if one takes the former position, one would need to embrace the reality of configuration space as well—an interesting variation on the themes of Chapters 2 and 3. In relativistic quantum field theory, the fields can be defined in the usual four spacetime dimensions of common experience, but there are also somewhat less widely used formulations that invoke generalized wavefunctions—so-called
wavefunctionals
defined on an even more abstract space,
field space.

7. The experiments I am referring to here are those on the
photoelectric effect,
in which light shining on various metals causes electrons to be ejected from the metal's surface. Experimenters found that the greater the intensity of the light, the greater the number of electrons emitted. Moreover, the experiments revealed that the energy of each ejected electron was determined by the color—the frequency—of the light. This, as Einstein argued, is easy to understand if the light beam is composed of particles, since greater light intensity translates into more light particles (more photons) in the beam—and the more photons there are, the more electrons they will hit and hence eject from the metallic surface. Furthermore, the frequency of the light would determine the energy of each photon, and hence the energy of each electron ejected, precisely in keeping with the data. The particlelike properties of photons were finally confirmed by Arthur Compton in 1923 through experiments involving the elastic scattering of electrons and photons.

8. Institut International de Physique Solvay,
Rapport et discussions du 5ème Conseil
(Paris, 1928), pp. 253ff.

9. Irene Born, trans.,
The Born-Einstein Letters
(New York: Walker, 1971), p. 223.

10. Henry Stapp,
Nuovo Cimento
40B (1977), 191-204.

11. David Bohm is among the creative minds that worked on quantum mechanics during the twentieth century. He was born in Pennsylvania in 1917 and was a student of Robert Oppenheimer at Berkeley. While teaching at Princeton University, he was called to appear in front of the House Un-American Activities Committee, but refused to testify at the hearings. Instead, he departed the United States, becoming a professor at the University of São Paulo in Brazil, then at the Technion in Israel, and finally at Birkbeck College of the University of London. He lived in London until his death in 1992.

12. Certainly, if you wait long enough, what you do to one particle can, in principle, affect the other: one particle could send out a signal alerting the other that it had been subjected to a measurement, and this signal could affect the receiving particle. However, as no signal can travel faster than the speed of light, this kind of influence is not instantaneous. The key point in the present discussion is that at the very moment that we measure the spin of one particle about a chosen axis we learn the spin of the other particle about that axis. And so, any kind of "standard" communication between the particles—luminal or subluminal communication—is not relevant.

13. In this and the next section, the distillation of Bell's discovery which I am using is a "dramatization" inspired by David Mermin's wonderful papers: "Quantum Mysteries for Anyone,"
Journal of Philosophy
78, (1981), pp. 397-408; "Can You Help Your Team Tonight by Watching on TV?," in
Philosophical Consequences of Quantum Theory: Reflectionson Bell's Theorem,
James T. Cushing and Ernan McMullin, eds. (University of Notre Dame Press, 1989); "Spooky Action at a Distance: Mysteries of the Quantum Theory," in
The Great Ideas Today
(Encyclopaedia Britannica, Inc., 1988), which are all collected in N. David Mermin,
Boojums All the Way Through
(Cambridge, Eng.: Cambridge University Press, 1990). For anyone interested in pursuing these ideas in a more technical manner, there is no better place to start than with Bell's own papers, many of which are collected in J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge, Eng.: Cambridge University Press, 1997).

14. While the locality assumption is critical to the argument of Einstein, Podolsky, and Rosen, researchers have tried to find fault with other elements of their reasoning in an attempt to avoid the conclusion that the universe admits nonlocal features. For example, it is sometimes claimed that all the data require is that we give up so-called realism—the idea that objects possess the properties they are measured to have independent of the measurement process. In this context, though, such a claim misses the point. If the EPR reasoning had been confirmed by experiment, there would be nothing mysterious about the long-range correlations of quantum mechanics; they'd be no more surprising than classical long-range correlations, such as the way finding your left-handed glove over here ensures that its partner over there is a right-handed glove. But such reasoning is refuted by the Bell/Aspect results. Now, if in response to this refutation of EPR we give up realism— as we do in standard quantum mechanics—that does nothing to lessen the stunning weirdness of long-range correlations between widely separated
random
processes; when we relinquish realism, the gloves, as in endnote 4, become "quantum gloves." Giving up realism does not, by any means, make the observed nonlocal correlations any less bizarre. It is true that if, in light of the results of EPR, Bell, and Aspect, we try to maintain realism—for example, as in Bohm's theory discussed later in the chapter—the kind of nonlocality we require to be consistent with the data seems to be more severe, involving nonlocal interactions, not just nonlocal correlations. Many physicists have resisted this option and have thus relinquished realism.