By the time Compton did his experiments in 1923, this was the expected result. Einstein won his first Nobel Prize for describing the related photoelectric effect, explaining the way individual electrons are knocked from solid materials by individual photons. Planck performed the first theoretical calculations of photon momentum and energy, although he did not take his hypothetical photons seriously.

A more advanced mental picture I like to use, which catches both the surfer and the wave in a single system, is a hoop which, like a Mobius band, has a twist in it. Imagine that the hoop is made of very stretchable material but is resistant to being twisted, so that it stores some elastic energy in the twist. The twist is not uniformly distributed round the hoop. At any given point, the degree of twisting corresponds to the amplitude of the wave. Sooner or later, the ring snaps at some point—most likely somewhere the local twisting is greatest—and untwists itself, reforming as a simple hoop, no longer a Mobius strip, and no longer storing any elastic energy. The hoop-with-twist metaphor works only in two dimensions, but physics-knowledgeable readers can think in terms not of a Mobius strip but a skyrmion, a corresponding kind of topological knot in three-dimensional space.

For example, if the electron detector is a passive loop of wire that has a current induced in it only when a charged particle passes nearby, it still has some effect on its neighborhood at other times, because random thermal motions of electrons in the wire loop will produce a tiny, fluctuating magnetic field.

Including more-sophisticated experiments involving three particles rather than two, whose results are even harder to quibble with.

Howard, D. 2003. Who invented the Copenhagen Interpretation? A study in mythology. Available at: http://www.nd.edu/~dhoward1/Copenhagen%20Myth%20A.pdf

Bohm, D., and B. J. Hiley. 1993. The Undivided Universe. New York: Routledge.

Price, H. 1996. Time’s Arrow and Archimedes’ Point: New Directions for the Physics of Time. Oxford: Oxford University Press. The constraint in our future would probably be different from the known constraint in the past, the pointlike Big Bang. It would be a state of micro order rather than macro order. A visual analogue would be a clump of seaweed at low tide. At the seabed the strands all start at the same point (macro order, the Big Bang); at the surface the strands are spread apart, but wind and buoyancy force them to lie exactly parallel to one another (micro order).

For example, the existence of particle interactions that exhibit what is called CPT violation are a problem for Price’s version. This stands for charge-parity-time violation. The particles do not behave in a fully time-symmetric manner.

There are many possible quibbles with the exact figure. Cosmologists can feel free to add a few orders of magnitude.

Joos, E. 1999. Elements of environmental decoherence. In P. Blanchard, D. Giulini, E. Joos, C. Kiefer, and I.-O. Stamatescu (eds). Decoherence: Theoretical, Experimental, and Conceptual Programs. Heidelberg, Germany: Springer.

See www.lhup.edu/~dsimanek/fe-scidi.htm.

Russell, J. B. 1991. Inventing the Flat Earth: Columbus and Modern Historians. New York: Praeger.

Gribbin, J. 2002. Science: A History 1543-2001. London: Penguin Books, pp. 421-424.

Hoping that you can ignore the effects of far-off things because their influence is relatively small is not necessarily justified. For example, the inverse-square law tells you that many forces diminish by a factor of four for a doubling of distance, but a doubling of distance implies that you must then take into account the effects of objects in an eightfold greater volume of space. If the action is instantaneous, you can get the kind of self-reinforcing interactions that we nowadays call positive feedback. There is never a guarantee that the universe will be comprehensible, but a universe incorporating instantaneous long-range interactions is likely to be almost impossible to get to grips with.

Turnbull, C. M. 1961. The Forest People. New York: Simon & Schuster, quoted in R. D. Gross. 1987. Psychology, the Science of Mind and Behaviour. London: Hodder & Stoughton, p. 129. I am indebted to Claire Chambers for tracking down the source of this story.

Deutsch, D., and P. Hayden. 2000. Information flow in entangled quantum systems. Centre for Quantum Computation, The Clarendon Laboratory, University of Oxford. Proceedings of the Royal Society of London, Ser. A 456:1759-1774.

Tegmark, M. 2003. Scientific American, May. An expanded version appears in the online physics archive http://www.arxiv.org.

Kwiat, Zeiliger et al., High-efficiency quantum interrogation measurements via the quantum Zeno effect, arXiv:quant-ph/9909083 v1 27 Sep 1999.

Paul, H., and M. Pavicic. 1997. Nonclassical interaction-free detection of objects in a monolithic total-internal-reflection resonator. Journal of the Optical Society of America B 14:1273-1277.

Kent, A., and D. Wallace. Quantum interrogation and the safer X-ray. Quantum Physics, abstract quant-ph/0102118 v1.

Feynman, R. 1982. Simulating physics with computers. International Journal of Theoretical Physics 21 (6/7):467-488.

Deutsch, D. 1985. Quantum theory, the Church-Turing principle, and the universal quantum computer. Proceedings of the Royal Society of London, Ser. A 400:97-117.

http://www.chem.ox.ac.uk/curecancer.html.

http://www.climateprediction.net/index.php.

Other discoveries such as Grover’s search algorithm still require further work before they can truly be said to do anything “useful.”

Vaidman, L. 2002. “Many-worlds interpretation of quantum mechanics.” In E. N. Zalta (ed.),The Stanford Encyclopedia of Philosophy (Summer ed.), Available at: http://plato.stanford.edu/archives/sum2002/entries/qm-manyworlds/.

Deutsch, D. 1985. Quantum theory, the Church-Turing principle and the universal quantum computer. Proceedings of the Royal Society of London, Ser. A 400:97-117.

Deutsch, D., and P. Hayden. 2000. Information flow in entangled quantum systems. Proceedings of the Royal Society of London, Ser. A 456:1759-1774. Available at: http://xxx.lanl.gov/abs/quant-ph/9906007.

Deutsch, D. 2004. Qubit field theory, January. Available at: http://arxiv.org/ftp/quant-ph/papers/0401/0401024.pdf.

Wallace, D. 2003. Everettian rationality: Defending Deutsch’s approach to probability in the Everett interpretation. Quantum Physics, abstract quant-ph/0303050 revised March 11.

Another notable British example is Jim Lovelock, famous for his discovery that an ecosystem is unstable until it becomes limited by the chemical resources available to it. A consequence is that the atmosphere of any life-bearing planet should deviate from chemical equilibrium, so planets with ecosystems should be detectable from afar by looking for excesses of such gases as ozone and methane. Lovelock’s concept of “Gaia” to describe the Earth’s dynamic equilibrium made him a darling of the early eco-movement. His income from ingenious patents made an academic post unnecessary.

Barbour’s more technical work, which is too complex for us to go into here, essentially concerns the problem of how we can specify the state of the whole universe at a particular instant when, due to relativity, different observers do not agree on what constitutes a simultaneous instant.

Gell-Mann, M. and J. B. Hartle “Strong Decoherence” In D.-H. Feng and B.-L. Hu (eds). Proceedings of the 4th Drexel Conference on Quantum Non-Integrability: The Quantum-Classical Correspondence. Hong Kong: International Press of Boston. arXiv:gr-qc/9509054 v4 23 (Nov).

http://www.hep.upenn.edu/~max/index.html.

Lewis, D. 2004. How many lives has Schrödinger’s cat? Australasian Journal of Philosophy 82:3-22.

In the full and nightmarish version of Jonathan Swift’s Gulliver’s Travels, which is not normally given to children to read, the plight of these immortal but terribly enfeebled and senile persons is graphically described.

Sebastian Sequoia-Jones, conversation with the author, March 2004.

David Wallace, conversation with the author, November 2003.

Piccione, M., and A. Rubinstein. 1997. On the interpretation of decision problems with imperfect recall. Games and Economic Behavior 20:3-24.

Vaidman, L. 2001. Probability and the MWI. In A. Khrennikov (ed.), Quantum Theory: Reconsideration of Foundations. Vaxjo, Sweden: Vaxjo University Press, pp. 407-422.

Penrose, R. 1989. The Emperor’s New Mind. New York: Oxford University Press.

Marshall W., C. Simon, R. Penrose, and D. Bouwmeester. 2002. Towards quantum superpositions of a mirror, Quantum Physics, abstract quant-ph/0210001, revised September 30.

To a many-worlder like myself, this “tip-of-the-iceberg-effect,” the discrepancy between the large amount of information that the universe needs to know about the particle (the exact angle of its spin) to make it behave appropriately, and the single bit that can be read out in any given “world,” can be seen as further evidence for the existence of the multiverse.

For further discussion of this lattice-based approach, including a description of Planck lengths and the holographic principle, see Chapter 16.

Normal tolerances in the process of printing, folding, and binding these book pages may result in an inexact superimposition of Figures 15-2 and 15-3, thus preventing the stated effect from occurring. To observe it, the reader may photocopy both figures and hold them back to back against a strong light, adjusting the superimposition carefully until the effect appears.

Many readers will have realized that this is just a variant of the one-time-pad still used for sending secure messages today.

Zeilinger has attempted to develop his system using an alternative measure of information to that given by conventional Shannon

information theory. He believes that this approach is justified because the classical “ignorance” interpretation of probability described in Chapter 5 is not adequate in a quantum context. The validity of this claim is vigorously disputed by many theorists.

Shahriar, A. 2004. “Quantum Rebel.” New Scientist, July 24, 2004, p. 30.

Plaga, R. 1997. “Proposal for an experimental test of the many-worlds interpretation of quantum mechanics” Found.Phys. 27 559. http://xxx.lanl.gov/PS_cache/quant-ph/pdf/9510/9510007.pdf.

Vaidman, L. 1996. On schizophrenic experiences of the neutron, Quantum Pysics, abstract quant-ph/9609006, revised September 7.

Tegmark, M. Does the universe in fact contain almost no information? Foundations of Physics Letters 9:25-42.

This statement of course needs qualifications. For example, if the galaxies involved contain not just pointlike stars but clouds of gas and dust, as most or all galaxies do, there will be significant interactions between those entities that can trigger bursts of star formation and other effects. But the point I am trying to make is that perfectly classical physics can include things that share the same volume of space, but interact relatively little with one another.

Feynman, R. 1994. The Character of Physical Law. Cambridge, Mass.: Modern Library.

Bekenstein, J. D. 1973. Black holes and entropy. Physics Review D7:2333-2346.

Deutsch, D. 2004. Qubit field theory, January. Available at http://arxiv.org/ftp/quant-ph/papers/0401/0401024.pdf.

We could take this anthropic argument a step further. One of Oxford’s most famous authors, C.S. Lewis, speculated that the vastness of cosmic distances might represent “God’s quarantine regulations,” ensuring that an imperfect species such as our own could not extend its influence to other worlds. We now know that his hope was false: Travel over interplanetary and even interstellar distances is defi-

nitely possible for a technologically advanced species. Indeed, astronomers wondering how many intelligent species our universe may contain have seriously considered what is called the Queen Bee hypothesis. There is normally only one queen in a hive of bees, because the first new queen to be born promptly stings any potential rivals to death in their larval cells. An intelligent species that develops interstellar travel might well use its power similarly to ensure that it would never have any dangerous competitors. In that case, there will usually be only one intelligent species per universe.

The same logic would apply to the multiverse as a whole—if there was any way at all in which creatures occupying one small slice of it could reach out to affect other “parallel worlds.” For a multiverse to support a huge number of species, we do not need merely laws of physics that efficiently support multiple processes. They must embody a very special combination of properties, for they must also in some subtle way make it not just technologically difficult, but fundamentally impossible, for a being, however intelligent, to systematically affect world lines far removed from its own. That is exactly what we are currently discovering.