Abstract
The aim of this chapter is to introduce, in concrete physical terms, quantum phenomena, by which I, again, mean those physical phenomena in considering which Planck’s constant h cannot be neglected. I shall do so by way of the double-slit experiment, a paradigmatic or, it is sometimes argued, even the paradigmatic quantum experiment, in which the famously strange features of quantum phenomena manifest themselves. This experiment and the way it reflects such key features of quantum phenomena as the uncertainty relations and the probabilistic nature of our quantum predictions are considered in Sections 2.1 and 2.2. Sections 2.3 and 2.4 discuss two other experiments that are closely related to the double-slit experiment: the delayed-choice experiment, due to John A. Wheeler, and the quantum eraser experiment, due to Marlan Scully and his coworkers. Section 2.5 uses the quantum eraser experiment to establish the fundamental difference between classical and quantum physics by considering the repetition of the identically prepared experiments in each domain.
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Notes
- 1.
Cf. Bohr’s comments on the subject in (Bohr 1935b, 698, n.). This is not unusual in dealing with thought experiments. The EPR experiment, as originally proposed by EPR, cannot be performed in a laboratory, though this has never put in question its legitimacy for the theoretical arguments concerning or based on it. Related experiments, most famously those by Alain Aspect, based on Bohm’s version of the EPR experiment for spin (Aspect et al. 1982), have subsequently been performed, as were experiments statistically approximating the EPR experiment.
- 2.
Technically, one does not need the first diaphragm and can merely use the source itself to define the initial stage of the experiment. The arrangement described here is sometimes convenient, however, especially if one wants to relate the experiment to the uncertainty relations. Bohr uses this arrangement in most of his arguments (Bohr 1935b, p. 697; Bohr 1949, PWNB 2, pp. 45–46, Fig. 3, pp. 47–48, Fig. 4).
- 3.
Dirac contended that “each photon … interferes only with itself. Interference between different photons never occurs” (Dirac 1958, p. 9). Dirac is correct on the second point, and he shows that making the assumption of interference between different photons “would contradict the conservation of energy” (p. 9). That interference between different photons does not occur is made clear by the fact that the interference pattern would emerge even if the interval between each emission were sufficiently large for the next photon to be emitted only after the previous photon has hit the screen and been destroyed by the collision. To assume interference between different photons under these circumstances would amount to rather radical assumptions concerning the collective behavior of photons. On the other hand, Dirac’s statement that “each photon … interferes only with itself” may not be sufficiently precise or sufficiently explained. It does, however, capture something essential about the situation. Part of the problem here is, again, the language of “interference,” borrowed from classical wave physics. Dirac grounds his contention in the following point: “Some time before the discovery of quantum mechanics people realized that the connexion between light waves and photons must be of a statistical character. What they did not clearly realize, however, was that the wave function gives information about the probability of one photon being in a particular place and not the probable number of photons in that place” (p. 9). This is a profound statement which, apart from capturing the probabilistic nature of the wave function, suggests a Bayesian view of quantum probability adopted here, by linking the wave functions to the probabilities of individual events. The statement concerning each photon interfering only with itself could then be read as follows. (I am not sure whether Dirac says only this, rather than making further claims concerning the physical behavior of photons, but he appears to say at least this.) The probabilities encoded in the wave function enabling our predictions concerning where each photon will hit the screen correspond to the interference-pattern distribution of the traces left on the screen that will, inevitably, emerge in the corresponding setup. The probabilities are different in the alternative (no-interference-pattern) setup of the double-slit experiment and are differently predicted by quantum mechanics. Dirac also says that “[quantum mechanics] gets over the difficulty by making each photon go partly into each of the two components [of equal intensity]” into which a beam of light is split by a beam-splitter device (p. 9). As I shall argue below, that statement is difficult to sustain in this form, and Dirac does not appear to properly support it. While somewhat ambiguous, his overall analysis of the situation does not appear to necessarily imply that this statement is meant in a physical sense; rather, it concerns the linear superposition of quantum states defined by the wave function, which, again, deals with probabilities concerning the outcome of experiments (pp. 11–14). I shall explain these concepts below, and I shall revisit Dirac’s argument in Chapter 6.
- 4.
Even in Bohmian theories, where both concepts are used in describing the behavior of quantum objects, these concepts are not fused in a single entity: A wave accompanies or/and guides the particle in question, following de Broglie’s idea, in turn inspired by Einstein’s earlier suggestion, which was discarded by Einstein himself.
- 5.
Among the more intriguing alternatives is Anthony J. Leggett’s argument for “macrorealism,” an argument he advanced for over two decades (e.g., Leggett 1988). It can be summarized as follows: While quantum mechanics adequately describes the workings of nature at its ultimate micro-level, it may be incorrect at the macro-level. In other words, the question is whether quantum mechanics has a limited (micro)scale of application, rather than properly reflecting the constitution of all physical objects. Leggett designed clearly defined experiments for testing his proposal, although these experiments are difficult and as yet remain unperformed. This argument relates to a thorny and still unresolved problem of the transition from the quantum to the classical domain—a problem addressed with, in the present view, at most limited success by decoherence theories (e.g., Zurek 2003; Schlosshauer 2007), on which I shall comment in Chapter 10. More accurately, one should speak of the transition from the domain treated by quantum mechanics to that treated by classical physics, assuming, again, that the ultimate constitution of nature is quantum.
- 6.
It may be noted that, while Feynman states more unequivocally that “light behaves like particles,” and not like waves, his actual interpretation is not that far from the one offered here, and his “like particles” already qualify his claim (Feynman 1985, p. 15).
- 7.
Cf. famous pictures found in Tonomura et al. (1989) and displaying, in the title of their important paper itself, a “demonstration of single-electron buildup of an interference pattern.”
- 8.
These traces are not really “points” either; they appear as discrete entities (“dots” on the screen in the double-slit experiment) only at a low resolution, and they actually comprise millions of atoms (Ulfbeck and Bohr 2001; Bohr et al. 2004).
- 9.
When elementary particles are considered in quantum theory, even when assigned a mass, they are idealized as zero-dimensional, point-like objects (or possibly one-dimensional strings). Such objects can be given a rigorous mathematical meaning but not a rigorous physical meaning. It is true that this type of point-like (mathematical) idealization of physical objects is also used in classical physics. There, however, this idealization allows one to approximate the actual behavior of the objects considered and, on the basis of this descriptive approximation, to make excellent predictions concerning this actual behavior. The physical objects themselves thus considered may be, and usually are, assumed to have extension, the property that has defined physical objects or, more generally, material bodies (res extensa) at least since Descartes. In the case of quantum objects, such an assumption is difficult to sustain. For example, in the case of electrons it leads to well-known contradictions with classical electrodynamics, since, if assumed to have extension, an electron would be torn apart by its negative charge. It is this circumstance that led to the idealization of the electron even before quantum mechanics. Accordingly, the nature of the point-like idealization of elementary quantum objects is different in classical and quantum physics. Quantum physics gives reasons for and logic to a still more radical idealization found in nonclassical interpretations of quantum objects, which keeps us from idealizing them or their behavior on any conceivable model—physical, mathematical, or other. Importantly, this view applies to composite quantum objects as well, including those that reach the level of macro-objects, such as the “squids,” or even more interestingly, carbon 60 fullerenes, which can be observed either as classical or as quantum objects (Arndt et al. 1999). That is, we can also observe such objects, as concerns their macro-aspects and behavior, as classical macro-objects, which we cannot do with the elementary quantum objects, such as electrons and photons. On the other hand, just as in the case of these elementary constituents themselves, the constitution of such quantum macro-objects as quantum is beyond our capacity to observe and only manifest in their effects upon our measuring instruments.
- 10.
As noted in the Introduction, technically, we measure the momentum in a given direction, and the uncertainty relations apply to this momentum and the corresponding coordinate. In the uncertainty relations for the position and the momentum associated with a quantum object in the three-dimensional space, each quantity will have three components defined by the chosen coordinate system.
- 11.
The comment is reported in Mehra and Rechenberg’s The Historical Development of Quantum Theory (MR 6, p. 43).
- 12.
Yet another possibility to explain the situation would be a retroaction in time, which is hardly less problematic, although it is not inconceivable and is entertained by some (cf. Stapp (1997) and, for counterarguments, Mermin (1998b) and Shimony and Stein (2001)). As will be seen below, a retroaction in time also follows from the assumption that a quantum object can pass through both slits in the delayed-choice experiment. It is true that the possibility of retroaction in time is a mathematical consequence of general relativity, that is, a possible solution of its equations, as was demonstrated by Gödel (Gödel 1949). There are also arguments concerning the “wormholes” in general-relativistic physics that draw this implication. As things stand now, however, very few would accept retroaction at time as physically possible, given both the logical consequences involved, such as that of potentially changing the past, and the limits of the theories involved, such as the fact that general relativity is incompatible with quantum theory (there is, again, no quantum gravity as yet).
- 13.
See Busch and Shilladay (2006) for an illuminating discussion of the relationships between uncertainty relations and complementarity.
- 14.
See again Feynman’s accounts of the situation in Feynman (1951) and Feynman et al. (1977, vol. 3, pp. 1–11).
- 15.
Wheeler actually uses the beam-splitter experiment, but it does not affect the argument given here (Wheeler 1983, p. 183).
- 16.
Again, I leave aside Bohmian theories, to which my argument does not apply but which are manifestly nonlocal in any event.
- 17.
The delayed-choice version of the quantum eraser experiment uses half-silvered mirrors and EPR-type entangled photon pairs (Scully and Drühl 1982; Greene 2004, pp. 182–213). This setup allows us to gain or erase the knowledge in question (which way a given photon goes) without examining and hence in any way interfering with that given photon. We do this by interfering with and examining its EPR companion photons. This examination can, in principle, take place in a delayed-choice manner, indeed with arbitrary delay—for example, years after the actual events of the experiment have physically taken place. The immediate examination of the medium (screen) with traces of photons will not reveal any interference pattern. However, the subsequent (delayed) examination of the traces left by their companions—whose Scully markings have been erased, thus disabling our knowledge concerning which way these particular photons went (again, possibly years ago)—will show the interference pattern of the corresponding subset of the traces left on the screen. I shall not discuss this version of the experiment further. While its features may appear even more striking than those of the standard version, they are consistent with the nature of quantum phenomena as manifest in the double-slit and other experiments, and as such, they are, again, more expected than unexpected.
- 18.
On further connections to Bohr’s complementarity, see Herzog et al. (1995).
- 19.
This point also applies to the delayed-choice version of quantum eraser. As explained in note 17, in this case those photons that are marked and those that are unmarked are sorted out later, thus enabling us to “carve out” the interference in the overall pictures related to those individual runs of the experiment in which the erasure of the Scully marking took place. However, each set is defined strictly in accordance with the marking or unmarking pertaining to particular photons from the two respective different sets, which thus disconnects them.
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Plotnitsky, A. (2010). Quantum Phenomena and the Double-Slit Experiment. In: Epistemology and Probability. Fundamental Theories of Physics, vol 161. Springer, New York, NY. https://doi.org/10.1007/978-0-387-85334-5_2
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