In “Quantum Weirdness? It's All in Your Mind,” Hans Christian von Baeyer describes quantum Bayesianism (QBism) as a model of quantum mechanics in which the wave function exists only as a mathematical tool employed by an observer to assign his or her personal belief that a quantum system will have a particular property.
But what about the famous two-slit experiment in which the wave function of an electron interferes with the portion of itself going through the other slit? Can my belief about which slit the electron went through interfere with itself?
Von Baeyer often employs straw men in his criticisms of frequentist probability. For instance, he cites the University of London's Marcus Appleby's example of a lottery won by the same person each week for 10 years. Appleby and von Baeyer ridicule the frequentist who would bet in this lottery in spite of the evidence that it is rigged. Their imaginary frequentist is made to assume that each draw is an independent event, while they afford themselves the luxury of suspecting dependence.
Both frequentists and Bayesians accept independence and use Bayes' law to deal with conditional probabilities. Von Baeyer fails to explore their real differences.
VON BAEYER REPLIES: Hazen is correct that the wave function for a single electron in a two-slit experiment passes through both slits. QBists agree; they differ from other interpreters of quantum mechanics in their insistence that the wave function itself resides only in the agent's mind and that it does not describe the actual path of the electron. It is a calculational device for determining the betting odds the agent should assign for the outcomes of future experiments to detect the electron and is no more substantial than the number on a laundry ticket.
The example I chose to illustrate the difference between Bayesian and frequentist probability, which Miller finds unfair, is perhaps too extreme. Consider instead a series of real coin tosses made by a real person. Ten heads in a row is rare but not unusual. How about a 100, or 1,000, or a million? There is no rational reason to suspect foul play if any of these cases occur because all are possible even under fair conditions. Yet a reasonable person would begin to smell a rat after some (implausible) number of heads. The value of that number differs from observer to observer and is therefore subjective. Frequentism makes no allowance for this normal human behavior, but Bayesianism does.
“Cracks in the Periodic Table,” by Eric Scerri, is especially interesting for three reasons: the periodic table is often regarded as the symbol of science; the article highlights the problems associated with the current classification approach, which is based on chemical properties of the elements; and, correct me if I am wrong, for the first time since its introduction in 1928, the Janet left-step periodic table is prominently displayed on the pages of a popular scientific magazine.
The periodic system has two levels of classification: a primary level, based on atomic numbers of the elements, and a secondary one, based on chemical properties. Just as imprecise atomic weights were replaced with precise atomic numbers for the primary classification, the loosely defined “chemical properties” should be replaced with more precise characteristics of the elements based on spectroscopic signatures and/or physical attributes of the atoms, such as electron orbitals. The left-step table is the first step in achieving this goal.
Nowadays the Janet left-step table seems to be the favorite of physicists. In that chart, helium is placed above the alkaline earth elements, contrary to its usual position as a member of the noble gases family in conventional tables. It is difficult to see what the chemical similarity between helium and alkaline earth metals is, however. Despite several advantages of the left-step table when compared with the traditional one, I wonder whether adoption of the left-step formulation amounts to putting the cart of quantum mechanics before the horse of chemistry.
National Scientific and Technical Research Council and National University of Quilmes, Argentina
SCERRI REPLIES: The left-step periodic table actually has been featured in a magazine article before; I discussed it in some detail in the British magazine Education in Chemistry in 2005. One might argue, however, over how “popular” that periodical is.
Labarca's comment serves as an apt response to Tsimmerman's suggestion that the classification of the elements should be based exclusively on, say, electronic configurations. The chemistry of the elements may not be fully reducible to quantum mechanics. If electronic configurations were all that mattered, chemists, physicists and designers of the periodic table would long ago have agreed to the placing of helium among the alkaline earth metals in view of its two electrons in a shell configuration.
The article's discussion of “relativistic” electrons causing certain atoms to behave differently than their position on the periodic table was, in part, intended to illustrate why it is not safe to extrapolate based simply on the number of outer-shell electrons in any atom.