Abstract
The innovations had come thick and fast since the beginning of the century. From Planck’s proposal that energy is transferred in discrete bundles to Einstein’s introduction of photons, from Rutherford and Bohr’s analyses of the atom to de Broglie’s proposal that waves are omnipresent, and from Heisenberg’s H-technique (which presumed discontinuous processes) to Schrödinger’s wave equation (which presumed that all processes are smooth)—all the powerful new tools for probing the nature of the universe had come piling in, ready for use.
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Endnotes
[Cropper 1970:78].
[Gibbins 1987:48].
The announcement was made in an article in the prestigious joumal Zeitschrift für Physik 43, with the title, “Uber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik” (On the visualizable content of quantum-theoretical kinematics and mechanics).
[Margenau 1954:9].
[Margenau 1954:9].
Mass is mentioned as a possessed quality, because it varies continuously, depending on speed, but is otherwise determinate. (The distinction seems to me to be less than sharp.)
The word is based on the Latin com- (together) and -jugum (ox yoke). Conjugate factors such as x and px are yoked together (but not quite as two people who have become conjugal partners are joined). This sense of conjugate is one of many slightly different senses employed in scientific practice. All carry the meaning of mutually associating two quantities in some special relation.
It follows from the UP that there is, strictly speaking, no such thing as perfect pitch, in the musical sense of estimating perfectly the frequency of a tone. And this is so, no matter how long you listen to a tone. However, I believe the term is usually applied to identifying a tone as one of the discrete notes of the harmonic scale (a much different proposition). If that is the case, it suffices if your error in estimating the frequency is less than about one-quarter interval.
There are two essential points in this assertion: (1) that the electron must be perturbed, and, (2) that the perturbation must be unpredictable to some degree. The first point is obvious: if we do not hit the electron with at least one photon, we will have no information about its position. The second point is less obvious but may become acceptable as details of the microscope unfold.
Classically, granted enough resources (“Had we but funds enough and time… ”), Ax could be reduced to as small a finite value as desired. Whether it could be reduced to zero is debatable and unimportant.
Named after Sir George Biddell Airy (1801–1892), an English scientist and Astronomer Royal for most of his active life. He calculated the minute details of the blur of light produced by an optical instrument focusing on a point source, and classified the aberrations and distortions in such instruments. Millar et al. [1996] record that “he was remarkably precise, to the extent of labelling empty boxes ‘empty.”’
Most texts on optics derive this formula. See, for example, [Towne 1967].
Weisskopf [1989:57] reports this saying, ascribing it to “a Danish humorist.” Who but Borge could it be?
You may wish to juggle with the algebra to get a feel for the numbers. Thus, if the electron is initially located to within an uncertainty Ax (centered at x = 0, say) and is known to have a speed v with an associated uncertainty of Av, then its location at some later time, t,is nominally x(t) = t x v, with an uncertainty of Ax(t) = Ax + t x Av. Insert plausible values to learn how rapidly the electron (its wave packet, if you prefer) disperses. Notice that, the more closely you locate the electron initially, the more rapid the dispersion.
Pierre Simon, Marquis de Laplace, Philosophical Essay on Probabilities, 1816.
qu [Jammer 1989:349].
[Margenau 1954]. Cropper adopts this metaphor; see his [1970:110].
From Through the Looking Glass,this is the song, “A-Sitting on a Gate,” which the Knight sings to comfort Alice. Their preceding conversation, concerning various ways to refer to the song, is incomparable.
qu [Cropper 1970:109], no source.
[Cropper 1970:75].
The gedanken experiment has been subject to repeated and varied analyses; indeed, it is sometimes difficult to recognize that we are reading about the same confrontation at the same conference. Several analysts have pointed out that the experiment as presented by Einstein was unnecessarily complicated and that he could have made as strong an argument by treating a photon which traverses a mask with only one slit. However, we shall discuss his original configuration.
The verbal exchanges between Einstein and Bohr at the Solvay Conference have not been recorded verbatim. If I seem to be telling you what either physicist said at the time, you must chalk it up to artistic license. All is paraphrasing.
If anyone invents a measuring device which is not subject to the UP, it could be used to make all sorts of measurements with indefinitely fine precision.
qu [Baggott 1992:94].
Recently, Plenum Press published the proceedings of a symposium on the history of the UP under the title, Sixty-Two Years of Uncertainty: Historical, Philosophical, and Physical Inquiries into the Foundations of Quantum Mechanics [Miller 1989]. Note the correlation assumed between the UP and “the foundations” of quantum mechanics.
End notes
B. Stevenson, ed., The Home Book of Quotations,New York: Dodd, Mead, 1958.
[Rigden 1987:58].
[Weisskopf 1985].
[Cropper 1970:36].
qu [Feshbach & 1985:18].
[Peierls 1985:55–56].
[Crease & 1986:21].
[Kafatos & 1990:79].
[Rozental 1967]; qu [Powers 1993:77].
Gamow’s anecdote is related without specific source in [Cole 1985:203].
[Cole 1985:203].
[Gamow 1961:237].
[Pais 1991:227].
[Peierls 1985:55].
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Grometstein, A.A. (1999). Copenhagen Takes Over (1925-?). In: The Roots of Things. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4877-5_16
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