Abstract
This chapter aims to demonstrate that both Eddington’s use of a priori methods, in the deduction of constants and the related analysis of measurement of observables, are the result of a kind of extreme analysis based around the question what really happens when we perform a measurement? The apparent craziness of the deductions is significantly reduced when it is realised that the qualitative principles flowing into the quantitative deductions have the status of broad physical generalities. At the root of the principles lies an analysis of measurement and observables that was decades ahead of its time, and was an interpretation of the physical content of generallyrelativistic theories that philosophers are only very recently rediscovering.
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- 1.
Edmund Whittaker refers to the problem of “the respective shares of reason and sense-perception in the discovery of the laws of nature” ([15], p. 185).
- 2.
In truth, it is simply a bad use of terminology, bound to confuse readers acquainted with standard discussions of the a priori.
- 3.
Note that this was written in the days when Woolworth’s was solely a threepence and sixpence arcade.
- 4.
We might note, that Wheeler’s‘it from bit’ notion, though very similar, denies the lack of objectivity of such knowledge, promoting the information (as encoded in apparatus-elicited answers to ‘yes-no’ questions) to the most objective facts of the world. I have a feeling that Eddington would not have disagreed, however, and was using ‘subjective’ and ‘objective’ in an idiosyncratic manner: if subjective for Eddington means ‘relative to observers,’ then I think Wheeler and Eddington are on the same page. The real difference in their positions, however, stems from the fact that quantum mechanics plays the central (essential) role in Wheeler’s approach, whereas in Eddington’s it is considerations of a more general sort, having to do with measurables and observables that are crucial.
- 5.
He describes PPS as a study of “principles of philosophic thought associated with the modern advances of physical science.” He argued that “philosophic truth should be reached by the same method of progressive advance” as in the sciences.
- 6.
Freeman Dyson once wrote: “The crazy ideas about calculating the constants of nature from first principles had roughly the same place in Eddington’s life that alchemy had in Newton’s. \(\ldots \) Unfortunately Eddington spoiled his reputation by publishing his crazy ideas; in this respect Newton was wiser.” [Applications of Group Theory in Particle Physics, SIAM Review, 8(1): 1].
- 7.
I note that Poincaré presented a very similar view: “Since the enunciation of our laws may vary with the conventions that we adopt, since these conventions may modify even the natural relations of these laws, is there in the manifold of these laws something independent of these conventions and which may, so to speak, play the role of universal invariant? For instance, the fiction has been introduced of beings who, having been educated in a world different from ours, would have been led to create a non-Euclidean geometry. If these beings were afterwards suddenly transported into our world, they would observe the same laws as we, but they would enunciate them in an entirely different way. In truth there would still be something in common between the two enunciations, but this is because the beings do not yet differ enough from us. Beings still more strange may be imagined, and the part common to the two systems of enunciations will shrink more and more. Will it thus shrink in convergence to zero, or will there remain an irreducible residue which will then be the universal invariant sought?” ([13], p. 334). He seemed to provide a broadly similar conclusion to Eddington, based on his notion of ‘convention’: “What now is the nature of this invariant it is easy to understand, and a word will suffice us. The invariant laws are the relations between the crude facts, while the relations between the ‘scientific facts’ remain always dependent on certain conventions” (ibid, p. 336).
- 8.
Whittaker points out that many qualitative features can shift during theory change, so since the quantitative assertions are based on qualitative features in Eddington’s scheme, they too must be incomplete. Postulates of Impotence are supposed to be more stable.
- 9.
Of course, the complaint would be that he sneaked a peek at the various pages of the book in the postulates of impotence he employs. However, this is by the by. Eddington admits to using such qualitative assertions. What he doesn’t do is find quantitative values of constants in this way: these he formally deduces from his qualitative assertions.
- 10.
Numbers that’s don’t depend on units of Mass, Length, and Time are said to be pure (of dimension 1 in dimensional analysis). So, for example, the ratio of proton mass and electron mass is pure since it is invariant under alterations in the system of units.
- 11.
This is very similar to the way that one forms a gauge-invariant physical quantity from a pair of gauge-variant quantities: it is a form of gauge-invariance.
- 12.
He famously initially derived 136, but later modified his reasoning as a result of experiment. He claimed a permutation invariance had been neglected—see below.
- 13.
Expanded out the number is: 15 747 724 136 275 002 577 605 653 961 181 555 468 044 717 914 527 116 709 366 231 425 076 185 631 031 296.
- 14.
Of course, we now have reason to believe that baryonic matter accounts for only a very small fraction of the total mass of the universe, with the majority comprising dark matter and, more still, dark energy.
- 15.
As Bergmann and Smith put it, “[m]easurability analysis identifies those dynamic field variables that are susceptible to observation and measurement (“observables”), and investigates to what extent limitations inherent in their experimental determination are consistent with the uncertainties predicted by the formal theory” ([2], p. 1131).
- 16.
I save an analysis of his approach to quantum gravity for a later paper. I will note, however, that the complexities come from the fact that a physical reference frame used to localise observables, to build relative quantities such as velocities and positions, in measurements for example, will be described by a wave function.
- 17.
Of course, we will often adopt the practice of supposing that one or other factor is ‘really’ the one that has some property (that really moves, or is located, etc.). But this is a facon de parler: either could be viewed as the reference factor: “we can no more contemplate an atom without a physical universe to put it in than we can contemplate a mountain without a planet to stand it on”.
- 18.
In Fundamental Theory Eddington invokes the cosmological term to function as a “comparison fluid” (an “all-pervading entity”), thus grounding a physical reference frame capable of localising observables.
- 19.
We perhaps need a better term to describe these “conjunctions”. I called them ‘correlations’ elsewhere, but neither adequately captures the mutual embrace and lack of ontological priority of the factors in such entities.
- 20.
See Unruh’s comments in the proceedings of the Conference on Conceptual Issues in Quantum Gravity (A. Ashtekar and J. Stachel, eds., Birkháuser, 1989, p. 267).
- 21.
“We have to express in mathematical symbolism what we think we are doing when we measure things” ([9], p. 266).
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Rickles, D. (2017). All Possible Perspectives: A (Partial) Defence of Eddington’s Physics. In: Durham, I., Rickles, D. (eds) Information and Interaction. The Frontiers Collection. Springer, Cham. https://doi.org/10.1007/978-3-319-43760-6_4
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