Gruenbaum on Reichenbach's "Universal Forces"
Gruenbaum on Reichenbach's "Universal Forces"
Many students who have read Reichenbach's Philosophy of Space and Time (Reichenbach 1958) may have felt some perplexity with his concept of universal forces, especially because Carnap, in his "Introductory Remarks" praised Reichenbach's use of this concept (Reichenbach 1958, vii). I was confused by some passages, because what Reichenbach says seemed contradictory, in view of his definition of universal forces.
Now anyone who has had similar experiences should consult Gruenbaum's chapter 3 of Philosophical Problems of Space and Time. Gruenbaum points out that there are two senses of "universal forces" in Reichenbach, one literal and the other metaphorical.
At issue are the metrical amorphousness and the alternative metrizability of the spatial (and/or temporal) continuum. That is, as Gruenbaum thinks Riemann first pointed out, metric relations "must come from somewhere else in the case of a continuous manifold" (Riemann 1854), not intrinsically contained in the manifold itself; and this applies to physical space and time. "Amorphous" because there is no intrinsic metric, and "alternatively metrizable" because there are alternative possibilities open for choice. Riemann did not use the word "convention" in this context; Poincare explicitly introduced this word; for instance in his Science and Hypothesis (chap. 2), he argues that in order to obtain measurable quantities, one must be able to compare two intervals between a term and another, and one can do this only by the aid of a special convention. Combining these two insights, Gruenbaum claims:
Only the choice of a particular congruence standard which is extrinsic to the continuum itself can determine a unique congruence class, the rigidity or self-congruence of that standard under transport being decreed by convention, and similarly for the periodic devices which are held to be isochronous (uniform) clocks. (Gruenbaum 1963, 11-2)
On this basis Gruenbaum tries to reconstruct Reichenbach's contention in terms of universal forces. Reichenbach first introduces the distinction between "differential forces" and "universal forces" (Reichanbach 1958, 13). Some forces, such as those produced by heat, affect different materials (mercury and glass, for instance) differently, so that one can tell their presence by comparing such differences (as is the case with a mercury thermometer). Universal forces, unlike differential forces, cannot be demonstrated directly, since they are supposed to have the following two properties:
(a) They affect all materials in the same way.
(b) There are no insulating walls. (Reichenbach 1958, 13)
And here is a famous figure for illustrating the action of a universal force. (Reichenbach 1958, 11)
Imagine two surfaces G and E as in the figure, where G has a hump in the middle part, and all its points are projected onto E. Suppose G-people (two dimensional creatures on G) measure the distance between two points on G by a rigid rod. They find A'B' and B'C' to be equal, but the projections AB and BC on E would look unequal; but the rigid rod is also projected onto E, so that the length of its shadow changes accordingly below the hump. Now Reichenbach invites us to consider the following possibility: Suppose, on the surface E, a strange force is in action (below the hump area), and everything (including measuring rods) changes its length, so that E-people find AB and BC to be equal! This strange force is an instance of a universal force. And our question is: what is the real geometry on G and on E? How can we distinguish real distance from apparent distance on either?
On Gruenbaum's diagnosis, these questions should be dealt with, without invoking the notion of universal forces.
The legitimacy of making a distinction between the real (true) and the apparent geometry of a surface turns on the existence of an intrinsic metric. If there were an instrinsic metric, there would be a basis for making the distinction ... But inasmuch as there is not, the question as to whether a given surface is really a Euclidean plane with a hemispherical hump or only apprently so must be replaced by the following question: on a particular convention of congruence as specified by a choice of one of Carnap's functions f, does the coincidence behavior of the transported rod on the surface in question yield the geometry under discussion or not?
Thus the question as to the geometry of a surface is inherently ambiguous without the introduction of a congruence definition. And in view of the conventionality of spatial congruence, we are entitled to metrize G and E either in the customary way or in other ways so as to describe E as a Euclidean plane with a hemispherical hump R in the center and G as a Euclidean place throughout. To assure the corectness of the latter non-customary descriptions, we need only decree the congruence of those respective intervals which our questioner called "really equal" as opposed to apprently equal ... respectively. (Gruenbaum 1963, 84)
On the other hand, Reichenbach himself chose to state the thesis of this conventionality in terms of univeral forces, as was explained in the preceding. But, according to Gruenbaum, in this context "universal forces" is used only metaphorically, since the whole point was to illustrate the conventionality of congruence.
However, when Reichenbach begins to speak of gravitation (in particular), universal forces appear again both in literal and metaphorical sense. On this point, Gruenbaum argues as follows:
It is entirely correct, of course, that a uniform gravitational field (which has not been transformed away in a given space-time coordinate system) is a universal force in the literal sense with respect to a large class of effects such as the free fall of bodies. But there are other effects, such as the bending of elastic beams, with respect to which gravity is clearly a differential force in Reichenbach's sense: a wooden book shelf will sag more under gravity than a steel one. And this shows, incidentally, that Reichenbach's classification of forces into universal and differential is not mutually exclusive. ...
The issue is therefore twofold: first, does the fact that gravitation is a universal force in the literal sense indicated above have a bearing on the spatial geometry, and second, in the presence of a gravitational field is the logic of the spatial congruence definition any different in regard to the role of metaphorical universal forces from what it is in the absence of a gravitational field? (91-2)
For Gruenbaum's answer to these questions, the reader is referred to his book. All I wish to say here is that, by keeping Gruenbaum's distinction and diagnosis in mind, many confusions can be avoided, and it becomes easier to make sense of many of Reichenbach's assertions.
I know that Gruenbaum's view on conventionality is criticized by younger philosophers such as Friedman (Friedman 1983, 294-309); but Friedman's objections against conventionality crucially depend on his own assumption that the power of theoretical unification is essential for saying the existence of anything postulated in a theory (Friedman 1983, 236ff., 241ff., 305). I am skeptical about this; and to the extent that this assumption is problematic, the thesis of conventionality is not refuted, as Friedman would like us to belive.
References
Friedman, M. (1983) Foundations of Space-Time Theories, Princeton Univ. Press.
Gruenbaum, A. (1963) Philosophical Problems of Space and Time, Alfred A. Knopf.
Gruenbaum, A. (1974) Philosophical Problems of Space and Time, 2nd ed. (1st edition is reprinted, with extensive supplementary materials), Reidel.
Poincare, H. (1902) Science and Hypothesis, Japanese translation from Iwanami, 1959.
Reichenbach, H. (1958) The Philosophy of Space and Time, Dover.
Riemann, G. F. B. (1854) "On the Hypothesis which lie at the Foundations of Geometry", Japanese translation by K. Yano, Kyouritsu, 1971. （現代数学の系譜10）
For websites related to Gruenbaum, see:
Last modified March 30, 2003. (c) Soshichi Uchii
