Abstract
At the end of the Scholium Newton includes a long paragraph about two globes revolving around their center of gravity and held together by a tensed cord. It has been interpreted as a thought experiment (Sect. 6.2) meant to show how the properties of true circular motion defined as absolute motion can be determined in a three-dimensional empty universe. I start by showing that this reading of Newton’s example as a bona fide thought experiment is riddled with interpretation problems and that it is less straightforward than so far assumed (Sect. 6.3).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Some of the novel quantities, such as the quantity of matter and the various quantities of centripetal force, are described in the set of definitions at the beginning of the Principia. The space-time Scholium, as it is now called, is a commentary pertaining to the set of definitions. The definitions are of: quantity of matter, quantity of motion, inherent force of matter (vis insita), impressed force, centripetal force and three measures of it (absolute quantity of centripetal force, accelerative quantity and motive quantity). (See Newton 1999, 403–408)
- 2.
“Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly and by another name is called duration.” (Newton 1999, 408)
- 3.
“Absolute space, of its own nature and without reference to anything external, always remains homogenous and immovable. Relative space is any movable measure or dimension of this absolute space; such a measure or dimension is determined by our senses from the situation of the space with respect to bodies and is popularly used for immovable space.” (Newton 1999, 408–9)
- 4.
“Place is the part of space that a body occupies, and it is, depending on the space, either absolute or relative.”(Newton 1999, 409)
- 5.
“Absolute motion is the change of position from one absolute place to another; relative motion is change of position from one relative place to another.” (Newton 1999, 409)
- 6.
- 7.
See, for instance Maudlin (2012, 15): “Newton produces powerful empirical evidence for the existence of absolute motion (and hence absolute space and time) using considerations of the causes of motion.”
- 8.
- 9.
Rynasiewicz (2019) understands the distinction between the true and absolute motion of a body on the one hand, and the apparent and relative motions, on the other hand, as one of a metaphysical kind. The former has an elevated ontological status, more reality or existence perhaps, than the latter. See also Huggett (2012) and DiSalle (2002, 2006) on the connection between true and absolute motion. The clearest presentation I found in Brading, Philosophy and the Physics Within, Ch 3 (ms). My own view departs from all of these, but this is not the place to develop it. I take it from the recent literature that, at least in the case of the globes, Newton builds the description such that there is a single quantity of true motion pertaining to each globe, and that the challenge is to capture the factors which change this quantity, and only those.
- 10.
- 11.
A side note: we immediately face the question of how to understand the gravity of those two globes in such an empty universe.
- 12.
There is a great similarity between this strategy and current methodology of studying the properties of binary star systems. Most stars are in fact binary systems. (csiro.au)
- 13.
For instance, Mach (1919) faults Newton with the assumptions entering into this thought experiment because it looks like the universe assumed is very different in crucial aspects from the universe we know to observe and inhabit. As he puts it, “the universe is not given twice.”
- 14.
On the contrary, Newton says that the example aims to “actually” (actu) distinguish apparent and true motions. (See Sect. 6.4)
- 15.
The model I have in mind is akin the two-body problem in physics, and not, say, mechanical models for causal interaction of two bodies. Newton, of course, does not use the word “model.” For recent work on this understanding of Newtonian models see Ducheyne (2005) and Ducheyne (2012, esp. chap. 2). Ducheyne focuses on planetary models. I share much with Ducheyne’s arguments, especially the idea that the models in Book 1 are not restricted to mathematics. But I also think that the two features which I introduce here are to be more systematically applied and embedded into Newton’s natural philosophy, going beyond models of planetary motions.
- 16.
This claim will be developed elsewhere. This paper restricts itself to arguing that the presentation of the globes scenario is best understood as an illustration of the result of applying these two features. Specifically, it demotes the understanding of the scenario as a thought experiment. (That is not say that thought experiments in natural science do not use models.) Briefly put, this scenario is closer to reasoning in physics proper than we have seen it so far represented in the literature.
- 17.
?- shows insertions
- 18.
The adverb deleted and replaced by “actu” cannot quite be made out, and hence this translation is a guess.
- 19.
In the second edition of the Principia Newton inserted at this point the further clause, “and that the bodies were at rest.”
- 20.
These passages are quoted from a longer manuscript by George Smith and Anne Whitman. Appendix 5 consists of variorum translations of selections from the version of Liber Primus Newton submitted to Cambridge Library under the auspices of Lucasian Lectures, Dd. 9.46 (pp. 36–215 of Whiteside 1989). See Whiteside (1989, 45–6), translated by George E. Smith; and the folio numbers (11 and 12) in Dd. 9.46. Smith (in press-b).
- 21.
This question has often showed up during George’s course and it is a recurrent pattern in the history of testing Newtonian gravity. See Smith 2014.
- 22.
The preceding paragraph stressed again the distinction between relative and “actual” quantities. The former are sensible measures of the latter. When we refer to quantities involving time, space, place, motion in the absolute sense, we use a “manner of expression which is out of the ordinary and purely mathematical.”
- 23.
According to the reading on offer here, the bucket experiment follows the same method.
- 24.
Focusing on changes in the motions of bodies as quantities also shows how specifying the bodies the motion to take place in a vacuum is a significant detail. It points out to the lack of resistance for the motions and, therefore, it provides a separate reason for considering the bodies a system unto itself. That is, the isolation of the system is well supported from a dynamical point of view as well.
- 25.
- 26.
See Newton’s discussion of the distinction between absolute space and relative space. Newton (1999, pp. 409–10)
- 27.
“Thereupon if?no matter what? equal forces were to be impressed [imprimerentur] at the same time on alternate faces of the globes increasing or lessening the circular motion, the increase or decrease of the motion
could be still be learned?would become known? from the added or diminished tension in the cord, and therefrom?finally? on which faces of the globes the forces would have to be [deberent] impressed for the motion to be increased maximally could be found, that is, the posterior faces, or those which follow [sequuntur] in the circular motion.” (See Sect. 6.4) - 28.
The general hypothetical form is basically an inference: if such-and-such effects are present, then such-and-such claims are true. See Sect. 6.5.
- 29.
Smith (in press-a), ‘Liber secundus.’
- 30.
The bolded emphasis is mine throughout.
- 31.
This is yet another one of the great contributions for which I am grateful to George Smith. On the one hand, there is the dedication to the analysis of the text. On the other hand, there is the generosity in sharing these materials with generations of researchers.
- 32.
Recall that the two globes were taken to revolve around their center of gravity (and not some arbitrary point), a well-defined mathematical point which assumes some understanding of gravity.
- 33.
Newton proposes here a view of analyzing the motion of an isolated system of two bodies acting through a central potential. Our current physics sensibilities recognizes this as a two-body problem and it is one the paradigmatic examples taught in celestial physics. Yet until Newton there was nobody who formulated the motion of two bodies under gravity in this manner.
- 34.
Law 3 is inevitably included in the model.
References
Arthur, R., 2018. Thought experiments in Newton and Leibniz. In Routledge companion to thought experiments, ed. M. Stuart, Y. Fehige and J. R. Brown, 111–127. Routledge.
Bacon, F. 1620/2000. The new Organon, ed. L. Jardine and M. Silverthorne. Cambridge University Press.
Barbour, J.B. 1989. Absolute or relative motion? A study from a Machian point of view of the discovery and the structure of dynamical theories, The discovery of dynamics. Vol. I. Cambridge University Press.
Berkeley, G. 1721/1992. De Motu and the analyst, ed. and trans. D. Jesseph, Dordrecht: Kluwer.
DiSalle, 2002. Newton’s philosophical analysis of space and time. Cambridge companion to Newton, ed. I. B. Cohen & G. E. Smith, 33–56. Cambridge University Press.
DiSalle, R. 2006. Understanding spacetime. The philosophical development of physics from Newton to Einstein. Cambridge University Press.
Ducheyne, S. 2005. Mathematical models in Newton’s Principia. A new view of the ‘Newtonian Style.’. International Studies in the Philosophy of Science 19: 1–19.
———. 2012. The main business of natural philosophy. Springer.
Earman, J. 1989. World enough and space-time: Absolute versus relational theories of space and time. Cambridge, MA: MIT Press.
Hoek, D. 2022. Forced changes only: A New Take on the Law of Inertia. Philosophy of Science, 1–17. https://doi.org/10.1017/psa.2021.38. https://www.cambridge.org/core/journals/philosophy-of-science/firstview/firstview
Huggett, N. 2012. What did Newton mean by ‘absolute motion’? Interpreting Newton: Critical essays, ed. E. Schliesser and A. Janiak, 196–218. Cambridge University Press.
Laymon, R. 1978. Newton’s bucket experiment. Journal of the History of Philosophy 16: 399–413.
Mach, E. 1893/1902/1919. The science of mechanics. A critical and historical account of its development. Translated from German by Thomas J. McCormack, The Open Court Publishing Company.
Maudlin, T., 2012. Philosophy of Physics: Space and time, Princeton University Press.
Nagel, E. 1961. The structure of science. Harcourt. Brace & World.
Newton, I. 1718/1730. Opticks, based on fourth ed. London, 1730. Reprinted by Dover, 1952.
Newton, I. 1999. The principia: Mathematical principles of natural philosophy. Trans. I. Bernard Cohen and Anne Whitman. University of California Press.
Rynasiewicz, R. 1995a. ‘By their properties, causes and effects.’ Newton’s Scholium on space, time, place and motion – I. The text. Studies in History and Philosophy of Science 16: 133–153.
———. 1995b. ‘By their properties, causes and effects.’ Newton’s Scholium on space, time, place and motion – II. The context. Studies in History and Philosophy of Science 26: 295–321.
Rynasiewicz, R. 2014. Newton’s views on space, time, motion. Stanford encyclopedia of philosophy, ed. E.N. Zalta, Summer 2014 Edition. http://plato.stanford.edu/entries/newton-stm/
———. 2019. Newton’s Scholium on time, space, place and motion. Oxford handbook of Newton, ed. E. Schliesser and Chr. Smeenk.
Smith, G.E. 2007. Newton’s Philosophiae Naturalis Principia Mathematica. Stanford Encyclopedia of Philosophy, ed. E.N. Zalta. https://plato.stanford.edu/entries/newton-principia/
———. 2012. How Newton’s Principia changed physics. Interpreting Newton. Critical essays, ed. A. Janiak and E. Schliesser, 360–395. Cambridge University Press.
———. 2014. Closing the loop. Newton and Empiricism, ed. Z. Biener and E. Schliesser, 262–345. Oxford University Press.
———. 2020. Experiments in the principia. Oxford handbook to Newton, ed. E. Schliesser and Chr. Smeenk. https://doi.org/10.1093/oxfordhb/9780199930418.013.36.
Smith, G.E. (in press-a). ‘Liber secundus: A variorum translation,’ with Anne Whitman.
Smith, G.E. (in press-b). A variorum translation of several pages from The preliminary manuscripts for Isaac Newton’s 1687 principia, 1684–1686, ed. D. T. Whiteside, Cambridge University Press, 1989, (p. 45–46), corresponding to folio numbers (11 and 12) in Dd. 9.46.
van Fraassen, B. 1970. An introduction to the philosophy of time and space. New York: Random House.
Westfall, R. 1971. Force in Newton’s physics. New York: Wiley.
Whiteside, D.T. 1989. The preliminary manuscripts for Isaac Newton’s 1687 principia, 1684–1686. New York: Cambridge University Press.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Solomon, M. (2023). Newton’s Example of the Two Globes. In: Stan, M., Smeenk, C. (eds) Theory, Evidence, Data: Themes from George E. Smith. Boston Studies in the Philosophy and History of Science, vol 343. Springer, Cham. https://doi.org/10.1007/978-3-031-41041-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-031-41041-3_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-41040-6
Online ISBN: 978-3-031-41041-3
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)