{"id":3619,"date":"2014-05-14T14:00:05","date_gmt":"2014-05-14T02:00:05","guid":{"rendered":"https:\/\/blogs.otago.ac.nz\/emxphi\/?p=3619"},"modified":"2014-05-14T15:17:56","modified_gmt":"2014-05-14T03:17:56","slug":"are-newtons-laws-experimentally-confirmed","status":"publish","type":"post","link":"https:\/\/blogs.otago.ac.nz\/emxphi\/are-newtons-laws-experimentally-confirmed\/","title":{"rendered":"Are Newton’s Laws Experimentally Confirmed?"},"content":{"rendered":"

Kirsten Walsh writes…<\/strong><\/em><\/p>\n

Previously on this blog, I have argued <\/a>that the combination of mathematics, experiment and certainty are an enduring feature of Newton\u2019s methodology.\u00a0 I have also highlighted the epistemic tension between experiment and mathematical certainty found in Newton\u2019s work.\u00a0 Today I shall examine this in relation to Newton\u2019s \u2018axioms or laws of motion\u2019.<\/p>\n

In the scholium to the laws, Newton argues that his laws of motion are certainly true. \u00a0In support, however, he cites a handful of experiments and the agreement of other mathematicians: surprisingly weak justification for such strong claims!\u00a0 In this post, I show how Newton\u2019s appeals to experiment justify the axioms\u2019 inclusion in his system, but not with the certainty he claims.<\/p>\n

Newton begins:<\/p>\n

    \u201cThe principles I have set forth are accepted by mathematicians and confirmed by experiments of many kinds.\u201d<\/ol>\n

    Newton expands on this claim, discussing firstly, Galileo\u2019s work on the descent of heavy bodies and the motion of projectiles, and secondly, the work conducted by Wren, Wallis and Huygens on the rules of collision and reflection of bodies. \u00a0He argues that:<\/p>\n

      \n
    1. The laws and their corollaries have been accepted by mathematicians such as Galileo, Wren, Wallis and Huygens (the latter three were \u201ceasily the foremost geometers of the previous generation\u201d);<\/li>\n
    2. The laws and their corollaries have been invoked to establish several theories involving the motions of bodies; and<\/li>\n
    3. The theories established in (2) have been confirmed by the experiments of Galileo and Wren (which, in turn confirms the truth of the laws).<\/li>\n<\/ol>\n

      These claims show us that Newton regards his laws as well-established empirical propositions.\u00a0 However, Newton recognises that the experiments alone are not sufficient to establish the truth of the laws.\u00a0 After all, the theories apply exactly<\/i> only in ideal situations, i.e. situations involving perfectly hard bodies in a vacuum.\u00a0 So Newton describes supplementary experiments that demonstrate that, once we control for air resistance and degree of elasticity, the rules for collisions hold.\u00a0 He concludes:<\/p>\n

        \u201cAnd in this manner the third law of motion \u2013 insofar as it relates to impacts and reflections \u2013 is proved by this theory [i.e. the rules of collisions], which plainly agrees with experiments.\u201d<\/ol>\n

        This passage suggests that the rules of collisions support a limited version of law 3, \u201cto any action there is always an opposite and equal reaction\u201d, and that the rules themselves appear to hold under experimental conditions.\u00a0 However, this doesn\u2019t show that law 3 is universal<\/i>: which Newton needs to establish universal gravitation.\u00a0 This argument is made by showing how the principle may be extended to other cases.<\/p>\n

        Firstly, Newton extends law 3 to cases of attraction.\u00a0 He considers a thought experiment in which two bodies attract one another to different degrees.\u00a0 Newton argues that if law 3 does not hold between these bodies the system will constantly accelerate without any external cause, in violation of law 1, which is a statement of the principle of inertia.\u00a0 Therefore, law 3 must hold.\u00a0 As the principle of inertia was already accepted, this supports the application of law 3 to attraction.<\/p>\n

        Newton then demonstrates law 3\u2019s application to various machines.\u00a0 For example, he argues that two bodies suspended from opposite ends of a balance have equal downward force if their respective weights are inversely proportional to the distances between the axis of the balance and the points at which they are suspended.\u00a0 And he argues that a body, suspended on a pulley, is held in place by a downward force which is equal to the downward force exerted by the body.\u00a0 Newton explains that:<\/p>\n

          \u201cBy these examples I wished only to show the wide range and the certainty of the third law of motion.\u201d<\/ol>\n

          What these examples in fact <\/i>show is the explanatory power of the laws of motion \u2013 particularly law 3 \u2013 in natural philosophy.\u00a0 Starting with collision, which everyone accepts, Newton expands on his cases to show how law 3 explains many different physical situations.\u00a0 Why wouldn\u2019t a magnet and an iron floating side-by-side float off together at an increasing speed?\u00a0 Because, by law 3, as the magnet attracts the iron, so the iron attracts the magnet, causing them to press against one another.\u00a0 Why do weights on a balance sometimes achieve equilibrium?\u00a0 Because, by law 3, the downward force at one end of the balance is equal to the upward force at the other end of the balance.\u00a0 These examples demonstrate law 3\u2019s explanatory breadth.\u00a0 But these examples do not give us a compelling reason to think that law 3 should be extended to gravitational attraction (which seems to require some kind of action, or attraction, at a distance).<\/p>\n

          Newton, clearly, is convinced of the strength of his laws of motion.\u00a0 But this informal, discussion of the experiments he appeals to shows that he ought not<\/i> be so convinced.\u00a0 As I see it, Newton has two projects in relation to his laws:<\/p>\n

          1)\u00a0\u00a0\u00a0\u00a0\u00a0 The specification of the laws as the axioms of a mathematical system; and<\/p>\n

          2)\u00a0\u00a0\u00a0\u00a0\u00a0 The justification of laws as first principles in natural philosophy.<\/p>\n

          I suggest that the experiments discussed give strong support for the laws in limited cases.\u00a0 This justifies their application in Newton\u2019s mathematical model, but it does not justify Newton\u2019s claims to certainty. \u00a0In modern Bayesian terms, we might say that Newton\u2019s laws have high subjective priors.\u00a0 In my next post, I shall sketch an account in which Newton\u2019s laws gain epistemic status by virtue of their relationship to the propositions they entail.<\/p>\n","protected":false},"excerpt":{"rendered":"

          Kirsten Walsh writes… Previously on this blog, I have argued that the combination of mathematics, experiment and certainty are an enduring feature of Newton\u2019s methodology.\u00a0 I have also highlighted the epistemic tension between experiment and mathematical certainty found in Newton\u2019s […]<\/p>\n","protected":false},"author":4582,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[113],"tags":[274,276,16427,224,4406],"class_list":["post-3619","post","type-post","status-publish","format-standard","hentry","category-ideas","tag-certainty","tag-experiment","tag-laws-of-motion","tag-newton","tag-principia"],"_links":{"self":[{"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/posts\/3619","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/users\/4582"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/comments?post=3619"}],"version-history":[{"count":0,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/posts\/3619\/revisions"}],"wp:attachment":[{"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/media?parent=3619"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/categories?post=3619"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.otago.ac.nz\/emxphi\/wp-json\/wp\/v2\/tags?post=3619"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}