{"id":3775,"date":"2016-06-07T18:45:08","date_gmt":"2016-06-07T23:45:08","guid":{"rendered":"http:\/\/huewhite.com\/umb\/?p=3775"},"modified":"2016-06-07T18:45:08","modified_gmt":"2016-06-07T23:45:08","slug":"free-will","status":"publish","type":"post","link":"https:\/\/huewhite.com\/umb\/2016\/06\/07\/free-will\/","title":{"rendered":"Free Will"},"content":{"rendered":"

Continuing an old discussion<\/a> under a more apropos name,\u00a0quantum physicist Nicolas Gisin writes a summary of his position<\/a> on free will in NewScientist<\/strong><\/em> (21 May 2016, paywall):<\/p>\n

But are the mathematical real numbers physically real? Certainly not! Most real numbers are never-ending strings of digits. They can be thought of as containing an infinite amount of information \u2013 they could, for example, encode the answers to all possible questions that can be formulated in any human language. Yet a finite volume of space-time can only hold a finite amount of information. So the position of a particle, or the value of any field or quantum state in a finite volume, cannot be a real number. Real numbers are non-physical monsters.<\/p><\/blockquote>\n

That’s a bit puzzling. Sure, they can<\/strong><\/em> be thought of containing an infinite amount of information, but that’s just one interpretation, one amongst many. He’s posted a longer paper<\/a> to the academic pre-print server arxiv:<\/p>\n

The use of real numbers in physics, and other sciences,\u00a0is an extremely efficient and useful idealization, e.g. to\u00a0allow for differential equations. But one should not make\u00a0the confusion of believing that this idealization implies\u00a0that nature is deterministic. A deterministic theoretical\u00a0model of physics doesn\u2019t imply that nature is deterministic.\u00a0Again, real numbers are extremely useful to\u00a0do theoretical physics and calculations, but they are not\u00a0physically real.<\/p>\n

The fact that so-called real numbers have in fact random\u00a0digits, after the few first ones, has especially important\u00a0consequences in chaotic dynamical systems. After a\u00a0pretty short time, the future evolution would depend on\u00a0the thousandth digit of the initial condition. But that
\ndigit doesn\u2019t really exist. Consequently, the future of\u00a0classical chaotic systems is open and Newtonian dynam-ics is not deterministic. Actually most classical systems\u00a0are chaotic, at least the interesting ones, i.e. all those\u00a0that are not equivalent to a bunch of harmonic oscillators.\u00a0Hence, classical mechanics is not deterministic,\u00a0contrary to standard claims and widely held beliefs.<\/p><\/blockquote>\n

Discerning the difference between reality and modeling is interesting, but I can’t help but notice the argument is merely symmetrically applicable, i.e., you also can’t use the argument to disprove the suggestion the Universe is deterministic. The rest of his argument is either way beyond me, or gibberish – I can’t tell.<\/p>\n

On an unrelated note, he also gives the reason for the name real numbers<\/em>, which I thought was interesting. From the NewScientist<\/strong><\/em> article:<\/p>\n

It took me a long time to identify what I believe is the key to the problem: a crucial detail of the mathematics we use to describe the world. Fittingly, it goes back again to Descartes. He gave the name \u201creal\u201d to the numbers commonly used in science: 1, 2, \u00be, 1.797546\u2026 His point was to distinguish them from the imaginary numbers based on the square root of -1, numbers that intuitively cannot exist in the real world.<\/p><\/blockquote>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Continuing an old discussion under a more apropos name,\u00a0quantum physicist Nicolas Gisin writes a summary of his position on free will in NewScientist (21 May 2016, paywall): But are the mathematical real numbers physically real? Certainly not! Most real numbers are never-ending strings of digits. They can be thought of \u2026 Continue reading → <\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3775","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/huewhite.com\/umb\/wp-json\/wp\/v2\/posts\/3775","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/huewhite.com\/umb\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/huewhite.com\/umb\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/huewhite.com\/umb\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/huewhite.com\/umb\/wp-json\/wp\/v2\/comments?post=3775"}],"version-history":[{"count":1,"href":"https:\/\/huewhite.com\/umb\/wp-json\/wp\/v2\/posts\/3775\/revisions"}],"predecessor-version":[{"id":3776,"href":"https:\/\/huewhite.com\/umb\/wp-json\/wp\/v2\/posts\/3775\/revisions\/3776"}],"wp:attachment":[{"href":"https:\/\/huewhite.com\/umb\/wp-json\/wp\/v2\/media?parent=3775"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/huewhite.com\/umb\/wp-json\/wp\/v2\/categories?post=3775"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/huewhite.com\/umb\/wp-json\/wp\/v2\/tags?post=3775"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}