{"id":10842,"date":"2019-02-19T12:15:27","date_gmt":"2019-02-19T17:15:27","guid":{"rendered":"http:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=10842"},"modified":"2019-02-19T12:15:27","modified_gmt":"2019-02-19T17:15:27","slug":"the-mathematical-question-from-which-all-answers-flow","status":"publish","type":"post","link":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/?p=10842","title":{"rendered":"The Mathematical Question From Which All Answers Flow"},"content":{"rendered":"

I’m beginning to suspect that there are actually (at least) two different theoretical HEP physicists named Nima Arkani-Hamed out there. One of them (who I’ll call Nima1) believes the way to understand the fundamental nature of physical reality involves extremely complicated extensions of the Standard Model, with large numbers of parameters tuned to avoid conflict with observation, and possibly hundreds or thousands of extra fields thrown in for good measure. He also seems to like the multiverse and anthropic explanations. I have a lot of disagreements with Nima1, most recently discussed here<\/a>.<\/p>\n

The second Arkani-Hamed (Nima2) has a completely different point of view, one quite close to my own, although he may be even more of a mathematical mystic than I am. Natalie Wolchover has recently talked to Nima2 and written about it for the New Yorker<\/a>. Nima2 is in love with the deep mathematical structure of physics and the way it appears in different aspects:<\/p>\n

Nima Arkani-Hamed, a physicist at the Institute for Advanced Study, is one of today\u2019s leading theoreticians. \u201cThe miraculous shape-shifting property of the laws is the single most amazing thing I know about them,\u201d he told me, this past fall. It \u201cmust be a huge clue to the nature of the ultimate truth.\u201d<\/p><\/blockquote>\n

Wolchover expands on this idea of multiple ways of expressing the same underlying mathematical structure:<\/p>\n

The existence of this branching, interconnected web of mathematical languages, each with its own associated picture of the world, is what needs to be understood.<\/p>\n

This web of laws creates traps for physicists. Suppose you\u2019re a researcher seeking to understand the universe more deeply. You may get stuck using a dead-end description\u2014clinging to a principle that seems correct but is merely one of nature\u2019s disguises. It\u2019s for this reason that Paul Dirac, a British pioneer of quantum theory, stressed the importance of reformulating existing theories: it\u2019s by finding new ways of describing known phenomena that you can escape the trap of provisional or limited belief. This was the trick that led Dirac to predict antimatter, in 1928. \u201cIt is not always so that theories which are equivalent are equally good,\u201d he said, five decades later, \u201cbecause one of them may be more suitable than the other for future developments.\u201d<\/p>\n

Today, various puzzles and paradoxes point to the need to reformulate the theories of modern physics in a new mathematical language. Many physicists feel trapped. They have a hunch that they need to transcend the notion that objects move and interact in space and time. Einstein\u2019s general theory of relativity beautifully weaves space and time together into a four-dimensional fabric, known as space-time, and equates gravity with warps in that fabric. But Einstein\u2019s theory and the space-time concept break down inside black holes and at the moment of the big bang. Space-time, in other words, may be a translation of some other description of reality that, though more abstract or unfamiliar, can have greater explanatory power.<\/p><\/blockquote>\n

Nima2 is obsessed with exactly the same mystical mathematical issue that I am: what’s the right mathematical question that has as answer the Standard Model and GR?<\/p>\n

To Arkani-Hamed, the multifariousness of the laws suggests a different conception of what physics is all about. We\u2019re not building a machine that calculates answers, he says; instead, we\u2019re discovering questions. Nature\u2019s shape-shifting laws seem to be the answer to an unknown mathematical question…<\/p>\n

Arkani-Hamed now sees the ultimate goal of physics as figuring out the mathematical question from which all the answers flow. \u201cThe ascension to the tenth level of intellectual heaven,\u201d he told me, \u201cwould be if we find the question to which the universe is the answer, and the nature of that question in and of itself explains why it was possible to describe it in so many different ways.\u201d It\u2019s as though physics has been turned inside out. It now appears that the answers already surround us. It\u2019s the question we don\u2019t know.<\/p><\/blockquote>\n

I’m not sure the Amplituhedron is the right path to the “tenth level of intellectual heaven” and finding the “mathematical question from which all the answers flow”, but I’m completely sympathetic with Nima2’s motivation and quest. <\/p>\n","protected":false},"excerpt":{"rendered":"

I’m beginning to suspect that there are actually (at least) two different theoretical HEP physicists named Nima Arkani-Hamed out there. One of them (who I’ll call Nima1) believes the way to understand the fundamental nature of physical reality involves extremely … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[1],"tags":[],"class_list":["post-10842","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/10842","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=10842"}],"version-history":[{"count":5,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/10842\/revisions"}],"predecessor-version":[{"id":10847,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/10842\/revisions\/10847"}],"wp:attachment":[{"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10842"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10842"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.math.columbia.edu\/~woit\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10842"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}