{"id":1017,"date":"2013-06-03T12:33:46","date_gmt":"2013-06-03T19:33:46","guid":{"rendered":"https:\/\/mathrising.com\/?p=1017"},"modified":"2013-06-03T12:33:46","modified_gmt":"2013-06-03T19:33:46","slug":"multiverse-busses-and-emergent-space-time","status":"publish","type":"post","link":"https:\/\/mathrising.com\/?p=1017","title":{"rendered":"Multiverse, busses and emergent space-time"},"content":{"rendered":"

There was once what many call a ‘foundational crisis in mathematics’<\/a> – disputes among mathematicians about both their ideas and their methods.\u00a0 But while one needn’t now address the relationship between mathematics and reality in order to pursue a successful career in mathematics, the conceptual and experimental puzzles of modern physics likely reflect a similar difficulty that we have reconciling our ideas with our reality.<\/p>\n

Some of these puzzles are addressed in a recent article appearing on the Simons Foundation<\/a> website by Natalie Wolchover.\u00a0 The article was given the title Is Nature Unnatural?\u00a0 In it Wolchover describes difficulties that physicists have reconciling very effective mathematical models with experimental data.\u00a0 The accuracy with which the mathematics of the Standard Model represents experimental results has forced the consideration of some fairly radical ideas about the nature of our reality.\u00a0 Some physicists find these alternatives unacceptable, while others see them as inevitable.<\/p>\n

With the discovery of only one particle, the LHC experiments deepened a profound problem in physics that had been brewing for decades. Modern equations seem to capture reality with breathtaking accuracy, correctly predicting the values of many constants of nature and the existence of particles like the Higgs. Yet a few constants \u2014 including the mass of the Higgs boson \u2014 are exponentially different from what these trusted laws indicate they should be, in ways that would rule out any chance of life, unless the universe is shaped by inexplicable fine-tunings and cancellations\u2026..<\/p>\n

Physicists reason that if the universe is unnatural, with extremely unlikely fundamental constants that make life possible, then an enormous number of universes must exist for our improbable case to have been realized.<\/p><\/blockquote>\n

It’s interesting that this multiverse possibility is essentially a product of missing pieces in our ‘breathtakingly accurate’ model of the universe taken together with what we understand about probabilities. Shifting the attention of the mind’s eye a bit, a well investigated pattern in mathematics, that characterizes quantum chaotic systems, has also been observed in the departure times of busses at a specific location in Mexico, where drivers alter their behavior based on information they receive about busses that are ahead of them.\u00a0 In another article<\/a> by Wolchover,\u00a0 she explains:<\/p>\n

Subatomic particles have little to do with decentralized bus systems. But in the years since the odd coupling was discovered, the same pattern has turned up in other unrelated settings. Scientists now believe the widespread phenomenon, known as \u201cuniversality,\u201d stems from an underlying connection to mathematics, and it is helping them to model complex systems from the Internet to Earth\u2019s climate.<\/p><\/blockquote>\n

The concept of universality is grounded in the purely mathematical exploration of an eigenvalue<\/a> whose roots are traced back to the late 18th century.<\/p>\n

\u201cIt seems to be a law of nature,\u201d said Van Vu, a mathematician at Yale University who, with Terence Tao of the University of California, Los Angeles, has proven universality for a broad class of random matrices.<\/p>\n

Universality is thought to arise when a system is very complex, consisting of many parts that strongly interact with each other to generate a spectrum. The pattern emerges in the spectrum of a random matrix, for example, because the matrix elements all enter into the calculation of that spectrum. But random matrices are merely \u201ctoy systems\u201d that are of interest because they can be rigorously studied, while also being rich enough to model real-world systems, Vu said. Universality is much more widespread. Wigner\u2019s hypothesis (named after Eugene Wigner, the physicist who discovered universality in atomic spectra) asserts that all complex, correlated systems exhibit universality, from a crystal lattice to the Internet.
\nThe more complex a system is, the more robust its universality should be, said L\u00e1szl\u00f3 Erd\u00f6s of the University of Munich, one of Yau\u2019s collaborators. \u201cThis is because we believe that universality is the typical behavior.\u201d
\nIn many simple systems, individual components can assert too great an influence on the outcome of the system, changing the spectral pattern. With larger systems, no single component dominates. \u201cIt\u2019s like if you have a room with a lot of people and they decide to do something, the personality of one person isn\u2019t that important,\u201d Vu said.<\/p><\/blockquote>\n

The technique is being applied to the analysis of the evolution of the Internet, climate change models, and tests of bone tissue related to an understanding of osteoporosis.<\/p>\n

Another take on the current state of affairs is given in an interview with Nobel Prize-winning physicist David J. Gross<\/a> by Peter Byrne (also on the Simons Foundation website)\u00a0 Byrne tells us:<\/p>\n

Gross characterizes theoretical physics as rife with esoteric speculations, a strange superposition of practical robustness and theoretical confusion.<\/p><\/blockquote>\n

In response to the question “Is there a crisis in physics?”\u00a0 Gross says:<\/p>\n

I do not view the present situation as a crisis, but as the kind of acceptable scientific confusion that discovery eventually transcends.<\/p><\/blockquote>\n

But I found the next question unexpected and the answer provocative.<\/p>\n

What does it mean to say that space-time is an emergent phenomenon?<\/em>
\n[Chuckles.] That is a very sophisticated concept, which takes from about birth until the age of two to grasp. We do not really experience space-time; it\u2019s a model. It describes how to get that piece of food that\u2019s on the rug over there: crawl.
\nOur model of space-time, as amended by Einstein, is extremely useful, but perhaps it is not fundamental. It might be a derived concept. It seems to emerge from a more fundamental physical process that informs the mathematical pictures drawn by string theory and quantum field theory.<\/p><\/blockquote>\n

It seems that the conceptual difficulties in modern physics cannot avoid an intriguing question about us, namely, “What are we doing when we build a concept?”\u00a0 Gross also says this:<\/p>\n

There are frustrating theoretical problems in quantum field theory that demand solutions, but the string theory \u201clandscape\u201d of 10500 solutions does not make sense to me. Neither does the multiverse concept or the anthropic principle, which purport to explain why our particular universe has certain physical parameters. These models presume that we are stuck, conceptually.<\/p><\/blockquote>\n

When asked about human consciousness and objective reality, Gross sounds like a Platonist.<\/p>\n

I believe that there is a real world, out there, and that we see shadows of it: our models, our theories. I believe that mathematics exists. It may be entirely real in a physical sense; it may also contain \u201cthings\u201d that are ideal. But, to be clear, the human mind is a physical object. It\u2019s put together by real molecules and quarks.<\/p><\/blockquote>\n

One of the more aggressive moves toward an interdisciplinary look at how our views of reality are constructed was demonstrated by the 2011 International and Interdisciplinary Conference<\/a> organized by the Foundational Questions Institute which I plan to go back to in a future post:
\nSetting Time Aright: An international and inter-disciplinary meeting investigating the Nature of Time.<\/p>\n","protected":false},"excerpt":{"rendered":"

There was once what many call a ‘foundational crisis in mathematics’ – disputes among mathematicians about both their ideas and their methods. But while one needn’t now address the relationship between mathematics and reality in order to pursue a successful career in mathematics, the conceptual and experimental puzzles of modern physics likely reflect a similar […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5,32,26],"tags":[70,74,49],"class_list":["post-1017","post","type-post","status-publish","format-standard","hentry","category-mathematics","category-philosophy-of-mathematics","category-physics","tag-mathematics","tag-physics","tag-quantum-mechanics","odd"],"_links":{"self":[{"href":"https:\/\/mathrising.com\/index.php?rest_route=\/wp\/v2\/posts\/1017","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathrising.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathrising.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathrising.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathrising.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1017"}],"version-history":[{"count":3,"href":"https:\/\/mathrising.com\/index.php?rest_route=\/wp\/v2\/posts\/1017\/revisions"}],"predecessor-version":[{"id":1020,"href":"https:\/\/mathrising.com\/index.php?rest_route=\/wp\/v2\/posts\/1017\/revisions\/1020"}],"wp:attachment":[{"href":"https:\/\/mathrising.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1017"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathrising.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1017"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathrising.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1017"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}