{"id":1367,"date":"2016-04-01T12:00:10","date_gmt":"2016-04-01T17:00:10","guid":{"rendered":"https:\/\/blogs.mathworks.com\/cleve\/?p=1367"},"modified":"2016-11-13T07:49:10","modified_gmt":"2016-11-13T12:49:10","slug":"dark-energy-gravitational-waves","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/cleve\/2016\/04\/01\/dark-energy-gravitational-waves\/","title":{"rendered":"Dark Energy Gravitational Waves"},"content":{"rendered":"<div class=\"content\"><!--introduction--><p>Recent theoretical, observational and computational results establish the possibility that gravitational waves produced by the dark energy created at the dawn of the universe affect the clock rate of silicon digital processors operating at very low temperatures.<\/p><!--\/introduction--><h3>Contents<\/h3><div><ul><li><a href=\"#c0d7b135-a443-4e2f-a001-41a4a2aa2f36\">Ed Plum<\/a><\/li><li><a href=\"#675b7c50-ccb6-4694-9873-48b0e468ce1d\">LIGO<\/a><\/li><li><a href=\"#eb6843aa-8c08-459f-b6ec-32575512656f\">LIGO Labs<\/a><\/li><li><a href=\"#6f362e6a-567d-4f46-8495-42a1e71a71ab\">LIGO Gravitational Waves<\/a><\/li><li><a href=\"#566391b6-0168-48d2-95d7-dedee4632c58\">Dark Energy Gravitational Waves<\/a><\/li><li><a href=\"#1fecae63-0555-4094-88d6-3d174e5e4f38\">The signal<\/a><\/li><li><a href=\"#5126e2ba-860b-4fb3-a255-ba8529261b04\">The sound<\/a><\/li><li><a href=\"#6aec9f6b-0188-46e5-94cd-243443875d18\">The spectrogram<\/a><\/li><li><a href=\"#0445fdfd-d898-4ad7-8833-76b28f26a03f\">Expectations<\/a><\/li><\/ul><\/div><h4>Ed Plum<a name=\"c0d7b135-a443-4e2f-a001-41a4a2aa2f36\"><\/a><\/h4><p>Ed Plum is a professor in the Institute for Theoretical Physics at the U. C. Santa Barbara.  He is also a long-time friend of mine and an avid MATLAB fan.<\/p><p>Ed and his colleagues are publishing an important paper today. Here is a link to the journal, <a href=\"https:\/\/blogs.mathworks.com\/images\/cleve\/Plum_et_al.pdf\"><i>Physical Review Communications<\/i><\/a>.  Ed has shared an advanced copy with me.  They have found convincing evidence that the gravitational waves predicted by Einstein's General Theory of Relativity and emanating from \"Dark Energy\" affect the operating frequency of silicon computer chips.  The effect can be observed in experiments operating at temperatures below 2 degrees Kelvin.<\/p><h4>LIGO<a name=\"675b7c50-ccb6-4694-9873-48b0e468ce1d\"><\/a><\/h4><p>The announcement on February 11 of the detection of gravitational waves by the LIGO team thrilled scientists and the public at large worldwide. LIGO stands for Laser Interferometer Gravitational-Wave Observatory. Here is the <a href=\"http:\/\/www.ligo.caltech.edu\/\">link to the LIGO home page<\/a>. Here is their scientific paper in <a href=\"http:\/\/dx.doi.org\/10.1103\/PhysRevLett.116.061102\"><i>Physical Review Letters<\/i><\/a>.  Excellent survey articles were published in <a href=\"http:\/\/www.nytimes.com\/2016\/02\/14\/opinion\/sunday\/finding-beauty-in-the-darkness.html?_r=4\"><i>The New York Times Sunday Review<\/i><\/a> and <a href=\"http:\/\/www.newyorker.com\/tech\/elements\/gravitational-waves-exist-heres-how-scientists-finally-found-them\"><i>The New Yorker<\/i><\/a>.<\/p><p>Here is a <a href=\"https:\/\/en.wikipedia.org\/wiki\/General_relativity#\/media\/File:Gravwav.gif\">Wikipedia animated graphic<\/a> depicting gravitational waves in the article on General Relativity.<\/p><h4>LIGO Labs<a name=\"eb6843aa-8c08-459f-b6ec-32575512656f\"><\/a><\/h4><p>The LIGO experiment is designed to detect powerful one-time astrophysical events such as colliding black holes.  The gravitational waves involved have wave lengths that require L-shaped detectors with legs four kilometers long.  A wave passes through the detector just once, in a fraction of a second.  There are two detectors, located in Washington State and Louisiana.<\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"https:\/\/blogs.mathworks.com\/images\/cleve\/LIGOs_Dual_Detectors.jpg\" alt=\"\"> <\/p><p>Photo: <a href=\"http:\/\/www.ligo.caltech.edu\">&lt;http:\/\/www.ligo.caltech.edu<\/a> &gt;<\/p><h4>LIGO Gravitational Waves<a name=\"6f362e6a-567d-4f46-8495-42a1e71a71ab\"><\/a><\/h4><p>This beautiful graphic from the <i>Phys. Rev. Letters<\/i> paper shows the event detected by the LIGO team.  The top two figures show the actual signals recorded at the two labs.  The next two figures show the results from supercomputer runs for the numerical solution of Einstein's equations.  The small pair of figures show that the difference between the observations and the simulations is noise.  The two color figures show the \"chirps\", spectrograms plotting frequency versus time. These chirps are readily audible to the human ear.<\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"https:\/\/blogs.mathworks.com\/images\/cleve\/LIGO_graph.png\" alt=\"\"> <\/p><p>Source: <a href=\"http:\/\/www.ligo.caltech.edu\">&lt;http:\/\/www.ligo.caltech.edu<\/a>&gt;<\/p><h4>Dark Energy Gravitational Waves<a name=\"566391b6-0168-48d2-95d7-dedee4632c58\"><\/a><\/h4><p>The most commonly accepted model of cosmology hypothesizes <i>dark energy<\/i>, formed at the origin of the universe and permeating all of space, but invisible to optical observation.  According to Einstein's General Theory of Relativity, this energy constantly produces short wave length, very low energy gravitational waves.  These waves continuously interact with all mass in the universe, but on a scale that is almost impossible to detect.<\/p><p>Plum and his colleagues have evidence from both numerical simulations and actual observations that the dark energy gravitational waves affect the operating frequency of commercial microprocessors.  Very slight changes in processor speed can be detected, provided the silicon is exceptionally pure and the observations are made at very low temperatures.  It's like immersing a high-end laptop in liquid nitrogen. Here is one of the detectors.<\/p><p><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"https:\/\/blogs.mathworks.com\/images\/cleve\/microprocessor.jpg\" alt=\"\"> <\/p><p>Photo: <a href=\"http:\/\/www.canstockphoto.com\/images-photos\/microprocessor.html\">Plum <i>et al<\/i><\/a><\/p><h4>The signal<a name=\"1fecae63-0555-4094-88d6-3d174e5e4f38\"><\/a><\/h4><p>Some time ago, Ed gave me access to one of the first signals his group had detected and we have been quietly including it as one of sample sounds on recent MATLAB distributions.  The file is <tt>chirp.mat<\/tt>.  We have reversed the signal to disguise it until now.  You should be able to load a copy on your own machine.<\/p><pre class=\"codeinput\">    clear\r\n    which <span class=\"string\">chirp.mat<\/span>\r\n    load <span class=\"string\">chirp.mat<\/span>\r\n    y = flipud(y)';\r\n    t = (1:length(y))\/Fs;\r\n    whos\r\n<\/pre><pre class=\"codeoutput\">C:\\Program Files\\MATLAB\\R2016a\\toolbox\\matlab\\audiovideo\\chirp.mat\r\n  Name      Size                Bytes  Class     Attributes\r\n\r\n  Fs        1x1                     8  double              \r\n  t         1x13129            105032  double              \r\n  y         1x13129            105032  double              \r\n\r\n<\/pre><p>The first plot is the entire signal.  Since the waves are arriving continuously, we see several peaks.  The second plot zooms in on one of the peaks.<\/p><pre class=\"codeinput\">    subplot(2,1,1)\r\n    plot(t,y)\r\n    axis([0 t(end) -1 1])\r\n\r\n    subplot(2,1,2)\r\n    plot(t,y)\r\n    axis([.75 .80 -1 1])\r\n    xlabel(<span class=\"string\">'Time (secs)'<\/span>)\r\n<\/pre><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"https:\/\/blogs.mathworks.com\/images\/cleve\/gravwave_blog_01.png\" alt=\"\"> <h4>The sound<a name=\"5126e2ba-860b-4fb3-a255-ba8529261b04\"><\/a><\/h4><p>I hope you can run this <tt>sound<\/tt> yourself and hear the chirps. If you are just reading this on the Web, you will have to imagine what this sounds like.<\/p><pre class=\"codeinput\">    sound(y,Fs)\r\n<\/pre><h4>The spectrogram<a name=\"6aec9f6b-0188-46e5-94cd-243443875d18\"><\/a><\/h4><p>Here is the picture of one chirp, the spectrogram of about one-eighth of the signal.<\/p><pre class=\"codeinput\">    clf <span class=\"string\">reset<\/span>\r\n    spectrogram(y(1:2048),kaiser(128,18),120,128,Fs,<span class=\"string\">'yaxis'<\/span>)\r\n<\/pre><img decoding=\"async\" vspace=\"5\" hspace=\"5\" src=\"https:\/\/blogs.mathworks.com\/images\/cleve\/gravwave_blog_02.png\" alt=\"\"> <h4>Expectations<a name=\"0445fdfd-d898-4ad7-8833-76b28f26a03f\"><\/a><\/h4><p>This is just be beginning. We expect to learn much more about our universe as we are able to refine the silicon in the microprocessors and lower the temperature of the operating environment.<\/p><script language=\"JavaScript\"> <!-- \r\n    function grabCode_a7e8ba3b6a45440894a54653fefb0ea6() {\r\n        \/\/ Remember the title so we can use it in the new page\r\n        title = document.title;\r\n\r\n        \/\/ Break up these strings so that their presence\r\n        \/\/ in the Javascript doesn't mess up the search for\r\n        \/\/ the MATLAB code.\r\n        t1='a7e8ba3b6a45440894a54653fefb0ea6 ' + '##### ' + 'SOURCE BEGIN' + ' #####';\r\n        t2='##### ' + 'SOURCE END' + ' #####' + ' a7e8ba3b6a45440894a54653fefb0ea6';\r\n    \r\n        b=document.getElementsByTagName('body')[0];\r\n        i1=b.innerHTML.indexOf(t1)+t1.length;\r\n        i2=b.innerHTML.indexOf(t2);\r\n \r\n        code_string = b.innerHTML.substring(i1, i2);\r\n        code_string = code_string.replace(\/REPLACE_WITH_DASH_DASH\/g,'--');\r\n\r\n        \/\/ Use \/x3C\/g instead of the less-than character to avoid errors \r\n        \/\/ in the XML parser.\r\n        \/\/ Use '\\x26#60;' instead of '<' so that the XML parser\r\n        \/\/ doesn't go ahead and substitute the less-than character. \r\n        code_string = code_string.replace(\/\\x3C\/g, '\\x26#60;');\r\n\r\n        copyright = 'Copyright 2016 The MathWorks, Inc.';\r\n\r\n        w = window.open();\r\n        d = w.document;\r\n        d.write('<pre>\\n');\r\n        d.write(code_string);\r\n\r\n        \/\/ Add copyright line at the bottom if specified.\r\n        if (copyright.length > 0) {\r\n            d.writeln('');\r\n            d.writeln('%%');\r\n            if (copyright.length > 0) {\r\n                d.writeln('% _' + copyright + '_');\r\n            }\r\n        }\r\n\r\n        d.write('<\/pre>\\n');\r\n\r\n        d.title = title + ' (MATLAB code)';\r\n        d.close();\r\n    }   \r\n     --> <\/script><p style=\"text-align: right; font-size: xx-small; font-weight:lighter;   font-style: italic; color: gray\"><br><a href=\"javascript:grabCode_a7e8ba3b6a45440894a54653fefb0ea6()\"><span style=\"font-size: x-small;        font-style: italic;\">Get \r\n      the MATLAB code <noscript>(requires JavaScript)<\/noscript><\/span><\/a><br><br>\r\n      Published with MATLAB&reg; R2016a<br><\/p><\/div><!--\r\na7e8ba3b6a45440894a54653fefb0ea6 ##### SOURCE BEGIN #####\r\n%% Dark Energy Gravitational Waves\r\n% Recent theoretical, observational and computational results establish\r\n% the possibility that gravitational waves produced by the dark energy\r\n% created at the dawn of the universe affect the clock rate of silicon\r\n% digital processors operating at very low temperatures.\r\n\r\n%% Ed Plum\r\n% Ed Plum is a professor in the Institute for Theoretical Physics at the\r\n% U. C. Santa Barbara.  He is also a long-time friend of mine and an avid\r\n% MATLAB fan.\r\n\r\n%%\r\n% Ed and his colleagues are publishing an important paper today.\r\n% Here is a link to the journal, \r\n% <https:\/\/blogs.mathworks.com\/images\/cleve\/Plum_et_al.pdf\r\n% _Physical Review Communications_>.  Ed has shared\r\n% an advanced copy with me.  They have found convincing evidence that\r\n% the gravitational waves predicted by Einstein's General Theory of\r\n% Relativity and emanating from \"Dark Energy\" affect the operating\r\n% frequency of silicon computer chips.  The effect can be observed in\r\n% experiments operating at temperatures below 2 degrees Kelvin.\r\n\r\n%% LIGO\r\n% The announcement on February 11 of the detection of gravitational waves\r\n% by the LIGO team thrilled scientists and the public at large worldwide.\r\n% LIGO stands for Laser Interferometer Gravitational-Wave Observatory.\r\n% Here is the <http:\/\/www.ligo.caltech.edu\/ link to the LIGO home page>.\r\n% Here is their scientific paper in\r\n% <http:\/\/dx.doi.org\/10.1103\/PhysRevLett.116.061102\r\n% _Physical Review Letters_>.  Excellent survey articles were published\r\n% in <http:\/\/nyti.ms\/1Xmh2ot _The New York Times Sunday Review_> and\r\n% <http:\/\/www.newyorker.com\/tech\/elements\/gravitational-waves-exist-heres-how-scientists-finally-found-them\r\n% _The New Yorker_>.\r\n\r\n%%\r\n% Here is a\r\n% <https:\/\/en.wikipedia.org\/wiki\/General_relativity#\/media\/File:Gravwav.gif\r\n% Wikipedia animated graphic> depicting gravitational waves in the article\r\n% on General Relativity.\r\n\r\n%% LIGO Labs\r\n% The LIGO experiment is designed to detect powerful one-time\r\n% astrophysical events such as colliding black holes.  The gravitational\r\n% waves involved have wave lengths that require L-shaped detectors with\r\n% legs four kilometers long.  A wave passes through the detector just\r\n% once, in a fraction of a second.  There are two detectors, located\r\n% in Washington State and Louisiana.\r\n% \r\n% <<LIGOs_Dual_Detectors.jpg>>\r\n%\r\n% Photo: <http:\/\/www.ligo.caltech.edu http:\/\/www.ligo.caltech.edu >\r\n\r\n%% LIGO Gravitational Waves\r\n% This beautiful graphic from the _Phys. Rev. Letters_ paper shows the\r\n% event detected by the LIGO team.  The top two figures show the actual\r\n% signals recorded at the two labs.  The next two figures show the results\r\n% from supercomputer runs for the numerical solution of Einstein's\r\n% equations.  The small pair of figures show that the difference between\r\n% the observations and the simulations is noise.  The two color figures\r\n% show the \"chirps\", spectrograms plotting frequency versus time.\r\n% These chirps are readily audible to the human ear.\r\n%\r\n% <<LIGO_graph.png>>\r\n%\r\n% Source: <http:\/\/www.ligo.caltech.edu http:\/\/www.ligo.caltech.edu>\r\n\r\n%% Dark Energy Gravitational Waves\r\n% The most commonly accepted model of cosmology hypothesizes _dark energy_,\r\n% formed at the origin of the universe and permeating all of space, but\r\n% invisible to optical observation.  According to Einstein's General \r\n% Theory of Relativity, this energy constantly produces short wave length,\r\n% very low energy gravitational waves.  These waves continuously interact\r\n% with all mass in the universe, but on a scale that is almost impossible\r\n% to detect.\r\n\r\n%%\r\n% Plum and his colleagues have evidence from both numerical simulations\r\n% and actual observations that the dark energy gravitational waves affect\r\n% the operating frequency of commercial microprocessors.  Very slight \r\n% changes in processor speed can be detected, provided the silicon is\r\n% exceptionally pure and the observations are made at very low\r\n% temperatures.  It's like immersing a high-end laptop in liquid nitrogen.\r\n% Here is one of the detectors. \r\n%\r\n% <<microprocessor.jpg>>\r\n%\r\n% Photo: <http:\/\/www.canstockphoto.com\/images-photos\/microprocessor.html\r\n% Plum _et al_>\r\n\r\n%% The signal\r\n% Some time ago, Ed gave me access to one of the first signals his group\r\n% had detected and we have been quietly including it as one of sample\r\n% sounds on recent MATLAB distributions.  The file is |chirp.mat|.  We\r\n% have reversed the signal to disguise it until now.  You should be able\r\n% to load a copy on your own machine.\r\n\r\n    clear\r\n    which chirp.mat\r\n    load chirp.mat\r\n    y = flipud(y)';\r\n    t = (1:length(y))\/Fs;\r\n    whos\r\n    \r\n%%\r\n% The first plot is the entire signal.  Since the waves are arriving\r\n% continuously, we see several peaks.  The second plot zooms in on one\r\n% of the peaks.\r\n \r\n    subplot(2,1,1)\r\n    plot(t,y)\r\n    axis([0 t(end) -1 1])\r\n    \r\n    subplot(2,1,2)\r\n    plot(t,y)\r\n    axis([.75 .80 -1 1])\r\n    xlabel('Time (secs)')\r\n    \r\n%% The sound\r\n% I hope you can run this |sound| yourself and hear the chirps.\r\n% If you are just reading this on the Web, you will have to imagine\r\n% what this sounds like.\r\n\r\n    sound(y,Fs)\r\n\r\n%% The spectrogram\r\n% Here is the picture of one chirp, the spectrogram of about one-eighth\r\n% of the signal.\r\n\r\n    clf reset\r\n    spectrogram(y(1:2048),kaiser(128,18),120,128,Fs,'yaxis')\r\n    \r\n    \r\n%% Expectations\r\n% This is just be beginning. We expect to learn much more about our\r\n% universe as we are able to refine the silicon in the microprocessors\r\n% and lower the temperature of the operating environment.\r\n##### SOURCE END ##### a7e8ba3b6a45440894a54653fefb0ea6\r\n-->","protected":false},"excerpt":{"rendered":"<div class=\"overview-image\"><img src=\"https:\/\/blogs.mathworks.com\/cleve\/files\/gravwave_blog_02.png\" class=\"img-responsive attachment-post-thumbnail size-post-thumbnail wp-post-image\" alt=\"\" decoding=\"async\" loading=\"lazy\" \/><\/div><!--introduction--><p>Recent theoretical, observational and computational results establish the possibility that gravitational waves produced by the dark energy created at the dawn of the universe affect the clock rate of silicon digital processors operating at very low temperatures.... <a class=\"read-more\" href=\"https:\/\/blogs.mathworks.com\/cleve\/2016\/04\/01\/dark-energy-gravitational-waves\/\">read more >><\/a><\/p>","protected":false},"author":78,"featured_media":1382,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[5,4,8],"tags":[],"_links":{"self":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/1367"}],"collection":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/users\/78"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/comments?post=1367"}],"version-history":[{"count":6,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/1367\/revisions"}],"predecessor-version":[{"id":2098,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/posts\/1367\/revisions\/2098"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/media\/1382"}],"wp:attachment":[{"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/media?parent=1367"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/categories?post=1367"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.mathworks.com\/cleve\/wp-json\/wp\/v2\/tags?post=1367"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}