{"id":2651,"date":"2016-02-12T17:13:32","date_gmt":"2016-02-12T22:13:32","guid":{"rendered":"https:\/\/scottaaronson.blog\/?p=2651"},"modified":"2017-01-12T18:17:24","modified_gmt":"2017-01-12T23:17:24","slug":"the-universe-has-a-high-but-not-infinite-sleep-number","status":"publish","type":"post","link":"https:\/\/scottaaronson.blog\/?p=2651","title":{"rendered":"The universe has a high (but not infinite) Sleep Number"},"content":{"rendered":"

As everyone knows, this was a momentous\u00a0week in the history of science. \u00a0And I don’t need to tell you why: the STOC<\/a> and CCC<\/a> accepted paper lists finally came out.<\/p>\n

Haha, kidding! \u00a0I meant,\u00a0we learned this week that gravitational waves were directly detected for the first time, a hundred years after Einstein first predicted them (he then reneged on the prediction, then reinstated it, then reneged again, then reinstated it a second time—see Daniel Kennefick’s article<\/a>\u00a0for some of the fascinating story).<\/p>\n

By now, we all know some of the basic parameters here: a merger of two black holes, ~1.3 billion light-years away, weighing ~36 and ~29 solar masses respectively, which (when they merged) gave off 3 solar masses’ worth of energy in the form of gravitational waves—in those brief 0.2 seconds, radiating more watts of power\u00a0than all the stars in the observable universe combined. \u00a0By the time the waves reached earth, they were only stretching and compressing space by 1 part in 4\u00d71021<\/sup>—thus, changing the lengths of the 4-kilometer arms of LIGO by 10-18<\/sup> meters (1\/1000 the diameter of a proton). \u00a0But this was detected, in possibly the highest-precision measurement ever made.<\/p>\n

As I read the historic news, there’s one question that kept gnawing at me: how close would you need to have been to the merging black holes\u00a0before you could, you know, feel<\/em> the distortion of space? \u00a0I made a guess, assuming the strength of gravitational waves fell off with distance as\u00a01\/r2<\/sup>. \u00a0Then I checked Wikipedia<\/a> and learned that the strength falls off only as 1\/r, which completely changes the situation, and implies that the answer to my question is: you’d need\u00a0to be very<\/strong>\u00a0close. \u00a0Even if you were only as far from the black-hole cataclysm as the earth is from the sun, I get that you’d be\u00a0stretched and squished by a mere ~50 nanometers (this interview with Jennifer Ouellette and Amber Stuver<\/a>\u00a0says 165 nanometers, but as a theoretical computer scientist, I try not to sweat factors of 3). \u00a0Even if you were 3000 miles from the black holes—New-York\/LA distance—I get that the gravitational waves would only stretch and squish you by around\u00a0a millimeter. \u00a0Would you feel<\/em> that? \u00a0Not sure. \u00a0At 300 miles, it would be maybe\u00a0a centimeter—though presumably\u00a0the linearized approximation is breaking down by\u00a0that point. \u00a0(See also this Physics StackExchange answer<\/a>, which reaches similar conclusions, though again off from mine by factors of 3 or 4.) \u00a0Now, the black holes themselves were orbiting about 200 miles from each other before they merged. \u00a0So, the distance at which you could safely\u00a0feel<\/em> their gravitational waves, isn’t too far from the distance at which they’d rip you to shreds and swallow you!<\/p>\n

In summary, to stretch and squeeze spacetime by just a few hundred nanometers per meter, along the surface of a sphere whose\u00a0radius equals our orbit around the sun, requires more watts of power than all the stars in the observable universe give off as starlight. \u00a0People often say that the message of general relativity is that matter bends spacetime “as if it were a mattress.” \u00a0But they should add that the reason it took so long for humans to notice this, is that it’s a really friggin’ firm\u00a0mattress<\/strong>, one that you need to bounce up and down\u00a0on unbelievably hard before it quivers, and would probably never want to sleep on.<\/p>\n

As if I needed to say it, this post is an invitation for experts to correct whatever I got wrong. \u00a0Public humiliation, I’ve found, is a very<\/em> fast and effective way to learn an unfamiliar field.<\/p>\n","protected":false},"excerpt":{"rendered":"

As everyone knows, this was a momentous\u00a0week in the history of science. \u00a0And I don’t need to tell you why: the STOC and CCC accepted paper lists finally came out. Haha, kidding! \u00a0I meant,\u00a0we learned this week that gravitational waves were directly detected for the first time, a hundred years after Einstein first predicted them […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"advanced_seo_description":"","jetpack_seo_html_title":"","jetpack_seo_noindex":false,"jetpack_seo_schema_type":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"{title}\n\n{excerpt}\n\n{url}","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"_wpas_customize_per_network":false,"jetpack_post_was_ever_published":false},"categories":[18,19,3],"tags":[],"class_list":["post-2651","post","type-post","status-publish","format-standard","hentry","category-embarrassing-myself","category-physics-for-doofuses","category-procrastination"],"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/2651","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2651"}],"version-history":[{"count":3,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/2651\/revisions"}],"predecessor-version":[{"id":2655,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=\/wp\/v2\/posts\/2651\/revisions\/2655"}],"wp:attachment":[{"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2651"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2651"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/scottaaronson.blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2651"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}