{"id":1155,"date":"2016-04-24T21:09:20","date_gmt":"2016-04-25T04:09:20","guid":{"rendered":"https:\/\/dubinko.info\/blog\/?p=1155"},"modified":"2016-04-24T21:09:20","modified_gmt":"2016-04-25T04:09:20","slug":"the-physics-of-the-impossibly-tiny","status":"publish","type":"post","link":"https:\/\/dubinko.info\/blog\/2016\/04\/the-physics-of-the-impossibly-tiny\/","title":{"rendered":"The physics of the impossibly tiny"},"content":{"rendered":"

According to Newtonian gravitation, the attraction between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. Einstein refined this somewhat, but as long as there aren\u00e2\u20ac\u2122t crazy speeds or non-flattish spacetime\u00c2\u00a0involved, Newton\u00e2\u20ac\u2122s formulation is accurate. As far as we know.<\/p>\n

I read this interesting article<\/a>, which spun off the thought experiment\u00c2\u00a0below. The EM Drive mechanism keeps confounding some Really Smart people who would genuinely like to discredit it. What\u00e2\u20ac\u2122s going on here? I\u00e2\u20ac\u2122m probably butchering the explanation, but the article posits that very small accelerations don\u00e2\u20ac\u2122t behave in a completely smooth manner. In other words, they\u00e2\u20ac\u2122re subject to quantum effects.<\/p>\n

Here\u00e2\u20ac\u2122s a thought experiment. What is the Newtonian gravitational attraction between this hydrogen atom in my little finger, and one in, say, the Andromeda galaxy? (Pedantically, one that was in the Andromeda galaxy 2.5 million years ago, from the Earth\u00e2\u20ac\u2122s frame of reference)<\/p>\n

I put this into Wolfram Alpha<\/a> (which helpfully supplied an value for the big-G constant) and came up with an answer of:<\/p>\n

1.419 * 10-109<\/sup>\u00c2\u00a0N (newtons)<\/p>\n

That\u00e2\u20ac\u2122s not a typo. There\u00e2\u20ac\u2122s 109 places to the right of the decimal.<\/p>\n

I don\u00e2\u20ac\u2122t even have a good analogy for how slight that force is. A trillionth\u00c2\u00a0trillionth of the seismic energy\u00c2\u00a0of a dandelion seed landing, measured\u00c2\u00a0from a trillion\u00c2\u00a0km away?? Still too much, by a\u00c2\u00a0lot<\/em>. It\u00e2\u20ac\u2122s a reasonable question whether the universe even goes to that level of detail. Could such a slight force even be said to exist in a meaningful sense? In other words, could it be measured, even in principle? I\u00e2\u20ac\u2122m no expert, but I doubt it. So maybe physics isn’t\u00c2\u00a0completely smooth down to that level.<\/p>\n

Is there a limit to how small a force can be and still act like a force?<\/p>\n

To accurately compute the complete gravitational affect on this hydrogen atom in my little finger, I\u00e2\u20ac\u2122d have to take into account the 1080<\/sup> particles in the observable universe, the vast majority of which make unmeasurably tiny contributions to the overall sum. That\u00e2\u20ac\u2122s for a single instant. For a continuous number, I\u00e2\u20ac\u2122d need to repeat this enormous calculation something like 1043<\/sup> times per second. So all you universe simulator writers out there, take note. Some simplification is probably warranted. :)<\/p>\n

(A realistic simulator would only need to take into account the mass of the Earth, Moon, Sun, and for a few decimal places more, Jupiter. But I\u00e2\u20ac\u2122m talking about laws running the universe, not engineering hacks.)<\/p>\n

It seems there are still some quite\u00c2\u00a0interesting things left to discover in the universe. I keep going back to the chapter Surprises from the Real World<\/em>\u00c2\u00a0in Lee Smolin\u00e2\u20ac\u2122s Trouble With Physics<\/a>. Exciting times ahead! -m<\/p>\n","protected":false},"excerpt":{"rendered":"

According to Newtonian gravitation, the attraction between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. Einstein refined this somewhat, but as long as there aren\u00e2\u20ac\u2122t crazy speeds or non-flattish spacetime\u00c2\u00a0involved, Newton\u00e2\u20ac\u2122s formulation is accurate. As far as we know. I read this…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","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_publicize_message":"","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},"jetpack_post_was_ever_published":false},"categories":[28],"tags":[642,295,1182,1181],"class_list":["post-1155","post","type-post","status-publish","format-standard","hentry","category-everythingismiscellaneous","tag-gravity","tag-physics","tag-simulator","tag-universe"],"aioseo_notices":[],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p8eo8l-iD","_links":{"self":[{"href":"https:\/\/dubinko.info\/blog\/wp-json\/wp\/v2\/posts\/1155","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dubinko.info\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dubinko.info\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dubinko.info\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/dubinko.info\/blog\/wp-json\/wp\/v2\/comments?post=1155"}],"version-history":[{"count":1,"href":"https:\/\/dubinko.info\/blog\/wp-json\/wp\/v2\/posts\/1155\/revisions"}],"predecessor-version":[{"id":1156,"href":"https:\/\/dubinko.info\/blog\/wp-json\/wp\/v2\/posts\/1155\/revisions\/1156"}],"wp:attachment":[{"href":"https:\/\/dubinko.info\/blog\/wp-json\/wp\/v2\/media?parent=1155"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dubinko.info\/blog\/wp-json\/wp\/v2\/categories?post=1155"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dubinko.info\/blog\/wp-json\/wp\/v2\/tags?post=1155"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}