Alternate Title: It's a point, dammit!
Why do physicists consider higher-order (beyond our standard three) dimensions to be "rolled up" into a small space within the existing three dimensions? They even spend a lot of time working out just how small this space must be given various theoretical and experimental results. Yet if these additional dimensions are anything like the dimensions we know and love, I don't think there's any reason to think of them this way. If they are orthogonal to the existing three dimensions, just extending in a direction we happen to be unable to perceive, then they needn't have any size at all in our existing set of dimensions.
I mean, if you look at a two-dimensional painting and then examine a line extending out of the plane of the painting into the third dimension, does it make any sense to think of that third dimension as somehow rolled up into the two dimensions of the painting? No, it doesn't. The third dimension is orthogonal to the other two dimensions. It's kind of what orthogonal means--the new dimension does not align with the other two. There is no overlap between the new and old dimensions. Similarly, if the fourth spatial dimension is orthogonal to the first three, then I think it makes precisely as much sense to discuss its size in those original three dimensions as it actually takes up in those dimensions: None at all.
This comment has been removed by a blog administrator.
ReplyDeleteThis comment has been removed by a blog administrator.
ReplyDeleteThis comment has been removed by a blog administrator.
ReplyDeleteThis comment has been removed by a blog administrator.
ReplyDeletePerhaps in the beginning, right after the big bang, while 3 of the spatial dimensions grew to astronomical size, others were compactified; so the higher dimensions may be compact like a circle or ellipse with a very small size.
ReplyDeleteWe can see the 3 independent directions of 3D space by examining the corner of a room. Any other direction in 3D space is a linear combination of x,y and z, i.e; ax+by+cz, where a,b,c are any scalars. It’s not possible to orient a ruler perpendicular to all three edges at the corner of a room. If it is perpendicular to two edges, it would be parallel to the third. But if it could move in the fourth dimension we could get the ruler perpendicular to all three edges and meeting at a corner of a 3D room. The ruler would then be parallel to the 'fourth direction'. A particle that travels in 4D space, for example, can move along any linear combination of four independent directions. In addition to moving north/south & east/west, there is a fourth direction in the 4D space perpendicular to each of these other directions.
Your first observation is how I think physicists currently imagine events to have unfolded (and folded :)). Your second observation is more in line with what I had in mind... Orthogonal should really mean orthogonal. If you tilt that ruler so it lies along the fourth dimension you might see only a cross section of it (since we can't perceive that fourth dimension), just the way the residents of Flatland would see only the outline of a ruler poking through their world and aligned with the third dimension, perpendicular to their world. Maybe I've read too much science fiction in general and Rudy Rucker in particular, but I don't have much trouble imagining additional dimensions. I even have what I think is a pretty unusual take on the idea that might be suitable for a science fiction story of my own, but who knows if it'll ever get written, sigh.
ReplyDeleteThis comment has been removed by a blog administrator.
ReplyDeleteThis comment has been removed by a blog administrator.
ReplyDelete若對自己誠實，日積月累，就無法對別人不忠了。........................................
ReplyDelete路過--你好嗎..很棒的BLOG.........................................
ReplyDeleteNice Post~!!!. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ReplyDelete很高興見到你哦!!. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ReplyDelete0401影音成人影片交流愛撫淫叫色情照片性愛圖片女生如何自慰激突成人論壇美女脫胸罩走光一夜正妹視訊情人性愛論壇85cc影城性伴侶85cc色情影片打手槍情色視訊聊天室色情a片色情色情圖片限制級照片色情電話520sex免費色情網情色性愛一夜情聊天網成人聊天網視訊成人台灣性網av一夜女情色av淫女免費視訊美女挑逗情色影音聊天作愛影片辣妹清涼秀美女做愛成人自拍貼圖成人資訊色論壇台灣色情成人網站色情視訊聊天露三點打砲情色性愛貼圖av成人網成人影片
ReplyDelete教育無他，愛與榜樣而已...............................................................
ReplyDeleteHey!Nice post~........................................................
ReplyDelete來問個安，誰不支持這個部落格，我咬他.........................
ReplyDelete要求適合自己的愛情方式，是會得到更多，還是會錯過一個真正愛你的人。..................................................
ReplyDelete我在戀愛著？--------是的，因為我在等待著..................................................
ReplyDelete良言一句三冬暖，惡語傷人六月寒。...........................................................................
ReplyDeleteConstant dripping wears away the stone. 滴水穿石！加油！..................................................
ReplyDelete微風成人 ut視訊交友 彩虹聊天 a免費線上 手機視訊交友 女優露點影片 性感車展美女 av影片下載 走光+偷拍+自拍 彩虹視訊聊天室 85cc 情趣 18h 可愛視訊少女 85ccst影城 歐美a片論壇 007情色小說 自拍色情圖 彰化一夜情聊天室 s383影城 完美女人工廠 影音視訊聊天 做愛美女 視訊辣妹網 人妻自拍 歐美熟女做愛成人 視訊成人網 空姐性愛影片 aa圖免費看 美女寫真貼圖 85cc免費成人 成人短片 情色貼圖 視訊聊天 杜蕾斯貼圖區正妹牆 正妹援交 嘟嘟情人色網貼圖 鋼管秀 avvcd 洪爺影片城 國中大奶f sex888免費影片 色遊戲下載區 巨乳人妻影片 性貼圖 後宮 限制級遊戲 0204成人電影 免費性愛貼片 走光照
ReplyDelete你不能左右天氣，但你可以改變心情.............................................................
ReplyDelete看看blog放鬆一下，工作累死了.................................................................
ReplyDeletePoverty tries friends..................................................................
ReplyDelete良言一句三冬暖，惡語傷人六月寒。.................................................................
ReplyDelete向著星球長驅直進的人，反比踟躕在峽路上的人，更容易達到目的。............................................................
ReplyDelete安一估~你也安一估哦~............................................................
ReplyDeletethx rfor you sharing~~learn it by heart..................................................................
ReplyDelete真是太有道理了~~我支持你~~~............................................................
ReplyDeleteNecessity is the mother of invention.......................................................................
ReplyDeleteRiches serve a wise man but command a fool.............................................................
ReplyDelete當最困難的時候，也就是離成功不遠的時候。..................................................
ReplyDeleteNever hesitate to hold out your hand; never hesitate to accept the outstretched hand of another..................................................................
ReplyDelete享受你自己的生活,不要與他人相比。............................................................
ReplyDelete文章是心情的反應~~祝妳天天寫的都是讓人開心的好文章哦!!...............................................................
ReplyDelete一時的錯誤不算什麼，錯而不改才是一生中永遠且最大的錯誤..................................................
ReplyDelete謝謝大大的分享 我會學會反省與寬容 感恩 ∩△∩............................................................
ReplyDelete愛情不是慈善事業，不能隨便施捨。......................................................................
ReplyDeletemay the blessing be always with you!!............................................................
ReplyDelete原來這世上能跟你共同領略一個笑話的人竟如此難得......................................................................
ReplyDelete唯有用熱情、用智慧去觀察事物，這事物才會把他的秘密，洩漏給我們......................................................................
ReplyDeleteMany a little makes a mickle..................................................................
ReplyDeleteLearning makes life sweet.......................................................................
ReplyDelete說「吃虧就是便宜的人」，多半不是吃虧的人。......................................................................
ReplyDelete