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最小作用量原理被称为物理中的“第一性原理”，其地位可见一斑。我出于对物理规律普适性的向往，折腾了三个多月写出这篇三万七千字的长文，终于了却了自己的这个心愿。目录02 并不可怕的微积分04 初识变分06 横空出世的拉格朗日方程08 最小作...

拉格朗日函数 最速降线 理论力学 物理科普 最小作用量原理 中学物理

赞同2  717浏览  0评论 music 2022-05-18 14:38

林威 回复了问题 2022-06-02 23:08 站务: 问答请问萌新应该怎么学习家庭网络搭建呢？

林威 :以个人经验为例，理论+实践是最佳选择。比如最常见的，你购置了一台电脑和一个路由器。目的是把这些设备都通电用起来。那么，这些设备都有什么功能，有什么作用？硬件怎么连接？请先看“说明书”了解设备功能。最开始可以不求甚解，先把网络通起来，剩下就可以一步步挖掘路由器中每一个设置的名词定义和功能。这时候就是理...; 赞同0 反对 0人感谢 0评论 1回复

文章静电计为什么可以反映电容器两极板间的电压

“典例问答”栏目将不定期剖析典型问题，把最本质的方法与规律呈现给读者。欢迎大家关注“因物悦理”，我将持续分享高中物理的干货哟。问：如图，静电计的这种接法为什么可以反映出电容器两极板间的电压呢？为什么不直接用电压表去测量电容器两极板间的电压呢...

静电计 电容器

赞同1  1092浏览  1评论 music 2022-05-30 23:51

文章你也能懂的微积分

前面接连发了三篇麦克斯韦方程组的文章（积分篇、微分篇和电磁波篇），从理论上来说，讲麦克斯韦方程组不讲微积分是不行的，因为人家本来就是一组积分方程和一组微分方程。但是，为了让更多人，尤其是中学生也能理解这“最美的公式”，长尾君还是预设不懂微积...

数学 微积分

赞同3  905浏览  0评论 长尾科技 2022-05-16 17:24

文章如何理解麦克斯韦方程中的不对称性

物理 麦克斯韦方程组

赞同1  964浏览  0评论 yubr 2022-05-23 00:01

文章有史以来最伟大的方程

有史以来最伟大的方程写在前面的话本文译自Robert P Crease所撰写的The greatest equations ever一文，发表在Physics World, 2004, 17(10):14–15上，为同年5月份作者请读者为...

物理

赞同2  843浏览  0评论 redcrag 2022-06-06 00:08

林威 回复了问题 2022-05-20 00:06 流形 激发态 光化学: 问答如何通俗地理解分子激发态动力学中所谓的“流形”（manifold）

林威 : Manifold日语翻译：多样体。这是比较符合原意的。Mani-多，fold-折叠。中文译法为啥叫“流形”，当年的翻译者江泽涵老先生并没有给出明确答案。但我们也不能说这词很有逼格。见江泽涵，《我国数学名词的早期工作》，载《数学通报》，1980年，第12期，第23-24...; 赞同0 反对 0人感谢 0评论 2回复

文章顶注册后迷茫不知干啥的朋友，你想要的答案在这里

悟理wuphys是啥？悟理是一个发源于长尾科技社群的邀请制知识平台，倡导用户使用费曼学习法，真正学懂自己提出的问题。当前入口有：国际域名：www.wuphys.com 中文域名：悟理.中国 &n...

公告站务

赞同6  1897浏览  0评论 林威 2022-06-03 01:39

文章光学前沿—OAM光通讯

写在前面的话本文译自Alan Eli Willner所撰写的OAM Light for Communications一文，文章发表在Optics & Photonics News, 2021, 32(6):34–42上。翻译目的为...

光学物理

赞同0  1175浏览  0评论 redcrag 2022-06-05 23:59

长尾科技 发起了提问 2022-06-07 11:12 相对论: 问答如何看待汪洁的相对论科普书《时间的形状》？

《时间的形状》是一本比较通俗的相对论科普书，零基础的朋友基本上也能看得懂。此问题隶属于更高层级的问题《相对论的【学习路径图】是什么样的？如何系统地学习相对论？》，属于相对论学习路径图的一部分。大家可以在这里讨论这两篇文章的相关内容，也可以去更高层级的问题讨论相对论的学习路径图。上层链接：相对论的【学...; 关注问题 1 0人感谢 0评论

文章深度：杨-米尔斯理论说了啥？为什么说这是杨振宁超越他诺奖的贡献？

在上一篇文章《深度：宇称不守恒到底说了啥？杨振宁和李政道的发现究竟有多大意义？》里，长尾君用了很长的篇幅跟大家聊了聊宇称不守恒的事。大家也知道杨振宁和李政道先生因此斩获了全球华人的第一个诺贝尔奖，然而，对杨振宁关注多一点的人就会经常听到这样...

杨振宁 杨米尔斯理论

赞同2  970浏览  0评论 长尾科技 2022-05-16 17:26

文章最美的公式：你也能懂的麦克斯韦方程组（积分篇）

2004年，英国的科学期刊《物理世界》举办了一个活动：让读者选出科学史上最伟大的公式。结果，麦克斯韦方程组力压质能方程、欧拉公式、牛顿第二定律、勾股定理、薛定谔方程等”方程界“的巨擘，高居榜首。麦克斯韦方程组以一种近乎完美的方式统一了电和磁...

狭义相对论 麦克斯韦方程组

赞同1  721浏览  0评论 长尾科技 2022-05-16 17:24

文章啊对对对(2)

42688010005∑n=0∞(6n)!(545140134n+13591409)(3n)!(n!)3(−640320)3n\section{3}测试\textbf{鬼影}，这个命令可以生成一段指定长度的空白：c~k1k2⋯kpk1k2⋯...

数学学习

赞同0  2200浏览  0评论 Adele 2022-06-10 12:17

林威 回复了问题 2022-05-29 01:05 站务公式: 问答如何在悟理上发带公式的文章？

林威 :最简便的方法：用LaTeX。LaTeX是科研界最常用的公式语法。学习资料很多，后续悟理平台也会逐步搬运一些LaTeX相关的文章。1、需要假设我们已经会用LaTeX来描述需要打出的公式了。或者已经手写公式，由自动化网站或朋友转换出了LaTeX代码。2、我们可以访问Markdown Nice，这是一个支...; 赞同4 反对 0人感谢 0评论 1回复

文章《人类司机》- 第三部分：宇航篇

本文由 @林威（我的朋友）/ UnknownID（我自己）合写而成，为长篇科幻。本文分为四个部分：地面篇，UAM篇，宇航篇，未来篇。本文最初灵感与初版大纲，以及地面篇（全部）和UAM篇（绝大部分）的作...

人类司机 科幻

赞同0  806浏览  0评论 无名_unknownID 2022-05-28 19:08

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CONNECT:[ UseTime:0.000476s ] mysql:host=127.0.0.1;port=3306;dbname=wuphysthink;charset=utf8mb4
SHOW FULL COLUMNS FROM `aws_hook_plugins` [ RunTime:0.000691s ]
SELECT `hook`,`plugins` FROM `aws_hook_plugins` WHERE `status` = 1 ORDER BY `sort` DESC [ RunTime:0.000405s ]
SHOW FULL COLUMNS FROM `aws_config` [ RunTime:0.000725s ]
SELECT * FROM `aws_config` [ RunTime:0.000594s ]
SHOW FULL COLUMNS FROM `aws_forbidden_ip` [ RunTime:0.000703s ]
SELECT `ip` FROM `aws_forbidden_ip` [ RunTime:0.000244s ]
SHOW FULL COLUMNS FROM `aws_admin_group` [ RunTime:0.000513s ]
SELECT `permission` FROM `aws_admin_group` WHERE `id` = 5 LIMIT 1 [ RunTime:0.000339s ]
SHOW FULL COLUMNS FROM `aws_users_online` [ RunTime:0.000561s ]
DELETE FROM `aws_users_online` WHERE `last_login_time` < 1746492226 [ RunTime:0.003068s ]
SHOW FULL COLUMNS FROM `aws_menu_rule` [ RunTime:0.000616s ]
SELECT * FROM `aws_menu_rule` WHERE `status` = 1 AND `group` = 'nav' ORDER BY `sort` ASC,`id` ASC [ RunTime:0.000400s ]
SELECT * FROM `aws_menu_rule` WHERE `status` = 1 AND `group` = 'footer' ORDER BY `sort` ASC,`id` ASC [ RunTime:0.000349s ]
SHOW FULL COLUMNS FROM `aws_links` [ RunTime:0.000491s ]
SELECT * FROM `aws_links` WHERE `status` = 1 [ RunTime:0.000279s ]
SHOW FULL COLUMNS FROM `aws_post_relation` [ RunTime:0.000531s ]
SELECT COUNT(*) AS think_count FROM `aws_post_relation` WHERE `item_type` IN ('question','article','') LIMIT 1 [ RunTime:0.000360s ]
SELECT `id`,`item_id`,`item_type`,`uid` FROM `aws_post_relation` WHERE `item_type` IN ('question','article','') ORDER BY RAND(),`is_recommend` DESC LIMIT 90,15 [ RunTime:0.000388s ]
SHOW FULL COLUMNS FROM `aws_question` [ RunTime:0.000597s ]
SELECT `last_answer` FROM `aws_question` WHERE `id` IN (17,8,24,15) AND `status` = 1 [ RunTime:0.000311s ]
SHOW FULL COLUMNS FROM `aws_answer` [ RunTime:0.000522s ]
SELECT * FROM `aws_answer` WHERE `status` = 1 AND `id` IN (9,17,26,0) [ RunTime:0.000377s ]
SHOW FULL COLUMNS FROM `aws_topic_relation` [ RunTime:0.000434s ]
SELECT `topic_id`,`item_type`,`item_id` FROM `aws_topic_relation` WHERE `item_id` IN (17,8,24,15) AND `item_type` = 'question' [ RunTime:0.000361s ]
SHOW FULL COLUMNS FROM `aws_topic` [ RunTime:0.000463s ]
SELECT * FROM `aws_topic` WHERE `id` IN (47,48,49,5,71,18) [ RunTime:0.000327s ]
SELECT * FROM `aws_question` WHERE `status` = 1 AND `id` IN (17,8,24,15) [ RunTime:0.000643s ]
SELECT `topic_id`,`item_type`,`item_id` FROM `aws_topic_relation` WHERE `item_id` IN (28,57,11,33,71,62,67,20,12,79,49) AND `item_type` = 'article' [ RunTime:0.000618s ]
SELECT * FROM `aws_topic` WHERE `id` IN (13,28,19,29,32,33,43,44,45,46,40,26,2,65,57,75,76,16,5,80,82) [ RunTime:0.000573s ]
SHOW FULL COLUMNS FROM `aws_article` [ RunTime:0.000848s ]
SELECT * FROM `aws_article` WHERE `status` = 1 AND `id` IN (28,57,11,33,71,62,67,20,12,79,49) [ RunTime:0.015992s ]
SHOW FULL COLUMNS FROM `aws_users` [ RunTime:0.003163s ]
SELECT `uid`,`nick_name`,`user_name`,`salt`,`email`,`mobile`,`sex`,`is_first_login`,`inbox_unread`,`notify_unread`,`fans_count`,`friend_count`,`available_invite_count`,`is_valid_email`,`is_valid_mobile`,`integral`,`reputation`,`reputation_update_time`,`avatar`,`signature`,`verified`,`group_id`,`integral_group_id`,`reputation_group_id`,`last_login_time`,`last_login_ip`,`reg_ip`,`money`,`frozen_money`,`deal_password`,`birthday`,`url_token`,`views_count`,`agree_count`,`question_count`,`answer_count`,`article_count`,`draft_count`,`topic_focus_count`,`column_count`,`extend`,`status`,`theme`,`create_time`,`update_time` FROM `aws_users` WHERE `status` = 1 AND `uid` IN (65,155,5,55,56,12,1,62,90) [ RunTime:0.000664s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 1 LIMIT 1 [ RunTime:0.000317s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 1 LIMIT 1 [ RunTime:0.000288s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 5 LIMIT 1 [ RunTime:0.000241s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 5 LIMIT 1 [ RunTime:0.000250s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 12 LIMIT 1 [ RunTime:0.000240s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 12 LIMIT 1 [ RunTime:0.000225s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 55 LIMIT 1 [ RunTime:0.000240s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 55 LIMIT 1 [ RunTime:0.000231s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 56 LIMIT 1 [ RunTime:0.000257s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 56 LIMIT 1 [ RunTime:0.000254s ]
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SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 62 LIMIT 1 [ RunTime:0.000252s ]
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SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 65 LIMIT 1 [ RunTime:0.000237s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 90 LIMIT 1 [ RunTime:0.000243s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 90 LIMIT 1 [ RunTime:0.000231s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 155 LIMIT 1 [ RunTime:0.000241s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 155 LIMIT 1 [ RunTime:0.000239s ]
SHOW FULL COLUMNS FROM `aws_article_vote` [ RunTime:0.000722s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 28 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000369s ]
SHOW FULL COLUMNS FROM `aws_question_vote` [ RunTime:0.000464s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 26 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000303s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 17 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000270s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 57 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000293s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 11 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000338s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 33 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000304s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 71 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000352s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 9 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000318s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 8 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000290s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 62 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000276s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 67 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000305s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 24 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000278s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 20 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000311s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 12 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000288s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 79 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000300s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 17 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000281s ]
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SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 49 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000364s ]
SHOW FULL COLUMNS FROM `aws_announce` [ RunTime:0.000628s ]
SELECT * FROM `aws_announce` WHERE `status` = 1 ORDER BY `set_top_time` DESC,`sort` DESC LIMIT 0,3 [ RunTime:0.000372s ]
SELECT COUNT(*) AS think_count FROM `aws_topic` WHERE `status` = 1 AND `discuss_month` > 0 LIMIT 1 [ RunTime:0.000463s ]
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SHOW FULL COLUMNS FROM `aws_topic_focus` [ RunTime:0.000443s ]
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SHOW FULL COLUMNS FROM `aws_column` [ RunTime:0.000514s ]
SELECT * FROM `aws_column` WHERE `verify` = 1 ORDER BY RAND(),`view_count` DESC LIMIT 0,5 [ RunTime:0.000477s ]
SELECT * FROM `aws_users` WHERE `uid` <> 0 AND `status` = 1 AND `reputation` > 0 ORDER BY RAND(),`reputation` DESC,`answer_count` DESC LIMIT 5 [ RunTime:0.001088s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 35 LIMIT 1 [ RunTime:0.000273s ]
SHOW FULL COLUMNS FROM `aws_users_follow` [ RunTime:0.000496s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 35 LIMIT 1 [ RunTime:0.000261s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 44 LIMIT 1 [ RunTime:0.000245s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 44 LIMIT 1 [ RunTime:0.000240s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 15 LIMIT 1 [ RunTime:0.000247s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 15 LIMIT 1 [ RunTime:0.000235s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 17 LIMIT 1 [ RunTime:0.000227s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 17 LIMIT 1 [ RunTime:0.000233s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 12 LIMIT 1 [ RunTime:0.000235s ]

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