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文章邮箱帐号绑定微信

手机端访问悟理知识平台，可以关注公众号“悟理wuphys”，或者直接用浏览器访问 http://www.wuphys.com微信关注公众号后，点击“知识平台”按钮，即可访问。但登录时，如您的微信未绑定账号，将提示“您的微信未绑定悟理账号”。...

站务

赞同0  1065浏览  1评论 林威 2022-05-08 23:40

文章闵氏空间和洛伦兹变换

作者：yubr编辑：Trader Joe's四维闵可夫斯基时空我们在本科阶段接触的经典力学和经典电动力学里的物理规律，都是以三维矢量方程的形式描述的。无论是牛顿运动定律，还是麦克斯韦方程组，其基本的物理对象都是三维欧式空间的矢量（例...

洛伦兹变换 闵氏空间

赞同1  1208浏览  0评论 yubr 2022-05-24 23:00

Giacomo 回复了问题 2022-05-23 19:58 物理: 问答广义相对论里曲率张量该如何理解？

Giacomo :有一个概念叫截面曲率（sectional curvature），是说在黎曼流形里面一点截取一个二维的子切空间，对应一个实数。这个概念是经典微分几何里面的高斯曲率的拓展; 赞同5 反对 0人感谢 0评论 1回复

文章伽利略逝世的那年牛顿诞生，真的是这样吗？

历法

赞同3  1074浏览  0评论 traderjoes 2022-05-17 01:55

粽子 回复了问题 2022-06-02 11:45 数学: 问答求教个人业余想学习数学的路径

粽子 :哈哈哈我很想放一个@Vladimir的路径图呢。首先声明，学习路径是个很个人的事情。（当然这也意味着，大家容易有不同意见。我先抛砖引玉，还请友善交流）看看你喜欢什么方向咯。不算应用，数学大致可以分为代数和数论，几何和拓扑，当然还有分析类。当然也有很多其他分支，也有很多交叉性的东西。所以弄清楚自己对什...; 赞同4 反对 2人感谢 1评论 3回复

Jakob齐斋 回复了问题 2022-05-27 23:01 配位化学 化学: 问答在配位化学中，主族金属配位和过渡金属的配位有什么本质区别？

Jakob齐斋 :区别在于，过渡金属和主族元素与配体相互作用的轨道不同。一般过渡金属（3d,4d）形成配合物是过渡金属的d轨道和配体p轨道作用。一般过渡金属（副族）和配体成键，电子只填充在了成键轨道，成键轨道填满，配合物就稳定。常用的经验定律18电子规则也是基于此，即中心原子和配体合力填满9个成键轨道就是稳定的。一般...; 赞同3 反对 2人感谢 0评论 1回复

文章 2022年5月11日，悟理公测

各位朋友们，经过紧张的技术准备工作和小范围内测，悟理知识平台定于2022年5月11日，以邀请制注册的方式开始公测。公测期间，各位朋友可以通过公众号“悟理wuphys”，以及网站 http://www.wuphys.com 、悟理.中国来访...

公告站务

赞同5  1436浏览  4评论 林威 2022-05-11 02:31

林威 回复了问题 2022-06-09 17:53 数学学习: 问答这好丑啊

林威 : 略丑$$\int_{-\infty}^{+\infty} {1 \over 1 + x^2} d x$$$$\int_{-\infty}^{+\infty} {1 \over 1 + x^2} d x$$不丑&nbs...; 赞同0 反对 0人感谢 0评论 2回复

文章拿什么喜欢你，物理？

《学习高中物理会有哪些坑？》连载文章将会分享一些学习高中物理时所面临的典型问题与困惑。欢迎大家关注“因物悦理”，我将持续分享高中物理的干货哟。任何事情都是由...

物理 高中物理

赞同1  1064浏览  0评论 music 2022-05-31 23:15

一块石头 回复了问题 2022-05-17 20:02 化学: 问答如何理解pH或者酸碱值？

一块石头 :我们熟知的酸碱理论有丹麦化学家Brønsted和英国化学家Lowry各自独立提出的酸碱质子理论，和和美国化学家Lewis提出的酸碱电子理论，人们也称之为狭义酸碱理论和广义酸碱理论。酸碱质子理论认为：凡是可以释放质子（氢离子）的分子或离子为酸（ Brønsted 酸），凡是能接受氢离子的分子或离子则...; 赞同5 反对 1人感谢 0评论 1回复

文章最美的公式：你也能懂的麦克斯韦方程组（微分篇）

在上一篇文章《最美的公式：你也能懂的麦克斯韦方程组（积分篇）》里，长尾科技带着大家从零开始一步一步认识了麦克斯韦方程组的积分形式，这篇文章我们就来看看它的微分形式。在积分篇里，我们一直在跟电场、磁场的通量打交道。我们任意画一个曲面，这个曲面...

电动力学 狭义相对论 麦克斯韦方程组

赞同0  1236浏览  0评论 长尾科技 2022-05-16 17:24

文章为什么我们的宏观世界是三维的（附答疑）

作者| yubr编辑| Trader Joe's经验表明，我们所生活的这个宏观世界是一维时间+三维空间所组成的四维时空的有机整体，这一点是狭义相对论的基本观点，也已经被无数的实验所验证（例如，LHC上每时每刻都在以无数微观粒子“尸骨”来...

物理

赞同1  1243浏览  0评论 yubr 2022-05-24 22:34

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  1180浏览  0评论 redcrag 2022-06-06 00:08

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  2733浏览  0评论 林威 2022-06-03 01:39

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CONNECT:[ UseTime:0.000445s ] mysql:host=127.0.0.1;port=3306;dbname=wuphysthink;charset=utf8mb4
SHOW FULL COLUMNS FROM `aws_hook_plugins` [ RunTime:0.000586s ]
SELECT `hook`,`plugins` FROM `aws_hook_plugins` WHERE `status` = 1 ORDER BY `sort` DESC [ RunTime:0.000360s ]
SHOW FULL COLUMNS FROM `aws_config` [ RunTime:0.000629s ]
SELECT * FROM `aws_config` [ RunTime:0.000502s ]
SHOW FULL COLUMNS FROM `aws_forbidden_ip` [ RunTime:0.000565s ]
SELECT `ip` FROM `aws_forbidden_ip` [ RunTime:0.000203s ]
SHOW FULL COLUMNS FROM `aws_admin_group` [ RunTime:0.000461s ]
SELECT `permission` FROM `aws_admin_group` WHERE `id` = 5 LIMIT 1 [ RunTime:0.000260s ]
SHOW FULL COLUMNS FROM `aws_users_online` [ RunTime:0.000412s ]
DELETE FROM `aws_users_online` WHERE `last_login_time` < 1773992463 [ RunTime:0.003350s ]
SHOW FULL COLUMNS FROM `aws_menu_rule` [ RunTime:0.000501s ]
SELECT * FROM `aws_menu_rule` WHERE `status` = 1 AND `group` = 'nav' ORDER BY `sort` ASC,`id` ASC [ RunTime:0.000338s ]
SELECT * FROM `aws_menu_rule` WHERE `status` = 1 AND `group` = 'footer' ORDER BY `sort` ASC,`id` ASC [ RunTime:0.000337s ]
SHOW FULL COLUMNS FROM `aws_links` [ RunTime:0.000583s ]
SELECT * FROM `aws_links` WHERE `status` = 1 [ RunTime:0.000267s ]
SHOW FULL COLUMNS FROM `aws_post_relation` [ RunTime:0.000611s ]
SELECT COUNT(*) AS think_count FROM `aws_post_relation` WHERE `item_type` IN ('question','article','') LIMIT 1 [ RunTime:0.000351s ]
SELECT `id`,`item_id`,`item_type`,`uid` FROM `aws_post_relation` WHERE `item_type` IN ('question','article','') ORDER BY RAND(),`is_recommend` DESC LIMIT 45,15 [ RunTime:0.000444s ]
SHOW FULL COLUMNS FROM `aws_question` [ RunTime:0.000590s ]
SELECT `last_answer` FROM `aws_question` WHERE `id` IN (9,4,12,35,7,15) AND `status` = 1 [ RunTime:0.000329s ]
SHOW FULL COLUMNS FROM `aws_answer` [ RunTime:0.000536s ]
SELECT * FROM `aws_answer` WHERE `status` = 1 AND `id` IN (24,7,12,15,17,34) [ RunTime:0.000461s ]
SHOW FULL COLUMNS FROM `aws_topic_relation` [ RunTime:0.000486s ]
SELECT `topic_id`,`item_type`,`item_id` FROM `aws_topic_relation` WHERE `item_id` IN (9,4,12,35,7,15) AND `item_type` = 'question' [ RunTime:0.000369s ]
SHOW FULL COLUMNS FROM `aws_topic` [ RunTime:0.000491s ]
SELECT * FROM `aws_topic` WHERE `id` IN (13,3,2,61,5,71,82) [ RunTime:0.000335s ]
SELECT * FROM `aws_question` WHERE `status` = 1 AND `id` IN (9,4,12,35,7,15) [ RunTime:0.000701s ]
SELECT `topic_id`,`item_type`,`item_id` FROM `aws_topic_relation` WHERE `item_id` IN (2,37,24,5,60,13,36,71,62) AND `item_type` = 'article' [ RunTime:0.000567s ]
SELECT * FROM `aws_topic` WHERE `id` IN (5,16,30,19,29,38,2,53,54,27) [ RunTime:0.000394s ]
SHOW FULL COLUMNS FROM `aws_article` [ RunTime:0.000820s ]
SELECT * FROM `aws_article` WHERE `status` = 1 AND `id` IN (2,37,24,5,60,13,36,71,62) [ RunTime:0.003211s ]
SHOW FULL COLUMNS FROM `aws_users` [ RunTime:0.001004s ]
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 (1,55,42,9,28,12,35,65,4,5,56,13,36) [ RunTime:0.000613s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 1 LIMIT 1 [ RunTime:0.000295s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 1 LIMIT 1 [ RunTime:0.000243s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 4 LIMIT 1 [ RunTime:0.000281s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 4 LIMIT 1 [ RunTime:0.000234s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 5 LIMIT 1 [ RunTime:0.000260s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 5 LIMIT 1 [ RunTime:0.000233s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 9 LIMIT 1 [ RunTime:0.000231s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 9 LIMIT 1 [ RunTime:0.000221s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 12 LIMIT 1 [ RunTime:0.000239s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 12 LIMIT 1 [ RunTime:0.000221s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 13 LIMIT 1 [ RunTime:0.000248s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 13 LIMIT 1 [ RunTime:0.000219s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 28 LIMIT 1 [ RunTime:0.000242s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 28 LIMIT 1 [ RunTime:0.000221s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 35 LIMIT 1 [ RunTime:0.000225s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 35 LIMIT 1 [ RunTime:0.000216s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 36 LIMIT 1 [ RunTime:0.000218s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 36 LIMIT 1 [ RunTime:0.000237s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 42 LIMIT 1 [ RunTime:0.000242s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 42 LIMIT 1 [ RunTime:0.000233s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 55 LIMIT 1 [ RunTime:0.000226s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 55 LIMIT 1 [ RunTime:0.000219s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 56 LIMIT 1 [ RunTime:0.000224s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 56 LIMIT 1 [ RunTime:0.000219s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 65 LIMIT 1 [ RunTime:0.000224s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 65 LIMIT 1 [ RunTime:0.000231s ]
SHOW FULL COLUMNS FROM `aws_article_vote` [ RunTime:0.000555s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 2 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000307s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 37 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000297s ]
SHOW FULL COLUMNS FROM `aws_question_vote` [ RunTime:0.000486s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 12 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000296s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 9 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000272s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 24 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000301s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 24 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000256s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 4 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000266s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 15 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000256s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 12 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000249s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 5 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000257s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 34 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000249s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 35 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000260s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 60 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000285s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 7 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000264s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 7 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000249s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 13 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000273s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 36 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000278s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 71 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000289s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 17 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000284s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 15 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000260s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 62 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000275s ]
SHOW FULL COLUMNS FROM `aws_announce` [ RunTime:0.000927s ]
SELECT * FROM `aws_announce` WHERE `status` = 1 ORDER BY `set_top_time` DESC,`sort` DESC LIMIT 0,3 [ RunTime:0.000391s ]
SELECT COUNT(*) AS think_count FROM `aws_topic` WHERE `status` = 1 AND `discuss_month` > 0 LIMIT 1 [ RunTime:0.000474s ]
SELECT * FROM `aws_topic` WHERE `status` = 1 AND `discuss_month` > 0 ORDER BY RAND(),`top` DESC,`focus` DESC,`discuss_month` DESC LIMIT 0,5 [ RunTime:0.001013s ]
SHOW FULL COLUMNS FROM `aws_topic_focus` [ RunTime:0.000553s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 66 LIMIT 1 [ RunTime:0.000369s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 26 LIMIT 1 [ RunTime:0.000370s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 84 LIMIT 1 [ RunTime:0.000360s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 29 LIMIT 1 [ RunTime:0.000310s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 72 LIMIT 1 [ RunTime:0.000339s ]
SHOW FULL COLUMNS FROM `aws_column` [ RunTime:0.000685s ]
SELECT * FROM `aws_column` WHERE `verify` = 1 ORDER BY RAND(),`view_count` DESC LIMIT 0,5 [ RunTime:0.000657s ]
SELECT * FROM `aws_users` WHERE `uid` <> 0 AND `status` = 1 AND `reputation` > 0 ORDER BY RAND(),`reputation` DESC,`answer_count` DESC LIMIT 5 [ RunTime:0.001156s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 33 LIMIT 1 [ RunTime:0.000325s ]
SHOW FULL COLUMNS FROM `aws_users_follow` [ RunTime:0.000542s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 33 LIMIT 1 [ RunTime:0.000312s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 35 LIMIT 1 [ RunTime:0.000340s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 32 LIMIT 1 [ RunTime:0.000302s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 32 LIMIT 1 [ RunTime:0.000328s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 5 LIMIT 1 [ RunTime:0.000304s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 17 LIMIT 1 [ RunTime:0.000301s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 17 LIMIT 1 [ RunTime:0.000310s ]

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