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一、误差误差测量值真实值想必大家都知道对同一对象多次测量取其算术平均值就能很好的减小随机误差。不过在历史上这个观念可曾备受质疑，为啥呢？这得从误差的认识说起。据悉是伽利略首次提出了观测误差（就是随机误差的...

物理测量

赞同1  1384浏览  0评论 music 2022-05-29 21:46

文章什么是量子力学？

提到量子力学，很多人的第一反应是微观、不连续、不确定，然后就是玄乎、奇怪、诡异，乃至恐怖。有这样的想法并不奇怪，毕竟，它跟经典物理的确不太一样，大家也乐于相信玻尔说的：“如果谁不为量子力学感到困惑，他就还没理解它。”许多文章、视频也喜欢把量...

量子力学

赞同2  1030浏览  0评论 长尾科技 2022-05-16 16:07

长尾科技 回复了问题 2022-06-07 10:32 相对论: 问答相对论的【学习路径图】是什么样的？如何系统地学习相对论？

长尾科技 :1、完全零基础的朋友可以先看看长尾科技的四篇关于狭义相对论的主线文章。相对论的历史):1.2、相对论诞生：爱因斯坦是如何创立狭义相对论的？| 主线（3.3万字）然后是关于关于质能方程的讨论（想进一步讨论质能方程可以来这里：如何看待长尾科技的《你也能懂的质能方程E=mc²》？）：1.4、《...; 赞同4 反对 0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  1302浏览  4评论 林威 2022-05-11 02:31

长尾科技 发起了提问 2022-06-07 11:53 相对论: 问答如何看待格里菲斯的《电动力学导论》？

因为狭义相对论主要是从电动力学发展出来的，所以一般电动力学的最后一章都会讲狭义相对论的内容，从这个角度去理解狭义相对论会更加自然。格里菲斯的《电动力学导论》就是其中非常好的一本书，大家可以在这里一起学习这本书，有什么问题和想法都可以在这里讨论。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...; 关注问题 1 1人感谢 0评论

文章见证奇迹的时刻：如何从麦克斯韦方程组推出电磁波？

在前两篇文章里，长尾君给大家介绍了麦克斯韦方程组的积分和微分形式。大家也都知道麦克斯韦从这套方程组里推导出了电磁波，然后通过计算发现电磁波的速度正好等于光速。于是，麦克斯韦就预言“光是一种电磁波”，这个预言后来被赫兹证实。电磁波的发现让麦克...

电动力学 狭义相对论 麦克斯韦方程组

赞同0  948浏览  0评论 长尾科技 2022-05-16 17:24

文章运动的分解为啥这样干？

“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，速度的分解为啥一定得这样干？相信读者不用想就能正确写出上图的速度分解的关系式：。不过我也确信总有人会疑惑...

高中物理 中学物理

赞同2  1033浏览  0评论 music 2022-05-23 00:16

文章为什么微型黑洞可以作为能量源？

（文章为我原创，封面来自生活大爆炸）在目前的理论体系之下，人类可以应用的最强能量源是什么？核聚变？对于“最强”来说，他不太够。从能层提取克尔黑洞（旋转黑洞）的角动量？有那么点意思了，但他还不是最强的...

霍金辐射 量子力学

赞同0  917浏览  0评论 无名_unknownID 2022-05-27 23:11

文章光学前沿—驾驭太赫兹空隙

写在前面的话本文译自Sidney Perkowitz所撰写的Navigating the terahertz gap一文，文章发表在Physics World, 2020, 33(3):37–40上。翻译目的为分享知识，欢迎指正。如有侵权...

光学物理

赞同0  1160浏览  0评论 redcrag 2022-06-06 00:03

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  1103浏览  0评论 长尾科技 2022-05-16 17:24

文章简谐振动的运动学方程是怎么来的？

简谐振动是最简单最基本的振动，它的典型例子是弹簧振子。水平弹簧振子什么是弹簧振子呢？一个不考虑质量的弹簧连接一个有质量的小球或物块，然后把它沿着弹簧的方向压缩或者拉伸一定的距离（不要拉得太狠，悠着点儿）后松手，那么物块就会只在弹簧弹力的作用...

振动 牛顿力学

赞同3  975浏览  1评论 小熊君 2022-05-18 16:02

zhu 发起了提问 2022-06-07 19:27 物理: 问答土星有固体核心吗？

土星有固体核心吗？有什么证据？; 关注问题 1 0人感谢 0评论

长尾科技 发起了提问 2022-06-07 11:50 相对论: 问答一起学习周磊老师的《电动力学》视频教程

因为狭义相对论主要是从电动力学发展出来的，所以一般电动力学的最后一章都会讲狭义相对论的内容，从这个角度去理解狭义相对论会更加自然。周磊老师的视频《电动力学周磊复旦大学-HD》讲得非常好，大家在学习过程中有什么问题和想法可以来这里讨论。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？...; 关注问题 1 0人感谢 0评论

文章什么是高中物理？

很多同学初中时很喜欢物理，觉得物理很简单也很有意思。但一到高中就感觉跟不上了，感觉跟自己以前认识的物理不是一个东西，不再那么直观，也不再那么简单有趣。于是，在一些可以自由选择高考科目的地方，大量考生纷纷放弃物理，“弃考物理”曾一度成为热门话...

中学物理 高中物理

赞同0  1010浏览  0评论 长尾科技 2022-05-16 17:24

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  2409浏览  0评论 林威 2022-06-03 01:39

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CONNECT:[ UseTime:0.000419s ] mysql:host=127.0.0.1;port=3306;dbname=wuphysthink;charset=utf8mb4
SHOW FULL COLUMNS FROM `aws_hook_plugins` [ RunTime:0.000639s ]
SELECT `hook`,`plugins` FROM `aws_hook_plugins` WHERE `status` = 1 ORDER BY `sort` DESC [ RunTime:0.000357s ]
SHOW FULL COLUMNS FROM `aws_config` [ RunTime:0.000674s ]
SELECT * FROM `aws_config` [ RunTime:0.000664s ]
SHOW FULL COLUMNS FROM `aws_forbidden_ip` [ RunTime:0.000611s ]
SELECT `ip` FROM `aws_forbidden_ip` [ RunTime:0.000218s ]
SHOW FULL COLUMNS FROM `aws_admin_group` [ RunTime:0.000605s ]
SELECT `permission` FROM `aws_admin_group` WHERE `id` = 5 LIMIT 1 [ RunTime:0.000304s ]
SHOW FULL COLUMNS FROM `aws_users_online` [ RunTime:0.000579s ]
DELETE FROM `aws_users_online` WHERE `last_login_time` < 1765003035 [ RunTime:0.003420s ]
SHOW FULL COLUMNS FROM `aws_menu_rule` [ RunTime:0.000649s ]
SELECT * FROM `aws_menu_rule` WHERE `status` = 1 AND `group` = 'nav' ORDER BY `sort` ASC,`id` ASC [ RunTime:0.000468s ]
SELECT * FROM `aws_menu_rule` WHERE `status` = 1 AND `group` = 'footer' ORDER BY `sort` ASC,`id` ASC [ RunTime:0.000470s ]
SHOW FULL COLUMNS FROM `aws_links` [ RunTime:0.000701s ]
SELECT * FROM `aws_links` WHERE `status` = 1 [ RunTime:0.000398s ]
SHOW FULL COLUMNS FROM `aws_post_relation` [ RunTime:0.000690s ]
SELECT COUNT(*) AS think_count FROM `aws_post_relation` WHERE `item_type` IN ('question','article','') LIMIT 1 [ RunTime:0.000521s ]
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:0.000665s ]
SHOW FULL COLUMNS FROM `aws_question` [ RunTime:0.000666s ]
SELECT `last_answer` FROM `aws_question` WHERE `id` IN (21,31,32,30) AND `status` = 1 [ RunTime:0.000399s ]
SHOW FULL COLUMNS FROM `aws_answer` [ RunTime:0.000737s ]
SELECT * FROM `aws_answer` WHERE `status` = 1 AND `id` IN (32,0) [ RunTime:0.000499s ]
SHOW FULL COLUMNS FROM `aws_topic_relation` [ RunTime:0.000639s ]
SELECT `topic_id`,`item_type`,`item_id` FROM `aws_topic_relation` WHERE `item_id` IN (21,31,32,30) AND `item_type` = 'question' [ RunTime:0.000501s ]
SHOW FULL COLUMNS FROM `aws_topic` [ RunTime:0.000660s ]
SELECT * FROM `aws_topic` WHERE `id` IN (18,2) [ RunTime:0.000421s ]
SELECT * FROM `aws_question` WHERE `status` = 1 AND `id` IN (21,31,32,30) [ RunTime:0.000751s ]
SELECT `topic_id`,`item_type`,`item_id` FROM `aws_topic_relation` WHERE `item_id` IN (55,8,5,14,34,44,69,11,31,10,62) AND `item_type` = 'article' [ RunTime:0.000557s ]
SELECT * FROM `aws_topic` WHERE `id` IN (16,20,26,27,13,28,30,19,29,5,42,23,62,2,74,80) [ RunTime:0.000449s ]
SHOW FULL COLUMNS FROM `aws_article` [ RunTime:0.001668s ]
SELECT * FROM `aws_article` WHERE `status` = 1 AND `id` IN (55,8,5,14,34,44,69,11,31,10,62) [ RunTime:0.005767s ]
SHOW FULL COLUMNS FROM `aws_users` [ RunTime:0.001471s ]
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 (65,5,1,90,56,10,42) [ RunTime:0.000669s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 1 LIMIT 1 [ RunTime:0.000331s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 1 LIMIT 1 [ RunTime:0.000289s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 5 LIMIT 1 [ RunTime:0.000300s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 5 LIMIT 1 [ RunTime:0.000306s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 10 LIMIT 1 [ RunTime:0.000271s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 10 LIMIT 1 [ RunTime:0.000283s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 42 LIMIT 1 [ RunTime:0.000268s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 42 LIMIT 1 [ RunTime:0.000272s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 56 LIMIT 1 [ RunTime:0.000275s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 56 LIMIT 1 [ RunTime:0.000283s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 65 LIMIT 1 [ RunTime:0.000282s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 65 LIMIT 1 [ RunTime:0.000268s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 90 LIMIT 1 [ RunTime:0.000276s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 90 LIMIT 1 [ RunTime:0.000271s ]
SHOW FULL COLUMNS FROM `aws_article_vote` [ RunTime:0.000554s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 55 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000356s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 8 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000352s ]
SHOW FULL COLUMNS FROM `aws_question_vote` [ RunTime:0.000600s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 32 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000365s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 21 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000357s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 5 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000350s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 31 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000380s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 14 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000344s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 34 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000317s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 44 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000317s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 69 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000393s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 11 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000425s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 31 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000399s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 32 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000379s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 30 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000359s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 10 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000400s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 62 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000371s ]
SHOW FULL COLUMNS FROM `aws_announce` [ RunTime:0.000655s ]
SELECT * FROM `aws_announce` WHERE `status` = 1 ORDER BY `set_top_time` DESC,`sort` DESC LIMIT 0,3 [ RunTime:0.000380s ]
SELECT COUNT(*) AS think_count FROM `aws_topic` WHERE `status` = 1 AND `discuss_month` > 0 LIMIT 1 [ RunTime:0.000542s ]
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:0.001047s ]
SHOW FULL COLUMNS FROM `aws_topic_focus` [ RunTime:0.000627s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 48 LIMIT 1 [ RunTime:0.000397s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 80 LIMIT 1 [ RunTime:0.000367s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 52 LIMIT 1 [ RunTime:0.000324s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 74 LIMIT 1 [ RunTime:0.000306s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 19 LIMIT 1 [ RunTime:0.000325s ]
SHOW FULL COLUMNS FROM `aws_column` [ RunTime:0.000672s ]
SELECT * FROM `aws_column` WHERE `verify` = 1 ORDER BY RAND(),`view_count` DESC LIMIT 0,5 [ RunTime:0.000616s ]
SELECT * FROM `aws_users` WHERE `uid` <> 0 AND `status` = 1 AND `reputation` > 0 ORDER BY RAND(),`reputation` DESC,`answer_count` DESC LIMIT 5 [ RunTime:0.001511s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 15 LIMIT 1 [ RunTime:0.000374s ]
SHOW FULL COLUMNS FROM `aws_users_follow` [ RunTime:0.000451s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 15 LIMIT 1 [ RunTime:0.000303s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 17 LIMIT 1 [ RunTime:0.000289s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 17 LIMIT 1 [ RunTime:0.000300s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 36 LIMIT 1 [ RunTime:0.000279s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 36 LIMIT 1 [ RunTime:0.000297s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 55 LIMIT 1 [ RunTime:0.000284s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 55 LIMIT 1 [ RunTime:0.000307s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 5 LIMIT 1 [ RunTime:0.000277s ]

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