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长尾科技 发起了提问 2022-06-07 11:23 相对论: 问答如何看待布莱恩·格林的《宇宙的琴弦》？

格林的《宇宙的琴弦》是超弦理论的经典科普书，但它在前面也会科普相对论相关的内容。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...; 关注问题 1 0人感谢 0评论

“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：静电场里的公式那么多，电荷又有正负之分，令人抓狂的符号怎么处理？说到公式问题，咱得先申明一个立场：所有公式不分...

物理电场

赞同0  1027浏览  0评论 music 2022-05-25 19:02

文章一文看懂测量的误差与估读

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  1513浏览  0评论 music 2022-05-29 21:46

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

文章人踢足球，弹力对足球做不做功？

“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：人踢足球，弹力存在时认为球没有位移；等球有位移时，弹力又不存在了。那么弹力到底有没有做功？足球的动能哪来的？问...

物理弹力

赞同3  1032浏览  0评论 music 2022-05-29 20:25

文章闵氏几何是什么？它是如何统一时空并极大简化狭义相对论的？

1905年，爱因斯坦正式提出了狭义相对论；1908年，闵可夫斯基给出了狭义相对论的几何表述，也就是我们这里说的闵氏几何。爱因斯坦一开始对这套几何语言很反感，认为这些纯数学上的“花架子”没什么用，还增加了相对论的复杂度。但是，他很快就发现闵氏...

闵氏几何 狭义相对论

赞同2  982浏览  0评论 长尾科技 2022-05-16 17:24

林威 发起了提问 2022-05-31 01:29 温度计 物理: 问答极低温的温度计测温的原理是什么？

在0.1K以下的极低温环境，是由什么仪器可以测量出如此低的温度？仪器的实现原理是什么？; 关注问题 1 0人感谢 0评论

文章越之文章整体

一维单$\delta$势一维单$\delta$势的哈密顿量为$$H=-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}+\gamma\delta(x),$$它描述了一个在$x=0$处趋于无穷的势，发散的方向取决于“强度”...

物理

赞同0  3235浏览  0评论 林威 2022-07-18 11:48

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  988浏览  0评论 长尾科技 2022-05-16 17:24

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 10:29 相对论: 问答如何看待长尾科技的《你也能懂的质能方程E=mc²》？

长尾科技科技关于质能方程的文章：《你也能懂的质能方程E=mc²》（2.1万字）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...; 关注问题 1 0人感谢 0评论

林威 回复了问题 2022-05-23 01:20 天文黑洞: 问答事件视界望远镜（EHT）公布的银河系中心黑洞照片，和M87黑洞有什么区别？

林威 :以下回答总结于Core的描述：严格上说这并不能算是黑洞的照片，而是黑洞的事件视界附近的物质的照片。照片于黑洞本身更相关的信息是：阴影区域的大小，限制了黑洞事件视界的尺度。即便拍了黑洞照片，对于黑洞科普来说并没有加什么新料。这次发布，更有价值的事情，应该是EHT望远镜观测技术和数据到图像的处理过程。处...; 赞同0 反对 0人感谢 0评论 1回复

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  1123浏览  0评论 redcrag 2022-06-06 00:08

文章规范场论发展简史

规范场论发展简史作者 | yubr 规范场论起源于20世纪20年代Weyl关于电磁场规范对称性的基本思想，1954年杨振宁和Mills将规范对称性推广到了非阿贝尔场的情形。从Yang-Mills理论1954年被提出，一直到1971年非阿贝...

物理 规范场论

赞同2  1096浏览  0评论 yubr 2022-05-16 22:50

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CONNECT:[ UseTime:0.000375s ] mysql:host=127.0.0.1;port=3306;dbname=wuphysthink;charset=utf8mb4
SHOW FULL COLUMNS FROM `aws_hook_plugins` [ RunTime:0.000506s ]
SELECT `hook`,`plugins` FROM `aws_hook_plugins` WHERE `status` = 1 ORDER BY `sort` DESC [ RunTime:0.000303s ]
SHOW FULL COLUMNS FROM `aws_config` [ RunTime:0.000475s ]
SELECT * FROM `aws_config` [ RunTime:0.000433s ]
SHOW FULL COLUMNS FROM `aws_forbidden_ip` [ RunTime:0.000431s ]
SELECT `ip` FROM `aws_forbidden_ip` [ RunTime:0.000178s ]
SHOW FULL COLUMNS FROM `aws_admin_group` [ RunTime:0.000381s ]
SELECT `permission` FROM `aws_admin_group` WHERE `id` = 5 LIMIT 1 [ RunTime:0.000239s ]
SHOW FULL COLUMNS FROM `aws_users_online` [ RunTime:0.000389s ]
DELETE FROM `aws_users_online` WHERE `last_login_time` < 1769880156 [ RunTime:0.005368s ]
SHOW FULL COLUMNS FROM `aws_menu_rule` [ RunTime:0.000433s ]
SELECT * FROM `aws_menu_rule` WHERE `status` = 1 AND `group` = 'nav' ORDER BY `sort` ASC,`id` ASC [ RunTime:0.000319s ]
SELECT * FROM `aws_menu_rule` WHERE `status` = 1 AND `group` = 'footer' ORDER BY `sort` ASC,`id` ASC [ RunTime:0.000293s ]
SHOW FULL COLUMNS FROM `aws_links` [ RunTime:0.000449s ]
SELECT * FROM `aws_links` WHERE `status` = 1 [ RunTime:0.000238s ]
SHOW FULL COLUMNS FROM `aws_post_relation` [ RunTime:0.000454s ]
SELECT COUNT(*) AS think_count FROM `aws_post_relation` WHERE `item_type` IN ('question','article','') LIMIT 1 [ RunTime:0.000336s ]
SELECT `id`,`item_id`,`item_type`,`uid` FROM `aws_post_relation` WHERE `item_type` IN ('question','article','') ORDER BY RAND(),`is_recommend` DESC LIMIT 75,15 [ RunTime:0.000384s ]
SHOW FULL COLUMNS FROM `aws_question` [ RunTime:0.000535s ]
SELECT `last_answer` FROM `aws_question` WHERE `id` IN (28,4,16,31,32,23,5) AND `status` = 1 [ RunTime:0.000312s ]
SHOW FULL COLUMNS FROM `aws_answer` [ RunTime:0.000468s ]
SELECT * FROM `aws_answer` WHERE `status` = 1 AND `id` IN (24,11,1,0) [ RunTime:0.000359s ]
SHOW FULL COLUMNS FROM `aws_topic_relation` [ RunTime:0.000408s ]
SELECT `topic_id`,`item_type`,`item_id` FROM `aws_topic_relation` WHERE `item_id` IN (28,4,16,31,32,23,5) AND `item_type` = 'question' [ RunTime:0.000356s ]
SHOW FULL COLUMNS FROM `aws_topic` [ RunTime:0.000444s ]
SELECT * FROM `aws_topic` WHERE `id` IN (13,24,25,78,2,18) [ RunTime:0.000311s ]
SELECT * FROM `aws_question` WHERE `status` = 1 AND `id` IN (28,4,16,31,32,23,5) [ RunTime:0.000756s ]
SELECT `topic_id`,`item_type`,`item_id` FROM `aws_topic_relation` WHERE `item_id` IN (40,55,54,18,84,14,71,22) AND `item_type` = 'article' [ RunTime:0.000862s ]
SELECT * FROM `aws_topic` WHERE `id` IN (30,19,29,31,2,35,55,73,74) [ RunTime:0.001668s ]
SHOW FULL COLUMNS FROM `aws_article` [ RunTime:0.000939s ]
SELECT * FROM `aws_article` WHERE `status` = 1 AND `id` IN (40,55,54,18,84,14,71,22) [ RunTime:0.002449s ]
SHOW FULL COLUMNS FROM `aws_users` [ RunTime:0.001057s ]
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 (5,65,28,1,42,56,55,32,36) [ RunTime:0.000855s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 1 LIMIT 1 [ RunTime:0.000367s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 1 LIMIT 1 [ RunTime:0.000317s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 5 LIMIT 1 [ RunTime:0.000305s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 5 LIMIT 1 [ RunTime:0.000325s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 28 LIMIT 1 [ RunTime:0.000329s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 28 LIMIT 1 [ RunTime:0.000295s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 32 LIMIT 1 [ RunTime:0.000316s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 32 LIMIT 1 [ RunTime:0.000328s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 36 LIMIT 1 [ RunTime:0.000292s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 36 LIMIT 1 [ RunTime:0.000292s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 42 LIMIT 1 [ RunTime:0.000283s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 42 LIMIT 1 [ RunTime:0.000271s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 55 LIMIT 1 [ RunTime:0.000298s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 55 LIMIT 1 [ RunTime:0.000276s ]
SELECT `last_login_time` FROM `aws_users_online` WHERE `uid` = 56 LIMIT 1 [ RunTime:0.000305s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 56 LIMIT 1 [ RunTime:0.000267s ]
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:0.000265s ]
SHOW FULL COLUMNS FROM `aws_question_vote` [ RunTime:0.000694s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 28 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000369s ]
SHOW FULL COLUMNS FROM `aws_article_vote` [ RunTime:0.000810s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 40 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000375s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 55 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000346s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 24 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000351s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 4 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000315s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 54 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000332s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 18 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000382s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 16 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000329s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 84 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000345s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 31 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000332s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 14 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000748s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 32 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000355s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 23 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000369s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 11 AND `item_type` = 'answer' LIMIT 1 [ RunTime:0.000469s ]
SELECT `vote_value` FROM `aws_question_vote` WHERE `uid` = 0 AND `item_id` = 5 AND `item_type` = 'question' LIMIT 1 [ RunTime:0.000326s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 71 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.022335s ]
SELECT `vote_value` FROM `aws_article_vote` WHERE `uid` = 0 AND `item_id` = 22 AND `item_type` = 'article' LIMIT 1 [ RunTime:0.000388s ]
SHOW FULL COLUMNS FROM `aws_announce` [ RunTime:0.000926s ]
SELECT * FROM `aws_announce` WHERE `status` = 1 ORDER BY `set_top_time` DESC,`sort` DESC LIMIT 0,3 [ RunTime:0.000425s ]
SELECT COUNT(*) AS think_count FROM `aws_topic` WHERE `status` = 1 AND `discuss_month` > 0 LIMIT 1 [ RunTime:0.000545s ]
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:0.001056s ]
SHOW FULL COLUMNS FROM `aws_topic_focus` [ RunTime:0.000588s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 34 LIMIT 1 [ RunTime:0.000348s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 17 LIMIT 1 [ RunTime:0.000337s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 67 LIMIT 1 [ RunTime:0.000311s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 49 LIMIT 1 [ RunTime:0.000368s ]
SELECT `id` FROM `aws_topic_focus` WHERE `uid` = 0 AND `topic_id` = 16 LIMIT 1 [ RunTime:0.000320s ]
SHOW FULL COLUMNS FROM `aws_column` [ RunTime:0.000948s ]
SELECT * FROM `aws_column` WHERE `verify` = 1 ORDER BY RAND(),`view_count` DESC LIMIT 0,5 [ RunTime:0.000588s ]
SELECT * FROM `aws_users` WHERE `uid` <> 0 AND `status` = 1 AND `reputation` > 0 ORDER BY RAND(),`reputation` DESC,`answer_count` DESC LIMIT 5 [ RunTime:0.015860s ]
SHOW FULL COLUMNS FROM `aws_users_follow` [ RunTime:0.000639s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 56 LIMIT 1 [ RunTime:0.000363s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 17 LIMIT 1 [ RunTime:0.000315s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 17 LIMIT 1 [ RunTime:0.000308s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 12 LIMIT 1 [ RunTime:0.000295s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 12 LIMIT 1 [ RunTime:0.000328s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 1 LIMIT 1 [ RunTime:0.000335s ]
SELECT `user_name`,`url_token` FROM `aws_users` WHERE `uid` = 35 LIMIT 1 [ RunTime:0.000299s ]
SELECT `id` FROM `aws_users_follow` WHERE `fans_uid` = 35 LIMIT 1 [ RunTime:0.000311s ]

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