量子力学中的波动性的一种解释,我觉得靠谱。非常靠谱!这个想法太酷了!

YouTube视频源地址:https://www.youtube.com/watch?v=WIyTZDHuarQ

The standard theory of quantum mechanics leaves a bit to be desired. As Richard Feynman put it, “I think I can safely say that no one understands quantum mechanics.” This is because observations of experiments have led us to a theory that contradicts common sense. The wave function contains all the information that is knowable about a particle, yet it can only be used to calculate probabilities of where a particle will likely turn up. It can’t give us an actual account of where the particle went or where it will be at some later time.

Some have suggested that this theory is incomplete. Maybe something is going on beneath the radar of standard quantum theory and somehow producing the appearance of randomness and uncertainty without actually being random or uncertain. Theories of this sort are called hidden variable theories because they propose entities that aren’t observable. One such theory is pilot wave theory, first proposed by de Broglie, but later developed by Bohm. The idea here is that a particle oscillates, creating a wave. It then interacts with the wave and this complex interaction determines its motion.

Experiments using silicone oil droplets on a vibrating bath provide a remarkable physical realization of pilot wave theories. They give us a physical picture of what the quantum world might look like if this is what’s going on – and this theory is still deterministic. The particle is never in two places at once and there is no randomness.

视频:(提示,可以选择中文字幕,非常感谢酆正玄的翻译

该项目主页:http://dualwalkers.com/ 强烈推荐!

Silicone oil droplets provide a physical realization of pilot wave theories.

播主主页:https://www.patreon.com/veritasium

Check out Smarter Every Day: http://bit.ly/VeSmarter

Support Veritasium on Patreon: http://bit.ly/VePatreon

还有一个视频主用水做的实验演示:(视频地址:https://www.youtube.com/watch?v=KJDEsAy9RyM

这种视频扬声器的制作者是Nighthawkinlight,其播客页面是 https://www.youtube.com/user/Nighthawkinlight

 

GRTensor 下载地址:https://github.com/grtensor/grtensor

GRTensor 博客:https://hyperspace.uni-frankfurt.de/2016/12/07/grtensoriii-for-maple-has-been-released/

GRTensor wiki介绍:https://github.com/grtensor/grtensor/wiki

GRTensor 官方网站:http://grtensor.phy.queensu.ca/


本段摘选自GRTensor wiki介绍,链接在上面已经给出。

GRTensorIII is provided as Maple package in the  lib/  directory of the project. This lib directory needs to be included in your Maple library path.

This can be accomplished in a Maple session with a command like (changing the path to the directory on your system):

For Windows users (DOUBLE backslashes!!):

If the library is not found the cryptic error message will say something like: “with expects it’s first argument to be of type….”

Alternately, this command can be placed in the Maple init file in the home directory on your computer. See Maple Init File

GRIII can then be loaded via:

And the output will be:

It is then useful to ensure you have a suitable path set for loading and saving metrics. This is controlled by the global variable  grOptionMetricPath . The current option settings are displayed with the command  groptions(); . The grtensor distribution includes a directory with some useful metrics in  metrics/ .

grOptionMetricPath can be configured by assignment in the Maple session or set in your  .mapleinit  file.

GRTensorIII contains a new option variable  grOptionMapletInput  (default  true ). More recent Maple releases have made dialog box input the default mode. The interactive routines in GRTensorIII now use these dialogs by default. If this is not desired, set this option variable to  false . See  ?groptions for a description of all the options for GRTensorIII.

Getting Started

There are multiple approaches to get started with GRTensor:

  • consult the built in help.  ?grtensor  and  ?grt_commands  are a good starting point
  • open one of the sample worksheets in the  worksheets  directory
  • read the PDF docs, typically starting with  grIntro.pdf  in the  docs/  directory.

软件制作界面:

注意,首先设置视频长度(按按帧数设置,比如每秒30帧,共900帧,则一共30秒)

然后按F3开始录制,

在时间轴上将进度条拖动到某一部位,比如300处,再框选局部区域,双击放大,则插入该区域的关键帧。

依此类推,直到末尾。

然后渲染,生成视频,这一步非常耗时。下面的视频一共三十秒,耗时2小时。

不过在这两小时可以做别的事,比如我看完了这本书《Wolfram语言入门》的部分章节,认识到“纯虚函数”的重要性,以及Mathematica中实现流程编程并不方便这一事实。还学到了如何用Mathematica制作声音, 特别有趣!

视频结果:

如何理解四维球体? 十维球体呢?

视频源地址:https://www.youtube.com/watch?v=zwAD6dRSVyI

https://brilliant.org/3b1b尝试基于问题的学习方式! https://www.benbenandblue.com/

特别感谢以下赞助者:http://3b1b.co/high-d-thanks

看看Ben Eater的通道:https://www.youtube.com/user/eaterbc

音乐: 文森特·鲁宾蒂 https://soundcloud.com/vincerubinetti…