The extend of independence is the very thing that all scholars have to handle. A lack of independence can cause parroting and too much of it will lead to a break-away from academic society. Yet science needs an academic society to recognize the works, and thus most scientists choose being more docile for academic safety. This functions, but it brings about another problem. If all scientists conduct that way, the progress can be quite slow, since everybody has to step little enough.

Therefore, some scholars choose to be more independent. But this takes risks. It is not so hard to propose breaking views. Nonetheless, a large portion of them can not be supported by scientific facts and society. Halfhearted denial of previous scientific works is a disrespect of science. We have seen lots and lots of failures in the way towards independence, so much that it is now even claimed to be dangerous. However, we also believe that this kind of danger can be avoided by certain means.

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Recently I came across several elucidations about symmetry and conservation laws, within which numerous errors occur. So I write this post to make some clarifications.

Before proceeding this, we need to retrospect the famous Noether’s Theorem:

Every continuous symmetry of theory corresponds to a conservation law.

We hope you can recite every word carefully before reading the following content, since this is a mathematical theorem and no mathematical statements contain redundant words.

Symmetry of Matter and Conservation Law

There are no direct links between symmetry of matter field and conservation laws

The relationship between matter field and conservation law is one of the leading fallacies in Physics. The correspondence of symmetry and conservation laws has been introduced widely in physical courses. However, Continue reading →