Can Isotropy of Time Lead to New Conservation Laws in Landau's Mechanics?

[zerokool]

In Landau's Mechanics he derives the three conservation laws of energy, linera momentum and angular momentum from three principles respectivly: homogeneity of time, homogeneity of space and isotrophy of space

To complete the symmetry could there be a law derived from the isotrophy of time?

 

[voko]

There is no such thing as "isotrophy". The word is "isotropy", which means that all the ways (orientations) are equal. Time, unlike space, is one-dimensional, so the concept is simply inapplicable.

 

[zerokool]

Thanks for the speling lesson.

I know what isotrophy means. Please assume the person asking the question know what the terms they are using mean. I don't want to feel insulted when I come here and you may not know how much I've thought about my question.

 

[voko]

Thanks for the speling lesson.

I know what isotrophy means.

You have been told, it means nothing. Insisting on your mistakes won't get you anywhere.

Please assume the person asking the question know what the terms they are using mean. I don't want to feel insulted when I come here and you may not know how much I've thought about my question.

I have addressed the essence of your question. You have chosen to pay attention only to the note on grammar. This is not productive.

 

[Dale]

Please assume the person asking the question know what the terms they are using mean.

We generally do assume that unless there is evidence to the contrary. In this case, voko correctly pointed out that the term you are using is inapplicable to the context in which you are using it. You need at least two dimensions for the term "isotropy" to apply and time has only one dimension.

The question itself indicates that you didn't know the meaning of the terms you were using, so voko correctly explained. That is the purpose of the forum, to help educate people on scientific concepts. It isn't an insult to be instructed in something you don't know or corrected in a mistake, that is just education.

 

[zerokool]

I was here raising a question to stimulate discussion. Do you think I can't bring up points you will have difficulty answering? You see, with deep thinking and experience comes the humility that knowledge of anything like physics is a complicated and complex affair. And if you probe deeply you find many difficult questions that are not easy to answer.

I am a Buddhist monk and part of a living debate tradition going back thousands of years. My training is in probing deeper and deeper and hitting on one point until one reachs a point where the surface answer is no longer clear. Easy questions have easy answers, deep questions have deep answers.

In terms of credentials I have a BS in physics and an MS in maths. I taught HS physics for four years. I've challenged physics professors who could only answer by telling me I was wrong without any proof.

@Voko, before you go around insulting my level of thinking compare your answer in the "Lagrangian equation of motion" post. You did not even understand what the poster mean by kinetic energy being independent of position yet I did and I even mentioned the section of Landau where you could read more on this. If you had read Landau's Mechanics or actually understood the basics of the Lagrangian you would have seen this is what the poster was asking. So yeah I guess I know a little physics.

I know that time is only is only one dimensional. I know you need at least two dimentions to define a rotation which is how you can derive conservation of angular momentum via isotropy of space.

My question is still not answered as far as I'm concerned.

 

[Dale]

I was here raising a question to stimulate discussion.

The purpose of this forum is for education on existing mainstream physics, not for discussion of new physical theories. The only answers which are possible within the rules of this forum have already been given: the term isotropy is simply inapplicable in the context of your question.

 

[D H]

The only answers which are possible within the rules of this forum have already been given: the term isotropy is simply inapplicable in the context.

Another way to look at it: Homogeneity does not necessarily imply isotropy for a multidimensional space, but it does for a one dimensional space. If a one dimensional space is homogeneous it is also isotropic, and vice versa.