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## Main Question or Discussion Point

Hi,

I have a question and I was hoping for some help. The reasoning goes something like this:

There appears to be two fundamental types of coordinates

x - space

t - time

and there appears to be three types of fundamental transformations

- translations

- rotations

- boosts

If we ignore boosts for the moment, then combining these gives four combinations

- space translations

- time translations

- space rotations

- time rotations

Applying Noether's theorem to the first three gives us three fundamental laws of physics

invariance under space translations -> conservation of linear momentum

invariance under time translations -> conservation of energy

invariance under space rotations -> conservation of angular momentum

I guess my question is: If we apply Noether's theorem to invariance under time rotations, how likely is it that we will get another fundamental law of physics?

invariance under time rotations -> conservation of ???

Thanks.

I have a question and I was hoping for some help. The reasoning goes something like this:

There appears to be two fundamental types of coordinates

x - space

t - time

and there appears to be three types of fundamental transformations

- translations

- rotations

- boosts

If we ignore boosts for the moment, then combining these gives four combinations

- space translations

- time translations

- space rotations

- time rotations

Applying Noether's theorem to the first three gives us three fundamental laws of physics

invariance under space translations -> conservation of linear momentum

invariance under time translations -> conservation of energy

invariance under space rotations -> conservation of angular momentum

I guess my question is: If we apply Noether's theorem to invariance under time rotations, how likely is it that we will get another fundamental law of physics?

invariance under time rotations -> conservation of ???

Thanks.