Homogeneity and isotropy of space and time

[quasar987]

Landau's Mechanics and also a cranky book on waves & oscillation I read some time ago talks about space and time being homogeneous and isotropic.

I assume that the homogeneous property of space means that it does not matter where the motion of a closed dynamical system unfolds, the result will be the same.

Homogeneity of time means that given a certain state of a mechanical system, it does not matter what time your clock shows, the unfolding will be the same.

As for isotropic, I know it means "same in all direction" but what does that means specifically in terms of space and times?

Also, feel free to correct or put in more formal terms my definition of homogeneity of space and time.

thx!

 

[Gokul43201]

As for isotropic, I know it means "same in all direction" but what does that means specifically in terms of space and times?

When you say "space is isotropic" it means you can take the isolated system you are performing the experiment on and rotate it through an arbitrary angle, and the outcome of the experiment would be unchanged.

 

[quasar987]

And for time... it could be referring to the fact that given a mechanical system evolving in time. If the time arrow would be reversed, we would not notice. There could be a universe with the same physical laws as ours, in which everything that happens to us happens to them but in the reverse order.

 

[Gokul43201]

And for time... it could be referring to the fact that given a mechanical system evolving in time.

I have not come across the term 'isotropic' used in the context of time alone. But there is such a thing as a time-reversal symmetry, as you've hypothesized above. Many physical processes however, do not exhibit such a symmetry.

 

[gispiamp]

thx for your Q&A!