Homogeneity and isotropy of space and time

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Discussion Overview

The discussion centers on the concepts of homogeneity and isotropy of space and time, exploring their definitions and implications within the context of mechanics and physical laws. Participants examine these properties theoretically, with a focus on their meanings and applications in dynamical systems.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that homogeneity of space implies that the results of a closed dynamical system are independent of the location where the motion occurs.
  • Homogeneity of time is suggested to mean that the evolution of a mechanical system is unaffected by the specific time indicated on a clock.
  • Isotropy in space is described as the property that allows an isolated system to yield the same experimental outcomes regardless of its orientation.
  • One participant hypothesizes that isotropy of time could relate to time-reversal symmetry, suggesting that a universe with reversed temporal events could still follow the same physical laws.
  • Another participant notes that while time-reversal symmetry is a concept, many physical processes do not exhibit this symmetry.

Areas of Agreement / Disagreement

Participants express varying interpretations of isotropy in the context of time, with some uncertainty regarding its application. There is no consensus on the implications of time-reversal symmetry, as some argue for its existence while others point out exceptions.

Contextual Notes

Participants acknowledge limitations in their definitions and understanding, particularly regarding the application of isotropy to time and the existence of time-reversal symmetry in various physical processes.

quasar987
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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!
 
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quasar987 said:
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.
 
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.
 
quasar987 said:
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.
 
Last edited:
thx for your Q&A!
 

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