Homogeneity and isotropy of space and time

In summary, Landau's Mechanics and the book on waves and oscillation discuss the properties of space and time being homogeneous and isotropic. Homogeneity refers to the idea that the outcome of a closed dynamical system will be the same regardless of where it takes place or what time it occurs. Isotropy means that space and time are the same in all directions, allowing for experiments to be rotated without affecting the outcome. Additionally, the concept of time-reversal symmetry is mentioned, where a universe with the same physical laws as ours could exist but with time moving in the opposite direction.
  • #1
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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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 
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  • #5
thx for your Q&A!
 

1. What is the concept of homogeneity in space and time?

Homogeneity refers to the uniformity or sameness of a physical property in a given space or time. In the context of space and time, it means that the properties of space (such as density or curvature) and the passage of time are consistent and do not vary in different regions or at different times.

2. What is the significance of homogeneity and isotropy in the study of the universe?

Homogeneity and isotropy are important concepts in cosmology, the study of the universe. They serve as the basis for the cosmological principle, which states that the universe is uniform and consistent on a large scale. This principle is crucial in developing models of the universe and understanding its evolution.

3. How do scientists test for homogeneity and isotropy in space and time?

Scientists use various observational methods, such as measuring the distribution of galaxies or the cosmic microwave background radiation, to test for homogeneity and isotropy in space. They also use precision instruments to measure the passage of time and look for any variations or patterns that may indicate a violation of homogeneity and isotropy.

4. Are there any known violations of homogeneity and isotropy in space and time?

So far, there have been no major violations of homogeneity and isotropy in the observable universe. However, on a smaller scale, there are some variations and structures in the universe, such as galaxy clusters and filaments, that may suggest slight deviations from perfect homogeneity and isotropy.

5. What are the implications of a non-homogeneous or anisotropic universe?

A non-homogeneous or anisotropic universe would challenge our understanding of the universe and its fundamental laws, such as the laws of gravity and thermodynamics. It could also have significant implications for our understanding of the Big Bang theory and the evolution of the universe. However, most current evidence supports the notion of a homogeneous and isotropic universe on a large scale.

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