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As far as I remember, the above-mentioned statement in L-L's book takes place in the first volume thus regarding classical mechanics.

Even if I dislike Landau-Lifschitz' approach, the requirements of homegeneity and isotropy of the space uniquely determine the inertial reference frames in classical mechanics.

That is because

(a) inertial forces are both homogeneous and isotropic only in those reference frames, as they vanish there;

(b) the remaining general dynamical laws are already homogeneous and isotropic in the inertial reference frames.

Homogeneity and isotropy of space in dynamics means the following in practice.

Consider an isolated (sufficiently far from the other bodies of the universe) mechanical system made of an arbitrary number of interacting bodies.

Prepare it with some initial conditions and record the dynamical evolution of the parties of the system with a fixed camera.

Next prepare a similar experiment with initial conditions translated (homogeneity) and/or rotated (isotropy) and perform the same action on the position of the camera.

Finally, compare the recorded movies: it turns out that you cannot distinguish them.

This happens only in inertial reference frames. If you try to do the same in non-inertial ones, you get different movies even if the dynamical systems are identical (including the interactions). That is because the apparent forces act differently in different places of the space (translated and/or rotated with respect to the initial ones).

Inertial reference frames posses also a further property: time homogeneity. The practical explanation is similar to the one above just considering translations in time.

Finally there is a further invariance property related to the boost translations, but it changes the (inertial) reference frame.

(As is well known, each of these (3+3+1+3=10 scalar) symmetries implies the existence of a corresponding (scalar) dynamically conserved quantity. But this is another story.)

Passing to more modern formulations, like special and general relativity, the issue becomes much more delicate in view of the notion of rest frame with an observer which should deserve a deeper discussion.

As far as I remember, the above-mentioned statement in L-L's book takes place in the first volume thus regarding classical mechanics.

Even if I dislike Landau-Lifschitz' approach, the requirements of homegeneity and isotropy of the space uniquely determine the inertial reference frames in classical mechanics.

That is because

(a) inertial forces are both homogeneous and isotropic only in those reference frames, as they vanish there;

(b) the remaining general dynamical laws are already homogeneous and isotropic in the inertial reference frames.

Homogeneity and isotropy of space in dynamics means the following in practice.

Consider an isolated (sufficiently far from the other bodies of the universe) mechanical system made of an arbitrary number of interacting bodies.

Prepare it with some initial conditions and record the dynamical evolution of the parties of the system with a fixed camera.

Next prepare a similar experiment with initial conditions translated (homogeneity) and/or rotated (isotropy) and perform the same action on the position of the camera.

Finally, compare the recorded movies: it turns out that you cannot distinguish them.

This happens only in inertial reference frames. If you try to do the same in non-inertial ones, you get different movies even if the dynamical systems are identical (including the interactions). That is because the apparent forces act differently in different places of the space (translated and/or rotated with respect to the initial ones).

Inertial reference frames posses also a further property: time homogeneity. The practical explanation is similar to the one above just considering translations in time.

Finally there is a further invariance property related to the boost translations, but it changes the (inertial) reference frame.

(As is well known, each of these (3+3+1+3=10 scalar) symmetries implies the existence of a corresponding (scalar) dynamically conserved quantity. But this is another story.)

Earth's frame is not inertial so that it is not a problem.

Passing to more modern formulations, like special and general relativity, the issue becomes much more delicate in view of the notion of rest frame with an observer which should deserve a deeper discussion.

As far as I remember, the above-mentioned statement in L-L's book takes place in the first volume thus regarding classical mechanics.

Even if I dislike Landau-Lifschitz' approach, the requirements of homegeneity and isotropy of the space uniquely determine the inertial reference frames in classical mechanics.

That is because

(a) inertial forces are both homogeneous and isotropic only in those reference frames, as they vanish there;

(b) the remaining general dynamical laws are already homogeneous and isotropic in the inertial reference frames.

Homogeneity and isotropy of space in dynamics means the following in practice.

Consider an isolated (sufficiently far from the other bodies of the universe) mechanical system made of an arbitrary number of interacting bodies.

Prepare it with some initial conditions and record the dynamical evolution of the parties of the system with a fixed camera.

Next prepare a similar experiment with initial conditions translated (homogeneity) and/or rotated (isotropy) and perform the same action on the position of the camera.

Finally, compare the recorded movies: it turns out that you cannot distinguish them.

This happens only in inertial reference frames. If you try to do the same in non-inertial ones, you get different movies even if the dynamical systems are identical (including the interactions). That is because the apparent forces act differently in different places of the space (translated and/or rotated with respect to the initial ones).

Inertial reference frames posses also a further property: time homogeneity. The practical explanation is similar to the one above just considering translations in time.

Finally there is a further invariance property related to the boost translations, but it changes the (inertial) reference frame.

(As is well known, each of these (3+3+1+3=10 scalar) symmetries implies the existence of a corresponding (scalar) dynamically conserved quantity. But this is another story.)

Passing to more modern formulations, like special and general relativity, the issue becomes much more delicate in view of the notion of rest frame with an observer which should deserve a deeper discussion.

As far as I remember, the above-mentioned statement in L-L's book takes place in the first volume thus regarding classical mechanics.

Even if I dislike Landau-Lifschitz' approach, the requirements of homegeneity and isotropy of the space uniquely determine the inertial reference frames in classical mechanics.

That is because

(a) inertial forces are both homogeneous and isotropic only in those reference frames, as they vanish there;

(b) the remaining general dynamical laws are already homogeneous and isotropic in the inertial reference frames.

Homogeneity and isotropy of space in dynamics means the following in practice.

Consider an isolated (sufficiently far from the other bodies of the universe) mechanical system made of an arbitrary number of interacting bodies.

Prepare it with some initial conditions and record the dynamical evolution of the parties of the system with a fixed camera.

Next prepare a similar experiment with initial conditions translated (homogeneity) and/or rotated (isotropy) and perform the same action on the position of the camera.

Finally, compare the recorded movies: it turns out that you cannot distinguish them.

This happens only in inertial reference frames. If you try to do the same in non-inertial ones, you get different movies even if the dynamical systems are identical (including the interactions). That is because the apparent forces act differently in different places of the space (translated and/or rotated with respect to the initial ones).

Inertial reference frames posses also a further property: time homogeneity. The practical explanation is similar to the one above just considering translations in time.

Finally there is a further invariance property related to the boost translations, but it changes the (inertial) reference frame.

(As is well known, each of these (3+3+1+3=10 scalar) symmetries implies the existence of a corresponding (scalar) dynamically conserved quantity. But this is another story.)

Passing to more modern formulations, like special and general relativity, the issue becomes much more delicate in view of the notion of rest frame with an observer which should deserve a deeper discussion.

As far as I remember, the above-mentioned statement in L-L's book takes place in the first volume thus regarding classical mechanics.

Even if I dislike Landau-Lifschitz' approach, the requirements of homegeneity and isotropy of the space uniquely determine the inertial reference frames in classical mechanics.

That is because

(a) inertial forces are both homogeneous and isotropic only in those reference frames, as they vanish there;

(b) the remaining general dynamical laws are already homogeneous and isotropic in the inertial reference frames.

Homogeneity and isotropy in dynamics means the following in practice.

Consider an isolated (sufficiently far from the other bodies of the universe) mechanical system made of an arbitrary number of interacting bodies.

Prepare it with some initial conditions and record the dynamical evolution of the parties of the system with a fixed camera.

Next prepare a similar experiment with initial conditions translated (homogeneity) and/or rotated (isotropy) and perform the same action on the position of the camera.

Finally, compare the recorded movies: you cannot distinguish them.

This happens only in inertial reference frames. If you try to do the same in non-inertial ones, you get different movies even if the dynamical systems are identical (including the interactions). That is because the apparent forces act differently in different places of the space (translated and/or rotated with respect to the initial ones).

Passing to more modern formulations, like special and general relativity, the issue becomes much more delicate in view of the notion of rest frame with an observer which should deserve a deeper discussion.

As far as I remember, the above-mentioned statement in L-L's book takes place in the first volume thus regarding classical mechanics.

Even if I dislike Landau-Lifschitz' approach, the requirements of homegeneity and isotropy of the space uniquely determine the inertial reference frames in classical mechanics.

That is because

(a) inertial forces are both homogeneous and isotropic only in those reference frames, as they vanish there;

(b) the remaining general dynamical laws are already homogeneous and isotropic in the inertial reference frames.

Homogeneity and isotropy of space in dynamics means the following in practice.

Consider an isolated (sufficiently far from the other bodies of the universe) mechanical system made of an arbitrary number of interacting bodies.

Prepare it with some initial conditions and record the dynamical evolution of the parties of the system with a fixed camera.

Next prepare a similar experiment with initial conditions translated (homogeneity) and/or rotated (isotropy) and perform the same action on the position of the camera.

Finally, compare the recorded movies: it turns out that you cannot distinguish them.

This happens only in inertial reference frames. If you try to do the same in non-inertial ones, you get different movies even if the dynamical systems are identical (including the interactions). That is because the apparent forces act differently in different places of the space (translated and/or rotated with respect to the initial ones).

Inertial reference frames posses also a further property: time homogeneity. The practical explanation is similar to the one above just considering translations in time.

Finally there is a further invariance property related to the boost translations, but it changes the (inertial) reference frame.

(As is well known, each of these (3+3+1+3=10 scalar) symmetries implies the existence of a corresponding (scalar) dynamically conserved quantity. But this is another story.)

Passing to more modern formulations, like special and general relativity, the issue becomes much more delicate in view of the notion of rest frame with an observer which should deserve a deeper discussion.