What is isotropy: Definition and 5 Discussions

In physics and geometry, isotropy (from Ancient Greek ἴσος (ísos) 'equal', and τρόπος (trópos) 'turn, way') is uniformity in all orientations. Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix a- or an-, hence anisotropy. Anisotropy is also used to describe situations where properties vary systematically, dependent on direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented.

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    I Transformations for isotropy in terms of math

    Probably, my last question about isotropy. This is the last thing that I want to double check. We know that mathematically, passive and active transformation are both the same. In passive, coordinate frame is moved and nothing else, while in active frame, objects are moved and coordinate frame...
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    I Coordinate transformation for isotropy

    The following question struck me by accident. Would appreciate to let me know the flaw in my logic, no need to deviate from this approach. We know that on small-scale, experiment such as dropping ball from some height to the earth tells us that space is non-isotropic, because of preferred...
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    I Inertia/Non-inertial frame - isotropy

    It's known that in inertial frame, space is isotropic. (statement of this where I have taken out of is attached as image) When we talk about an uniform accelerated train, ground frame is considered as inertial frame(at least in newtonian mechanics). So if ground frame is considered such as...
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    I Reference frames in terms of homogenity/isotropy

    Question 1: in the non-inertial frame, space is non-isotropic. If we're in an accelerated train frame, and we face forward(the same direction where train is accelerating) and drop a ball, ball moves backward. If we face backward and repeat the experiment, dropped ball moves forward to us. So we...
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    I Doubts about isotropy of space

    I might have some other questions related to this topic, but I will ask them in further replies. Isotropy of space is explained such as it should look the same in every direction. It's not enough to imagine ourselves to be in the center of the sphere, because definition says that to call space...