Discrete Symmetries
A discrete symmetry is a symmetry that describes non-continuous changes in a system. For example, a square possesses discrete rotational symmetry, as only rotations by multiples of right angles will preserve the square's original appearance. Discrete symmetries sometimes involve some type of 'swapping', these swaps usually being called reflections or interchanges.
- Time reversal: Many laws of physics describe real phenomena when the direction of time is reversed. Mathematically, this is represented by the transformation, . For example, Newton's second law of motion still holds if, in the equation, is replaced by . This may be illustrated by describing the motion of a particle thrown up vertically (neglecting air resistance). For such a particle, position is symmetric with respect to the instant that the object is at its maximum height. Velocity at reversed time is reversed.
- Spatial inversion: These are represented by transformations of the form and indicate an invariance property of a system when the coordinates are 'inverted'.
- Glide reflection: These are represented by a composition of a translation and a reflection. These symmetries occur in some crystals and in some planar symmetries, known as wallpaper symmetries.
Read more about this topic: Symmetry (physics)
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