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Crystals of Time

Crystals of Time

Dimensional progressions grow across a spectrum that we describe beginning with points, then lines, then planes, and finally volumes. Time appears to us to be linear, so we call it 1-dimensional. Space appears to us to be mostly volume-like so we call it 3-dimensional. Many areas of geometry, algebra and more fields of science exhibit properties known as levels or types of symmetry. Simple geometric symmetries involve reflections and rotations that don’t change the properties of an object. More complex but similar symmetries have been noted in mathematical operations and projection transformations in physics.

If symmetries are built into the raw fabric of the time-space continuum, then it could make sense to expect to find them in time as well as space. A respected physicist has suggested that they do exist in time and may have properties similar to the way space and matter seem to use symmetries to form crystals.

Crystals may be possible in time as well as space – [sciencenews.org]

In two new papers, Nobel Prize–winning physicist Frank Wilczek lays out the mathematics of how an object moving in its lowest energy state could experience a sort of structure in time. Such a “time crystal” would be the temporal equivalent of an everyday crystal, in which atoms occupy positions that repeat periodically in space.

Physicists Predict The Existence of Time Crystals – [technologyreview.com]

If a system produces the same result regardless of when it takes place, it must obey the law of conservation of energy.

We have the German mathematician, Emmy Noether, to thank for this powerful way of thinking. According to her famous theorem, every symmetry is equivalent to a conservation law. And the laws of physics are essentially the result of symmetry.

Equally powerful is the idea of symmetry breaking. When the universe displays less symmetry than the equations that describe it, physicists say the symmetry has been broken.

A well known example is the low energy solution associated with the precipitation of a solid from a solution—the formation of crystals, which have a spatial periodicity. In this case the spatial symmetry breaks down.

Spatial crystals are well studied and well understood. But they raise an interesting question: does the universe allow the formation of similar periodicities in time?

Dimensionality is not Digital
1872 – Erlangen Program
1887 – E8

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