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Question:

Quartz crystals and other gemstones ?

Is there any scientific evidence that these eminate energy, such as for healing or psychic abilities ?

Answer:

Supply pulses of predetermined oscillations.
It's called the piezoelectric effect. When pressure is applied to a piezoelectric crystal like quartz, it creates a charge displacement which equates to a voltage. Oppositely, if you apply a voltage to it it will strain. Mechanically, if you strain something then let it go quickly or if you quickly strain something, it will vibrate at a frequency determined by the material (not quite the same as a pipe or a string, since the pipe vibrations depend on the shape and the string depends on the length and tension). The vibrations of quartz are very well documented and very consistent, and its consistent vibration can be used to time electronic transitions or mechanical motions.

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