A rose by any name
There is something amiss in the very way the idea of square root was named. This led to difficulties, some of which were swept under the carpet, others simply passed unnoticed. The first sign of trouble may have come when someone asked the question, “What then is the square root of -1?” This was an embarrassment on the way to becoming a full-blown debacle.
Based as it is on the number line it would better have been named “line root,” or “linear root,” or “1-dimension root” possibly. But “square root” is a misnomer and worse. Were it just a question of a wrong name involved we could simply accept the trival consequences and move on. But this is a misnomer with non-trivial consequences which makes it more like a serious mistake.
Next we will look more closely at how the younger algebraic square challenged the old geometric square and seized the power of the crown in the 1550s, taking exclusive ownership of the mathematical term “square root.” Algebra and all its successes notwithstanding, this choice of name set mathematics and physics on an illegitimate trajectory from which they have not yet recovered. The unfortunate consequences of this turn of events will be examined as well as a prescription for a corrective. It is a drama of epic Shakespearean dimension.
Sound amplification by stimulated emission of radiation
SASER is a device capable of emitting acoustic radiation. Acoustic radiation (sound waves) can be emitted by using the process of sound amplification based on stimulated emission of phonons. Sound (or lattice vibration) can be described by a phonon just as light can be considered as photons and therefore one can state that SASER is the acoustic analogue of the laser. In a – sound amplification by stimulated emission of acoustic radiation − device, a source (e.g. an electric field as a pump) produces sound waves (lattice vibrations, phonons) which travel through an active medium. In this active medium, a stimulated emission of phonons takes place which leads to amplification of the sound waves resulting in a sound beam coming out of the device. The sound wave beams emitted from such devices are highly coherent which briefly means that they have a zero phase difference.
Image: The structure of a superlattice of semiconductor layers (AlAs, GaAs). Acoustic waves undergo amplification. Click image for license details.
We all learn in high school science about the dual nature of light — that it exists as both waves and quantum particles called photons. It is this duality of light that enables the coherent transport of photons in lasers. Sound at the atomic-scale has the same dual nature, existing as both waves and quasi-particles known as phonons. Does this duality allow for phonon-based lasers? Some theorists say yes, but the point has been argued for years. Recently a large collaboration, in which Berkeley Lab scientists played a prominent role, provided the first “unambiguous demonstration” of the coherent transport of phonons. [ScienceDaily]