Coming down to Earth with Physics

Posted on by Chris Warburton
I read a blog post today where the writer imagined future computers being capable of unlimited calculations, storage, etc.

To quote the author: "Electricity and other force waves can be ?on? or ?off?, but they also have lots of other properties, many of which are sufficient to represent an infinity (or near-infinity). Frequency of any wave represents an infinity, for example?you can have a 1 Hz wave, a 1.1 Hz wave, a 1.15 Hz wave, a 1.151 Hz wave, etc.".

Disregarding the nonsense term "near-infinity", here an assumption has been made that waves have a continuous spectrum of frequencies, so that another decimal can always be added and allow ten times the number of frequencies to be used. Is this assumption valid? Physics says no. The frequency of a wave is equal to the energy of the wave divided by Planck's constant (f = E/h). Since Planck's constant is constant, for a wave to have a continuous spread of frequencies it must have a continuous spread of energies. Quantum mechanics shows us that energy occurs only in certain quantities ("quantity" making it "quantum"), for a very simple example see the quantum harmonic oscillator.

The author also states "the fact that waves take up essentially no space (only the medium that they vibrate takes up space)." To me this represents a complete misunderstanding of what a wave actually is. Wikipedia defines a wave as:

"A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium (which on deformation is capable of producing elastic restoring forces), waves of electromagnetic radiation (and probably gravitational radiation) can travel through vacuum, that is, without a medium. Waves travel and transfer energy from one point to another, often with little or no permanent displacement of the particles of the medium (that is, with little or no associated mass transport); instead there are oscillations around almost fixed locations."

Notice that two contradictions to the blog author appear here. Firstly the definition includes, straight away, the word space. Without space there are no waves. Secondly waves do not necessarily need a medium to exist in. A wave is not an entity of itself, it is an abstract concept which describes the oscillation of something.

Add to this the fact that analogue systems (ie. continuous valued measurables) suffer from noise in a non-recoverable way (unlike digital systems), which makes your measuring device limited to its resolving power, which once again is limited thanks to the effect of apertures (the smaller the worse, by the way, making smaller spaces less distinguishable), and this whole concept, whilst initially sciencey-sounding, is unfortunately a no-starter.