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The Quantum Theory of Laundry


(Thanks to Alex Kruppa for this link.) At last! Dr. Brian Reardon's QTL page* details a rigorous theoretical framework that explains the following formerly mysterious phenomena: The above site also many provides practical guidelines (some quite counterintuitive) for all users of modern automatic laundry equipment. It explains:
* - Dr. Reardon's original page seems to have vanished from the web, so I present a cached copy below. My annotations are in the form [annotation] :
Laundry: A Quantum Mechanical Approach

Laundry: A Quantum Mechanical Approach
by: Brian J. Reardon


Introduction

It has been argued that the act of doing laundry followed the discovery of clothing by only a few weeks. While this fact has been regarded to be fantastically trivial, one can not ignore the enigmas that the act of doing laundry has created. This is especially true in the age of high speed washers and dryers. In the early days, the disappearance of articles of clothing could simply be accounted for by saying that the sock was lost in the river. Unfortunately, such excuses can no longer be used today. The availability of high speed automated washers and dryers has provided a number of fundamental questions that can not be answered using the classical laundry theory (i.e.: the river washed the sock away). Such questions include:

The inability to answer these questions using the classical theory of laundry resulted in the development of new theories.

This paper is a simple introduction to the quantum theory of laundry. As a result, it only deals with the simplest example in which a sock is analyzed in either a washer or a dryer. The mathematics involved in the analysis of a sock in both a washer and dryer and in transition between the two is left for more advanced laundry courses.

The first modern attempt to explain the fundamental questions of laundry involved the decay theory. The decay theory states that the quantity of socks in a load can be expressed as a decreasing exponential function of time which is analogous to radioactive decay (see equation 1).

Nt = N0*exp(-pt).    (1)

The decay theory easily explains the origin of lint and why new socks tend to release more lint than old socks. However, according to this theory, socks should never completely disappear, or, more importantly, reappear. This clearly contradicts everyday experience.

The Quantum Theory of Laundry

The quantum theory of laundry (QTL), however, can explain the fundamental questions of laundry. The QTL is base on three intuitive assumptions.

These assumptions can be mathematically manipulated to provide a number of functions and conditions which are in close correspondence to quantum theory.

Using these assumptions, a general form of the wave function for the sock in the washer can be inferred. This function is identical to the standard solution to the Schrödinger Wave Equation (SWE) and can be expressed as two partial derivatives of time and space.

-h22Yih∂Y


+ V(x,t) =

    (4)
8mπ22x∂t

The sock wave functions that satisfy the SWE can take three forms that represent the three different possible places the sock can reside within the washing system. The entire system can be pictured as an infinite potential energy well that contains a finite energy barrier. The main washing compartment is represented as a potential well (5), the washing system is represented by the potential barrier (6), and the lint trap is represented by another, but narrower, potential well (7).

Y1(x,t) = A*sin(kx-wt) + B*cos(kx-wt)    (5)

Y2(x,t) = E*exp(-Fx-ut)    (6)

Y3(x,t) = C*sin(kx-wt) + D*cos(kx-wt)    (7)

Where, the constants A, B, C, D, E, and F, are material properties of the sockand washer system and w, k, and u are cyclic properties of the postion of the sock within the washer.

The QTL explains the fundamental of problems of laundry in a very direct manner. The origin of lint can now be defined as the sum of probabilities that a sock traveled or tunneled through the washing system into the lint trap. The sock tunneling phenomenon is analogous to the electron tunneling phenomena in quantum mechanics. The occasional presence of large quantities of lint is easily explained by the real likelihood that entire socks can spontaneously take on the wave function of the lint trap.

The QTL also explains that socks never actually disappear. Quite simply, at the time of disturbance or stopping of the machine they have a wave function that puts them temporarily in the washing system or completely converts them to lint.

Furthermore, if a machine is disturbed during a subsequent washing cycle there is a finite probability that a sock lost in previous cycles may reappear in the main washing compartment. This explains the appearance of other people's sock in your wash.

Lastly, the disappearance of entire loads can be explained by the existence of the finite probability that all of the socks in the main compartment have taken on the wave function of the lint trap and subsequently turned to lint. This further implies that instead of accusing someone of stealing your socks, running the machine while empty for long periods of time will increase the chances of retrieval of most of the socks.

While the current implications the QTL seem extraordinary, the far reaching implications may redefine laundromat etiquette for centuries to come.


Last modified: August 19, 1997
Keeper of the page: / Brian J. Reardon

http://mersenneforum.org/mayer/qtl.html -- Last Revised: 21 May 2005
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