Pdt

On The Phenomena of Precipitating Poo and Poo Dynamics Theory Anjan Soumyanarayanan∗ Cavendish Laboratory, University of Cambridge Submitted for publication to Reviews of Modern Physics Parodies in September 2005

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Introduction

Classical Poo Dynamics

The work of early physicists considered poo as

Newton’s theory of gravitation [1] was occa-

a rigid kinematic body. The elementary drag

sioned by a memorable incident - the falling of

equation:

bird poo on his head (the anecdote concerning

m¨ x = mg − B x˙

the apple is most certainly apocryphal according to most historians). Since then, such exotic

(1)

where x is the displacement of the poo particle

dynamic phenomena have puzzled experimen-

and B is the drag coefficient, constituted the

talists and theorists alike. The study of these

first physical analysis of the free fall of poo

phenomena evolved through the phases of clas-

(acted on by a drag force due to air). The rate

sical dynamics [2] and fluid mechanics [3]. The

of poo fall was found to depend on the mass of

advent of radical theories over the past century

poo, the surface area and orientation.

that have completely changed our perception of nature has forced the physics community

Further analysis using the Lagrangian and to modify the classical Poo Dynamics Theory Hamiltonian operators revealed that the tra(PDT) in certain extreme conditions. This ar- jectory of poo was such that the total energy ticle reviews the historical development of our of poo to be an extremum. Optimisation techunderstanding of the motion of poo and PDT niques [4] applied on poo fall by introducing in various situations.

various parameters discovered that if the excreting person minimises his effort in the process, the speed of the poo is maximised if the poo is long and thin and has minimal water

∗

content (around 10%).

Correspondence: [email protected]

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When the rigid poo body moves in water, it cakes (in the Bernoulli Limit of constant enthalpy). However, fart emissions were not ex-

obeys Stokes’ Law of drag F = 6πηrv

plained well due to the low viscosity of the

(2)

gaseous methane. The diffusion equation (4)

where η is the coefficient of viscosity of wa- and the Theory of Brownian Motion [7] of fart ter, which increases with increasing amount of gas molecules however proved to be a much poo in water, and r is the dimensional size of better model for this. the poo piece. A vertically oriented poo piece would hence travel much faster than a horizon-

∇2 u =

tal one. The study of nematic liquid crystals

1 ∂v κ ∂t

(4)

[5] draws analogy from these ancient studies of The temperature dependent effects are con-

PDT.

tained in the viscosity term ρ for Equation (3) and in the thermal conductivity term κ

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Poo as a Viscous Fluid

for Equation (4). These terms increase with temperature, and hence the mean square speed shows a corresponding increase.

The study of poo as a fluid began when scientists found that rigid body PDT could not explain the dynamics of diarrhoea, cow dung

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fart emissions. Initially, the studies were lim-

Relativistic Poo Dynamics

ited to hydrostatic effects, but the efforts of many mathematical physicists [6], culminating The Special Theory of Relativity forced us to in the famous Navier-Stokes equation (3), aug- abandon the notion of an absolute frame of refmented poo research. ∂v + ρv · ∇v = −∇P + η∇2 v + Fext ∂t

erence, and hence most problems in PDT were treated in the rest frame of the toilet. Circum-

(3)

stances did arise where poo traveled at rela-

tivistic speeds (close to the speed of light), and Extreme forms of poo were subsequently hence the theory had to be modified to account modeled as a highly viscous fluid (η À 1) and for this. These situations could include shitthe dynamics were studied applying suitable ting in an aeroplane or space shuttle, a man boundary conditions to the problem. The shitting in his pants while running away from a model of a viscous jet from a small source lion, or the emission from a highly constipated was found to explain the dynamics of diar- person upon administration of a laxative. rhoea and cow dung extremely satisfactorily, including the natural formation of round dung

It was instructive in these cases to consider 2

the motion in the rest frame of poo, using the This explains all modern poo observations well beyond our experimental constraints, and is

Lorentz Coordinate Transformations [8] ct0 = γ(ct − βx) x0 = γ(x − βct) y0 = y z0 = z

bound to revolutionise our quantum technol(5) ogy. (6) QPD introduces poo motion that obeys the (7) Heisenberg Uncertainty Relation. A precise (8) measurement of the motion of poo would result in its position being uncertain and vice

Where the relativistic factors

versa. As a result, QPD models nanopoo as a

β =

v c

γ =

p

(9) wavepacket that modulates in space. 1 1 − v 2 /c2

(10)

QPD has revolutionary quantum technology in store for the future. The current R&D in

It was found that a small clock attached to a Quantum Optics can be extended to QPD, and piece of poo was slower than a clock attached to we would soon see the introduction of Quanthe excreting human. The effects were slightly tum Poo Dots and Quantum Poo Wires. modified when experiments were conducted on elephants, as one had to take General Relativistic considerations into account [9].

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The past few centuries have seen the develop-

Quantum

Poo

Dynamics

Conclusion

ment of PDT using classical models, followed

(QPD)

by the incorporation of relativistic and quantum effects. However, the tremendous success

The theory of Quantum Mechanics, established of QPD and potential applications will ensure in 1926 following the Copenhagen Interpre- that in the future, poo will be much more than tation introduces an inherent uncertainty in just a pile of shit. measurements on the nanoscale. This has resulted in modifications to PDT. The advent of Quantum Electrodynamics (QED) and perspi-

References

cacious efforts by numerous theorists (mostly confined to the realms of their toilets) has resulted in the establishment of the infalli-

[1] I. Newton. Principia Mathematica. The

ble Quantum Poo Dynamics (QPD) [10, 11].

Royal Society Press, 1708. 3

[2] P.T. Jackson. The Complete Works of Euler, Lagrange and Hamilton. Oxford University Press, 1832. [3] G.K. Batchelor. An Introduction to Fluid Dynamics. Cambridge University Press, 1998. [4] G.W. Leibnitz. Optimising Poo Fall using Differential Methods. Eur. Phys. Mag. 23 (1701) 27. [5] P.M. Chaikin and T.C. Lubensky. Principles of Condensed Matter Physics. Addison-Wesley 1996. [6] G.G. Stokes. On the dynamics of nonviscous Newtonian Fluids. Proc. Roy. Soc. London 42 (1854) 71. [7] A. Einstein. Auf der Brownschen Bewegung der kleinen Scheißepartikel. Annalen der Physik 19 (1908) 328. [8] A. Einstein. Zur Elektrodynamik bewegter K¨orper. Annalen der Physik 17 (1905) 639. [9] W. Rindler. Relativity:

Special, Gen-

eral and Cosmological. Oxford University Press, 2001. [10] R.P. Feynman QPD: The Strange Theory of Quantum Poo and Energy. Addison Wesley 1974. [11] S. Weinberg. The Quantum Theory of Fields. Cambridge University Press, 1995.

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