View source for The Effect of Ordered Air Molecules on a Tumbling Cube

{{Infobox paper
| title = The Effect of Ordered Air Molecules on a Tumbling Cube
| url = [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_1289.pdf Link to paper]
| author = [[Jean E Burns]]
| keywords = [[Mental effects]], [[Uncertainty]], [[Randomness]], [[Tumbling cube]]
| published = 2002
| journal = [[Noetic Journal]]
| volume = 3
| number = 4
| num_pages = 13
| pages = 330-339
}}

'''Read the full paper''' [http://www.naturalphilosophy.org/pdf/abstracts/abstracts_1289.pdf here]

==Abstract==

A quantitative theory of the effects of mental influence outside the body, based on the idea that such influence consists of the ordering of random fluctuations within the limits of the uncertainty principle, is used to predict the effects of ordered air molecules on a tumbling cube. If the influence can act throughout the first tumble of a cube, the pressure necessary to produce the deviation effects achieved by Forwald (1959, 1969) is estimated to be 1.45 x 10<sup>-5</sup> dyne/cm<sup>2</sup>. The number of molecules which must be simultaneously influenced to produce this pressure is 2.41 x 10<sup>5</sup>. The trajectory of a tumbling cube must have a minimum number of steps s<sub>0</sub> in order for any substantial amount of magnification of a change in its trajectory to occur. (A step is a tumble from one corner to another.) When mental effects are produced by ordered molecules, s<sub>0</sub> depends logarithmically on cube parameters (mass, length of a side, velocity), the pressure of the surrounding gas, and the number of molecules a person can simultaneously influence. If a cube of mass M and half-length b is compared to a cube with mass M<sub>1</sub> and half-length b<sub>1</sub>, and all other parameters are constant, then s<sub>0</sub>(M,b) - s<sub>0</sub>(M<sub>1</sub>,b<sub>1</sub>) = log<sub>2</sub>(Mb<sub>1</sub><sup>2</sup>/M<sub>1</sub>b<sup>2</sup>). If different numbers of cubes n and n<sub>1</sub> are influenced, with all other parameters constant, then s<sub>0</sub>(n) - s<sub>0</sub>(n<sub>1</sub>) = log<sub>2</sub>(n/n<sub>1</sub>). If values for s<sub>0</sub> are compared at pressures P and P<sub>1</sub>, with all other parameters constant, then s<sub>0</sub>(P) - s<sub>0</sub>(P<sub>1</sub>) = log<sub>2</sub>(P<sub>1</sub>/P).

==Overview==

Jean E Burns' paper is the third instalment of a linked series (Burns 2002a, 2002b and the present work) that attempts something unusual in parapsychology: to make the psychokinesis (PK) hypothesis '''quantitative''' and therefore falsifiable, rather than leaving it as an unbounded claim. The physical setting is deliberately mundane — a cube tumbling down a ramp and across a surface, i.e. a die — because the classic experiments of Haakon Forwald (1959, 1969) used exactly that arrangement and reported systematic sideways deviations of the endpoint.

Burns' starting premise is that if mental influence exists at all, it must operate inside the latitude physics already allows, and the only such latitude is the [[Uncertainty Principle|uncertainty principle]]. Adopting the stochastic interpretation of [[Quantum mechanics|quantum mechanics]], in which all objects are subject to fluctuations bounded by ''δx δp''<sub>''x''</sub> = ''ħ''/2, she supposes that mental influence does not add energy but merely '''selects''' the most favourable fluctuation within those bounds — an ordering of randomness rather than a force. The paper then asks a purely mechanical question: given that budget, is the observed deviation of a tumbling cube achievable, and if so by what route?

The answer distinguishes the paper sharply from the earlier literature. Burns concludes that the route proposed by Evan Harris Walker (1975) — shifting the cube itself within the uncertainty limits appropriate to its own macroscopic mass — '''fails''' by a factor she computes explicitly, and that a different mechanism, the ordering of surrounding air molecules, is required. Rather than defending a favoured hypothesis she eliminates one, and derives testable scaling laws for the survivor.

==The argument==

===Quantum fluctuations as the available budget===

Under the stochastic interpretation (Chebotarev 2000; de la Peña and Cetto 1996; Jammer 1974), root-mean-square displacements and momentum changes obey ''δx'' = (''ħt''/''m'')<sup>1/2</sup> and ''δp''<sub>''x''</sub> = ½(''ħm''/''t'')<sup>1/2</sup>, where ''t'' is elapsed time and ''m'' the mass of the object. Burns notes that the fractional change in momentum and in energy both scale as ''t''<sup>−1/2</sup>, "so energy and momentum are conserved when ''t'' is large" — the mechanism is therefore not a hidden energy source. The crucial feature for what follows is the ''m''<sup>−1/2</sup> dependence of ''δx'': a molecule is enormously easier to nudge than a five-gram cube.

===Dynamics of the tumbling cube===

From the earlier paper (Burns 2002b), a small shift ''Δθ'' in the cube's initial angular orientation produces an average endpoint deviation ''ΔY'' = ''a''(''s'' − ''s''<sub>0</sub>), where ''a'' is the average sideways step length per tumble, ''s'' the total number of steps, and ''s''<sub>0</sub> = log(''π''/3''Δθ'')/log 2 is the minimum number of steps before any substantial magnification appears. The magnification is exponential — this is a chaotic amplification argument, and ''s''<sub>0</sub> is where the exponential finally clears the noise. For a cube of half-length ''b'' with forward velocity ''u'', the time for one tumble is ''τ''<sub>cube</sub> = 2''πb''/3''u'', and the forward distance is ''X'' = √3 ''bs''.

===Ruling out the macroscopic-mass shift===

If the cube of mass ''M'' is shifted directly within its own uncertainty limits, the angular shift over one tumble is ''Δθ''(''τ''<sub>cube</sub>) = (1/√3''b'')(''ħτ''<sub>cube</sub>/''M'')<sup>1/2</sup>. Forwald's cubes had ''M'' = 5 g and ''b'' = 0.8 cm; Burns takes the early-trajectory velocity as ''u'' = 100 cm/sec (noting that since ''s''<sub>0</sub> depends on the log, doubling or halving ''u'' changes it by only half a step). This gives ''τ''<sub>cube</sub> = 1.676 × 10<sup>−2</sup> sec, ''Δθ'' = 1.356 × 10<sup>−15</sup> radians, ''s''<sub>0</sub> = 49.4 steps, and a required forward travel of ''X''<sub>0</sub> = 68.5 cm.

Forwald's cubes travelled about 15 cm down a ramp plus 35 cm across a horizontal surface — 50 cm in total — and showed deviations of roughly 5 cm. Since 50 cm is well short of the 68.5 cm needed, Burns concludes that Walker's mechanism "cannot account for Forwald's experimental results", and that anecdotal "lucky" dice results occurring over even shorter distances make the problem worse. She is careful to credit Walker nonetheless: he was the first to see that a tumbling cube could exponentially magnify a tiny initial perturbation, and among the first to propose that mental influence acts within uncertainty-principle limits; his dynamical analysis "was simply too rough to show accurately the minimum distance of travel needed."

===Ordered air molecules as the alternative===

A freely travelling molecule whose momentum components fluctuate within uncertainty limits has those changes magnified by its next collision, so that after one mean free path its direction of travel can be anything (Burns 1998, 2002a) — the same mechanism she elsewhere invokes to account for [[Entropy|entropy]] increase. Ordering that redirection is therefore enough to bias molecules toward a surface and raise the pressure on it. Because the randomisation is continuous, each molecule must be influenced over its whole mean free path, and because a terminal collision is needed to magnify the change, twice as many molecules must be influenced as are ordered.

The excess pressure ''ΔP'' is given (Burns 2002a) by a relation proportional to ''N''<sub>''I''</sub>''Pσ''/''A'', where ''N''<sub>''I''</sub> is the number of simultaneously influenced molecules, ''P'' the ambient pressure, ''σ'' the molecular cross section and ''A'' the area the pressure acts on. (The exact numerical coefficient does not survive text extraction from the PDF and is not reproduced here.) If several objects are influenced at once, ''A'' is their total cross-sectional area, so ''A'' = ''nA''<sub>cube</sub> for ''n'' cubes. This pressure acts on the skew cross section (2''b'')(2√3''b'') of the tumbling cube, giving a torque ''L'' = ''ΔP A''√3''b'' about the corner, with moment of inertia ''I'' = 4''Mb''<sup>2</sup>. Assuming an exponentially decaying influence ''ΔP'' = ''ΔP''<sub>0</sub>exp(−''t''/''τ''<sub>''I''</sub>) with time constant ''τ''<sub>''I''</sub>, and noting that only the first few steps matter so that ''τ''<sub>''I''</sub> ≤ ''τ''<sub>cube</sub>, she obtains ''Δθ''(''τ''<sub>cube</sub>) = 2''πΔP''<sub>0</sub>''τ''<sub>''I''</sub>''b''<sup>2</sup>/''Mu'' and hence a closed expression for ''s''<sub>0</sub> in terms of ''Mu''/''b''<sup>2</sup>''ΔP''<sub>0</sub>''τ''<sub>''I''</sub>.

===The numbers===

Forwald's results correspond to ''s''<sub>0</sub> ≈ 29 ± 2 steps, i.e. ''X''<sub>0</sub> = 40 ± 3 cm. Inverting, ''ΔP''<sub>0</sub> = 2.42 × 10<sup>−7</sup>/''τ''<sub>''I''</sub> dyne/cm<sup>2</sup>; the ±2-step range multiplies or divides this by 4. Setting ''τ''<sub>''I''</sub> = ''τ''<sub>cube</sub> = 1.67 × 10<sup>−2</sup> sec gives ''ΔP''<sub>0</sub> = 1.45 × 10<sup>−5</sup> dyne/cm<sup>2</sup>, range 3.62 × 10<sup>−6</sup> to 5.79 × 10<sup>−5</sup>. Forwald released six cubes per trial, and with ''σ'' = 1.98 × 10<sup>−16</sup> cm<sup>2</sup> and atmospheric ''P'' = 1.103 × 10<sup>6</sup> dyne/cm<sup>2</sup>, the minimum number of molecules is 2.41 × 10<sup>5</sup>, range 6.02 × 10<sup>4</sup> to 9.62 × 10<sup>5</sup>.

Burns then checks this against her own biological estimate: about 80 ordered molecules break a chemical bond, ~400 open a sodium-channel gate, and ~8,000 must be influenced to initiate a physical action in the brain. The cube figure exceeds the single-action-potential figure by a factor of 30 — "reasonably compatible", she judges, given that both are rough. A harder problem she raises herself: a low-noise microphone detecting 1.5 × 10<sup>−4</sup> dyne/cm<sup>2</sup> over 0.10 cm<sup>2</sup> would need only ~10<sup>4</sup> influenced molecules, fewer than the cube requires, yet microphones do not register mental influence. Her proposed escape is that the ordering is spatially incoherent across a macroscopic surface.

===Testable scaling laws===

The payoff is a set of predictions independent of the individual acting, since person-specific quantities enter only through ''ΔP''<sub>0</sub> and ''τ''<sub>''I''</sub>: ''s''<sub>0</sub>(''M'',''b'') − ''s''<sub>0</sub>(''M''<sub>1</sub>,''b''<sub>1</sub>) = log<sub>2</sub>(''Mb''<sub>1</sub><sup>2</sup>/''M''<sub>1</sub>''b''<sup>2</sup>); ''s''<sub>0</sub>(''n'') − ''s''<sub>0</sub>(''n''<sub>1</sub>) = log<sub>2</sub>(''n''/''n''<sub>1</sub>) for ''n'' cubes; and ''s''<sub>0</sub>(''P'') − ''s''<sub>0</sub>(''P''<sub>1</sub>) = log<sub>2</sub>(''P''<sub>1</sub>/''P'') for a cube tumbling in a [[Vacuum|vacuum]] chamber. She adds practical cautions: cubes must be released within ''τ''<sub>cube</sub> ≈ 1.7 × 10<sup>−2</sup> sec of each other or the subject could act on them sequentially; at least six cubes should be the reference set; and below about 4.80 × 10<sup>−4</sup> torr in a one-metre chamber the mean free path exceeds the container and the effect should fall off. The logarithmic dependence, she argues, would explain the long-standing puzzle (Stanford 1977) that PK results appear insensitive to macroscopic variables. Finally, since 10<sup>5</sup> molecules are ordered over ~10<sup>−9</sup> sec each while conscious time resolution is a few tenths of a second, "if psi occurs at the molecular level, as is suggested herein, it must be carried out at a deeply unconscious level."

==Assessment==

The distinctive merit of this paper is its willingness to let its own hypothesis fail. Burns computes the macroscopic-mass mechanism honestly, finds it needs 68.5 cm of travel where 50 cm was available, and discards it — discarding in the process the specific proposal of the best-known theorist in the field. That is the opposite of the usual pattern in this literature. The scaling laws she derives are genuinely falsifiable and cheap to test: vary cube mass and size, vary the number of cubes, evacuate the chamber, and the predicted shifts in ''s''<sub>0</sub> are small integers, independent of who is doing the influencing. She also volunteers the microphone objection, which cuts against her, rather than suppressing it.

The difficulties are serious and mostly structural. The gravest is that the paper's empirical anchor is Forwald's data, and Burns herself notes that Forwald "took no precautions to shield against air currents from breath or hand movements which might have affected results", concluding that "we do not know whether that pressure was produced by molecules ordered by mental influence or by artifactual air currents." Since the entire quantitative content is a back-calculation from those deviations, the derived 1.45 × 10<sup>−5</sup> dyne/cm<sup>2</sup> may be a measurement of Forwald's breath. The pressures involved are far below anything a 1959 apparatus could exclude. Modern PK meta-analyses on dice have not sustained an effect of the size Forwald reported, and the paper does not engage the possibility that ''ΔY'' is zero.

Several steps are asserted rather than derived. The claim that mental influence can "select the most favorable change within these limits" is the whole mechanism, and it is imported from Burns (2002a) without argument here; the uncertainty principle bounds the ''magnitude'' of fluctuations but supplies no channel by which anything could select among them, and standard quantum mechanics contains no such selection operator. The exponential form ''ΔP'' = ''ΔP''<sub>0</sub>exp(−''t''/''τ''<sub>''I''</sub>) is admitted to be a guess ("we do not know how ''ΔP'' varies in time"), and the free parameter ''τ''<sub>''I''</sub> is then set equal to ''τ''<sub>cube</sub> precisely because that choice minimises the required pressure — a selection that flatters the result. There is also a real tension in the treatment of coherence: molecular ordering must be coherent enough to produce a net directional pressure on a tumbling cube, yet incoherent enough to escape a microphone that requires fewer molecules. Burns offers this as a possibility rather than a mechanism, and as it stands it is an unfalsifiable patch on an otherwise falsifiable framework.

The physics inside the chosen framework is, however, careful. The magnification argument, the moment-of-inertia treatment, the pressure-to-torque conversion and the insensitivity of ''s''<sub>0</sub> to poorly known parameters (because of the logarithm) are all handled competently, and the Appendix comparison with Walker shows that the two angular-shift expressions agree to within a factor near unity, so the disagreement in conclusions traces entirely to the dynamics, not the quantum input. Judged as physics conditional on the premise, the paper is sound; judged as evidence for the premise, it rests on a fifty-year-old dataset that the author's own text concedes was not shielded against the trivial alternative explanation.

==See also==

* [[Jean E Burns]]
* [[Uncertainty Principle]]
* [[Quantum mechanics]]
* [[Entropy]]
* [[Planck Constant]]
* [[Vacuum]]

[[Category:Scientific Paper|effect ordered air molecules tumbling cube]]

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