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Uncertainty principle

Despite the confirmation of previous neuroscientific results, and the apparent success of our quasi-quantum model, our research question as posed above remains only half answered. Using this model, we noted differences in the probability distributions and the phase space centroids in rest when compared to task. However, we still sought a parameter from the model that would remain the same in rest and task. To this end, we defined an analogous Heisenberg uncertainty principle of the form,

\bigtriangleup x(t)\bigtriangleup p_{x}(t)\geq K_{brain}

(5)

Table 2 displays the values of this constant ( $K_{brain}$ ) acquired in all conditions, as well as the maximum value, mean value, and standard deviation. We found that this quasi-quantum model leads to a constant minimum value across $\Delta x(t)\Delta p_{x}(t)$ and $\Delta y(t)\Delta p_{y}(t)$ of $0,78\pm 0,41{\tfrac {cm^{2}}{4ms}}$ with $T=0,P=1$ . Note the unit of ${\tfrac {cm^{2}}{4ms}}$ is a result of the EEG being sampled at 250 Hz and the mass being taken to be unity. Furthermore, the average value and standard deviation of these quantities remains consistent across conditions with an average value of $9,3\pm 4,4{\tfrac {cm^{2}}{4ms}}$ ( $T=0,P=1$ ) and a standard deviation of $18\pm 29{\tfrac {cm^{2}}{4ms}}$ ( $T=0,P=1$ ). Notably, the maximum value does vary between conditions, with the largest value occurring while subjects watched the intact clip from Bang! You’re Dead. Despite the average position of the signal along the y direction being different in rest than during a task ( $P<0.001$ ), the quasi-quantum mathematical methodology leads to a constant uncertainty value. Quite remarkably, the values in the table display that the average uncertainty and minimum uncertainty is the same across different conditions, despite maxima varying by over two orders of magnitude. Thus, giving further credence to the idea that this uncertainty relation captures the similarities of the brain across the vastly different conditions. Figure 3 displays the probability distribution at the time corresponding to the minimum in uncertainty for both $x$ and $y$ .