# Biophotons: A Hard Problem
## 3 Statistical Analysis of the Experimental Data
### The Diffusion Entropy Method
In fact, in the first three temporal regions, the same analysis produced a mean scaling factor \(\eta\) = 0.56 \(\pm\) 0.04, which corresponded to a mean \(\mu\) = 2.79 \(\pm\) 0.11, while the last three regions have a mean scaling factor \(\eta\) = 0.50 \(\pm\) 0.01, which corresponded to a mean \(\mu\) = 2.99 \(\pm\) 0.03. These results indicated that in the first three temporal regions, the departure from the condition of random diffusion was due to the presence of crucial events, while the FBM regime dominated in the last stage of seed growth. In other words, it seems that during the germination process, the nonergodic component tends to vanish with time, and complexity becomes dominated by stationary infinite memory. However, the DEA without stripes gave scaling factors significantly larger than those achieved with the use of the DEA with no stripes. This indicated that the germination process generates both crucial events and noncrucial events of the FBM type. Therefore, the complexity of the emission of biophotons can be thought of as a mixture between two dynamics: one associated with crucial events and the second with noncrucial events of the FBM type having infinite memory. The latter can be interpreted as a form of quantum coherence, which becomes predominant in the late germination phase. In the upper part in Figure 7, we show the different spectral components of the signal relating to the various wavelength intervals. The experimental data were obtained through the use of long-pass glass color filters, and the curves correspond to the average number of photons in each wavelength interval divided by the total signal without any filter. The complete analysis and a detailed description of the method can be found in Ref. [27]. It is clear that the different ratios changed as a function of time, according to the moment of germination. In particular, the high-energy components (green and violet curves) remained constant for the entire time of the measurement, while the lower-energy parts change in relative intensity; in detail, the orange part decreases at the beginning for a few hours, it remained constant for up to hours 20, and then it slowly decreased until reaching a constant value after 30 hours. This behavior was associated with a simultaneous increase in the yellow-green component of the spectrum at 10-30 hours. After this time interval, all spectral components remained essentially constant until the end of the experiment. It is interesting to note that hour 30 represents the border between the time region where complexity is due to the presence of crucial events and that instead dominated by the FBM type of fluctuations. In our opinion, all these results represent the first empirical data indicating that the germination process of lentil seeds is a process that presents phase transitions [11] accompanied by changes in patterns of complexity (crucial to noncrucial events). This type of behavior can also be found in the heartbeats of patients under the influence of autonomic neuropathy [48]. The increasing severity of this disease has the effect of making \(\mu\) move from the healthy condition close to \(\mu\) = 2 to the border with ordinary statistical physics \(\mu\) = 3, which corresponds to a pathological state. In human beings, the presence of crucial events is a necessary condition for different organs to \"talk\" to each other, for example, the heart [45] and brain [47; 48]; it is also the condition for maintaining good health [45; 48]. This may not be true for plants as they do not have well-defined organs; only at the beginning of the germination process is there a clear differentiation process that may require the presence of crucial events. However, to grow, plants need light to trigger the synthesis of chlorophyll, which is necessary to produce the appropriate nutrients; this did not happen in our experimental apparatus, which was a light-free environment.