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About a hundred years ago, the Russian biologist A. Gurwitsch, based on experiments with onion plants by measuring their growth rate, hypothesized that plants emit a weak electromagnetic field that somehow influences cell growth. This interesting observation remained fundamentally ignored by the scientific community; only in the 1950s the electromagnetic emission from some plants was measured using a photomultiplier used in single counting mode. Later, in the 1980s, several groups around the world started extensive work to understand the origin and role of this ultraweak emission, now called biophotons, coming from living organisms. Biophotons are an endogenous very small production of photons in the visible energy range in and from cells and organisms, and this emission is characteristic of living organisms. Today, there is no doubt that biophotons exist, this emission has been measured by many groups and for many different living organisms, from humans to bacteria. However, the origin of biophotons and whether organisms use them to exchange information is not yet well understood; no model proposed to date is capable of reproducing and interpreting the great variety of experimental data coming from the many different living systems measured so far. In this brief review, we present our experimental work on the biophotons coming from germinating seeds, the main experimental results, and some new methods we are using to analyze the data to open the door for interpretative models of this phenomenon clarifying its function in the regulation and communication between cells and living organisms. We also discuss ideas on how to increase the signal-to-noise ratio of the measured signal to open up new experimental possibilities that allow the measurement and the characterization of currently unmeasurable quantities.
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Appl. Sci. 2024, 14, 5496. https://doi.org/10.3390/app14135496 www.mdpi.com/journal/applsci
Review
Biophotons: A Hard Problem
Luca De Paolis 1, Roberto Francini 2, Ivan Davoli 3, Fabio De Maeis 2, Alessandro Scordo 1, Alberto Clozza 1,
Maurizio Grandi 4, Elisabea Pace 1,*, Catalina Curceanu 1, Paolo Grigolini 5 and Maurizio Benfao 1,*
1 Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, Via E. Fermi 40, 00044 Frascati, Italy;
luca.depaolis@lnf.infn.it (L.D.P.); alessandro.scordo@lnf.infn.it (A.S.); alberto.clozza@lnf.infn.it (A.C.);
catalina.curceanu@lnf.infn.it (C.C.)
2 Dipartimento di Ingegneria Industriale, Università di “Tor Vergata”, Via del Politecnico, 00133 Roma, Italy;
francini@roma2.infn.it (R.F.); demaeis@roma2.infn.it (F.D.M.)
3 Dipartimento di Fisica, Università di “Tor Vergata”, Via della Ricerca Scientica, 00133 Roma, Italy;
ivan.davoli@roma2.infn.it
4 Istituto La Torre, Via M. Ponzio 10, 10141 Torino, Italy; info@la-torre.it
5 Center for Nonlinear Science, University of North Texas, Denton, TX 76203-5017, USA;
paolo.grigolini@unt.edu
* Correspondence: elisabea.pace@lnf.infn.it (E.P.); maurizio.benfao@lnf.infn.it (M.B.)
Abstract: About a hundred years ago, the Russian biologist A. Gurwitsch, based on experiments
with onion plants by measuring their growth rate, hypothesized that plants emit a weak electro-
magnetic eld that somehow inuences cell growth. This interesting observation remained funda-
mentally ignored by the scientic community; only in the 1950s the electromagnetic emission from
some plants was measured using a photomultiplier used in single counting mode. Later, in the
1980s, several groups around the world started extensive work to understand the origin and role of
this ultraweak emission, now called biophotons, coming from living organisms. Biophotons are an
endogenous very small production of photons in the visible energy range in and from cells and
organisms, and this emission is characteristic of living organisms. Today, there is no doubt that
biophotons exist, this emission has been measured by many groups and for many dierent living
organisms, from humans to bacteria. However, the origin of biophotons and whether organisms use
them to exchange information is not yet well understood; no model proposed to date is capable of
reproducing and interpreting the great variety of experimental data coming from the many dierent
living systems measured so far. In this brief review, we present our experimental work on the bio-
photons coming from germinating seeds, the main experimental results, and some new methods
we are using to analyze the data to open the door for interpretative models of this phenomenon
clarifying its function in the regulation and communication between cells and living organisms. We
also discuss ideas on how to increase the signal-to-noise ratio of the measured signal to open up
new experimental possibilities that allow the measurement and the characterization of currently
unmeasurable quantities.
Keywords: biophotons; complexity; data analysis
1. Introduction
All living systems emit electromagnetic radiation, a small number of photons of
about 100 ph/sec per square centimeter of surface area, at least in the visible energy range.
The scientic community calls this emission by the name of biophotons [1,2].
This emission is present in all living organisms, at least in aerobic ones, and ends as
soon as the organism dies. This excludes the possibility that it derives from traces of the
radiative substances present in the organism or the passage of cosmic rays. The main char-
acteristics of biophotonic emission are a very low intensity and the absence of specic
emission lines; practically, we are in the presence of a at emission in the energy range
between 200 and 800 nm with a slight maximum around the orange area. It should also
Citation: Paolis, L.D.; Francini, R.;
Davoli, I.; De Maeis, F.; Scordo, A.;
Clozza, A.; Grandi, M.; Pace, E.;
Curceanu, C.; Grigolini, P.; et al.
Biophotons: A Hard Problem. Appl.
Sci. 2024, 14, 5496. hps://doi.org/
10.3390/app14135496
Academic Editors: Vladislav
Toronov and Jorge Bañuelos Prieto
Received: 22 February 2024
Revised: 12 June 2024
Accepted: 19 June 2024
Published: 25 June 2024
Copyright: © 2024 by the authors. Li-
censee MDPI, Basel, Swierland.
This article is an open access article
distributed under the terms and con-
ditions of the Creative Commons At-
tribution (CC BY) license (hps://cre-
ativecommons.org/licenses/by/4.0/).
Appl. Sci. 2024, 14, 5496 2 of 24
be noted that the contribution of the thermal part, calculated with the Planck distribution
in the visible energy range and at room temperature is practically zero [3]. Furthermore,
the presence of any type of stress, from chemical to a change in temperature, typically
induces an increase in emission, which can reach up to a few orders of magnitude greater
than the nonstressed baseline, followed by a decrease, which follows a nonexponential
power law, up to normal values [1,2].
In the 1920s, the Russian biologist A. Gurwitsch [4], observing the growth rate of on-
ion plants, hypothesized the existence of an electromagnetic eld responsible for the reg-
ulation of cellular growth in living systems, capable of inuencing the mitotic activity of
the surrounding tissues. He called this weak emission “mitogenetic radiation”. Despite
the conrmation of his results (see the article by Gabor and Reiter [5]), the scientic com-
munity completely ignored Gurwitsch’s results; therefore, his work faded into the back-
ground. Only thirty years later, Colli and Facchini [6,7] carried out the rst measurement
of electromagnetic emission from living organisms through the use of the rst photon
detectors used in single-photon counting mode. This work again fell into oblivion; only
thirty years later, F.A. Popp et al. [2] began a large experimental/theoretical research pro-
ject to understand the origin and signicance of biophoton emission in detail.
Nowadays, there are no longer any doubts about the experimental evidence of bio-
photonic emissions; however, questions related to their generation and the role they have
in biological processes remain open. There are currently several hypotheses [1,2] that try
to explain this surprising phenomenon that is typical of living beings. These can essen-
tially be divided into two categories: in the rst, the emission derives from the random
processes of the radiative decay of the molecules previously excited by metabolic pro-
cesses, while in the second, the theories are based on the existence of a coherent electro-
magnetic eld inside the cells that in some way generates the observed biophotonic emis-
sion. Both theories predict that any type of perturbation generated by nonspecic stress
gives rise to an increase in emission, as observed experimentally. The two hypotheses are
not mutually exclusive, and the emission could have a dual origin. There is also clear ex-
perimental evidence that biophotonic emission carries some type of biological information
[8–11]; for example, the emied radiation can increase the rate of cell division by up to
30% in similar organisms, which is the so-called mitogenetic eect [11–13].
Recently, biophotons are also revealing their ability to be used in noninvasive meth-
ods for research in biology from applications in toxicology [14] to human health monitor-
ing [15] as well as identication and treatment of diseases, especially cancer [16].
In this short review, we present the results we obtained by following the emission of
biophotons from various types of seeds during the germination process. Our experimental
apparatus essentially consists of a black PVC dark chamber appropriately made to avoid
any contamination from external light and a photomultiplier that works as a single-pho-
ton count device. The experimental data consist of the number of photons that arrived at
the sensitive part of the photomultiplier in a well-dened time window (1 sec. in our case)
and were stored as a function of time from the moment the experimental chamber was
closed and for the entire duration of the experiment, which could last from a few hours to
several days, depending on the seeds. Therefore, the experimental data are represented
by a time series in which the counts detected in the chosen time window are reported as
a function of time [1,6,7,17].
We recently analyzed these data using the diusion entropy analysis (DEA) method
[17]. This is based [18,19] on the determination of the scaling index η associated with the
time series, according to the complexity concept developed by Kolmogorov [20]. Using
the experimental data, it is possible to generate a diusive process [17–19], and the scaling
index is determined by calculating the associated Shannon entropy. The presence of an
anomalous complexity is highlighted by a deviation from the ordinary value η = 0.5. Our
analysis [17] indicates a clear deviation from the ordinary value η = 0.5 for the entire du-
ration of the experiment. At the beginning of germination, we found complexity essen-
tially due to the presence of so-called crucial events, while as the germination process
Appl. Sci. 2024, 14, 5496 3 of 24
progresses and leaves and roots develop, the type of complexity changes and we proceed
towards a Fractional Brownian Motion (FBM)-type regime [21].
Biophotons can be regarded as an index of thermodynamic activity [2], and changes
in emission rates over time (usually hours) result in changes in scaling parameters [17].
When biophoton emission rates are used in conjunction with an analytical technique like
DEA, they have the potential to document dynamic changes in complexity in a developing
organism or complex adaptive system.
From this point of view, the germination process could be seen as a process that has
a phase transition not yet known, accompanied by changes in complexity paerns (from
crucial to FBM condition). We can hypothesize that the process of cellular dierentiation
required for the development of leaves and roots leads to a criticality [11] driven by the
presence of crucial events. These results oer the possibility of investigating the existence
of variation in complexity paerns in a variety of dierent developing organisms and pro-
vide evidence of the importance of the exchange of information (entropy) transfer for cell-
to-cell communication during organismal development [11].
It can also be thought that the concept of swarm intelligence [22,23] may be associated
with the development of a root network of plants living in natural conditions, and the
presence of crucial events in the initial phase of germination may be associated with the
birth of this extraordinary radical intelligence.
In this paper, we present a brief review of our work on spontaneous emission coming
from seeds during the germination process. In particular, in Section 2, we present a new
method of analysis of experimental data based on the use of the logistic equation. This
allowed us to hypothesize that the germination process can also be thought of as the acti-
vation of dierent cell groups, each with its characteristic times, which are nodes of a
complex network that interact based on the increase or decrease in the global benet. Fur-
thermore, we describe the diusion entropy analysis method in detail; the results obtained
are related to the spectral and the logistic types of analysis, all of which create a fairly
coherent picture of how the germination process of various seeds should be thought.
A section is also dedicated to some new ideas for developing the experimental set-
up to increase the signal-to-noise ratio to have access to information that is dicult to
obtain today. Finally, a section is dedicated to a brief description of the role of stress in
biophotonic emission, with particular aention to delayed luminescence experiments,
while in another section, the main applications of biophotons in the life sciences are briey
described.
2. Methods and Experimental Data
Our experimental setup was formed by a germination chamber, a photon counting
system, and a turning lter wheel [17]. A drawing of the experimental setup we used to
measure the spontaneous emission of germinating seeds is shown in Figure 1.
The photon counting device a H12386-210 high-speed counting head (Hamamatsu
Photonic Italia S.r.l, Arese (MI), Italy) powered at +5 Vcc. The phototube is sensitive in the
wavelength range between 230 and 700 nm, with a peak sensitivity at 400 nm [24]. The
data acquisition and control of the experiment were achieved via an ARDUINO board and
a computer equipped with a LAB-VIEW system (National Instrument, Austin, TX, USA).
Appl. Sci. 2024, 14, 5496 4 of 24
Figure 1. Schematic view of the experimental setup used in our experiment. The germination cham-
ber is built with black PVC to avoid any contamination of light from outside. This gure is a part of
Figure 1 in [17].
The whole experimental setup work as a single-photon counting system and the de-
tector can see a single photon with just the quantum eciency of the photomultiplier. The
acquisition time window was xed at 1 s, and within this window, the entire system had
a dark count of approximately 2 counts/sec, perfectly in line with the datasheet of this
specic photomultiplier, which indicates 1.7 counts/sec [25]. A turning wheel holding a
few long-pass glass color lters placed between the germinating seeds and the detector.
The wheel had eight positions. Six were used for the color lters, one was empty, and the
last one was closed with a black cap; see [17] for details.
Seeds were kept in a humid coon bed and placed in a Petri dish; they were normal
seeds bought from a supermarket. Without any seed, the emission consists of a monotonic
decreasing tail due to the residual luminescence of the material, a consequence of the light
exposure of the experimental chamber. The emission tail arrives in a few hours at the dark
count value.
A typical measured signal with seeds and the wheel in the empty position is dis-
played in Figure 2. This signal (red points) refers to the emission of 76 lentil seeds for a
total duration of 72 h from the moment of closure of the experimental apparatus after
insertion of the Petri dish with the seeds into the measurement chamber.
The initial behavior (a few hours) is dominated by residual luminescence. The ger-
mination-triggered biophoton emission emerges about 5–7 h after closing the chamber
(the change in the slope of the counting curve), and then it became dominant for the entire
duration of the experiment, with a signal well above the detector’s dark counts.
The temporal evolution of biophoton emission (see Figure 2) have a shape that ap-
pears to be a universal characteristic in the germination phase of seeds. For example, emis-
sions from common wheat (Triticum aestivum) [14] and Arabidopsis thaliana seeds [26] are
very similar to those presented here. All this seems to indicate that the emission is sub-
stantially controlled by a completely general process, characteristic of the germination
phase and substantially independent of the type of seed. This is quite interesting and
needs a deeper discussion.
Appl. Sci. 2024, 14, 5496 5 of 24
Figure 2. Biophoton emission of germinating lentil seeds. In the insert, a comparison between the
emission of a single bean (orange curve) with that of lentil seeds (black curve); the two curves are
the raw data (count/sec) averaged over one minute. This gure is depicted using the time scale for
lentils. The capital leers in the gure indicate the main emission peaks observed in the experi-
mental data.
The comparison [27] between the emission of the 76 lentil seeds and that of a single
bean is reported in the inset in Figure 2. The emissions were analyzed for a fairly long
time, from the end of the residual luminescence until the moment of the generation of
leaves and roots. The time scales relating to the single bean and the 76 lentil seeds are
completely dierent; therefore, to highlight the common characteristics of the two emis-
sions, we rescaled the time scale of the bean by a factor of 0.164. This allowed us to align
the two maxima, the C peaks in the gure. The zero was placed in the rst minimum of
both emissions at the end of the residual luminescence; this means we subtracted the val-
ues 10 and 100 from the original time scales, respectively, for the lentils and the single
bean. Furthermore, to normalize the number of counts to the C peaks, we multiplied the
counting scale of a single bean by a factor 2.28.
The time-rescaling procedure used here is based on the popular logistic equation
[28,29], which can be used in dierent systems to describe the growth of a population that
reaches the nal steady-state value that is specic for any system. The logistic equation
plays an important role in biology, also contributing to the emerging science of chaos.
Here, the logistic equation takes the form
󰇗󰇛󰇜󰇛󰇜󰇛󰇜
(1)
Appl. Sci. 2024, 14, 5496 6 of 24
where n(t) is the number of cells growing because of watering the seeds [29], and the num-
bers a and b are constants that depend on the system. The solution to Equation (1) can be
wrien as:
󰇛󰇜

(2)
where C depends on the initial conditions n(0) through the relationship 󰇛󰇜
󰇛󰇜. We
made the conjecture that the rate of biophoton emission is proportional to the derivative
of the number of cells, i.e., to 󰇗󰇛󰇜:
󰇗󰇛󰇜
󰇛󰇜
(3)
Cells can be thought of as a kind of interacting unit in the living organism; for a single
type of unit, the time derivative reaches a maximum at a time determined by the param-
eters and b and the initial conditions. The corresponding emission has a regular trend,
with only one maximum reached at time 
󰇡
󰇢 and intensity 
. β is de-
ned as .
We hypothesized that the saturation time of the ordinary logistic equation in dierent
systems corresponds to the maximum emission peak, and we rescaled the time scale of
the bean so that its maximum photon emission rate coincided with that of the lentils. In
this way, we made a comparison between them, reducing the time of the slower growth
by a reducing factor: 0.164 in the case of the bean.
The fact that the emissions of dierent seeds have very similar temporal behavior led
us to hypothesize the existence of a sort of generalized logistic equation as a universal
property of the connection between the system growth and photon emission.
The experimental data show a wealth of structures with a succession of maxima and
minima distributed throughout the experiment. In detail, the lentil emission shows peaks
B and C, separated by about 5 h, between time 0 and 20 h, and the same two peaks (B’ and
C) are present in the emission of the single bean, but here they separated by about 14 h.
The biophoton emission of the bean has a further peak A at about 43 h (these values in the
bean time scale), which is absent in the lentil emission. Both emissions also show at least
two slopes in the growth phase, between zero and peak C.
In our opinion, this is clear evidence of the presence of dierent types of units in the
seeds that could be activated at dierent times on dierent time scales. The simplest gen-
eralization of Equation (3) that considers the presence of dierent types of units and with
which to make a phenomenological t of biophotonic emission as a function of time could
be of the following type:
󰇗󰇛󰇜
󰇛󰇜

(4)
where the dierent constants could be determined by a t procedure conducted by using
the experimental data. In Figure 3, we present such a type of analysis by comparing the
experimental data relating to the emission of the 76 lentils with the two ts made using
Equation (4) with J = 1 and J = 5.
Appl. Sci. 2024, 14, 5496 7 of 24
Figure 3. Comparison between the biophoton emission of the 76 lentils (red line) with two ts using
Equation (4) with J = 1 (blue dashed line) and J = 5 (green line). The experimental data are counts
per second averaged over 1 min. The time scale is now the original one used in the raw experimental
data presented in Figure 2.
The two ts were conducted using the experimental data in the time range of 10–60
h. We do not report the values obtained from the t procedure, both for brevity and be-
cause this analysis essentially aims to give a qualitative indication of the path to be fol-
lowed for the development of models capable of shedding light on the mechanisms un-
derlying the generation of biophotons. We also tested ts based on single-component
models. These did not seem to work. This is not surprising as the temporal distances be-
tween the various peaks in the emission spectrum are dierent, and this seems to suggest
the need for dierent frequencies.
It seems quite clear that only ts made based on many-component functions can re-
produce, at least qualitatively, the shape of the time series representing the measured ex-
perimental data, supporting the idea that the germination process can also be thought of
as the activation of dierent cell groups at dierent times characteristic for each group.
From this point of view, each unit can be thought of as a node in a network, where each
node can interact with its neighbors and make choices based on the increase or decrease
in global benet [30]. The system spontaneously evolves towards criticality, leading at the
same time to the emergence of cooperation and intelligence. By intelligence, we here mean
the fact that a local interaction changes into a long-term one, making the single units sen-
sitive not only to their nearest neighbors but also to the units very far away from them.
Analysis of single-bean experimental data produces the same type of ts and to the same
type of interpretation, which is why they are not shown in this work.
For a full understanding of the biophoton phenomenon, one also needs to consider
the processes of the excitation of molecules, which then give an emission during the radi-
ative decay process. All the details of the cellular environment, i.e., the spectral distribu-
tion of the density of states, are important and can inuence the excitation as well as the
emission of the molecules, and the processes related to biophoton emissions should be
essentially considered as connected to the nonthermal states occurring in the living cell.
The processes in nonliving substances are mostly related to thermal equilibrium states at
room temperature, and thus they cannot lead to molecular excitation and consequently to
the emission of biophotons in the optical region. There are many models in the literature
in this regard (see reference [31] for a review), essentially based on three processes. The
rst is DNA replication (it is considered a possible source of biophotons) during the cell
cycle, when the activation energy of DNA replication may be used to excite molecules,
Appl. Sci. 2024, 14, 5496 8 of 24
prior to cell division, which includes membrane formation. The second is the synthesis of
ATP that occurs during cellular metabolism, when the ion uxes through membrane (par-
ticularly in the mitochondrion); the last one is based on the oxidation process of some
biological molecules in the living system.
3. Statistical Analysis of the Experimental Data
In this section, we briey present the main results regarding the statistical properties
of the time series representing the experimental data using the probability distribution
function approach and the diusion entropy analysis method.
3.1. The Probability Distribution Function Approach
In a semiclassical picture of the optical detection process, a phototube converts the
continuous cycle-averaged classical intensity 󰇛󰇜 into a series of discrete photocounts.
Thus, the photocount m obtained in an integration time T is proportional to the intensity
of the light that arrives on the detector [32]. From the experimental data, it possible to
obtain the distribution function 󰇛󰇜, which counts how many times a number of pho-
tons n has been detected by the phototube in a given acquisition time T. Therefore, after
an appropriate normalization process, it gives the probability of obtaining m counts in the
chosen acquisition time window.
This function is analyzed by determining the mean, variance, and other moments of
higher order to highlight some statistical properties of emied light, considering that, at
least in some particular cases, there is a direct correspondence between the statistical prop-
erties of the light, the functional form of the 󰇛󰇜, and some characteristics of the physical
process behind the production of the measured light. We do not repeat here the entire
theoretical derivation that leads to the determination of 󰇛󰇜, but we want to remember
that there are only some cases that lead to an analytical form of this function. Details can
be found in the literature [27,33].
The simplest case is a stable classic light wave, where the cycle-averaged intensity
has a xed value independent of the time [33]. In this case, the distribution has a Pois-
sonian form:
󰇛󰇜
 󰇛󰇜
(5)
where . Factor α is a constant that depends on the construction characteristics
of the phototube. For a Poisson distribution, the variance is equal to the average .
It is convenient to dene the so-called Fano factor [32] through the relationship
to quantify some type of departure from the Poisson distribution; this could be an
indication of a nonclassical nature of the light. A Poisson distribution is a sign of a system
in coherent states; in this case, the quantum states correspond to classical electromagnetic
waves [27,32,33], but this distribution also occurs for experiments where the integration
time is much longer than the characteristic time of the intensity uctuations of the light
beam.
The photocount distribution can be also derived for complete thermal chaotic light
[28,32,34]. In this case, the distribution takes the form
󰇛󰇜󰇛󰇜
󰇛󰇜
󰇧
󰇨
(6)
where n is the average number of photons, and M is the number of eld modes. Thermal
states are classical, and there is the following relationship between average and variance:
(7)
In general, the M coecient could be huge, in this case, the variance becomes almost
equal to the average value, recovering the equation valid for the Poisson distribution.
Appl. Sci. 2024, 14, 5496 9 of 24
Therefore, for large M values, the thermal photocount distribution approaches the Poisson
distribution. This implies that it is dicult to discriminate between coherent and thermal
states when many modes are present, in agreement with the discussion of in Ref. [34].
In references [17,27], we have already presented a detailed analysis of the experi-
mental data relating to lentils and a single bean. For brevity, we present here only the
comparison between the 󰇛󰇜 obtained from the experimental data of lentil seeds related
to the time window between 20 and 30 h (original time scale in Figure 1) and two ts
performed using Equations (5) and (6). The results are presented in Figure 4. The two ts
have essentially the same , and there is no reason to prefer one over the other.
Figure 4. Comparison between the experimental count probability distribution function (red points)
relative to lentil emission with two ts using a Poisson function (solid blue line) and a many-mode
thermal function (dashed green line). The emission period is between 20 and 30 h.
In this case, the experimental average count is  and the variance is
. The Fano factor  indicates a photocount statistics of the super-Poissonian
type. The Poissonian type of the t gives an average count equal to ,
while the multimode thermal function gives  and ,
in this last case, Equation (7) is roughly satised. This result conrms what we have found
in previous works [17,27]. The experimental photocount distribution function always has,
at least for the time windows considered in our experiment, a variance greater than the
average value, indicating a super-Poissonian type of behavior, which is typical of either
thermal emission or emission with a very short coherence time compared to the time win-
dow of the measurement. Using this type of analysis, it is very dicult to discriminate
between coherent and thermal states, in agreement with the discussion in Ref. [32]. The
possibility of proving whether the biophotonic emission of living beings is coherent, so
measuring some parameters such as the coherence length and time is extremely important
for the implications that this type of nding would have in dening the role that coherent
processes have in biology. Coherence parameters can be measured using light interference
or light correlation functions [32,34]. The nonclassical nature of the emied light could be
assessed using the measure of the higher-order correlation functions associated with the
electromagnetic eld [33,34]. This type of measurement is extremely challenging with the
experimental setups used until now because we need to consider signals of very low in-
tensity and those coming from nonstationary processes.
Appl. Sci. 2024, 14, 5496 10 of 24
3.2. The Diusion Entropy Method
There is now clear evidence that biological systems cannot be described by the ordi-
nary prescriptions of equilibrium statistical mechanics. This indicates the need to have
analysis methods that can highlight all the deviations from the canonical form of equilib-
rium to understand the breakdown of the conditions on which Bolmann’s view is based:
no memory, short-range interaction, and no cooperation. Any deviation from the canoni-
cal form is a measure of the system’s complexity. There is still no unanimous consensus
on the origin of complexity. In our case, the idea that complexity emerges from self-or-
ganization seems to be the most appropriate. The seed can be thought of as a system that
self-organizes when it begins to germinate because of watering. In general, a complex sys-
tem is formed by several interacting units generating a whole with specic properties such
as nonlinearity, self-similarity, and self-organization, to quote just a few. Complexity can
be thought of as a delicate balance between order and randomness, and when one of the
two prevails, complexity turns into simplicity.
In the complexity literature, there exists wide consensus on the importance of Kol-
mogorov complexity [20], especially of Kolmogorov-Sinai entropy [35,36]. The evaluation
of Kolmogorov complexity has been the subject of many studies. A dedicated discussion
of this literature is out of the scope of this paper, we refer the reader to the discussion
presented in Ref. [19] for details. These authors illustrated two research directions aimed
at evaluating Kolmogorov complexity; one called compression, aiming to establish the
Lyapunov coecient directly, and the second one is called diusion, which is based on
converting the original time series into a diusion process. The Kolmogorov complexity
is turned into a scaling factor η, which is expected to depart from the ordinary value η =
0.5.
The technique of analysis used here is based on the diusion approach, and it is
called Diusion Entropy Analysis (DEA). This method was introduced in the literature in
the early 2000s [37–40], and it is based on converting experimental time series, like the
emission we recorded with our experimental setup, into a diusional trajectory and uses
the deviation of this diusion from that of ordinary Brownian motion as a measure of the
temporal complexity in the data. The complexity of the signal is determined through the
evaluation of the Shannon entropy associated with the diusional trajectory under the
assumption that the complexity of the signal may be revealed by the anomalous scaling
of the diusional trajectory.
The time axis is divided into bins of size s (in our case s = 1 sec), and we assign to the
nth bin the value ξ(n), which is the number of photons emied in that small time interval.
In total, we have a time series of length M. For notation simplicity, the time series is con-
sidered as a continuous time signal ξ(t), in this way, the diusional trajectory can be de-
ned as
󰇛󰇜 󰇛󰆒󰇜󰆒󰇛󰇜
(8)
It is convenient to consider the 󰇛󰇜 time series because it is directly related to the
correlation function of the original time series [17,37,38,40]. The scaling properties are de-
termined through the long-time limit behavior of the correlation function 󰇛󰇜󰇛󰇜
and the average can be made over a large number of realizations of 󰇛󰇜 using the mov-
ing window method. See references [37,39,40] for details. Following the standard ap-
proach of assuming that the correlation functions are stationary, it is possible to dene a
normalized correlation function totally independent of the absolute values of and :
󰇛󰇜󰇛󰇜󰇛󰇜
(9)
where , and it is related to the 󰇛󰇜 time series as
Appl. Sci. 2024, 14, 5496 11 of 24
󰇛󰇜 󰆒

󰆓
(10)
We can now relate the complexity of ξ(t) to the anomalous scaling of the diusion
trajectory x(t). Using FBM and Hurst notation [21,38], we indicate the scaling factor with
the symbol H, instead of η. Dierentiating Equation (10) twice with respect to the time
and supposing that , we obtain
󰇛󰇜󰇛󰇜
(11)
which, when H deviates from the ordinary value H = 0.5, has, in the long-time limit [40],
the structure 󰇛󰇜
,with δ = 22H. Any deviation from the value H = 0.5 indicates
the anomalous behavior of the time series, which therefore presents some type of com-
plexity even in the case of a stationary regime.
Although the conversion of the time series () into a diusion trajectory leads natu-
rally to relating the complexity of () to the Hurst coecient ≠ 0.5, there exists another
source of anomalous behavior [41] of the diusion trajectories that cannot be described
through stationary correlation functions.
One of the key features of most complex systems is the presence of renewal events
[41,42]. The presence of a renewal event resets the memory of the system, and the se-
quences of the waiting times between successive renewal events are completely uncor-
related and independent. Renewal events generate a rejuvenation of the system, giving
rise to a dynamic where, whenever an event of this type occurs, the system restarts from
a completely new state. Renewal events are characterized by the fact that the time interval
between successive events is described by a waiting-time probability density function,
which has the important asymptotic properties 󰇛󰇜
, with ranging from 1 to .
Crucial events are renewal events corresponding to the condition 1 < < 3.
A classic example of a crucial event is the sudden change in direction of the ight of
a swarm of birds. When such an event occurs, the global velocity of the swarm vanishes,
and the birds y in a new direction that does not correlate to the previous one [43,44].
These types of events are not conned only to the swarms of birds but can be found in
many biological and physiological processes [44] and play an essential role in the self-
organization process of the living system and in keeping it healthy [45,46].
For the analysis of data generated by the emission of biophotons, we have at our
disposal only one time series. To perform the statistical analysis, we convert the diu-
sional trajectory 󰇛󰇜into many realizations so as to make it possible to obtain an ensem-
ble average. These realizations are performed through a window of size that we move
along the trajectory (). Assuming a window of length ranging from to , the
value 󰇛󰇜 can be thought of as the initial position of a random walker that jumps in a
time from the origin to a value 󰇛󰇜󰇛󰇜 . This procedure is represented
graphically in Figure 5.
The dierent realizations obtained using the moving window method are dened as
󰇛󰇜 󰆒

󰇛󰆒󰇜
(12)
Note that the largest value of is where M is the number of bins in our time series,
and for any given window size , we can generate realizations changing the
initial position of the random walker, i.e., the t value. Some of these new realizations are
represented graphically in the inset in Figure 5 for a given value of . We are now ready
to calculate the probability distribution function 󰇛󰇜 and the related Shannon entropy
of our diusion process. For further details, see [18].
Appl. Sci. 2024, 14, 5496 12 of 24
Figure 5. Graphical representation of the algorithm underlying the DEA. The blue line represents
the diusional trajectory in Equation (8), while the red squares are the moving windows. The inset
represents a cloud of the various realizations obtained by moving a window of length and using
Equation (12).
With M being very large, as in our case, it is possible to create enough realizations so
as to be able to evaluate the probability distribution density 󰇛󰇜 with an accuracy high
enough to t the scaling coecient , assuming the scaling condition
󰇛󰇜
󰇛
󰇜
(13)
The Shannon entropy related to the probability distribution density 󰇛󰇜 can be
wrien as
󰇛󰇜 
 󰇛󰇜󰇟󰇛󰇜󰇠
(14)
and plugging Equation (13) into Equation (14), we obtain
󰇛󰇜󰇛󰇜
(15)
This equation means that the entropy 󰇛󰇜 increases linearly with 󰇛󰇜 and the
slope of the resulting straight line is the scaling factor , which must be found numerically
from the experimental data. The numerical results are expressed in a linear-log scale that
transforms the ing curve with the form 󰇛󰇜into a straight line. Of course, if the
FBM condition applies, 
The results in Figure 6 were obtained by examining portions of dierent lengths L of
the experimental sequence of the dark emission. The starting point of these dierent por-
tions is always the beginning of the experimental sequence. Increasing the length L, the
entropy S(l) derived with the DEA algorithm remains essentially the same, which is not
surprising as dark emission is stationary over time with an average count of about 2
counts/sec. The main eect is increasing the accuracy in determining the scaling factor
through the t procedure. In this case, we found an average value .
Appl. Sci. 2024, 14, 5496 13 of 24
Figure 6. Entropy S(l) as a function of window size l. This plot has a linear-log scale, in accordance
with Equation (15). The dierent curves illustrate S(l) for time series of dierent lengths obtained
using the experimental data from time origin up to L.
This method allowed us to nd the anomalous scaling associated with the experi-
mental data, but it was not able to discriminate whether the scaling factor was due to
stationary or nonstationary correlation functions. For this purpose, the DEA algorithm
must be modied by introducing the concept of stripes, as discussed in [18]. Rather than
converting the original experimental data into a diusion process () directly, we divide
the ordinate axis into many bins of size s and record the times at which the experimental
signal crosses the border of two neighboring stripes. In this way, we obtain a new time
series 󰇝󰇞. At any of these times, an event occurs. We replace the experimental time data
with a time series z(t) dened as follows: if time coincides with one of the times , we
set 󰇛󰇜, and 󰇛󰇜 otherwise. In other words, if time corresponds to the occur-
rence of an event, the random walker makes a step ahead by a xed quantity of one. The
diusion trajectory can be now obtained using Equation (8) again with the surrogate time
series 󰇛󰇜. This is a very short description of the DEA with and without stripes; details
can be found in Ref. [46].
To distinguish the anomalous scaling generated by crucial events from other types of
anomalous scaling, we denote it with the symbol η rather than H. It is possible to demon-
strate [40,41] that there are several dierent equations relating η and μ depending upon
their values. In detail: for ;
 for ; and  for
. If complexity is generated by crucial events, the region corresponds in any
case to stationary uctuations and is interpreted as the manifestation of ordinary equilib-
rium statistical physics; conversely, the region with is the area of nonstationary be-
havior, either temporary when or permanent for .
The experimental data showed extreme variability in terms of observed intensity; for
this reason, we decided to divide the total acquisition time of about 72 h into six regions,
the rst ve having a length of 10 h, while the last one was greater, being equal to 22 h.
The idea behind this way of analyzing data was to understand if μ changes with time
during the germination process, its value at dierent stages of germination, and how these
compare with the values obtained in the analysis of some other physiological processes,
like heartbeats [45] and brain dynamics studied via EEG recording [47].
In Figure 7, we show the six regions chosen for the analysis, separated by vertical
black lines. For each of these regions, we used DEA with and without stripes to determine
the various scaling factors. A similar analysis was also conducted for the dark counts to
enable a comparison with the experimental data coming from a case without any seeds.
Appl. Sci. 2024, 14, 5496 14 of 24
We found that the dark count yields the ordinary scaling, thereby showing that no
temporal complexity of either kind may occur in the absence of any seed in the chamber.
In the presence of seeds in the chamber, anomalous scaling emerged. The analysis with
no stripes yielded a scaling signicantly larger than the scaling obtained by DEA supple-
mented with stripes. Furthermore, while the scaling factor remained practically constant
in all the six dierent regions when obtained by using the DEA without stripes, there was
a signicant time dependence for the scaling factor obtained by the DEA with stripes. In
the rst phase of germination, within the three rst temporal regions, the value of μ was
signicantly less than three, a value that increased with the progress of the germination
process. Without stripes, the value increased from 0.694 (μ = 2.44) to 0.796 (μ = 2.25),
while with stripes, it increased from 0.496 (μ = 3.01) to 0.596 (μ = 2.67). For brevity, we do
not report here the complete analysis (see Ref. [17] for details), but we present a summary
using an average procedure on the dierent scaling factors. These numbers related to the
dierent temporal regions are divided into two sets: in the rst one, the average is deter-
mined using the scaling factors obtained in temporal regions #1–3, while in the second set,
the average is determined using the scaling factors coming from regions #4–6 (see Table 2
in Ref. [17] for the numbers).
Figure 7. Number of photons emied during the germination of lentil seeds (violet points). The
black lines represent the six dierent regions used for the DEA. The dierent spectral components
of the signal relating to four spectral windows are also indicated with dierent colors in the inset at
the top of the gure.
Using DEA without stripes, the average scaling index related to the rst 30 h (regions
#1–3) was η = 0.77 ± 0.03, which corresponds to a mean μ = 2.30 ± 0.05, while in the second
three regions (regions #4–6), the average scaling index was η = 0.72 ± 0.02, corresponding
to a mean μ = 2.39 ± 0.04. Essentially, there is no time dependence of the scaling factor
throughout the whole germination process. In contrast, when applying the DEA with
stripes, the results showed a clear and signicant time dependence. In fact, in the rst
three temporal regions, the same analysis produced a mean scaling factor η = 0.56 ± 0.04,
which corresponded to a mean μ = 2.79 ± 0.11, while the last three regions have a mean
scaling factor η = 0.50 ± 0.01, which corresponded to a mean μ = 2.99 ± 0.03.
Appl. Sci. 2024, 14, 5496 15 of 24
These results indicated that in the rst three temporal regions, the departure from
the condition of random diusion 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 innite memory. However, the DEA
without stripes gave scaling factors signicantly 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 asso-
ciated with crucial events and the second with noncrucial events of the FBM type having
innite memory. The laer 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 dierent spectral components of the signal
relating to the various wavelength intervals. The experimental data were obtained
through the use of long-pass glass color lters, and the curves correspond to the average
number of photons in each wavelength interval divided by the total signal without any
lter. The complete analysis and a detailed description of the method can be found in Ref.
[27]. It is clear that the dierent 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 simultane-
ous 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 domi-
nated by the FBM type of uctuations. In our opinion, all these results represent the rst
empirical data indicating that the germination process of lentil seeds is a process that pre-
sents phase transitions [11] accompanied by changes in paerns of complexity (crucial to
noncrucial events).
This type of behavior can also be found in the heartbeats of patients under the inu-
ence of autonomic neuropathy [48]. The increasing severity of this disease has the eect
of making μ move from the healthy condition close to μ = 2 to the border with ordinary
statistical physics μ = 3, which corresponds to a pathological state. In human beings, the
presence of crucial events is a necessary condition for dierent 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-dened organs; only at the
beginning of the germination process is there a clear dierentiation process that may re-
quire 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. There-
fore, the change in paerns of complexity may also be due to the beginning of a patholog-
ical process that leads to the death of the plant.
Discriminating between these two hypotheses is of extreme importance because it
could open up the possibility of using the emission of biophotons as a tool to understand
the state of health of a living organism through the determination of scaling indices and
therefore the presence or absence of crucial events. At the same time, as the emission of
biophotons is a universal characteristic of living organisms, this study can lead to conr-
mation that the presence of crucial events is a necessary condition for the health status of
any type of living organism.
Appl. Sci. 2024, 14, 5496 16 of 24
4. External Excitation and Biophoton Emission
One of the peculiar characteristics of biophotonic emission is its extreme sensitivity
to any type of stress that can be externally applied to a living organism. Typically, a stress
reaction is manifested by a sudden increase in the intensity of the emission, generally fol-
lowed by a decrease, and sometimes a return to the normal nonstressed baseline [1]. How-
ever, there is no univocal response to various types of external stimuli (typically mechan-
ical, electromagnetic, or chemical), and, in some cases, very small quantities of chemical
substances [49,50] may have the eect of increasing the intensity of the radiation emied
even by a few orders of magnitude, while in other cases, large concentrations of toxic
agents may cause small changes [14] in the emission that remain practically stable even
for long periods.
The biophotonic emission of plants presents a temperature dependence typical of
physiological processes, with the presence of an overshoot of emission when the temper-
ature increases and an undershoot when the temperature decreases [1,50,51]. In the be-
ginning, the emission rapidly increases, in accordance with the fact that the speed of phys-
iological processes typically increases with increasing temperature, obviously within bio-
logically acceptable limits; then, there are two characteristic peaks, followed by a slow
decrease to lower values. Very interesting is the hysteresis-like dependence of the emis-
sion on the temperature T, as T is cyclically changed. The presence of the two peaks and
the hysteresis loop clearly point to the nonlinear and collective behavior of the plant cells
and the presence of some type of memory. All this indicates a typical behavior of complex
systems, for which the phenomenon of biophoton emission is not the sum of a series of
independent microscopic biochemical processes but the result of a cooperative process
involving dierent groups of cells. The DEA supports this idea by highlighting the pres-
ence of a nontrivial temporal complexity in the time series representing biophotonic emis-
sion.
There is also clear evidence that any type of mechanical damage to some part of the
plant produces an eect on biophotonic emission [52,53]; in particular, there is an increase
in intensity. This also depends heavily on which part is damaged and on the kind of
wounding. For example, in Cucurbita pepo var. styriacae, cuing away part of the seed
leaves produces an increase in emission, which slowly reaches a constant value in approx-
imately hundreds of seconds after damage. Cuing the stem produces a rapid increase in
intensity followed by a decrease, which brings the emission to values similar to those it
had before the wound [53]. This study indicates that reversible perturbations of homeo-
stasis produce an increase in the intensity of the emission until a stationary value is
reached. On the contrary, damage that leads to death produces a rapid increase in the
intensity of the emission, followed by a decrease until the end of the emission at the mo-
ment of death. In other words, if the external stimulus is somehow “manageable” by the
plant, the plant reorganizes itself, with changes aiming to bring the organism to the max-
imum possible well-being considering the new external situation. A local stimulus, such
as damage to a small part of the plant, leads to biochemical and electrical events that aect
the entire plant and not just the part aected by the wound. Therefore, there must be a
very precise coordination of these adaptative events that must pass through a wide net-
work of signals and transduction pathways.
The experimental phenomenology associated with stress phenomena is very broad
and varied; at the same time, there is an equally wide variety of interpretative models that
aempt to explain the experimental data currently available [51]. In our opinion, much
remains to be achieved, especially with regard to the explanation of the temporal trend in
the emission following a stress of some kind.
As a nal example, let us now examine the phenomenon of delayed luminescence
(DL). Several experiments carried out in recent decades have demonstrated how a previ-
ous brief illumination of a biological sample can temporarily increase its subsequent emis-
sion of biophotons by important factors, up to a few orders of magnitude [54]. Further-
more, this signal lasts longer than usual uorescence and has been seen in virtually all
Appl. Sci. 2024, 14, 5496 17 of 24
biological systems studied up to now. DL emission is also very sensitive to the biological
state of the system [55], and, for this reason, it is now widely used as a noninvasive method
for obtaining biological information.
Typically, a sample is illuminated by a pulse of light generated by a nitrogen laser
equipped with a dye laser module to enable the possibility of varying the wavelength of
the exciting radiation. In this way, the system generates pulses with a 5 ns width, an en-
ergy of about 150 μJ/pulse, and a wavelength ranging from 360 to 710 nm. During this
illumination phase, the phototube is o to avoid any damage, and the acquisition starts
10 ms after the end of the laser pulse. Data analysis consists of studying the decay of the
emission after the sample was irradiated with the laser pulse, and the decay time to return
to normal emission can vary from a few tens of seconds to a few minutes, i.e., a much
faster time than the typical one in germination processes, which normally takes place over
tens of hours. The typical decay curve takes the form of a power law of the type [56].
󰇛󰇜
󰇛
󰇜
and the total number of emied photons is the integral of this function between a mini-
mum and a maximum observation time. Hyperbolic forms such as this have already been
used to describe the decay in delayed uorescence and the temporal decay of coherent
systems. The dierent parameters in this equation are determined from experimental data
with a ing procedure, and they characterize both the biological system under study and
its physiological state [55]. The main characteristics of DL, in particular its long decay
times and its existence at physiological temperatures, indicate that it can hardly be con-
nected with delocalized states such as normal electronic bands. On the other hand, it is
currently thought that DL is connected to the formation and dissociation of self-localized
nonlinear electronic states of the soliton type, which could form in the low-dimensional
macromolecular structures normally present within cellular structures [56,57].
This type of model has a more general value, and it is not only conned to the DL,
but, on the other hand, it is unable to explain cases of nonhyperbolic decay or the wide
variability in the observed decay times. For this reason, a two-phase model was recently
proposed: a stress transfer phase that transforms stress into a generation of photons, fol-
lowed by a photon propagation phase [58]. In our opinion, spontaneous and stimulated
emissions originate from substantially dierent excitation/deexcitation channels, alt-
hough they probably involve the same types of molecules.
5. Biophotons in Living Materials
In this short section, we give a brief overview of the use of biophotons in recent stud-
ies in living maer; biophotons are in fact emied by all living organisms. Since Gur-
witch’s rst studies, many groups all over the world have studied, and are currently stud-
ying, this phenomenon in completely dierent contests. Hundreds of articles have been
wrien. For an extensive review, see Ref. [31].
5.1. Seeds and Plants
Many groups are interested in studying germinating seeds for several reasons,
mainly to test the germinal goodness of the seeds and to verify how plant growth is af-
fected by pests, pollution agents, insecticides, fertilizers, and extreme atmospheric condi-
tions. The assessment of the quality of a seed is one of the most essential tasks for seed
certication: the study of the biophotons emied by a sample of seeds is a rapid method
to assess various seed-quality parameters, as Sarmah states in Ref. [59].
Extensive studies on the consequences of pests have been performed at the Hungar-
ian University of Agriculture and Life Sciences [60,61], observing plants in vivo. The same
group studied the eect of pollution agents, for example, cadmium on barley [62]. When
pests are present and insecticides are used, it is important to understand their eects on
Appl. Sci. 2024, 14, 5496 18 of 24
plants. For example, a group at the Universidade Tecnologica Federal do Paraná (Brazil)
is studying Triticum aestivum treated with thiamethoxam [63].
It is also important to know how fertilizers aect plants: Salieres’s group studied how
hydrogenated water acts on Medicago sativa plants, aecting growth and development
[64]. Kobayashi’s group studied azuki seeds and their behavior under heat shock [65].
Other studies were conducted for understanding which parts of plants emit biopho-
tons: Mackenzie’s group separately observed the biophotons emied by roots and the up-
per part of a-mung sprouts [66].
5.2. Food Quality
Observation of biophoton emission is widely used in this eld because it is a fast and
noninvasive technique. Recently, the Iranian-Brazilian group headed by Nematollahi pro-
duced an extended list of studies on food quality and food production quality [67]. For
example, biophoton emissions coming from chicken eggs were used regarding the possi-
bility for quality verication [68], while the emission from wine has been used to test the
dierent winery practices in France [69] and in Hungary [70] to improve the quality of
production.
Nowadays, food is stored for several days before arriving in our houses. Biophotons
can help in this case too. Several groups have used this emission to understand the degree
of freshness of several types of food in many dierent conditions [59,61,71] and the secu-
rity of storage of food, as in the study by Gong [72].
Pulsed electric eld technology is an important emerging modality for both biomed-
icine and the food industry, e.g., in medicine (electrochemotherapy, tissue ablation, novel
methods for drug and gene delivery and therapy), in the food industry (pasteurization,
food compounds extraction), and in biotechnology. Biophotons are used in this case for
sensing the protein oxidation generated by pulsed electric elds [73].
5.3. Humans and Animals
Many studies have been conducted on human beings and animals. The production
of biophotons inside the human body was demonstrated by Zangari’s group, observing a
signature left by biophotons, using a technique based on the principle that the ionic Ag+
in solution precipitates as insoluble Ag granules when exposed to light [74]. Other groups
have tried to understand why and where these biophotons are produced [75–77].
Some studies have observed biophotons emied by cell culture or tissue slices. Tu-
mor cells displayed increased photon emissions compared to nonmalignant cells: it is pos-
sible to use biophoton emissions as a noninvasive, early-malignancy detection tool, both
in vitro and in vivo [78]. Mice synaptosome and brain slice biophoton emissions were used
for studying the dierences between Alzheimer’s disease and vascular dementia, discov-
ering that communications and the information processing of biophotonic signals in the
brain are crucial for advanced cognitive functions [79]
Both in vivo and in vitro studies have been conducted to evaluate the oxidative stress
of human skin, which is important for skin cancer prevention [8082].
Many studies have been conducted on Traditional Chinese Medicine (TCM). Re-
cently, Wang and colleagues stated that “the study of the super weak glowing phenome-
non of biology and death of people’s thoughts, anger and death process is expected to
promote the combination of Chinese and western medicine” [83]. Guo and colleagues pro-
posed studying changes in the ultra-weak luminous intensity of acupuncture points and
meridians before and after needling stimulation [84]. Biophoton emission was measured
at four sites on the hands of people with type 2 diabetes before treatment and after 1 and
2 weeks of treatment with TCM: the biophoton emission intensity decreased gradually
over the course of the treatment [85].
Biophoton emission has been also correlated to mental states. An increase spontane-
ous human biophoton emission is caused by anger emotional states [51,86]. Stress levels
can be detected by making a specic analysis of biophoton emission (in conjunction with
Appl. Sci. 2024, 14, 5496 19 of 24
other physiological parameters; this kind of assessment is under study for Ukrainian mil-
itary personnel after frontline service) [87].
6. Future Experimental Upgrade and Perspective
For any experimental apparatus that aims to perform biophotonic measurements,
possible improvements involve two approaches: increasing the number of detectors to
enhance counts or enhancing the collection capacity. The rst approach may be a double-
edged sword. Biophotons are an endogenous production of a very small ux of photons,
of the order of 100 ph/sec, within an energy range between 200 and 800 nm. Even in the
darkest environment, a low background counter could have some spare counts per sec-
ond. Increasing the number of detectors means increasing the sources of background noise
and the covered solid angle, but this last can in practice be increased by a very small per-
centage, and therefore produce a modest gain in signal-to-noise ratio. In our opinion, en-
hancing the biophoton measurement capability of an experimental setup would be best
achieved by improving its collection capacity. In this section, we introduce and assess var-
ious upgrades aimed at increasing the ability to collect luminescence biophotons in a sci-
entic apparatus. Such improvements could also be applied to dierent apparatuses that
aim to make measurements of rare low-background luminescence processes.
A rst improvement is the introduction of a Fresnel lens to the apparatus. The Fresnel
lens is a “sectioned” convex lens with vertical parallel planes forming concentric rings.
Refraction bends the light rays and makes them converge into a single focus. Placing a
Fresnel lens in front of the emiing source (germinating plants, for example), lumines-
cence photons can be focused to the counter (distances can be evaluated with a simula-
tion), and thus the geometrical eciency of the apparatus can be improved up to two
orders of magnitude, as shown in Figure 8.
Figure 8. On the left, (a) a schematic view of the apparatus with a Fresnel lens inserted to improve
the number of light photons collected by the counter. On the right, (b) a schematic view of the ap-
paratus with an integrative sphere made of white Teon. The sphere allows the reection of the light
rays, enhancing the collection capability of the apparatus.
A second improvement would be the building of an integrating sphere made with
white Teon. Teon reects more than 99% of the incident light in the visible energy range,
so the light originally generated by the sample is reected many times by the walls and
nally reaches the hole where the photomultiplier is housed. In this way, it collects the
emission coming from every part of the sample, and it is as if we have increased the solid
angle of measurement by certain factors. The integrating sphere can be located inside a
black PVC chamber to avoid any light contamination (see the right panel in Figure 8).
The third improvement is the installation of light sources for calibration and valida-
tion testing of the experimental setup. Specically, the best solution would be the
Appl. Sci. 2024, 14, 5496 20 of 24
installation of two light sources: one emiing coherent light and another emiing inco-
herent light. This can be of extreme importance as there are many works investigating the
coherence state of biophotonic emission; we range from an analysis in terms of a totally
chaotic eld to those based on the presence of coherent and squeezed states. The intro-
duction of coherent and incoherent light sources in the apparatus can provide a reference
to compare the biophoton emission.
So far, we mentioned the upcoming improvements. However, several further im-
provements may be made. One is the installation of an infrared camera to obtain funda-
mental information about growing cells. Such an improvement can be tested in lentils, but
their chaotic vertical growth may produce an incomplete response collection. In cell cul-
tures, where the layer is uniform, an infrared camera can collect more complete and clean
information. Other improvements include the installation of devices and sensors to mod-
ify and monitor the temperature inside the chamber, the installation of irradiation sys-
tems, and the variation in atmosphere or pH and constituents of the soil of the plants to
characterize the spectrometric response of germinating seeds. In this way, the lentil exper-
iment represents a pioneering study on biophotons. In addition to being a valuable source
of information concerning plant growth, it also serves as a testing ground for evaluating
devices and solutions applicable in the future, extending to the study of biophotons emit-
ted by both healthy and cancerous cell cultures [88–90].
7. Conclusions and Suggestions for Future
There is growing interest in the literature in the role that biophotons appear to have
in biology, from studies on seeds and plants to those involving humans. In this short re-
view, we essentially presented the results that our group has obtained in the study of seed
germination processes, relating them to the results already reported in the literature. We
have seen a kind of phase transition during the germination process, highlighted by
changes in the complexity paerns (crucial and noncrucial events) and by a dierent be-
havior of the spectral components. At the same time, the analysis of the intensity and the
shape of the emission in terms of a generalized logistic equation seems to indicate that
during the germination period, the parts of the organism involved in the emission process
change according to the degree of plant development.
In this contest, the germination process can be thought of as a spontaneous organiza-
tion of a biological system generating nonequilibrium events and deviations from the dy-
namical processes of ordinary thermodynamics. The system evolution and the interaction
between the dierent units lead to criticality [41], which therefore emerges directly from
the processes of the spontaneous organization of biological systems as a delicate balance
between order and disorder.
The idea that biophotons, beyond the molecular mechanisms that generate them, are
also a manifestation of the degree of complexity of the system can help us answer the
question of how such a small signal can transmit information. This can be achieved using
complexity matching theory, which was introduced to extend linear response theory of
Kubo from the ordinary condition of thermodynamic equilibrium to the more general
condition of perennial nonequilibrium.
All living beings seem to emit biophotons, and this emission is extremely sensitive to
the “state” of the organism that is emiing them. Changes in biophoton emission spectra
under any type of stress indicate that something is happening in the living system; the
changes in paern complexity may be an indicator of a loss of cellular communication,
identied by crucial events [46], signaling a “loss of complexity”, with the disappearance
of crucial events, where loss of complexity may be an early sign of disease. From this point
of view, biophotons could have a role in establishing links between the units of the com-
plex living system, despite their ultra-weak intensity.
Following this line of thought, we can hypothesize that biophotons are another com-
munication route developed by nature to allow the exchange of information between dif-
ferent cells as well as organisms. If this is true, we can imagine an active role for
Appl. Sci. 2024, 14, 5496 21 of 24
biophotons in the treatment of various pathologies, cancer, or Alzheimer’s, just to give a
few examples, through the development of a system that emits biophotons of the right
degree of complexity and intensity and which therefore can be “interpreted” by diseased
cells to lead them through a healing process.
It is extremely important to increase the signal-to-noise ratio, and, in this review, we
proposed an extremely economical possibility that could open the doors for experiments
carried out on single seeds that have a beer energy resolution than the one we obtained.
We should also mention the possibility of using a CCD camera in experiments with plants
and seeds to map the emiing parts as already conducted in the case of human beings.
A lot has been achieved, and perhaps some answers are starting to emerge, but a lot
remains to be accomplished. This requires work and imagination, but this is the fun part
of the story.
Author Contributions: All authors contributed equally to this review. All authors have read and
agreed to the published version of the manuscript.
Funding: We acknowledge support from the Foundational Questions Institute, FQxI, a donor-ad-
vised fund of Silicon Valley Community Foundation (grant Nos. FQXi-RFP-CPW-2008 and FQXi-
MGB-2011), and from the John Templeton Foundation, Grant 62099. The opinions expressed in this
publication are those of the authors and do not necessarily reect the views of the John Templeton
Foundation.
Data Availability Statement: All relevant data are available from the authors upon request.
Acknowledgments: We warmly thank I. H. von Herbing, L. Tonello, and D. Lambert for the con-
versation we had during the writing of this paper.
Conicts of Interest: The authors declare no conicts of interest.
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This third edition, like its two predecessors, provides a detailed account of the basic theory needed to understand the properties of light and its interactions with atoms, in particular the many nonclassical effects that have now been observed in quantum-optical experiments. The earlier chapters describe the quantum mechanics of various optical processes, leading from the classical representation of the electromagnetic field to the quantum theory of light. The later chapters develop the theoretical descriptions of some of the key experiments in quantum optics. Over half of the material in this third edition is new. It includes topics that have come into prominence over the last two decades, such as the beamsplitter theory, squeezed light, two-photon interference, balanced homodyne detection, travelling-wave attenuation and amplification, quantum jumps, and the ranges of nonliner optical processes important in the generation of nonclassical light. The book is written as a textbook, with the treatment as a whole appropriate for graduate or postgraduate students, while earlier chapters are also suitable for final- year undergraduates. Over 100 problems help to intensify the understanding of the material presented.