by Ram Lakhan Pandey Vimal and Christopher James Davia

28 January 2008, posted 2 February 2008



Abstract: - Our goal is to investigate the biological correlates of the first-person experience of time or phenomenal time.  ‘Time’ differs in various domains, such as (i) physical time (e.g., clock time), (ii) biological time, such as the suprachiasmatic nucleus, and (iii) the perceptual rate of time.  One psychophysical-measure of the perceptual rate is the critical flicker frequency (CFF), in which a flashing light is perceived as unchanging. Focusing on the inability to detect change, as in CFF, may give us insight into phenomenal time.  CFF varies from 24 Hz for dim light and 60 Hz in bright light and is lower for colored lights.  We propose that problem of the phenomenal time can be addressed using (1) quantum coherence such as a soliton, a coherent state similar to a Bose-Einstein Condensate (BEC), the properties of which include temporal uncertainty, and (2) temporal frequency tuned mechanisms.  Phenomenal time may be quantized into ‘subjective occasions of experience’ (SE), which arise out of the interaction of the individual and situation.  The SEs for a subject who has CFF of 60 Hz are approximately 16.7 ms in duration.  Pioneering work examining the complex interaction of neurons suggests the possibility that macroscopic quantum states similar to a BEC may also occur in the brain (e.g., Vimal and Davia, 2008; Davia, 2006; Georgiev, 2004).


Key-Words: - Phenomenal time; Quantum coherence; Soliton; Bose-Einstein condensate; Critical flicker frequency (CFF);

Color fusion frequency; Temporal integration; Temporal frequency tuned mechanisms; Luminance and color channels;

Subjective passage of time; Past, present, or future; Linear and cyclic nature of time






Bergson argued that time could only be understood from the contemplation of the consciousness moment, i.e., time is “grasped by, and belongs only to, inner consciousness” [1]. According to James [2], in the context of phenomenal time, (i) Clay’s the obvious past, the specious present, the real present, and the future play important role in the stream of consciousness, (ii) the ‘sensible present’ and ‘spacious present’ have duration (a few seconds to a minute), which is in recent past , i.e., working memory, whereas the ‘the real present’ implies a durationless instant, the latter boundary of ‘specious present’, (iii) the perception of space and that of time interacts, i.e., “Date in time corresponds to position in space”, and (iv) a succession of thoughts is not a thought of successions. According to Vimal [3], phenomenal time can be defined as the subjective, personal, or first person experience of time.




Problem Formulation


Phenomenal time is a long standing problem for cognitive science and the philosophy of mind.  St Augustine argued that the experience of change must involve a connection between future events, present events, and past events.  However, if each moment comprised an infinitely thin slice of time, then such a connection seemed impossible.  One might argue that the experience of change emerges simply as a consequence of the causal relationships that effect transitions; however, “Change in our experience is not the same thing as experience of change” [4]. In physics, there is no absolute rate of time, i.e., although we may claim (within limits determined by relativity) that event A precedes event B, there is no criteria that determines how quickly or how slowly consecutive events should be experienced.  The concept of an absolute and fixed rate of time is wholly absent from our physical description of the universe.  The temporal passage has been considered a subjective illusion [5].  We shall argue that the problem of phenomenal time cannot be solved within the context of a classical physics.  An approach rooted in quantum coherence, such as a solitonic (traveling wave) coherent state similar to a Bose-Einstein condensate (BEC), may resolve the problem.  We shall point to a specific physical quantity as the principle factor, which determines the apparent rate that we experience time. We shall discuss the physiological correlates of cyclic and linear nature of time underlying temporal consciousness.  The fundamental problem is formulated as follows :  what are various aspects of time, what is phenomenal time and what are its neural correlates ?




Problem Solution



Aspects or forms of time and phenomenal time


The various forms of time are as follows: (i) Physical time: This is physical clock time.  The Planck time is the unit of time in the system of natural units known as Planck units, which is the time it would take a photon traveling at the speed of light in a vacuum to cross a distance equal to the Planck length; it is about 5.39 x 10-16 seconds; however, it has not been measured yet.  Images of electrons leaving atoms were produced by short pulses of laser light and recorded within 100 attoseconds (10-16 seconds); this is the shortest time measured so far. (ii) Biological time: although all brain areas can be considered as biological clocks, the suprachiasmatic nucleus is the master molecular clock; it is measured in msec. (iii) Perceptual rate of time: this is psychophysically measured in cycles per second (Hz) using luminance critical flicker frequency (CFF). It varies from 24 Hz in dim light and 60 Hz in bright light for normal humans to 80 Hz for Buddhist monks during meditation to 300 Hz for the honeybee.  Color fusion frequencies are lower than CFF.  Time can be integrated up to 160 msec for luminance stimuli, whereas integration time is longer for color stimuli. (iv) Relative positions in time: these can be distinguished in two ways: (a) Each position is either Past, Present, or Future.  This distinction varies continuously. (b) Each position can be earlier or later than positions.  This distinction is permanent. (v) Cyclic and linear nature of time: Time can be cyclic (day _ night) or linear (future _ present _ past). (vi) Subjective passage of time can be shorter or longer than physical time depending on the state of mind. Phenomenal time is subjective experience of time. It seems to speed up as we grow older, slow down in crisis, and slowing towards stopping, in some cases, such as at death, in near-death experience, meditation, and psychedelic drug use [6]. Furthermore, rather than focusing on the ability to detect change, insight into phenomenal time may come by focusing on the inability to detect change such as in CFF.  After every phenomenal time, there may be an ‘occasion of experience’ or SE, for example, Buddhist Monk who has CFF of 80 Hz may have SE every 12.5 msec whereas a subject who has CFF of 60 Hz may have SE every 16.7 msec.



Models and experiments related to time


In the dissipative quantum model of the brain [7], the brain is constantly entangled with its environment in a way that maintains the unified whole in time.  This entanglement causes our perceptions to be imprinted upon memory, which are then processed into the cognitive map of our environment.  This map appears to be in relative motion (‘relating the presence of consciousness to the contents consciousness is conscious of’) during the SE of passage of time.  The solitoncatalytic model [8] does not contradict the quantum-dissipative model [7], rather they are equivalent to each other; they try to connect discrete neural activities to classical field to quantum field [6].  Within the catalytic model [8], it is noted, that solitons are a classical analogue of quantum particles suggesting the possibility that solitons may ‘induce’ macroscopic quantum states (although solitons are often defined as non-dissipative, this is not true for similar phenomena that occur within dissipative media.  Within the soliton-catalytic model the brain is considered to be an excitable media and therefore a dissipative media).  In the soliton-catalytic model [8], energy is dissipated via structure (fixed points that do not change under transformation).  According to Vimal [3], the wriggles in Humphrey’s framework [9] of sensation from the internalization of action during evolution can be considered equivalent to the traveling wave in soliton-catalytic model [8].  One could argue that the apparent rate at which time is experienced (phenomenal time) depends on the spatiotemporal characteristics of visual mechanisms.  For example, human visual system has one luminance and two color (Red-Green and Yellow-Blue) psychophysical channels, each has spatial, temporal, and spectral frequency tuned mechanisms.  There are six bandpass spatial frequency tuned luminance mechanisms and six spatial frequency tuned Red-Green color mechanisms (one lowpass and five bandpass) [10,11]. There are four temporal frequency tuned luminance mechanisms:  one low-pass with a corner frequency of 8 Hz, and three bandpass with bandwidth of 2-2.5 octaves peaking between 4-8 Hz [12]. There are two temporal frequency tuned color mechanisms: one low-pass and other bandpass [13]. The above are threshold mechanisms, which have flattening effect and show color-contrast constancy at suprathreshold level [14,15].  The luminance channel showed no temporal integration beyond 160 msec, whereas color channels had longer integration time [16]. Our goal is to investigate a general unifying principle underlying these tuned mechanisms and to relate them to phenomenal time. In chaos theory, the balance between linear and nonlinear time involves (a) the changing demands as one approaches and departs bifurcation points, and (b) time dilation and contraction as a control parameter. For example, meditators self-organize time perception differently compared to non-meditators: critical flicker fusion frequency progressively increase by 11-15% following yoga training [17]. Buddhist monks show highly coherent, high amplitude gamma synchrony EEG about 80 Hz [18].




Continuous experiences and invariance related to time


One could hypothesize that the apparent rate at which time is experienced is dependant upon the lower limit of a subject’s sensitivity to change.  This hypothesis is based upon our own subjective experience of what it is like to ‘just about be able to see something move’ and relies upon our inability to conceive of what it might be like if our experience of change was not characterized by a continuum of experiential states – i.e. from almost stationary to moving very fast as we experience them.  But, our inability to conceive of what it might be like to experience change in a radically different way is not sufficient evidence that a very different relationship between changing stimuli and corresponding phenomenological states is not possible. Up until now we have been examining the problem of phenomenal time within the context of changing temporally structured experiences. However, there is a class of experiences that are completely invariant with respect to time.  When we listen to a sine wave above the critical frequency, the associated experience is completely invariant.  Can progress be made by considering the problem within the context of temporally invariant experiences ?  Having argued that change is not essential for an experience to involve phenomenal temporal flow, we may simplify the problem we are addressing by eliminating the need to consider change or ‘phenomenal change’ as a first order aspect of the problem.  We suggest that phenomenal temporal flow may exist without phenomenal change but phenomenal change cannot exist without phenomenal flow.  Invariant experience with respect to phenomenal time is related to perceiving steady light for all stimulus-flicker rates that are greater than critical flicker fusion frequency.  Thus, for a particular temporally structured stimulus there may be only one possible phenomenal state.



Quantum coherence and solitons in visual area – toward a solution


The inability to detect change beyond critical flicker fusion (CFF) frequency may be because our visual system is not sensitive to frequencies greater than CFF. In other words, visual system needs time to integrate information, which we have defined as phenomenal time and is about 16.7 msec for CFF = 60 Hz.  Alternatively, one can argue that rather than focus on the ability to detect change, insight into phenomenal time may come by focusing on the inability to detect change.  One operationalization of the inability to detect change is the CFF rate.  CFF may be correlated with a neural Bose-Einstein condensate (BEC) soliton, the properties of which include temporal uncertainty.  Quantum states are implicated in the phenomenon of consciousness [19]. Dynamic systems may give rise macroscopic states that resemble a phenomenon termed a Bose-Einstein condensate (a field that may exhibit invariance in time).  A Bose-Einstein condensate is a condensed phase of matter in which the individual identity of the comprising atoms is lost and forms a coherent unity – a single wave function.  This phase change is extremely difficult to bring about and usually requires temperatures very close to absolute zero.  However, there is a growing body of research that suggest that similar states may be brought about as a consequence of the behavior of nonlinear dynamic systems.  Studies into the behavior of complex networks like the World Wide Web, suggest that, under certain conditions, a change in the overall dynamic behavior of the network may occur that is a classical analogue of a Bose-Einstein condensate (BEC) and is mathematically modeled in the same way [20].  Macroscopic quantum states similar to a BEC may also occur in the brain [21].  If such macroscopic states do indeed form the neural correlate of consciousness then these states may be in the form of solitons [8].  A soliton is an extremely robust non-linear dynamic that preserves its structure as a consequence of a fine balance between linear dissipative and nonlinear compressive forces.  The fractal catalytic model [8] argues that non-linear interactions in the brain give rise to solitons (or robust traveling waves; they were observed in visual area V1 and are essential for the organization of retina to lateral geniculate nuclei connectivity prior to birth) that mediate energy dissipation as a macroscopic process of catalysis.  Traveling waves in the brain are observed [22] reported that (i) visually evoked primary wave originated in V1 and was ‘compressed’ (via GABA inhibition) when propagating to V2, which then reflected and propagated backward into V1, (ii) the compression/reflection pattern appears to be organized by an internal mechanism associated with visual processing.  Furthermore, [23] reported digital to analog transformations in living systems: action potentials are the primary binary (digital) signal used by neurons for communication within the central nervous system.  They showed that the site of action potential initiation in neurons, the axon initial segment, serves as a critical locus where these binary signals can be modified in a graded (analog) manner.  In the retina, spontaneous activity takes the form of traveling waves, which are essential for the organization of retina to lateral geniculate nuclei pre-birth connectivity [24].  Solitons require structure in the boundary conditions of their environments for the possibility of their emergence.  Furthermore, the fractal catalytic model [8] argues that the brain (which is considered to be an excitable medium) is structured in real time by the body and the environment (both immediately via the senses and historically via past experience) and that any spatio/temporal symmetries (invariance) implicit in the body, the senses and dynamics of interaction between body/senses and the environment may support soliton formation in the brain [8].  Within the context of this theory, consciousness is correlated with the spatio/temporal evolution of a coherent soliton.  If an invariant conscious state is to be correlated with a soliton in the form of a BEC, then, just as it is possible for a simple electromagnetic field to exhibit non-trivial invariance, so it is possible for non-trivial states to occur such that no matter at what rate we present the flickering stimulus the physical correlate of consciousness (the BEC soliton) may always appear exactly the same, as long as the flicker rate is greater than CFF frequency.


A BEC soliton is an interesting phenomenon when considered in the light of the problem we are addressing.  Unlike a classical soliton (e.g. a tsunami), a coherent soliton in the form of BEC exhibits properties quite different from a classical soliton.  Although complex – a BEC soliton is a probability wave function.  As such it embodies characteristics of any quantum probability wave function.  In addition to the uncertainty between position and momentum, the wave function also describes the uncertainty between energy and time.  So, a soliton in the form of a BEC is a four dimensional phenomena with extension in time as well as space.  The degree of this extension is determined by the Uncertainty Principle.  Correlating consciousness with a coherent BEC soliton does not immediately solve our problems.  Although, the uncertainty in time of the wave function may be significant with respect to the problem we are addressing, within the context of the potentially infinite number and variety of cognitive and behavioral states and the potentially infinite number of associated wave functions, it is difficult to see why our experience of temporal flow should exhibit such consistency.  However, progress may be made by considering research that provides evidence that there may be an underlying ‘carrier wave’ that supports other neurological processes – a carrier wave for consciousness.  The basis of this hypothesis is as follows :  The frequency of stimulus fusion in the tactile, auditory, and visual modality equals 18 Hz [25].  If film is shown at a frame-rate less than 16 Hz then ‘flicker’ becomes more pronounced.  Color flicker-fusion frequency is lower than luminance flicker-fusion frequency [26,27].  Thus, there is sufficient evidence pointing to a critical threshold that demarcates the boundary between continuous and discontinuous experience across sensory modes.  The flicker-fusion threshold demarcates the boundary between temporally modulated stimuli that can and cannot be sensed – it marks the limit above which change cannot be experienced. These findings support the hypothesis that there may be an important cycle rate or minimum unit of consciousness. For the argument that follows we shall assume that these findings point to an underlying coherent carrier wave for consciousness.




 Catalytic-soliton and temporal frequency tuned mechanisms models for phenomenal time


As discussed above, the fractal catalytic model of consciousness correlates mental states with the spatio-temporal evolution of a coherent soliton.  The underlying coherent soliton associated with consciousness may be continually adapting and changing its organization as a consequence of variations in the boundary conditions imposed upon it by the body and the senses.  If the temporal structure of the stimulus exhibits modulations that are greater than the uncertainty of the probability wave function of the BEC soliton then, a varying experience will be the result.  But, what of stimuli that exhibit temporal variations (DTs) that are smaller than the uncertainty of the wave function (DT) ?  Stimuli with temporal intervals smaller than the temporal uncertainty of the carrier wave function (i.e., when DTs < DT) may nevertheless give rise to unique and unvarying solitonic solutions.  Given the possibility that the neural correlate of temporal consciousness is a BEC soliton, and given the possibility that there may be unique solitonic solutions determined by temporal structures which fall below the uncertainty in time associated with its wave function (i.e., when DTs < DT), then those solutions cannot embody information that could be used to distinguish individual temporal components of the stimulus within the BEC’s soliton’s temporal uncertainty.  This hypothesis accords well with the phenomenology of experience.  Although we may be able to experience a high frequency stimulus, we are unable to distinguish its small scale structure.  Given that the flicker fusion frequency or CFF is a crucial quantity that represents the limit above which we cannot experience change (i.e., when stimulus flicker frequency FFs > CFF), then it would seem reasonable to conclude that the primary factor that determines the apparent ‘rate’ at which we experience time is the uncertainty in time associated with the carrier wave function of the BEC soliton.  The flicker-fusion frequency may be giving us very precise information about the way in which we (and other species) experience time.  It must be pointed out that a threat to this hypothesis exists as a consequence of a large body of research that seems to show that the flicker-fusion frequency depends upon factors such as intensity and wavelength of stimuli, adaptation condition, background condition and so on [26,27].  However, we could argue that uncertainty in time associated with the carrier wave function of the BEC soliton also similarly depends on the above factors.  Any attempt to interact with a coherent state that resulted in information being obtained that fell below the temporal uncertainty of the wave function (i.e., when DTs < DT) must cause it to collapse.  We suggest that the temporal uncertainty of the wave function demarks the boundary below which discriminations in time cannot be made.  We suggest that for this reason, time as it forms part of the wave function cannot be considered as a ‘duration’ as is normally conceived.  Alternatively, one could also argue that some of the temporal frequency tuned mechanisms that were sensitive at high suprathreshold luminance becomes less sensitive to the extent that they are non-functional at lower luminance.  This is in analogy to the number of luminance spatial frequency (SF) tuned mechanisms dropped down from 6 at photopic to 4 at mesopic level to 2 at scotopic level, where higher SF tuned mechanisms were first to drop [28,29].  It would be interesting to extract temporal frequency tuned mechanisms at mesopic and scotopic luminance levels.  One could further argue that if a subject’s CFF = 60 Hz, then the subject has Whitehead’s occasion of experience at every 16.7 msec.  The critical flicker fusion frequency (CFF) is the frequency at which a flickering light is indistinguishable from a steady, non-flickering light.  CFF depends on species, luminance level, color, and other conditions.  Frank [30] reported, “nocturnal insects tend to have lower CFFs [and lower temporal resolution] than diurnal insects”, and “there is a trend towards lower CFFs with increasing habitat depth”. Some of luminance CFFs are as follows [6]: (i) 60 Hz in bright light and 24 Hz in dim light for humans, (ii) 58 Hz for cat, (iii) 70 Hz for octopus in bright light, and (iv) 180-300 Hz for honeybee, dragon fly and blowfly flies. These data can also be explained by their temporal frequency tuned mechanisms, which needs further investigation.




Neural correlates of phenomenal time


The brain itself can be considered as a clock or ‘organ of time sense’ [31].  The biological circadian clock has an intrinsic period of about 24 hours, which synchronizes to the daily day-night (light–dark) cycle [32].  According to Herzog, “circadian clocks may be crucial for widespread changes in brain activity and plasticity.  These daily changes can modify the amount or activity of available genes, transcripts, proteins, ions and other biologically active molecules, ultimately determining cellular properties such as excitability and connectivity” [32].  For example, suprachiasmatic nucleus (SCN) tracks the cyclic form of time such as sleep-wake rhythms and regulates the biological need for sleep, food, and reproduction.  Activation of SCN and primary visual cortex depends upon time of day [33,34].  Whereas hippocampus and frontal cortex tag a linear cause-and-effect form of temporal information about the memories of the past and the expectancies for the future, respectively, and regulate neural nets that together form memories, consciousness, and the perception of past, present and future [31].  Both forms of biological time or clocks are critical in temporal consciousness; when one is turned on, other is turned off [31].  When these clocks are out of synchrony, both physical and mental disorder can occur [31]. Temporal disorganization of the brain is a characteristic of the aging process, such as a disruption of the sleep–wake cycle, ‘an increase in the subjective rate of time passage’, and a decline in future expectancies [31].  Time seems to speed up as we grow older and time appears to slow down in crisis [6], for example time seems 36% longer in free fall.1 Phenomenal time (subjective experience of time) slowing towards stopping, in some cases, such as at death, in near-death experience, meditation, and psychedelic drug use [35,36]. A player who has higher rate of conscious moments may win the game [19].  The temporal disorganization observed in schizophrenia, autism, and bipolar disorders may be partially due to genetic mutations in the human clock gene.  The brain is temporally organized via ‘temporal tagging’ and ‘re-entry’, which bind the wide range of spatiotemporal stimulus-features to a unified subjective experience that is held in synchrony with the external world [31,37].  Time and its neuroendocrine correlate melatonin are involved in binding the spatiotemporal stimulus features for subjective experience [31,37].  Melatonin decreases the desynchronization between internal circadian rhythms and the external environment, which occur in jet-lag, shift-work, blindness, and delayed sleep phase insomnia [34].  From the fMRI data for the phenomenological concepts of temporality i.e. phenomenal time, Northoff [38] wrote, “Lloyd [39] observed that the multivariate distance and changes between brain images is approximately linearly related to their temporal distance.  The more closer acquired in time the more similar the images.  Thus, the changes between the different images occur gradually over time.  Lloyd argues that these results are consistent with Husserl's description of time consciousness in that they reflect the inexorable temporal flux of the conscious state.  Analogous to the way that each moment of our phenomenological experience of time builds on foundation of the previous moment, the series of fMRI images appears to form a continuously evolving temporal pattern of global activity.”






We2 summarize our proposal as follows: (1) Rather than focus on the ability to detect change, insight into phenomenal time may come by focusing on the inability to detect change.  This is consistent with the ‘psychological present’: ‘there is always an experienced duration in which experience does not change’ [40,41]. (2) One operationalization of the inability to detect change is the critical flicker fusion (CFF) rate. (3) CFF may be correlated with a neural Bose-Einstein condensation (BEC) soliton (traveling wave), the properties of which include temporal uncertainty. (4) A single CFF (16-18 Hz) would be associated with an ‘underlying coherent carrier wave’ for consciousness; however, CFF may depend on many factors. (5) The subjective experience of time is phenomenal time; in terms of measurable physical time it is 1/CFF; it can be addressed by temporal frequency tuned mechanisms.  (6) After every phenomenal time; there may be an ‘occasion of experience’ or subjective experience (SE), i.e., Buddhist Monk who has CFF of 80 Hz may have SE every 12.5 msec whereas a subject who has CFF of 60 Hz may have SE every 16.7 msec.






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[Draft version 4, 28 January 2008. This paper has not been peer reviewed. Please do not copy or cite without authors’ permission]



Ram Lakhan Pandey Vimal and Christopher James Davia

Vision Research Institute, 428 Great Road, Suite 11, Acton, MA 01720 USA;


Dristi Anusandhana Sansthana (DAS), A-60 Umed Park, Sola Road, Ahmedabad-61, Gujrat, India;


DAS, c/o NiceTech Computer Education Institute, Pendra, Bilaspur, C.G. 495119, India; and


Dristi Anusandhana Sansthana, Sai Niwas, East of Hanuman Mandir, Betiahata, Gorakhpur, U.P. 273001, India.


1-4* (Vimal)


Centre for Research in Cognitive Science, University of Sussex, Brighton, BN1 9RH, UK (Davia)


     e-mail <rlpvimal (at) yahoo.co.in, c.j.davia (at) sussex.ac.uk; http://www.geocities.com/rlpvimal/