# The feeling of the passage of time against the time of the external clock

Sylvie Droit-Volet, Florie Monier, Natalia Martinelli

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Sylvie Droit-Volet, Florie Monier, Natalia Martinelli. The feeling of the passage of time against the time of the external clock. Consciousness and Cognition, 2023, 113, pp.103535. 10.1016/j.concog.2023.103535. hal-05500174

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# The feeling of the passage of time against the time of the external clock

Droit-Volet, S., Monier, F. & Martinelli, N.

In daily life, individuals often claim that time passes quickly or slowly. This phenomenological experience on the speed of the passage of time is well known and has been well described in the literature (Wearden, 2015). However, the mystery remains regarding the underlying psychological processes. This last decade has therefore seen a renewed of interest in the study of this temporal feeling in an experimental setting allowing us to further understand this human experience about the speed of the passage of time (PoT).

The feeling of the passage of time is complex. There is not one but several types of PoT judgment depending on the time period considered. Four types of PoT judgment have been identified (Droit-Volet & Martinelli, ). The first refers to a very long period of time covering several years ("do you find that time passes more quickly now than 5-10 years before") or even an entire lifetime (do you find that time passes more quickly as we get older) (Witmann, Jman, Droit-Volet & Wearden, ). The second refers to shorter periods covering the past year, month, week, or day. The third refers to the present PoT judgment also called the now PoT judgment, that is on the current activity or the one just before the temporal judgment. These different judgments are considered retrospective because participants are not aware in advance they will have to judge the time of past events. True retrospective temporal judgment requires only one trial because once people are aware of the purpose of the task, they pay attention to time and temporal judgment become prospective (Wearden 2005, Hicks et al., 1976). Also, for methodological reasons, laboratory studies often used several trials and accordingly assessed rather the prospective PoT judgment. There is thus a fourth judgment called the prospective PoT judgment, when participants are instructed that they must judge the passage of time for the task that they are going to do. However, it has been recently shown that the retrospective PoT judgment and the prospective PoT for the current task are closely correlated, at least for long task durations (Martinelli & Droit-Volet,). In addition, even in a so-called retrospective condition, some people spontaneously think about time as soon as the task gets a little longer (Martinelli & Droit-Volet, ; Wittmann). Therefore, in our study we examined the prospective PoT judgment on several trials. We nevertheless examined the relationship between this PoT judgment and the other types of PoT judgment.

The present PoT judgment in a prospective paradigm has been widely examined in different studies (e.g., Christandl et al. 2021; Odgen, ; ). Different predictors of PoT judgment have been identified which varied as a function of studies. However, the experimental procedures used also varied from a study to another one, such that no serious conclusion can be drawn. Recently, Martinelli and Droit-Volet carried out a series of experiments by controlling the various factors recognized as being at the source of the PoT judgment. They modified the level of difficulty of the task performed (Experiment 1), and the emotional value of stimuli (Experiment 2) while keeping their duration constant. They also varied the duration of the task while keeping the task difficulty level constant (Experiment 3). The results showed that the PoT judgment is highly contextual dependent, varying with the factor that varied, whatever it was. Therefore, they proposed a contextual self-duration theory of the passage-of-time (Martinelli & Droit-Volet, 2022a,b; Droit-Volet & Martinelli, 2023). According to this theory, the PoT judgment results from the individual introspective analysis of the effect of context on internal states, with the emotion induced that dominates as a factor.

The aim of the present study was to go further in understanding of this human experience of the speed of the passage of time. When participants express the feeling of a change in the speed of the passage of time, this involves a comparison with the
conventional time. To being able to tell that time goes faster or slower is necessarily in
relation to a temporal reference that goes slower or faster, i.e., the time indicated by the
external clocks (watches, mobile phones). The question is: what is the role of this
reference to the time of the clock on the PoT judgment? Does the reference to the clock
time have no impact on the subjective feeling of the speed of the passage of time? In this
case, it would only represent an abstract concept used in the linguistic metaphor of the
time motion (Boroditsky, 2000). On the contrary, does the reference to the clock time affect
this temporal judgment? In this case, what is the effect of the clock time on the PoT
judgment? Does it slow down or speed up the PoT judgment? We have all had the
experience of being engrossed in an activity (reading, for example), then looking up at a
clock and exclaiming "It's already x o' clock!", or being in a waiting room, looking at a clock
and thinking on the contrary that time drags. There is thus a comparison between clock-
measured time (objective time) and the felt time. There are few data on what happens in
these situations (Wearden et al., 2014). In the case of a boring task, looking at an external
clock can increase the feeling that time is dragging on, thus slowing down the PoT
judgment. Alternatively, it can increase the feeling that time is speeding up. Indeed, people
may become aware that time passes faster that they initially thought. They then adjust
their temporal judgment to a more "objective" time, thus saying that time passes quickly.

To test these alternative hypotheses, we decided to systematically examine the
effect of an external clock on the PoT judgment. There are very few studies that have
investigated this question in an experimental setting (for a review see Thönes et al., 2018).
To our knowledge, 3 studies have investigated its effect on the perception of durations
(Craik & Sarbin, 1963; Park et al., 2016; Rotter, 1969), but only 2 studies on the PoT
judgment (Rotter, 1969, Thönes et al., 2021). Moreover, the results of these 2 studies are
mixed, as discussed later. Thönes et al. (2021) did not observe significant effect of the
external clock on retrospective judgment of the passage of time for a working memory
task. On the contrary, Rotter (1969) found a significant effect of the external clock. By
modifying the speed of the clock hands, he observed a slowing down of the PoT judgment
with the decrease in the speed of the clock hands. This suggests a systematic adjustment
of PoT judgment to time indicated by the external clock.

In Experiment 1, we tested the role of an external clock on the judgment of the
passage of time when the participants carried out an easy and a difficult task with two
groups of participants: one with an external clock and the other without an external clock.
No explicit reference was made to the external clock. In Experiment 2, using a within-
subjects design, we examined the effect of introducing an external clock on adjustment of
participants' PoT judgment to objective time in the easy task. In Experiment 3, we tested
with the same within-subjects design the effect of different clock hand speeds. In addition,
in all these experiments, we assessed how often participants looked at their clock in daily
life to determine whether those who often look at their clock were less prone to distortions
in the sense of time, or if they experienced a stronger sense of dragging time. We also
examined the relationship between frequency of looking at the clock in daily life and the
different types of PoT judgment described above.

EXPERIMENT 1

METHOD

Participants

As a part of credit courses, 118 first-year psychology students (M<sub>age</sub> = 19.49, SD<sub>age</sub> = 1.53, 97 women) participated in this experiment after reading information and consent
form. This experiment respected the Helsinki ethical principles and was approved by the Research Ethics Committee of the University Clermont Auvergne (IRB 00011540-2022-06), which waived the need to collect written consent.

## Material

The experiment took place in a laboratory room. After giving to the experimenter their watch and mobile phone, the participants sat in front of a 17-inch computer screen (60-cm distance). Data collection and stimulus presentation were handled with E-prime software v 2.0 (Psychology Software Tools, Pittsburgh, PA, USA). A 5.5 inches mobile phone was used to display a programmed digital clock with an analog clock layout. It was a circular-faced clock with 3 hands, a shorter one for the hours and two longer ones, one black for the minutes and one red for the seconds (5.5 cm). This clock was placed at the bottom of the computer screen, either on the right side or the left side. For the non-temporal task, a number consisting of 2 or 6 randomly selected digits (black, size 24) was presented on a white background in the center of the computer screen. An SMI red eye tracking bar was also used in order to capture eye movements towards the clock (left or right visual area) or the center of the screen (central visual area). Eye tracking data was processed with SMI BeGaze (SensoMotoric Instruments, Teltow, Germany). The participants responded using the computer keyboard.

## Procedure

There were two groups of participants according to the presence or not of the external clock during the whole experimental session (clock vs. no-clock group). The clock side (left, right) was counterbalanced between the participants. No explicit reference to the clock was made. The experimental session was the same for all participants. After 2 demonstration trials with a duration of 7 s, the participants were given 10 trials, each of a duration of 90 s (1.5 min): 5 trials with an “easy” non-temporal task and 5 trials with a “difficult” non-temporal task. The task order was counterbalanced between the participants. The non-temporal task was to reproduce as quickly as possible 2-digit number in the easy task and 6-digit number in the difficult task. The analyses of non-temporal performance confirmed that easy task was effectively easy for the participants than the difficult task (mean number of correct reproduction: $M_{easy} = 0.95$, $SD_{easy} = 0.11$ vs. $M_{difficult} = 0.60$, $SD_{difficult} = 0.24$, $t(117) = 15.58$, $p < .001$); mean Reaction time: $M_{easy} = 0.984$, $SD_{easy} = 244$ vs. $M_{difficult} = 2978$, $SD_{difficult} = 502$, $t(117) = -50.05$, $p < .001$).

The trials were composed in the same way for the easy and the difficult task. A trial included 12 sequences of number presentation and reproduction (for a similar procedure see Martinelli and Droit-Volet, 2022). Each sequence consisted of (1) a 500-ms fixation cross followed by (2) a 500-ms blank screen, and (3) the number presented for 1000 ms. (4) After another blank screen of 500 ms, a text box appeared (“digit reproduction”) during 4500 ms for the participant’s reproduction. The participants triggered each trial by pressing a button after the word “ready”. After each trial, they gave their judgment on how the time passed for them during this trial from 1 “very slowly” to 7 “very fast”.

At the end of the experimental session, participants answered a series of additional questions about how often they look at the clock time and their feelings about the speed of the passage of time now, for the week, month, year, the last 5 years, when they age, and if they feel time pressure. They answered on a 7-point scales ranging from “never/very slow” to “always/very fast”.

## RESULTS
## Eyes fixation for the clock area

We calculated the average number of eye fixations to the left and the right area where the clock was located, as well as the total duration of these fixations. An ANOVA was performed on these 2 dependent variables (fixation number and duration) with the task as within-subject factor and the clock as between-subject factor. Initial analysis showed no effect of the clock side. The ANOVA found a significant main effect of the clock condition, *F*(1, 116) = 10.28, *p* = .002, η²_p = 0.08, and of the task, *F*(1, 116) = 4.26, *p* = .04, η²_p = 0.04, with no clock x task interaction, *F*(1, 116) = 2.89, *p* = .09, for the number of eye fixations, as well as for the total fixation duration: clock, *F*(1, 116) = 11.15, *p* = .001, η²_p = 0.09; task, *F*(1, 116) = 4.31, *p* = .04, η²_p = 0.04; clock x task, *F*(1, 116) = 3.02, *p* = .09. As illustrated Figure 1 and as expected, participants looked at the clock area more often and longer when the clock was present (M fix.number = 4.51, ES = 0.80; M fix duration = 1238.09, ES = 220.04) than when it was absent (M fix.number = 0.80, ES = 0.83; M fix duration = 180.74, ES = 147.91), and more often and longer for the easy task (M fix.number = 3.25, ES = 0.48; M fix duration = 885.54, ES = 147.91) than for the difficult task (M fix.number = 2.07, ES = 0.77; M fix duration = 533.26, ES = 206.46).

## Passage of time

An ANOVA was performed on the PoT judgment with the clock, the task, but also the trials (5 trials) as factors (Figure 2). There was a linear effect of trials, *F*(1, 116) = 22.18, *p* < .001, η²_p = 0.16, without interaction involving this factor (all *p* > .05). This indicates an increase in the feeling of a slowing down of the passage of time with increasing number of trials.

The ANOVA also showed a significant interaction between the clock and the task, *F*(1, 116) = 4.84, *p* = .029, η²_p = 0.04, with no main effect of the clock, *F*(1, 116) = 1.80, *p* = .18, but a significant main effect of the task, *F*(1, 116) = 214.54, *p* < .001, η²_p = 0.65. The time was indeed judged to pass slower with the easy task (M = 3.296, ES = 0.12) than with the difficult task (M = 5.445, ES = 0.11).

The significant clock x task interaction indicated that there was no effect of the clock on the PoT judgment for the difficult task (M clock = 5.40, SD = 1.25; M no-clock = 5.49, SD = 1.07, *F*(1, 116) = 0.16, *p* = .69, η²_p = 0.69, because the participants hardly looked at the clock when performing the difficult task. On the contrary, there was a significant effect of the clock for the easy task (M clock = 3.58, SD = 1.43; M no-clock = 3.01, SD = 1.24, *F*(1, 116) = 5.19, *p* = .025, η²_p = 0.043. The passage of time was indeed judged to go faster with than without the clock for the easy task.

## Relationships between how often participants watch the time and their feelings about the speed of the passage of time

Table 1 shows the mean of participants' answers on the 7-point scales for the different questions asked after the experimental session, i.e., the questions on how often they watch the clock time and their different feelings about the speed of the passage of time (now, for the week, month, year, the last 5 years, as one gets older) as well as on their feeling of time pressure. The mean PoT judgment for the easy task used in our experiment was added in Table 1 for comparison. It appears that the participants judged that the time passed faster now than during the easy task), thus confirming the impact of the current activity on the PoT judgment.

More interestingly, Table 2 shows correlations between the participants' answers to these different questions. It reveals that the frequency of looking the clock time in daily life were not correlated with the different judgments of the passage of time (all *p* > .05) (see
Table 2). Consequently, the PoT judgment in a specific context (i.e., the easy task used in our study) did not slow down more in the participants who often look at their clock (R = -0.02, *p* > .05). There was only a significant relationship between how often the participants looked at their clock and the feeling of being under time pressure (R = .26, *p* < .01).

The speed of the passage of time experienced during the current easy task was also no related to different retrospective judgments of the passage of time: i.e., now, week, month, year, last 5 years, as one gets older (all *p* > .05). In contrast, these retrospective PoT judgments were significantly correlated between them (all *p* < .05), such as the faster time flies for the week, the faster time flies for the year, for example. These results were replicated in Experiments 2 and 3 (see supplementary information), so we decided not to systematically report them to reduce the length of the article.

DISCUSSION

Our results showed that the PoT judgment in a specific context was not associated
with participants' tendency to look more or less at the clock time in daily life. In other
words, it is not because some participants often look at the time on their watch or their
mobile phone that they judge the passage of time more objectively than others or that they
have the feeling that time passes slower, feeling time dragging on more strongly. The high
frequency of clock checking was only related to the feeling of being under time pressure.

In line with the contextual self-duration theory of the passage of time (Martinelli &
Droit-Volet, 2022a,b; Droit-Volet & Martinelli, 2023), our results confirmed that PoT
judgment is highly context-dependent, thus depending in our study of the difficulty of the
activity performed, and this independently of its duration. This finding replicated those of
Martinelli and Droit-Volet that showed that time was judged to pass slower in an easy task
compared to a difficult task, although the durations of these tasks were similar. However,
these authors also showed that, in a prospective time judgment, when the participants
were instructed to judge time, PoT judgment could also result from processing of durations
when changes in stimulus durations formed the most salient contextual information. In
their experiment, the passage of time was judged to go slower for long durations than for
shorter durations. Therefore, in Experiment 2, we tested the PoT judgment with 2 different
durations in the same task, namely the easy task for which we found a clock effect. The
durations tested in Experiment 2 were nevertheless longer (between 4 and 6 min) than
that used in Experiment 1 (1.5 min) in order to check the generality of our clock-related
results with long-lasting durations.

Our results showed that the presence of an external clock had a significant effect on the judgment of the passage of time in the easy task but not in the difficult task. Monitoring eye movements with the eye tracker in our experiment allows us to simply explain the lack of significant clock effect in the difficult task by the fact that participants barely looked at the external clock in a highly demanding task. Therefore, the more the task requires attention for its completion, the less one looks at the clock. We can, of course, assume that the role of the clock time and its consultation is different for tasks under time pressure, when these must be completed in a given short time (e.g., Christandl et al., 2018), which was not the case in our experiment.

For the easy task, our results also showed that the time was judged to pass quickly
with the external clock than without the external clock. The presence of a clock did not
accentuate the feeling that time is dragging, as one might conceive. Furthermore, our
results suggest that the presence of the external clock did not radically modify the feeling
of the passage of time. Indeed, the PoT judgment remained different between the difficult
task and the easy task even in the clock condition, i.e., when the clock indicated an
objective time flow. Consequently, we assume that the judgment of the speed of the
passage of time has somehow nothing to do with our knowledge of clock time (see general
discussion), because it remains grounded in our internal states (emotion). Looking at the clock would only allow us to punctually adjust our feelings of the passage of time to standard time. In other words, with a clock in front of them, the participants would simply appreciate that time finally passed a little faster than they previously thought. In order to test this hypothesis, we also decided to examine how the introduction of a clock in the participants' environment modify their initial PoT judgment by using a within-subjects design. In Experiment 2, the participants therefore had to judge the speed of the passage of time when performing the easy task on a series of trials with two durations, firstly in the no-clock condition, and then in the clock condition.

# EXPERIMENT 2

## METHOD

### Participants

The sample was composed of 59 first-year psychology students who, after having read the information and consent form, participated in this experiment for course credits ($M_{age} = 18.71$, $SD = 2.08$, 56 women). The experimental procedure was validated by the Research Ethics Committee of the Clermont Auvergne University (IRB 00011540-2022-06).

### Material and procedure

The material and procedure were close to those used in Experiment 1, except that the participants performed only the easy task and that 2 durations were tested: 270 s (4.5 min) and 324 s (5.4 min). In addition, the participants were placed in the no-clock condition and then in the clock condition to examine how spontaneous PoT judgment was modified when a clock was introduced in the experimental environment. After the Clock condition, during a small break, the experimenter entered the room and placed the clock on the left or the right side of the computer (counterbalanced between the participants). No explicit reference to the clock was made.

The participants were given 8 trials, 4 trials in the no-clock condition followed by 4 trials in the clock condition. For each condition, 2 trials had a duration of 270 s and 2 trials of 324 s. The trials were randomly presented. As the trial duration was longer than in Experiment 1 and the number of presentation-reproduction sequence similar ($N = 12$), we added time to each sequence event. For both the 270-s duration and the 324-s duration, (1) a 1500-ms fixation cross appeared, then (2) a 1500-ms blank screen, and (3) the digit sequence for 3000 ms. (4) After a second 1500-ms blank screen, the "digit reproduction" text appeared during 13500 ms for the participant's reproduction. The inter-sequence intervals lasted between 1125 and 1875 seconds for the 270 s durations and between 3600 and 8250 seconds for the 324 s durations, such as the trial duration was of 270 and 324 s, respectively.

A series of 3 questions on how bored they felt during the trials was also added with a 7-point response scale going from "1 - not at all" to "7 - a lot": (1) "I was bored"; (2) "the task was not interesting"; (3) "I had difficulty fighting boredom".

## RESULTS

### Eyes fixation for the clock area
As in Experiment 1, the statistical analyses on the mean number of eye fixation and the duration of eye fixation towards the clock areas confirmed that participants look more often and longer at clock localization areas in the clock condition than in the no-clock condition: Number of fixation, *F*(1, 58) = 38.58, *p* < .001, η²_p_ = 0.40; fixation duration, *F*(1, 58) = 34.44, *p* < .001, η²_p_ = 0.37. A previous analysis showed no effect of the clock localization (right vs. left) (*p* > .10).

## Passage of time

An ANOVA was performed on the PoT judgment with 3 within-subjects factors (duration, trial, clock). It revealed a major main effect of the duration, *F*(1, 58) = 13.16, *p* < .001 η²_p_ = 0.19, and of the trial, *F*(1, 58) = 8.17, *p* < .006, η²_p_ = 0.124 (Figure 3A). The speed of the passage of time was indeed judged to go slower for the long duration (M = 2.86, ES = 0.16) than for the shorter one (M = 3.19, SE = 0.16). The feeling of a slowdown of time also increased with the increasing number of trials. The effect of the clock just failed to reach significance, *F*(1, 58) = 3.26, *p* = .076, η²_p_ = 0.05, with the passage of time that tended to be judged faster in the clock condition than in the no-clock condition. No interaction was significant (all *p* > .10).

However, when we included in the analyses the feeling of boredom (mean score for the 3 boredom-related questions) as covariable, the duration factor lost its significance, *F*(1, 57) = 0.86, *p* = .36, as well as the trial factor, *F*(1, 57) = 0.07, *p* = .80. In the within-subjects design used in our study, boredom and its increase with the length of the duration and the length of the experimental session constituted the main factor explaining the variations in the PoT judgment, *F*(1, 57) = 17.10, *p* < .001, η²_p_ = 0.23. Indeed, the more the participants were bored, the more they judged that time passed in slow motion (Figure 3B). However, with boredom as covariable, the clock x trial interaction reached significance, *F*(1, 57) = 4.65, *p* = .035, η²_p_ = 0.08, as well as the clock x trial x boredom interaction, *F*(1, 57) = 5.97, *p* = .018, η²_p_ = 0.10.

Figure 3C illustrates the succession of PoT judgments across the trials (regardless of the duration), with the first 4 trials (1-4) in the no-clock condition and the 4 following trials in the clock condition (5-8). This figure clearly indicates a cubic trial effect over the 8 trials, *F*(1, 58) = 9.70, *p* = .003, η²_p_ = 0.14. Indeed, the feeling of a slowdown of time increased linearly from the trials 1 to 4, *F*(1, 58) = 6.18, *p* = .016, η²_p_ = 0.10. However, a recalibration of this temporal feeling occurred with the presence of the clock in trial 5. Then, the feeling of slowing down time took over and increased linearly from trials 5 to 8, *F*(1, 58) = 8.58, *p* = .005, η²_p_ = 0.13. Consequently, the passage of time was judged faster for the first trial (trial 5) or the second trial (trial 6) in the clock condition than for the last trial in the no-clock condition (trial 4) (*t*(58) = -4.91, *p* > .0001, Cohen's d = 1.34, *t*(58) = -2.77, *p* = .008, d = 1.32, respectively).

However, as judgments of the passage of time based on participants' internal state (boredom) dominated even in the clock condition, the passage of time was then judged slower on trials 7 and 8, such as no difference in PoT judgment was observed between these clock trials and the no-clock trial 4 (*t*(58) = 1.26, *p* = .21, *t*(58) = -1.64, *p* = .11, respectively). This significant slowing down of the passage of time was observed in the clock condition (e.g., trial 8), while participants looked at the clock areas more often in this last trial in the clock condition than in the last trial (trial 4) in the no-clock condition, *t*(58) = 5.39, *p* < .001, *d* = 67.30), and they looked at the clock as often in trial 8 as in trial 5 (the first trial in the clock condition), *t*(58) = 1.59, *p* = .12, and even tended to look at the clock longer in trial 8 than in trial 5, *t*(58) = 1.74, *p* = .087, *d* = 20977.

## DISCUSSION
The results of Experiment 2 replicated those of Experiment 1 and showed that the feeling of the passage of time was contextual dependent and mainly based on the individual internal context, i.e., the emotion of boredom induced by the current activity.

Experiment 2 also showed that duration affected the passage of time experienced with the time being deemed slower for the long duration than for the shorter duration. This is consistent with the results from previous studies which found that participants were able to discriminate different paces in the passage of time for different durations both in the minutes and the seconds range (Martinelli & Droit-Volet, 2022; Droit-Volet & Hallez, 2022). However, in our experiment using long durations of several minutes, this temporal discrimination resulted more from felt differences in the internal state of boredom than from the processing of the duration itself. It would be nevertheless difficult to dissociate these 2 factors (boredom, duration), according to the theoretical idea that duration (especially long duration) would be grounded in sensory-motor experience, a loss of energy in the case of boredom (Droit, Witmman,).

Moreover, our results, obtained with a within-subjects design, allows us to better understand the effect of an external clock on PoT judgment. Our results showed that the participants often looked at the clock when it was present in their environment, at least in the easy and boring task used in our study (see Experiment 1). Consulting the clock allowed them to readjust their temporal judgment towards a more “objective” time, that indicated by the clock. Indeed, consistent with this idea of a readjustment of temporal judgment, in Experiment 2, as in Experiment 1, the participants did not report that time dragged on more (slower) when looking at the clock but passed faster. However, the emotion felt (boredom) had a predominant effect on the PoT judgment. When the experimental session extends over time, the participants reported a slow passage of time in the clock condition as well as in the no-clock condition, and this even when they looked at the clock frequently. This demonstrates that the clock did not have a simple distracting effect on the temporal judgment, and that variations in PoT judgment was fundamentally based on changes in felt emotion, i.e., boredom.

However, the major effect of boredom on the PoT judgment obtained in our experiment using a within-subject design could be due to the long durations used which accentuated the feeling of boredom and thus in turn its effect on the time judgment. Therefore, to verify our results, we performed a third experiment with a shorter duration than that used in Experiment 2: a duration of 90 s as in Experiment 1.

In addition, to examine in more details the effect of a clock on the PoT judgment, we decided to manipulate the clock speed. Very few experimental studies have systematically manipulated the clock speed (for a review see Thönes et al., 2018). Most of these studies have reduced the speed of clock hands to 80 or 50 % and increased it to 120, 150 or 200 %, and found that the participants did not notice these clock manipulations. The results of these studies suggest that the altered clock speeds modify duration judgment, with elapsed duration that was overestimated with a faster clock and underestimated with a slower clock rate (Craik & Sarbin, 1963, Park et al., 2016). It also modified the PoT judgment. Rooter (1969) found that “the slower the speed of a clock, the slower was experienced the flow of time” (p. 51). However, Thönes et al. (2021) did not replicate these results for the retrospective PoT judgment of a memory working demanding task. In our study, we therefore decided to test 3 different clock speeds: (1) a faster rate, (2) a slower rate, and (3) a normal rate (control condition). Our hypothesis was that the introduction of a clock in the experimental context would produce a readjustment of the PoT judgment, such as time would be judged to pass more quickly with than without a clock. However, the feeling of a slowing down of time based on boredom would quickly take over with the increasing number of trials, such as no difference in the PoT judgment would be observed between the condition with and without the clock for the last trials, even if the participants
always looked at the clock (see Experiment 1 and 2). In addition, the readjustment of the PoT judgment would be different depending on the clock speed with the experience of an acceleration of the passage of time higher with an external clock running at a higher rate than at a normal rate (control group), and with a normal rate than a slower rate.

# EXPERIMENT 3

## METHOD

### Participants

71 new students in psychology ($M_{age} = 18.52$, SD = 1.24, 65 women) participated in this experiment for course credits after the consent form reading. The experimental design was approved by the Research Ethics Committee of the Clermont Auvergne University (IRB 00011540-2022-06).

### Material and procedure

The material and procedure were also close to that used in Experiment 2 with only the easy task but a shorter duration of 90 s. The participants were given 10 trials, 5 in the No-Clock condition, and then 5 in the Clock-condition. There were 3 groups of participants as a function of the type of clock used: (1) with the clock hands turning at the normal rate, (2) at a faster rate, and (3) at a slower rate. The speed of movement of the seconds hand (red) was of: one movement for 1 second for the normal rate, one for 500 s seconds for the faster rate, and one for 1500 s for the slower rate.

## RESULTS

### Eyes fixation for the clock area

The results on the eye movements replicated those of Experiments 1 and 2 by indicating that participants looked more often at the visual areas of the localization of the clock in the clock condition than in the no-clock condition: Number of fixation, $F(1, 68) = 31.27, p < .001, \eta_p^2 = 0.32$; fixation duration, $F(1, 68) = 27.71, p < .001, \eta_p^2 = 0.29$. The clock location (right vs. left) had no effect on eye movements (all *p* > .10). There was also no difference in eye movements as a function of clock speed (*p* > .10), indicating that the participants did not look at the clock more often and longer when its speed was different from normal.

### Passage of time

Figure 4 shows the PoT judgment for the different trials in the no-clock condition followed by those in the clock condition, for the 3 groups of participants with different clock speeds (normal, faster, slower). Inspection of Figure 4 indicates a clock effect on the PoT judgment that decreased with increasing number of trials from trial 6 to trial 7, with a larger decrease between trial 8 and trial 9, particularly in the condition with faster clock. Therefore, and consistently with our hypothesis, we conducted two ANOVA with 3 factors (the clock speed as between-subjects factor, and the clock and the trials as within-subjects factors): a first ANOVA with the trials 3, 4, 5 and 6, 7, 8, in order to compare the 3 last trials without the clock (trial, 3, 4, 5) and the 3 first trials with the clock (trial 6, 7, 8), and
second ANOVA with the trials 4, 5, and 9, 10, to compare the last 2 trials without the clock (trial 4,5) and the last 2 trials with the clock (trial 9, 10).

The first ANOVA showed a significant effect of the clock, $F(1, 68) = 8.13, p = .006$, $\eta_p^2 = 0.11$, and of trials, $F(2, 136) = 3.02, p = .05$, $\eta_p^2 = 0.04$. The effect of the clock speed did not reach significance, $F(2, 68) = 0.26, p = .78$. There was also no 2- or 3-way interactions involving the different factors (all $p > .05$). This indicated that the time was judged to go faster in the clock condition (M = 4.46, ES = 0.17) than in the no-clock condition (M = 4.01, ES = 0.16) on the first trials. Post-doc analyses on the difference in PoT judgment between 2 trials, the last trial without a clock (trial 5) and the trial with the clock either the trial 6, 7 or 8, showed a significant effect of the clock speed for the trial 7, $F(2, 68) = 4.01, p = .02$, $\eta_p^2 = 0.11$, and the trial 8, $F(2, 68) = 3.90, p = .03$, $\eta_p^2 = 0.10$, but not for the trial 6, $F(2, 68) = 1.85, p = .17$. Bonferroni tests suggest that for the trials 7 and 8, the participants tended to judge that the time passed faster with the clock running with a faster rate than that with a normal pace ($p > .05$) (Trial 7, $M_{faster} = 1$ vs. $M_{normal} = -0.23$; Trial 8, $M_{faster} = 0.88$ vs. $M_{normal} = -0.36$). No difference in the PoT judgment was observed between the clock with the normal speed and that with the slower speed ($p > .05$) (Trial 7 and Trial 8, $M_{slower} = 0.21$ and $0.25$, respectively).

In contrast, the ANOVA comparing the last trials (trials 9, 10) with the clock to the last trials without the clock (trials 4, 5) did not find any significant results, neither effect of the clock, $F(2, 68) = 1.53, p = .22$, nor of the trial, nor of the clock speed, nor interaction between these factors (all $p > .05$). After 3 experimental trials, the participants judged that time passed slowly in all conditions, with the clock as well as without the clock. This feeling of time slowing down was observed even when the participants gaze more often and longer at the visual clock localization area (i.e., the clock) in the clock condition than in the no-clock condition (trial 5 vs trial 9, $t_{fix.number}(70) = 5.90, p < 0.001, d = 14.22$; $t_{fix duration}(70) = 5.61, p < 0.001, d = 4366$; trial 5 vs. trial 10, $t_{fix.number}(70) = 5.74, p < 0.001, d = 15.31$; $t_{fix duration}(70) = 5.50, p < 0.001, d = 4415$). It was also observed while the participants tended even to look more often and longer at the clock in the trial 9 and the trial 10 than in the trial 6 (the first trial with the clock) ($t_{fix.number}(70) = 1.77, p = .08$; $t_{fix.number}(79) = 1.97, p = .05$; $t_{fix duration}(70) = 1.9, p = .06$; $t_{fix duration}(79) = 1.82, p = .07$, respectively).

When we added the score of boredom (averaged score for the 3 questions on boredom) as covariate to this last ANOVA, boredom appeared to be the only factor explaining the PoT judgment, $F(1, 67) = 20.60, p < .001$, $\eta_p^2 = 0.24$. Moreover, the level of boredom did not change as a function of the clock speed, $F(2, 69) = 0.06, p = .95$. In sum, the more bored the participants felt, the more they felt that the passage of time was slowing down, and the presence of a clock did not change this feeling of boredom.

## DISCUSSION

The results of Experiment 3 replicated those of Experiments 1 and 2. They showed that the presence of a clock significantly impacted the judgment of the passage of time, leading the participants to claim that the time passed ultimately faster than that they had thought, that they had experienced previously.

Contrary to our assumptions, our results suggested that the type of clock used has little effect on the PoT judgment. Only a small difference in temporal judgment was observed for the trials 7 and 8 between the fast clock rate and the normal clock rate. In these trials, participants tended indeed to say that time passed faster with the fastest clock. No difference in the PoT judgment was nevertheless found between the normal clock and the slower clock. In accordance with the recent results of Thönes et al. (2021), our results did not replicate those of Rotter (1969) showing a significant decrease in the speed of time felt with the decrease in the movements of the clock hands.
A first explanation would be that the experimental differences in the clock rhythm used were not significant enough to find significant results. The methodological difficulty in the manipulation of the clock speed is that participants must not notice an alteration in clock speed for its effectiveness. With more altered speed of the clock hands, participants might not believe the time indicated by the clock. In addition, we no longer know whether it is the movement of the hands themselves or the actual time indicated by the clock that affect the temporal judgment.

A second explanation would be that participants know the normal rhythm of a clock and therefore intentionally ignore small differences in the movements of the clock hands. They may also have failed to pay attention to the movements of the clock hands due to their reduced alertness produced by boredom (..). However, in these 2 cases, no effect of the clock type would be observed, even in the condition with the faster clock rate. Moreover, the experiments that manipulated the speed of an external clock showed that participants did not notice changes in the speed of the clock hands in the ranges tested in our study (Thönes et al., 2018).

Another more believable explanation would be that the speed of the passage of time experienced by the participants was particularly very slow, so that a further decrease would be difficult to obtain, even if they noticed that in reality, less time has passed than they thought. An alternative and non-exclusive explanation would be that the external clock had finally little impact on the feeling of the passage of time during a task. Similarly, Thönes et al. (2021) did observe difference in retrospective judgment of the passage of time with different clock speed manipulations. Indeed, the results of Experiment 3, as those of other Experiments, demonstrated that the individual feeling of the passage of time primarily lies in emotion felt, boredom in the case of our easy task.

## GENERAL DISCUSSION

The results on the effect of an external clock on the judgment of the passage of time for a non-temporal task with two levels of difficulty (easy vs. difficult) were replicated in our 3 experiments and consistent. They showed that the present PoT judgment was primarily based on the emotion induced by the encountered context. In our study, it was the emotion of boredom associated with the easy task, regardless of its duration. The passage of time was indeed experienced as going more slowly in the easy task that in the difficult task. In addition, the more the individuals were bored, the more they judged that time passed in slow motion. Our experiment thus added data to growing database providing evidence of the key role of emotion (affective state) in the judgment of the passage of time, and, in particular, the emotion of boredom. For example, recent studies on people in lockdown during the Covid-19 pandemic have shown that boredom was the main predictor of their feeling that the time passed more slowly during the lockdown than before. Similarly, Witowska et al. (2020) showed that boredom was significantly associated with feeling that time passed slowly when people waited in an empty room for 7.5 minutes. Recently, Weiss et al. (2021) reproduced this type of results showing that the passage of time was associated to experience of boredom in a boring task, beyond individual differences in the experience of boredom. Boredom is the negative affective dimension of the lack of cognitive engagement in an activity. Therefore, our experiments provide support to theories of flow which emphasize the strong link between sense of time and occupational emotional and intellectual engagement (Larson, 2004; Larson & von Eye, 2006; Nakamura & Csikszentmihalyi, 2014; Csikszentmihalyi, 1990). However, the factors responsible of variations in the PoT judgment depend on context according to the contextual self-duration theory of the passage-of-time (Martinelli & Droit-Volet, 2022a,b; Droit-Volet & Martinelli, 2023). And, in the present case of a task that did not require a high cognitive engagement, and which extended over time, this factor is boredom.
The findings of our experiments also provided a series of arguments in favor of a reduced role of the reference to the time clock on the PoT judgment. Firstly, we found no significant relationship between the feeling of the passage of time in a given situation and individual tendencies to look more or less at the clock time in daily life. It is not because individuals often look at their clock that they are less prone to distortions in the sense of time or that they experienced a stronger feeling of dragging time. How often people looked at their clock was only systematically correlated with the feeling of time pressure. Obviously, time pressure can affect the PoT judgment for a task carried out under time pressure (Christandl, et al., 2018). Moreover, the frequency of looking at the clock can change depending on the situation encountered. For example, Experiment 1 showed that the participants looked at the clock more frequently and longer in the easy task than in the difficult task. In their boring waiting situation, Witowska et al. (2020) found that participants thought about time more often, and, consistent, we found in our experiments that they looked at the clock time more often. The reference to the clock time therefore depends on the situation, the activity, and the engagement of attention of participants in this activity.

Secondly, we found that the presence of a clock affected the PoT judgment, but only occasionally. Indeed, after a few trials, there was no longer any significant effect of the clock on the PoT judgment. Indeed, for the last trials, the participants experienced the same slowing down of time in the condition with and without the external clock. It was not because they were not looking at the clock anymore. The analysis of eye movements with the eye tracker demonstrated on the contrary that they always looked at the clock in the last trials or even more often and longer than in the first trials with the clock. Consequently, the time clock no longer had an impact on the judgment of passage of time. Only the emotion felt – boredom – was determinant.

This supports the idea that for the feeling of passage of time, we use a linguistic metaphor relative to the speed of motion (time speeds up or slows down) which implies an abstract concept of time (Boroditsky, 2000). However, this concept of something unobservable does not influence the subjective experience of the passage of time. We recently conducted a study on the PoT judgment in young children aged 4-5 years who were not able to tell the time on a clock. These young children nevertheless produced PoT judgments similar to those found in adults based on their emotion. They judged time to pass faster when they felt happier and more alert. As we have argued, the explicit experience of variation in time motion (acceleration and deceleration) reflects changes in self-movement, specifically in successions of individual states and their extension. The awareness of changes in the speed of the passage of time is thus rooted in perceived changes in emotional and sensory-motor experience. The theories of the embodiment of time encounter difficulties in finding empirical supports. Our results provide thus new support with regard to the awareness of the passage of time. They also provide support regarding the temporal judgment of long durations, when increasing the duration of activity has dynamic consequences on individual affects. Indeed, our study showed that the longer the duration, the more the participants were bored, and the slower the time was considered.

Our results showed the time of the clock has finally a small but significant effect on the PoT judgment. The clock effect observed in our studies systematically resulted in an acceleration of time flow felt. The passage of time was effectively judged as passing more quickly in the clock condition than in the no-clock condition. Whatever the speed of the clock used (fast, normal, slow), we found this speeding up of PoT judgment. The PoT was not judged to go slower with the clock hands than turned slower contrary to what Rotter (1969) found. As discussed previously, the lack of slowing down of subjective time with the clock may have several origins. A possible cause may be related to the easy task used in our experiments that produced a strong feeling of a slowed down time, such as an additional slowdown is difficult to envisage. In the mind of the participants, the time during
an activity, which naturally inflows over time, cannot slow down until it stops. A limitation of our studies is that we have not tested a series of the other tasks or other situations to further investigate the role of different clock speeds on the PoT judgment. Another limitation is not having tested longer durations of the order of a quarter of an hour, half an hour and an hour. The role of the clock time is probably more important in this temporal range. For example, Park et al. (2016) found participants modified the duration of an activity of 90 min when they were told that time passed 2 times faster (180 min) or 2 times slower (45 min). Other studies are needed to provide a complete picture of the role of clock time on PoT judgment.

However, thank to our Experiments 2 and 3 using a within-subject design, our findings clearly indicated that the clock effect was transient. Indeed, in these two experiments, we observed a significant effect of the clock only for the first trials in the clock condition. Consequently, we can assume that the acceleration of the PoT in presence of the clock results from an adjustment of subjective time to objective time, that displayed on the clock. Indeed, in front of the reality of time, the participants may become aware that time has passed finally faster than they initially though. Consequently, they judged that it passed faster in the clock condition than in the previous non-clock condition. However, the magnitude of this acceleration of the speed of the passage of time in presence of the clock remained limited at about 1 point on a 7-point scale. It is because the emotion (boredom) acts as an attractor, the PoT judgment being the mirror of affects perceived and of their changes, in other words, movements perceived in the self-duration (see Martinelli & Droit-Volet, submitted).

Our studies on the effect of clock time on the judgment of the passage of time allow us to understand that this temporal judgment is a spatial metaphor of time that serves to account for affects resulting from the introspective analysis of the self in a given situation. The clock then allows a simple and punctual adjustment of this subjective time to a more objective time, thus reducing the distortion of the sense of time. Our studies finally highlight the limited role of watches which are mainly used to adapt to social time (appointment time, finishing a task on time). However, the role of the clock time appeared limited in our study on the PoT judgment for short durations of a few minutes. Its role may be different for longer durations of several hours. This should be taken into account.

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