Droit-Volet

G T Lorandi

Sylvie Droit-Volet
email: sylvie.droit-volet@uca.fr

Running head: Judgment of the passage of time in the elderly The retrospective and present judgment of the passage of time in the elderly

Keywords: Time, Passage of time, Aging, Consciousness, Happiness, Memory

This study examined the judgment of the passage of time in elderly people living in retirement homes, focusing on the passage of time experienced in the present and that judged retrospectively for short periods (last day, week, month) and longer periods of life (year, now compared with 5 years before, as we get older). Participants' cognitive abilities and feeling of happiness were also assessed among other dimensions. Results showed no significant relationship between these three forms of judgment of the passage of time, except between the judgment of the passage of time for the present and for the day. In addition, the level of happiness was a significant predictor of both the momentary judgment of the passage of time and the retrospective judgment of the passage of time for shorter periods. In contrast, the individual differences in cognitive abilities better explained differences in the retrospective judgment of the passage of time for longer periods. As discussed, the different forms of judgments of the passage of time are therefore based on different cognitive mechanisms.

INTRODUCTION

How fast does time seem to pass for you? It makes no sense to ask people this question if we do not give them a time frame. Their answers can be based on their direct experience of the passage of time in the present moment or on comparisons between the rhythm of their lives in the present and in different past periods. And the underlying cognitive processes are likely to differ according to the type of judgment.

A distinction is made between two types of judgment of the passage of time: the retrospective passage-of-time judgment (retro-PoT) and the present passage-of-time judgment (present-PoT) [START_REF] Wearden | Passage of time judgements[END_REF]. The retro-PoT judgment is the judgment of the passage of time for an entire period of time that has already elapsed, i.e. in the past. The past period considered can be more or less long, covering a day, a week, a month or several years. The questions typically asked to participants are: How fast has time passed for you during the last week/month/year/5-10 years? The period considered can also cover an entire span of life as in the question "Do you think that time passes more quickly when one gets older? (e.g., [START_REF] Friedman | Aging and the speed of time[END_REF][START_REF] Janssen | Why does life appear to speed up as people get older[END_REF]Joubert, 1990;[START_REF] Lemlich | Subjective acceleration of time with aging[END_REF]Wittmann & Lehnoff, 2005;Wittmann et al., 2015).

The present-PoT judgment is the evaluation of the immediate sense of the speed of the passage of time, that is the momentary temporal judgment made in the present. It is closely linked to the context in which the judgment is made. To evaluate this type of temporal judgment, researchers have used Experienced Sampling Methodology (ESM), also called Ecological Momentary Assessment (EMA) (Droit-Volet, 2019;[START_REF] Droit-Volet | Experience Sampling Methodology reveals similarities in the experience of passage of time in young and elderly adults[END_REF][START_REF] Droit-Volet | Passage of time judgments are not duration judgments: Evidence from a study using Experience Sampling Methodology[END_REF][START_REF] Droit-Volet | Passage of time judgments in everyday life are not related to duration judgments except for long durations of several minutes[END_REF]. Indeed, this method permits the evaluation of the PoT judgment at different times of the day. In addition, each temporal question is associated with a series of other questions about the context (emotion, activity) in which the temporal judgment is made. Some researchers have also attempted to examine this temporal judgment by asking participants to answer one question on their current life: How fast does time usually pass for you? (Winckler et al., 2017;[START_REF] Janssen | Why does life appear to speed up as people get older[END_REF]. However, this judgment is ambiguous because it is not clear whether participants base their judgments on direct experience of the PoT at time t, or on a period of several days, weeks or months, i.e. on life in general.

The few studies on PoT judgments have found different results depending on the type of temporal judgment requested. Although the data are not always consistent across studies [START_REF] Droit-Volet | Experience Sampling Methodology reveals similarities in the experience of passage of time in young and elderly adults[END_REF], most of them have found an effect of age on the retro-PoT judgment when a long period of life was taken into account, i.e. for questions covering periods of 5 or 10 years and questions relating to changes in PoT with aging (e.g. [START_REF] Janssen | Why does life appear to speed up as people get older[END_REF][START_REF] Lemlich | Subjective acceleration of time with aging[END_REF][START_REF] Winkler | Has it[END_REF]Wittmann & Lehnhoff, 2005). For these two long periods, the PoT was judged faster by older participants (older than 50 years) than younger participants. In contrast, for the retro-PoT judgment of shorter time periods (day, week, month), no age effect has been observed [START_REF] Droit-Volet | Experience Sampling Methodology reveals similarities in the experience of passage of time in young and elderly adults[END_REF][START_REF] Droit-Volet | Passage of time judgments are not duration judgments: Evidence from a study using Experience Sampling Methodology[END_REF][START_REF] Friedman | Aging and the speed of time[END_REF][START_REF] Janssen | Why does life appear to speed up as people get older[END_REF][START_REF] Winkler | Has it[END_REF]Wittmann & Lehnhoff, 2005;Wittmann et al., 2015). Similarly, the ESM studies on the present-PoT judgment have not found any difference between older and younger participants [START_REF] Droit-Volet | Experience Sampling Methodology reveals similarities in the experience of passage of time in young and elderly adults[END_REF][START_REF] Droit-Volet | Passage of time judgments are not duration judgments: Evidence from a study using Experience Sampling Methodology[END_REF][START_REF] Droit-Volet | Passage of time judgments in everyday life are not related to duration judgments except for long durations of several minutes[END_REF]. A recent ESM study conducted by Droit-Volet (2019) even showed a reversal in the daily feeling of the passage of time toward a slowing down of time in the participants older than 75 years of age, and especially those living in retirement homes. In recent studies of PoT during the COVID lockdown using a large sample, [START_REF] Ogden | The passage of time during the UK Covid-19 lockdown[END_REF] and Droit-Volet et al.

(2020) also found a significantly slower passage of time with increasing age, alhough this age effect was not replicated in another COVID study [START_REF] Martinelli | Time and Emotion in the lockdown for the Covid-19 epidemic: The determinants of our experience of time?[END_REF]. One can therefore have the experience that the years flash past, but that the days last forever [START_REF] Droit-Volet | Experience Sampling Methodology reveals similarities in the experience of passage of time in young and elderly adults[END_REF].

The differences in the results according to the type of temporal judgment can be explained by the different psychological mechanisms that underlie each type of judgment. ESM studies have found that the main predictor of the present-PoT judgment was not age but the affect felt at the moment of the judgment, namely the level of happiness felt [START_REF] Droit-Volet | Experience Sampling Methodology reveals similarities in the experience of passage of time in young and elderly adults[END_REF][START_REF] Droit-Volet | Passage of time judgments are not duration judgments: Evidence from a study using Experience Sampling Methodology[END_REF][START_REF] Droit-Volet | Passage of time judgments in everyday life are not related to duration judgments except for long durations of several minutes[END_REF]Droit-Volet, 2019). Participants have indeed reported that time passes faster when they are happy and drags when they are sad (less happy).

The feeling expressed by seniors living in retirement homes that time slows down is therefore associated with a decrease in their level of happiness (Droit-Volet, 2019). Indeed, seniors living in retirement homes often present symptoms of depression or anxiety [START_REF] Seitz | Prevalence of psychiatric disorders among older adults in long-term care homes: A systematic review[END_REF]. Other significant predictors of the present-PoT judgment have nevertheless been identified, namely the level of arousal, the degree of attention devoted to the current task, the feeling of frustration [START_REF] Tipples | Increased frustration predicts the experience of time slowing-down: Evidence from an experience sampling study[END_REF], time pressure or the number of routines involved in daily life [START_REF] Janssen | Why does life appear to speed up as people get older[END_REF][START_REF] Winkler | Has it[END_REF]. The present-PoT judgment does indeed depend on the context in which it is made, and this varies according to the population tested and their lifestyle. However, as argued by [START_REF] Winkler | Has it[END_REF], the two main predictors of judgment of current passage of time are emotion and attention.

The present-PoT judgment is therefore closely related to the emotional state experienced by participants in the present moment. The relationship between the emotion felt (happiness) and the other forms of PoT judgment has not yet been investigated. Nevertheless, we can assume that the feeling of happiness is less related to the retro-PoT judgment than to the present-PoT judgment, with the latter being based on emotions experienced in the present moment and the former on recovery processes in long-term memory [START_REF] Friedman | Aging and the speed of time[END_REF][START_REF] Blas | L'évolution de la mémoire et de la notion de temps. L'Harmattan[END_REF]. However, there may also be a difference due to the period of time considered, i.e. whether it is short (day, week, month, year) or long (5-years, PoT with aging). Indeed, retro-PoT judgments for shorter periods (i.e., day, week, month, year) imply episodic memory, which is based on certain memories of personal events of daily life together with their emotional dimension [START_REF] Di Crosta | Commentary: Experience Sampling Methodology reveals similarities in the experience of passage of time in young and elderly adults[END_REF]. On the other hand, retro-PoT judgments for longer periods seem to be based more on knowledge of self in its temporality (narrative self, [START_REF] Gallagher | Philosophical conceptions of the self: implications for cognitive science[END_REF], detached from daily experiences. For example, most people think that time passes faster as they get older. But this thought does not correspond to any reality [START_REF] Miller | Does it really seem to us as though time passes?[END_REF]. In everyday life, time does not pass more quickly in older than in younger people (e.g., [START_REF] Droit-Volet | Experience Sampling Methodology reveals similarities in the experience of passage of time in young and elderly adults[END_REF]. As Pierre Janet (1928) said many years ago, it is a kind of "collective illusion": "There is no contradiction between us, we all have the same language about this optical illusion" (p. 43). This idea in fact comes from knowledge of self in its temporality, i.e., from the deduction in relation to our age that we have little time left to live before the probable date of our death [START_REF] Droit-Volet | Awareness of the passage of time and selfconsciousness: what do meditators report[END_REF]. Therefore, the retro-PoT judgment for long periods would depend on processes related to semantic memory rather than episodic memory with its emotional coloring, although the two do not operate separately. In this case, it can be assumed that the inter-individual differences in the retro-PoT judgment for long periods may be related to individuals' cognitive abilities rather than to the feeling of happiness experienced in everyday life. In contrast, the retro-PoT judgment of shorter periods (day, week, month) may also be related to individuals' level of happiness.

The aim of this study was to examine the different types of judgment of the passage of time (retro-PoT, present-PoT) and the links between them, as well as their predictors: the level of happiness felt and/or the cognitive capacities. We conducted this study with old participants living in the same retirement home for three main reasons. The first was to find participants with different cognitive abilities in order to examine our hypotheses. The second was to avoid differences in temporal judgments related to the place of residence. The third was to try to replicate the results found by Droit-Volet (2019) in elderly persons at different stages of dementia. Participants' cognitive abilities were assessed using the MoCA, which is used to diagnose dementia (Montreal Cognitive Assessment) [START_REF] Nasreddine | The Montreal Cognitive Assessment, MoCA: a brief screening tool for mild cognitive impairment[END_REF]. Participants' levels of depression and anxiety were also evaluated using the Beck Depression Inventory (BDI, [START_REF] Beck | Beck depression inventory (BDI)[END_REF]) and the State-Trait Anxiety Inventory (STAI, [START_REF] Spielberger | Manual for the State-Trait Anxiety Inventory[END_REF], respectively. We used ESM for the present-PoT judgment and a series of questions for the retrospective-PoT judgment. Self-reported level of happiness was assessed after each time question for the former and after the series of questions for the latter. All the participants volunteered to participate in this experiment and signed a consent form approved by the Sud-Est VI Statutory Ethics committee.

METHOD

Materials and Procedure

For the retrospective PoT judgments (retro-PoT), the participants responded to a series of 7 questions on a 7-point Likert-type scale (from 1 "not at all -very slow" to "very muchvery fast"): "Do you find that time has passed quickly today (1), this week (2), this month (3), this year? (4)'', ''Do you find that time passes more quickly now than 5 years ago (5), and that time is passing faster as you get older (6)?''. The retro-PoT for the day (7) was averaged over the responses given at the end of each of the five ESM testing days (between 7 and 8 p.m.).

After the retro-PoT questions, the participants answered another question on their level of happiness, again with a 7-point response scale.

For the present PoT judgment (present-PoT), the ESM adapted for very old people was used (Droit-Volet, 2019). The participants had to spontaneously answer a temporal question on a 7-point scale (from 1 very slow to 7 very fast): "Now, at this moment, how fast does time seem to be passing for you.'' They responded to this question twice a day for five consecutive weekdays (from Monday to Friday). The questions were asked by an experimenter. The questioning time had previously been fixed based on a random choice between 8 and 12 a.m.

for the first question, and between 12.30 and 6.30 p.m. for the second question. As in other ESM studies, after the temporal question, the participants answered the affective questions (happiness, high-arousal, low-arousal) and the attention-related questions (Is the activity that you are doing difficult? Does it capture your attention?). They also answered a final question about their level of pain, because focusing on their physical pain could change their relationship to time. They responded on a 5-point scale for the pain question and a 7-point scale for the other questions.

In addition to the MoCA [START_REF] Nasreddine | The Montreal Cognitive Assessment, MoCA: a brief screening tool for mild cognitive impairment[END_REF], symptoms of depression and anxiety were assessed using the BDI [START_REF] Beck | Beck depression inventory (BDI)[END_REF], and the STAI [START_REF] Spielberger | Manual for the State-Trait Anxiety Inventory[END_REF], respectively. These scales, as well as the MoCA and the retro-PoT questions, were administered two or three days before and after the ESM. An additional question was asked on the participants' judgment of their physical and psychological health: from very good to very bad.

Participants' responses to the question on psychological health were not taken into account because this variable was confused with the feeling of being happy (r = 0.84, p < 0.0001).

Statistical analyses

Different statistical analyses were conducted for the retrospective and the present PoT judgment. For the analyses on the retro-PoT judgment, we conduced a series of independent samples t-tests on this temporal judgment for each period considered (day averaged, week, month, year, 5 years, as you get older) to compare the groups of participants with moderate vs. mild/very mild cognitive impairments. In addition, we analyzed the correlations between the different retrospective time judgments and the scores for happiness, cognition (MoCa), depression and anxiety. Preliminary statistical analyses on the retro-PoT judgment showed no significant relationship between the self-reported level of physical health and the different judgments of the passage of time (all p > .05). This factor was thus excluded from the statistical analyses.

For the present-PoT judgment, there were multiple responses per participant for each testing trial. Therefore, we conducted regression analyses (Multi-Level Modeling, MLM) using SPSS with the present-PoT as dependent variable and the participants as random effect. Initial statistical analyses were conducted with the two repeated measures, i.e. the testing day (numbered from 1 to 5) and the moment of assessment (a.m. vs. p.m.), as fixed factors using the autoregressive covariance structure (AR(1)). The results showed neither an effect of the testing day (E = 0.18, SE = 0.11, 95% CI[-0.04; 0.40], t = 1.64, p = .10), nor of the assessment moment (E = 0.21, SE = 0.24, 95% CI[-0.25; 0.66], t = 0.90, p = .37), nor of their interaction (E = -0.09, SE = 0.07, 95% CI[-0.22; 0.66], t = -1.22, p = .23). Therefore, these factors were excluded from the subsequent MLM analyses testing the fixed effects (cognition, depression, anxiety, happiness, high-arousal, low-arousal, activity difficulty, activity attention, pain) entered in the same model.

To examine the relationship between the present-PoT judgment and each type of retro-PoT judgment, we also conducted a MLM analysis with the present PoT judgment as dependent variable and each type of retro-PoT judgment taken separately as fixed factor. The participants were always used as random factor.

Additional Bayesian analyses were conducted using JASP for the t-tests, the correlation matrix (BF10, Upper 95% CI, Lower 95% CI), and regression analyses to verify whether with Bayes Factors indicated that the significant and the non-significant results supported the alternative (H1) and the null hypothesis (H0), respectively [START_REF] Dienes | Using Bayes to get the most out of non-significant results[END_REF].

RESULTS

The retrospective judgment of the passage of time

The correlation matrix between the retro-PoT judgments and the scores on the different scales is presented in Table 1. Table 1 suggests some differences in the retrospective time judgments according to the periods considered, i.e., between the shorter periods (day, week, month) and the longer periods (year, now than 5 years before, as one gets older).

As illustrated in Figure 1, the PoT judgment did not change with the cognitive impairment scores (MoCA scores) for the short periods (day, week, month) (for all r, p > .05), although there was nevertheless moderate support for H0. The t-tests confirmed the similarity in the temporal judgment between the participants with moderate and mild cognitive impairment for the day (Mmod. = 4.92, SE = 0.02; Mmild = 5.08, SE = 0.02; t(51) = 0.62, p = 0.54; Cohen's d = 0.17; BF10 = 0.32), the week (Mmod. = 4.70, SE = 0.22; Mmild = 4.96, SE = 0.23; t(51) = 0.78, p = 0.44; d = 0.22; BF10 = 0.36), and the month (Mmod. = 4.75, SE = 0.23; Mmild = 5.04, SE = 0.25, t(51) = 0.85, p = .40; d = 0.22; BF10 = 0.37) (Figure 1). Bayes factors supported H0, albeit moderately. For these short periods, rather than individual differences in the cognitive abilities, it was the variations in the feeling of happiness that influenced the time judgment (day, r = 0.45, p = .001, BF10 = 38.45, 95% CI[0.64, 0.19]; week, r = 0.34, p = .05, BF10 = 3.41, 95% CI[0.56, 0.07]; month, r = 0.37, p = .01, BF10 = 5.26, 95% CI[0.57, 0.10]). Strong evidence for the correlation between the feeling of happiness and the PoT judgment was found for the day (BF10 > 30), and moderate evidence was found when the length of the period increased, i.e. for the week and the month (BF10 > 3). Therefore, the participants experienced a slowing-down of time when they felt less happy over different temporal periods ranging from one day to one month.

Unlike the time judgment for the short periods, the corresponding judgment for the longer periods (year, now-5 years, when people get older) was not significantly related to the feeling of happiness (Table 1, for all r, p > .05), as confirmed by the moderate evidence in support of H0 indicated by the Bayes factors (BF10 > 3), at least for the longest time period (5 years, when people get older). It was more related to mental capacities, i.e. the cognitive scores on the MoCA (year, r = 0.27, p < .05, BF10 = 1.14, 95% CI[0.49, 6.234 e-4 ]; now-5 years, r = 0.47, p > .001, BF10 = 82.29, 95% CI[0.65, 0.22]; aging, r = 0.28, p < .05, BF10 = 1.35, 95% CI[0.50, 0.01]). As confirmed by the t-test (see Figure 1), the participants with moderate cognitive impairment reported that time passed slower than those with mild cognitive impairment both when considering the past year (Mmod = 4.82, SEmod = 0.19; Mmild = 5.40, SE = 0.21, t(51) = 2.04, p = 0.046, d = 0.56, BF10 = 1.50), now versus 5 years before (Mmod = 2.75, SEmod = 0.28, Mmild = 4.6, SEmild = 0.298, t(51) = 4.51, p < 0.001, d = 1.24, BF10 = 511.87) and when people get older (Mmod = 2.75, SEmod = 0.32, Mmild = 3.92, SEmild = 6.36, t(51) = 2.52, p = .015, d = 0.694, BF10 = 3.52). However, the Bayes factor only provides evidence for a cognitive impairment effect on the retrospective PoT judgment over the longest periods (5 years, as we get older). The evidence in favor of H1 was anecdotal for the year, suggesting that this time period might be a transitory period between the short and the very long periods of time.

The present judgment of the passage of time

The MLM results (Table 2) indicate that the main factor that significantly predicted the present-PoT judgment was the level of happiness experienced by the participants at the moment of the time judgment (E = 0.037, SE = 0.05, 95% CI [0.27; 0.47], t = 7.13, p = .0001). The Bayesian analysis with happiness as the only factor confirmed this significant result (E = 0.44, SE = 0.06, 95% CI [0.32; 0.56], R-hat = 1.00, ESSbulk = 3295.45,ESStail = 4007.63). The attention devoted to the current activity also contributed to variation in PoT, albeit to a lesser extent (E = 0.079, SE = 0.036, 95% CI [0.09; 0.149], t = 2.22, p = .03). This was verified in the Bayesian analysis with the current activity as the only factor (E = 0.14, SE = .04, 95% CI [0.06; 0.23], R-hat = 1.00, ESSbulk = 3592.66, ESStail = 4121.39). As illustrated by the plots of the regression curve (Figure 2), at each moment of the day when the participants felt less happy, they expressed the feeling that time slowed down. Conversely, they reported that time passed faster as their level of happiness increased. As we will discuss later, the present-PoT judgment therefore fluctuated greatly in terms of the level of self-reported happiness over the days (M = 4.4, SD = 1.31, Min = 1, Maxi = 7).

The current feeling of happiness thus often alternated from pleasure to displeasure, with the result that there was no clear link between daily levels of happiness and the individual trait of

The relationship between the retrospective and the present judgment of the passage of time

The results of the regression analyses (MLM) on the present passage-of-time judgment show that the different retro-PoT judgments were not related to the present-PoT judgment (all p > .05) (Table 3). These non-significant results were verified in the Bayesian analysis (week, E = 0.13, SE = 0.10, 95% CI [-0.08; 0.34], month, E = 0.12, SE = 0.09, 95% CI [-0.06; 0.31],

year, E = -0.02, SE = 0.11, 95% CI [-0.24; 0.196], 5 years, E = -0.01, SE = 0.07, 95% CI [-0.14; 0.13], get older E = -0.03, SE = 0.07, 95% CI [-0.16; 0.10]). The only significant link was between the different momentary judgments of time and the temporal judgment reported retrospectively at the end of the day (E = 0.41, SE = 0.05, 95% CI [0.31; 0.51], t = 8.29, p = .0001). This was confirmed by the Bayesian analyses (E = 0.41, SE = 0.06, 95% CI [0.28; 0.52], R-hat = 1.00, ESSbulk = 3041.37, ESStail = 3954.54).

DISCUSSION

The results of our study on PoT judgment suggest that there was no significant relationship between the retrospective-PoT judgment and the PoT judgment at different present moments. The present-PoT judgment was only related to the judgment of the speed of the passage of time made retrospectively for the entire day. This supports the idea that PoT judgments involve different mechanisms depending on the time period under consideration.

Our results on the present-PoT judgment in everyday life obtained with the ESM are entirely consistent with the findings of other studies using this method (Droit-Volet, 2019;[START_REF] Droit-Volet | Experience Sampling Methodology reveals similarities in the experience of passage of time in young and elderly adults[END_REF][START_REF] Droit-Volet | Passage of time judgments are not duration judgments: Evidence from a study using Experience Sampling Methodology[END_REF][START_REF] Droit-Volet | Passage of time judgments in everyday life are not related to duration judgments except for long durations of several minutes[END_REF]. They confirm that the main predictor of the present-PoT judgment is the emotion felt at the moment of the temporal judgment. The activity carried out also plays a role, but to a lesser extent, probably because of the very wide range of activities performed. The emotion driving the variations in the PoT judgment in our study was the feeling of happiness. Participants reported that time passed faster when they felt happier and slowed down when their level of happiness decreased.

Consequently, as shown by Droit-Volet (2019), elderly people living in retirement homes, such as those tested in our study, experienced a daily slowing down of time that was greater than that of elderly people (same age) living at home due to their enjoyment of fewer moments of happiness. To improve their mental health (wellbeing), it is therefore important to try to make elderly people happier by restoring meaning to their lives and making them accept their agedrelated changes (loss of autonomy), as suggested by the Acceptance and Commitment Therapy (ACT) for the elderly [START_REF] Davison | A pilot trial of acceptance and commitment therapy for symptoms of depression and anxiety in older adults residing in long-term care facilities[END_REF]. The feeling of happiness is therefore a key factor in the variations in the experience of the passage of time in everyday life.

The feeling of being happy from day to day (emotion-state) is thought to change with general mental health, i.e. whether or not participants suffer from depression or anxiety (emotion-trait). It is well known that depressed people have a sad mood and lose interest in daily activities [START_REF] Rottenberg | Mood and Emotion in Major Depression?[END_REF]. However, our statistical analysis indicated that the PoT judgment varied little with the individual scores of depression and anxiety on the self-reported clinical scales used. Similarly, it did not depend on general cognitive capacities as assessed by the MoCA in our study. In their COVID study on time, [START_REF] Martinelli | Time and Emotion in the lockdown for the Covid-19 epidemic: The determinants of our experience of time?[END_REF] also found few relationships between the individual traits (durable happiness, impulsivity, depression, anxiety, alexithymia) and the momentary judgment of the passage of time, with this latter depending on the current emotional state (i.e., boredom, happiness) as in our study. Therefore, the emotional state always fluctuates from one moment to the next in everyday life according to the current context, despite a general personality trait. individual traits. This provides evidence in support of the distinction between "fluctuating happiness" in "which phases of pleasure and displeasure alternate repeatedly" and "authentic-durable happiness" which is "less dependent on circumstances" (Dambrun et al., 2012, p. 1). This also reinforces the idea that present-PoT judgment is effectively rooted in a unique experience carried out in a specific context (Martinelli & Droit-Volet, in press). Our idea [START_REF] Droit-Volet | Intertwined facets of subjective time[END_REF], 2019;[START_REF] Droit-Volet | Awareness of the passage of time and selfconsciousness: what do meditators report[END_REF] that the judgment of the passage of time in daily life is derived from the minimal self (subject of experience) [START_REF] Gallagher | Philosophical conceptions of the self: implications for cognitive science[END_REF][START_REF] Gallagher | A pattern theory of self[END_REF] and its temporally contraction and extension under the influence of the emotion experienced at a given moment is therefore confirmed in our study.

Our results identified the feeling of being more or less happy as the major predictor of variations in the present-PoT judgment. The recent studies on the PoT judgment during the COVID lockdown have confirmed the role of this critical emotion, but also found an effect of other feelings such as boredom and life satisfaction [START_REF] Ogden | The passage of time during the UK Covid-19 lockdown[END_REF]Droit-Volet et al. 2020;[START_REF] Martinelli | Time and Emotion in the lockdown for the Covid-19 epidemic: The determinants of our experience of time?[END_REF]. Although these factors likely fall into two main categories (affect and attention load), it will be interesting to examine the specificities of different dimensions (e.g., anger, fear, boredom, frustration) and their inter-relations in order to identify whether one category of factors prevails over the other in the momentary judgment of the passage of time.

However, as discussed above, the factors underlying this type of temporal judgment depend on the context in which the judgment is made [START_REF] Martinelli | Time and Emotion in the lockdown for the Covid-19 epidemic: The determinants of our experience of time?[END_REF]. In this respect, the life context differs greatly between young and very old people living in retirement home.

Our study also confirms the weak relationship between the present-and the retro-PoT judgment. This validates the hypothesis that the retro-PoT judgment is not based on short-term cognitive mechanisms involved in the current experience as for the present-PoT judgment, but on recollection processes in long-term memory. In addition, our study suggests some differences in the retro-PoT judgment depending on the time period considered. Indeed, there was no or little significant correlation between the temporal judgment for the shorter periods (day, week, month) and that for the longer periods (5-years, aging). The PoT judgment for the last year was at an intermediate point, being significantly correlated with both the temporal judgment for the shorter periods (week, months) and that for the longer periods (5-years, aging), except that for the day. The best predictor of variations in the PoT judgment also differed as a function of the temporal period considered, being the level of happiness for the shorter periods and the level of cognitive impairment, i.e. the MoCA scores, for the longer ones. This suggests that PoT judgment for periods covering the day, the week, but also the month, are based on memorable events of everyday life stored in episodic memory. However, since there was no significant relationship between the judgment of time in the present moment and that of the last week or month, we can easily assume that PoT judgments for the last week or the last month do not result from the sum either of PoT experiences at different moments or of PoT judgments at the end of each day of the week, but from certain remarkable and memorable days. The latter would provide an emotional color (feeling of happiness) to the elapsed temporal period (week, month), thus influencing in turn the retrospective judgment of the passage of time. Further experiments are nevertheless needed to better understand the interplay between the emotional judgment of different days of the week, and that of the week and of the month as a whole.

Our results showed that the retrospective judgment of the passage of time over longer periods (year, 5-years, aging) was significantly correlated with the MoCA scores, rather than with the retro-PoT judgment for shorter periods (day, week, month) or the feeling of happiness, which is a reliable predictor of this latter judgment. This result cannot be explained by the older participants' difficulties in understanding some of the temporal questions as no cognitive impairment effects were observed for most of the temporal questions, which were similarly worded. On the other hand, the existence of memory deficits in the early stages of dementia is well known. The differences in the retro-PoT judgment for the longer periods between people with mild and those with moderate dementia symptoms could therefore be explained by the latter's problems in remembering past events. Defending a memory-based theory of retro-PoT judgment, [START_REF] Fraisse | The psychology of time[END_REF] explained that time is thought to pass quickly with aging because the number of events retrieved in memory is smaller in older people than in younger people. The number of memories would therefore be even lower in people with more severe symptoms of dementia such as those tested in our study. However, this explanation is valid for the feeling of an acceleration of time with aging but not its slowing-down as was observed in our participants.

In addition, recent studies have questioned this memory theory and suggested that the speedingup of time with aging is rather related to the experience of time pressure in old people [START_REF] Blas | L'évolution de la mémoire et de la notion de temps. L'Harmattan[END_REF][START_REF] Friedman | Aging and the speed of time[END_REF][START_REF] Winkler | Has it[END_REF]Wittmann & Lehnhoff, 2005). However, it is hard to imagine that older people have a greater sense of time pressure when most of them no longer have the pressure of a job and/or family to manage. Is it the real pressure of everyday life or the pressure of life going by?

The difference in the PoT judgment for the longer periods between the groups of participants with moderate and mild dementia can be better explained by their different abilities to represent time. Indeed, people with dementia symptoms have trouble orienting themselves in time [START_REF] Eslinger | Neuropsychologic detection of abnormal mental decline in older persons[END_REF]. They have difficulties saying what day, month, year it is. Moreover, the questions on time orientation form an integral part of the MoCA test. However, although this explanation is valid, it is nevertheless also insufficient to account for the stronger sense of slowing down of time in the participants with the most severe dementia symptoms.

The problem with studies using elderly people living in retirement homes is the heterogeneity of the population used, which presents many different clinical problems. In our study, it would have been preferable to have a larger number of participants in order to obtain very strong rather than moderately significant effects like those found in our study and to permit the addition of an age-matched control group without cognitive difficulties.

Our results indicate that the judgment of the passage of time for long periods of time was related neither to the participants' current emotion, nor to pain, nor to their self-reported level of physical health. We can therefore simply assume that this subjective retrospective judgment of time for very long periods of life is rooted in the awareness of ineluctable changes in the self with aging. Participants would thus compare the pace of their lives before and after their psychological difficulties, thus resulting in the statement that the pace of life has slowed down. The retro-PoT judgment for long periods would thus be linked to the concept of self in its temporality. The knowledge of self in its temporality (past, present, future) is linked to the narrative self [START_REF] Gallagher | Philosophical conceptions of the self: implications for cognitive science[END_REF][START_REF] Gallagher | A pattern theory of self[END_REF].

Therefore, based on our results, we assume that both the representation of time and the concept of self take account of changes in the judgment of the passage of time for long periods (5-years, aging). Time representation and self-knowledge form part of the semantic memory system. This therefore supports our idea that the PoT-judgment for long periods of life involves semantic memory processes rather than episodic memory processes, as is the case for the time judgment of shorter periods (day, week, month). For future research, it therefore seems to be very important to evaluate participants' memory abilities by means of specific semantic memory tests and not only the MoCA, which rapidly evaluates cognitive function with different short subtests (visuo-spatial executive function, clock, time orientation, naming, short-term memory, attention, language, abstraction, memory recall) but not the cause of cognitive impairments. However, as already reported, it is obvious that episodic memory and semantic memory do not operate separately, as suggested by the findings showing the significant correlations between the PoT judgment for the last year and those for both the shorter and the longer periods.

In conclusion, our study has demonstrated that there is not one but several types of judgment of the passage of time depending on the temporal period taken as a reference and that these different time judgments are not or few related. This highlights the complexity of the PoT judgment in human consciousness [START_REF] Gruber | The illusory flow and passage of time within consciousness: A multidisciplinary analysis[END_REF]. Finally, talking about time would be a familiar way to account for ourselves, our moods and the way our difficulties increase with age.

The slowing down of time in very old people would a way of accounting for "things shipwrecked in the depths of the soul" in old age before death (Hugo, 1838).

really Been that Long? Why Time Seems to Speed up with Age. Timing & Time Perception, 5, 168-189. Wittmann, M., Rudolph, T., Gutierrez D., & Winkler, I. (2015). Time Perspective and Emotion Regulation as Predictors of Age-Related Subjective Passage of Time. Int. J. Environ. Res. Public Health, 12(12), 16027-16042. Wittmann, M., & Lehnhoff, S. (2005). Age effects in perception of time. Psychol. Rep.,97(3), 921-935.

Figure captions

Participants

  The final sample was composed of 53 elderly adults (40 women and 13 men) with a mean age of 87.5 years (SD = 7.62, Min = 65, Max = 100). They were all living in the same retirement home in Cusset in the Auvergne Rhône-Alpes Region of France. They were recruited in cooperation with the clinical psychologist of the retirement home. The MoCA was used to estimate their cognitive impairment (MMoCA = 16.06, SD = 5.77, Min = 4, Max = 29); lower scores indicating greater cognitive impairments. The MoCA scores allowed us to identify two groups of participants with significantly different levels of cognitive impairment: moderate cognitive impairments (N = 28, MMoCA = 11.68, SD = 3.15, Min = 4, Max = 16), and mild or very mild cognitive impairments (N = 25, MMoCA = 20.96, SD = 3.15, Min = 13, Max = 29), F(1, 51) = 97.18, p < .0001. Age and level of education were similar in these two groups (88 vs. 87 years, F(1, 51) = 0.73, p = .40; 8.59 vs. 8.8 years of education, F(1, 51) = 0.24, p = .62.

  depression, and a mild link between happiness and anxiety as indicted by the Bayesian MLM analyses (E = 0.04, SE = 0.02, 95% CI [-0.09; 0.02], R-hat = 1.02, ESSbulk = 170.25, ESStail = 215.31; E = -0.03, SE = 0.01, 95% CI [-0.05; -0.01], R-hat = 1.00, ESSbulk = 12547, ESStail = 2084.68, respectively).

Figure 1 .

 1 Figure1. Mean (standard error) retrospective judgment of the passage of time from 1 (very slow) to 7 (very fast) made by the old participants with moderate cognitive impairment and those with mild or very mild cognitive impairments for the temporal questions on the day (averaged on the responses given at the end of 5 testing days), the week, the month, the year, now than 5 years ago, and as you get older.

Figure 2 .

 2 Figure 2. Plot of the regression (MLM) between the present judgment of the passage of time from 1 (very slow) to 7 (very fast) and the level of self-reported happiness (standardized) assessed using the Experience Sampling Methodology.

Figure 2

 2 Figure 2

Table 1 .

 1 Correlation matrix, including Pearson's r, the Bayesian factor (BF10), the Upper and the Lower 95% Confident Interval (CI), between retrospective judgments of the passage of time for different time periods (day, week, month, year, now compared to 5 years before, as people get older) and scores of happiness, cognition (MoCA), depression and anxiety.

	Variable		D	W	M	Y	5-y	A	H	C	D
	Week	r	0.24	-
		BF₁₀	0.70	-
		U 95% CI	0.47	-
		L 95% CI	-0.04	-
	Month	r	0.33*	0.81*** -
		BF₁₀	2.64	2.683 e +10 -
		U 95% CI	0.54	0.88	-
		L 95% CI	0.06	0.67	-
	Year	r	0.25	0.54*** 0.70*** -
		BF₁₀	0.82	777.40	2.297 e +6 -
		U 95% CI	0.48	0.70	0.81	-
		L 95% CI	-0.02	0.30	0.51	-
	5-years	r	0.10	0.25	0.16	0.31*	-
		BF₁₀	0.22	0.81	0.32	2.07	-

Note. Pearson'r; Bayes Factor; Upper 95% CI; Lower 95% CI; * p < .05; ** p < .01; *** p < .001

Table 2 .

 2 Results of the regression analysis (MLM) on the present passage-of-time judgments with the different factors entered in the same model.

	95% CI

a Dependent variable: Present-PoT judgment

Table 3 .

 3 Results of the regression analyses (MLM) on the present passage-of-time judgment with each type of retrospective passage-of-time judgment considered as factor taken separately.

				95% CI
		Estimate a	SE	Lower	Upper	t	p
	Day	0.4081	0.0492	0.3112	0.5049	8.29	0.0001
	Week	0.1291	0.1010	-0.0736	0.3317	1.28	0.21
	Month	0.1207	0.0931	-0.0662	0.3075	1.30	0.20
	Year	-0.0158	0.1101	-0.2368	0.2052	-0.14	0.89
	5-years	-0.0025	0.0669	-0.1368	0.1319	-0.04	0.97
	Aging	-0.0277	0.0658	-0.1599	0.1044	-0.42	0.68

a Dependent variable: Present-PoT judgment


N And Droit-Volet

Sylvie Droit-Volet
email: sylvie.droit-volet@uca.fr.

Running head; What factors underlie our experience of the passage of time? What factors underlie our experience of the passage of time? Theoretical consequences

Keywords: Time, Experience of time, Consciousness

The aim of this study was to examine the factors that explain variations in the conscious experience of time. The level of difficulty of the task, emotional valence and duration of stimuli were tested in three different experiments with two ranges of durations, one of seconds and the other one of minutes. The results showed that the passage of time was judged faster with durations in the seconds than in the minutes range. However, for all duration values, each change in the features of the task produced changes in the judgment of the passage of time.

The subjective feeling of an acceleration of the passage of time therefore increased linearly with the increase in the level of difficulty of the task and with the positive valence of the emotional stimuli. It also varied linearly with the length of real time, increasing in the same proportion as the decrease in stimulus duration, regardless of the associated range (seconds or minutes). Our theory is that the judgment of the passage of time might be a generic way of describing the most salient internal or external contextual changes experienced.

Judging the different aspects of time is part of our daily activities. Every day, we estimate the duration of events or that of the interval between two events. Every day, we notice that time passes faster or slower than it really does. For decades, researchers have used an experimental approach to examine human abilities to judge durations and the factors explaining their variations. However, the judgment of the passage of time (PoT) has not been subject to the same experimental analysis involving supposedly more objective tests [START_REF] Larson | The time of our lives: The experience of temporality in occupation[END_REF][START_REF] Wearden | Passage of time judgements[END_REF][START_REF] Droit-Volet | Intertwined facets of subjective time[END_REF]. The aim of this exploratory study was to fill this gap in the literature by experimentally examining the factors behind variations in our awareness of changes in the speed of the passage of time.

Nonetheless, in recent years, the PoT judgment has been examined in more details in correlation studies using the Experience Sampling Method (ESM), which makes it possible to evaluate PoT judgments in daily life [START_REF] Larson | Predicting the perceived flow of time from qualities of activity and depth of engagement[END_REF][START_REF] Droit-Volet | Experience sampling methodology reveals similarities in the experience of passage of time in young and elderly adults[END_REF]. With this method, participants are informed that they will have to judge the speed of the passage of time at different times of the day, for several days of the week. They receive phone calls during which they have to rate the speed of the passage of time using a Likert scale going from "very slow" to "very fast". They also have to answer a series of questions designed to assess the context in which the temporal judgment is made. Droit-Volet and [START_REF] Wearden | Passage of time judgements[END_REF] asked participants questions about the valence of their emotion at the time of the temporal judgment as well as about the difficulty of the activity they had just been performing and its level of attentional demand. Larson and van Eye (2006) asked about "emotional engagement" ("how emotionally involved were you in the activity") and "intellectual engagement" ("how intellectually involved or 'into' the activity were you?") (p. 124). The statistical analyses performed in these ESM studies have shown that the activity undertaken and the emotion felt are significant predictors of the judgment of the passage of time. Indeed, the participants experienced an acceleration of the passage of time when the activity performed was judged difficult and attentionally demanding or required more "intellectual engagement". They also reported that time passed more quickly when they felt happier, and that it slowed down when they felt sadder.

These results have been replicated in subsequent ESM studies demonstrating that emotions and task difficulty are two major predictors of PoT judgment in daily life [START_REF] Droit-Volet | Passage of time judgments are not duration judgments: evidence from a study using experience sampling methodology[END_REF][START_REF] Droit-Volet | Passage of time judgments in everyday life are not related to duration judgments except for long durations of several minutes[END_REF]Droit-Volet 2019a).

To account for fluctuations in the awareness of the passage of time with activity and emotion, Droit-Volet juxtaposed the PoT judgment based on "Self-duration" with that based on "World-duration" (e.g., [START_REF] Droit-Volet | Intertwined facets of subjective time[END_REF][START_REF] Droit-Volet | Awareness of the passage of time and self-consciousness: What do meditators report[END_REF]. The first corresponds to judgments of the passage of time resulting from intra-individual analyses of a temporal extension or contraction of the minimal self. The minimal self is the consciousness of oneself as an immediate subject of experience [START_REF] Gallagher | Philosophical conceptions of the self: implications for cognitive science[END_REF][START_REF] Gallagher | A pattern theory of self[END_REF]. In other words, the passage of time is judged to accelerate or decelerate relative to participants' awareness of changes in their different states, including the prevailing emotional feelings. The second is the representation of external time, as indicated by our watches, that flows at a constant rate in a uniform and universal way. World-duration is therefore used as a reference allowing individuals to state that time passes faster or slower than it really does. In sum, according to this theoretical approach, the awareness of the passage of time would be based on the introspective analysis of the self in its context and not the processing of event-durations.

This assumption is supported by the results of ESM studies which have found that the PoT judgment in everyday life was related to the non-temporal context of judgment (activity, emotion) and not to temporal information [START_REF] Droit-Volet | Passage of time judgments are not duration judgments: evidence from a study using experience sampling methodology[END_REF][START_REF] Droit-Volet | Passage of time judgments in everyday life are not related to duration judgments except for long durations of several minutes[END_REF]. Indeed, these studies showed no relationship between the feeling about the speed of the passage of time at a given time and the values of estimated durations (< 60 s); An overestimation of short durations did not translate into the feeling that time is passing faster.

The ESM studies nevertheless found that the PoT judgment was significantly correlated with the judgment of long durations of several minutes. The mechanisms underlying estimates of short and long durations are likely to differ.

The processing of short durations involves an internal clock-like system, as has been well established in the literature (e.g., [START_REF] Gibbon | Scalar timing in memory[END_REF], for a review [START_REF] Merchant | Neural basis of the perception and estimation of time[END_REF]. In contrast, the processing of long durations of several minutes would involve memory reconstruction processes that make use of non-temporal information stored in memory during the interval to be processed [START_REF] Droit-Volet | The explicit judgment of long durations of several minutes in everyday life: conscious retrospective memory judgment and the role of affects?[END_REF]. Similar results on the dependence of time estimates on non-temporal information have been found in studies on retrospective timing in which participants do not know in advance that they will have to judge time events and the internal clock is not activated [START_REF] Block | Prospective and retrospective duration judgment: the role of information processing and memory[END_REF][START_REF] Block | Prospective and retrospective timing processes: Theories, methods, and findings[END_REF]. Therefore, [START_REF] Droit-Volet | Passage of time judgments in everyday life are not related to duration judgments except for long durations of several minutes[END_REF] concluded that the PoT judgment, even in a prospective timing condition, would be based on memory mechanisms like in the retrospective time judgment.

The hypothesis that there is no relationship between PoT judgment and duration processing is deduced from ESM findings on the lack of correlation between the PoT judgment and the judgment of short durations (< 60). However, although interesting, the ESM studies pose various methodological problems. First, the interval duration considered by participants in their PoT judgments was not controlled, even if we may suppose that in their everyday lives, they considered the duration of their current activity, i.e. a period of several minutes. Second, the results of these ESM studies are based on correlation analyses, and not the causal link between the nontemporal factors and the PoT judgment. There are very few studies that have experimentally investigated PoT judgments in the laboratory [START_REF] Sucala | Psychological time: interval length judgments and subjective passage of time judgments[END_REF][START_REF] Wearden | Subjective duration in the laboratory and the world outside[END_REF]). As in the ESM studies, they showed that the task was perceived as passing faster when it was difficult than when it was easy. However, these studies have only examined one factor (task difficulty) and not other factors on which PoT judgments could also depend, such as emotion. In addition, and more critically, they have only examined one duration, namely of several minutes.

The participants had to judge the passage of time for a single interval of 4 minutes in Sucala et al.'s study (2011), and of 3 minutes in Wearden et al.'s study (2014). None of these studies tested different durations in different time ranges from a few seconds to several minutes, as would be necessary in order to examine the real influence of durations on PoT judgments.

There still has not enough laboratory-based research into PoT judgments. The aim of the present study was thus to begin to investigate the effect on the PoT judgment of different types of non-temporal factors, i.e. task difficulty (Experiment 1) and the emotional valence of the stimuli (Experiment 2), with the duration maintained constant, for durations in the range of seconds and minutes. Another aim was to examine the effect on the PoT judgment of varying temporal information (Experiment 3) when the non-temporal information was controlled for.

Our hypothesis was that the PoT judgment would vary with the changes in the non-temporal factors, whatever they were (task difficulty or emotion) for the interval durations in the minutes range, and those in the seconds range. However, in a prospective PoT judgment paradigm, i.e. when participants know that they have to judge the passage of time, we can assume that stimulus durations have a greater influence on the PoT judgment in the seconds than the minutes range because the former involves the mobilization of an internal clock system as explained above.

Experiment 1 -Task Difficulty

Method

Participants

The final sample was composed of 83 participants (72 women and 11 men), all of them students at University Clermont Auvergne (mean age = 19.10, SD = 1.49), who received a course credit for their participation.

All individual participants signed an informed consent form describing the procedure used, that was in accordance with the 1964 Helsinki declaration and approved by the Research Ethics Committee of the University Clermont-Auvergne (IRB00011540-2019-33) following the French Ethical law.

Material

The experiment was presented on a 17-inch PC screen with a 1920x1080-pixel resolution, and a 60 Hz refresh rate. Obviously, no temporal information (clock, watch, etc.) was available. Data collection and stimuli presentation were handled with E-prime software v 2.0 (Psychology Software Tools, Pittsburgh, PA, USA). The participants sat in front of the screen (50-cm distance) and responded using the computer keyboard. For the nontemporal task, we used sequences of digits displayed (black on a white background) in "Courier New", font size 18, in the center of the screen. Based on a pilot study involving five participants, the non-temporal task was subdivided into 3 levels of difficulty. The difficulty level was defined in terms of the number and order of the digits to be reproduced. The digit sequences contained different numbers presented in random order. For the first level of difficulty of the non-temporal task, named "Easy", a sequence consisted of two digits (e.g., 85), and the participants had to type the digits on the normal computer keyboard in the same order in which they had appeared.

For the second level, "Medium", a sequence consisted of six digits (e.g., 716483) and the participants again had to reproduce it in the correct order. For the "Difficult" level, six digits were also presented per sequence (e.g., 284106), but the participants had to reproduce it in the reverse order (601482). As explained in the procedure, the number of digit sequences per trial obviously depended on the trial duration.

Procedure

All the participants performed 18 trials, i.e. 6 trials for each of the 3 difficulty levels of the non-temporal task (easy, medium, and difficult). Each trial therefore consisted of a series of 2-or 6-digit sequences to be reproduced either in the forward order or in the backward order. The trials were presented randomly. For each digit sequence, the participants were presented with a fixation mark (+) displayed for 500 ms in the center of the screen. The digit sequence then appeared for up to 1000 ms followed by a 500-ms blank screen. A text box was then presented for 5000 ms with the response instruction and the participant reproduced the digit sequence as quickly as possible. The inter-sequence interval varied according to the trial duration.

The participants were randomly assigned to one of two duration groups, one with trial durations in the range of seconds (N = 42) and the other with trial durations in that of minutes (N = 41). In the seconds group, the trials varied between 30 s, 33 s and 36 s, and in the minutes group between 90, 99 and 108 s. Consequently, the number of digit sequences to be reproduced per trial varied as a function of the trial duration. To avoid the methodological bias linked to the number of sequences, we maintained the same number of sequences for the different trial durations by varying the length of the inter-sequence intervals. In the seconds group, all trials contained 4 digit sequences with an inter-sequence interval varying between 400 and 650 ms for 30 s, 1000 and 3000 ms for 33 s, and 1000 and 3000 ms for 36 s. In the minutes group, the trials were composed of 12 digit sequences with inter-sequence intervals between 375 and 625 ms for 90 s, 1000 and 1450 ms for 99 s, and 1200 and 2750 ms for 108 s. The 6 trials for each task-difficulty level therefore consisted of two trials for each of the 3 trial durations. However, the trial durations were similar across the different levels of difficulty of the nontemporal task.

After each trial, the participants gave their judgment of the passage of time. The question "How did time pass for you during the activity compared to the time of a clock?" appeared with a 7-point Likert-type scale going from (1) "very slowly" to (7) "very fast", and the participants responded on the computer keyboard. Before the testing trials, the participants were given 2 demonstration trials.

Results & Discussion

Non-temporal performance

For each participant, we calculated the number of correctly reproduced digit sequences as a proportion of the total number of sequences presented in each difficulty condition of the non-temporal task. An ANOVA was carried out on the non-temporal performance with the level of task difficulty (easy, medium, difficult) as withinsubjects factor and the duration group (seconds, minutes) as between-subjects factor. The ANOVA showed a significant main effect of task difficulty, F(1.88, 151.93) = 888.12, p < .0001, ηp 2 = .92 (Fig. 1). The non-temporal performance therefore decreased with the level of task difficulty, as indicated by the linear effect of task difficulty (Measy = .96 SEeasy = .004, Mmediun = .57, SEmedium = .02, MDifficult = .18, SEdifficult = .017, F(1, 81) = 2067.01, p < .0001, ηp 2 = .96). The main effect of duration also reached significance F(1, 81) = 9.22, p = .003, ηp 2 = .10, as did the duration x task difficulty interaction, F(1.88, 151.93) = 3.20, p = .045, ηp 2 = .038, although the effect size was low. This indicates that the proportion of correct responses tended to be higher in the minutes range (Mlong = .60, SElong = .017) than in the seconds range (Mshort = .533, SEshort = .017), especially for the highest task-difficulty level.

PoT judgment Seconds Minutes

The material used was the same as that used in Experiment 1, except for the emotional stimuli. The emotional stimuli used consisted of videos from 3 emotional categories with a different emotional valence:

negative, neutral and positive. Videos were used instead of static images in order to maintain the emotion induced in the case of long durations of several minutes (Droit-Volet et al. 2019b). The videos were composed of pictures of a given emotional valence extracted from the International Affective Picture System (IAPS; [START_REF] Lang | International affective picture system (IAPS): Affective ratings of pictures and instruction manual[END_REF]. All the pictures were thus assessed as positive on a 9-point emotional valence scale (from 7.01 to 8.28) for the positive videos, or as neutral (from 4.03 to 4.99) and negative (from 2.06 to 3.16) for the neutral and the negative videos, respectively. The positive pictures showed people enjoying themselves, baby animals and facial expressions of joy. The neutral valence pictures represented inanimate objects and neutral facial expressions, and the negative pictures presented landfill sites, war images and people with sad expressions and/or crying. The negative pictures were thus associated with the emotion of sadness. To create smooth animated transitions between the images presented in the videos, we used the software OpenShot Video Editor (OpenShot Studios, Rockwall, TX, USA). The number of images used was similar for the different emotional videos, varying between 12, 14 or 16 images for the durations in seconds and 36, 42 and 48 images for those in minutes. The presentation duration of the images as well as the duration of the animated transition between the images varied between the videos. For each duration range (seconds, minutes), we created 27 videos (54 in total): 9 videos for each of the 3 emotional valences (negative, neutral and positive valence), i.e. 3 for each of the 3 durations (30, 33, 36 seconds or 90, 99, 108 seconds).

Procedure

The participants were randomly assigned to the seconds (N = 41) or the minutes group (N = 42). The presentation duration of the emotional stimuli varied between 30, 33 and 36 seconds in the seconds group, and 90, 99 and 108 seconds in the minutes group. In each group, the participants were presented with 18 trials, with 6 trials for each of the 3 emotional stimuli (negative, neutral, positive), i.e. 3 trials per tested duration. The trial order was random. The emotional stimuli were also randomly chosen for each trial among the videos in such a way that the number of images and their presentation duration varied from one trial to another but were similar across the emotional conditions. On each trial, the participants pressed the space bar to watch the emotional stimuli when ready. Then, as in Experiment 1, they gave their judgment on the passage of time on a 7-point scale going from (1) "very slowly" to (7) "very fast".

Results & Discussion

We performed an ANOVA on the PoT judgment with the emotion as within-subjects factor and the duration group as between-subjects factor. The analysis showed a significant main effect of the emotion on the PoT judgment, F(1.67, 134.99) = 8.17, p = .001, ηp 2 = .092. As in Experiment 1, there was also a main effect of the duration group, F(1, 81) = 10.74, p = .002, ηp 2 = .117, indicating that time was judged to pass slower in the range of minutes (M = 3.74, SE = .107) than in that of seconds (M = 4.24, SE = .108). The emotion x duration interaction also reached significance, F(2, 134,99) = 6.28, p = .002, ηp 2 = .07.

Parsing the emotion x duration interaction indicated that the effect of the emotion was significant in all the duration groups, and was so for both the seconds and the minutes ranges F(1, 81) = 18.93, p < .001, ηp 2 = .189). In fact, the PoT judgment for the neutral emotional stimuli did not differ from that for the negative emotional stimuli in the seconds condition (Bonferroni test, p > .05), or from that for the positive emotional stimuli in the minutes condition (p > .05). This suggests that the negative emotional effect is reduced with the short durations and that the positive emotional effect is reduced with the long durations.

Nevertheless, whatever the duration condition (seconds or minutes), the passage of time was always judged faster with the positive than the negative emotional stimuli (4.565 vs. 4.093; 3.81 vs. 3.43, respectively, all p < .05).

Material and procedure

The materiel and the procedure were the same as those used in the previous experiments, except that the stimuli to be judged were static neutral images representing a geometric pattern in black and white. The image size was 21.77° x 16.1°. There were 54 images with different geometric patterns, i.e. 27 for each duration group.

As in Experiments 1 and 2, there were therefore two groups of participants depending on whether the duration of the stimuli was in the seconds (N = 41) or minutes range (N = 41). However, in the present study, the manipulated factor was neither the task difficulty nor the emotional valence but the stimulus duration per se. The stimulus durations were of 22, 33 and 44 seconds in the seconds group and of 66, 99 and 132 seconds in the minutes group.

The participants were thus presented with 18 blocks of trials, i.e. 6 trials per stimulus duration. The trial order was random and the image presented on each trial was randomly chosen in such a way that the images used were similar for the different temporal conditions. As in Experiments 1 and 2, the participants gave their judgments going from 1 "very slowly" to 7 "very fast" after each trial.

Results

An ANOVA was performed on the PoT judgments with the stimulus duration (short, medium, long) as within-subjects factor and the duration group (seconds, minutes) as between-subjects factor. As illustrated in Fig. 4, the main effect of the stimulus duration was significant, F(1.70, 135,69) = 120.92, p < .0001, ηp 2 = .602. No stimulus duration x duration group interaction was found (F > 1). There was only an additional main effect of the duration group, testifying to the fact that the stimulus durations in seconds (M = 3.40, SE = .17) were judged as passing faster than those in minutes (M = 2.91, SE = .17), F(1, 80) = 4.17, p = .04, ηp 2 = .05.

Consequently, whatever the duration range tested, the subjective experience of the speed of time varied linearly with the real time, as indicated by the linear effect of the stimulus duration, F(1, 80) = 176.978, p < .0001, ηp 2 = .69. Indeed, as confirmed the Bonferroni tests, the PoT was considered to be faster for the shortest duration (M = 3.79, SE = .136) than for the medium (M = 3.24, SE = .133) or the longest duration (M = 2.44, SE = .125), and also for the medium than for the longest duration (all p < .0001). In addition, and as indicated by the nonsignificant interaction between the stimulus duration and the duration group, the experience of an acceleration of time with the changes in real time was similar for a wide range of durations as long as the ratio between stimulus durations was the same. This is, to our knowledge, the first demonstration of the scalar property of time in the domain of the subjective passage of time.

Seconds Minutes

In three different experiments, we examined variations in the PoT judgment when the difficulty of the task varied (Experiment 1), when the emotion valence of the stimuli shifted from negative to positive (Experiment 2), while stimuli durations were controlled and, finally, when the duration itself varied (Experiment 3). Our results

showed that time was judged to pass more slowly for durations in the minutes than for those in the seconds range.

However, for all duration ranges, we observed that each change in the feature of a given task (difficulty of the task, emotional valence, duration) produced a change in the PoT judgment. The judgment of the speed of the passage of time therefore increased linearly with the increase in the level of difficulty of the task, although the duration of the task did not change. This result is consistent with those obtained by [START_REF] Sucala | Psychological time: interval length judgments and subjective passage of time judgments[END_REF] and [START_REF] Wearden | Subjective duration in the laboratory and the world outside[END_REF] showing, with a single interval of 3-4 minutes, that the passage of time was felt to be faster as the task difficulty increased. Moreover, our results showed that the PoT was judged to change not only depending on the level of task difficulty but also the emotional valence of the stimuli. Indeed, the speed of the passage of time was judged to increase with the positive valence of the emotional stimuli, regardless of their presentation duration. The participants therefore judged the passage of time independently of durations on the basis of non-temporal information. Nevertheless, when the stimulus durations changed, while the other characteristics of the task remained constant, the PoT judgment also varied according to the duration values. We observed that the speed of the PoT judgment increased as the stimulus durations decreased.

In an experimental prospective timing paradigm such as the one used in our studies, it is assumed that the internal clock system is activated and that it processes time. In other words, participants experience durations by focusing their attention on time (Zakay andBlock 1996, 1997;[START_REF] Zakay | Prospective and retrospective duration judgments: an executive-control perspective[END_REF]). However, our results revealed that even if the participants were aware that time was an important feature of the task, their judgments of the passage of time were not always based on temporal information. Indeed, in Experiments 1 and 2, the PoT judgment varied in response to changes in non-temporal information while the target duration remained constant (randomly controlled throughout the non-temporal conditions). We expected that the effect of temporal information on the PoT judgment would be higher for the short durations of a few seconds than for the long durations of several minutes since the mechanisms responsible for processing short and long duration do indeed

differ. An internal clock system is thought to provide an accurate representation of time in the case of short durations (for reviews, [START_REF] Merchant | Neural basis of the perception and estimation of time[END_REF][START_REF] Wearden | The Psychology of Time Perception[END_REF]. By contrast, memory-based processes are thought to be involved in the judgment of long durations [START_REF] Droit-Volet | The explicit judgment of long durations of several minutes in everyday life: conscious retrospective memory judgment and the role of affects?[END_REF]. However, for the PoT judgment, and contrary to our hypothesis, we obtained the same results for all durations. Indeed, a significant main effect of task difficulty on the PoT judgment was observed in Experiment 1, regardless of the duration of the task and the duration range (seconds vs. minutes). A main effect of emotion was also observed on the PoT judgment for the different duration range in Experiment 2 as well as in Experiment 1. In Experiment 2, a significant interaction between emotion and duration range was nevertheless found. However, this interaction only indicated that the participants felt that time passed faster for positive emotional stimuli when presented for a few seconds than for several minutes. Overall, therefore, our results in Experiment 1 and 2 suggest that PoT judgments obtained for a wide range of durations were based on something other than duration processing itself.

However, in our study, the PoT judgment also changed with the real time when the duration was the only feature of the situation that varied. Indeed, in Experiment 3, we found a linear relationship between the stimulus duration and the experience of the passage of time when the difficulty of the task was experimentally controlled.

In particular, the participants experienced an acceleration of the passage of time as the duration decreased from one value to the next, i.e. with a time step of 11 s in the range of seconds and of 33 s in the minutes range.

Therefore, a time-measurement mechanism (internal clock) may also contribute in part to the prospective judgment of the passage of time. The fact that the PoT judgment varied in our studies not only when we manipulated all the non-temporal information but also the temporal information suggests that the PoT judgment is not based on a specific factor, but on a number of different factors depending on the salience of the context encountered, i.e. the nature of the experienced or perceived changes. For example, in Experiment 3, the stimulus duration might have influenced the PoT judgment because the variation in the duration of stimulus was the most salient. But, in another context, time would have little or no influence on the prospective judgment of the passage of time, being the level of task difficulty and emotion. Some correlation studies have suggested that other factors may also play a role in PoT judgment such as time pressure, routine of everyday life [START_REF] Winkler | Has it really been that long? Why time seems to speed up with age[END_REF][START_REF] Wittmann | Time perspective and emotion regulation as predictors of age-related subjective passage of time[END_REF], and boredom [START_REF] Droit-Volet | The explicit judgment of long durations of several minutes in everyday life: conscious retrospective memory judgment and the role of affects?[END_REF][START_REF] Jokic | Individual differences in self-rated impulsivity modulate the estimation of time in a real waiting situation[END_REF][START_REF] Witowska | What happens while waiting? How self-regulation affects boredom and subjective time during a real waiting situation[END_REF][START_REF] Wittmann | Time perspective and emotion regulation as predictors of age-related subjective passage of time[END_REF]. Consequently, one can assume that PoT judgments are inferred not from one and always the same dimension (i.e. task difficulty) but from the most salient contextual (temporal or not) changes encoded and memorized during the interval. PoT judgment would therefore be a generic way of describing the most salient internal or external contextual changes experienced.

Our results therefore suggest that the PoT judgment can also be based on the processing of durations, at least in the prospective PoT judgment paradigm. Finally, the PoT judgment is multi-faceted. We have identified three main types of PoT judgment: Self-duration, World-duration and Self-time perspective. As reported in the introduction, the first of these refers to the intra-subject malleability of time related to introspective analyses of internal states. The second is the representation of external time as indicated by our watches and the third is related to temporality of self in the past-present-future. We may add a fourth type of PoT judgment, namely the event duration measured by an internal clock mechanism: "Event-duration". In this last case, there would be an association between the speed of the passage of time and the measured event-duration values. As found in the present study, the participants had no difficulty judging that time passed faster with short durations than with long durations. In summary, many factors underlie PoT judgments. This would imply that there are different types of PoT judgment, depending on the context and its significance during the interval to be judged as well as on whether the PoT judgment is prospective or retrospective. Further studies are nonetheless needed to determine which of the factors we have seen prevail over the others in the different types of PoT judgment and why.

Furthermore, our studies point out a linear relationship between the PoT judgment and the different levels of any tested factor, regardless of the factor examined. However, it is likely that the PoT judgment curve might not be as linear as observed in our experiments in other circumstances. Under extreme conditions, with a task that is too difficult, or in the presence of more intense emotions, the participants might no longer be able to experience the movements of time with its compression or extension. They could experience timelessness, a time that no longer exists, a time that no longer flows at different speeds (Csikzentmihalyi and Csikzentmihalyi 1988). This is what is reported in deep states of meditation experienced by meditation experts [START_REF] Droit-Volet | Awareness of the passage of time and self-consciousness: What do meditators report[END_REF] or in car accidents [START_REF] Noyes | Depersonalization in response to life-threatening danger[END_REF][START_REF] Arstila | Time slows down during accidents[END_REF].

Fig. 1 .

 1 Fig. 1. Proportion of correct responses for the non-temporal task plotted against the task-difficulty level for the durations in the seconds and the minutes ranges.

Fig. 2 .

 2 Fig. 2. Mean passage of time judgments plotted against task-difficulty level for the durations in the seconds and the minutes ranges.

  (F(1.773, 70.92) = 7.45, p = .001, ηp 2 = .16; F(1.446, 59.27) = 7.04, p = .002, ηp 2 = .15, respectively). However, there was no difference in the PoT judgment for the neutral stimuli between the two duration ranges (Mseconds = 4.057, SEseconds = 0.144; Mminutes = 3.992, SEminutes = 0.142, F > 1), while the PoT was judged slower in the minutes range than in the seconds range for both the negative emotional stimuli (Mmin. = 3.425, SE = 0.146; Msec. = 4.093, SE = 0.148; F(1, 81) = 10.38, p = .002, ηp 2 = .114), and the positive emotional stimuli (Mmin. = 3.806, SE = 0.123; Msec. = 4.565, SE = 0.124);

Fig. 3 .

 3 Fig. 3. Mean passage of time judgments plotted against emotional stimuli of negative, neutral or positive valence in the seconds and the minutes ranges.

Fig. 4 .

 4 Fig. 4. Mean passage of time judgments plotted against stimulus durations in the seconds and the minutes ranges.

  Further experimental investigations are thus required to better understand what lies behind our awareness of variations in the speed of the passage of time and why we translate our experience in the present into movements of time and self-duration. Compliance with Ethical Standards: For the 3 experiments conduced in human adults, all individual signed an informed consent form presenting the procedure validated by the Research Ethics Committee of the University Clermont Auvergne (IRB00011540-2019-33) and conducted in accordance with the 1964 Helsinki declaration.

Conflict of Interest: Natalia Martinelli and Sylvie Droit-Volet declare that their have no conflict of interest.