Time slows down on a crowded train

Numerosity, complexity and affect are among factors known to dilate perceived time. While such objective and subjective factors are usually tested in isolation with simple stimuli in the lab, here we examined the perceived passage of time in the ecology of daily social life: crowded public transit. Higher crowding level denotes a higher numerosity along with increased negative affect. Accordingly, we hypothesized that crowding lengthens subjective trip duration. Participants (N=41) experienced short (between 1 to 2 minutes) immersive subway trips using Virtual Reality (VR). Each individual experienced multiple virtual trips with different crowding levels. After each trip, they were asked to estimate the trip duration and rate its affective pleasantness. Presence of one additional person per square meter of the train significantly increased perceived travel time by an average of 1.8 seconds. Rather than objective factors, this effect was mediated by subjective negative feelings induced by crowding. Analysis of cardiac data also revealed the slope of change in heart rate during a trip as a physiological source of perceived travel time, independent of the crowding level. This study is an example of bringing basic psychological and physiological findings into an ecologically valid setting using VR technology. Findings have broader implications for the effects of disliking social crowding on our daily perceptions, which is likely more pronounced during or even after the COVID-19 pandemic.


Introduction
If we consider time as one dimension of existence, then passage of each and every along with negative emotional influences, especially during the age of Covid-19 pandemic. Both sensory and emotional aspects of crowding could contribute to a distortion of the perceived time.
The visual aspect of crowding is the view of a higher number of individuals in a limited space. According to A Theory Of Magnitude, Those questions of how many and how long, how fast, and how far are tightly related to each other (Walsh, 2003). Estimating time, space and quantity share a common underlying system in the parietal cortex (Walsh, 2003), the region that also supports the directing of attention to spatiotemporal features (Coull et al., 2004). Aligned with this theory, various studies have demonstrated that higher magnitude or numerosity of items presented during an interval, lead to a longer perceived duration. For example, a physically larger stimulus has a lengthened duration compared to a smaller stimulus (Rammsayer & Verner, 2014;Xuan et al., 2007). Higher numbers of dots are perceived longer than fewer dots with the same objective duration (Dormal et al., 2006;Hayashi et al., 2013;Long & Beaton, 1981;Xuan et al., 2007). Even a digit is perceived temporally longer the larger the value it represents (Oliveri et al., 2008). Complexity of stimuli has also been shown to increase perceived duration (Aubry et al., 2008;Roelofs & Zeeman, 1951;Schiffman & Bobko, 1974). More dynamic visual displays with more complex motion are perceived longer compared to more static ones or with simpler movements (Brown, 1931).
The role of distinct stimulus characteristics on time perception has been commonly examined with simplistic stimuli such as dots, simple geometrical shapes, or characters shown on a computer screen and usually tested with intervals shorter than a couple of seconds. It is unknown how these factors scale up to more complex real-world conditions, and durations with magnitudes of consequence for choice and behavior. Here we examine whether the effects of stimulus factors, such as numerosity and complexity shown to regulate perception of brief Crowding is not only a different sensory experience but it also causes an internal subjective unpleasant feeling. In a crowded environment an individual might experience a violation of personal space, which serves as an imaginary buffer around the self. When violated, our defense systems, which have evolved to deal with threats to physical survival, are likely to be activated (Todd & Anderson, 2009). This is only more prevalent in the age of the COVID-19 pandemic, where personal space (6ft or less) highlights potential viral exposure.
Activating defense systems generates tense arousal, leading to avoidant motivational states.
Social crowding in public transit is indeed associated with negative arousal (Cheng, 2010;Cox et al., 2006;Kalb & Keating, 1981;Stokols, 1972). Several components of affective reactions to crowding in public transit include feeling uncomfortable, distracted, frustrated, and irritated, which have been associated with higher levels of stress and somatic symptoms such as headache, tension, and stiff muscles (N. D. M. Mahudin et al., 2012;N. M. Mahudin et al., 2011).
Negatively arousing stimuli are perceived longer in duration than neutral stimuli (Droit-Volet, 2013). For instance, a sound that induces negative affect is perceived longer than a neutral one (Noulhiane et al., 2007). Observers overestimate the duration of time looking at angry faces compared to neutral faces (Droit Volet et al., 2004) -. In the most prominent model of time perception, the pacemaker accumulator model, dilation of time in emotional contexts is thought to reflect arousal increasing the rate of the internal clock (Treisman et al., 1990) (Cacioppo et al., 2000).
However, the exact mechanisms of affective modulation of time perception are still debated , as is the relation between time perception and autonomic states that regulate physiological pacemakers, such as heart rate (Schwarz et al., 2013).
As reviewed above, previous works show that these physical and affective characteristics of social crowding lengthen experience of time, although tested in isolation with simple stimuli and usually in intervals of shorter than a few seconds. Here we examined the objective factors of passenger density or physical closeness to others to regulate an internal subjective factor of crowding discomfort. We hypothesized that social crowding in an ecologically valid virtual context leads to negative feelings and accordingly a lengthened perceived travel time at durations in the order of minutes. In order to examine this hypothesis, we used immersive VR technology, simulating a realistic social setting with controlled manipulation of crowding levels, i.e., number and closeness. While participants were physically in the lab, they experienced short (1 to 2 minutes) immersive trips in the VR environment of a subway train with specific densities of virtual passengers sitting or standing around. We examined perception of duration and affective ratings after each of 5 virtual trips that had 5 different crowding levels (figure 1). Our VR environment was sufficiently realistic, that conditions with higher levels of crowding were perceived as more emotionally negative. We hypothesized that a higher crowding level makes a trip be perceived longer, and that this effect is, at least partially, mediated by the negative feelings induced by crowding.
The homeostatic time perception theory associates temporal perception to integration of bodily signals over time (Craig, 2009) . Based on this theory, dilation of duration in emotional conditions may be linked to the integration of peripheral physiological signals such as heart rate 138 (Craig, 2009;Meissner & Wittmann, 2011). We also recorded heart rate data during the experiment using a wristband pulse device. The purpose of heart rate recording was to explore the potential link between objective physiological changes and subjective travel time perception and its affective components.

Results
Each participant experienced five VR trips with five different crowd density levels ( Figure 1; also see supplementary video). Net emotional valence of a trip, defined as pleasantness rating minus unpleasantness rating is represented in Figure 2.A, averaged for each density level across participants. As we can see, valence of an experience decreased, as a function of increase in density level (β=-1.03, SE=0.099, p<0.0001). However, arousal level, estimated by summing up the pleasantness and unpleasantness ratings was not significantly predictable from density (β=2.4e-3, SE=0.033, p=0.94).
Observers were able to assess objective differences in temporal durations, with perceived duration increasing with objective duration of train ride (β=0.76, SE=0.14, p<0.0001). We defined a measure of time perception bias as the actual duration of a trip subtracted from the participant's perceived duration. However, there was a significant overall decrease in IBI during a trip (β=-5e-4, SE=8.7e-5, p<0.0001), indicating an increase in heart rate. As shown in Figure 4, a larger slope of this IBI change, i.e., more deceleration of heart rate during the trip, was associated with longer perceived travel duration (β=3870, SE=1721, p=0.026). This was the case even though the IBI slope was not explained by subjective valence of the trip (β=2.8e-8, SE=2.1e-5, p=0.90) and its effect on perceived travel duration was significant even when controlling valence (slope β=3746, SE=1704, p=0.029); therefore, heart rate had a unique contribution to variability in perceived trip duration.

Discussion
In a VR simulation of a subway ride, we examined the relationship between density of passengers and perceived duration of short immersive trips. Results showed that crowding level inside the subway car had a significant effect on one's perception of travel time: one additional passenger per square meter on average increased perceived duration of a 1-2 minutes trip by around 1.8 seconds. This effect was explained by subjective feelings. While passenger density is an objective measure (here only a visual factor), it regulated an internal sense of the passage of time and affective feelings. Increased virtual crowding made a trip feel longer and more unpleasant. It was this latter subjective feeling that mediated the former effect of crowding on time perception: A more crowded trip was perceived longer to the extent that it induced negative feelings. This result is in agreement with previous evidence that negative emotions lengthen perceived duration (Droit-Volet, 2013;Droit Volet et al., 2004;Noulhiane et al., 2007;Rey et al., 2017), indicating that crowding, as an affectively negative factor could have such an effect on time perception. Conversely, a less crowded trip was judged as a more positive experience.
Positive experiences were associated with a greater contraction of time relative to objective durations. As such, time flew by, i.e., greater contraction relative to objective duration, the more pleasant the trip. Independently of crowding and valence, analysis of the cardiac data showed a significant decrease in IBI (i.e. increase in heart rate) during a trip, suggestive of sympathetic arousal and stress (Kirschbaum et al., 1993). A positive rate of change in IBI, i.e. less increase or more decrease in heart rate explained lengthened perceived travel time. Sympathetic heart rate acceleration facilitates action in an urgent situation (fight or flight), while the parasympathetic deceleration facilitates higher sensory intake during passive attention (Graham & Hackley, 1991;Vila et al., 2007). Our results, therefore suggest that in this sympathetic-parasympathetic compromise, a less sympathetic or more parasympathetic dominance is associated with a lengthened perception of time. As this effect was independent of the effect of valence on perceived travel time, the role of heart rate change is probably a marker of attentional rather than affective processes. This finding is aligned with an ample amount of evidence that increased attention lengthens subjective time (Grondin, 2010).
The majority of previous experiments on time perception have been administered in the lab setting using computerized tasks with discrete relatively short stimuli. Our experiment took place in the lab as well, but it simululated an experience approximating more closely the ecology of daily-life in an urban center. VR is an excellent tool for creating social stimuli that are more controlled than real stimuli, are replicable, and may be impractical or too expensive to attain in the real-world (Fox et al., 2009). Increased density of virtual avatars caused an increase in negative feelings during the trip, validating that they were sufficiently realistic to induce the negative feelings associated with overcrowding in real-world commuting trips (Cheng, 2010;Cox et al., 2006;Kalb & Keating, 1981;N. D. M. Mahudin et al., 2012;N. M. Mahudin et al., 2011;Stokols, 1972). Despite the efficiency of the VR environment in simulating a relatively realistic travel experience, our experiment had several limitations that made it different from daily-life settings.
In a real social setting, crowding has other components such as smell and noise that are beyond the visual closeness to strangers (Haywood et al., 2017). Here, however, we only manipulated the visual aspect of crowding in different passenger density levels. Virtual experience with the current VR technology, even though highly realistic, also differs in critical ways from a real experience, including vibratory, kinesthetic and exterior visual cues that can signal travel time.
Virtual avatars were also visually distinguishable from real humans. Participants did not actually intend to travel to a destination, and were only asked to imagine so. Furthermore, the duration of subway trips in the current study were in the range of one to two minutes. This allowed for testing a higher number of conditions in the limited duration of the experiment session, at the expense of having unrealistically short trips. Another limitation of this study was the undergraduate demographics of our sample. While crowding is an unpleasant phenomenon worldwide (Evans et al., 2000), its perception as more or less unpleasant may depend on different demographics characteristics such as age, occupation, or culture. Nonetheless, we posit that the underlying effect of valence to dilate or contract time, would be universal. Therefore, considering this interaction term in these choice models might be beneficial to obtain a better fit to humans' behavior. Furthermore, our results suggest that the impact of crowding on perceived travel time can be alleviated if public vehicles target design features to make the experience of crowding less unpleasant. As we showed, crowd density itself does not regulate perceived trip duration, but rather it is the affective impact of crowding. Design engineering can focus on regulating subjective rather than physical factors, which may in turn have objective consequences for decreased physiological stress.
Data collection of the current experiment was conducted before the COVID-19 outbreak.
During the pandemic, authorities and scientists all across the world gave extensive warnings to avoid large crowds and comply with social distancing. This portrayal of the crowd as a source of disease could cause it to trigger defense systems even more intensely, leading to heightened negative feelings (Chapman & Anderson, 2013;Curtis et al., 2004Curtis et al., , 2011Curtis & Biran, 2001).
Therefore, the influence of passenger density and its subjective affective impact on perceived travel time is likely only to get stronger. The emphasized negativity of crowding during the pandemic could be even more long-term carrying on in a post-pandemic age when the threat of the virus is alleviated. It will be critical for future studies to shed light on the short-and longterm effects of COVID-19 pandemic on perceptions of crowding, and its consequences on use of public transit.

VR environment
The VR environment was developed to simulate the inside of a subway car, including moving avatars of passengers (Supplementary video S1). The dimensions and the interior of the subway car were created to represent the New York City subway car R160 model (13.61m × 2.59m, 35.25m 2 ) currently in service. Five conditions were used in the experiment to present five different levels of passenger density.
The number of passengers in the car in each condition was determined to have one, two, three, four, and five passengers per square meter. For example, the lowest density condition was created with one passenger per square meter, i.e., 35 passengers in 35 m 2 , and the highest density condition was with five passengers per square meter, i.e., 175 in 35m 2 . Seating and standing passengers were placed with random distributions to look natural while keeping the total number in the car in the incremental ratios. The 3D computer model of the environment was created in Autodesk 3DS Max, then converted into Twinmotion software where real-time interaction and avatars were added.
Interactions allowed a viewer to walk in the subway car and look around the environment and passenger avatars. The avatars were animated to simulate naturalistic behaviors of passengers such as occasionally changing postures, looking at phones, and reading books or magazines.
To experience the virtual environment, we used the HTC VIVE  subway car (5 density levels). Participants were informed that the trip duration is the time between the first bell and the second bell ringing sounds.
Upon arrival at the lab and signing the consent form, participants were given an oral description of a trip. They then experienced three practice trips with density levels 1, 3, and 5 and of 100 second duration. The purpose of the practice trip was to familiarize them with the environment and the concept of a virtual trip. During demo runs, participants were asked to estimate the duration following the trips . They did not receive any feedback about the accuracy of their estimates. After the demo trips they performed the main VR task and then answered several surveys about transportation preferences. All questions asked during the VR task and the following surveys were computer administered through the Qualtrics online survey platform.

VR task
The VR task included experiencing 5 trips with all 5 different passenger density levels in a randomized order, each having a randomly selected duration among 60, 70, or 80 seconds (with equal probability). After each trip, participants were asked to take off the headset and sit at a computer to answer the questions about their experience. These questions included the following: 1) Indicate how pleasant you felt during the virtual trip experience you just had, by a number between 1 and 7.
2) Indicate how unpleasant you felt during the virtual trip experience you just had, by a number between 1 and 7.
3) How long was the trip you just experienced? Type your estimate in seconds. Pleasantness and unpleasantness were asked in two unipolar scales (questions 1 and 2), to allow for assessment of mixed feelings and while also allowing derivation of arousal levels (Kron et al., 2013(Kron et al., , 2015. Magnitude and direction of net valence was defined as pleasantness rating (question 1) minus unpleasantness rating (question 2). Arousal, which is defined by the overall intensity of one's affective experience, was estimated by summing pleasantness and unpleasantness ratings (Kron et al., 2013).

Physiological recording and analysis
Cardiac data was recorded during the experiment using the Empatica E4 wristband. E4 is a wireless bluetooth wearable device that detects pulse using Photoplethysmogram (PPG).
Participants were instructed to rest their hand on a stand during the virtual trip (supplementary video S1) in order to reduce movement of the wristband and prevent noise in physiological data.
Interbeat intervals (IBI) are the duration of the interval between two consecutive heartbeats.
IBI's recorded during each trip were extracted based on the logged start and end time of the trip.
Average IBI for each trip (i.e. inverse of heart rate), was then estimated as an inverse measure of autonomic cardiac arousal during the trip. We also estimated the average slope of change in heart rate during each trip using a linear model with timestamp of each beat as the independent variable and the corresponding IBI as the dependent variable.

Statistical analysis
We used mixed-effects regression models for statistical analyzes since the task design between subjects variability, by including a random intercept that depends on subject ID in addition to fixed effects for conditions. We used these models for all tests on the relationship between trip-related measures (unless otherwise stated), for example, testing whether crowding would explain valence or time perception bias or in models ran for the mediation analysis.
Statistical significance of models' fixed-effects (slopes of independent variables) were estimated using t-tests with Satterthwaite's method to approximate degrees of freedom. Whether the average of a trip measure such as time perception bias was different from zero was tested using a random effect model predicting the variable from an intercept (significance of intercept would show systematic difference of the variable from zero).
All data analysis was performed using the R programming software. The gmnl package in R was