# Cognitive load, fatigue, and aversive simulator symptoms, but not manipulated zeitgebers, affect perception of duration in virtual reality

### Duration judgments

The sun was a constant component of the environment and was designed to either move at its natural speed over the horizon or not move at all. Participants completed 8 trials in total, lasting 6 minutes each, and were not told that the trials were of equal length or how many trials they would complete. Additionally, throughout the experiment, participants listened to ambient sounds of sea waves and wind through headphones.

We experimentally manipulated the level of immersion by asking participants to perform the task in a non-immersive and immersive environment, in front of the LCD screen or with the head-mounted device (HMD) respectively. In order to probe the effect of cognitive load, as in the original study, in half of the trials participants were asked to perform the classic n-back task30. These experimental conditions amount to 2 (immersion) × 2 (movement of the sun) × 2 (cognitive load) of design. At the end of each trial, participants were asked to estimate the duration of the successful trial in seconds, following Schatzschneider et al. Design 2016. At the beginning and end of the experimental session, participants were also asked to complete a Simulator Sickness Questionnaire (SSQ), the change in this score is used as the Simulator Sickness Score. To test the effects of each experimental condition, we run a 2 × 2 × 2 repeated measures ANOVA, with the simulator disease score as a covariate in a separate run. Results were adjusted for multiple comparison with Bonferroni correction if necessary.

#### Sun

First, we tested the effect of manipulating the sun. In the original study, the authors found that when no task was being performed, participants felt that time was longer when the sun was stationary than when it was moving at its natural speed. We found no significant effect of manipulating the speed of the sun’s motion on time estimation (F(1.36) = 0.103, p = 0.750, Fig. 1A) even when we only look at the task-free condition (two-tailed you(36) = − 0.191, p = 1, adjusted for multiple comparisons, Fig. 2). To ensure that the effect was not inhibited by the unpleasant simulator effect, we included the score as a covariate in the ANOVA analysis. Although adding the SSQ score improves the fit of the model (residuals (full + SSQ) < residuals (full), where residual = data - fit), it has no significant effect on sun, immersion or the interaction between the sun and immersion.

We have reproduced the classical result of the cognitive load11 and found a significant task effect on trial duration estimation (F(1,36) = 69.013; p = 6.874e-10, ηp2= 0.657). A post-hoc test found that the duration estimate was shorter when participants performed a task than when they were passively present in the environment (you(36) = 8.307, p = 6.876e−10,D= 0.59, Figure 1B).

#### Immersion

Schatzschneider et al.28 reported shorter duration estimation in non-immersive (LCD) environments than in immersive (HMD) environments. We did not reproduce this result and no effect of the environment was found on the duration estimate (F(1,36) = 0.588; p= 0.448, Fig. 1C), however, we found a significant interaction between cognitive load and immersion (F(1,36) = 6.854; p= 0. 013, $$\upeta _{P}^{2} = 0.16$$) – when no task was assigned, participants felt the time was longer in an immersive environment, but when participants performed a task, they felt the time was longer in a non-immersive environment ( Fig. 3A). We first thought this was again a cognitive load effect – in an immersive environment, participants were exposed to fewer distractors and could focus more on the task and engage more cognitive resources. However, the performance was slightly better in the LCD condition (matching you(73) = 2.7156, p= 0. 0083 Fig. 3A insert). In light of these results, we hypothesize that HMD was somehow a more challenging environment. In the non-immersive environment, in the no-task condition, participants were exposed to the rest of the experimental room, which resulted in a more complex environment as opposed to the HMD condition where only the virtual island could be observed.

#### Symptoms of simulator sickness – physiological arousal

Although the negative symptoms of the simulator did not specifically affect the effect of the sun on the time estimate, we tested if it had an effect on the average time estimate. To assess the statistical significance of this relationship, we regressed the SSQ score on the duration estimation measures. The SSQ score explained a significant portion of the variance in the duration estimate (F(1,294) = 9. 590, p= 0.002,R = 0. 178,R2 = 0.032). The regression coefficient (B= 3.765,95%,THIS= [1.372,6.156]) reported that an increase in SSQ score by 1 increased, on average, the duration estimate by 4 seconds (Fig. 3C). We hypothesize that this effect of aversive symptoms of simulator sickness, such as nausea or dizziness, is mediated by the link between physiological arousal and time perception. Various types of excitation have previously been shown to affect interval timing4,5,6especially unpleasant stimuli dilate the perception of time31. Although Schatzschneider et al.28 also collected SSQ responses, they did not provide analysis beyond score change.

#### Fatigue

As noted above, we did not reproduce the effect of immersion on the duration estimate. Although the effect reported in the original article is not significant, it appears to be a strong trend, at least for the conditions with a task. In the original paradigm, participants had always started with a non-immersive block and continued on to an immersive block. Such a linear design is distorted by fatigue. At the beginning of the experiment, participants may feel that the duration is shorter simply because they are less tired than at the end, so we hypothesize that this is the reason why we did not reproduces the immersion effect reported by Schatzschneider et al.28. In our design, we controlled for this effect by randomizing the dip blocks. Irrespective of the condition in which the participants started or ended the experiment, they estimated that the time was shorter at the beginning of the experiment than at the end (Fig. 3B) with a transitory restriction effect of the change of environment in the middle of the experiment.

### Bayesian analysis

Non-significant results of frequentist tests do not distinguish between “absence of evidence” and “evidence of absence”. To test our ability to present evidence in favor of the null hypothesis (no effect of the movement of the sun on the perception of time), we went beyond the frequentist approach, we turned to Bayesian inference and performed repeated Bayesian ANOVA and separate paired-samples Bayesian t-tests for each state. We first performed a Bayesian repeated measures ANOVA on the data with the experimental conditions [immersion (2) × task (2) sun (2)] as within-subjects factors. We used the a priori default options for effects (i.e., r= 0.5 for fixed effects). To assess the robustness of the result, we also repeat the analysis for two different a priori specifications (details in the ”Methods” section). Analysis of effects indicates moderate to strong evidence for excluding immersion (BFexcept = 4.803, where BFexcept is the change between the before and after exclusion probabilities for the model-averaged results, our notation follows the JASP Handbook), sun (BFexcept = 16.815), and all interactions between the two. In fact, only the model with a single cognitive load term had BFexcept less than 1 (BFexcept = 3.724e−13). Post-hoc tests indicated the robustness of these results to anterior width (Figs. 4, S2). We can therefore conclude that in our data we can observe moderately strong evidence for no effect of sun manipulation or immersion on duration estimation.