Learning Special Relativity Energy Laws Using Visio-haptic Illusion Nicolas Ladeveze * APC – Paris 7 University, Paris, France Tony Doat † CNRS/LIMSI/VENISE group, Orsay, France Etienne Parizot ‡ APC – Paris 7 University, Paris, France Jean-Marc V ´ ezien § CNRS/LIMSI/VENISE group, Orsay, France ABSTRACT Visual analysis of complex scientific simulation data often gain to be completed by an exploration with advanced Virtual Reality modalities as the haptic channel. But exploiting the haptic channel with a force-feedback device can be problematic when the profile of the forces to be conveyed to the user is inherently nonlinear. As application domain we are interested in learning relativity. Specifi- cally, we focused our interest in studying the evolution of the kinetic energy of an object approaching the speed of the light. Indeed, the divergent value of momentum for a fast moving object is a difficult concept to understand for students in theoretical physics. In this didactic context, we propose to use a spring launcher based visuo- haptic metaphor to allows a user to i) intuitively set the speed of objects in a relativistic framework and ii) access to the law beside the momentum value through this interactive experience. In this context, we imply that a user could interpret and remember an ab- stract mathematical concept by experiencing it in a VR simulation without having any knowledge and experience neither with haptic rendering nor with special relativity knowledge. In this paper, the contribution of visuo-haptic illusion and pseudo-haptic techniques is analysed with respect to a standard visual-haptic coupling. Af- ter formulating the laws of haptic control for this specific problem, a first evaluation is presented with preliminary results. These first results highlight the effectiveness of pseudo-haptic rendering tech- nique used for the interaction design with a complex force profiles and its interpretation taking into account a didactic goal. Index Terms: H.5.2 [User Interfaces]: Haptic I/O; I.3.6 [Methodology and Techniques]: Interaction techniques; I.3.6 [Methodology and Techniques]: Ergonomics; 1 I NTRODUCTION The context of the present study is a more global project called EVEILS (french acronym for Virtual Spaces for Scientific Explo- ration and Education), supported by an interdisciplinary team gath- ering VR specialists, physicists and didacticians. One of the goals of EVEILS is to combine advanced 3D graphics with VR inter- faces in order to create an appropriate environment to study Rela- tivity as well as to help students to develop some intuition of the quadri-dimensional structure of space-time. In a previous work [2] a physical simulator, tested in a CAVE-like setup, was introduced. It enables users to explore relativistic worlds in an immersive simu- lation of a carom billiard application. At this stage, the information about relativistic laws was purely visual, coupled with some basic navigation interaction. It allows a single user to observe special relativity induced phenomenas such as length contraction, time di- lation and relativity of simultaneity applied in a well known game * e-mail: ladeveze@apc.univ-paris7.fr † e-mail: tony.doat@limsi.fr ‡ e-mail: parizot@apc.univ-paris7.fr § e-mail: jean-marc.vezien@limsi.fr like simulation. The goal of EVEILS is to develop some intuitions of relativity and the 4D structure of spacetime by accessing and in- teracting with relativistic virtual world. For this, it was identified that other modalities can be used to access to extra information; for example, the link between energy and speed of objects moving at velocities close to the speed of light barrier. In particular, a user, using the sense of touch, could feel the en- ergy cost of interacting with relativistic objects. He may also under- stand how and why reaching a velocity equal to the velocity of light is impossible in a more tangible fashion (think about moving an ob- ject with extreme inertia). We choose to use an haptic device linked to a specific virtual object in order to allow the user to simultane- ously choose the speed of this object while perceiving information about energy cost through the force feedback. For this purpose, we designed a pseudo-haptic spring-launcher metaphor allowing the user to transmit a velocity to an object close to the speed of light, in an efficient way from a sensory-motor per- spective. We evaluate this metaphor using a visio-haptic illusion effect and pseudo-haptic rendering in comparison to a classic visuo- haptic coupling. The remaining of the article is organized as follows: First, sec- tion 2 makes a comprehensive review of related works both with respect to VR in Special Relativity as well as pseudo-haptic / visuo- haptic illusions and present our approach. Section 3 introduces the spring launcher metaphor allowing the user to control velocity of relativistic objects. Section 4 follows to present a pseudo-haptic spring control metaphor exploiting visuo-haptic illusion. Section 5 details the experimental protocol while section 6 presents and dis- cuss the results of the evaluation itself. Section 7 summarizes the work and open up new perspectives. 2 PREVIOUS WORK AND BASIS OF OUR STUDY The combination of advances in Virtual Reality and Computer Graphics make possible user’s immersion into complex virtual worlds. Our previous work [2, 3] allow a user to experiment differ- ent phenomenas according to the theory of special relativity. But, at this stage, only the sense of sight is used to apprehend the im- plication of this theory (e.g. the photon propagation delay, the aberration of light, the relative implication of space and time). To complete this sensitive experiment with a multi-modal interaction we focussed on using haptics. This kind of device usually allows to achieve various kind of interactions with the virtual scene such as navigation, selection [1] and manipulation of 3D objects [7]. Through the force feedback, haptic device can enhance proprieties perception such as their physical structure, viscosity or pressure. Also, Haptic device have already been used to learn Newtonian physics by experiments on topics such as dynamics [5, 6]. In our context of special relativity, we propose to use it in order to allow a user to access usually unreachable information: the dynamic law of fast moving objects. Unfortunately, Haptic device also have strong intrinsic limita- tions such as a maximum applicable force feedback value and a limited workspace size. As an alternative solution, Pseudo-Haptic 1 rendering [8] can be used as a way of rendering force feedback 1 Please note that in this paper we focus using illusion principles of pseudo-haptics and not on the cognitive interpretation of pseudo-haptics 13