Figure 2. Heaviness ratings averaged over subjects. (A) Judged mass for pushing the objects with full visual feedback expressed as z- scores. (B) Judged mass expressed in grams for pushing with full visual feedback (black) and pushing without visual feedback of the trajectory (dark grey). The scores were normalised in such a way that the judgments for the medium and reference object corresponded to 250 g and 200 g, respectively, so that the standard error for these objects is zero. (C) Judged mass expressed in grams for subjects that performed both the pushing with full visual feedback (black) as well as the lifting (grey) task. In all panels the error bars represent the between–subjects standard error. doi:10.1371/journal.pone.0042518.g002 pushing with full visual feedback conditions showed only an effect of object size (F (2,14)~197,pƒ0:001). There was no effect of task nor was there an interaction effect (p~0:43 and p~0:15, respectively). Size-Mass Illusion Discussion First, we have shown that perception of weight is not at all necessary for the size–weight illusion to occur. The illusion should therefore be interpreted as a size–mass illusion. The results also show that the magnitude of the illusion was similar for lifting and pushing. This demonstrates that weight is not only unnecessary for the illusion to occur, but that also the magnitude of the illusion does not depend on providing weight as a cue. An explanation for the fact that the illusion size reported here is large compared to what has been reported previously is that we have used a set containing one cube, while the other objects had the same height and depth but were elongated compared to the cube. In other studies usually a set of cubes in different sizes was used. Possibly the visual estimate of the volume differences between the shapes was therefore more pronounced in our study. Anyway, the constancy of the magnitude of the illusion across lifting and pushing indicates that the size–mass illusion is independent of the basis of the heaviness percept. Our results show that the objects with different sizes reached different peak velocities. There was no adaptation of the peak velocities over trials, i.e. participants didn’t adapt their pushing force such that all object sizes were pushed with the same amount of force after a number of trials. It has been shown that the maximum grip and load force rates adapt within as little as five trials such that there are no differences in these values anymore for lifting small and large objects [12]. This suggests that a mismatch between lifting force and an object’s weight is not an explanation for the size–weight illusion. It has, however, also been shown that the grip and load forces themselves do not adapt or at least do not adapt as fast as the peak grip and load force rates [18]. Since the peak velocity of the objects in our study is directly coupled to the amount of force applied (and not to its rate), adaptation is not to be expected for the peak velocities. Generally, the size-weight illusion is explained in terms of a discrepancy between prior expectations and sensory information [6,10]. This means that the perceptual system uses knowledge from prior experiences such as that larger objects are heavier than smaller ones [6]. Therefore different forces are used to lift small and large objects with the same mass [11,12]. In daily life situations we perceive either only gravitational forces when statically holding an object or a combination of gravitational and inertial forces while moving an object, but we rarely experience inertial forces alone. Nonetheless, we found that prior experience handling objects results in the same illusion magnitude for lifting and pushing of objects. This shows that the size–weight illusion is not caused by a perceptual prior for the lifting forces directly associated with weight, but by a more general prior related to the mass of objects instead. Several researchers have used the size–weight illusion to investigate the mechanisms underlying heaviness perception [19,20]. The present study demonstrates that the size–weight illusion is very robust, and is independent of the mechanism underlying the heaviness percept. We found that the magnitude of the illusion is the same for lifting and pushing whereas the heaviness percept (and the mechanism it is based on) differs between these modes of exploration. Apparently, there is a discrepancy, because both modes of exploration show a large difference in perceived heaviness, but not in the magnitude of the size–weight illusion. This indicates that one should be careful when drawing conclusion about heaviness perception in general from results obtained from studying size–weight illusion. In the physical world gravitational and inertial mass are the same according to Einstein’s equivalence principle. Mass is, PLoS ONE | www.plosone.org 4 August 2012 | Volume 7 | Issue 8 | e42518