Hubbard, T. L. (2005). Representational momentum and related displacements in spatial memory: A review of the findings. Psychonomic Bulletin And Review, 12(5), 822–851. doi:10.3758/BF03196775

Summary

Hubbard consolidates a huge body of literature regarding the phenomena of displacement. While this has sometimes been referred to as representational momentum, Hubbard prefers the term “displacement” because the effect can be found in many domains:

Forward displacement (in the direction of motion)
Downward displacement (due to gravity)
Reduced displacement after contact (due to friction)
Inward displacement along a curved trajectory (due to centripetal force)
Displacement in auditory pitch

There are many variables that seem to influence the amount and direction of displacement:

Target velocity (increased velocity increases displacement)
Direction of motion (horizontal displacement is typically greater than vertical displacement, and vertical displacement is affected by gravity)
Target identity and shape (displacement tends to be consistent with the typical direction certain shapes move)
Target weight (larger downward displacement for larger objects)
Target animacy
Surrounding context (e.g. if there are “landmarks”, if the stimuli are realistic scenes, if the motion is from the point of view of an observer, etc.)
Physical constraints (e.g. walls that the object can bounce off of)
Structure of the motion (e.g. oscillitory motion)
Internal vs. externally caused motion, as in the launching task

It is also influenced by factors applying to the participant themselves:

Attention
Fixation point (eye movements)
Action plans

Methodologically, displacement has been found for smooth-moving targets, for sequential series of discrete stimuli, for static images that imply motion, and for targets whose motion is controlled by the participant. The effect of displacement seems to decay after a period of time, though the results on this are somewhat mixed. Response measures have included judging same/different, clicking on the remembered position of the target, or reaching for the target.

Hubbard suggests that displacement does not solely reflect objective physical laws, though it might strongly be influenced by them. Importantly, this is because displacement can be affected by other factors (such as landmarks, or whether the motion is internally or externally caused) besides just kinematics and dynamics. Regarding naive physics, he suggests that “displacement might reflect subjective consequences of physical principles, rather than objective physical principles per se” (pg. 842).

In terms of a computational-level theory of displacement, Hubbard suggests that displacement serves the purpose of bridging the gap between perception and action by helping to localize the future spatial locations of objects. This is consistent with the idea of forward models, though displacement seems to often be less than what one would expect from an accurate prediction into the future. Hubbard suggests this might be a tradeoff for prediciting motion that is either predictable or unpredictable: some displacement helps bias action towards predictable motion, but it is also less than what would be expected, which makes it easier to recover when the motion is unpredictable.

Takeaways

I would be really curious to see if you could get the effects of displacement from a computational-level model whose goal is to execute an action to “catch” a moving object. This would involve predicting the next state of an object based on a variety of factors (position, rotation, velocity, shape, etc.) but also executing the action (with a latency similar to that found in humans). Would you end up finding the same types of displacement effects? Would this model predict new things about displacement?

Additionally, I wonder to what extent displacement/prediction is used simply as a tracking device. That is, it’s not used to inform the motor system of where to execute its action—just to help the perceptual system track the object through time.