A system for virtual interaction, comprising two or more portable electronic devices, is provided. Each device comprises, in turn, coordinate referencing means operable to define a coordinate system common to the portable electronic devices with respect to a physically defined reference position, position estimation means operable to detect a the physical position of its respective portable electronic device with respect to the reference position, virtual environment generation means operable to generate a virtual environment, and communication means operable to transmit positional data using the common coordinate system from that portable electronic device to another portable electronic device. The virtual environment is shared in common between the portable electronic devices. The virtual environment uses the common co-ordinate system within which each portable electronic device defines a position for itself responsive to its physical position with respect to the reference position.