October 1988 | D. Amati, M. Ciafaloni, G. Veneziano
The paper explores the possibility of probing distances below the string size in string theory through scattering processes at Planckian energies. The authors show that this is feasible if the energy is not so extreme as to cause gravitational instability and when the scattering angle approaches a critical value from below. Above this angle, the distance starts increasing, deviating from the usual position-momentum uncertainty relation, and the resolution is never smaller than the string length. This suggests that below the Planck scale, the concept of space-time changes meaning. The study is based on explicit calculations of scattering amplitudes in string theory, which reveal that the string's soft nature and the gravitational radius \( R(E) \) play crucial roles in determining the behavior at short distances. For \( R(E) > \lambda_s \), a classical gravitational instability occurs, leading to black-hole formation. However, for \( R(E) < \lambda_s \), no such instability arises, allowing for the exploration of short distances. The analysis of the angle-distance relationship indicates a modification of the uncertainty relation at the Planck scale, suggesting the existence of a minimal observable length of the order of the string size.The paper explores the possibility of probing distances below the string size in string theory through scattering processes at Planckian energies. The authors show that this is feasible if the energy is not so extreme as to cause gravitational instability and when the scattering angle approaches a critical value from below. Above this angle, the distance starts increasing, deviating from the usual position-momentum uncertainty relation, and the resolution is never smaller than the string length. This suggests that below the Planck scale, the concept of space-time changes meaning. The study is based on explicit calculations of scattering amplitudes in string theory, which reveal that the string's soft nature and the gravitational radius \( R(E) \) play crucial roles in determining the behavior at short distances. For \( R(E) > \lambda_s \), a classical gravitational instability occurs, leading to black-hole formation. However, for \( R(E) < \lambda_s \), no such instability arises, allowing for the exploration of short distances. The analysis of the angle-distance relationship indicates a modification of the uncertainty relation at the Planck scale, suggesting the existence of a minimal observable length of the order of the string size.