We consider a quantized massless and minimally coupled scalar field within a (1+1)-dimensional spacetime described by a circle with a time-dependent radius R(t). Within the semi-classical treatment, the back-reaction of the quantum field onto the R(t)-dynamics is taken into account in terms of the renormalized expectation value of the energy–momentum tensor including the trace anomaly. In case the classical energy of the circle is positive, the results indicate that the back-reaction (induced by the trace anomaly) could prevent the collapse of the spacetime R ↓ 0; however, the semi-classical picture fails to describe the R(t)-dynamics at the turning point (i.e., possible bounce) at finite values of R and . The fate of the interacting system after that point (e.g., oscillation or eternal acceleration) cannot be determined within the semi-classical picture and thus probably requires the full quantum treatment. Allowing also for negative classical energies (similar to the Newtonian gravitational energy, for example), the Casimir effect yields the dominant back-reaction contribution and might also prevent the collapse of the spacetime—leading to eternal oscillations of R(t) ≠ 0.