Final answer:
Spacetime's existence and its curvature are determined by the presence of matter, as per Einstein's general relativity, which states that matter influences the way spacetime curves, influencing how matter moves. In the classical sense, temperature does not directly affect this curvature, but energy distribution can influence spacetime due to mass-energy equivalence. In quantum theories, extreme temperatures can affect spacetime through interactions with quantum fields.
Step-by-step explanation:
The considerations for the existence of spacetime and its interaction with matter and temperature are rooted in the principles of Einstein's general relativity. According to Einstein, it is the presence of matter that warps or curves the fabric of spacetime, and this curvature is what we experience as gravity.
Rather than serving as a static background, spacetime is dynamic, responding to the presence of matter and energy. When a particle, such as light or an electron, moves through a region of distorted spacetime, its trajectory is altered. John Wheeler encapsulated this idea by stating, "Matter tells spacetime how to curve; spacetime tells matter how to move."
Temperature itself does not directly affect the curvature of spacetime in classical relativity; however, the distribution of energy, which can include thermal energy, influences the curvature of spacetime due to mass-energy equivalence. In quantum theories, temperature relates more intricately to spacetime through quantum fields and particles.
In the realms of high energy physics—like those present during the early moments of the Big Bang—extreme temperatures influence the behavior of these quantum fields and consequently spacetime itself.
The study of these interactions is complex and requires a sophisticated understanding of both thermal physics and quantum field theory.
Speaking to classical and quantum considerations, while general relativity gives us the understanding that matter distribution determines spacetime curvature, in quantum gravity theories, the quantum state of matter-energy fields can lead to more nuanced behaviors of spacetime at very small scales, which could be affected by temperature and other quantum effects.