The scenario you described, where there is a planet or dwarf planet on the opposite side of the Sun from Earth, moving and rotating at the exact same speed, is extremely unlikely based on our current understanding of planetary dynamics. Here's why:
Stability of orbits: Planetary orbits are governed by the laws of gravity and follow predictable patterns. For a planet to maintain a stable orbit directly opposite Earth, it would need to have a very specific set of initial conditions and finely-tuned parameters. Any perturbation or deviation from those conditions would cause the orbit to become unstable, and the planet would drift away from the exact opposite side.
Gravitational influences: The presence of other planets and celestial bodies in the solar system would exert gravitational forces on any object located on the opposite side of the Sun. These influences would disrupt the delicate balance required for a planet to remain precisely opposite Earth.
Detection through gravitational effects: Even if a hypothetical planet existed on the other side of the Sun, its gravitational influence would still be detectable. Observations of the orbits of other planets and spacecraft in the solar system would reveal gravitational perturbations caused by the hidden planet's presence.
Advances in observational technology: Over the years, our ability to observe distant celestial bodies has improved significantly. Astronomers utilize telescopes, space probes, and advanced techniques to detect and study planets in our own solar system and beyond. It is highly unlikely that a planet hiding directly opposite Earth would remain completely unnoticed by these observational efforts.
In summary, while it is theoretically possible for a planet to exist on the opposite side of the Sun, moving and rotating at the same speed as Earth, the likelihood of such a scenario is incredibly low based on our current understanding of planetary dynamics and observations.