There are several reasons why it would be highly challenging, if not impossible, for a spacecraft to travel across the entire Solar System or the entire galaxy within a single day, even at speeds exceeding the speed of light:
Vast distances: The scales involved in interstellar or intergalactic travel are immense. Even within the relatively small Solar System, the distances between planets are significant. For example, the average distance between Earth and Mars is about 225 million kilometers (140 million miles). To travel across the entire Solar System, which extends to the outer reaches of the Kuiper Belt, would require covering distances on the order of billions of kilometers.
Energy requirements: Traveling at extremely high speeds, such as faster than light, would require an enormous amount of energy. The energy required to accelerate a massive spacecraft to such speeds, overcome inertia, and counteract the effects of acceleration and deceleration would be astronomical. We currently do not possess any known energy sources or propulsion systems that could provide the necessary energy levels.
Relativistic effects: As an object approaches the speed of light, the relativistic effects become more pronounced. Time dilation, length contraction, and increased relativistic mass are among these effects. These would introduce significant challenges for the passengers or crew on board the spacecraft, as well as potential issues with navigation, communication, and even the structural integrity of the spacecraft itself.
Technical limitations: Achieving speeds faster than light, as currently understood, violates our current understanding of physics. The theory of relativity, a cornerstone of modern physics, sets an upper limit on the speed of light as an absolute cosmic speed limit. It suggests that as an object with mass approaches the speed of light, its energy requirements become infinite. Additionally, other physical phenomena, such as the gravitational effects of massive objects, pose additional challenges to FTL travel.
It's important to note that our understanding of physics and technology may evolve in the future, potentially leading to new discoveries and breakthroughs that could change what we consider possible. However, based on our current understanding and technological capabilities, interstellar or intergalactic travel within a single day, even at faster-than-light speeds, remains highly unlikely, if not impossible.