Traveling across the entire Solar System or the entire Galaxy within just a single day is currently considered highly implausible, if not impossible, for several reasons:
Vast distances: The scale of the Solar System and the Galaxy is immense. The Solar System spans a distance of about 2 light-hours from the Sun to the outermost planet, Neptune. The Galaxy, the Milky Way, has a diameter of about 100,000 light-years. Even at the speed of light, it would take light itself thousands of years to traverse such distances. Overcoming these vast distances in a single day would require speeds far exceeding the speed of light.
Special theory of relativity: According to Einstein's special theory of relativity, the speed of light in a vacuum is the ultimate speed limit in the universe. As an object with mass approaches the speed of light, its mass increases, and its energy requirements become infinitely high. Breaking the speed of light barrier would require infinite energy, which is currently beyond the realm of known physics.
Time dilation: As an object approaches the speed of light, time dilation occurs. Time slows down for the object relative to an observer at rest. This means that even if a spacecraft could travel close to the speed of light, from the perspective of someone on board, the journey would still take a considerable amount of time. Therefore, it wouldn't be possible to complete interstellar or intergalactic travel in a single day, even at such high speeds.
Technological limitations: Even if we were to imagine a hypothetical propulsion system capable of achieving speeds close to the speed of light, we currently lack the technology and understanding of physics to build such a spacecraft. The enormous energy requirements, potential dangers associated with high speeds, and the need for shielding against interstellar debris pose significant engineering challenges that are currently beyond our capabilities.
It's important to note that our understanding of physics and technology could evolve in the future, potentially opening up new possibilities for interstellar or intergalactic travel. However, based on our current scientific knowledge, traveling across the Solar System or the Galaxy within just a single day or faster than the speed of light remains highly unlikely, if not impossible.