If a spacecraft were to hypothetically travel close to the speed of light, the crew inside would not be crushed by the acceleration itself. According to Einstein's theory of relativity, as an object with mass approaches the speed of light, its mass appears to increase, and it requires more and more energy to accelerate it further. This phenomenon is known as relativistic mass increase.
However, the crew's experience of acceleration depends on their reference frame. From their own perspective inside the spacecraft, they would not feel any crushing forces due to the acceleration itself. They would experience the acceleration as normal, similar to how we feel acceleration in our everyday lives. The forces they experience inside the spacecraft would be relative to the spacecraft itself.
That said, traveling at speeds close to the speed of light would introduce other relativistic effects that could impact the crew. Time dilation is one such effect, where time appears to pass more slowly for objects moving relative to an observer at rest. As the spacecraft approaches the speed of light, time dilation would become significant. From the perspective of someone on Earth, time would appear to pass slower for the crew on board the spacecraft. This means that while the crew might not feel crushed by acceleration, they would experience time passing differently compared to someone on Earth.
Additionally, there would be other challenges associated with traveling at such high speeds, including the need for immense amounts of energy, potential impacts from interstellar dust or particles, and the effects of high-energy radiation. These factors would need to be considered when designing and planning for relativistic space travel.
It's worth noting that current technology is far from achieving speeds anywhere close to the speed of light, and there are many technological and theoretical challenges that would need to be overcome to make relativistic travel a reality.