Einstein's development of the theory of general relativity, which describes gravity as the curvature of spacetime caused by mass and energy, was a groundbreaking and highly creative achievement. The concept of mass creating a well in spacetime can indeed be challenging to visualize since it involves abstract mathematical ideas and a departure from classical notions of space and gravity. Here's a simplified explanation of how Einstein arrived at this idea:
Equivalence Principle: One key concept that influenced Einstein's thinking was the equivalence principle. It states that the effects of gravity and acceleration are indistinguishable. Einstein reasoned that if an observer in a closed box cannot distinguish between being in a gravitational field and being in an accelerating frame of reference, then gravity must be a manifestation of something more fundamental.
Thought Experiments: Einstein employed various thought experiments to explore the consequences of the equivalence principle. One famous example is the "elevator thought experiment." Imagine an observer in an elevator without windows. If the elevator is at rest on the surface of the Earth, the observer feels a force pulling them downwards (gravity). Now, imagine the elevator is freely falling in a gravitational field. In this case, the observer would experience weightlessness, as if there were no gravity at all. Einstein pondered the question: What would happen if the observer dropped an object inside the elevator? He realized that the object would appear to be floating, just as it would in the absence of gravity. This led him to conclude that the sensation of gravity could be explained by the curvature of spacetime.
Mathematics of Curved Spacetime: Einstein developed a mathematical framework to describe the curvature of spacetime caused by mass and energy. He utilized sophisticated mathematical equations, known as tensor calculus, to express the relationship between the distribution of matter and the geometry of spacetime. The presence of mass and energy bends the fabric of spacetime, creating a "well" or curvature. Objects then move along the curved paths determined by this curvature, producing the effects of gravity.
It's important to note that Einstein's understanding of gravity was not based solely on visual observations but on a combination of thought experiments, logical reasoning, and mathematical formalism. His theory of general relativity has been remarkably successful in explaining a wide range of gravitational phenomena, including the bending of light, the motion of planets, and the behavior of black holes.