This is the nature of science, which in many respect only fully matured at beginning of the 20th century when all this was happening. It depends on observation, and without observation all one has is religion.
Here is what is now thought when science is done. An observation is made. If we take Galileo as an example, he observed bones in animals. Then We make a mathematical model. In that case it was the relationship between mass the bone volume that was needed to support the mass. Then we make testable predictions based on that model, Galileo made the prediction that Giants do not exist, which is true, and could not have existed, which is one of the things that made the Church mad.
Relativity and Quantum mechanics both depend heavily on the mathematical model to make predictions on things that are not part of our everyday experience. This is different from classical physics where the mathematical models were based on things that most people observe.
Classical physics is a ball falling and bouncing off the floor or light refracting through a prism. Quantum mechanics is a ball tunneling through the floor or light refracting around a galaxy.
What I find interesting is that people take Relativity at face value and have a problem with Quantum Mechanics. It is true that we see a limit in velocity in the macroscopic world, but that has to do with friction, not relativity. There is nothing in our experience that says we cannot go as fast as we have the energy to accelerate. Certainly our mass does not increase if we are traveling at 80 miles and hour in a car instead of 30 miles an hour.
OTOH, our experience does tell us that second and third hand information is unreliable, and we are often better off making direct observations if possible. Are we just going to let some stranger bury our cat on the statement the cat fell off the roof and died? No, we want to see the cat, and until we do we hope the cat is alive, but there is chance the cat is dead. Is it both? No, it is uncertain, which is the key thing that people do not learn about science. Uncertainty.
In Quantum Mechanics this is called a wave function, and the cat is in a superposition of wave functions that represent all possible states. The wave function collapses when we make an observation.
Here is another interesting thing. Quantum Mechanics came about to a problem with infinity. Relativity never solved it's problem with infinity, at least not completely, and when combined with Quantum Mechanics develops more infinities. This is what does not make sense.