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Well..
If physicists were sticking to what feels right, we would have still been at the Aristotle's level of understanding the physical world. Like, heavier things fall quicker than lighter ones... and so on.
I know, it is not a good attitude to accept just everything from "big guys because they know better", but it is not good either not to try to understand why they say things are what they are... However, what we can grasp (if we can not fully understand the mathematical models they are playing with) is the process, how they come up with their conclusions, this is not beyond average person's understanding, if the fine details and tools (math) are.. There are plenty of reading on the web, which can help here. The main thing is not to dig in our own ways of understanding things. Because there must be something in the fact that "big guys" thik otherwise...
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