I think thoughts are brain activities, and these can be measured. I think that if pictures fitting Dante's Inferno were entered into a brain scan, with the instruction that the scanee is supposed to think about that, we could probably detect the difference. We might even be able to detect the difference between the response of the scanee who believes in that version of hell and the response of someone who doesn't.
would that equate to measuring the energy of beliefs? I don't think it would. That would be measuring brain activity connected to thoughts, which in itself is a very intriguing thing.
The other thing you asked about, the early Church (significant because they got the point) didn't much care about our modern concept of "beliefs." To them, beliefs were demonstrated by action. And you don't need a brain scan to measure those. This didn't change until Constantine felt it politically necessary to codify this servant's religion.
Looking at Jesus' own statements about believing, one very much gets the idea that if it could register on a brain scan, it would be at least similar if not identical to meditation; a blank slate, or approaching it. So I think "beliefs" would be a lack of energy, if we could measure them. This too is consistent with Scripture: we are to labor to enter into rest. Ultimately this is what the Sabbath has always been about.