I'm not woo at all and also think that surely there would be 'proof' by now, however I have had several experiences that I haven't been able to explain to myself entirely comfortably.
Many years ago as a teenager, I was in a house after a party. Four of us in one room about to go to sleep, one other couple (boyfriend/girlfriend) in another room. Suddenly: screaming -went rushing in to the other room to find that all the posters from one wall ( think entirely covered wall) had been ripped off and thrown against the farthest wall. The couple were cowering under the duvet gibbering. They'd been having sex when all the posters just tore from the wall and flew across the room.
In my Gran's house there was (apparently) a little white dog that sat beside the front door. Invisible to everyone but children under the age of 4 or so. Generations of children in the family commented on the dog, as did other children who were visiting.
In the house I grew up in we used to hear footsteps on the stairs most nights. My mum would tell me that we were hearing footsteps from the adjoining house ( staircases on either side of the wall) so as not to terrify me, when in fact she was scared stiff as the footsteps would also be heard when there was no one next door and would sometimes continue into her bedroom.
When I was a teenager I was in the house alone and went into the kitchen with the feeling that something was 'off.' The dining room led from the kitchen and I often used to feel that something was standing just out of sight in the dining room. As I stood in the middle of the kitchen that day, the mugs that were hanging on hooks under the cupboards all started to slowly bump against the wall. Very deliberate bumps, not the shaking you would get from an earth tremor. Nothing else was shaking or rattling and the area affected was on the other side of the wall to where I used to feel the presence. I just stood in absolute terror for about a minute while this happened. Couldn't go in the dining room for ages afterwards.
Interestingly years later when I mentioned to my mum about this she said " Oh Christ, I remember you being terrified of the ghost at our first house, I didn't want to tell you the was something in the dining room in this one!"
The feeling of dread in that room disappeared immediately they had the downstairs remodelled to remove that wall.
I used to work in a shop that was actually a 17th century house, with a cellar and lots of floors. We regularly used to see a figure in black in the cellar. And several of us had our names whispered in our ears while we were down there. Which was simply terrifying!
I often worked late there on my own, and I used to hear footsteps regularly going up and down the stairs and see movement in the cellar on these occasions but I used to talk to 'her' as I went about the shop in a very cheerful voice, telling her what I was doing, why I needed to pop upstairs etc. I think she got quite attached to me as the more I talked to her the more I felt she was following me around.
One particular night she seemed very active, lots of running up and down the stairs and bumps from upstairs floors. I heard her come into the shop, which she rarely did, and as I looked towards the door, there seemed to be a patch of air that was just a shimmery type of darkness in the air which seems to glide right up to where I was standing. I was in a part of the shop that was a 20th century addition. If I moved back into the 'old' part of the shop she would move away from me but if I went to the new part she only seemed able to be able to come as far as the wall and then moved around restlessly. I wondered if to her I was coming in and out of focus as I moved between the two sites.
I'm sure that energy and memory are linked in some way. I also think that it is naive and arrogant to say that we have discovered all there is to know about the world. A vast amount of our brains remains a mystery still.