God may or may not be true, but I do believe in Karma, and I do believe in, for a lack of better word 'Ghost', as I do with ESP.
Why? They do have scientific backing.
Our brains emit radio waves. Ever thought or mental process causes a sort of energy radiation from our brains, which can be measured, and are constantly vary (How and why they vary we don't know).
Now, at the same time, it's been proven that our brains are receptive to radio waves and energy from outside of us.
The theory is, experiences like ESP, mind reading, fore-telling the future in dreams, and deja-vu is due to our brain receiving radio waves from our surroundings, and our sub-concious processing them.
Also, by scientific research, it has been shown that energy can, in a sense, 'pass through time'. There was this complicated physics theory I read about in a book by Hawking - I borrowed it from a friend, so I can't exactly quote it now, but am going off what I remember. The essence was that a quark or something has an identical 'twin' of sorts. Each sub-atomic particle has an identical pair particle that rotates and acts in the opposite direction to it, such that if you rotate said particle in one direction, it's pair gets automatically rotated in the other direction at the same instant.
Maths managed to prove that this is real, however, practically, it was difficult to prove. They did, I think, manage to prove this, but realised that the math means that this can apply to two pair particles that are like a million lightyears away from each other. But how does that work, considering that energy will have to be transferred from one to another in order to cause the other particle to rotate?
Enter a theory about energy being able to travel, in a sense, through time.
Add this to the 'Infinite dimensions' theory which states that there are tiny, sub-atomic size portals to different dimensions opening and closing all the time in our surroundings, and for all we know 'Ghosts' and 'ESP' and all that could just be some very, very complicated science involving energy transfer, radiation, and time travel.
After all, Mirages and those lights in the sky seemed so strange until they were revealed to be some complicated scientific phenomenon, maybe deja-vu and ghosts are similar but just far more complicated?