The double slit experimentJust read the Wikipedia article which explains four possible explanations for this phenomena.
Here's my take on it.
The exact location of quantum particles such as electrons, photons atoms... is a probability distribution explained by Heisenbergs uncertainty principle - a bell curve.
Quantum tunneling is the phenomena where particles can appear on the other side of a barrier without having sufficient energy to do so.
It also demonstrates that the uncertainty principal isn't just an idea, it explains phenomena observable in nature.
By the conservation of mass-energy particles such as electrons and atoms aren't cancelling themselves out due to interference as this would release a lot of energy.
If electrons aren't canceling themselves out and their hitting the detector in bright and dark bands then their probability distribution function is being affected by the slits.
They either hit the slit mask where they are absorbed or reflected or travel through it.
Quantum tunneling even allows them to reach the other side of the slits by traveling some non-zero distance inside the slit mask that classical physics would prohibit.
Somewhere in this journey from one side of the slit mask to the other the probability distribution of the particles is affected making their final trajectory different to that of a particle traveling in a straight line without the double slit barrier.
If these particles have mass then it's at the quantum level.
If some thing's changing the direction of such a particle and it's not one of the other atomic forces then were left with one conclusion - quantum gravity.