It is not difficult for modern western scientific reductionists to understand the most coarse and obvious meaning of anatta: the lack of a permanent, unitary, and independent person.
In this culture, we are trained to look at the world from the default viewpoint of scientific reductionism. That people can be viewed as a composite of sub-atomic particles governed by the laws of chemistry and physics. We learn in elementary and middle school about caloric intake, cellular division (mitosis and meiosis), evolution, genetics and epigenetics which all make it trivial to ascertain that the person is thoroughly non-permanent, non-unitary, and dependent.
So if modern culture makes it so easy to arrive at the coarse meaning of anatta, then why aren't we all Arhats??
Because there is much more to realizing emptiness than just this very coarse and trivial understanding of anatta. For the wisdom realizing emptiness to have its soteriological effect the following must be true:
- It can not be trivial. If it were trivial, then it would not have any power whatsoever to cure our suffering or pull us out of this endless cyclic existence.
- It can not be mere word games or simply an intellectual philosophical exercise. If it were, then again it would not have any ability to end our suffering.
- It can not mean that nothing exists. If we come to the conclusion that nothing exists, then there can be no clearer guidepost saying “turn around!” as it is stated over and over in the Dharma that this is manifest evidence that the reasoning on emptiness has gone astray.
- Still, it must be something that can be inferred from reasoning. It is not a completely obscure phenomena.
Even a mere correct inferential understanding of emptiness or the object of negation should rock something deep inside of you. If it doesn't absolutely shake your deeply ingrained ignorance, then how could it ever have the power to uproot suffering?
Similarly, if you become convinced that some understanding of emptiness is leading you to believe that the world does not exist, or that karma does not exist, or rebirth does not exist, then you can be absolutely sure that there is some mistake in your understanding. The Virtuous Teachers warn again and again that the true meaning of emptiness does not equate to nihilism or the repudiation of the Four Noble Truths in any shape or form. In other words, keep looking.
So, looking to modern science - including psychology or neuroscience - to help arrive at coarse level of anatta is fine.
To arrive at the subtler levels will require more powerful tools. In terms of modern science, Relational QM is perhaps one of those tools. See an article by Carlo Rovelli here.
But looking towards modern science to provide even a glimpse of the subtlest meaning of anatta or emptiness is unfortunately (so far) futile. Which is evident by looking around to see how many modern scientists appear to be highly realized beings teaching the Dharma...