Right off, let me be clear that I am a journalist, not a philosopher or scientist, so the following discussion is that of an interested layman who makes no claims of special insight.
That said, I often hear in discussions with atheists and agnostics that Quantum Mechanics (QM) renders much of the conventional wisdom about the physical universe obsolete.
As an example, Kenneth Samples of Reasons To Believe, who is both a philosopher and theologian, considers the argument that QM specifically renders the Law of Non-Contradiction (LNC) old news.
Samples quotes Live Science’s definition of QM as the branch of physics concerned with the smallest things in the physical universe:
“It results in what may appear to be some very strange conclusions about the physical world. At the scale of atoms and electrons, many of the equations of classical mechanics, which describe how things move at everyday sizes and speeds, cease to be useful.
“In classical mechanics, objects exist in a specific place at a specific time. However, in quantum mechanics, objects instead exist in a haze of probability; they have a certain chance of being at point A, another chance of being at point B and so on.”
According to LNC, that which is A cannot also be Non-A. To illustrate, the claim of Christianity that Jesus is God Incarnate (A) and Islam’s claim that Jesus is not God Incarnate (Non-A) cannot both be true.
“the claim of Christianity that Jesus is God Incarnate (A) and Islam’s claim that Jesus is not God Incarnate (Non-A) cannot both be true.”
But if things at the atomic level simultaneously have multiple probabilities, then where does that leave LNC? “The challenge of QM in the context of the LNC is that light (a subatomic object) seems to be both a wave and a particle simultaneously, thus A and non-A,” Samples explains.
Samples offers what seems to this observer to be a reasonable explanation for why the LNC is not actually contradicted by QM, but I don’t want to give it away here.
But he also offers an observation on why the LNC and indeed the rest of the laws of logic are absolutely essential to any discussion of their relationship to QM:
“The fundamental problem with any denial of the LNC is that the laws of logic make rational thought possible. In this very case, both a scientist and a philosopher exchanged ideas under the assumption of existing laws of logic.
“Thus, philosophers need input from scientists just as scientists need input from philosophers. And Christians would do well to populate both critical disciplines.”
Go here for the first part of Samples’ three-part discussion of these issues. I will add the links to the remaining two as they appear on his blog.