The philosophy of Advaita Vedanta is one of the few spiritual philosophies that conform to science. It is however contradicted by nor contradicts present scientific positions.
In Advaita Vedanta, the world is said to have two levels of reality, the level of the world that we see around us which has relative reality, and the level of Brahman or Oneness, which has absolute reality.
The world around us is said to be only relatively real. This does not mean that it does not exist or is unreal, but only that its level of reality is not perfect, it is an ambiguous reality. It has an indistinct reality, nothing that we examine in the world can be shown to have a definite reality. Whenever we analyze anything in the world down to its roots, we will find that it degenerates into an ambiguous reality. It is only when we reach the level of Brahman or Oneness that we will find a definite reality.
Brahman in Advaita is considered to be the absolute reality. It is not affected by time or space and hence is homogeneous, non-discrete and beyond this everyday world.
Now, coming to present science, we find that as far as the first part of the Advaita proposition, quantum physics defines the world in the same way. In quantum physics also, the ultimate reality of the world is said to be quantum particles. At present, the particles of the Standard Model, a table that defines about 50-60 subparticles like quarks, muons and bosons, are considered to be the fundamental particles that institute all of the world. Now, it is interesting that the reality of these quantum particles is described in very much the same terms that Advaita Vedanta used to describe the relative reality of the world. In quantum physics also, it is recognized that the reality of these quantum particles is not well defined, and they have an ambiguous, 'smudged' reality.
Again, it is well recognized in present science that the Standard Model is not complete, and there is a sub-structure below it. What exactly this is still not known, various theories like String theory, Technicolor theory, etc. are proposed. These propose entities which define, if possible, entities which are even more ambiguous in their reality! Thus both Advaita Vedanta and modern quantum physics assert that the world has an ambiguous reality.
However, here the similarity between present science and Advaitism ends. Quantum Physicspite proposing particles with ambiguous reality at the base, does not go on to propose anything which has absolute reality and says it is this ambiguous reality which holds at the base.
Advaita Vedanta would not say that present quantum physics is wrong. Instead what it says is that it is incomplete. It is the assertion of Advaita Vedanta that regardless of the Standard Model nor other theories like String theory that propose discrete, 'atomic' particles will be the final answer and they will be found to be incomplete with further sub structures beyond them. Advaita Vedanta asserts that when the final root is discovered of this world, it will be an entity which is homogeneous, continuous and not discrete, and which is independent of time and space, in other words, Brahman.
Here Advaita Vedanta does not contradict science at all, in fact present quantum physics is a vindication of its assertion that the world is only relatively real. But it encompasses quantum physics and goes beyond it and says there is a further truth beyond its presentories, and that is an absolute entity.
The greatness of this theory is that not only does it not contradict science but science also does not contradict it. It is well recognized in quantum physics that the present Standard Model is not sufficient since there are too many loose ends in it and it is widely accepted that there is a further sub structure below it. The alternatives like String Theory which are proposed as this sub structure have already developed problems even before they are fully accepted. Here quantum physics would not say that the Absolute of Advaita Vedanta is false, at best it would say that this absolute has not been delivered as yet. But since the journey of quantum physics is not complete and there is a long way to go, quantum physicists would still consider proving or disproving the Advaita Vedanta theory to be far into the future. Of course, if the Standard Model had been completely proved, or its substructure, the String Theory is completely provided sometimes in the future, then we would say that Advaita is opposed by science. But at present at least, this does not seem likely at all and String Theory in its turn is likely to be as incomplete as the present Standard Model.
Here Advaita Vedanta is in harmony with science and believers in Advaita Vedanta can still persist in a scientific outlook even as they follow the path of spirituality of Brahman or Oneness.