From a philosophical point of view Sartre created the idea of Nothingness as the antimony of Heidegger’s Process Being. For Heidegger in Being and Time Being was a monolith with two modalities present-at-hand (Pure Being) and ready-to-hand (Process Being). See Henry’s critique of Heidegger’s Ontological Monism in his book The Essence of Manifestation (one difficult book to read, but I got through it). Nothingness is more or less the same idea as the black hole, in as much as it is continually involuting into itself. Nothingness is the process of making absent, just as Process Being is the process of making present. Everyone more or less agreed that Sartre misunderstood Heidegger and more or less got it wrong, and so his popularity with scholars have waned. But personally I like the Sartre of the Critique of Dialectical Reason the best. He tries to rescue the dialectic by treating it dialectically, rather than the normal mechanistic treatment that was the norm under Communism. But treating the dialectic dialectically is merely the positive version of nothingness in many way. Sartre thought we could get at existence through the active negation of Being and putting that at the center of consciousness. Now that I understand Hegel a little better, I think Sartre needs to be reconsidered because I think he understood Hegel better than Heidegger did. We can see Being and Nothingness as an attempt to bring Hegel up to date, in light of Being and Time. Heidegger repudiated Sartre’s form of Existentialism. Heidegger’s form of Existentialism interprets the ecstasy of the projection of Being from Dasein as existence. Sartre’s form of Existentialism focuses on groundlessness and radical freedom. (See http://www.iep.utm.edu/sartre-ex/) Sartre uses Hegels’s terminology of the in-itself and for-itself to describe the modalities of consciousness and being as separate. The relation between the two is nothingness.
For Heidegger Being is “No Thing” which means the same as ontological difference between Being and the ontic beings, because Being itself is no specific thing, but a generalization of all things that stands independently from the things.
For Hegel being and nothing are equals at the root of the logical tree in the Science of Logic. Nothing is specifically identified with the Buddhist idea of emptiness (which is nondual) and thus existent. From being and nothing comes becoming which is Heraclitian becoming, and from that comes the determinate thing dasein.
For Sartre there are two realms, one of Being and the other of consciousness and they have a relation though active negation. Heidegger more or less assumes that consciousness is the same as Being but he avoids the term so prevalent in Husserl’s work and uses the term dasein instead and concentrates on the dynamic upwelling of Being through our being-in-the-world.
So none of these philosophers say that Nothingness is the root of Being. Nothingness is basically the antipode or dual inverse of Process Being of Heidegger. At least that is what Merleau-Ponty thought when he talked about Hyper Being as the hyper-dialectic between Being (in Heidegger’s Process sense) and Nothingness of Sartre.
Nothingness is active self-negating that produces groundlessness. But that groundlessness points to existence, but is not the same as existence, but rather another face of Being. Sartre assumes that Being and Consciousness are two different things and the difference that makes a difference between this is the radical active negation that keeps them apart, and produces groundlessness. It points toward the bedrock of existence but does not ever arrive there because it exemplifies the groundlessness of Being.
The root of Being is Existence as nondual, either empty or void. And how we get there is by traversing the meta-levels of Being because at the fifth meta-level of Being we run into existence at the heart of Being. But we don’t need Nothingness to get there. Rather nothingness is self-negation of the projection process of Being, while Heidegger’s Process Being is the active projection that produces the world. So from my point of view Sartre’s nothingness is just another way to look at Being as self-destroying. And that self-destroying is what keeps consciousness apart from the realm of beings.
The root of Being is Existence as nondual. In fact, Being itself has a core which is nondual, and these nonduals have a specific structure as determined in the Indo-european worldview as seen in myth, which is the series Order, Right, Good, Fate, Source, Root. Each of these concepts are designated as nondual in the Western worldview. Thus there are stages to the unfolding of the core of the Western worldview from its nondual root in the deeper nonduals of Manifestation and the Amanifest.
The key idea that Sartre put forward with Nothingness is the groundlessness of Being, which today is called Anti-foundationalism (http://en.wikipedia.org/wiki/Ant…). There have been doubts about the foundations of Being since Nietzsche. In a sense Nothingness is the anti-foundation of Being, and not its root. The lack of a foundation is why it is a groundless projection normally thought of as an illusion, or an illusory continuity (like we see when we watch a film). Existence is what is left when the anti-foundation annihilates with the search for a first philosophy that is perennial in our tradition, and which anti-foundationalism gives up on.