Why is there something rather than nothing?

Martin Heidegger claimed that this is the most important question in philosophy. Here I wish to focus on a special case of this question, namely: 'Why is there something physical rather than nothing physical?' The implicit assumption which underlies this question is that the existence of the physical universe is contingent. If one rejects this assumption, then one possible answer to the question is that the physical universe exists necessarily. Mathematical structures exist necessarily because mathematical existence is merely absence from contradiction, and modern theoretical physics represents the physical universe as a mathematical structure, hence the physical universe exists necessarily as a special case of mathematical existence.

Another implicit assumption which underlies the question is that something physical does indeed exist! This assumption was questioned some time ago by David Z. Albert, a one-time advocate of the many-worlds interpretation of quantum theory. Albert's argument pertains to the Fock space formalism of relativistic quantum field theory, which represents the vacuum state of a system as a non-zero vector in a subspace called the vacuum sector. This is crucial, because in non-relativistic quantum mechanics, the vacuum vector of a system is represented by the zero vector. The vacuum vector in Fock space can be expressed as a non-zero linear combination of orthogonal vectors belonging to subspaces outside the vacuum sector. (Intuitively, orthogonal vectors are at right-angles to each other). In contrast, the zero vector in non-relativistic quantum mechanics cannot be expressed as a non-zero linear combination of orthogonal vectors. An advocate of the many-worlds interpretation holds that each vector in an orthogonal linear combination represents a different branch of the universe. Hence Albert claims that whilst the global state of the universe can be the vacuum, something can physically exist in the different local branches of the universe:

"Observers such as ourselves cannot establish, by any practical means, that our experience is not merely a constituent, merely a branch, of that vacuum...What if the Creator, the Selector of Initial Conditions, had decided not to create; to create nothing, to create the vacuum? That vacuum would already have contained us and what we see around us. The option not to create some world like ours, given the physics [of] relativistic quantum field theory,...is not a logical possibility." (PSA 1988, Volume 2, p129).

It's an ingenious argument, although one which founders upon the assumption that the vacuum vector in quantum field theory represents a state of physical nothingness. For a start, quantum field theory pre-supposes the existence of a background space-time, and a space-time is something physically. Moreover, the vacuum of Fock space quantum field theory is the idealised vacuum of a free field, a field free from interactions with other systems. Notoriously, the vacuum of interacting quantum field theory is considered to be a seething torrent of evanescent particles, popping in and out of existence. Whilst there is, as yet, no well-defined theoretical structure to represent this interacting vacuum, the general belief in the existence of such an interacting vacuum poses a considerable problem for Albert's idea.

David Z.Albert Heidegger Nothing Something