Before Jung's scientific concept of synchronicity can be precisely defined, I will require a definition and a metaphysical model. The definition will make apparent the need for the first digression and the model will make apparent the need for both digressions.
I will define what is scientific as simply the recognition of some phenomenon along with the subsequent attempt to identify and define that phenomenon. This is a definition that was much more prevalent and widely accepted, more or less, at the beginning of the 20th century than it is today. The name that is sometimes given to what is considered to be scientific today, at least by those who wish to deride it, is Scientism. The label Scientism represents a science that has fully embraced rational reductionism in an attempt to firmly and conclusively establish the dogma of materialism or physicalism, which is the dogma that asserts that the physical world is the
fundamental ground of all reality.
Scientism was not foreign to the science that existed at the beginning of the 20th century it simply had not yet become the established dogma. Although I would go so far as to say that the dogma underlying Scientism is the natural evolution of the dogma that embraces and seeks to firmly and conclusively establish the dogma of the absolute existence of the metaphysical idea of some external objective, deterministic world. This dogma, which is to some extent related to what has been called "the clockwork universe", was quite prevalent and widely accepted, more or less, at the beginning of the 20th century.
It is within this context that the metaphysical model of a dual-aspect monism may be introduced, which is described in the book, The Pauli-Jung Conjecture - and its impact today, edited by Harald Atmanspacher and Christopher A. Fuchs. In essence, a dual-aspect monism proposes the existence or reality of an underlying monism, which may be characterized as the alchemical
Unus Mundas, and that monism gives rise to two distinctly different aspects of itself as mind and matter.
(The Pauli-Jung Conjecture contains the correspondence between Jung and
Wolfgang Pauli who, after being a student of the psychiatrist Jung, became a strong proponent of Jung's philosophy. Wolfgang Pauli was a famous physicist who, along with Heisenberg and Bohr, was a principal proponent of quantum physics in opposition to Einstein.)
With the definition of what is scientific along with the metaphysical model of a dual-aspect monism, the definition of Jung's concept of synchronicity immediately follows. In essence, synchronicity is when “some event” occurs in our inner or outer world that has a direct and
obvious correspondence with “some event” in the other world. Synchronicity then proposes that those events are
actually connected even though they are clearly not, and cannot be, physically connected via a casual relationship. Within the context of a dual-aspect monism, synchronicity may be characterized as asserting that all reality occurs at the level of the
Unus Mundas and those occurrences gain expression or manifestation in either one or both of its aspects. In other words, the inner and outer worlds are not actually distinct realities, but are merely distinct expressions or manifestations of
the one underlying reality.
The fundamental point that is the basis of the scientific definition of Jung's concept of synchronicity is that the definition merely identifies a specific type of phenomenon that is inherent to the reality that we live in and experience. No proof of this phenomenon can possibly exist; it can only be experienced. And it is only in this sense that Jung’s concept of synchronicity can be considered to be scientific.
In closing it should be mentioned that a dual-aspect monism should merely be taken to be some sort of thought experiment and not in any way taken to be an expression of how
reality (whatever
that is or no matter how
that is interpreted or defined)
actually is. In addition, I think Jung would agree and would possibly go even further by characterizing any relation between his concepts and a dual-aspect monism as simply some type of failed attempt to make his ideas correspond in some substantial way with the then burgeoning quantum theory. A dual-aspect monism is a useful metaphor that is employed to illustrate the concept, nothing more.
If you want to acquire more understanding of Jung's
model of reality I would advise directly reading Jung's works, specifically CW 8, The Structure and Dynamics of the Psyche, and CW 9 (I), The Archetypes and the Collective Unconscious. (Note that although I may be (legitimately) criticized for postulating an invalid objectification of the model, I will again note that the postulate is purposefully chosen to undermine the subjectification that is inherent to the common interpretation, which is also equally invalid. As a matter of fact, in the book, Projection and Re-Collection in Jungian Psychology, some type of direct relationship or correspondence is postulated to exist between Jung's collective unconscious and matter/objective reality, which may also be considered to be an invalid objectification by some.)
As an aside, when I said that Tarot, through
reflection, is capable of showing us what is beyond awareness, it appears that statement may have been interpreted to mean that Tarot
reflects what is "inside" us. That is unequivocally inaccurate. I consider the Hermetic axiom, "as above, so below" to be equivalent to and thus also, to some extent, to be synonymous with "as within, so without". I do not think that the objective/subjective dichotomy can be effectively or accurately employed to characterize or limit what Tarot can
actually reflect.
The reasons for my implicit derision of
the fundamental duality is of no relevance to the definition of Jung's concept of synchronicity and thus will not be addressed. I will only mention that it is based on the simple fact that I find the Western definitions of consciousness to be patently ridiculous, such as defining consciousness as our personal awareness, our sense of “I” (or ego or agency), as our qualitative experience, and so forth. The Eastern definitions are much more rationally and logically tenable as well as being much more intellectually coherent.