You ask me to compare two ways of saying something:

• that there exists at T1 some set of facts S describing the state of the world (including my mind), and that E2a|b and E1a|b both depend on S

• that E2a|b exerts an acausal atemporal influence on E1a|b

What, you ask, does that second formulation buy us? My answer, of course, is that the second is more concise and it avoids mentioning either T1 or S (good, among other reasons, because there might be multiple times T1, T2, and T3, as well as state vectors S1, S2, and S3 at those times). The second formulation is even more economical if you leave off that extraneous word "atemporal".

What you pay for this economy is a prior climb up a pretty rugged learning curve. Is it worth it? It is hard to say at this point. However, I should point out the irony that I have cast myself in the role of a defender of all this "acausal" mumbo-jumbo; ironic because I usually play your role - a fierce skeptic of the local zeitgeist and defender of the old-fashioned, orthodox approach.