Spacetime as a causal set: Universe as a growing block?

Spooky Action at a Temporal Distance

“…Furthermore, to ensure that the growth process satisfies general covariance, it is necessary to impose the requirement of discrete general covariance on the dyamics, meaning that the probability of reaching a particular final causet is independent of the path taken to reach that final causet—i.e., the probability does not depend on the order in which the elemets of the causet were “birthed”. It is standard to interpret this by saying that there is no fact of the matter about which path was taken—the choice of path is pure gauge [ 61 ]—but this makes it implausible to regard the growth of the causal set as a real physical process, since probabilities are ultimately attached to the causal sets themselves rather than to the transitions that occur during the supposed growth [ 65 , 66 ]. Wütrick and Callender argue that these considerations simply show that modern physics requires us to adopt a ‘novel and exotic’ notion of becoming in which we are generally prohibited from saying which elements of the causal set exist at any stage of its growth [ 66 ].…”

What Becomes of a Causal Set?

“…The claim is routinely made in the pertinent physics literature, and has even found its way into popular science magazines. 1 One might not believe that our intuitive notion of time needs or deserves rescuing, but there is no denying that if this claim is correct it would have significant consequences for the philosophy of time. Specifically, it may underwrite a 'growing block' model of the metaphysics of time, as John Earman (2008) has speculated.…”

“…This is his first interpretive option (page 16); the second augments the kinematical causal structure with a gauge-invariant dynamics, to be discussed below.16 That local, asynchronous becoming is closely analogous to worldline or lightcone becoming is also noted byArageorgis (2016).17Huggett (2014) argues that unless the background 'time' relative to which events are born can somehow be shown to be physical, i.e., not mere gauge, the dynamics is fully analogous to what we find in GR and so not hospitable to a substantive notion of passage. Showing background time to be physical…”