Superluminal Transformations and Indeterminism

TL;DR

The paper investigates whether superluminal transformations (SpTs) can ground quantum-like indeterminism within a finite-information classical framework. It develops a no-go theorem under natural assumptions—non-order-preserving SpTs, finite information density, time-symmetric total information, past memory, and a defined arrow of time—showing that SpTs and finite information cannot coexist; any SpT-extended theory would require unbounded information content, yielding a deterministic classical ontology. By contrasting this with quantum indeterminism, the work argues that SpTs do not straightforwardly reproduce quantum randomness unless one abandons finite-information constraints, shifting the source of indeterminism to epistemic limitations. The findings clarify the limits of relativistic extensions as explanations for quantum indeterminism and highlight a tension between symmetry, information bounds, and the arrow of time, with implications for interpreting probabilities as either ontic or epistemic.

Abstract

Quantum theory is widely regarded as fundamentally indeterministic, yet classical frameworks can also exhibit indeterminism once infinite information is abandoned. At the same time, relativity is usually taken to forbid superluminal signalling, yet Lorentz symmetry formally admits superluminal transformations (SpTs). Dragan and Ekert have argued that SpTs entail indeterminism analogous to the quantum one. Here, we derive a no-go theorem from natural assumptions, which can be interpreted as: superluminal transformations (SpTs) and finite information cannot coexist. Any theory accommodating SpTs must therefore allow unbounded information content, leading to a deterministic ontology akin to that of classical theories formulated over the real numbers. Thus, any apparent indeterminism arising from superluminal transformations reflects only probabilities arising from subjective ignorance, unlike the objective nature of probabilities in quantum theory, indicating that the claimed indeterminacy from superluminal extensions is not quantum.

Figures (3)

• Figure 1: Past and Future of Information: The nodes represent events, the red edges connect events that have already actualised, while the blue edges represent potential causal connections, associated with a weight that represents the propensity for an event to actualise. The dotted edges going out of the information cones (which are bounded by the lightcone) of the multigraph are causal connections that either never actualise or do not actualise to observable interaction, hence, for our consideration, the propensity of such events is zero.
• Figure 2: Past in SpLT in green. The coordinate in purple denotes the reference frame of a subluminal observer, and the one in green represents a superluminal observer. We note that under superluminal transformation, the past and the future seem to have equal distribution of events and information, unlike subluminal reference frames.
• Figure 3: On the left we have the total information structure in pink with events $E_1$ to $E_7$ which undergo an SpT transformation (A0) on the right, where the lightcone is given in the direction of geometric time (A4).

Theorems & Definitions (2)

• Theorem
• proof