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REVIEW 4 major objections 6 minor 40 references

The paper proves that any theory with superluminal transformations must give up finite information, time-symmetric information, past memory, or time's special role.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-03 08:53 UTC pith:MN5EYBFT

load-bearing objection A genuinely new disjunctive no-go claim, but the proof has a load-bearing gap that needs real work before the theorem is established. the 4 major comments →

arxiv 2601.15263 v2 pith:MN5EYBFT submitted 2026-01-21 quant-ph gr-qcphysics.hist-ph

Superluminal Transformations and Indeterminism

Amrapali Sen , Flavio Del Santo This is my paper
classification quant-ph gr-qcphysics.hist-ph
keywords superluminal transformationsfinite informationindeterminismno-go theoremopen pastpropensitiestime symmetrycausal structure
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper aims to show that superluminal transformations — velocity boosts beyond the speed of light that reverse the temporal order of some events — cannot coexist with a set of otherwise natural assumptions about finite information, the time-symmetry of stored information, a past that remembers, and a distinguished role for time. If the theorem is right, any consistent theory containing such transformations is forced to abandon at least one of these pillars, and the authors' favored escape is to abandon finite information: a world with superluminal observers would then require infinite-precision, real-number physics, making any apparent randomness from such boosts a matter of ignorance rather than ontic chance. A sympathetic reader would care because this undercuts recent claims that superluminal transformations explain quantum indeterminism.

Core claim

The central claim is the theorem that the conjunction of assumptions A0–A4 cannot hold. A0 asserts the existence of a superluminal transformation that does not preserve temporal order; A1 asserts the total information in the universe is finite; A2 asserts stored information is roughly split equally between past and future in every inertial frame; A3 asserts the past records actualized events with extremal propensities while the future carries non-extremal rational propensities, making the future informationally richer; A4 asserts time keeps its causal role under any physical transformation. The proof shows that under A1–A3 the past must contain more events than the future to compensate for t

What carries the argument

The argument runs on an information-theoretic causal graph G(t) = (E(t), Ω(t), P(t)) whose information content I(G(t)) is measured by Kolmogorov complexity. The load-bearing asymmetry is A3: past propensities are extremal (0 or 1, one bit each) while future propensities range over rationals in [0,1], so the future's propensity information strictly exceeds the past's. To keep total informations equal (A2), the past must hold more events than the future. A superluminal transformation — specifically the antisymmetric Lorentz extension with v → ∞, which swaps the t and x coordinates in 1+1 dimensions — converts this required event-count imbalance into an equal count, breaking the balance. The pr

Load-bearing premise

The load-bearing premise is A2, the asserted approximate time-symmetry of total stored information about past and future in every inertial frame; the paper gives no derivation for it, and the proof also quietly assumes that event-count contributions are time-translation symmetric. If A2 (or that extra symmetry) fails, superluminal transformations and finite information can coexist without contradiction.

What would settle it

Construct an explicit finite-information causal model (e.g., a sparse event graph with rational-valued propensities) that includes a non-order-preserving superluminal boost and check whether the equality I'(E)_past = I'(E)_future actually holds for the transformed graph. If a graph can be found where the boost does not equalize past and future event counts (e.g., because the finite speed of the boost leaves the counts imbalanced), then the proof's central step fails and A0–A4 may be jointly satisfiable. Conversely, if one can prove the equality holds for all SpTs, the theorem is strengthened.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • Any theory with non-order-preserving superluminal transformations cannot simultaneously be finite-information, time-symmetric in stored information, and have a memory-like past; at least one of these pillars must fall.
  • If one keeps superluminal transformations, the natural cost is infinite information content, which restores classical determinism and makes superluminal randomness epistemic.
  • The claimed quantum-like indeterminism from superluminal boosts would not be ontic; the probabilities would reflect observer ignorance, not fundamental chance.
  • The theorem extends beyond SpTs to any non-order-preserving transformation of events, such as certain causal-loop scenarios.
  • Rejecting superluminal transformations outright (¬A0) keeps A1–A4 intact and is a free epistemic option.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The proof leans on an unstated assumption that event-count contributions are symmetric under time translation; without it, the inference from equal total information to equal event counts fails, so the theorem's force rests partly on this extra premise.
  • A2 is not derived from more basic principles; the paper itself notes that dropping it is consistent, so the theorem does not by itself rule out finite-information SpT theories with an asymmetric past/future split.
  • A testable extension would be to construct an explicit model with SpTs and finite information that violates A2 in a controlled way; if such a model is consistent and reproduces known physics, the theorem shows which assumption has to give, not that SpTs are impossible.
  • The argument could be translated to quantum reference frames in superposition: if such frames include superluminal components, the same informational tension might constrain quantum reference frame theories.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper aims to prove a theory-independent no-go theorem connecting superluminal transformations (SpTs) with finite information. The authors introduce an information-theoretic framework in which the state of the universe is a directed acyclic multigraph G(t) of events, causal connections, and propensities. They then list four assumptions: A0 (existence of non-order-preserving SpTs), A1 (finite information), A2 (time symmetry of total information), A3 (the past holds memory, so past propensities are extremal and cheaper to encode), and A4 (time has a special causal role). The main claim is that A0–A4 cannot all hold; in particular, any theory admitting SpTs must sacrifice at least one of these assumptions, and the authors' preferred reading is that SpTs require unbounded information, implying that SpT-related indeterminism is epistemic rather than quantum. The paper concludes by discussing what happens when each assumption is relaxed.

Significance. If the theorem were sound, it would connect two active research lines — finite-information classical indeterminism and superluminal extensions of relativity — and would offer a criterion for interpreting the indeterminism proposed by Dragan and Ekert. The paper engages with a genuinely interesting conceptual problem and surveys relevant literature. However, the central proof contains serious gaps: a key inequality is derived only under an unstated symmetry assumption, and the crucial equality in the superluminal frame is asserted from a diagram rather than proved. Moreover, the contradiction appears to be generated largely by the authors' own time-asymmetric assumptions (A2 and A3), so the no-go result, as stated, is not established. The paper's conceptual ambition is commendable, but the technical execution does not yet support the claimed theorem.

major comments (4)
  1. [Section V, step after Eq. (11)] The proof infers I(E(t))_past > I(E(t))_future from Eqs. (10) and (11) by adding 'Assuming that the contributions of events are symmetric under time translation.' This symmetry assumption is not part of A0–A4 and is not justified. Without it, the equality in (10) could be satisfied by different per-event complexities or by different constants C_P and C_F. The sentence about 'comparable C_P and C_F' does not fix this; the embedding-scheme dependence of Kolmogorov constants cannot be used to force an inequality that is not otherwise derived.
  2. [Section V, Eq. (12) and the following paragraph] The equality I(G)=I'(G) is stated without argument. If it is intended as frame-independence of total information, it is already part of A1, but it does not imply the needed claim that in the superluminal frame I'(E)_past = I'(E)_future. The text says this 'we see' from Fig. 3, but a non-order-preserving transformation does not, by itself, guarantee that the information content of past and future event sets becomes equal. This is a load-bearing assertion, not a derived result.
  3. [Section VI, ¬A2] The paper concedes that if A2 is dropped, SpTs can coexist with finite information (A1), memory (A3), and a meaningful arrow of time (A4). Since A2 is an unproven, highly nontrivial assumption about the universe's memory distribution, the strong conclusion that SpTs require infinite information does not follow from the no-go theorem. At most, the theorem shows a specific package of assumptions is internally inconsistent. The authors should not present ¬A2 as a mere alternative without acknowledging that it undermines the advertised implication.
  4. [General framing of A2 and A3] The contradiction seems to be driven by the assumptions themselves: A3 asserts the past is informationally poorer (extremal propensities, one bit) and the future richer; A2 asserts total past/future information equality. A transformation that swaps past and future then necessarily conflicts with A2. This raises a circularity concern: the no-go is built into the chosen informational asymmetry. To make the theorem nontrivial, the authors would need to justify A2 and A3 from more basic principles or show they are independently necessary; otherwise the result is largely a restatement of the assumptions.
minor comments (6)
  1. [Abstract] Typo: 'superluminal extensions isnotquantum' should read 'is not quantum'.
  2. [Section II and throughout] The notation for subscripts is inconsistent: 'past' and 'future' appear as words, as 'p', and as 'fut' (e.g., I(G(t))_past vs. I(G(t))_fut). Please standardize.
  3. [Section IV, equations after Eq. (7)] The additive constants C_P and C_F are said to 'depend on the embedding scheme' and later to be 'comparable' to obtain the desired inequality. This is problematic: the choice of embedding scheme should not be used as a free parameter to enforce a physical inequality. Please clarify the role of these constants.
  4. [Section V, A2] A2 states 'approximately symmetric' but Eq. (10) uses exact equality. Please make the logical relation precise or adjust the equation to reflect the intended approximation.
  5. [Section V and VI] Assumption A4 is very vague and is never used substantively in the proof. If it is not needed, it should be removed; if it is needed, its precise role should be spelled out.
  6. [General] Several sentences are grammatically awkward, e.g., 'we can always have at least one scenario with comparable C_P and C_F to get this relation because the constants are subject to the embedding scheme chosen by the observer.' Please revise for clarity.

Circularity Check

0 steps flagged

No significant circularity: the no-go theorem is a conditional inconsistency argument, not a prediction reduced to its own inputs.

full rationale

The paper's central result is a proof by contradiction from explicitly stated assumptions A0–A4; its conclusion is the negation of their conjunction, not an empirical prediction fitted from data. The key inequality I(P|E)_past < I(P|E)_future is written directly into assumption A3 as the definition of 'the past holds memory', and the subsequent contradiction is a logical consequence of combining that assumption with A0, A2, and A4. This is the normal structure of a no-go theorem, not a circular reduction: the theorem is exactly a demonstration that these assumptions are mutually inconsistent. The proof does contain an extra, unstated premise — 'Assuming that the contributions of events are symmetric under time translation' — and it asserts I'(E)_past = I'(E)_future from Fig. 3 rather than deriving it generally; these are logical-gap or correctness concerns, not circularity. Likewise, the paper's stronger interpretive claim that SpTs require infinite information is not forced by the derivation: Section VI explicitly discusses ¬A2 as a viable alternative preserving finite information, so preferring ¬A1 is an interpretive choice, not a conclusion entailed by the proof. Self-citations to the authors' prior propensity framework supply background and motivation, but the theorem's assumptions are stated in this paper and are not justified by a load-bearing self-citation or by a uniqueness theorem imported from the authors' own prior work. No fitted parameter is renamed as a prediction, and no known result is merely relabeled. Thus no circular step is exhibited.

Axiom & Free-Parameter Ledger

0 free parameters · 7 axioms · 3 invented entities

The central claim rests entirely on the authors' information-theoretic apparatus: the multigraph state G(t), rational propensities, and the four assumptions A0–A4. A2 and A3 are not derived from external physics; they are stipulated within the authors' framework and are what produces the contradiction. No empirical data, fitted parameters, or code are involved.

axioms (7)
  • domain assumption A0: Existence of non-order-preserving superluminal transformations (SpTs).
    Assumed to hold for the no-go; SpTs are a formal extension of the Lorentz group, not empirically established.
  • domain assumption A1: Principle of finite information: any finite spacetime region contains at most N<∞ bits; total information is finite and frame-independent.
    Adopted from the finite-information program; no independent evidence is given in this paper.
  • ad hoc to paper A2: Time symmetry of total information: I(G(t))_past ≈ I(G(t))_future in every inertial frame.
    Stipulated as 'expected' with no derivation; the paper's Section VI acknowledges that dropping A2 dissolves the contradiction.
  • domain assumption A3: The past holds memory: past propensities are extremal {0,1}, future propensities are rational, so I(P|E)_past < I(P|E)_future.
    Core of the authors' propensity framework; not an external constraint and not derivable from A0 or A1.
  • domain assumption A4: Time has a specific causal role in every reference frame; it is the parameter along which deterministic equations evolve and lightcones are defined.
    Interpretive assumption about time; Section VI discusses what happens if it is abandoned.
  • standard math Kolmogorov complexity chain rule: I(G)=I(E)+I(P|E)+C0.
    Standard information-theoretic identity used in Eqs. (7)-(9); assumed up to additive constants.
  • ad hoc to paper The state of a system is fully described by the multigraph G(t) of events, causal connections, and propensities.
    This representational postulate is required for the information accounting; it comes from the authors' prior work and is not independently justified.
invented entities (3)
  • Superluminal transformations/observers (SpTs) no independent evidence
    purpose: Formal extensions of Lorentz transformations with |v|>c that can reverse temporal order; the theorem's subject matter.
    No empirical evidence; purely mathematical extension of special relativity.
  • Propensities no independent evidence
    purpose: Rational weights attached to potential causal connections, encoding objective tendencies; they make the past/future information asymmetry A3 meaningful.
    Borrowed from the authors' prior framework; not observable independently and not required by the external SpT literature.
  • Creative time no independent evidence
    purpose: A temporal flow associated with actualisation of indeterminate events, distinct from geometric time; used to interpret A4 and the SpT paradoxes.
    Conceptual construct from prior work, not a measured quantity.

pith-pipeline@v1.3.0-alltime-deepseek · 11695 in / 16663 out tokens · 171595 ms · 2026-08-03T08:53:30.898735+00:00 · methodology

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Cite this review

Pith. "Pith review of Superluminal Transformations and Indeterminism." pith.science (2026). https://pith.science/paper/MN5EYBFT

@misc{pith2026260115263,
  author       = {Pith},
  title        = {Pith review of: Superluminal Transformations and Indeterminism},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MN5EYBFT}},
  note         = {Machine review of arXiv:2601.15263}
}
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read the original 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, although Lorentz symmetry formally admits superluminal transformations (SpTs). Dragan and Ekert have argued that SpTs entail a form of indeterminism analogous to that encountered in quantum theory. Here, we derive a theory-independent no-go theorem from a set of natural assumptions: any framework admitting non-order-preserving SpTs must either abandon finite information, relinquish time-symmetric informational content, deny that the past stores memory, or abandon the notion that time determines a preferred causal ordering. In particular, one possible implication is that any theory accommodating SpTs suggests an ontology with unbounded informational content, akin to deterministic classical theories formulated over the real numbers. Consequently, any ontic indeterminacy associated with superluminal transformations cannot originate from finite information.

Figures

Figures reproduced from arXiv: 2601.15263 by Amrapali Sen, Flavio Del Santo.

Figure 1
Figure 1. Figure 1: FIG. 1: Past and Future of Information: The nodes [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Past in SpLT in green. The coordinate in [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: On the left we have the total information [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

discussion (0)

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Reference graph

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