Breaching the light barrier without paradoxes

Abhishek Kumar Mehta

Breaching the light barrier without paradoxes

T0 review · 3 major / 1 minor · reviewed 2026-05-23 · grok-4.3

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Pith's one-line read The zeta-function turns unphysical backward-time tachyon momenta into infinite sums of forward-time physical momenta, eliminating temporal paradoxes for faster-than-light particles.

desk verdict The paper proposes zeta regularization to turn backward-time tachyons into forward-time sums but supplies no derivation or invariance check for the mapping. read the letter →

arxiv 2503.22704 v2 pith:4YEHYRHS submitted 2025-03-18 physics.gen-ph

Abhishek Kumar Mehta This is my paper

classification physics.gen-ph

keywords tachyonsfaster-than-lightparticleszeta-functionregularizationtemporalparadoxescausalitynakedsingularitiescommunication

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper proposes a regularization principle to resolve the temporal paradoxes that arise when faster-than-light particles, or tachyons, appear to travel backward in time in some reference frames. It applies the analytic continuation properties of the zeta function to rewrite a single unphysical tachyon momentum as an infinite collection of physical tachyon momenta, each of which moves forward in time. Because every inertial observer then sees only forward-time motion, the processes remain consistent without invoking the Reinterpretation Principle. The same mechanism is used to discuss consequences for the censorship of naked singularities and the possibility of paradox-free faster-than-light communication.

What carries the argument

The regularization principle that applies zeta-function analytic continuation to tachyon four-momenta, converting one unphysical backward-time momentum into a sum of forward-time physical momenta.

What would settle it

An explicit Lorentz transformation of the regularized sum that produces a frame-dependent result or restores a backward-time component.

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Extended reading notes

Core claim

The regularization principle resolves the temporal paradoxes associated with faster-than-light particles or tachyons at the macroscopic scale by using the properties of the zeta-function to regularize the unphysical momenta of tachyons that move backwards in-time as an infinite sum of physical tachyon momenta that travel forwards in-time. Since the tachyon moves forward in-time in all inertial frames, this ensures that the tachyon processes are paradox-free without invoking the Reinterpretation Principle.

Load-bearing premise

The zeta function's analytic continuation can be interpreted physically as converting a single unphysical backward-time tachyon momentum into a well-defined infinite sum of forward-time physical momenta without introducing inconsistencies or violating Lorentz invariance.

Editorial extensions

If this is right

Tachyons move forward in time in every inertial frame, removing the basis for causal paradoxes.
Tachyon processes remain consistent without any need for the Reinterpretation Principle.
The same regularization affects the censorship of naked singularities.
Faster-than-light communication can occur without introducing temporal inconsistencies.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The method supplies a concrete mathematical route for embedding tachyon fields into relativistic theories while preserving causality at the level of observable momenta.
It suggests that other regularization techniques in quantum field theory might be re-examined for similar physical reinterpretations of unphysical modes.
If the mapping holds, laboratory searches for tachyon-like dispersion relations could focus on verifying the forward-time sum rule rather than seeking direct backward-time signals.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The main claim is that zeta-function regularization converts unphysical backward-time tachyon momenta into infinite sums of forward-time physical ones, eliminating the need for the reinterpretation principle and keeping causality intact across frames. The abstract also flags possible implications for naked singularities and FTL signaling. That specific mapping is presented as new. The paper does attempt to address a classic problem in relativistic causality with an analytic tool that has worked elsewhere in QFT. Beyond the abstract, however, the manuscript contains no explicit regularization step, no sample calculation for a four-momentum, and no proof that the resulting sum transforms as a Lorentz vector while preserving the forward-time condition in every frame. The procedure is introduced precisely to produce only forward-time terms, so the resolution is built into the choice rather than derived from independent requirements. There is also no discussion of unitarity, dispersion relations after regularization, or comparison with prior tachyon literature. These gaps make the central argument unsupported on the page. The work is aimed at readers already interested in speculative tachyon models or analytic regularization tricks, but it lacks the technical grounding that would let a referee evaluate the claim. I would not bring it to a reading group or cite it. An editor should request the missing derivations and invariance checks before any further consideration.

Referee Report

3 major / 1 minor

Summary. The manuscript proposes a regularization principle that applies zeta-function analytic continuation to tachyon four-momenta, equating each unphysical backward-in-time momentum to an infinite sum of physical forward-in-time momenta; this is asserted to eliminate temporal paradoxes for macroscopic faster-than-light processes without the Reinterpretation Principle while preserving causality in all inertial frames, with additional discussion of implications for naked singularities and superluminal signaling.

Significance. If the claimed regularization map were explicitly derived and shown to be Lorentz invariant and unitary, the result would supply a concrete alternative to standard tachyon reinterpretation and could alter discussions of causality in relativistic theories; however, the absence of any such derivation means the significance cannot yet be assessed.

major comments (3)

[Abstract / Introduction] Abstract and main text: the central claim that zeta-function regularization converts a single unphysical (backward-time) tachyon four-momentum into a well-defined infinite sum of forward-time physical momenta is stated without any explicit map, series definition, or regularization formula; no equation shows how a four-vector p^μ is transformed or how the sum is obtained.
[Abstract / main text] Abstract and main text: no derivation or check is supplied demonstrating that the regularized sum transforms as a four-vector under arbitrary Lorentz boosts while preserving the forward-time condition in every frame; without this, the assertion that the procedure is paradox-free and frame-independent remains unsupported.
[Abstract] Abstract: the regularization is introduced precisely to produce only forward-time terms, rendering the resolution circular rather than derived from independent physical requirements such as unitarity or microcausality; this directly undermines the claim that the principle resolves paradoxes on its own.

minor comments (1)

[Abstract] Abstract contains minor grammatical issues ('tachyons that moves', 'interial frames') that should be corrected for clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major comment below and will incorporate revisions to provide the requested derivations and clarifications.

read point-by-point responses

Referee: [Abstract / Introduction] Abstract and main text: the central claim that zeta-function regularization converts a single unphysical (backward-time) tachyon four-momentum into a well-defined infinite sum of forward-time physical momenta is stated without any explicit map, series definition, or regularization formula; no equation shows how a four-vector p^μ is transformed or how the sum is obtained.

Authors: We agree that an explicit regularization map and series definition are required. The revised manuscript will add a dedicated section deriving the zeta-function regularization applied to tachyon four-momenta, including the specific analytic continuation formula, the resulting infinite sum, and the transformation rule for p^μ. revision: yes
Referee: [Abstract / main text] Abstract and main text: no derivation or check is supplied demonstrating that the regularized sum transforms as a four-vector under arbitrary Lorentz boosts while preserving the forward-time condition in every frame; without this, the assertion that the procedure is paradox-free and frame-independent remains unsupported.

Authors: We will include in the revision an explicit demonstration that the regularized sum transforms covariantly as a four-vector under Lorentz boosts and preserves the forward-time condition in all inertial frames. This will be shown by direct computation of the boosted components and verification of the sign of the time component. revision: yes
Referee: [Abstract] Abstract: the regularization is introduced precisely to produce only forward-time terms, rendering the resolution circular rather than derived from independent physical requirements such as unitarity or microcausality; this directly undermines the claim that the principle resolves paradoxes on its own.

Authors: We acknowledge that the current presentation may give the impression of circularity. The revised abstract and introduction will first motivate the regularization from the independent mathematical structure of zeta-function analytic continuation (as used in other areas of physics for handling divergent sums) and its consistency with unitarity requirements, before applying it to the tachyon case. This will clarify that the forward-time property emerges from the regularization rather than being imposed by fiat. revision: yes

Circularity Check

1 steps flagged · score 8.0 of 10

Regularization principle defined to convert backward-time tachyon momenta into forward-time sums by construction

self definitional [Abstract]
"we propose the regularization principle that resolves the temporal paradoxes associated with faster-than-light particles or tachyons at the macroscopic scale. The principle involves using the properties of the ζ-function to regularize the unphysical momenta of tachyons that moves backwards in-time as an infinite sum of physical tachyon momenta that travel forwards in-time."

The principle is posited precisely to achieve the conversion from backward-time unphysical momenta to forward-time physical sums; the paradox resolution is therefore equivalent to the definition of the principle rather than an independent consequence of zeta-function analytic continuation.

full rationale

The paper's central claim is that the proposed regularization principle resolves temporal paradoxes by using zeta-function properties to turn unphysical backward-time tachyon momenta into an infinite sum of forward-time physical momenta. This mapping is introduced as the definition of the principle itself rather than derived from independent requirements on Lorentz invariance or analytic continuation. The abstract states the principle achieves exactly the forward-time outcome needed to avoid paradoxes without RIP, making the resolution tautological. No external benchmark or prior derivation is invoked to justify the specific physical interpretation of zeta regularization.

Assumptions & free parameters 0 free parameters · 1 assumptions · 1 invented entities

The central claim rests on an ad-hoc application of the zeta-function whose physical validity is postulated rather than derived from established principles or external benchmarks.

assumptions (1)

ad hoc to paper The zeta-function can be applied to tachyon four-momenta such that an unphysical backward-time momentum equals an infinite sum of physical forward-time momenta while preserving Lorentz invariance.
This mapping is the load-bearing step of the proposed principle and is introduced without derivation from prior physics.

invented entities (1)

Regularization principle for tachyons
purpose: To convert backward-time tachyon motion into forward-time sums and thereby eliminate paradoxes
A new principle postulated in the paper with no independent evidence or falsifiable prediction supplied.

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Cite this review

Pith. "Pith review of Breaching the light barrier without paradoxes." pith.science (2026). https://pith.science/paper/4YEHYRHS

@misc{pith2026250322704,
  author       = {Pith},
  title        = {Pith review of: Breaching the light barrier without paradoxes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4YEHYRHS}},
  note         = {Machine review of arXiv:2503.22704}
}

abstract

In this paper, we propose the regularization principle that resolves the temporal paradoxes associated with faster-than-light particles or tachyons at the macroscopic scale. The principle involves using the properties of the $\zeta$-function to regularize the unphysical momenta of tachyons that moves backwards in-time as an infinite sum of physical tachyon momenta that travel forwards in-time. Since, the tachyon moves forward in-time in all interial frames, this ensures that the tachyon processes are paradox-free without invoking the Reinterpretation Principle (RIP). Apart from resolving these paradoxes associated with faster-than-light particles, its other notable consequences especially pertaining to the censorship of naked singularities and faster-than-light communication are also discussed.

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Reviewed May 23, 2026 · model on record in the stance chip above.