Covariant quantum field theory of tachyons is unphysical (2406.14225v5)

Abstract: Tachyons have fascinated generations of physicists due to their peculiar behavior, but they did not solve any real physical problem. This may have changed with the recent works of Dragan et al., who have shown that superluminal observers may be related to the foundations of quantum mechanics (QM) because they require introducing non-determinism and wave-like behavior at the fundamental level. Unfortunately, we show that the tachyon quantum field theory proposed as a part of this program is not quantum since the tachyon field commutes at all points and the canonical commutations relations of a quantum scalar field are not satisfied. We also discuss other authors' theories, e.g., we show that the Dhar-Sudarshan's formula for the Feynman propagator violates unitarity, and we apply the LSZ formalism to tachyons for the first time, where we find that one cannot prove the LSZ asymptotic condition just by replacing plane waves with wavepackets.

• The paper demonstrates that existing covariant quantum field theories for tachyons are unphysical, failing fundamental quantum criteria like canonical commutation relations.
• The analysis shows that tachyon propagators lead to theories violating unitarity and conservation laws, rendering them unphysical under current QFT frameworks.
• The study argues that the standard LSZ formalism cannot be applied to tachyons, preventing the construction of a valid interaction framework for their covariant QFT.

Examination of "Covariant quantum field theory of tachyons is unphysical"

The paper under discussion provides a critical exploration of the covariant quantum field theory (QFT) of tachyons, challenging its validity within the framework of established physical theories. Tachyons, characterized as hypothetical particles that travel faster than light, have long intrigued physicists due to their unusual properties, including negative mass squared, potential causality paradoxes, and non-deterministic attributes. The authors address the arguments presented by Dragan et al. regarding the role of tachyons in quantum mechanics (QM) and explore the feasibility of constructing a coherent, covariant QFT for these particles.

Covariant Quantum Field Theory of Tachyons

The primary assertion in this paper is the inadequacy of existing tachyon QFTs to satisfy fundamental quantum criteria. The analysis begins with a critical look at the commutation relations in the twin space, arguing that the framework proposed by Dragan et al. fails to meet the canonical commutation relations required for fields to be truly quantum in nature. The paper underscores that the proposed tachyon field theory is not quantum because the field commutes at all points, disallowing the necessary quantum dynamics.

Problematic Propagators

The paper further challenges the legitimacy of the Feynman propagator adapted for tachyons by referring to the works of Dhar-Sudarshan. It is revealed that the methodologies relying on the inclusion of both subluminal and superluminal states to maintain Lorentz invariance (LI) result in an unphysical theory that breaches unitarity. Specifically, the critique highlights that allowing virtual tachyons to act within interactions results in observable predictions that contravene the conservation laws intrinsic to unitary theories.

Incompatibility with LSZ Formalism

An important aspect of the analysis involves the Lee-Schwinger-Zimmermann (LSZ) formalism, a crucial component for constructing scattering matrices in QFT. This paper claims that the LSZ formalism, as framed for subluminal quantum fields, cannot be straightforwardly adapted to tachyons. By demonstrating that the LSZ asymptotic conditions cannot be met simply by the inclusion of wave packets transformed from plane waves, the authors contend that the postulation of tachyonic QFT is blocked from establishing a reliable interaction framework.

Implications and Speculation

These findings prompt reflection on the speculative pursuit of uncovering superluminal influences within quantum mechanics. While the introduction of nondeterministic physics by Dragan et al. remains an intellectually stimulating proposal, the present analysis casts doubt on its viability through rigorous mathematical examination. Theoretical aspirations to reconcile superluminal observers with quantum theory could necessitate reformulating notions of space-time similarly to challenges encountered with general relativity, or perhaps exploring alternative theoretical constructs beyond those considered.

Conclusion

In summary, this paper scrutinizes the notion of a covariant QFT for tachyons and raises substantial doubts regarding its physicality under current theoretical structures. It posits that aspirations to treat tachyons as legitimate quantum fields encounter insurmountable barriers within Minkowski space, given present-day understandings of unitarity and quantum field dynamics. Thus, the paper contributes to the discourse on hypothetical supraluminal phenomena, urging continued critical assessment and innovation within theoretical physics.