[Paper Review] Comment on 'Time-energy uncertainty relations for neutrino oscillations and the Mossbauer neutrino experiment'

Evgeny Akhmedov, Joachim Kopp+1 more|ArXiv.org|Mar 10, 2008

Neutrino Physics Research2 references3 citations

TL;DR

This paper challenges the claim that time-energy uncertainty relations forbid neutrino oscillations in Mössbauer neutrino experiments. By re-evaluating the quantum field theory framework and emphasizing spatial evolution over time-only approximations, the authors demonstrate that oscillations are fully consistent with quantum principles, resolving a contradiction with prior work that incorrectly assumed x ≈ t for long-wavepacket neutrinos.

ABSTRACT

We discuss the implications of the time-energy uncertainty relation to recoillessly emitted and captured neutrinos (Mossbauer neutrinos) and show that it does not preclude oscillations of these neutrinos, contrary to a recent claim (J. Phys. G35 (2008) 095003, arXiv:0803.0527).

Motivation & Objective

• To resolve a contradiction between the time-energy uncertainty principle and Mössbauer neutrino oscillations as claimed in a prior study.
• To demonstrate that the standard time-energy uncertainty relation remains valid for Mössbauer neutrinos despite their long coherence lengths.
• To show that the assumption x ≈ t, often used in conventional neutrino oscillation theory, is invalid for Mössbauer neutrinos due to their macroscopic wave packets.
• To establish that proper quantum field theory treatment—incorporating source and detector localization—restores physical consistency to oscillation probabilities.
• To refute the claim that Mössbauer neutrino experiments could test the applicability of the time-energy uncertainty relation, by proving it is already valid in this regime.

Proposed method

• Re-analyzes the Mandelstam-Tamm time-energy uncertainty relation in the context of Mössbauer neutrinos using the Heisenberg picture and flavor projection operators.
• Uses the survival probability $ P_{\nu_l \to \nu_l}(x,t) = |\langle \nu_l | \Psi(x,t) \rangle|^2 $ as the observable to derive the uncertainty relation in coordinate- and time-dependent form.
• Rejects the time-only integration approach of prior work by arguing that the coordinate-independent survival probability $ P(t) $ lacks physical meaning for Mössbauer neutrinos.
• Applies the full quantum field theory framework, explicitly including production and detection processes to ensure asymptotic states are mass eigenstates.
• Demonstrates that the coherence length $ L_{\text{coh}} \sim 1/\Delta E \Delta v_g $ leads to wave packet sizes $ \sigma_x \sim \sigma_t \sim 10 \text{ km} $, invalidating the x ≈ t assumption.
• Compares QFT results with QM predictions, confirming consistency in wave packet size and coherence length across frameworks.

Experimental results

Research questions

• RQ1 Does the time-energy uncertainty relation forbid neutrino oscillations in Mössbauer neutrino experiments?
• RQ2 Is the assumption x ≈ t valid for describing the evolution of Mössbauer neutrinos in space and time?
• RQ3 Why do prior claims conclude that Mössbauer neutrino oscillations violate the time-energy uncertainty relation?
• RQ4 How does the inclusion of source and detector localization affect the oscillation probability in quantum field theory?
• RQ5 What is the physical meaning and validity of the time-only survival probability $ P(t) $ used in previous analyses?

Key findings

• The time-energy uncertainty relation does not preclude oscillations of Mössbauer neutrinos; the prior claim is incorrect due to flawed application of the formalism.
• The assumption $ x \simeq t $, which equates spatial and temporal evolution, is invalid for Mössbauer neutrinos because their wave packets are much longer than the baseline (10 km vs. tens to hundreds of meters).
• The survival probability $ P_{\nu_l \to \nu_l}(x,t) $ must depend on both space and time; treating it as a function of time alone leads to unphysical results.
• Wave packet size $ \sigma_x \sim \sigma_t \sim 10 \text{ km} $ arises from $ \Delta E \lesssim 10^{-11} \text{ eV} $, confirming macroscopic coherence lengths in Mössbauer neutrinos.
• Proper quantum field theory treatment, including source and detector localization, ensures that oscillation probabilities exhibit correct spatial dependence and are consistent with the uncertainty principle.
• The authors' QFT calculation confirms that coherence and localization conditions are well satisfied in realistic Mössbauer neutrino experiments, validating the occurrence of oscillations.