— The Temporal Structure of Low-Energy Gamma Emission and the Physical Reality of Lattice Response

By Yian Lei

I. Introduction: The Hidden Temporal Reality Behind the “Instantaneous” Picture

The Mössbauer effect is usually described as a nuclear process in which a bound nucleus emits a low-energy γ-ray without recoil, because the entire crystal lattice absorbs the momentum.

In conventional quantum theory, this process is modeled as an instantaneous transition:

• The γ photon is emitted instantaneously during a nuclear “jump”;

• The lattice instantaneously absorbs the recoil momentum;

• The emitted photon is treated as a perfect energy eigenstate with zero time width.

But this idealization conceals the real physics.
Every energy-defined emission must take finite time,
and every momentum transfer requires a continuous field interaction.

II. The Natural Quantum Theory (NQT) Foundation

In Natural Quantum Theory,

• “Emission” is not a sudden quantum jump but a gradual redistribution of field energy;

• A photon is not a particle created at an instant, but a continuously forming electromagnetic wave packet;

• The energy–time relationship

  $$\Delta t\cdot \Delta E\gtrsim \hslash$$

  reflects a causal dynamical constraint, not a fundamental randomness.

Therefore, a γ photon with a very narrow linewidth must take a correspondingly long formation time.
The Mössbauer effect, which depends on ultra-narrow γ lines,
necessarily implies a finite emission duration.

III. Recoil and Lattice Response: From Instantaneous to Temporal Cooperation

The standard explanation claims that:

The lattice “instantaneously absorbs the recoil,” thus no kinetic energy is lost.

But this rests on two contradictory assumptions:

1. Emission is instantaneous (Δt → 0), yet the lattice reacts as a whole;

2. The photon energy is precisely defined (ΔE ≈ 0), yet it forms instantly.

Both cannot be true.

In the NQT framework:

• The γ field forms gradually during emission;

• The nucleus experiences a recoil force transmitted continuously via its electromagnetic coupling to neighboring atoms;

• If the lattice response time τₗ (set by sound propagation and elastic rearrangement) is shorter than the photon formation time τγ,
  the recoil is collectively absorbed by the lattice during the emission.

Thus, the Mössbauer condition emerges naturally:

Recoilless emission occurs not because recoil is absent, but because it is distributed in time and coherently shared by the surrounding lattice.

IV. The Natural Quantum Condition

Define:

• Photon formation time:

  τγ≈ℏΔE\tau_\gamma \approx \frac{\hbar}{\Delta E}τγ≈ΔEℏ

• Lattice response time:

  τL≈avs\tau_L \approx \frac{a}{v_s}τL≈vsa

  where a is the lattice spacing and vₛ the sound velocity.

The Mössbauer condition is simply:

τγ>τL.\tau_\gamma > \tau_L.τγ>τL.

When this inequality holds, the recoil is smoothly transferred to the lattice as the field builds up, avoiding local excitation.

This explains why only low-energy, narrow-linewidth γ rays can exhibit Mössbauer recoil-free emission —
and why the effect disappears at higher energies, where τγ becomes too short.

V. Critique of the “Instantaneous Transition” Assumption

In standard quantum theory, the emission process is written symbolically as:

∣ψi⟩→∣ψf⟩+γ,|\psi_i\rangle \to |\psi_f\rangle + \gamma,∣ψi⟩→∣ψf⟩+γ,

as if the photon appears at an instant.

This is a mathematical fiction.
It lacks any causal mechanism connecting the initial and final states.

In contrast, Natural Quantum Theory describes a continuous field evolution:

• Energy and momentum flow gradually through the electromagnetic field;

• The γ wave packet forms as part of this redistribution;

• The recoil momentum is transmitted progressively into the crystal through lattice coupling.

Hence, the Mössbauer effect is not a quantum miracle,
but a manifestation of time-extended energy–momentum exchange in a coherent medium.

VI. Implications for the Nature of Light

The Mössbauer effect demonstrates that:

1. Light emission is not instantaneous;

2. The photon cannot be an independently existing particle detached from its source;

3. The emission process inherently couples to its environment over finite time;

4. The concept of a “photon” must represent a localized excitation of a continuous field, not a pointlike particle event.

Therefore, the existence of recoil-free γ emission contradicts the particle-photon hypothesis.

It instead supports a field-based, continuous picture:

Light is a structured field excitation that forms over time,
and matter responds coherently to that process.

VII. Comparison of Interpretations

Aspect	Conventional QED Interpretation	Natural Quantum Theory Interpretation
Emission Duration	Instantaneous	Finite and causal
Recoil Absorption	Instantaneous lattice response	Time-distributed collective transfer
Recoilless Condition	Momentum sharing by crystal	Temporal coherence between emission and lattice response
Photon Nature	Discrete quantum particle	Continuous wave packet of the EM field
Energy Conservation	Statistical	Local and dynamical

This reinterpretation not only aligns with all known experimental results,
but also restores physical causality and spatial realism to the emission process.

It is noteworthy that the Mössbauer effect occurs only for low-energy gamma emission, while high-energy gamma decays exhibit no recoil-free resonance.
This fact serves as a crucial piece of evidence:
According to conventional quantum mechanics, if a nuclear transition emits a photon instantaneously,
the emission energy should not fundamentally affect the possibility of recoil-free absorption.
Any nucleus embedded in a lattice should, in principle, transfer recoil momentum to the lattice as a whole, regardless of gamma energy.

However, experiments show that only low-energy gamma rays (typically tens of keV) can be absorbed collectively by the lattice,
whereas high-energy gamma rays (hundreds of keV and above) do not exhibit any Mössbauer resonance at all.
This indicates that the emission of radiation is not an instantaneous quantum jump,
but rather a finite-time field process during which the surrounding lattice dynamically responds to the gradual buildup of electromagnetic energy.

At lower energies, the emission time is long enough for the lattice to reorganize and collectively absorb the recoil.
At higher energies, the process is too rapid for such coordination; the recoil is thus localized on a single nucleus.

In other words,
the upper energy limit of the Mössbauer effect reveals that
low-energy gamma radiation is not a particle-like instantaneous emission but a continuous field reconfiguration.
This observation strongly supports the Natural Quantum Theory perspective:
light (and radiation in general) is a continuous field phenomenon, not a discrete quantum event.

VIII. Conclusion: From “Recoil-Free Miracle” to Temporal Realism

The Mössbauer effect does not reveal a magical “recoil-free quantum jump.”
It reveals that nature never acts instantaneously.

Energy and momentum are transmitted continuously through space,
and the coherence between emission and lattice response ensures that recoil is not localized but shared.

The photon is not a pointlike particle escaping the atom,
but a slowly forming field pulse whose creation time exceeds the lattice’s ability to respond.

Thus, the Mössbauer effect stands as compelling evidence for the Natural Quantum Theory view:
that light and matter are continuous, interacting fields,
and that the apparent discreteness of quantum events arises from the spectral constraints of continuous processes, not from ontological discontinuity.

In short:
The Mössbauer effect is not proof of quantum mysticism—it is proof of temporal realism.
It shows that even at the quantum scale,
the universe remains causal, continuous, and beautifully intelligible.