How the meaning of time changes across scales
Time is often treated as a single, universal quantity—but in reality, its meaning depends on scale.
At ultrafast scales, time appears as a phase difference that can be measured with extraordinary precision.
At intermediate scales, such as nanoseconds, time shifts become difficult to detect because signals overlap and
standard tools lose sensitivity. At biological scales, time is no longer a simple delay at all—
it emerges through changes in system state, such as activation, depletion, or recovery.
Figure 1 provides a conceptual map of how temporal information is encoded differently across scales,
forming the foundation of the Noir time hierarchy and guiding how we should interpret timing in physical and biological systems.
attoNoir (aN°) — When time becomes phase
Time scale: 10⁻¹⁸ seconds (attoseconds)
At the attoNoir level, time can no longer be observed as a simple shift along a timeline.
Instead, ultrafast dynamics are encoded in the phase of oscillating signals.
The figure above shows a zoomed-in RABBITT-like measurement.
Two signals differ by only 1 attosecond, yet their time-domain profiles almost perfectly overlap.
What distinguishes them is a systematic phase shift of the oscillation.
What does this mean?
At attosecond scales, classical time delays are too small to be seen directly.
Instead, timing information is recovered from the relative phase of the signal.
This phase shift can be translated into an attosecond delay, even when no visible time displacement exists.
Why is this important?
Electron motion and energy redistribution occur on attosecond timescales.
These processes define the initial conditions for all later chemical and biological reactions.
In this sense:
At the attoNoir level, systems do not respond yet —
they set the rules for how they will respond later.
Key takeaway
At the smallest time scales, time is not measured directly —
it is inferred from phase.
femtoNoir (fN°) — When phase becomes time
Time scale: 10⁻¹⁵ seconds (femtoseconds)
At the femtoNoir level, time begins to take a recognizable form.
Ultrafast signals now consist of a rapidly oscillating carrier embedded in a slower envelope.
A delay of 1 femtosecond does not simply shift the signal in time.
Instead, it appears as a relative shift of the carrier phase within the envelope.
What changes compared to attoseconds?
At attosecond scales, time exists only as phase.
At femtosecond scales, this phase becomes anchored to a temporal structure.
The system still behaves quantum-mechanically, but the concept of “before” and “after” starts to emerge.
Why is this important?
Femtosecond dynamics govern:
bond formation and breaking,
energy transfer within molecules,
and the earliest steps of biochemical reactions.
In this sense:
FemtoNoir is the bridge between quantum coherence and biological time.
Key takeaway
At femtosecond scales, time becomes visible —
but only through the internal structure of the signal.
picoNoir (10⁻¹² s): the reference
unit of the Noir time system
At the pico-second scale, physical time delays are already present in the system,
but they no longer appear as clean, directly measurable shifts along the time axis.
In the figure above, two signals are shown: a reference waveform and a second waveform that is
physically delayed by a small amount (hundreds of femtoseconds). Despite this real delay, the two
signals remain highly overlapping in the time domain. Their oscillatory structure and noise level
make it impossible to identify a single, unambiguous time offset by direct comparison or correlation.
This regime plays a special role in the Noir framework.
The picoNoir scale defines the base unit of Noir time.
It represents the smallest temporal unit at which time is still physically meaningful,
yet no longer directly observable as a unique shift in a signal.
At this boundary:
Time delays exist, but become correlation-limited.
Phase-based extraction methods begin to lose uniqueness.
The signal no longer carries sufficient independent temporal
information to support a single, well-defined delay estimate.
This makes picoNoir a reference unit rather than a measurement target.
In other words, picoNoir is not the scale at which time is most precisely measured; it is the
scale at which the concept of measurable time transitions into system behavior.
This distinction is fundamental to the Noir hierarchy:
Atto- and femto-Noir: time can be accessed through phase-sensitive observables.
picoNoir (Noir base unit): time exists, but cannot be uniquely read out.
Nano-Noir and beyond: time must be inferred indirectly, through dynamics, state transitions, and system-level responses.
By defining picoNoir as the reference unit, the Noir system anchors all higher temporal scales to
a physically meaningful boundary—one that separates time as a measurable quantity from time as an emergent property.
This transition naturally motivates the next level, nanoNoir, where temporal information
is no longer encoded as shifts, but as changes in dynamical state.
nanoNoir (10⁻⁹ s) – When time is no longer
a shift, but a divergence
At the nanoNoir scale, classical time-shift concepts begin to lose their meaning.
Even though two biochemical signals may start at the same time, their subsequent
evolution can differ profoundly due to altered molecular dynamics.
Panel A shows extracellular ATP dynamics measured at nanosecond resolution
for a control system and for a system with inhibited ecto-ATPase activity.
Both signals initiate simultaneously—there is no detectable delay or classical Δt between them.
However, as time progresses, their trajectories diverge: the inhibited system exhibits a slower decay
and a modified rebound profile. This difference cannot be captured as a simple time shift.
To make this divergence explicit, Panel B visualizes the dynamic difference between the two signals over time.
Instead of asking “how much is the signal shifted?”, this representation answers a different question:
When does the system begin to behave differently?
The dashed vertical line marks the onset of dynamic divergence, where the inhibitor-induced modification
becomes measurable. From this point onward, time is encoded not as alignment
between curves, but as a persistent state-dependent separation.
At the nanoNoir level, time is no longer read from synchronization,
but from how system states diverge over time.
This transition marks a conceptual boundary between reference-based time (picoNoir)
and dynamics-based time encoding, preparing the ground for higher biological timescales
where memory, feedback, and state-dependent behavior dominate.
microNoir (10⁻⁶ s) – When time emerges as recovery,
memory, and state-dependent dynamics
At the microNoir scale (10⁻⁶ seconds), divergence-based temporal encoding becomes biologically accessible.
Here, molecular-scale differences have propagated far enough to reshape system-level behavior,
allowing temporal effects to be observed through recovery dynamics rather than direct delays.
In extracellular ATP signaling, inhibition of ecto-ATPase activity does not introduce a rigid time shift
of the ATP trace. Instead, it modifies the entire response trajectory, including:
the depth of ATP depletion,
the timing of the rebound minimum,
and the rate of return toward baseline.
These features define a state-dependent temporal signature.
Time at the microNoir level is no longer a point on an axis, but a property of the recovery process itself.
The system effectively integrates earlier nano-scale divergences into macroscopic behavior,
transforming imperceptible timing differences into measurable changes in rebound shape, duration, and stability.
As a result, microNoir captures time not as delay, but as functional memory encoded in system dynamics.
milliNoir (10⁻³ s) – When time becomes a decision
At the millisecond scale, biological systems no longer represent perturbations as precise temporal shifts.
Instead, they integrate dynamic signals over extended time windows and convert them into discrete outcome decisions.
Extracellular ATP dynamics at this scale reveal that control and ecto-ATPase–inhibited systems may
respond similarly at early times, yet diverge markedly during recovery. These differences cannot be attributed
to a simple delay between signals. Rather, the entire response trajectory is reshaped,
reflecting how the system accumulates and processes information over time.
To capture this integration explicitly, the response is summarized using an integrated decision metric
—the normalized ATP rebound area. This metric reveals a clear, dose-dependent bias: increasing
perturbation strength progressively shifts the system toward a different outcome state,
even though no well-defined time shift can be assigned to individual events.
At the milliNoir level, time is no longer the primary observable variable.
What becomes measurable instead is the decision the system makes after integrating its internal dynamics.
Millisecond-scale behavior thus reflects not when something happens, but which state the system ultimately selects.
Why This Matters
Time is one of the most fundamental quantities in science—yet it is often treated as a single, universal variable.
The Noir framework challenges this assumption. What emerges is not a loss of time, but a change in how time can be meaningfully represented and measured.
At ultrafast scales, time exists as phase and coherence. At intermediate scales, classical time shifts dissolve into ambiguity. At biological scales, time reappears as memory, recovery, and decision-making.
Time-shift failure in biology
Below certain scales, time is no longer encoded as a shift. Searching for delays becomes conceptually misguided.
Unified language
Noir bridges ultrafast physics, molecular dynamics, and integrated cellular behavior without distortion.
Time as function
In living systems, time is used—not merely measured. It enables memory, integration, and decision-making.
New strategies
Focus shifts to state transitions, recovery dynamics, and stable, interpretable quantities.
Time is not a single concept.
It is a scale-dependent property of systems.