emergent-time-framework

emergent-time-framework.org

Welcome to emergent-time-framework.org

Here you will find links to my research papers and a blog for ongoing commentary on issues related to the Emergent Time Framework. As with all new scientific endeavours, the Emergent Time Framework represents a journey of learning and discovery, and I invite you to explore this new paradigm with me.

I am not the first person to have noticed that MOND’s $a_0$ appears to be mathematically linked to $\frac{c H_0}{2\pi}$ or, as later derivations show, $\frac{c H_0}{6}$ . Milgrom pointed this out in 1983, postulating that there was a deeper global cosmological property at work, linking the two. Current mainstream cosmology (2026) treats $a_0$ as an effect arising from within galaxy structures due to dark matter or, as in the case of MOND, a required modification to Newton’s laws in the weak field. The expanding cosmos is attributed to a separate component, called ‘dark energy’, with the two taken together referred to as the ‘dark sector’.

What makes the ETF unique is that it mathematically derives from first principles, $a_0$ as the 2D manifestation of the Planck power flux operating through the metric. In the unconstrained 3D isotropic vacuum, the acceleration floor is $a_F = \frac{c H_0}{12\pi}$ . This floor rate requires that any gravitational potential must accelerate matter above this rate if it is to move. This gives the 3D isotropic vacuum a property we call ‘metric stiffness’, denoted by $S_T$ , emulating dark matter. The Planck power is also responsible for driving the expansion of the universe through the process of vector-mediated energy exchange or transformation, giving rise to time dilation, as explained in the papers and blog elsewhere on this website. So the underlying driver of dark energy and dark matter is unified in the ETF. Enormous energies are stored within the manifold, and the values of $a_F$ and its 2D nucleated version $a_0$ are not static numbers but have evolved with the age of the cosmos. We use all of the above insights to explain some of the enduring challenges facing modern cosmology: the galaxy rotation anomaly, dark energy, dark matter, the lithium abundance problem and the impossible early galaxies imaged by the JWST, to name but a few.

What is the ‘Emergent Time Framework’, aka ETF?

The ETF is a novel interpretation of General Relativity that places primary emphasis on the energy-stress tensor, $T_{\mu\nu}$ . Rather than treating the spacetime manifold (aka ‘the vacuum’) as a passive stage shaped almost exclusively by mass, and time as a passive, pre-existing ‘canvas’ upon which physical action plays out, the framework posits that the geometry of the universe is a dynamic result of the continuous Planck power flux operating through the metric.

At its core, the framework is built upon the foundational principle

Vector-Mediated Energy Exchange: Every energy transformation or exchange process is strictly vector-mediated.
Inertial Response: These energy transitions generate an inertial response within all mass-bearing matter.
Time Dilation as a Fundamental Metric: Every inertial response induces a relative time dilation within the local proper time field during the vector-mediated exchange process.
Universal Dilation: Because this continuous energy exchange operates across all scales—from subatomic interactions to the largest cosmic structures—all matter in the universe exists in a perpetual state of dilated time relative to all other matter, and to the background proper time rate
The process is relative, and fully honours the precepts of General Relativity

Consequently, energy transformation acts as the fundamental physical bridge between inertial and gravitational equivalence. In flat spacetime, the energy transformation inducing an inertial response is transient; for any matter to be accelerated, it must do so above the 3D isotropic acceleration floor ( $a_F = \frac{c H_0}{12\pi}$ ). Conversely, within a massive body like the Earth, this energy transformation process is continuous, dynamically curving the cosmic-wide background proper time field. Because time is a proxy for distance and vice versa, using c as our cosmic ruler, we can say energy transformation as described above also yields geometry.

Time as a Field

The ETF proposes that we view time as a field rather than a dimension. In accordance with General Relativity, the rate of proper time is directly related to the local power flux. Proper time passes more slowly in regions of higher power density, such as the vicinity of a star or planet. In this model, energy transformation curves the existing background time field. This provides a phenomenological explanation for gravity: matter and photons encountering a gradient in the proper time rate will naturally follow a geodesic.

The Driver: Planck Power Flux

What powers the expansion of the cosmos and gives rise to the proposed time field and cosmic-wide acceleration floor? The ETF identifies the Planck Power $P_L$ —derived from fundamental constants as $P_L = \frac{c^5}{G} \approx 3.6 \times 10^{52}$ Watts—as the fundamental power flux to manifold geometry, i.e., expansion, driver.

Because $P_L$ is anchored to $c$ and $G$ , the power flux of the cosmos is maximised at this level, and it is invariant. If this flux were structurally lower, the fundamental constants of nature would not hold the values we measure today, and the universe would face significant entropic instability.

Space, Distance, and the Illusion of Time as a Dimension

The framework suggests that distance as measured by $c$ cannot exist without the prior energy transformations that caused space to arise between matter. Distance is, therefore, a spatial proxy for the proper time difference between objects, which is a manifestation of energy transformation.

The ETF does not recognise time as a dimension. The concepts of ‘yesterday’ and ‘tomorrow’ are viewed as constructs of human cognition and memory—evolutionary advantages that allow for learning and agency. Nature, however, operates only in the ‘now’ through continuous energy transformation.

We instead view time as a proper time-rate field overlaying the $x, y,$ and $z$ dimensions. This is not a hypothetical field; we already utilise this interpretation in technologies like GPS, where every point in space has a unique proper time rate relative to every other point within the bounds placed on the propagation of information at c. The proper time rate at any point in space is linked to the total power flux at that point.

Metric Stiffness ( $S_T$ ) and the Acceleration Floor

General Relativity does not mandate zero time dilation in flat spacetime. The ETF proposes a floor time dilation rate driven by cosmic expansion, which carries an associated background acceleration floor, $a_F$ . In 2D nucleated structures like galaxies, the floor acceleration rate is $a_0$ .

The 3D acceleration floor, from which the 2D galaxy acceleration floor is derived, is the minimum acceleration threshold required to move matter, and in the ETF, it is derived from first principles. In its 2D guise it is remarkably congruent with the empirical MOND figure of $1.2 \times 10^{-10} \text{ m/s}^2$ , yielding a calculated value of $1.133 \times 10^{-10} \text{ m/s}^2$ . Unlike MOND and ${\Lambda\text{CDM}}$ , this acceleration floor is not recognised as a property emerging from within galaxy structures (as a required modification to Newton’s laws or the need for a non-baryonic dark matter halo) but as the result of Planck power operating through the metric, driving cosmic expansion.

The acceleration floor confers the property of metric stiffness ( $S_T$ ) on the manifold. This stiffness is topological and evolves with the age of the cosmos ( $z$ ):

3D Isotropic Ground State: $S_T(3\text{D}) \to a_F = \frac{cH_0}{12\pi}$
2D Nucleated State (Galaxies): $S_T(2\text{D}) \to a_0 = \frac{cH_0}{6}$

Resolving Modern Cosmology Tensions

By recognising the metric as inherently constrained by the background Planck power and applying the property of evolving metric stiffness to the manifold, the ETF addresses the following areas:

Dark Matter & Dark Energy: These phenomena are reinterpreted as physical manifestations of Planck power driving cosmic expansion, with metric stiffness mimicking the gravitational effects traditionally attributed to dark matter. The cause of these observational phenomena is one and the same: Planck power operating through the metric.
The Hubble Tension: This long-standing tension is resolved by identifying the physical mechanisms driving measurement bias. The high metric stiffness of the early universe and the dense cosmic nucleation of the Local Group act as observational “bookends” that skew local versus cosmic measurements. The ETF derives mathematically from first principles and zero free parameters that within unconstrained, flat spacetime, the true Hubble constant resolves cleanly to $70.04 \text{ km s}^{-1}\text{Mpc}^{-1}$ .
The Primordial Lithium Abundance Problem: The higher acceleration floor and energy partitioning between the thermal-kinetic and manifold expansion present during Big Bang Nucleosynthesis (BBN) provided a natural temporal quench, inherently suppressing lithium production to the levels currently observed in the universe. The Standard Model BBN element inventories, other than lithium, remain unaffected.
CMB Homogeneity and Smoothness: The framework significantly relaxes the extreme fine-tuning requirements of standard cosmic inflation epoch models. Because the cosmic expansion rate and potential metric stiffness are coupled in a tight feedback loop, the early universe behaves as a self-regulating thermal-geometric system. This feedback loop naturally smooths out primordial anisotropic variances, elegantly explaining the exceptional cosmic microwave background (CMB) homogeneity observed by the Planck collaboration. This epoch of structural self-regulation governed the hot plasma-metric coupling from the electroweak horizon ( $t \approx 10^{-12}\text{ s}$ , $z \sim 10^{15}$ ) until the era of recombination ( $t \approx 380,000\text{ years}$ , $z \approx 1100$ ), at which point the universe became transparent, allowing primordial light to break free and lock in the cosmic temperature floor we observe today.
High-Redshift Massive Galaxies: Because the baseline acceleration floor ( $a_0$ ) evolved with the age of the cosmos, the ETF provides a natural evolutionary mechanism for the unexpectedly massive, well-formed galaxies observed at high redshifts.

The ETF paradigm offers a zero-free-parameter, first principles solution to some of modern science’s most challenging questions. It suggests that these exist because we have not yet factored in the role of metric stiffness or treated time as a physical field rather than a passive dimension. In doing so, the ETF extends the reach and explanatory power of General Relativity.

I invite researchers to explore the ETF paradigm. If you have any questions, please feel free to email me at andrewc.russell(at)gmail.com or post your queries on the question board.

Thank you for visiting emergent-time-framework.org.

emergent-time-framework.org

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