Today, I was watching https://www.youtube.com/watch?v=iUgqNu9cOEA related to #Astrum . I though to prepare a blog to solve it for them. Creation law and blops powering up our universe :).
So like other blogs, our reference: https://doi.org/10.5281/zenodo.17594186
Standard cosmology says the universe is expanding faster and faster, driven by a mysterious “dark energy” with almost constant density. At the same time, measurements of today’s Hubble constant \(H_0\) disagree depending on how you measure it: the CMB prefers a lower value, while local distance ladders prefer a higher one. This is the Hubble tension.
Quantum Traction Theory (QTT) offers a different perspective:
- the universe in its absolute clock is on a coasting expansion,
- apparent acceleration comes from a creation–driven time drift,
- and the Hubble tension is a manifestation of environment‑dependent drift, not conflicting values of a fundamental constant.
Crucially, the same creation law that slows down cosmic acceleration also naturally spreads measured \(H_0\) values between different probes.
1. Two clocks and coasting expansion in QTT
QTT distinguishes between:
- an absolute background clock \(T\) (ABC time), and
- local laboratory time \(t_{\rm lab}\), the time we actually measure.
Axiom A1 gives:
\[ d\tau = N(x^\mu,v)\,dT, \]
where \(N(x^\mu,v)\) is the usual gravitational/kinematic lapse; in cosmology we can take \(N\simeq 1\) at the background level. The second key choice is the coasting gauge:
\[ a(T) \propto T, \qquad H_\tau(T) := \frac{1}{a}\frac{da}{dT} = \frac{1}{T}. \]
So in ABC time the expansion is exactly coasting:
- no acceleration: \(d^2 a/dT^2 = 0\),
- Hubble in ABC time: \(H_\tau(T) = 1/T\).
The observational drama enters when we ask:
What is the Hubble parameter when measured in lab time, not in ABC time?
2. Time Tilt, Time Drift, and the mapping t ↔ T
In QTT, lab time is a tilted, drifting axis inside a 2D time plane spanned by \(T\) and a hidden reality direction \(w\). The local relation between lab time and ABC time is:
\[ dt_{\rm lab}(x,v;a) = I_{\rm clk}\,F_{\rm drift}^{\rm (time)}(a,x)\,N(x^\mu,v)\,dT. \]
- Tilt: a universal factor \(I_{\rm clk} = \cos(\pi/8)\), fixed by QTT’s discrete time‑plane symmetry.
- Drift (time version): \(F_{\rm drift}^{\rm (time)}(a,x)\), a slow, environment‑dependent factor coming from the Law of Creation.
- Dilation: \(N(x^\mu,v)\), the usual GR/SR lapse (≈1 for background cosmology).
For cosmological backgrounds we drop \(x,v\) and set \(N\simeq 1\), so
\[ dt_{\rm lab}(a) = I_{\rm clk}\,F_{\rm drift}^{\rm (time)}(a)\,dT. \]
For rates like Hubble, it is convenient to invert this and package Drift as a factor multiplying H rather than time intervals. Define the rate–drift factor:
\[ F_{\rm drift}^{\rm (rate)}(a) := \frac{I_{\rm clk}}{F_{\rm drift}^{\rm (time)}(a)}. \]
Then
\[ \frac{dT}{dt_{\rm lab}} = \frac{1}{I_{\rm clk}\,F_{\rm drift}^{\rm (time)}} = \frac{F_{\rm drift}^{\rm (rate)}}{I_{\rm clk}^2}. \]
For our purposes we only need the combination that multiplies \(H_\tau\), so we simply write:
\[ H_{\rm lab}(a,{\rm env}) = \frac{1}{a}\frac{da}{dt_{\rm lab}} = \frac{H_\tau(T)}{I_{\rm clk}}\,F_{\rm drift}^{\rm (rate)}(a,{\rm env}), \tag{1} \label{eq:Hlab-def} \]
where “env” labels the astrophysical environment behind the probe (CMB, TRGB, Cepheids, etc.). The key point:
- Coasting in \(T\): \(H_\tau(T) = 1/T\) is universal.
- Differences in measured \(H_0\) come entirely from \(F_{\rm drift}^{\rm (rate)}\), which depends on creation and environment.
3. Creation law and the drift integral
Where does \(F_{\rm drift}\) come from? QTT ties it directly to the Law of Creation via a time‑plane angle \(\theta(a)\). The lab axis \(u_t\) sits at an angle \(\theta(a)\) relative to the absolute axis \(u_\tau\). We write:
\[ \theta(a) = \theta_\ast + \delta(a), \qquad \theta_\ast = \frac{\pi}{8}, \]
with \(\theta_\ast\) the universal tilt and \(\delta(a)\) a slow, creation‑driven drift. The macroscopic QTT drift law is:
\[ \boxed{ \delta(a) \simeq \frac{1}{3} \int_0^{a} \Bigl[ \Omega_m(\tilde a) + \tau(\tilde a)\,\Omega_{\rm cre}(\tilde a) \Bigr]\, d\ln\tilde a, } \tag{2} \label{eq:delta-drift} \]
with
- \(\Omega_m(a)\) = matter fraction,
- \(\Omega_{\rm cre}(a)\) = effective “creation” / vacuum fraction,
- \(\tau(a) = 1 – 3w(a)\) = trace weight,
- radiation: \(w=1/3\Rightarrow \tau=0\), no drift,
- dust: \(w\simeq 0\Rightarrow \tau\simeq 1\),
- vacuum‑like: \(w\simeq -1\Rightarrow \tau=4\), dominates late drift.
This integral is “creation‑driven” in the precise sense that:
- it vanishes in a pure radiation era,
- grows slowly in the matter era,
- is boosted when the creation/vacuum channel becomes important.
The rate‑drift factor that enters \eqref{eq:Hlab-def} is then
\[ F_{\rm drift}^{\rm (rate)}(a,{\rm env}) = \frac{\cos\theta_\ast}{\cos\theta(a,{\rm env})} = \frac{\cos\theta_\ast}{\cos\bigl(\theta_\ast + \delta(a,{\rm env})\bigr)}. \tag{3} \label{eq:Fdrift-rate} \]
Environment (host galaxy type, star‑formation rate, etc.) enters because the effective creation density \(\Omega_{\rm cre}(a,{\rm env})\) is larger in star‑forming regions (more “white void” activity) than in passive environments.
4. Apparent acceleration and its slowing in lab time
In ABC time:
- \(a(T)\propto T\),
- \(H_\tau = 1/T\),
- the ABC deceleration parameter is \(q_\tau = 0\) (pure coasting).
In lab time we observe \(H_{\rm lab}(a)\) from \eqref{eq:Hlab-def}:
\[ H_{\rm lab}(a,{\rm env}) = \frac{H_\tau(T)}{I_{\rm clk}}\, F_{\rm drift}^{\rm (rate)}(a,{\rm env}) = \frac{1}{I_{\rm clk} T}\, F_{\rm drift}^{\rm (rate)}(a,{\rm env}), \]
with \(a\propto T\). The observed deceleration parameter in lab time is
\[ q_{\rm lab}(a) := -\frac{\ddot a\,a}{\dot a^{2}} = -\Bigl(1 + \frac{d\ln H_{\rm lab}}{d\ln a}\Bigr). \]
Using \(a\propto T\) and \(H_{\rm lab}\propto F_{\rm drift}^{\rm (rate)}/T\), we get
\[ \frac{d\ln H_{\rm lab}}{d\ln a} = \frac{d\ln H_{\rm lab}}{d\ln T} = -1 + \frac{d\ln F_{\rm drift}^{\rm (rate)}}{d\ln T}, \]
so
\[ q_{\rm lab}(a) = -\Bigl(1 + [-1 + d\ln F_{\rm drift}^{\rm (rate)}/d\ln T]\Bigr) = -\,\frac{d\ln F_{\rm drift}^{\rm (rate)}}{d\ln T}. \tag{4} \label{eq:q-lab} \]
This is the key QTT relation:
- if \(F_{\rm drift}^{\rm (rate)}\) grows with \(T\) (\(d\ln F/d\ln T>0\)), then \(q_{\rm lab} < 0\) → apparent acceleration;
- if the growth of \(F_{\rm drift}^{\rm (rate)}\) slows, \(d\ln F/d\ln T\to 0\), then \(q_{\rm lab}\to 0\) → acceleration slows and the universe tends back toward coasting in lab time;
- if \(F_{\rm drift}^{\rm (rate)}\) were to decrease, \(q_{\rm lab}>0\) → apparent deceleration.
In QTT, the creation law \eqref{eq:delta-drift} predicts:
- In the early radiation era, \(\tau=0\), so \(\delta(a)\approx 0\), \(F_{\rm drift}^{\rm (rate)}\approx 1\), \(q_{\rm lab}\approx 0\) (coasting).
- In the matter era, \(\tau\simeq 1\), and creation still small, so \(\delta(a)\) grows slowly, a mild \(q_{\rm lab}<0\) (weak acceleration).
- In the late vacuum‑like/creation era, \(\tau=4\) and \(\Omega_{\rm cre}\sim O(1)\), so \(\delta(a)\) grows faster: \(F_{\rm drift}^{\rm (rate)}\) ramps up and we see a stronger apparent acceleration.
- As the creation rate saturates or declines (fewer new white voids per Hubble time), the growth of \(\delta(a)\) slows, and \(\frac{d\ln F_{\rm drift}^{\rm (rate)}}{d\ln T}\to 0\). Equation \eqref{eq:q-lab} then predicts \(q_{\rm lab}\to 0\) again: the acceleration of the universe’s expansion slows down.
So in QTT, a slowing of acceleration is not a surprise: it’s a direct consequence of the creation law once the white‑void creation channel starts to run out of effective fuel.
5. Hubble constant tension as environment-dependent drift
Now plug the drift factor into the present‑day lab Hubble \(H_0\). Evaluate \eqref{eq:Hlab-def} at today’s scale factor \(a_0\):
\[ H_0^{({\cal P})} := H_{\rm lab}\bigl(a_0,{\rm env}={\cal P}\bigr) = \frac{H_{\tau 0}}{I_{\rm clk}}\, F_{\rm drift}^{\rm (rate)}(a_0,{\cal P}), \tag{5} \label{eq:H0-probe} \]
where \({\cal P}\) labels a particular probe family:
- \({\cal P} = {\rm CMB}\) (early–time, smooth background),
- \({\cal P} = {\rm BAO}\) (intermediate structures),
- \({\cal P} = {\rm TRGB}\),
- \({\cal P} = {\rm Cepheids+SNe}\) in star–forming hosts, etc.
Here \(H_{\tau0} = 1/\tau_0 \approx 63.5\ {\rm km\,s^{-1}\,Mpc^{-1}}\) and \(I_{\rm clk} = \cos(\pi/8)\) are universal QTT ledger values, fixed by the coasting and baryon identities. All the probe‑to‑probe variation lives in \(F_{\rm drift}^{\rm (rate)}(a_0,{\cal P})\).
Qualitatively:
- CMB: probes the smooth early background, where effective creation is small and homogeneous. QTT predicts \(F_{\rm drift}^{\rm (rate)}(a_0,{\rm CMB})\approx 1\), so \(H_0^{\rm (CMB)}\approx H_{\tau0}/I_{\rm clk}\).
- BAO / cosmic chronometers: sample large‑scale structure where creation activity has been moderate, giving a slightly larger drift factor: \(F_{\rm drift}^{\rm (rate)}(a_0,{\rm BAO})>1\) and thus a modestly larger inferred \(H_0\).
- TRGB / passive hosts: live in relatively quiescent environments with lower white‑void creation, so \(F_{\rm drift}^{\rm (rate)}(a_0,{\rm TRGB})\) is closer to the CMB value.
- Cepheid‑calibrated SNe in star‑forming hosts: sit in environments with enhanced creation (ongoing star formation, lots of small white‑void events). QTT predicts the largest drift factor here: \(F_{\rm drift}^{\rm (rate)}(a_0,{\rm SF})\) gives the highest inferred \(H_0\).
So the “Hubble tension” becomes:
a statement that our late‑time probes sample different values of \(F_{\rm drift}^{\rm (rate)}(a_0,{\cal P})\), not a fundamental inconsistency in the underlying expansion rate \(H_{\tau0}\).
The same creation law \eqref{eq:delta-drift} that drives the apparent acceleration— and eventually slows it via \eqref{eq:q-lab}—also explains why some probes “see” a larger \(H_0\) than others.
6. Summary: one creation law, two puzzles
Quantum Traction Theory weaves together three ideas:
- Coasting background in ABC time: \(a(T)\propto T\), \(H_\tau(T)=1/T\), no intrinsic acceleration.
- Creation‑driven time drift: the tilt angle \(\theta(a)=\theta_\ast+\delta(a)\) obeys the integral \eqref{eq:delta-drift}, and the rate‑drift factor \(F_{\rm drift}^{\rm (rate)}\) is \(\cos\theta_\ast/\cos\theta\).
- Environment dependence: creation density \(\Omega_{\rm cre}(a,{\rm env})\) is bigger in star‑forming regions and smaller in passive ones, feeding through into \(F_{\rm drift}^{\rm (rate)}(a_0,{\cal P})\) for each probe.
From these, QTT predicts:
- An apparent acceleration in lab time whenever \(F_{\rm drift}^{\rm (rate)}\) grows with cosmic time.
- A natural mechanism for slowing that acceleration as creation saturates, because equation \eqref{eq:q-lab} sends \(q_{\rm lab}\to 0\) when \(d\ln F_{\rm drift}^{\rm (rate)}/d\ln T\to 0\).
- A structural explanation for the Hubble constant tension: different probes sample different effective drifts \(F_{\rm drift}^{\rm (rate)}(a_0,{\cal P})\), so they infer different lab‑frame \(H_0^{({\cal P})}\) even though the underlying coasting rate \(H_{\tau0}\) is unique.
The same creation law responsible for the universe’s late‑time acceleration is also responsible for its eventual slowing and for spread in measured Hubble constants. In QTT, these are not three unrelated problems (dark energy, slowing of acceleration, \(H_0\) tension); they are three faces of one underlying structure: the way creation of space‑quanta tilts and drifts the time axis we use to talk about cosmic history.
QTT - Quantum Traction Theory 