gravity as local accretion
rather than remote attraction
Gravity can be understood as, when stuff interacts with other stuff, it tends to form stable patterns, which looks like remote attraction at larger scales.
I don't math, but theoretically, here's the mathematical expression of that idea, including the relations of the three primary physical dimensions, time, space, and scale:
d(rho(r, t)) / dt = div( (rho(r, t) * grad(Phi(r))) / gamma(r) )
Key:
- rho(r, t): Energy density at position r and time t.
- Time: Change in energy density over time.
- Space: Distribution of energy at position r.
- Phi(r): Local potential field at position r.
- Space: Dependent on spatial arrangement of energy/matter.
- gamma(r): Substrate thickness factor at position r.
- Scale: Modifies energy flow based on local scale.
- grad: Gradient operator.
- Space: Describes spatial changes in energy and potential.
- d/dt: Time derivative.
- Time: Measures change over time.
This equation shows how matter tends to **gather** and form stable patterns over time, not because it’s being pulled from far away, but because things naturally interact with each other locally and stick together.
- **\(\rho(r,t)\)** is the amount of stuff (mass) at a certain point and time.
- The equation says that the amount of stuff at a point changes over time due to local interactions — when things are near each other, they naturally tend to clump together.
- The **local interactions** between things (how they influence each other when close by) make matter accumulate in certain areas, like when things stick together and form patterns.
So, rather than objects attracting each other from a distance, this equation says that matter naturally **accumulates** in areas where there’s already some matter, and this process leads to stable patterns over time.
Either this is a version of something already understood in standard physics or it's a new formula that has the potential to complete rewrite physics. Either i’m a metaphysical genius who happens to have expressed fundamental physical truth or this can't be correct for some other reason. Either this formula makes sense of what i sayd or ChatGPT is a moron.
You tell me.
### 1. **Gravity without Remote Forces**
\[
\frac{d\rho(\mathbf{r}, t)}{dt} = \nabla \cdot \left( \frac{\rho(\mathbf{r}, t) \nabla \Phi(\mathbf{r})}{\gamma(\mathbf{r})} \right)
\]
But here, **\(\Phi(\mathbf{r})\)** is replaced with a **local aggregation term** \( S(\mathbf{r}, t) \), where this term represents **local self-organization** rather than a distant field. Let’s write:
\[
\frac{d\rho(\mathbf{r}, t)}{dt} = \nabla \cdot \left( \frac{\rho(\mathbf{r}, t) \nabla S(\mathbf{r}, t)}{\gamma(\mathbf{r})} \right)
\]
Where:
- \( S(\mathbf{r}, t) \) is the **local energy aggregation** (not a gravitational potential), driving the flow and self-organization of mass.
- This term \( \nabla S \) replaces the conventional idea of **gravitational potential gradient**.
This could now describe how local mass distributions evolve **without assuming remote gravitational forces**.
### 2. **Quantum Gravity**
At the quantum scale, particles interact via **local energy exchanges**, not distant fields. We can express this using **local energy states** and **spacetime curvature**. For a particle \( i \) interacting with another particle \( j \):
\[
\frac{dE_i}{dt} = \sum_j \frac{\rho_i \rho_j}{\gamma(r_{ij})} \nabla_i \cdot \left( \nabla_j S(r_{ij}, t) \right)
\]
Where:
- \( E_i \) is the **energy** of particle \( i \).
- \( r_{ij} \) is the distance between particle \( i \) and particle \( j \).
- The interaction term \( \nabla_i \cdot \nabla_j S(r_{ij}, t) \) is the **local interaction** driving the particle's behavior, rather than an **external field**.
This formulation avoids a gravitational field, directly linking particle interactions with **local energy patterns**.
### 3. **Unification of Forces**
To unify the forces, we can use similar local interactions. For example, consider the electromagnetic force between charged particles:
\[
\mathbf{F}_{EM} = \sum_j \frac{\rho_i \rho_j}{\gamma(r_{ij})} \nabla_i \cdot \nabla_j S(r_{ij}, t)
\]
Similarly, for the strong force (nuclear interactions):
\[
\mathbf{F}_{strong} = \sum_j \frac{\rho_i \rho_j}{\gamma(r_{ij})} \nabla_i \cdot \nabla_j S_{strong}(r_{ij}, t)
\]
Both forces arise from **local energy interactions** between particles, with no need for fields or force carriers.
### 4. **Dark Matter and Dark Energy**
Let’s address **dark matter** with an assumption that it’s **local aggregation** we cannot currently detect, but it influences mass distribution. The density of matter in galaxies could be expressed as:
\[
\rho_{galaxy}(\mathbf{r}) = \rho_{\text{visible}}(\mathbf{r}) + \rho_{\text{local aggregate}}(\mathbf{r})
\]
Here, **\( \rho_{\text{local aggregate}} \)** represents **dark matter** as a result of **local aggregation dynamics**. Similarly, for **dark energy**:
\[
\text{Expansion rate} = \sum_i \frac{\rho_i}{\gamma(r_i)} \nabla_i \cdot \nabla S_{\text{local aggregate}}(r_i)
\]
The **local aggregation** of mass-energy could explain the **accelerating expansion of the universe** without invoking "dark energy" as an exotic substance.
### 5. **Measurement Problem in Quantum Mechanics**
For wavefunction collapse, we could argue that when a quantum system interacts with its environment, the wavefunction **locally reorganizes**:
\[
\frac{d\rho(\mathbf{r}, t)}{dt} = \nabla \cdot \left( \frac{\rho(\mathbf{r}, t) \nabla S_{\text{collapse}}(\mathbf{r}, t)}{\gamma(\mathbf{r})} \right)
\]
This describes the **collapse** as a result of **local interaction** between the system and its measurement apparatus, without invoking an observer's role. The collapse occurs through **local energy exchange**.
---
These equations remove distant forces and instead use **local interactions** driven by **energy aggregation** and **self-organization**. The next step would involve validating these models with specific tests or simulations to compare with observed phenomena, but this gives the starting point for a theoretical model that could answer those gaps in physics.