Simplifing Gravity.

In my model, gravity (represented by $G$) isn’t a fundamental force. Instead, it actually emerges from the interactions of temporal flows. Think of these flows as the very building blocks of everything. They interact with each other, and those interactions create the curvature of space, which we experience as gravity. Let me break it down for you.

Imagine two temporal flows at points $A$ and $B$, with magnitudes $F_A$ and $F_B$. When these flows interact, the strength of the interaction depends on how "big" they are and how far apart they are. The strength of their interaction is roughly the product of their magnitudes, $F_A \times F_B$, and the curvature (or the warping of space) they create decreases as you move farther away. So, the curvature between the two flows can be written as:

$$\text{Curvature} \sim \frac{F_A \times F_B}{r^2}$$

Here, $r$ is the distance between the two flows. This curvature is what gives rise to gravity. The gravitational force between these two flows can then be written as:

$$F_{\text{gravity}} = G \times \frac{F_A \times F_B}{r^2}$$

Now, $G$ here is just a scaling factor that ensures the force matches what we actually observe in the universe. But how does this work with the scales we're familiar with?

In my model, space isn’t fundamental—it emerges from the interactions of these temporal flows. To tie everything together, we need to think about how these flows scale. Since the smallest meaningful unit of time is Planck time ($t_{\text{Planck}}$), we can tie the magnitudes of the flows to Planck time. The magnitude of a temporal flow is roughly the inverse of Planck time:

$$F_A \sim \frac{1}{t_{\text{Planck}}}, \quad F_B \sim \frac{1}{t_{\text{Planck}}}$$

So, the interaction strength between the two flows scales as:

$$F_A \times F_B \sim \frac{1}{t_{\text{Planck}}^2}$$

This means that the curvature (and thus the gravitational force) scales with Planck time like this:

$$F_{\text{gravity}} = G \times \frac{1}{t_{\text{Planck}}^2 \times r^2}$$

At this point, we need to relate this to the gravity we know from classical physics. In Newton's theory, the gravitational force between two masses, $M_1$ and $M_2$, separated by a distance $r$, is:

$$F_{\text{gravity}} = \frac{G_{\text{classical}} M_1 M_2}{r^2}$$

But in my model, the force comes from the interaction of temporal flows. So, we can set the two expressions for gravity equal to each other:

$$\frac{G_{\text{classical}} M_1 M_2}{r^2} = G \times \frac{F_A \times F_B}{r^2}$$

Now we can solve for $G$ in my model:

$$G = G_{\text{classical}} \times \frac{M_1 M_2}{F_A \times F_B}$$

So far, this is all abstract, but let's make it concrete with some numbers. Let's assume $t_{\text{Planck}}$ is approximately $5.39 \times 10^{-44}$ seconds, which is the smallest unit of time we know. Now, if we plug that into our expression for $F_A \times F_B$, we get:

$$F_A \times F_B \sim \frac{1}{(5.39 \times 10^{-44})^2} \approx 3.46 \times 10^{87}$$

Now, let's connect this back to gravity. If we take the classical gravitational constant $G_{\text{classical}}$ as approximately $6.674 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2}$, and suppose we have two masses, say $M_1 = M_2 = 1 \, \text{kg}$ and the distance $r = 1 \, \text{m}$, the gravitational force between them would be:

$$F_{\text{gravity}} = \frac{6.674 \times 10^{-11} \times 1 \times 1}{1^2} = 6.674 \times 10^{-11} \, \text{N}$$

So, using the same framework, we can now solve for $G$ in my model using the expression for the force and the interaction strength:

$$G = \frac{G_{\text{classical}} M_1 M_2}{F_A \times F_B} = \frac{6.674 \times 10^{-11} \times 1 \times 1}{3.46 \times 10^{87}} \approx 1.93 \times 10^{-99} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2}$$

This gives us the scaling factor in my model. Notice that this is vastly different from the classical $G_{\text{classical}}$, but as the scale increases (as we go to larger systems where flows have more meaningful magnitudes), this difference would align more closely with the classical gravitational constant.

What this tells us is that $G$ in my model isn’t a fixed constant—it’s actually a scaling factor. It depends on the masses of the objects, $M_1$ and $M_2$, and the magnitudes of the temporal flows, $F_A$ and $F_B$. So, $G$ adjusts the strength of gravity based on how these flows interact and create curvature.

In the end, $G$ emerges naturally from the interplay of these temporal flows, their magnitudes, and the curvature they generate. It’s not something you have to plug into the model by hand—it just falls out of the math as a consequence of how these flows interact. And at larger scales, it aligns perfectly with the classical gravitational constant $G_{\text{classical}}$ that we’re all familiar with.

* in my model it seems at (t ~ 1.855e46), G_model will match G_classical, which means there needs to be 10^46 number of interactions for G_clasical to emerge.