Just another minercraft Idea, with Bing

That’s an interesting question. To calculate the minimum density of the Schwarzschild radius in a Minecraft world, we need to use the formula for the Schwarzschild radius and the formula for density. The Schwarzschild radius is given by:

rs​=c22GM​

where rs​ is the Schwarzschild radius, G is the gravitational constant, M is the mass of the object, and c is the speed of light. The density is given by:

ρ=VM​

where ρ is the density, M is the mass, and V is the volume. Assuming that the object is spherical, we can use the formula for the volume of a sphere:

V=34​πr3

where r is the radius of the sphere. Substituting this into the density formula, we get:

ρ=4πr33M​

Now, we can use the Schwarzschild radius formula to eliminate M and get an expression for the density in terms of the Schwarzschild radius:

ρ=32πGrs2​3c4​

This formula tells us that the density depends inversely on the square of the Schwarzschild radius. The smaller the Schwarzschild radius, the higher the density required to form a black hole.

To apply this formula to a Minecraft world, we need to know some parameters of the game. According to one of my sources1, a Minecraft world stretches for roughly 30 million blocks in each direction from the spawn point, and one block in Minecraft is equivalent to one meter in real life. This means that a Minecraft world has a width and length of 60 million meters. The height limit for all Minecraft worlds is 320 blocks or meters2. Therefore, we can assume that a Minecraft world has a rectangular prism shape with dimensions of 60 million by 60 million by 320 meters.

To find the minimum density of the Schwarzschild radius in a Minecraft world, we need to find the maximum possible mass of a Minecraft world. This depends on what materials are used to fill up the world. According to another source3, there are different types of blocks in Minecraft with different densities. For example, stone has a density of 2.4 g/cm^3, iron has a density of 7.87 g/cm^3, and gold has a density of 19.3 g/cm^3. To get an upper bound on the mass of a Minecraft world, we can assume that it is made entirely of gold blocks, which have the highest density among all blocks.

The mass of one gold block is equal to its volume times its density. Since one block is one meter cubed, its volume is 1 m^3. The density of gold is 19.3 g/cm^3, which is equivalent to 19.3 x 10^6 g/m^3 or 19.3 x 10^3 kg/m^3. Therefore, the mass of one gold block is 19.3 x 10^3 kg.

The total number of blocks in a Minecraft world is equal to its volume divided by the volume of one block. Since one block has a volume of 1 m^3, we can simply use the volume of the world as the number of blocks. The volume of a rectangular prism is equal to its length times its width times its height. Therefore, the volume of a Minecraft world is:

V=60×106×60×106×320

V=1.152×1015m3

The total mass of a Minecraft world made entirely of gold blocks is equal to its volume times the mass of one gold block. Therefore, the mass of a gold Minecraft world is:

M=V×mgold​

M=1.152×1015×19.3×103

M=2.22336×1019kg

This is an extremely large mass, comparable to that of some asteroids or moons in our solar system.

Using this mass, we can calculate the Schwarzschild radius of a gold Minecraft world using the formula:

rs​=c22GM​

We need to use consistent units for this calculation. The gravitational constant G is approximately 6.674 x 10^-11 N m2/kg2 and the speed of light c is approximately 2.998 x 10^8 m/s. Therefore, the Schwarzschild radius of a gold Minecraft world is:

rs​=(2.998×108)22×6.674×10−11×2.22336×1019​

rs​=0.066m

This is a very small radius, about the size of a tennis ball.

Finally, we can use this radius to calculate the minimum density of the Schwarzschild radius in a gold Minecraft world using the formula:

ρ=32πGrs2​3c4​

Substituting the values of c, G, and rs​, we get:

ρ=32π×6.674×10−11×(0.066)23×(2.998×108)4​

ρ=1.212×1020kg/m3

This is an extremely high density, about 10^17 times higher than the density of gold.

Therefore, the minimum density of the Schwarzschild radius in a Minecraft world is approximately 1.212 x 10^20 kg/m^3, assuming that the world is made entirely of gold blocks and has a rectangular prism shape with dimensions of 60 million by 60 million by 320 meters. This density is so high that it is impossible to achieve with any known material in the universe.

Source: Conversation with Bing, 10/7/2023

(1) How big is a Minecraft world? - Sportskeeda. https://www.sportskeeda.com/minecraft/how-big-minecraft-world.

(2) How Big Is a Minecraft World? - Lifewire. https://www.lifewire.com/how-big-is-a-minecraft-world-5212822.

(3) World size – Minecraft Wiki. https://minecraft.fandom.com/wiki/World_size.

(4) Schwarzschild radius - Wikipedia. https://en.wikipedia.org/wiki/Schwarzschild_radius.

(5) Schwarzschild Radius Calculator. https://www.omnicalculator.com/physics/schwarzschild-radius.

(6) Schwarzschild Radius - vCalc. https://www.vcalc.com/wiki/MichaelBartmess/Schwarzschild+Radius.

(7) Schwarzschild Radius Calculator - PhysicsCalc.com. https://physicscalc.com/physics/schwarzschild-radius-calculator/.

(8) How Big Is Minecraft World? The Answer Will Shock You. https://gurugamer.com/pc-console/how-big-is-minecraft-world-19364.

(9) How Big Is Minecraft? Is It Really Bigger Than Earth - Fiction Horizon. https://fictionhorizon.com/how-big-is-minecraft/.