Inverse Square Law

The Inverse Square Law pops up everywhere. Everytime you have a "force field" you see the inverse square law describe how the force drops away as objects get further and further away from each other. But most graphs you see of the law conveniently mislead the person looking at them. Because most graphs show the line peter out to zero on the far right hand side of the graph.

This is a lie! Take that graph, see how it's about 20 cm wide on the screen. Now imagine extending the Y axis to the right by say 10 km. Even at that distance, if you zoom in to the line on the graph enough it will never touch the Y axis. At least as far as we know. If you simulated this on a computer the computer would eventually tell you that the line reaches zero. But this is a failing of the computer, not the mathematics. Because computers can only represent a finite range of values eventually the computer will just give in to the lie and tell you the line reached zero!

But the universe is not like a computer. As far as we know the universe can represent any number. That is it can represent an infinite range. Well, at least as far as we know. And what does it actually mean that the universe can represent any number? Once we get down to the smallest possible unit of measurement (the Planck Length) we still don't reach the limit of what the universe can represent (whatever that means). To quote a random page from The Internet: "There are a lot of misconceptions that generally overstate its physical significance, for example, stating that its the inherent pixel size of the universe.".

This has very disturbing consequences. It means that every "bit" of mass in the universe has a gravitational affect on every other "bit" of mass in the universe. If that is the case and the universe is like a computer, calculating how things move over time to generate reality, then this computer has infinite computational power and infinite memory. Yikes!

But what if this inverse square line does actually hit zero? How would we know it doesn't?