Comment by MadnessASAP
12 hours ago
I am somewhat curious where the math on a perfect rigid rod breaks down (that is, where does the 0 end up under the line)
12 hours ago
I am somewhat curious where the math on a perfect rigid rod breaks down (that is, where does the 0 end up under the line)
My gut instinct is you’d really need perfect incompressibility such that pushing one end of the rod would propagate the pressure wave to other end instantaneously. In other words, you have to make the speed of sound faster than the speed of light. I have no idea what the physical construction would look like. Maybe a string of singularities lined up and touching (hey, there’s your 0!) without tearing spacetime apart?
I think this is where the math breaks down:
> you’d really need perfect incompressibility such that pushing one end of the rod would propagate the pressure wave to other end instantaneously
I.e. by pushing an abstraction of "perfect incompressibility" and "instantenous propagation of pressure waves" to the point stops corresponding to reality. Those ideas are descriptive simplifications, abstracting away the underlying process of matter / fields interacting sequentially, an interaction that propagates at the speed of light.
It's the same kind of thing like assumption that array access is O(1). It is, until the array gets so large the process of finding the right place in memory becomes visibly O(n).
Or, on a more basic level, arithmetic on numbers seems to be O(1) with respect to the values of the numbers. Almost all programming practices and popular algorithms depend on that assumption, but it only holds for numbers that the hardware can process in one go. Adding 64-bit numbers is constant-time. Adding 64000-bit numbers isn't.
Right. "Let's assume force propagates instantaneously--" "Let me stop you there."
> Maybe a string of singularities lined up and touching (hey, there’s your 0!) without tearing spacetime apart?
At that point it's starting to sound less like a rigid rod and more like changing spacetime itself so that the two locations are closer together. :p
Force cannot transmit through the material faster than the speed of sound and because fundamentally at a subatomic level, mechanical force is the interaction of electromagnetic and gravitational fields between molecules, the speed of sound cannot exceed the speed of light in a material. The rod will compress or physics breaks down. Solid particles are an abstraction.
I think the math is fine, but a perfectly rigid rod cannot exist in our universe, so there's no paradox, even though it would let you send messages faster than light. It's like calculating how strong of a hydraulic press you'd need to compress matter into neutronium in your garage, or claiming that if a spaceship could travel at 2x light speed, then it could fly its way back out of a black hole.
There simply are no such things as rigid bodies in this universe. Everything is composed of particles that act on each other with forces, which take time to transmit the information that something is pushing on the other side.
My guess is that the Pauli exclusion principle would ultimately come into play, the same thing that keeps stuff from falling through other stuff. Electrons will shove other electrons out of the way, which isn't a lossless process or an instantaneous one. So a perfectly rigid rod would run afoul of special relativity if you pushed on one end.