- When you point your flashlight at the wall and turn it on, it seems
the light ray reaches the wall instantaneously, and so "speed of light for everyone watching" = c = ∞. Or equivalently c⁻¹ = 1/c = 1/∞ = 0.
- When you cut a stick in half, then cut the half in half, then get a
knife, cut the rest into something even smaller, sharpen the knife, and
so on, it feels like you can do this for ever, and with infinite time
"it makes sense to have something infinitely small to almost size zero" and we note this idea ħ = 0.
to have laws governing something infinitely small. Surprising, yes, but
it works for really small things and that's proven. No biggie.
- When a needle falls to the ground, it is pulled down by the gravity
from entire Earth (and that's really really big). But you can pick it up
with a tiny magnet. So gravity seems so ridiculously small compared to
other forces that in this perspective, we are almost tempted to ignore
it as if it didn't exist: G = 0.
So we thought that c⁻¹ = 0, ħ = 0 and G = 0, but we now know that c⁻¹ = 1, ħ = 1 and G = 1 and we want one consistent theory starting from there.
The theory behind c⁻¹ = 1, ħ = 0 and G = 0 is called Special Relativity.
The theory behind c⁻¹ = 0, ħ = 1 and G = 0 is called Quantum Mechanics.
The theory behind c⁻¹ = 0, ħ = 0 and G = 1 is called Newton's law of universal gravitation.
The theory behind c⁻¹ = 1, ħ = 0 and G = 1 is called General Relativity.
Other combinations have different theory names, but the one you asked for was:
The theory behind c⁻¹ = 1, ħ = 1 and G = 0 is called Relativistic Quantum Mechanics.
We have no consistent theory for c⁻¹ = 1, ħ = 1 and G = 1, even
though we know it is true. This problem is called "quantization of
gravity". A candidate theory is Loop Quantum Gravity. Another, more famous one is String Theory.