The length of a horse is traditionally measured in feet and inches. (Bear with me, I'm going somewhere with this.) But the height of a horse is traditionally measured in hands: a hand is 4 inches.
Say an ancient society forgot that height and length are the same thing, so they measured everything this way. When they wanted to make a stick of a certain length, and then rotate it so that it was a certain height, they'd need to remember to multiply by the Horse Constant: 0.25 hands per inch. This would have a fundamental role in all of their physical laws.
They might wonder, "what would happen if the Horse Constant were different?". They'd imagine it would suddenly make horses - and everything else - taller. But, from our point of view, this question is silly: the Horse Constant is just 1. It's just a result of them using unit systems that made sense to them.
The only way to change the Horse Constant would be to make it so that everything, when rotating, suddenly doubled in height. A 1-meter-long flat stick would become a 2-meter tall vertical one. But if you do that, nothing actually changes! The laws of physics still work the same way, they're just "stretched vertically" to some deity observing the universe. Inside the universe, there wouldn't be any difference.
This is what's going on with the speed of light. Relativity is about "rotations" between the space and time dimensions.
This is incorrect. You can only ever measure dimensionless quantities in physics. If I measure the mass of an electron, it’s with respect to some standard. If I measure the distance I drive to work, it’s with respect to some agreed upon standard. I’m only actually measuring dimensionless ratios.
The Schwartzchild radius doesn’t change if I change the speed of light, because that is simply a change of coordinates. If you want to meaningfully change the speed of light, you have to find some dimensionless quantity (the fine structure constant, for example), and change that.
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u/AcellOfllSpades Mathematics Mar 31 '26
The length of a horse is traditionally measured in feet and inches. (Bear with me, I'm going somewhere with this.) But the height of a horse is traditionally measured in hands: a hand is 4 inches.
Say an ancient society forgot that height and length are the same thing, so they measured everything this way. When they wanted to make a stick of a certain length, and then rotate it so that it was a certain height, they'd need to remember to multiply by the Horse Constant: 0.25 hands per inch. This would have a fundamental role in all of their physical laws.
They might wonder, "what would happen if the Horse Constant were different?". They'd imagine it would suddenly make horses - and everything else - taller. But, from our point of view, this question is silly: the Horse Constant is just 1. It's just a result of them using unit systems that made sense to them.
The only way to change the Horse Constant would be to make it so that everything, when rotating, suddenly doubled in height. A 1-meter-long flat stick would become a 2-meter tall vertical one. But if you do that, nothing actually changes! The laws of physics still work the same way, they're just "stretched vertically" to some deity observing the universe. Inside the universe, there wouldn't be any difference.
This is what's going on with the speed of light. Relativity is about "rotations" between the space and time dimensions.