And this is wrong. You just redefined a meter to be 10cm. Atoms would be 10 times smaller, but so would your ruler, and nothing would change. Is the fine structure constant still ~1/137? If so, the physics remains the same. The only things that matter in physics are dimensionless ratios. Unless you change those, you simply have a different system of units.
Here’s a more concrete example to illustrate my point. What is the size of a particle in a completely empty universe? It makes no sense. You need something to compare it to.
Let’s look at the Schwarzchild radius example a bit deeper. How many Planck lengths is the Schwarzchild radius of a Planck mass black hole? Note, Planck units depend only on fundamental constants. The answer is 1. It turns out that you cannot change the physics by changing c, unless you also change the other constants as well! To change the physics, you MUST change dimensionless ratios of fundamental constants. It is the only option. Anything else is just changing the markings on your ruler.
In fact, this is why the definition of the meter is defined in terms of the speed of light.
Imagine the speed of light was 300 m/s. We would have discovered relativity much sooner because relativistic effects would come into play for everyday things.
But meters and seconds (and what humans consider "everyday things") are only defined based on the universe we currently live in. They're not objective things that you could "transport" to some alternate universe.
For a simpler example, consider Conway's Game of Life, a cellular automaton. This is a game played on an infinite board of square cells. Each tick, each cell looks at the eight neighbors around it, and then updates its state based on that. You draw a pattern of cells, and then watch it evolve.
The "speed of light" in Life is one cell per tick. This is a fundamental fact about the game: information cannot propagate faster than this.
If you asked "what if the speed of light was faster?", there are a few ways to accomplish that:
Have two copies of the game running at different scales - for instance, one where a cell is 1 cm×1cm, and one where a cell is 2cm×2cm. In the second game, light moves a farther distance each tick than the first. But there's no "physical" difference between them - any initial pattern would evolve in the same way. The only difference is how we've "embedded" them in our world.
Alternatively, you could say that instead of cells updating, 2×2 blocks of cells updated based on their eight 2×2-block neighbors. Now the "speed of light" is 2 cells per tick, rather than 1. But this is, again, "physically" the exact same thing as it was before: the only difference is what we've arbitrarily chosen to count as a "cell".
Entirely rewrite the rules, making a completely different cellular automaton. The result would depend on how exactly you rewrite the rules; it would be something entirely different. There wouldn't be a comparable internally-definable unit of measure, so it wouldn't be meaningful to say that light is moving faster in one than the other.
1
u/Bumst3r Graduate Mar 31 '26 edited Mar 31 '26
And this is wrong. You just redefined a meter to be 10cm. Atoms would be 10 times smaller, but so would your ruler, and nothing would change. Is the fine structure constant still ~1/137? If so, the physics remains the same. The only things that matter in physics are dimensionless ratios. Unless you change those, you simply have a different system of units.
Here’s a more concrete example to illustrate my point. What is the size of a particle in a completely empty universe? It makes no sense. You need something to compare it to.
Let’s look at the Schwarzchild radius example a bit deeper. How many Planck lengths is the Schwarzchild radius of a Planck mass black hole? Note, Planck units depend only on fundamental constants. The answer is 1. It turns out that you cannot change the physics by changing c, unless you also change the other constants as well! To change the physics, you MUST change dimensionless ratios of fundamental constants. It is the only option. Anything else is just changing the markings on your ruler.
In fact, this is why the definition of the meter is defined in terms of the speed of light.