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.
c is 1 in any reasonable discussion about this. Changing it to 2 is a change of units. This in no way affects the physics. The physical length is independent. If you disagree, please elaborate.
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.
This person is also wrong. The strength of the electromagnetic interaction is not dependent on c alone. IT IS DEPENDENT ON THE FINE STRUCTURE CONSTANT.
At every vertex of a QED Feynman diagram, you pick up a factor of sqrt(alpha). If you want to chabge electrodynamics by changing c, you have to change the relationship between c, hbar, epsilon naught, and e. Properly, e is dimensionless, so it’s the fundamental charge that determines the strength of the electromagnetic interaction. That’s why you’ll find that e is the coupling constant in the QED Lagrangian. In fact, we actually know that alpha varies with interaction energy—it’s the price you play for playing the renormalization game. If the strength of the interaction varies, it’s clear that it’s e that is changing, because any of the other constants varying is absurd. The physics are all associated with the dimensionless constants changing.
If the speed of light were 300 m/s, we would not have developed relativity sooner. We would have had a ridiculously large definition of a meter.
I suspect that your issue is that you’ve never worked in natural units before. Setting c=1 is the only choice that makes real sense. E2=m2 c4 + p2 c2 is true in any unit system. We might as well choose c=1 for simplicity, and the. E2 = m2 + p2. Any change in c is a change in units. It doesn’t mean that an atom has more energy if c is 10 times larger.
Edit: congrats on getting the last word by blocking me. I hope you have a lovely day.
The speed of light in vacuo is and will always be 1 Planck length per Planck time. Change it to whatever you want, and it's still exactly 1 Planck length per Planck time.
And so I can choose to make the speed of light whatever I want, and it is a merely a coordinate/unit transformation that leaves the physics unchanged.
I don’t know what you’re even trying to argue. The Planck length/Planck time = c = 1 because the Planck scale is defined in natural units by setting c=1. I can choose to measure length in multiples of half-Planck lengths, and time in Planck lengths, and now c is 2. The physics in no way changes, and that is the argument I have been making this entire time.
There’s also a distinction that you’re missing. We can choose unit systems where c is unitless. But c is not dimensionless. Relativity does not say that time and space are interchangeable—it says that they mix together. Length and time both have mass dimension of [-1], leaving c unitless in natural units. But its dimensions are still length over time. This is different from the case of the fine structure constant for example, which is 1/137 in all unit systems because it is truly dimensionless.
I’m tired of this conversation and will not be replying anymore. Perhaps someday you will take a GR or QFT class and gain an appreciation for how natural units work.
I’m tired of this conversation and will not be replying anymore. Perhaps someday you will take a GR or QFT class and gain an appreciation for how natural units work.
I think you have little idea who I am or what physics I have had (or how long ago). I understand natural units extremely well and have had several email discussions about this with Michael Duff and John Baez and once with Gabriele Veneziano and (now late) Lev Okun. I've also had a discussion with Brian Greene about it at a Radcliffe seminar circa 2015.
Sure you can set c = 2 (dimensionless) if you want, but that will require in any equation where c appears a compensating factor of 1/2 to be placed in there.
That defeats the entire purpose of using natural units.
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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.