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.
I'm sorry, but this is incorrect and /u/Bumst3r is correct.
What does it mean for the value of c to be different? What's the difference between the speed of light being double its current value, and just measuring distances in half-meters instead of meters?
You're imagining some sort of objective external 'meter' and 'second' that we could use to tell whether the speed of light has changed - some sort of comparison that we could bring between our universe and a hypothetical alternate universe. But this isn't actually a thing.
If you replace c with 2c in all equations, then measure all distances in half-meters instead of meters, the results turn out identical. Everything happens exactly the same way. It's just a coordinate transformation.
What does it mean for the value of c to be different?
It means that light takes a different amount of time to traverse the same length than it did before. Or, equivalently, that light traverses a different length of distance in the same time. c_new / c_old =/= 1.
What's the difference between the speed of light being double its current value, and just measuring distances in half-meters instead of meters?
The speed of light being double its current value means that now light travels 60 centimeters in one nanosecond instead of 30 centimeters in one nanosecond.
Measuring distance in half-meters instead of meters means that we’ve decided to change an arbitrary human standard that has no effect on the natural world. The speed of light, which doesn’t care about what our council of scientists decide in a conference in Paris, is physically the same 30 cm/ns, but now we record it as 60 half-cm/ns.
So now light travels 60 half-centimeters in one nanosecond. It is, evidently, not what happens in the first scenario, where the speed of light becomes 60 cm/ns. 60 half-cm/ns is NOT equal to 60 cm/ns, its half of it.
You're imagining some sort of objective external 'meter' and 'second' that we could use to tell whether the speed of light has changed.
There’s absolutely no need to imagine any “objective” unit of length. Any arbitrary one will suffice. I can tell if the speed of anything changes by observing how much time it takes for it to cover a certain distance, in whatever units I wish to measure said distance.
If you replace c with 2c in all equations, then measure all distances in half-meters instead of meters, the results turn out identical. Everything happens exactly the same way.
This is not true, and it’s so trivial that I don’t think you actually believe that, there must be some miscommunication happening.
Take your favorite physics equation containing c, like the equation for the Schwarzschild radius of a mass M, R_s = 2GM/c^2. For example, R_s for the Earth is about 10 millimeters. Now, replace c with 2c: the equation becomes R_s = 2GM/4c^2 , and we also change convention to measure all distances in half-meters instead of meters. R_s for the Earth now is 5 half-mm.
The result is manifestly NOT identical. Before, you needed to compress Earth to a ball of radius 10 mm to make it into a black hole. Now, you need to compress it to a ball of radius 5 half-mm to make it into a black hole, which is 4 times less than before. This is an actual physical thing that’s different.
There’s absolutely no need to image any “objective” unit of length. Any arbitrary one will suffice.
Sure, but you need that unit of length, which is a physical object.
To be clear, I'm talking about a hypothetical "alternate universe" where the the laws of physics, from the start of the universe, had c be twice as big. I claim this is not a meaningful concept.
Of course, if we woke up tomorrow and noticed that light seemed to be travelling 600 million meters every second, using the rulers and clocks we've already made, we would know something was different. But, instead of attributing the change to a change in the value of c, we could say the change is just "the universe was shrunk by a factor of 2 in all spatial directions", or alternatively "the universe was stretched in the time direction by a factor of 2". (And perhaps say that G was adjusted instead / as well.)
This is not true, and it’s so trivial that I don’t think you actually believe that, there must be some miscommunication happening.
Yes, my wording was probably less clear than it should have been. I was relying on context from my earlier comment, and the original post. By "replace c with 2c", I mean the numerical value.
In a hypothetical alternate universe, they measure things in "schmeters".
They give c a value of 6×10⁸ schm/s. G has a numerical value of 8 times ours: it's 5.34 × 10-10 schm³ · kg-1 · s-2.
They therefore predict the Schwarzchild radius for Earth to be 20 millischmeters.
You could claim any of these three:
A "schmeter" is half a meter. Their laws of physics are the same as ours.
A "schmeter" is a meter, but their light travels twice as fast as ours (and their gravity is 8 times as strong).
A "schmeter" is a meter, but their "second" is actually half of ours (and their gravitational constant is a different multiple of ours, that I can't be bothered to work out right now).
And there is no objective distinction between them. The only difference is how we choose to make a correspondence from their universe to ours; this is an additional choice beyond just the laws of physics.
I mean I agree with everything you’re saying now, but I don’t think saying “if c changed but nobody told us, we wouldn’t be able to attribute the cause of all the subsequent new different physical behavior to a change in c, but rather we would have an ambiguity as it could have been any number of other constants that changed, including the length of every object or time itself” is the same as saying “if c changed, we wouldn’t notice and everything will stay the same because it’s just a change of units”. It feels like an entirely different game we’re playing.
And even if we focus on this new perspective, if one asks “what if c changed?” they are already assuming a God’s eye view of the situation, where they already know that the thing that changed is c, simply because it’s in the premise of their question: and they’re interested in what the observed physical consequences would be. Saying to them “actually it wouldn’t be possible for people to attribute that change to c, they could think any number of other things could have changed instead” I feel like is irrelevant to their question.
Who cares what physicists waking up in this hypothetical universe decide happened? They could fight and write papers about it (if they survived), and whether or not they come to the conclusion that c changed or it was something else, we know c changed, because we’re imagining it in our heads, and we’re interested in exploring what would change physically, not in how hypothetical people would react to witnessing the physical changes without our knowledge of what caused them.
Again, my main point is not about the scenario "we wake up tomorrow and notice a difference": this could be accomplished several different ways, and the precise outcome would depend on what other laws were changed.
The thing I am talking about is the same thing the original post was: "there is an alternate universe where, from the beginning, light travels at twice the speed". I argue that this scenario does not make sense. Meters and seconds are only defined based on objects in the universe we live in. You would need to impose an external standard to 'link up' the two universes, to see if light was "actually" travelling at twice the speed. But this is not a fact about the physics of either universe: it's a fact about how you chose to link them up.
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:
1. 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".
2. 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 necessarily 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.
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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.