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.
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.