It is quite inaccurate to say this. The correct way to phrase this is that the speed of light is 1/sqrt(permeability * permittivity) of the medium through which the light is traveling.
For a perfect vacuum, these two properties of that vacuum give a result as specified above. For other specified medium, you will get a different value, which could be greater than or less than the above figure.
Little technicalities matter in such cases, as it opens up the discussion. Part of that discussion is that solar space or interstellar space or intergalactic space will have distributions of matter that can alter what the speed of light is away from the assumed perfect vacuum speed of light.
Simple assumptions such as perfect vacuum are quite likely to affect how accurate our models of the universe are. The problem for us is that we are here and not out there making actual on location measurements of the permittivity and permeability of the relevant regions. The assumptions made in our models can come back and bite us in the long term.
Now as for the models we use currently for proton and neutron structure, there are assumptions here that could well be misleading us even though our models appear to work. There are alternate models available (since at least the early 20th century) which have, as far as I know, not been investigated with any detailed effort. Now, of course, it doesn't mean that these alternatives are actually viable, but we don't really know at this time.
The obvious way in which those constants are arbitrary is that the meter is just a random length we compare other lengths to (and the gram is an arbitrary mass we use). So, the precise numbers are only meaningful as part of a system built on these units
"Since 2019 the metre has been defined as the length of the path travelled by light in vacuum during a time interval of
1/299792458 of a second, where the second is defined by a hyperfine transition frequency of caesium."
Some of you are talking past each other. The speed of light being exactly the number c is arbitrary, because the choice to use the ephemeris second as the base unit of time (regardless of the precision we get by now using cesium atom “beats”) is arbitrary even though it’s based on something real. That’s just standardizing our arbitrary choice.
The charge of an electron is also effectively arbitrary for the same reason. We can have our units based on whatever real thing we want.
What isn’t arbitrary is that, whatever units we use and whatever number we arrive at for the charge of the electron, it true that the quark charge units are (1/3)e. Thus, as the poster pointed out there is a fundamental difference in asking why it works out that way compared to asking why the speed of light is a particular derived number.
tldr: The poster above is wrong about his claim that it’s like asking “Why is the speed of light…” because he’s comparing a number to a relationship.
OP: "It’s essentially asking why is the speed of light 299,798,452 m/s or the gravitational constant 6.67x10-11 Nm2/kg2
I’m sure a universe could work with those constants varied but that’s the one we have in our universe.
There could be hypothetical universes with protons being half of electron and atoms would have twice the protons.
However the fundamental constants are just that. A number that allows us to reason about how the universe works.
As to why the number is that, gotta ask your God why they chose that specific value."
And so the post I responded too said these constants are totally RANDOM / ARBITRARY.
But they cannot be otherwise the universe wouldn't work (as far as we know).
The measurements or units we use to express these are arbitrary-- but the constants themselves are DERIVED from the system we call the universe. Without them the system wouldn't work.
As I said, people were talking past each other. I don’t agree with the guys argument as to why that matters. I just don’t agree with your explanation.
My objection to your post is that the meter being defined based on physical reality isn’t meaningful. It isn’t the same thing as saying “the speed of light is c because c is the speed of light and we’ve derived it to be c (in our system of units).”
The relation between the meter as defined and the speed of light isn’t arbitrary. But the value of c in terms of meters isn’t really privileged compared to the value of c in parsecs: both numerical values are only the number they are because you’ve picked an arbitrary unit to measure them by.
Right. It's not so much that the speed of light itself is arbitrary, it's that the number 299,798,452 is arbitrary. Humans picked it because they liked those units for distance and time.
If we had two different types of universal-constant speed, we could measure the ratios between them. But there's only c.
Charges of elementary particles, on the other hand, we do have multiple examples. And whether we call an electron "-1" or "4895", there is an exact ratio between different particles that is an intriguingly simple number.
The ratio being such a simple number tells us something about the universe, in the way that most constants don't.
Or to put that another way, "299,798,452" is derived from both facts about the universe and arbitrary human choices. "1/3" is only derived from facts about the universe. It being such a simple number then begs for explanation, because humans didn't intervene to make it such a simple number.
And on top of that, if the speed of light or gravitational constant changed by .00001, nothing would happen. If the electron and proton didn't match perfectly, a ton of stuff would break.
Or, there's some more fundamental rule that's being followed that we haven't discovered yet that explains these numbers.
Physicists have been searching for the Grand Unified Theory since forever, and so far, no real luck. The closest is something i'm not too familiar with called M-theory (which is a derivative(?) of string theory).
'Grand Unified Theory' or the 'Theory of Everything' is to unite Quantum Mechanics with General/Special Relativity.
At scale of things in space (asteroids, planets, satellites, stars, galaxies) - We only need two constants (speed of light, and gravitational constant). The spacetime fabric bending explains everything we see at the scale. Things are very deterministic and have been verified with tons of experiments for decades around the globe.
At the quantum scale, gravity is an extremely weak force but it is still there. We have planks constant (h), elementary charge (e), speed of light.
You are right, that someday we may derive gravitational constant from another elementary particle constant.
I’m sure a universe could work with those constants varied but that’s the one we have in our universe.
There could be hypothetical universes with protons being half of electron and atoms would have twice the protons.
However the fundamental constants are just that. A number that allows us to reason about how the universe works.
As to why the number is that, gotta ask your God why they chose that specific value.