Bob: Alice, tell me, why do the fundamental constants have the value they have? Why is the speed of light what it is?
Alice: That is not a very meaningful question.
Bob: What do you mean?
Alice: Physics is the art of mathematically quantifying the universe we live in. So physicists map their observations to numbers. Dimensionless numbers. And as a consequence, all fundamental constants in physics are represented by dimensionless numbers.
Bob: Wo, wo, woo... stop! How can you maintain that in experiments we deal solely with dimensionless numbers? If, for instance, I measure my own length, surely I express the result in some length unit! Length measurements come with the dimension of length, duration measurements come with the dimension of time, and so on. Virtually all measurements in physics are expressed in dimensionfull numbers.
Alice: Indeed, expressing measurements in dimensionfull numbers is a common way of communicating physics results. But we should not forget that this represents nothing more than a useful abbreviation. If I make the statement "my length is 1.7 m" what I really mean is that the dimensionless ratio of my length to the length travelled by light in vacuum during 9,192,631,770 periods of the transition between the two hyperfine levels of the ground state of the caesium 133 atom, equals 1.7 divided by 299,792,458. Really, if you give it some thought, only dimensionless measurements make operational sense.
Bob: But surely the fundamental constants $c$, $G$ and $\hbar$ are all three dimensionfull, and a lot of effort goes into accurately measuring their values.
Alice: If you think about it, also these measurements boil down to quantifying dimensionless ratios.
Bob: How can that be? No matter how you take ratios between these constants such ratios end up being dimensionfull. And you should not forget that these are our most fundamental constants, we have nothing more fundamental that we can use to try and build dimensionless ratios.
Alice: You don't need anything 'more fundamental'. If you are quantifying the three parameters $c$, $G$ and $\hbar$, really what you are doing is specifying units. You are specifying the way you abbreviate the results of physical measurements. There is nothing fundamental associated with such a units specification.
Bob: But the fundamental constants are fundamental. They have an intrinsic meaning and knowing their values represents fundamental knowledge.
Alice: I beg to differ. The values for the three parameters $c$, $G$ and $\hbar$ are purely conventional constructs. Their values act as conversion factors. The term 'fundamental constants' is hardly appropriate here. The only fundamental aspect associated with these conversion factors is the fact that their values are finite. Look at it like this: you can set $c$, $G$ and $\hbar$ all equal to unity. It is very common for physicists to make such substitution. This does not change any of the physics.
Bob: That is not true. If you change the fundamental constants, you change everything. If the speed of light would change, all of physics would change. Suppose the speed of light would be 300,000 mm/s instead of 300,000 km/s. This would cause us to live in a relativistic world. A window seat in an airplane would give a spectacular experience of the laws of relativity.
Alice: If the physics has changed, that means you have changed some dimensionless constants. You have done more than just changing units. Again, physics is all about quantifying dimensionless ratios. There is no other quantification that can be operationalized.
Bob: So you are saying that if I would change $c$, $G$ and $\hbar$, such that no dimensionless ratio changes, there would be no observable consequences?
Alice: try it.