Are physical constants determined by their observation?

Question

In common interpretations of quantum mechanics, it can only be said that objects exist once I observe them - it is not legitimate to ask where an object was before I observed it.

Does this point of view extend to measurements of physical constants? Do physical constants exist or have definite values before we measure them? Do they have definite values when we aren't measuring them? For example, which of the following statements is correct?

1. A Measurement determines the speed of light
2. The speed of light determines the outcome of a measurement
3. Nobody knows, but somebody will know
4. Nobody will ever know

I think this is a legitimate question, since how could I know that the speed of light is constant, if I am not measuring permanently. Might it only be constant/meaningful to speak of the speed of light the moments I look at it?

Answer 1

Let us divide a calculation in physics into two pieces: the dynamics, which describes how a state changes with time, and the initial conditions, which describes the state at a particular time.

In quantum mechanics, the dynamics are described by a Hamiltonian, $H$. The initial conditions are described by a quantum state, $\psi(t_0)$. We evolve the state at time $t_0$ to a later time $t_1$ with the Hamilton $$ \psi(t_1) = \exp(-iH(t_1-t_0)) \psi(t_0) $$ Of course, in QM there is also measurement, a non-unitary process that isn't described by the Hamiltonian.

Physical constants are not part of a quantum state that is evolving in time; they are constants in the Hamiltonian. We determine physical constants by observing the dynamics. For this reason, the usual philosophical conundrums in QM concerning the existence of something prior to measurement (for example, of the properties of an electron) don't apply to physical parameters in the Hamiltonian.

Answer 2

Some physical constants, such as the speed of light $c$, are not measured but are defined to be a certain value. In the case of $c$, it's defined by way of the current definition of the meter. Other physical constants that are measured are always measured against a like-dimensioned standard. All physical measurements are fundamentally of dimensionless values.