Was Planck's constant $h$ the same when the Big Bang happened as it is today? Was Planck's constant $h$ the same when the Big Bang happened as it is today?
Planck's constant :
$$h= 6.626068 × 10^{-34}\, m^2 kg / s,$$
$$E=n.h.\nu,$$
$$\epsilon=h.\nu$$
 A: There is no invariant meaning to the statement that $\hbar$ changes as a function of time. $\hbar$ is a dimensional constant, like the speed of light $c$ and the gravitational constant $G$. The units of $\hbar$ are $kg m^2\over s$, so one way for $\hbar$ to change is that the unit of time was doubled, but everything happened twice as fast numerically (meaning at the same rate with respect to the unit of time) so that all physical times are unchanged, and nothing is different. This would also halve the speed of light and divide G by 4.
To make a unit change which only alters $\hbar$, you can alter length unit and time unit by the same amount (to fix c) and alter the mass unit by the same amount (to fix G). The $\hbar$ is altered without c or G getting altered.
The issues with dimensional constants and the system of units is discussed here: What is the proof that the universal constants ($G$, $\hbar$, $\ldots$) are really constant in time and space? . In order to be precise about what it means for $\hbar$ to change, you have to say relative to which system of units. If you do this, you will be able to translate this to some dimensionless constants changing together in ordinary natural units. If you ask the question about the combination of dimensionless constants changing, it will have an unambiguous answer, and the bounds from experiment will be severe. As it stands, the question is meaningless.
A: A quick Google will find you no end of papers reporting no variation e.g. this one, so there is no evidence for any variation in Planck's constant. I would guess (it's not my area) that any big variation would affect the evolution of the universe and be observable today, so if there was a variation it would have to be small.
There is no theoretical reason to expect a variation on Planck's constant, so although we can't absolutely rule it out, any variation seems unlikely.
