If Planck's Constant Were Larger than it is?

Question

A. Moving bodies would have longer wavelengths

B. Moving bodies would have smaller energies

C. Moving bodies would have higher speeds.

D. The uncertainty principle would be more significant.

Answer 1

The question is not meaningful.  The value of dimensionful constants is not real in any significant way--it is a relic of the units we use to measure.  You can give the same answer to the question "what if the speed of light changed?"

The only physical constants that matter are dimensionless.  For example, the fine structure constant.  Or the number of planck masses in a proton's mass.  Planck's constant appears in those expressions in combination with other physical quantities.  If you increased h and held the electron's charge, the speed of light, and the permittivity of free space constant, then that would decrease the fine structure constant, which would decrease the strength of the electromagnetic coupling.  If you increased h and held the speed of light and Newton's G constant, that would increase the planck mass.  If you did that and held the masses of particles constant, that would have the impact of making quantum effects more significant.  This would correspond to option d, which I think was where the questioner is naively trying to go with this.  But in all likelihood, the particle masses (which are the result of some unknown interaction--maybe with the Higgs field) are going to be proportional to square root of planck's constant and therefore to the planck mass.  So raising planck's constant doesn't really do anything.

So you just can't take one dimensionful physical constant and ask what would happen if you tweaked it.  The question just doesn't make sense.  To any actual physicist doing quantum mechanics, planck's constant is just 2 pi.  You base your system of units on it.  So it's like asking what would happen to physics if the meter were suddenly half a meter.  Maybe a lot.  Maybe nothing.  Maybe everything would just shrink along with the meter and it wouldn't matter.  Only dimensionless quantities have a real, non-arbitrary value.