Is Planck's Constant Constant, or Does it Vary Through Spacetime?

[Pademelon]

I would like to know whether it is possible that Planck's constant is not constant but varies throughout spacetime. For example if we were to travel linearly 'backward' through spacetime toward the big bang, would Planck's constant decrease until at the big bang singularity, Planck's constant would = 0.

Traveling further 'backward' linearly 'past' the big bang, Planck's constant would be negative and the 'arrow of time' would be opposite to that observed in our part of spacetime, similar to what would be expected within the event horizon of a black hole.

As Planck's constant underpins thermodynamics and quantum theory, this could have profound implications for cosmology.

 

[Sheyr]

There are some interesting theories based on variable constants. Look here http://www.arxiv.org/abs/astro-ph/0511440 and at other papers of John Barrow

 

[Chronos]

A variation in time of Planck's constant would have many observabale effects in the present day universe. It is, however, not impossible it could have varied in the very early universe: and the same goes for alpha. Scientists have good reasons to rule out variation of any fundamental constants beyond current observational limits [z~6].