Is it a reasonable conjecture [as suggested by Lee Smolin] to assume that hbar is proportional to the ....?

Question

... inverse of the square root of N (where N is the number of degrees of freedom in The Universe)?

Thank you for your comments!

.

Answer 1

I don't think there's any way to find out.  However, if you're interested in the idea, you might want to look at the  (now discredited) theories of Sir Arthur Eddington.  

Answer 2

...-Again, You're a few hundred Light Years shy of the Correct Location for finding an Answer to your Question. Try the Hyper-Mathematics Blog- at Harvard...  :)

Answer 3

I think this is a meaningless conjecture for two reasons.

1. sqrt(N) is a dimensionless number. In a sense, everything is proportional to this number.

2. If you are thinking that perhaps hbar is equal to 1/sqrt(N). In that case you must consider that hbar has dimensions and your choice of units would be critical.