How can Bitcoin change the world? Let's think of a hypothetical scenario if Bitcoin becomes the world's major (most used + highest market cap) currency one day. How will it change the world? The obvious point is cheaper money transfers, but what about its impact on the global economy? Is a "deflationary" currency better for the world? Is quantitative easing really that bad?
I like this question1 - we don't get many big picture questions. 


  How could Bitcoin change the world?



A mature digital cryptocurrency could reduce trade barriers and thus
increase the rate of productivity dispersion throughout society. As
money is a form of fungible authenticated information2, 
non-proprietary digital money gets to take advantage of the 
information age to rapidly democratise trade with lower 
transactional friction.
It could encourage governments to move towards a more rational global
currency or currency basket for sovereign wealth reserves, trade
imbalances and protection from commodity price shocks. In effect the
phenomena of democratised digital currencies, if not Bitcoin
specifically, could accelerate global cooperation and democracy in
macroeconomic practices badly in need of an overhaul.
It could provide an excellent educational opportunity for teaching
and learning macroeconomics. As the cryptocurrencies are moving
though the stages of currency development so fast as to eliminate
most of the confounding factors of studying more mature currencies
that evolved over several centuries of political and socio-economic
change.
It could enrich a very small minority of early adopters. Depending on
what these early adopters do with their new found wealth, they could
bootstrap other social improvements.
It will probably not result in increased (effective) tax evasion due
to the wide range of levers available to collect tax revenue.
Although an increased informal sector may result in governments
shifting towards regressive taxation such as consumption taxes to
offset the evasion of progressive taxation.
It will probably not result in a cap on the money supply due to the
ability to establish fractional reserve banking on top on any specie
currency if legally permitted. Off-block chain Bitcoin clearing
houses may evolve into fractional reserve banks to avoid on-block
chain costs. In either case, it will not provide an economic solution
to a political problem (deficit spending).
It will not create a libertarian or objectivist paradise. Such a
shift in socio-economic paradigm will require both economic and
social consensus. Cyptocurrencies can provide an economic consensus
only.



  What about its impact on the global economy?


Probable impact: Low to Medium. Possible impact: High. 

It really depends on how willing various cryptocurrencies are to absorb certain "bad" aspects of fiat currencies in order to grow into a major currency with global volume. At current, I don't know what level of actual impact is likely - since you have to predict not just technology but the behaviour of people: Both of those that use or might use Bitcoin and the adaptations of its traditional and contemporary competitors and their mindshare.


  Is a "deflationary" currency better for the world?


A qualified no3.


  Is quantitative easing really that bad?


A qualified no3.

1. In case people think I'm a curmudgeon.
2. Each coin I have is information that the world currently owes me X amount of    goods and services.
3. I can't do these questions justice in an answer primarily about how Bitcoin might change the world. Suffice to say we are currently trapped within a "growth" orientated socio-economic model which is incompatible with non-inflating money supply. The lack of true democratic control over the objectives and priorities of these federalised economic levers is a problem.