I guess that the simplest answer to this would be: 'Yes, everything is quantized.' However,
unfortunately this is one of the biggest problems in modern physics. No-one is really sure
how it should be quantized but the idea of quantized time as well as quantized space and
quantized gravity is part of the elusive theory of quantum gravity.
Some of the best minds in the world have been tackling the problem for years now. Einstein
failed to united quantum theory with his own relativity, Richard Feynman couldn't do it
(although QED was a definite step forwards) and even today some of our most famous
physicists such as Kip Thorne, Stephen Hawking and Roger Penrose are still unable to unite
quantum theory and relativity.
In answer to your question then. Yes, time is theoretically quantized and in an ultimate
field theory it would be a quantized field much the same as the particle fields that we can
already see in unified field theories. However, no-one has yet been able to come up with a
consistent theory of space, time, fields and matter which shows exactly how time is
quantized.
Answered by: Edward Rayne, Physics Undergraduate Student, Cambridge UK
'A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data. God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.'