In the last five decades various attempts to formulate theories of
quantum gravity have been made, but none has fully succeeded in
becoming "the "quantum theory of gravity. One possible explanation
for this failure might be the unresolved fundamental issues in
quantum theory as it stands now. Indeed, most approaches to quantum
gravity adopt standard quantum theory as their starting point, with
the hope that the theory's unresolved issues will get solved along
the way. However, these fundamental issues may need to be solved
before attempting to define a quantum theory of gravity.
The present text adopts this point of view, addressing the
following basic questions: What are the main conceptual issues in
quantum theory? How can these issues be solved within a new
theoretical framework of quantum theory?
A possible way to overcome critical issues in present-day quantum
physics - such as "a priori "assumptions about space and time that
are not compatible with a theory of quantum gravity, and the
impossibility of talking about systems without reference to an
external observer - is through a reformulation of quantum theory in
terms of a different mathematical framework called topos theory.
This course-tested primer sets out to explain to graduate students
and newcomers to the field alike, the reasons for choosing topos
theory to resolve the above-mentioned issues and how it brings
quantum physics back to looking more like a "neo-realist" classical
physics theory again.
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