| Summary: | We argue that, in a theory of quantum gravity in a four dimensional
asymptotically flat spacetime, all information about massless excitations can
be obtained from an infinitesimal neighbourhood of the past boundary of future
null infinity and does not require observations over all of future null
infinity. Moreover, all information about the state that can be obtained
through observations near a cut of future null infinity can also be obtained
from observations near any earlier cut although the converse is not true. We
provide independent arguments for these two assertions. Similar statements hold
for past null infinity. These statements have immediate implications for the
information paradox since they suggest that the fine-grained von Neumann
entropy of the state defined on a segment $(-\infty,u)$ of future null infinity
is independent of u. This is very different from the oft-discussed Page curve
that this entropy is sometimes expected to obey. We contrast our results with
recent discussions of the Page curve in the context of black hole evaporation,
and also discuss the relation of our results to other proposals for holography
in flat space.
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