diff --git a/synapse/storage/schema/main/delta/72/03bg_populate_events_columns.py b/synapse/storage/schema/main/delta/72/03bg_populate_events_columns.py
new file mode 100644
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+++ b/synapse/storage/schema/main/delta/72/03bg_populate_events_columns.py
@@ -0,0 +1,47 @@
+# Copyright 2022 The Matrix.org Foundation C.I.C
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+import json
+
+from synapse.storage.types import Cursor
+
+
+def run_create(cur: Cursor, database_engine, *args, **kwargs):
+ """Add a bg update to populate the `state_key` and `rejection_reason` columns of `events`"""
+
+ # we know that any new events will have the columns populated (and that has been
+ # the case since schema_version 68, so there is no chance of rolling back now).
+ #
+ # So, we only need to make sure that existing rows are updated. We read the
+ # current min and max stream orderings, since that is guaranteed to include all
+ # the events that were stored before the new columns were added.
+ cur.execute("SELECT MIN(stream_ordering), MAX(stream_ordering) FROM events")
+ (min_stream_ordering, max_stream_ordering) = cur.fetchone()
+
+ if min_stream_ordering is None:
+ # no rows, nothing to do.
+ return
+
+ cur.execute(
+ "INSERT into background_updates (ordering, update_name, progress_json)"
+ " VALUES (7203, 'events_populate_state_key_rejections', ?)",
+ (
+ json.dumps(
+ {
+ "min_stream_ordering_exclusive": min_stream_ordering - 1,
+ "max_stream_ordering_inclusive": max_stream_ordering,
+ }
+ ),
+ ),
+ )
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