Serializable isolation fails even for unrelated rows

Question

I have this table

create table "tasks" (id SERIAL PRIMARY KEY, user_id int REFERNCES "user"(id), title TEXT);

I also created index on "tasks"(user_id)

Then I open two transactions simultaneously. t0 t1.. denote series of time snapshots in increasing order

Transaction 1

begin; --T0
set transaction isolation level serializable; --T2
select * from "tasks" where user_id=1; --T4
insert into "tasks" (user_id, title, content, created_time) VALUES (1, 'abc'); --T6
end; --T8

Transaction 2

begin; --T1
set transaction isolation level serializable; --T3
select * from "tasks" where user_id=2; --T5
insert into "tasks" (user_id, title, content, created_time) VALUES (2, 'abc'); --T7
end; --T9

Transactions 1 succeeds but transaction 2 fails. But if i change the where user_id=? of the select statements to where id=?, it works.

So does SSI allow only unrelated primary key changes and still fails with unrelated indexed columns?

The situation is similar to this question Isolation level serializable not working as expected?. But I have created an index on my column.

Answer 1

Ok, turns out I needed to create more data for my test table, otherwise postgres will opt to use sequential scan instead of index scan and thus causes conflict.