Active Record nil timestamp

I have a table created like shown below.

CREATE TABLE foo(
  id INT PRIMARY KEY AUTO_INCREMENT,
  num INT,
  created_at TIMESTAMP DEFAULT CURRENT_TIMESTAMP,
  updated_at TIMESTAMP ON UPDATE CURRENT_TIMESTAMP
);

After I insert and edit a few values I get the table below.

+----+------+---------------------+---------------------+
| id | num  | created_at          | updated_at          |
+----+------+---------------------+---------------------+
|  1 |   15 | 2020-06-22 11:19:56 | 2020-06-22 11:20:20 |
|  2 |   13 | 2020-06-22 11:19:58 | 0000-00-00 00:00:00 |
|  3 |   14 | 2020-06-22 11:20:01 | 0000-00-00 00:00:00 |
+----+------+---------------------+---------------------+

Then I have the class:

require 'active_record'

class Foo < ActiveRecord::Base
  self.table_name = 'foo'
end

1 Foo.all # => [#<Foo:0x000056314a734188 id: 1, num: 15, created_at: 2020-06-22 11:23:40 UTC, updated_at: 2020-06-22 11:23:48 UTC>, #<Foo:0x000056314a7340c0 id: 2, num: 13, created_at: 2020-06-22 11:23:43 UTC, updated_at: nil>, #<Foo:0x000056314a743f98 id: 3, num: 14, created_at: 2020-06-22 11:23:46 UTC, updated_at: nil>]

2 Foo.where(updated_at: nil) # => []

3 Foo.where.not(updated_at: nil) # => [#<Foo:0x000055aafe3ba6d8 id: 1, num: 15, created_at: 2020-06-22 11:23:40 UTC>, #<Foo:0x000055aafe3ba5e8 id: 2, num: 13, created_at: 2020-06-22 11:23:43 UTC>, #<Foo:0x000055aafe3ba520 id: 3, num: 14, created_at: 2020-06-22 11:23:46 UTC>]

4 Foo.where(updated_at: '0000-00-00 00:00:00') # => []

5 Foo.where.not(updated_at: '0000-00-00 00:00:00') # => []

6 Foo.where("updated_at = '0000-00-00 00:00:00'") # => [#<Foo:0x000056314a8857d0 id: 2, num: 13, created_at: 2020-06-22 11:23:43 UTC, updated_at: nil>, #<Foo:0x000056314a885708 id: 3, num: 14, created_at: 2020-06-22 11:23:46 UTC, updated_at: nil>]

7 Foo.where("updated_at != '0000-00-00 00:00:00'") # => [#<Foo:0x000056314a8d7878 id: 1, num: 15, created_at: 2020-06-22 11:23:40 UTC, updated_at: 2020-06-22 11:23:48 UTC>]

• Foo.all returns all default ('0000-00-00 00:00:00') updated_at columns as nil.
• On line 2 I try to get rows where updated_at is nil by passing a hash then I get an empty array. Then on lines 4 and 5 I try to get rows where updated_at is either '0000-00-00 00:00:00' or not. I still get empty arrays for both queries.
• Passing a string like on lines 6 and 7 seems to work as expected.

+------------------------------------------------------------------------------------------------------------------------------+
| @@global.sql_mode                                                                                                            |
+------------------------------------------------------------------------------------------------------------------------------+
| ONLY_FULL_GROUP_BY,STRICT_TRANS_TABLES,NO_ZERO_IN_DATE,ERROR_FOR_DIVISION_BY_ZERO,NO_AUTO_CREATE_USER,NO_ENGINE_SUBSTITUTION |
+------------------------------------------------------------------------------------------------------------------------------+

+------------------------------------------------------------------------------------------------------------------------------+
| @@session.sql_mode                                                                                                           |
+------------------------------------------------------------------------------------------------------------------------------+
| ONLY_FULL_GROUP_BY,STRICT_TRANS_TABLES,NO_ZERO_IN_DATE,ERROR_FOR_DIVISION_BY_ZERO,NO_AUTO_CREATE_USER,NO_ENGINE_SUBSTITUTION |
+------------------------------------------------------------------------------------------------------------------------------+

+-------------------------+
| @@version               |
+-------------------------+
| 5.7.30-0ubuntu0.18.04.1 |
+-------------------------+

My questions

1. Is it the normal behavior that you get nils when the timestamp is 0000-00-00 00:00:00?
2. Why didn't the code on lines 4 and 5 work as expected?