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On December 31st, 1974, The clocks struck midnight in Wizarding Britain - and peculiar things started happening. Most noticeable - depending on the area - were aurora borealis-like lights, strangely south, and all clocks started to wind backwards, most of them eventually breaking.
Those in Wizarding areas were unlikely to notice any additional changes - the buildings are old, well-built. The same in the 70's as they had been in the 30's, so any news of a Time Warp seemed far-fetched and ridiculous.
Those outside of Wizarding Areas, however, found themselves, all of a sudden, standing in the exact same spot - 38 years earlier. Housing estates seemingly dissipated into thin air; interiors dated, and strange people lived in these houses and they weren't happy (and were most likely terribly confused as to how and why this random stranger was now taking up space in their abodes) to see the time-travellers.
All that was magic had slid back in time - leaving the muggles and all the muggle innovation behind. This meant that muggleborn (or muggle-related) sons and daughters found themselves separated from their parents without explanation - and now all the newspapers were declaring that it was January 1st, 1937.
The Ministry were curiously silent; they offered no explanation for the sudden disappearance of muggles or muggle items; for the lights in the sky; the clocks breaking; the sickness that some suffered after the reversal.
But times had changed, and so had the Ministry.
In August, 1937, the Ministry released a Census, which all persons were legally required to fill out.
In Autumn, 1937, it decreed through the Wizengamot that Blood Status Badges - these are bright red and are marked 'M' or 'H' - must be worn by all Muggleborns and Purebloods, and to not wear them was treason. This law caused outrage amongst the masses; especially as the Ministry then went on to decree that no-one bearing an 'M' badge could work for the Ministry. Blood Status testing ensued, with people found to have declared themselves as the wrong blood status in their census forms being put to Wizengamot Trial.
In January, 1939, after the assassinations of Ellerie Malthus and Lysander Ellwood-Luxe, the new Minister for Magic and his Senior Under-secretary responded to what they felt to be threats from the Muggleborn community and their sympathizers by:
Closing Magical Borders - WiSA permission - the wizarding equivalent of a Visa - is required to leave Wizarding Britain for Muggle Britain, and Britain all together. Of course, people are free to leave without one - but they face exile for doing so.
Requiring retail vendors to apply for a license to sell goods to muggleborns.
Banning several potions, including Felix Felicis and Polyjuice Potion.
Banning prank items which could be used to distract and/or conceal.
These laws have since been repealed, but the damage still lingers.
Young muggleborns were assigned Orphanages by the ministry, the biggest and best known of which was attached to St. Mungo's Hospital. They were forced to wear badges; they were subjected to racism from people of more magical backgrounds; and they were forcibly segregated in many ways, whilst left underrepresented in the Ministry.
Muggleborns at Hogwarts School might've taken interest in FEW - For the Equality of Wizards. FEW is a group set up by Charles Kedding with help from Cedric Galyn, and it's cause is for the removal of the blood status badges.
Older Muggleborns and sympathizers took their protests to the Ministry.
For some purebloods, the Time-Warp remained a confusing myth. This is because, as time moved on and everyone assimilates into the 30's / 40's, memories of the 70's have warped or changed. For example, you might remember your first kiss; you might remember it took place in a cinema (or picturehouse, as they were called); but you won't remember the style of clothing you were wearing, or what film you were seeing. Similarly, you might remember dancing, but you won't remember the song.
Some more clued-up purebloods believe the Time-Warp Theory.
Following the time-warp, the magical defence charms around Wizarding Germany disappeared, leaving them exposed to Nazi German Muggles. They joined forces, and so Muggle politics began to threaten the Wizarding World.
Wizarding France, whilst still defended, took to being Muggleborn Sympathizers. Beauxbatons - previously an elitist school - began to positively discriminate muggleborns, and the French were offended by Britain closing their borders. This led them to start researching into Time Warp Theory - which they begun to blame on the British Ministry of Magic - and they aligned with Wizarding Germany. This separated Muggle France - which was aligned with Britain - and Wizarding France. Beauxbatons Academy became a base for the Gestapo in Cannes.
The time-warp diffused slowly from it's origin in London. It took a total of twelve hours to complete, with Australia being the last country to be affected.
Some believe the time-warp happened; some don't.
Everyone who is currently alive has either witnessed 1974, or was born after the time-warp.
The 'warp' itself was really more of a 'slide' - it pushed everything in Wizarding history back 38 years, for example, the publication of a (wizarding) book in 1968 became a book published in 1930. Someone born in 1960's birth certificate read 1922 instead.
Muggle items which weren't around before 1937 disappeared.