Chess Blitz vs. Classical Ratings

It is obvious that, for example, Carlsen's 2862 classical rating represents a higher quality of play than his 2948 blitz rating. My question is: how does quality of play scale with time control? e.g. if someone plays as good classical chess as Carlsen plays blitz, what, approximately, would his classical rating be?

Blitz and classical are on different scales, but I will just say 3000 cause I want to.

It should be less than 2862, no? I highly doubt Carlsen gets better as he gets less time.

Ratings pools are relative.  2948 in blitz and 2862 in classic have no actual performance implications at all except relative to others in that pool.  There is only a loose correlation between pools.

If Carlsen were playing in a ratings pool with a million 6 year olds all rated 1000, his rating would cap out at about 1500-1600, and this would also be...relative.

Yes; I understand this; this is exactly the reason I am asking the question.

Let me reword: Suppose, hypothetically, that Carlsen's brain were magically slowed down 95% during a chess tournament, so that he effectively must play blitz. At about what rating would he play?

EDIT: Oh, and I highly doubt there are a million six-year-olds rated 1000. Just saying 

Just find out how Carlsen performs in simuls ;)...

I think if he played classical games like they were blitz, he would be around 2500 rating, or about as good as the worst grandmasters.

There's no easy answer to this question. OTB in my most recent blitz tournament I crushed multiple players rated just over 2000 (my blitz rating OTB in last rating list is high 1700s but I improved a lot since then).

However online I can't focus, play terribly at blitz and constantly blunder, miss tactical chances and make poor decisions. Yet some players play better online.

In classical chess I'm around 2000 strength OTB because I'm a slow thinker, but when I have time to think I tend to make very strong decisions. However some people are relatively worse at classical chess because they rely on intuition and seeing superficial things fast instead of making deep strategic decisions (meaning they might crush someone in blitz who in turn crushes them in classical chess).

Point being everyone has different strengths / weaknesses so what is true for some people is not true for others

Just dug up this post from many years ago. It seems like everybody misunderstood OP's question. I understand the question to be: if how Magnus played blitz were how someone else played in a classical chess, then what would their rating be?
To "there's no easy answer to this question", I think this is perfectly answerable (though i do not know the answer). I have heard of programmatic analyses that estimate what level a player played at.

The only way to know with any certainty is have two grandmasters of approximately the same playing strength with one having 5 minutes on his clock and the other with classical time controls and play a series of matches. I was trying to express this in a post but maybe not that clearly. I don't know if it has ever been done but I believe it would generate a lot of interest for some chess YouTuber.