Why was 20.Qe3 so good in Botvinnik-Sorokin? Why was 20.Qe3 so good in Botvinnik-Sorokin?

It doubles the pawns, and doesn’t do much else.
First of all, it was played by Botvinnik, a strong World Champion, and one of the most logical players ever, so it clearly has to do more than just let black ruin the white pawns.

It does many things:


It trades off black’s best piece, the active Qc5, and it cannot be
avoided with Qc7? Nxe5!. Trading your opponent's active pieces is very desirable, and I suspect this was the primary motivation for Botvinnik even looking at Qe3.
Despite the fact that those pawns have been weakened, they control
many critical squares. They are also very hard to get at, so
although they may matter in the endgame, black cannot attack them
anytime soon, and other factors will be much more important.
This is a principle that is not seen often, and often missed by
weaker players, but sometimes when you trade down material when attacking,
particularly, trading off a good defender, it allows the remaining pieces to
strengthen, and they become unopposed. In this case, the doubled
rooks are now monsters, and white’s significant lead in development
is going to show even more.
How does black develop the Bc8? In the game, he chose g4 but soon
actually had to strengthen white’s pawns after all.
Lastly, black is going to have a hard time defending e5, and it is
attacked immediately.


The minor weakness, that black can't even get near, was nothing compared to the weaknesses that were exposed when the black queen was no longer on the board to defend them. In short, the Qc5 was the glue that held the black position together, and without it, there was no defense.

 [FEN ""]
 [Event "URS-ch07 Final"]
 [Site "Moscow"]
 [Date "1931.10.25"]
 [Round "2"]
 [White "Botvinnik, Mikhail Moisevich"]
 [Black "Sorokin, Nikolay Tikhovich"]
 [Result "1-0"]
 [ECO "D60"]

 1. d4 d5 2. Nf3 Nf6 3. c4 e6 4. Nc3 Nbd7 5. Bg5 Be7 6. e3 O-O 7. Bd3 c6 8. O-O a6 9. a4 dxc4 10. Bxc4 c5 11. dxc5 Bxc5 12. Qe2 h6 13. Bh4 Be7 14. Rfd1 Nh5 15. Bxe7 Qxe7 16. Rd2 Nb6 17. Rad1 Qc5 18. Ba2 Nf6 19. e4 e5 20. Qe3 Qxe3 (20...Qc7? 21. Nxe5!) 21. fxe3 Bg4 22. a5 Nc8 23. Rc1 Bxf3 24. gxf3 Ne7 25. Nd5 Nc6 26. Nxf6+ gxf6 27. Rd7 Rab8 28. Kf2 Nxa5 29. Rcc7 Rbc8 30. Rxf7 Rxc7 31. Rxc7+ Kh8 32. Bd5 b5 33. b3 Rd8 34. Kg3 f5 35. Kh4 fxe4 36. fxe4 Rd6 37. Kh5 Rf6 38. h3 Rd6 39. h4 Rb6 40. Kg4 Rf6 41. Ra7 Rb6 42. Re7 Rd6 43. Rc7 Rf6 44. Ra7 Rb6 45. Rc7 Rf6 46. Kh5 Rd6 47. Bf7 Rf6 48. Bg6 Nxb3 49. Kxh6 Rf8 50. Rh7+ Kg8 51. Rg7+ Kh8 52. Bf7 Rxf7 53. Rxf7 Kg8 54. Kg6 Nd2 55. Rd7 1-0