ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ

ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠪᠣᠯ ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠦᠨᠳᠦᠰᠦᠨ ᠣᠢᠢᠯᠠᠭᠠᠯᠲᠠ ᠨᠤᠭᠤᠳ ᠤᠨ ᠨᠢᠭᠡ ᠶᠤᠮ᠃ ᠡᠨᠡᠬᠦᠦ ᠵᠠᠷᠴᠢᠮ ᠢᠢᠠᠷ ᠪᠠᠢᠢᠷᠢᠯᠠᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠬᠣᠣᠰ ᠹᠢᠽᠢᠻ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠨᠤᠭᠦᠳ ᠢ ᠨᠢᠭᠡᠨ ᠵᠡᠷᠭᠡ ᠨᠠᠷᠢᠨ ᠬᠡᠮᠵᠢᠬᠦ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ ᠭᠡᠵᠦ ᠦᠵᠡᠳᠡᠭ᠃ ᠨᠢᠭᠡ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠢᠢ ᠬᠡᠳᠦᠢ ᠴᠢᠨᠡᠭᠡ ᠢᠯᠡᠭᠦᠦ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠬᠡᠮᠵᠢᠨ᠎ᠡ᠂ ᠨᠥᠭᠦᠭᠡ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠢᠢᠨ ᠬᠡᠮᠵᠢᠯᠲᠡ ᠢᠢᠨ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠡᠳᠦᠢ ᠴᠢᠨᠡᠭᠡ ᠪᠠᠭᠤᠷᠠᠨ᠎ᠠ᠃ ᠡᠨᠡ ᠪᠣᠯ ᠠᠯᠢᠪᠠ ᠢᠢ ᠳᠤᠷᠠ ᠢᠢᠨ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠪᠠᠷ ᠬᠡᠮᠵᠢᠬᠦ ᠪᠣᠯᠤᠮᠵᠢᠲᠠᠢ ᠰᠣᠩᠭᠤᠳᠠᠭ ᠹᠢᠽᠢᠻ ᠦᠨ ᠰᠢᠰᠲ᠋ᠧᠮ ᠡᠴᠡ ᠻᠸᠠᠨ᠍ᠲ ᠹᠢᠽᠢᠻ ᠢᠯᠭᠠᠭᠳᠠᠬᠤ ᠭᠣᠣᠯ ᠣᠨᠴᠠᠯᠢᠭ ᠶᠤᠮ᠃ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠢ 1927 ᠣᠨ ᠳᠤ ᠭᠧᠷᠮᠠᠨ ᠤ ᠹᠢᠽᠢᠻᠴᠢ ᠸᠢᠷᠨᠢᠷ ᠾᠠᠢᠢᠰᡝᠨᠪᠢᠷᠭ᠌Werner Heisenberg ᠲᠣᠮᠢᠶᠠᠯᠠᠭᠰᠠᠨ᠃

ᠾᠠᠢᠢᠰᡝᠨᠪᠢᠷᠭ᠌ ᠦᠨ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ

ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠤᠨ ᠬᠠᠮᠤᠭ ᠤᠨ ᠲᠦᠭᠡᠮᠡᠯ ᠵᠢᠱᠢᠶ᠎ᠡ ᠲᠠᠲᠤᠳᠠᠭ ᠬᠡᠪᠡᠷᠢ ᠨᠢ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠦᠨ ᠲᠤᠬᠠᠢ ᠳᠤ ᠶᠠᠷᠢᠭᠳᠠᠳᠠᠭ᠃ ᠡᠭᠦᠨ ᠦ ᠮᠠᠲ᠋ᠧᠮᠠᠲᠢᠻ ᠢᠯᠡᠷᠡᠬᠡᠢᠢᠯᠡᠯ ᠨᠢ:

Δ𝑥⋅Δ𝑝≥ℏ/2​

ᠡ᠊ᠨᠳᠡ:

Δx ᠨᠢ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠳ᠋ᠠᠬᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ᠃

Δp ᠨᠢ ᠢᠮᠫᠦ᠋ᠯᠰ ᠳ᠋ᠠᠬᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ᠃

ℏ ᠨᠢ ᠪᠠᠭᠠ ᠫᠯᠠᠠᠨ᠍ᠻ ᠤᠨPlank ᠲᠣᠭᠲᠠᠮᠠᠯ (ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠦᠨᠳᠦᠰᠦᠨ ᠲᠣᠭᠲᠠᠮᠠᠯ).

ᠡᠨᠡ ᠲᠡᠩᠴᠡᠳᠬᠡᠯ ᠪᠢᠰᠢ ᠨᠢ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠦᠨ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠦᠷᠡᠵᠢᠪᠦᠷᠢ ᠨᠢ ᠶᠠᠮᠪᠠᠷ ᠨᠢᠭᠡ ᠲᠣᠭᠲᠠᠮᠠᠯ ᠤᠳᠬ᠎ᠠ ᠡᠴᠡ ᠢᠮᠠᠭᠲᠠ ᠶᠡᠬᠡ ᠪᠤᠶᠤ ᠲᠡᠩᠴᠠᠭᠦᠦ ᠪᠠᠢᠢᠬᠤ ᠶᠣᠰᠤᠲᠠᠢ ᠢᠢ ᠬᠠᠷᠠᠭᠤᠯᠵᠤ ᠪᠠᠢᠢᠭ᠎ᠠ ᠪᠥᠭᠡᠳ ᠡᠨᠡ ᠨᠢ ᠬᠣᠶᠠᠷ ᠬᠡᠮᠵᠢᠭᠳᠡᠬᠦᠨ ᠦ ᠤᠳᠬ᠎ᠠ ᠢᠢ ᠨᠢᠭᠡᠨ ᠵᠡᠷᠭᠡ ᠲᠡᠭᠦᠰ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯᠲᠠᠢ ᠮᠡᠳᠡᠬᠦ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ ᠭᠡᠰᠡᠨ ᠦᠭᠡ ᠶᠤᠮ᠃

ᠵᠦᠢᠯᠴᠢᠯᠡᠪᠡᠰᠦ

1. ᠳᠣᠯᠭᠢᠶᠠᠯᠢᠭ - ᠪᠥᠭᠡᠮᠯᠢᠭ ᠬᠣᠶᠠᠷᠳᠠᠮᠠᠯ ᠴᠢᠨᠠᠷ: ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠻ ᠲᠤ ᠡᠯᠧᠻᠲᠷᠣᠨ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠪᠥᠭᠡᠮᠰ ᠳᠣᠯᠭᠢᠶᠠᠯᠢᠭ ᠬᠢᠭᠡᠳ ᠪᠥᠭᠡᠮᠯᠢᠭ ᠴᠢᠨᠠᠷ ᠲᠠᠢ ᠪᠠᠢᠢᠳᠠᠭ᠃ ᠪᠥᠭᠡᠮ ᠦᠨ ᠪᠠᠢᠢᠷᠢᠯᠠᠯ ᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠭᠡᠵᠦ ᠦᠵᠡᠵᠦ ᠪᠣᠯᠬᠤ ᠪᠥᠭᠡᠳ ᠢᠮᠫᠦ᠋ᠯᠰ ᠢ ᠨᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠤᠷᠲᠤ ᠲᠠᠢ ᠬᠣᠯᠪᠤᠵᠤ ᠦᠵᠡᠳᠡᠭ᠃ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠢ ᠨᠠᠷᠢᠨ ᠲᠣᠳᠤᠷᠬᠠᠢᠢᠯᠠᠪᠠᠯ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠨᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠪᠣᠯᠬᠤ᠂ ᠬᠠᠷᠢᠨ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠢ ᠨᠢ ᠴᠢᠨᠠᠳᠤ ᠲᠣᠭᠲᠤᠭᠠᠭᠰᠠᠨ ᠪᠥᠭᠡᠮ ᠦᠨ ᠳᠣᠯᠭᠢᠶᠠᠨ ᠤ ᠤᠷᠲᠤ (ᠢᠮᠫᠦ᠋ᠯᠰ) ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠪᠠᠢᠢᠳᠠᠭ ᠡᠴᠡ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠤᠷᠭᠤᠨ ᠭᠠᠷᠴᠤ ᠪᠠᠢᠢᠨ᠎ᠠ᠃
2. ᠵᠥᠪᠬᠡᠨ ᠪᠠᠢᠢᠷᠢᠰᠢᠯ ᠪᠠ ᠢᠮᠫᠦ᠋ᠯᠰ ᠢᠢᠡᠷ ᠬᠢᠵᠠᠭᠠᠷᠯᠠᠭᠳᠠᠬᠤ ᠦᠭᠡᠢ: ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠡᠨᠧᠷᠭᠢ ᠪᠠ ᠴᠠᠭ ᠬᠤᠭᠠᠴᠠᠭ᠎ᠠ ᠭᠡᠬᠦ ᠮᠡᠲᠦ ᠪᠤᠰᠤᠳ ᠬᠣᠣᠰ ᠬᠤᠪᠢᠰᠠᠭᠴᠢ ᠨᠤᠭᠤᠳ ᠲᠤ ᠪᠠᠰᠠ ᠢᠯᠡᠷᠡᠨ᠎ᠡ᠃ ᠵᠢᠱᠢᠶᠡᠯᠡᠪᠡᠯ᠂ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠡᠨᠧᠷᠭᠢ ᠪᠣᠯᠤᠨ ᠡᠨᠧᠷᠭᠢ ᠢᠢ ᠬᠡᠮᠵᠢᠭᠰᠡᠨ ᠴᠠᠭ ᠤᠨ ᠬᠣᠭᠤᠷᠤᠨᠳᠤ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠬᠠᠷᠢᠴᠠᠭ᠎ᠠ ᠦᠢᠯᠡᠴᠢᠯᠡᠳᠡᠭ᠌ :

ΔE⋅Δt≥ℏ2

ᠡᠨᠡ ᠨᠢ ᠡᠨᠧᠷᠭᠢ ᠢᠢ ᠨᠡᠩ ᠪᠣᠭᠤᠨᠢ ᠬᠤᠭᠠᠴᠠᠭᠠᠨ ᠤ ᠬᠦᠷᠢᠶᠡᠨ ᠳᠦ ᠥᠨᠳᠦᠷ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠬᠡᠮᠵᠢᠬᠦ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ᠂ ᠬᠠᠷᠢᠨ ᠡᠨᠧᠷᠭᠢ ᠢᠢ ᠥᠨᠳᠦᠷ ᠨᠠᠷᠢᠪᠴᠢᠯᠠᠯ ᠲᠠᠢ ᠬᠡᠮᠵᠢᠪᠡᠯ ᠴᠠᠭ ᠢ ᠨᠠᠷᠢᠨ ᠲᠣᠭᠲᠤᠭᠠᠬᠤ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠭᠡᠢ ᠭᠡᠰᠡᠨ ᠦᠭᠡ᠃

1. ᠦᠯᠦ ᠰᠢᠯᠲᠠᠭᠠᠴᠠᠯ: ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠤᠭ ᠤᠨ ᠴᠢᠨᠠᠷ ᠪᠣᠯᠬᠤ ᠦᠯᠦ ᠰᠢᠯᠲᠠᠭᠠᠴᠠᠯ ᠤᠨ (non-determinism) ᠲᠤᠰᠬᠠᠯ ᠶᠤᠮ᠃ ᠰᠥᠩᠭᠤᠳᠠᠭ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠲᠤ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠪᠦᠬᠢ ᠦᠵᠡᠭᠦᠯᠡᠯᠲᠡ ᠢᠢ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠳᠦᠷᠰᠦᠯᠡᠳᠡᠭ ᠪᠣᠯ ᠻᠸᠠᠨ᠍ᠲ ᠰᠢᠰᠲ᠋ᠧᠮ ᠦᠨ ᠬᠤᠪᠢ᠋ ᠳᠤ ᠡᠨᠡ ᠨᠢ ᠪᠣᠯᠤᠮᠵᠢ ᠦᠡᠭᠢ ᠠᠵᠡᠢ᠃ ᠻᠸᠠᠨ᠍ᠲ ᠰᠢᠰᠲᠧᠮ ᠢ ᠵᠥᠪᠬᠡᠨ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠤᠨ ᠤᠳᠬ᠎ᠠ ᠪᠠᠷ ᠯᠠ ᠲᠣᠳᠤᠷᠬᠠᠢᠢᠯᠠᠳᠠᠭ᠃
2. ᠤᠳᠬ᠎ᠠ ᠤᠴᠢᠷ ᠨᠢ: ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠲᠠᠯᠠ ᠪᠠᠷ ᠬᠢ ᠻᠣᠫᠢᠨ᠍ᠾᠠᠭᠢᠨ ᠤ ᠲᠠᠢᠢᠯᠠᠪᠦᠷᠢ᠋ ᠳᠤ ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠴᠢᠨᠠᠷ ᠨᠢ ᠪᠢᠳᠡᠨ ᠦ ᠬᠡᠮᠵᠢᠬᠦ ᠬᠡᠷᠡᠭᠰᠡᠯ ᠦᠨ ᠲᠡᠭᠦᠰ ᠪᠤᠰᠤ ᠡᠴᠡ ᠡᠭᠦᠳᠡᠯ ᠲᠡᠢ ᠪᠢᠰᠢ᠂ ᠬᠠᠷᠢᠨ ᠪᠠᠢᠢᠭᠠᠯᠢ ᠢᠢᠨ ᠰᠠᠭᠤᠷᠢ ᠰᠢᠨᠵᠢ ᠭᠡᠵᠦ ᠥᠬᠦᠯᠡᠳᠡᠭ᠃ ᠥᠭᠡᠷ᠎ᠡ ᠪᠤᠰᠤᠳ ᠲᠠᠢᠢᠯᠠᠪᠦᠤᠷᠢ ᠨᠤᠭᠤᠳ ᠡᠭᠦᠨ ᠲᠡᠢ ᠤᠭᠯᠠᠭᠤᠷᠭ᠎ᠠ ᠪᠠᠷ ᠢᠢᠠᠨ ᠨᠡᠢᠢᠴᠡᠬᠦ ᠪᠠ ᠦᠯᠦ ᠶᠠᠯᠢᠭ ᠢᠯᠭᠠᠭ᠎ᠠ ᠪᠤᠢ᠃

ᠲᠣᠳᠤᠷᠬᠠᠢ ᠦᠭᠡᠢ ᠢᠢᠨ ᠵᠠᠷᠴᠢᠮ ᠨᠢ ᠠᠯᠢᠪᠠ ᠹᠢᠽᠢᠻ ᠰᠢᠰᠲᠧᠮ ᠢ ᠮᠠᠳᠠᠭ ᠦᠭᠡᠢ ᠲᠣᠳᠤᠷᠬᠠᠢᠢᠯᠠᠬᠤ ᠪᠣᠯᠤᠮᠵᠢᠲᠠᠢ ᠭᠡᠳᠡᠭ ᠲᠦ ᠵᠤᠷᠰᠢᠭᠰᠠᠨ ᠪᠢᠳᠡᠨ ᠦ "ᠰᠣᠩᠭᠤᠳᠠᠭ" (classical) ᠬᠤᠷᠠᠨ ᠮᠡᠳᠡᠬᠦᠢ ᠢᠢ ᠡᠪᠳᠡᠵᠦ᠂ ᠮᠠᠭᠠᠳᠯᠠᠯ ᠢᠢᠠᠷ ᠳᠦᠷᠰᠦᠯᠡᠭᠳᠡᠬᠦ ᠻᠸᠠᠨ᠍ᠲ ᠮᠧᠻᠠᠨᠢᠭ᠌ ᠦᠨ ᠤᠭ ᠴᠢᠨᠠᠷ ᠤᠨ ᠲᠣᠳᠤ ᠲᠣᠮᠤᠷᠠᠭᠤᠨ ᠢᠯᠡᠷᠡᠯ ᠪᠣᠯᠳᠠᠭ᠃