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Time at the Quantum Scale

์–‘์ž ๊ทœ๋ชจ์˜ ์‹œ๊ฐ„

Quantum mechanical foundations of temporal phenomena. Exploring time's nature at the smallest scales of reality.

์‹œ๊ฐ„์  ํ˜„์ƒ์˜ ์–‘์ž์—ญํ•™์  ๊ธฐ์ดˆ. ํ˜„์‹ค์˜ ๊ฐ€์žฅ ์ž‘์€ ๊ทœ๋ชจ์—์„œ ์‹œ๊ฐ„์˜ ๋ณธ์งˆ์„ ํƒ๊ตฌํ•ฉ๋‹ˆ๋‹ค.

Key Features

์ฃผ์š” ๊ธฐ๋Šฅ

๐ŸŒŠ

Wave Function Temporal

ํŒŒ๋™ ํ•จ์ˆ˜ ์‹œ๊ฐ„

Time evolution of quantum wave functions and temporal superposition states.

์–‘์ž ํŒŒ๋™ ํ•จ์ˆ˜์™€ ์‹œ๊ฐ„์  ์ค‘์ฒฉ ์ƒํƒœ์˜ ์‹œ๊ฐ„ ์ง„ํ™”.

๐Ÿ”—

Temporal Entanglement

์‹œ๊ฐ„์  ์–ฝํž˜

Quantum entanglement across different temporal coordinates.

๋‹ค๋ฅธ ์‹œ๊ฐ„ ์ขŒํ‘œ์— ๊ฑธ์นœ ์–‘์ž ์–ฝํž˜.

๐Ÿ“ˆ

Time Operators

์‹œ๊ฐ„ ์—ฐ์‚ฐ์ž

Mathematical operators for quantum time measurements and predictions.

์–‘์ž ์‹œ๊ฐ„ ์ธก์ • ๋ฐ ์˜ˆ์ธก์„ ์œ„ํ•œ ์ˆ˜ํ•™์  ์—ฐ์‚ฐ์ž.

๐ŸŽฒ

Temporal Uncertainty

์‹œ๊ฐ„์  ๋ถˆํ™•์ •์„ฑ

Energy-time uncertainty principle applications in temporal physics.

์‹œ๊ฐ„ ๋ฌผ๋ฆฌํ•™์—์„œ ์—๋„ˆ์ง€-์‹œ๊ฐ„ ๋ถˆํ™•์ •์„ฑ ์›๋ฆฌ ์ ์šฉ.

๐Ÿ”€

Path Integrals

๊ฒฝ๋กœ ์ ๋ถ„

Feynman path integral formulations for temporal trajectories.

์‹œ๊ฐ„์  ๊ถค์ ์— ๋Œ€ํ•œ ํŒŒ์ธ๋งŒ ๊ฒฝ๋กœ ์ ๋ถ„ ๊ณต์‹ํ™”.

๐ŸŒŒ

Quantum Gravity Time

์–‘์ž ์ค‘๋ ฅ ์‹œ๊ฐ„

Integration of quantum mechanics with gravitational time dilation.

์–‘์ž์—ญํ•™๊ณผ ์ค‘๋ ฅ ์‹œ๊ฐ„ ์ง€์—ฐ์˜ ํ†ตํ•ฉ.

Statistics

ํ†ต๊ณ„

โ„
Planck Constant
ํ”Œ๋ž‘ํฌ ์ƒ์ˆ˜
ฮ”Eฮ”t
Uncertainty Relation
๋ถˆํ™•์ •์„ฑ ๊ด€๊ณ„
|ฯˆโŸฉ
State Vector
์ƒํƒœ ๋ฒกํ„ฐ
โˆž
Hilbert Dimensions
ํž๋ฒ ๋ฅดํŠธ ์ฐจ์›

Quick Start

๋น ๋ฅธ ์‹œ์ž‘

import { QuantumTimeTheory } from '@wia/time-003';

const quantum = new QuantumTimeTheory({
  hilbertSpace: 'infinite',
  temporalResolution: 1e-44 // Planck time
});

// Create temporal superposition
const state = await quantum.createSuperposition({
  times: [-1, 0, 1], // seconds relative to now
  amplitudes: [0.33, 0.34, 0.33]
});

// Measure temporal position
const measurement = await quantum.measure(state, {
  observable: 'time-position',
  basis: 'standard'
});

console.log('Collapsed time:', measurement.value);
console.log('Uncertainty:', measurement.uncertainty);