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Quantum mechanics allows the calculation of properties and behaviour of physical systems. It is typically applied to microscopic systems: molecules, atoms and sub-atomic particles. It has been demonstrated to hold for complex molecules with thousands of atoms,[4] but its application to human beings raises philosophical problems, such as Wigner's friend, and its application to the universe as a whole remains speculative.[5] Predictions of quantum mechanics have been verified experimentally to an extremely high degree of accuracy.[note 1] A fundamental feature of the theory is that it usually cannot predict with certainty what will happen, but only give probabilities. Mathematically, a probability is found by taking the square of the absolute value of a complex number, known as a probability amplitude. This is known as the Born rule, named after physicist Max Born. For example, a quantum particle like an electron can be described by a wave function, which associates to each point in space a probability amplitude. Applying the Born rule to these amplitudes gives a probability density function for the position that the electron will be found to have when an experiment is performed to measure it. This is the best the theory can do; it cannot say for certain where the electron will be found. The Schrödinger equation relates the collection of probability amplitudes that pertain to one moment of time to the collection of probability amplitudes that pertain to another. One consequence of the mathematical rules of quantum mechanics is a tradeoff in predictability between different measurable quantities. The most famous form of this uncertainty principle says that no matter how a quantum particle is prepared or how carefully experiments upon it are arranged, it is impossible to have a precise prediction for a measurement of its position and also at the same time for a measurement of its momentum.

INTO JAPANESE

量子力学では、物理システムの特性と動作を計算できます。通常、分子、原子、亜原子粒子などの微視的システムに適用されます。数千の原子を持つ複雑な分子に適用できることが実証されていますが [4]、人間への適用は、ウィグナーの fr のような哲学的な問題を引き起こします。

BACK INTO ENGLISH

Quantum mechanics allows us to calculate the properties and behavior of physical systems. It is usually applied to microscopic systems such as molecules, atoms and subatomic particles. Although it has been demonstrated to be applicable to complex molecules with thousands of atoms [4], its application to humans is a philosophical question like Wigner's fr.

INTO JAPANESE

量子力学により、物理システムの特性と動作を計算できます。通常、分子、原子、素粒子などの微視的システムに適用されます。数千の原子を持つ複雑な分子に適用できることが実証されていますが [4]、人間への適用は、Wigne のような哲学的な問題です。

BACK INTO ENGLISH

Quantum mechanics allows us to calculate the properties and behavior of physical systems. It is usually applied to microscopic systems such as molecules, atoms and subatomic particles. Although it has been demonstrated to be applicable to complex molecules with thousands of atoms [4], its application to humans is a philosophical question like Wigne's.

INTO JAPANESE

量子力学により、物理システムの特性と動作を計算できます。通常、分子、原子、素粒子などの微視的システムに適用されます。数千の原子を持つ複雑な分子に適用できることが実証されていますが [4]、人間への適用は、Wigne のような哲学的な問題です。

BACK INTO ENGLISH

Quantum mechanics allows us to calculate the properties and behavior of physical systems. It is usually applied to microscopic systems such as molecules, atoms and subatomic particles. Although it has been demonstrated to be applicable to complex molecules with thousands of atoms [4], its application to humans is a philosophical question like Wigne's.