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普朗克质量

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预备知识
平方根
约化普朗克常数
真空中光速
引力常数

普朗克质量质量自然单位,常记为,是粒子的约化康普顿波长等于史瓦西半径的一半时的质量(此质量的约化康普顿波长为普朗克长度,而史瓦西半径则是2个普朗克长度)。

2010年CODATA所建议的普朗克质量值为:2.176 51(13) × 10-8千克,圆括号中的部分是要显示最后几位数字的不确定性—亦即数值为21.7651 ± 0.0013 微克。

粒子物理学宇宙学常用到约化普朗克质量,为普朗克洛伦兹-亥维赛单位制的质量单位,其值为:

≈ 6.1397 微克。

加上因子可以简化引力中的数个方程

不像其他多数的普朗克单位,普朗克质量的尺度对人类而言或多或少是能够体会的,因为它大约是跳蚤质量的四千到五千分之一。当所讨论的尺度与粒子的史瓦西半径相当时,由于质量造成的时空弯曲比较明显。而康普顿波长代表粒子的量子不确定性起作用的范围。当粒子的质量小于普朗克质量时,由于不确定性的作用范围超过史瓦西半径,点粒子不会坍缩成黑洞,因此普朗克质量可以认为是黑洞的最小质量。目前发现的基本粒子质量都远远小于普朗克质量。

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普朗克质量
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