Массивные частицы

Чтобы сделать определенные выводы о существовании пятого измерения, можно воспользоваться менее прямым способом. Подобно тому как стационарные волновые образования в атоме соответствуют долгоживущим состояниям движения электрона, стационарные волны на окружности в пятом измерении соответствуют частицам, которые в принципе можно обнаружить в лаборатории Волновой пакет должен целиком поместиться на окружности. Следовательно, либо амплитуда волны должна быть постоянной, либо по длине окружности должно уложиться целое число колебаний.

Масса каждой частицы зависит от длины волны, которая равна длине окружности, деленной на число колебаний волны, помещающейся на ней. Чем короче длина волны, тем больше ее энергия и тем больше масса сопоставляемой волне частицы. В теории Калуцы частицам с минимальной массой сопоставляется бесконечная длина волны. Другими словами, амплитуда таких волн в пятом измерении постоянна. Масса таких частиц равна нулю.

Первая массивная частица — это та, длина волны которой равна длине окружности; ее масса обратно пропорциональна размеру окружности. Масса следующей частицы в два раза больше массы первой, так как этой частице соответствует волна, два раза укладывающаяся вдоль окружности в пятом измерении. Таким образом, разрешенному набору стационарных волн можно сопоставить целое семейство частиц с массами, кратными массе первой тяжелой частицы.

Клейн высказал соображения, которые позволяют оценить массу первой тяжелой частицы. Так как теория Калуцы пытается объединить силы гравитации и электромагнетизма, первая тяжелая частица имеет электрический заряд, который тоже обратно пропорционален длине окружности. Заряды всех наблюдаемых частиц есть целые кратные заряда электрона. Если предположить, что первая тяжелая частица несет именно этот заряд, то можно вычислить ее массу. Получающееся значение поразительно велико: масса частицы в 1016 раз больше массы протона, что тяжелее, чем 10 000 бактерий.

 

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