Phần III: Động lực học tương đối tính
1. Phương trình cơ bản của động lực trong cơ học tương đối tính.
Ta hãy xét các phương trình cơ bản của cơ học. Dĩ nhiên các phương trình cơ bản của cơ học Newton bất biến với phép biến đổi Gallilei sẽ không bất biến đổi với phép biến đổi của thuyết tương đối, ta phải biến đổi dạng của những phương trình đó cho thích hợp.
Kết quả là, Einstein đã giả thiết rằng nếu đa vào định nghĩa mới xem xung lượng như là , trong đó m là khối lượng tương đối tính.
Thì các định luật cơ bản của động lực học trong cơ học tương đối tính giữ nguyên dạng như trong cơ học Newton, cụ thể là độ biến thiên xung lượng của chất điểm bằng xung của lực tác dụng : , hay
![](data:image/png;base64,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)
Kết hợp (3.1) và (3.2):
Trong công thức (3.1) và (3.2) , v là vận tốc của vật đối với hệ K, còn m0 là khối lượng nghỉ, tức là khối lượng của vật khi vận tốc của nó rất nhỏ so với c, m là khối lượng của vật đối với hệ K.
Trong cơ học cổ điển, khối lượng là lượng bất biến, là số đo lượng vật chất chứa trong vật. Ở đây, Einstein đã quan niệm rằng khối lượng là số đo mức quán tính của một vật, là đặc trưng của sự hấp dẫn. Khối lượng không phải là số đo lượng vật chất, vì vậy khi vật chuyển động với vận tốc lớn, quán tính của nó, tính hấp dẫn của nó tăng, không phải là lượng vật chất tăng.
Công thức (3.1) còn chứng tỏ rằng vật không thể có vận tốc lớn hơn vận tốc ánh sáng, bởi vì khi , điều đó không thể được.
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