therefore Δs simply reduces to

因此 Δs 就简化为
c times the time elapsed according to the particle.

c 乘以根据质点所过的时间
So, dτ is the time elapsed according to the particle itself.

dτ 是质点在自身参考系里过去的时间
According to the particle.

是在质点参考系里
That's what we're going to divide by.

那是我们拿来当分母的量
So, it's a very clever way to circumvent the question of

这个方法可以很好地回避
what should I take the derivative respect to.

"我应该对哪个量求导"这个问题
My time and your time all are variable.

我的时间和你的时间都是变量
we don't agree on it.

我们并没有达成共识
But let's ask

但我们可以问
how much time elapsed according to the one thing we are studying,

对于我们共同研究的东西所过去的时间
and let's divide by that time.

并除以那个时间