I have completely understood the time dilation topic along with its mathematical derivation and consequences. And we know due to time dilation a person's biological clock slows down.So I am not getting that point how slowing down of time in physical clocks affects the slowing down of our biological clock. I don't think that rate of metabolism inside our body is dependent on frame of reference.Please explain this.Are there any kind of biological explanation to this?
Your body is essentially a clock, ticking at the rate at which you age. Regardless of what reference frame you are in, you always find yourself to be aging at the same rate, so your "biological clock" does not slow down at all. This is your "proper" rate of aging. If however you are in motion with respect to some other observer, the observer will see you aging more slowly than the "proper" rate. So your "biological clock" will appear to have slowed down relative to this observer, and it is in this sense that your "rate of metabolism" depends on the observer.