When discussing how time slows down when you are going very fast, it's always explained with a clock, the clock slows down, cetera.
But is it possible that a human cell, or molecules in general don't necessarily work or slow down the same speed as a clock does?
The clock analogies when explaining Special Relativity work because the clocks we imagine (ie. the ones with ticking hands and a face, or even digital ones) are physical objects built according to physical laws. For example, a mechanical clock depends on a spring's motion, while an electric clock depends on the vibration of crystals.
All physical laws undergo "time dilation" in conceptually the same way: the spring would take "longer" to unwind the same distance, and the crystal would take "longer" to vibrate (the exact details are unimportant). These macro-scale physical effects are in fact macro-scale manifestations of time dilation effects on a quantum-mechanical level, to do with the momenta of subatomic particles. Momentum, of course, depends on time, and so is not exempt from time dilation just because the particle in question exists on a quantum scale.
Cells, molecules, etc. are all made of atoms which are made of subatomic particles. Their functioning depends on the kind of processes just mentioned, occurring at the quantum level. For example, the rate of functioning of mitochondria depends on chemical reaction rates, which in turn depend on the same quantum-level effects. Anything made up of subatomic particles will thus be subjected to time dilation in the same way, so (in identical situations) a human cell would age at the same speed as a quartz clock.
Thoughts along these lines afford us an understanding of an experimentally motivated meaning of time.
It is precisely because the ratios of rates of progression of physical processes are always the same for the same pairs of processes that happen in the same inertial frame that we have a well defined meaning for "time".
The cells of your body will undergo roughly the same number of mitotic splits for every tick of your quartz clock in all circumstances, as long as both share the same frame. My Grandfather's Clock will always number my Grandfather's life with the same number of ticks if both share the same frame. Why this is so is simply an experimentally observed fact.
And the ratio of the number of ticks to my grandfather's life's length changes if they don't share the same inertial frame. The change in ratio is governed by the Lorentz transformation. This is the experimental meaning of the notion of time dilation. It doesn't matter whether this shift is measured by lifetimes or clock ticks: if the pair of physical processes is the same, the ratio will be the same.
It is difficult to think of any plausible, rational reason why say, your leg bones, would age at any different rate than a clock, if you could make one, composed of biological parts.
Time dilation effects everything exactly the same way, humans cells are not exempt, although I am not sure this has ever been tested, as it is impossible to measure cell aging in these conditions.
Clocks are made of atoms, (and molecules) and we know they undergo time dilation, humans are made of atoms, (and molecules), so it seems very , very likely that they undergo the same effect.
If you read about this experiment Time dilation , it will add more details to this brief answer.
