[olla]

Every time some limit is reached in a physics equation, dilation, contraction or even moving in time is taken as a measure to rescue. It all sounds like a convenient method for explaining something we can not explain. It all comes from the fact that time is defined through speed and speed depends on space, thus time cannot describe dimensions not dependant of space.

[snarfy]

I believe you are referring to velocity = distance/time. This is the non-relativistic view of velocity. It makes more sense when you define what distance is.

When you push something with your finger and move it, you do not change it's velocity. You change it's acceleration. It's a small but important distinction. Under relativity, the distance between two points in spacetime is defined by the minkowski metric:

    d = sqrt( x^2 + y^2 + z^2 - (ct)^2 )

Notice time is negative/imaginary. The tl;dr of this is that an object at rest is still has a velocity along the time plane at the speed c, and any non rest velocity is relative to that (which affects d), which is where length contraction comes from. You're right in you can't define one without the other, so it's redefined around the constant c and the minkowski metric. It's why they call it spacetime.

[one-more-minute]

In what sense is time defined by speed? Surely it's the other way around?

Currently the second is defined by a number of oscillations of a known wavelength of radiation, which explicitly avoids any dependence on space / measurement of spatial speed.

[olla]

Isn't wavelength as such dependant on space? It all seems to come together as A is defined by B and B is defined by A.

[one-more-minute]

Yes, but the standard second doesn't depend on wavelength (maybe I should have said "known energy"). You take a Caesium-133 atom, look at it's emission spectrum, isolate the ground state radiation and time a number of oscillations. Of course, the radiation has a specific wavelength/energy, but the calculation doesn't depend on it.

Once you know about time, you can start talking about distance – a meter is defined as the distance light travels in a given time. Given that the meter is defined this way, defining time in terms of speed would be a bit circular.

[olla]

Ok, the time dilation makes actually sense now. So like chemical reactions depend on temperature and pressure, physical reactions (if they can be called this way) are dependant on gravity and velocity (dependance on the last I can not quite get still). By physical reactions I mean the transitions between the ground states that time is defined by.

[one-more-minute]

Sure, local velocity at any rate. If someone goes past you in a rocket, you'll notice that their Caesium radiation is oscillating slower than yours, so their second will appear to take longer than yours.