Time Dilation, Clocks, & Gravity

[Pushoam]

In the rest frame , the measured time interval is the time elapsed between the two ticks (so two events T1and T2) of one clock.
In moving frame,the time elapsed between the two ticks T1and T2 are measured by the two synchronized clocks kept at two different places x'₁ and x'₂.
The information that the rest clock has ticked first time reaches to the clock at x'₁ at some time say t'₁ and the information that the rest clock has ticked the second time reaches to the clock at x'₂ at some time say t'₂.
The information reaches in such a way that t'₂ - t'₁> t₂ -t₁.
If the information can travel with infinite speed , there will be no time - dilation.

But in this case , for different kinds of clocks e.g. sound and light clock, time dilation should be different.
So, this reasoning is wrong.
Should I simply take it for granted that time - dilation is property of space - time?

 

[FactChecker]

The only reason to imagine time dilation was all the experiments that measured the speed of light as the same no matter what inertial reference frame the measurement instruments were in. That is why the time dilation is tied to the speed of light. The same can not be said about the speed of sound. The argument for time dilation must reference the constant speed of light or it is flawed. Just talking vaguely about "information" is not enough.

 

[Mister T]

The phrase "speed of light" refers to the speed, not the light. This speed is the fastest speed possible because it's the speed that's the same in all inertial reference frames. Thus information cannot travel faster than this speed, and that is the crux of this argument. It has nothing to do with the fact that light happens to have this speed. If we were to discover that light travels slower than this speed it woud change nothing in the theory. We'd just refer to $c$ as the invariant speed rather than the speed of light, as many people already do so as to avoid these types of misunderstandings.

 

[FactChecker]

The phrase "speed of light" refers to the speed, not the light. This speed is the fastest speed possible because it's the speed that's the same in all inertial reference frames. Thus information cannot travel faster than this speed, and that is the crux of this argument. It has nothing to do with the fact that light happens to have this speed. If we were to discover that light travels slower than this speed it woud change nothing in the theory. We'd just refer to $c$ as the invariant speed rather than the speed of light, as many people already do so as to avoid these types of misunderstandings.

Good point. Light was the focus of the experiments, but it was not specifically essential to the theory. But neither was "information". The OP puts too much reliance on information speed regardless of means of transmission. Comparing information transmitted electromagnetically with information transmitted by sound is very wrong for understanding SR.