Arguments referring atomic clock supports time dilation is error, not dilated time:

It's interesting to find that Einstein published his paper on special relativity in 1905 and someone submitted that atomic clocks support time dilation, funny.

When the atomic clock was invented in 1945, how could a paper in 1905 rely on an atomic clock experiment discovered in 1945? Did the author use a time machine?

Listen, the practice is that when someone submits a scientific theory, even in applied science, the author himself has to show valid experimental results to support a claim, such as time dilation.

Obviously the author of Special Relativity never provided valid experimental results in support of time dilation. So author essentially failed to claim time dilation in his paper because he did not provide valid experimental results supporting time dilation when he submitted his paper on special relativity.

So I wonder, how did time dilation come about in the 1905 publication of spatial relativity without a supporting test for time dilation?

Also, the mathematical representation of time dilation that the author gave is bad, for physical gravitational effects or even speed dilating time (which is a mathematical parameter). Physical influences cannot modify conceptual time. Men do not marry a ghost wife!

However, the most interesting fact about the atomic clock mentioned is that it defines the frequency of specific atom representing unit of time in the SI system, and is therefore frequency, not speed or gravitational potential difference, corresponding time.

This means that Relativistic speed  or gravitational potential differences cannot represent time and so nor its dilation, unless they are considered as external influences that can cause distortions of time. Also other effects such as temperature variations or mechanical misalignment of clocks etc.

Neither of these effects causes time dilation but causes errors in the clock oscillation, resulting in timing errors.

This is exactly what my paper showed how time dilation is illegal.

Therefore, the atomic clock is the correct example to represent what is time and what is dominant error, but not time dilation. Time is not something to stretch.

Reference Relativistic effects on phase shift on frequencies invalidate time dilation Ii