How do I define a second properly?

[BananaChris]

I recently thought about time.
And I know from my days in school, that a second is determined by the radiation of Caesium-133. But I also know, that the duration of a second depends of where you measure it...like on a planet with a huge mass traveling very fast OR on a planet with low mass traveling slowly.

So I thought, that our second isn't actually a "real" second...it's more or less a "cousin" of a "real" second. Or just the time we have to use because it fits our system?!
So to find out what a "real" second is, we have to get in a system where we don't move and no gravity is pulling us. for example in space (i know there is also some gravity; but at least it is very small so we get as close as possible to a "real" second).

Is this a legitimate thought, or am I completely wrong??Sorry for my english; it's not my mother tongue! ;-)
br Chris

 

[HallsofIvy]

All of those things are addressed in the definition of "second".

According to Wikipedia: "since 1967 the second has been defined as the duration of 7009919263177000000♠9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. In 1997 CIPM added that the periods would be defined for a caesium atom at rest, and approaching the theoretical temperature of absolute zero (0 K), and in 1999, it included corrections from ambient radiation.

As far as a "real second" is concerned, I have no clue what you are talking about. A "real second" is whatever we define it to be.

 

[mfb]

Everyone can measure a second in their reference frame. Different observers won't agree on their clocks, but that is nothing you could fix. Physics is the same in all reference frames, you cannot pick one and say "this is right".

For time-keeping, we have the International Atomic Time, which is based on seconds at sea level on Earth.

 

[f95toli]

Yes, you are sort of correct.

However, you need to differentiate between the second (as defined by the SI) and the TAI/UTC which mfb linked to. The former is always with respect to a reference frame so relativistic effects won't change the results.
That said, relativistic effects do come into play for the UTC. It is not so much of a problem for the current definition of the second. but when the clocks are eventually replaced by optical clocks (which are about 1000x as accurate) it will be an issue. Time synchronization is very active research field and no one has really figures out how to synchronize optical clocks over large distances, one of the problem is indeed how to determine the relative positions of the clocks with respect to the geodesic (the positions changes due to e.g. tidal effects) accurately enough to compensate for relativistic effects.
The UTCis more or less given by averaging the results form lots of clocks from many different countries that report their results to the BIPM outside Paris meaning the distances involved are very large,

 

[StanEvans]

Previously time was measured by the sun and our rotation of it, but like other former SI unit measurements this is unreliable and changes, which is why we sometimes have leap seconds. I believe that the actual second is the duration of 9,192,631,770 periods of radiation of a caesium 133 atom and so this is our attempt to relate a quantity of the natural world to a quantitative measurement.

 

[pixel]

...So to find out what a "real" second is, we have to get in a system where we don't move and no gravity is pulling us. for example in space...

All motion is relative. There is no place in space where you can say you are absolutely at rest.