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Andre' Quanta
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Starting from the general expression of the metric in coordinates, what is the time misured by a clock in a non inertial reference sistem?
wabbit said:The clock measures proper time, which is in essence the metric itself ##\tau=\int ds=\int\sqrt{g_{ij}dx^idx^j}## (using c=1 units).
Andre' Quanta said:Starting from the general expression of the metric in coordinates, what is the time misured by a clock in a non inertial reference sistem?
Andre' Quanta said:I still have problem in defining the time in a curved space-time.
What i read from wabbit is the expression of the proper time in a general coordinates, but this is only the time measured by a free falling observer, what i need is a more general definition of time, not only for free falling observers.
Anyway if that expression is true, what rapresents the differential of dx-mu (dt, dx, dy, dz) related to the clock in that reference system (locally)?
I need an operative way to the define the time of the clock starting from that expression: if i can t say that the dx mu is physical, what do they rapresent?
Andre' Quanta said:What i read from wabbit is the expression of the proper time in a general coordinates, but this is only the time measured by a free falling observer, what I need is a more general definition of time, not only for free falling observers.
Andre' Quanta said:I still have problem in defining the time in a curved space-time.
What i read from wabbit is the expression of the proper time in a general coordinates, but this is only the time measured by a free falling observer, what i need is a more general definition of time, not only for free falling observers.
Anyway if that expression is true, what rapresents the differential of dx-mu (dt, dx, dy, dz) related to the clock in that reference system (locally)?
I need an operative way to the define the time of the clock starting from that expression: if i can t say that the dx mu is physical, what do they rapresent?
Great minds think alike. And I do, too.Nugatory said:[Rats! Beaten by Ibix!]
Andre' Quanta said:In general relativity i can t say that the time measured by the clock is simply the differential dt in the expression of the metric, because it changes under diffeomorfisms and this means that it is not measurable.
The main difference is that in a non-inertial system, time is affected by acceleration and motion, while in an inertial system, time is constant. This is due to the effects of gravity and the curvature of spacetime in a non-inertial system.
Yes, a clock in a non-inertial system can still be considered accurate as long as it is calibrated and functioning properly. However, the time measured may differ from that of an inertial system.
The Theory of Relativity explains that time is relative and can be affected by gravity and motion. In a non-inertial system, the curvature of spacetime caused by acceleration and motion can cause time to pass at a different rate compared to an inertial system.
Yes, time dilation is a factor in a non-inertial system. This is because the speed of an object in a non-inertial system can affect the perception of time for an observer in an inertial system.
The measurement of time in a non-inertial system is important for understanding the effects of gravity and motion on the universe. It helps us to make accurate predictions and calculations in fields such as astrophysics and cosmology.