Distance time travels per second

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If at the big bang, space and time began, would time not travel at a certain rate? Such as, light travels at 299792458m/sec. The solar system has been here for some 5 billion years and we are looking into outerspace at light that has taken 5 billion years to reach us. Would that not mean that time has reached here twice as quickly (if not more)? would that then mean that time is the fastest that anything can travel, and that light speed can be breeched?
 
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space and time are intimately tied together by the spacetime metric which is analogous to the pythagorean theorem and so Physicists don't talk about space and time as being separate but as an entity spacetime. The expansion of the universe in theory is the expansion of spacetime. It is not dictated by limits like the speed of light but particles traveling within spacetime are.
 
Time does not travel anywhere. Time is what a clock measures. A clock is an instrument with three basic parts: an oscillator, a counter, and a display. In the macroscopic world time has a direction which is forward, it continues forward at 1 sec/sec. Time is a measure of the "distance" between events.
 
Space and time are not "things" that move around and interact, they are the framework or background by which we are able to label systems of objects and how they move and interact. As such neither space nor time can move, attain velocities, accelerate, etc. All these happen to objects within spacetime such as an electron or proton.
 

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