You should at least try to quote me accurately. I've said the basis for the GPS has been around for 50 year. Not that the systems itself has. If we use a current scientific majority consensus, the earth has been around for what? 12 Billion years? What is 50 years to that? Your statement that our Global Positioning Systems (which is effected by HEIGHT, not Speed) proves that the speed of light was the same 10,000 years ago does not establish your belief.
Science can't actually prove that the sun will be there tomorrow let alone that the light from the sun tomorrow will travel at the same speed as it does today. It's a reasonable assumption though. In my lifetime I've not known of any evidence of any change to the speed of light. But then, does that mean that light traveled precisely at 299,792,458 m/s 10,000 years ago?
Let's assume it didn't for the sake of argument. Now it's your turn. Show how a change in the speed of light in times past would negate our ability to use Energy=8.987551787 E16 meters /second times Matter equation.
You're trying to say that if the speed of Light were different 10,000 years ago (or any arbitrary time in the past) our GPS and our Nuclear Reactors would not work. Based on what? Your belief? So far, you've established that the speed of light has no appreciable change in the past few decades. I will of course admit that any new speed of light, even if the change were just a few parts per billion, would seriously throw off the accuracy of GPS.