What speed of light means?

Question

speed of light means moving through space with the same speed you move through time?
or to move "only" through space and not through time?
Does this mean that you exist in two (or more) places at the same time?

Answer 1

The meaning of physical concepts comes from experiments and observations. The earliest observation demonstrating that light isn't an instantaneous phenomenon was Romer's discovery that the timing of observed eclipses of Jupiter's moon Io depends on how far Jupiter is from Earth.

Later experiments sent light pulses on round trips of known distance and measured the time it took. Light behaves as a thing that moves with a definite speed: we call that the "speed of light".

But speed relative to what? All measurements involved observers on Earth, in a similar state of motion. Attempts to figure this out led to Einstein's Special Relativity, and then Minkowski showed that theory could be interpreted geometrically, with every object "moving" through spacetime at the speed of light, but in different directions.

Light remains a phenomenon that is associated with a definite speed in the laboratory. As measurements of that speed improved, the speed of light became known as well as it could be, given the accuracy of distance measurements based in the international length standard, a piece of metal in Paris. So, taking into account relativity, we redefined distance based on an adopted speed of light. Thus, for the last 50 years, our fundamental measurements of both space and time have been based on our best clocks, with space and time thus abstractly the same thing.

It's a lot like mariners measuring location in nautical miles (by measuring star locations in the sky) and depth in fathoms (using ropes or poles). They understood that in theory they were both spatial measurements, but in practice they were different, requiring different tools and concepts.

So, to answer your questions, Minkowski's geometry does not change your normal qualitative experience. You move through time as you age, and through space as you travel. You exist where you exist, not elsewhere. Physical theory does not change the way the world works.