Are there any proof of the speed of light being constant?
The speed of light is a physical quantity, so it is not subject of a mathematical proof but subject to measurement.
Interesting enough your demand to proof this particular physical statement is like asking for a proof of a mathematical axiom in the realm of mathematics:
If you hit an axiom in mathematics you can not proof it. An axiom is a statement independent from all other axioms and their derived mathematical truths.
In this regard it is a starting point of mathematical reasoning, a fundamental, basic
You can accept a mathematical axiom as true or false and then go away with the more or less interesting or useful consequences of that choice.
The speed of light being constant is a physical principle.
A physical principle is believed to be true and (unlike a mathematical axiom) has to pass all known observations. It shares the fundamental, basic nature of a mathematical axiom in that it is used to derive other physical insights.
All i hear is that light travels at a constant speed because that's an
The famous Michelson-Morley interferometer experiment proved that speed of light did not depend on the orientation of the experiment's axes relative to the earth's movement through space. Which surprised the experimentators themselves quite a lot.
There were clever attempts to explain this observation by mechanical argumentations, e.g. the ether wind compressing the axis similiar to the Lorentz contraction.
Hendrik Lorentz and the great mathematician Henri Poincaré came up with the correct formulas, but not with the correct physics.
The only satisfiying explanation came through Albert Einstein's special theory of relativity.
A and that it fits in a coherent theory with all sorts of
other detailed observations.
Einstein's insight was that the experimental data only made sense if the speed of light is constant in all inertial systems, and that this leads to modifications of the prior known laws for time, length, mass, energy, and addition of velocities.
Is there no like mathematical proof or
something or is it just purely based on observations/measurements
No that would require a identification of the observed physical reality with one of the many possible mathematical universes (and its set of mathematical axioms).
Maybe someone pulls this off in the future, but right now, we are not there.
But even then that identification must be rooted on observation.
why is the speed the same for all observers?
This is a as true believed physical truth, in accordance with all observations.
A physical principle.
Einstein got the credit and not Lorentz or Poincaré, who certainly was the better mathematician, because of his formulations of physical principles.
The physical principles Einstein gave at that time was the
- The special principle of relativity: physical laws should have the same form in all inertial systems (systems at constant speed).
- The speed of light (in vacuum) is constant for every observer, independent of the movement of the light's sources.
From this he was the one to drop the ether hypothesis: Before it was assumed, even by Lorentz and Poincaré, that electromagnetical waves need a mechanical medium which does the vibrating and propagating like the media for water or gas waves.
That hypothetical medium was the ether. The dropping of the ether hypothesis was a physical insight, not a mathematical one.