What does it mean for the speed of light to be constant?

An extremely dangerous argument (Einsteinians are careless sometimes):

http://www.forbes.com/sites/startswi...perience-time/
"If all we did was adhere to the Newtonian definition of time - with the notion that time was an absolute quantity - this would be true for absolutely anything in the Universe: everyone, everywhere would experience time passing at the same rate in all circumstances. But if this were the case, the speed of light couldn't be a constant."

Here is where the danger comes from:

https://www.perimeterinstitute.ca/re...essons-quantum
Perimeter Institute: "Quantum mechanics has one thing, time, which is absolute. But general relativity tells us that space and time are both dynamical so there is a big contradiction there. So the question is, can quantum gravity be formulated in a context where quantum mechanics still has absolute time?"

http://arxiv.org/pdf/gr-qc/0610057.pdf
"One one hand, time in quantum mechanics is a Newtonian time, i.e., an absolute time. In fact, the two main methods of quantization, namely, canonical quantization method due to Dirac and Feynman's path integral method are based on classical constraints which become operators annihilating the physical states, and on the sum over all possible classical trajectories, respectively. Therefore, both quantization methods rely on the Newton global and absolute time. [...] The transition to (special) relativistic quantum field theories can be realized by replacing the unique absolute Newtonian time by a set of timelike parameters associated to the naturally distinguished family of relativistic inertial frames."

http://www.hindawi.com/journals/isrn/2013/509316/
"In quantum mechanics, time is absolute. The parameter occurring in the Schrödinger equation has been directly inherited from Newtonian mechanics and is not turned into an operator. In quantum field theory, time by itself is no longer absolute, but the four-dimensional spacetime is; it constitutes the fixed background structure on which the dynamical fields act. GR is of a very different nature. According to the Einstein equations (2), spacetime is dynamical, acting in a complicated manner with energy momentum of matter and with itself. The concepts of time (spacetime) in quantum theory and GR are thus drastically different and cannot both be fundamentally true.."

Pentcho Valev