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In relativity and quantum field theory, the vacuum speed of light is assumedto be constant; the range of validity of general relativity is determined bythe Planck length. However, there has been no convincing theory explaining theconstancy of the light speed. In this paper, we assume a five dimensionalspacetime with three spatial dimensions and two local time coordinates givingus a hint about the constancy of the speed of light. By decomposing the fivedimensional spacetime vector into four-dimensional vectors for each timedimension and by minimizing the resulting action, for a certain class ofadditional time dimensions, we observe the existence of a minimal length scale,which we identify as the Planck scale. We derive an expression for the speed oflight as a function of space and time and observe the constancy of the vacuumspeed of light in the observable universe.

The Planck length and the constancy of the speed of light in five dimensional space parametrized with two time coordinates