Ok this might explain it, it might not, or it might be total BS but here goes

The relative speeds depends on the observer, and that relative speed will always be the same. If an observer witnesses light travel past from stand still it will be seen to be travelling at the same speed to an observer, to the extreme, travelling with the light. The quicker the observer travels, the slower time will be, although it will appear normal. So at stand still time will be as normal, and for the observer travelling at the speed of light time will stop meaning it doesn't matter anyway . This I do believe is then proportional in between so travelling very close to the speed of light, time will travel so slow that it would still seem even though there is actually a small difference in speed that the speed of light is the same. Thus explaining speed of light is constant (I hope).

Now the others physical properties are not constant for various reasons, speed of sound affected by speed of travel (doppler effect), weight takes into affect gravitational pull so depends where you are, etc etc

Done