Laws of motion are the same in all inertial frames.
In a reference at rest, Newton's equation of motion of a body is d²x/dt².
If a body is in an inertial reference frame moving with a constant velocity k, then its x coordinate becomes x+kt. So, we replace "x" with "x+kt" in Newton's law of motion. Doing that we get d² (x + kt)/dt². We notice that this is equal to d² (x)/dt² which is the equation of motion for a body at rest.
We call this replacement of "x" with "x+kt" as a transformation. Newton's laws of motion do not change with this transformation. In technical words, it is invariant under this transformation.]
Measuring relative to space
- Galilean Relativity or simply Relativity doesn’t hold to these equations. It means that if we replace “x” with “x+kt” in these equations, we get different equations, unlike Newton’s law where we got the original equation back. Thus, Maxwell’s equations are not invariant to space.
- One can derive the speed of the wave with electric and magnetic components. It turned out that the speed of this wave is precisely equal to the speed of light.
- Galilean Relativity or simply Relativity applies only to laws of motion, not to laws of electricity and magnetism.
- From the fact that the wave with electric and magnetic components described by Maxwell’s equation travels at the speed of light — Maxwell postulated that the electromagnetic wave described by his equations is light itself. Light is an electromagnetic wave.
- One could measure the speed of light (electromagnetic wave described by Maxwell’s equations which M called as light) from Maxwell’s equation but the problem was that the equation doesn’t tell — speed relative to which reference frame? Maxwell hypothesised that there exists a medium called ether through which light passes and speed of light given by Maxwell’s equation was relative to this medium. Just like Newton hypothesised an absolute reference frame relative to which objects move, Maxwell’s ether is the absolute reference frame relative to which light’s speed is measured.
- How do we explain the speed of light given by Maxwell’s equations without a reference point?
- Why don’t Maxwell’s equations follow the principle of Relativity?
Einstein and Spacetime
All of us not just have our own positions (x,y,z), we also have our own time. We carry our own time, like we carry our own positions.
Note the transition. Newton considered an absolute reference frame of space relative to which bodies move. For Maxwell, ether was the absolute reference frame relative to which light moves. Einstein discarded both. For Einstein, spacetime is the absolute reference frame relative to which we have to make the observations. In this spacetime framework, speed of light is constant in all inertial reference frames.
- Laws of physical systems don’t change in inertial reference frames.
- Speed of light is the same in all reference frames. Further, nothing in space can travel more than the speed of light.
Intuitive understanding of spacetime
c = distance/time = space/time.
"c" remains constant because as a body gets into motion, length contracts and time slows down (dilates), keeping the ratio of length and time (speed) constant.
“c”, the speed of light is the thread that binds “space” and “time” and makes “space-time”.