Take a look at this addition to Special Relativity:
Doubly special relativity
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Now, doubly special relativity, proposes that not only is the speed of light always the same regardless of your frame of reference, but Planck units of mass and energy are also always the same. This means that relativistic effects (like mass appearing to increase on the train) do not occur at the Planck (i.e. very small) scale – although at larger scales, doubly special relativity should deliver results indistinguishable from conventional special relativity.
It turns out that at the Planck scale e = m, even though at macro scales e=mc^2. And at the Planck scale, a Planck mass is 2.17645 × 10^-8 kg ... supposedly the mass of a flea’s egg … and has a Schwarzschild radius of a Planck length … meaning that if you compressed this mass into such a tiny volume, it would become a very small black hole containing one Planck unit of energy.
To put it another way, at the Planck scale, gravity becomes a significant force in quantum physics. Although really, all we are saying that is that there is one Planck unit of gravitational force between two Planck masses when separated by a Planck length … and by the way, a Planck length is the distance that light moves within one unit of Planck time!
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Here we go … those damned mathematicians at it again ….
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It all sounds terribly exciting, but this line of thinking has been criticized as being just a trick to make the math work better, by removing important information about the physical systems under consideration.
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Interesting article. The idea that a Planck length can be considered an invariable constant independent of an observer’s frame of reference, whilst light speed isn't, is one of those counterintuitive thingys ..
Cheers