How Does Doubly-Special Relativity Redefine Space and Time?

[granpa]

http://en.wikipedia.org/wiki/Double_special_relativity

Doubly-special relativity (DSR)— also called deformed special relativity or, by some, extra-special relativity — is a modified theory of special relativity in which there is not only an observer-independent maximum velocity (the speed of light), but an observer-independent minimum length (the Planck length).

DSR is based upon a generalization of symmetry to quantum groups. The Poincaré symmetry of ordinary special relativity is deformed into some noncommutative symmetry and Minkowski space is deformed into some noncommutative space.

http://en.wikipedia.org/wiki/Noncommutative_space

In Mathematics, Noncommutative geometry, or NCG, is concerned with the possible spatial interpretations of algebraic structures for which the commutative law fails; that is, for which xy does not always equal yx. For example; 3 steps of 4 units and 4 steps of 3 units length might be different in noncommutative spaces.



in other words the distance between points a and b can take one of two values depending on how you calculate it. now the math is far beyond me but it occurs to me that one could see this as an explanation for why moving objects contract. the distance across a region of space occupied by an object as seen by the object itself would be different from the distance across the same space as seen by photons.

 

[cristo]

I'm moving this to BtSM, since I think people there will be better suited to comment on this thread.

 

[Entropia]

this difference in perception could be due to the noncommutative nature of space in DSR.

I find the concept of DSR intriguing and potentially groundbreaking. It challenges our traditional understanding of space and time, and opens up new possibilities for studying the fundamental structure of the universe. The idea of a minimum length scale, the Planck length, suggests that there may be a fundamental limit to how small we can measure distances, and this could have implications for our understanding of quantum mechanics.

The application of noncommutative geometry to DSR also offers a fascinating connection between mathematics and physics, showing that seemingly abstract mathematical concepts can have real-world implications. This could lead to further developments in both fields, as well as potential applications in other areas of science.

However, as with any new theory, DSR will require further research and experimentation to fully understand its implications and test its predictions. It is also important to consider how DSR fits in with other theories, such as general relativity, and whether it can be reconciled with them. But overall, I believe that DSR is a promising avenue for exploring the nature of space and time, and has the potential to greatly advance our understanding of the universe.