## The Einstein's formula proven but it could be just outdated

Experimental proof of the Einstein's famous formula E=mc^2 was given directly and indirectly thousand of times. Every day in particle accelerators Scientists are studying nuclear phenomena using the Einstein's formula and particle accelerators itself have been designed taking into account the Einstein Formula itself.

But could be the Einstein's Formula, E=mc2, generalized in a more general scenario? As it is well established by the Heisenberg indetermination principle the more our instruments approaches high energy the more is possible to investigate short distance. So high energy and short distance are indissolubly interconnected between them by mean of a Scale factor called h-cut (Planck constant).

There are a lot of Theories trying to embed Einstein Special Relativity in a more general theory. The most argue that violation from Special Relativity could occur if we investigate short distances / high energies. Technically speaking when the Energy involved in the experiments is near to the Planck Energy, it is postulated that some changes in the Special Relativity could happen.

### Generalization of the Special Relativity

According to those special relativity violation theories, Special Relativity is an approximation of a more general theory, valid at high energy (The Planck Energy), but embedded in it and still valid at lower energies. Since today instruments can approach many order of magnitude less the Planck Energy we do use special relativity laws in our experiments and everything works fine since it is an approximation whose errors are significantly smaller compared to our instruments preciseness errors.

The situation is equivalent to which of special relativity and newtonian mechanics. Newtonian mechanics explains fine every phenomena until that we approach to investigate phenomena at higher energy compared to the standard mechanics deal with.

### Doubly Special Relativity. Relativity with 2 independent observer scales

We're talking about a new relativistic theory outlined by 2 Italian Physicists and a Polish, based on non-commutative geometry. According to this theory, geometry at high energy is not as smooth as generally thought.

The space-time continuum at high energy could not be smooth but is thought to be discrete and therefore intrinsically quantum. Our vision of standard geometry changes according to new quantum rules.

To give an example consider 2 point in space time. It is argued to arrive from point A to point B following different paths could lead to some new phenomena in respect to our natural geometrical perception.

In a more wide scenario the aim of this new theory would be to start as a building block for a new theory capable to reconcile gravity (The Einstein's General Relativity) with Quantum Theory of the Fundamental Interactions i.e. the building block for a quantum gravity theory.

The results are presented in a famous paper published in 2001 on Physics Letters B, one of the most important scientific journals in physics, and followed by a multitude of papers that have been inspired from it.

Here are the title and the abstract:
Deformed Boost Transformations That Saturate at the Planck Scale
Authors: N.R. Bruno, G. Amelino-Camelia, J. Kowalski-Glikman
We derive finite boost transformations based on the Lorentz sector of the bicross-product-basis $\kappa$-Poincare' Hopf albegra. We emphasize the role of these boost transformations in a recently-proposed new relativistic theory. We find that when the (dimensionful) deformation parameter is identified with the Planck length, which together with the speed-of-light constant has the status of observer-independent scale in the new relativistic theory, the deformed boosts saturate at the value of momentum that corresponds to the inverse of the Planck length.
6 pages, LaTex (revtex)
Subjects:
High Energy Physics - Theory (hep-th)
Journal reference:
Phys.Lett. B522 (2001) 133-138
Among the other achievements obtained in this paper, the most important one is the new space-time transformations, that are valid at the Planck Energy but reduce to the usual Lorentz transformation at low energy and a new formula, valid at high energy, that corrects the famous E=mc2 Einstein's Formula. Thanks to the growing audience around those arguments, I will deeper treat the results of this new theory known as Deformed Special Relativity (DSR) in the future.