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[Phys-l] Double ( or Deformed) Special Relativity




Linked below is an excellent summary paper on Double Special Relativity. DSR
while not as glamorous as string theory ( which got its own PBS special
which neglected to mention all the other approaches to a Quantum gravity theory)
is a modest effort to modify the Relativistic transformations between inertial
observers when taking into account the possibly discrete nature of space
time once gravity is considered for inertial frames.

The basic idea is that the dispersion relationship needs additional
invariants , the Planck scale parameters of energy, the Planck length and Planck
time. Actually DSR is a name for several different approaches to deform the
Lorentz transforms to include these Planck scale parameters as additional
invariants. While there is no agreement on the exact form the new dispersion
equation would take it's basic structure would likely be

c^4*m^2=E^2-P*c^2+ f(E,E_qc,P^2)

Where E_qc would be either the Planck scale or possible the string
scale.

So the modified transform equations might look like

E= gamma*m^c^2/ ( 1+ gamma&M^c^2/ E_qc)

t= t_0/ (gamma-gamma*t_qc/t_0)


L= L_0/ (gamma-gamma*L_qc/L_0)

This model makes contact with observation in that space time becomes a
dispersion inducing background for wave packet propagation predicting a
anomalous dispersion for light , an observable effect. For this and other reasons
DSR is a far less theological approach toward a quantum theory of gravity then
string theory and more conservative than other approaches like Loop Quantum
Gravity. DSR appears compatible with one model of noncommutative space time
where

[ x_j,t]= i*lambda*x_j and [x_j,x_k] = 0



The effects predicted by the various DSR models may possibly be detected
by GLAST and the Pierre Auger Observatory in the next few years.

Bob Zannelli


_http://arxiv.org/abs/gr-qc/0210063_
(http://arxiv.org/abs/gr-qc/0210063)








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