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Lorentz invariance with an invariant energy scale
1Theoretical Physics, The Blackett Laboratory, Imperial College, Prince Consort Road, London SW7 2BZ, United Kingdom.
Physical Review Letters
|May 15, 2002
Summary
This study modifies special relativity by introducing Planck energy as an invariant alongside the speed of light. This modification maintains relativity principles and Einstein
Area of Science:
- Theoretical Physics
- Relativity
- Quantum Gravity
Background:
- Special relativity postulates the constancy of the speed of light.
- The Planck energy represents a fundamental scale in quantum gravity theories.
- Reconciling general relativity and quantum mechanics remains a significant challenge.
Purpose of the Study:
- To propose a modified theory of special relativity.
- To incorporate Planck energy as a physical invariant.
- To ensure consistency with Einstein's theory at low energies.
Main Methods:
- Nonlinear modification of the Lorentz group's action on momentum space.
- Introducing a dilatation alongside boosts to preserve Planck energy invariance.
- Analyzing the structure constants of the associated algebra.
Main Results:
- A modified special relativity where Planck energy is an invariant.
- The Lorentz group's action is modified nonlinearly.
- The associated algebra retains unmodified structure constants.
Conclusions:
- The proposed theory offers a new framework for high-energy physics.
- It suggests modifications to field theory and the equivalence principle.
- This provides a potential pathway for unifying general relativity and quantum mechanics.
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