Inverse results in special relativity

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SUMMARY

The discussion centers on the relationship between mass, energy, and frequency in the context of special relativity. It highlights the equation for relativistic mass increase, $$\frac{m'}{m}=\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$$, and the corresponding frequency decrease, $$\frac{\nu'}{\nu}=\sqrt{1-\frac{v^{2}}{c^{2}}}$$. The participants clarify that the energy of an object with mass is not equal to the energy of a photon, represented by $$E = h\nu$$, and that the de Broglie wavelength concept does not apply directly to massive objects. The conversation emphasizes the importance of using relativistic formulations, such as the Klein-Gordon and Dirac equations, for accurate descriptions of particles at high velocities.

PREREQUISITES
  • Understanding of special relativity concepts, including relativistic mass and energy.
  • Familiarity with the equations of energy-momentum relationships, particularly $$E = mc^2$$ and $$E = h\nu$$.
  • Knowledge of the de Broglie wavelength and its implications for quantum mechanics.
  • Basic grasp of relativistic wave equations, such as the Klein-Gordon and Dirac equations.
NEXT STEPS
  • Study the implications of the relativistic Doppler effect on frequency and wavelength shifts.
  • Learn about the Klein-Gordon and Dirac equations for relativistic quantum mechanics.
  • Explore the relationship between energy, frequency, and wavelength in both classical and quantum contexts.
  • Investigate the limitations of classical mechanics when applied to relativistic speeds and massive particles.
USEFUL FOR

Physicists, students of quantum mechanics, and anyone interested in the principles of special relativity and their applications in modern physics.

  • #31
But my point is that there is a relativistic analogue of the de Broglie relation. It just relates 4-frequency to 4-momentum.
 

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