Doppler effects and relativity

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SUMMARY

The discussion centers on the implications of the Doppler effect and wavefront behavior in a medium moving at relativistic speeds, specifically when the speed of the medium approaches the speed of light (c). It is established that massive particles, such as water molecules, cannot reach the speed of light, and thus sound waves in such a medium would appear to "stand still" when traveling at sound speed (v_sound). The conversation also touches on the complexities of electron movement within atoms in a moving medium, indicating that quantum mechanics may be necessary to fully understand these interactions.

PREREQUISITES
  • Understanding of the Doppler effect in wave mechanics
  • Familiarity with special relativity and the velocity addition formula
  • Basic knowledge of sound propagation in fluids
  • Introduction to quantum mechanics and atomic behavior
NEXT STEPS
  • Research the implications of the Doppler effect at relativistic speeds
  • Study the velocity addition formula in the context of special relativity
  • Explore sound wave behavior in different mediums, particularly at high velocities
  • Investigate quantum mechanics principles related to electron movement in moving frames
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Physicists, students of relativity, and anyone interested in the intersection of wave mechanics and quantum theory, particularly in the context of relativistic speeds.

arnesinnema
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I’ve got a question.

Say we have a medium traveling through a pipe at speed v. The soundspeed of the medium is vs. The speed of the wavefronts to an stationary are approximately v-vs and v+vs when both v and vs are much smaller than the lightspeed c. However what happens when v=c? Do the wavefronts move with apparent speed v-vs and v+0 or do they appear to be frozen i.e. v-0 and v+0.

On a similar note, say an electron is traveling around one of the medium atoms in a plane parallel to the direction of movement of the atom. Say the electron is first placed at the front, can it than move backwards? But will stay there? I.e. it cannot move forwards since than the combined speed (relative to the stationary observer) would exceed the speed of light.
I.e. what happens to the Doppler effect at relativistic speeds?

Admittedly I’m not an expert ;).

Regards Arne Sinnema
 
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However what happens when v=c?

For a medium like water?
Water consists of massive particles (molecules/atoms), which cannot travel at the speed of light.
Nothing massive (m > 0) can reach the speed of light.

If your water goes at ##v_{sound}##, your sound wave should "stand still".

For combined speed you might want to check http://en.wikipedia.org/wiki/Velocity-addition_formula#Special_theory_of_relativity.

traveling around one of the medium atoms

That is not easy to answer, you will probably need quantum mechanics for that.
 

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