Phase velocity faster than light?

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SUMMARY

The discussion centers on the concept of phase velocity in electromagnetic waves, specifically addressing the assertion that phase velocity can exceed the speed of light (c). It is established that while phase velocity can surpass c in certain media, such as glasses at X-ray frequencies, this phenomenon does not allow for the transmission of information at superluminal speeds. The conversation emphasizes that this is a mathematical artifact rather than a physical reality, and encourages a focus on Quantum Mechanics as the foundational theory beyond historical concepts like matter waves.

PREREQUISITES
  • Understanding of phase velocity and group velocity in wave mechanics
  • Familiarity with electromagnetic wave propagation
  • Basic knowledge of Quantum Mechanics principles
  • Concept of monochromatic waves and their properties
NEXT STEPS
  • Study the implications of phase velocity in different media, focusing on electromagnetic waves
  • Explore Quantum Mechanics fundamentals, particularly the transition from classical to quantum theories
  • Investigate the mathematical models that describe wave functions and their velocities
  • Review historical theories in physics, including matter waves and their relevance to modern physics
USEFUL FOR

Students in atomic physics, physicists interested in wave mechanics, and anyone seeking to understand the nuances of Quantum Mechanics and its historical context.

shanepitts
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I am currently taking an undergrads course in atomic physics, and I have just grazed the concepts of matter wave functions, group waves, group velocity, and phase velocity. For the latter, it has been stated that phase velocity can exceed the speed of light. I don't fathom this. Could anyone please help me with this concept?
 
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Per wiki: http://en.wikipedia.org/wiki/Faster-than-light#Phase_velocities_above_c

The phase velocity of an electromagnetic wave, when traveling through a medium, can routinely exceed c, the vacuum velocity of light. For example, this occurs in most glasses at X-ray frequencies.[11] However, the phase velocity of a wave corresponds to the propagation speed of a theoretical single-frequency (purely monochromatic) component of the wave at that frequency. Such a wave component must be infinite in extent and of constant amplitude (otherwise it is not truly monochromatic), and so cannot convey any information.[12] Thus a phase velocity above c does not imply the propagation of signals with a velocity above c.[13]
 
Thanks
 
shanepitts said:
I am currently taking an undergrads course in atomic physics, and I have just grazed the concepts of matter wave functions, group waves, group velocity, and phase velocity. For the latter, it has been stated that phase velocity can exceed the speed of light. I don't fathom this. Could anyone please help me with this concept?

Its purely a mathematical artefact - nothing is really traveling FTL.

Also matter waves was simply an interim theory on the way to full blown Quantum Mechanics that appeared when Dirac published his transformation theory.

Don't spend too long on what is just really of historical interest. Try, as soon as possible, to come to grips with the correct theory. So you understand its REAL basis check out:
http://www.scottaaronson.com/democritus/lec9.html

Your course may not get to this for a while, or indeed at all, depending on its depth, but just keep in the back of your mind this is what QM is REALLY about - the rest is basically historical background.

Thanks
Bill
 
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