The discussion centers on the relationship between the wavelength of a photon and its energy, exploring concepts from quantum mechanics, wave-particle duality, and the implications of these properties in various contexts. Participants examine the mathematical relationships involved and seek to understand the underlying reasons for these relationships.
Participants express various viewpoints on the relationship between wavelength, frequency, and energy, with no consensus reached on the deeper reasons behind these relationships. Some participants agree on the mathematical relationships, while others seek further clarification and understanding.
Some discussions involve assumptions about the definitions of terms like wavelength and frequency, and there are unresolved questions regarding the nature of wave behavior and the implications of wave-particle duality.
This discussion may be of interest to those studying quantum mechanics, wave theory, or anyone curious about the fundamental properties of light and energy.
marlon said:A smaller wavelength corresponds to a higher frequency via the deBroglie-relations. This way of looking at a particle as if it were a wave is the basic property of QM. Just think of the amount of energy of a certain foton as represented by a wave with corresponding frequency.
mee said:Thank you for showing what is the relationship, but why this relationship?
so-crates said:Remember that the speed of photons is the constant c. The speed of any wave is equal to the wavelength times the frequency, so c = lf. (l = lambda, the wavelentgth, f is frequency). Rearranging, f = c/l. If E = hf for a photon, then E = hc/l. So energy increaes with smaller l (wavelength).
Are you asking why c = lf, or why E = hf?
µ³ said:Remember how light has properties of a wave (wave/particle duality)? Well that's what the wavelength is, the wavelength of the property aspect of the photon. This helps predict such outcomes as the interference pattern in double-slit experiments.
Gravitational waves are another example of how spacetime can be curved even in the vacuum. General relativity predicts that when any heavy object wiggles, it sends out ripples of spacetime curvature which propagate at the speed of light. This is far from obvious starting from our formulation of Einstein's equation! It also predicts that as one of these ripples of curvature passes by, our small ball of initially test particles will be stretched in one transverse direction while being squashed in the other transverse direction. From what we have already said, these effects must precisely cancel when we compute .
Hulse and Taylor won the Nobel prize in 1993 for careful observations of a binary neutron star which is slowly spiraling down, just as general relativity predicts it should, as it loses energy by emitting gravitational radiation. Gravitational waves have not been directly observed, but there are a number of projects underway to detect them. For example, the LIGO project will bounce a laser between hanging mirrors in an L-shaped detector, to see how one leg of the detector is stretched while the other is squashed. Both legs are 4 kilometers long, and the detector is designed to be sensitive to a -meter change in length of the arms.
© 2004 John Baez and Emory Bunn
selfAdjoint said:The EM wave is a transverse vibration. No longitudinal component has ever been observed.