group velocity

[AntonioLao]

Without directions the group velocity of electromagnetic waves is the speed of the envelope of wave packets, while each packet would be the superposition of infinitely many individual uniform waves having the same amplitude, wavelength, and frequency. However, two of these waves could want to share the same space-time coordinate even though at every instant many do share the same time but at different places. This allows reality to separate into past, present and future for those waves who wanted to share the same space.

On the other hand, for those waves, being able to share the same time would be forced to possess the same energy. Nevertheless, these singular wave energies could be added if and only if these waves also share the same space.

Two waves are said to be in phase if the difference of their phase angles is zero. Then they travel at superluminal phase velocity. If all waves travel at the same phase velocity then they form continuous space-time (true vacuum). Otherwise, if the phase angle difference is exactly 180° or p radians then they are completely out of phase. If all waves are completely out of phase then they form stationary quantized space and both their group and phase velocities are all zero. If the phase angle difference is exactly 90° or p/2 radians then they form electromagnetic waves of photons whose group and phase velocities are equal to the speed of light measured relative to the true vacuum. For all other phase angles between 0° and 90°, between 90° and 270°, between 270° and 360°, the superposed waves are standing matter waves whose group velocities never exceed the speed of light.

[mkirkpatrick]

Thank you for your first post in the league Antonio,you are most welcome.

A question comes to mind,in regard electromagnetic waves,and the speed that they move
at,the question is this;if we accept the premise of a background field,that of the etheric
field or web,and further postulate that this etheric field is ubquitous by nature,and therefore stationary,what then if any,would be the effect on magnetic waves?

It would seem that the etheric field would enable the waves to purchase a pathway
through the vacuum,but would there be any charge made?


regards michael.

[AntonioLao]

what then if any,would be the effect on magnetic waves?

The magnetic waves are always perpendicular to the electric waves. But only the electric waves can be quantized unless someone detected the magnetic monopole. For what it's worth I think magnetic monopoles do not exist.

[Lloyd Gillespie]

Antonio, this is a post from the NASA site about scientific investigations of superluminal velocity and group velocity. My reading is the superluminal is still not confirmed;

Detection of Superluminal propagation at low or near resonance frequencies and the dynamics of the Forerunners

Principle Investigator: Kevin Y. Malloy, University of New Mexico, Albuquerque, MN
(Text excerpted and adapted from proposal summary.)
In recent years, the subject of superluminal propagation has received much attention. A complete review of this field is provided in reference [1]. At the present, a body of experimental evidence [2-7] suggests the reality of superluminal group velocities for tunneling photons (and perhaps electrons); however, there is no universal agreement on the interpretation of these facts. In all of the above experiments, the magnitude of the incoming wave is attenuated upon tunneling and consequently the energy velocity remains subluminal. [8].
In principal, a rather more striking superluminal behavior can be exhibited in the case of inverted medium. Under special circumstances photons can travel through an inverted medium with phase, group, energy, and signal velocities all exceeding the velocity of the light in vacuum [1, 9]. This phenomenon can occur either at low frequencies or at frequencies close to resonance. While the low- frequency behavior is easier to understand (the index becomes less than 1), the higher frequency response can be understood in terms of tachyon-like excitation process, in which undamped atomic polarization waves are strongly coupled to electromagnetic waves. This phenomenon is different in nature from the previously studied tunneling effects and in principal can be observed over long distances. While the theoretical foundation for the above anomalous effect is well established [9], as to date, there has not been any experimental verification. We propose exploring the above possibility via experiments with inverted media such as fiber amplifiers or rubidium vapor. Since both the low frequency and the tachyonic propagation involves exchange of energy between the wave and matter resulting in superluminal energy velocities, it is perhaps necessary to redefine energy velocity such that this rather anomalous effect is properly explained [ 10].
It is believed that in all superluminal propagation (low frequency, tachyonic or tunneling), the very front of the optical or microwave signal shall remain luminal in order to properly address the requirements of the special relativity and causality. Therefore, a careful investigation of these early parts of the signal, so called "forerunners" is of tremendous importance in regard to propulsion "make-or-break" issues. The form of the forerunners is dictated by the details of the dispersion relation and the incoming wave. Since in our tunneling experiments and many others, the optical multi-layers, also known as one dimensional photonic crystals (1DPC), are used [11], it is natural that we investigate the dynamics of forerunners for this particular structure. In this proposal, we envision a theoretical formulation of the forerunner's field and the possible experimental detection of these fields for the case of 1DPCs. Clearly, a correct mathematical formulation of the forerunners and possible consequent detection of these disturbances strongly suggests that, regardless of superluminal observation of group, signal, or even energy velocity, the requirements of causality is fully observed, and no violation of principal axioms are allowed.
Although it is premature and non-scientific at present to suggest a detailed and direct connection between the proposed tasks and possible future BPP devices, the suggested tasks are in close correlation with the expressed desire of "conducting experiments or advancing theories that address critical unknowns, make-or-break issues or curious effects." In other words, while the proposed ideas are far from becoming breakthroughs in near future, they provide a starting point for scientifically assessing the ideas regarding the application of theses anomalous effects to propulsion physics.

• [1] Chiao and Steinberg, Progress in Optics, 37, 345 (1997).
• [2] Steinberg, Kwiat, and Chiao, Phys. Rev. Lett., 71, 708 (1993); Steinberg and Chiao, Phys. Rev. A., 51, 3525 (1995).
• [3] Enders and Nimtz, J. Phys. I France, 2, 1693 (1992).
• [4] Ranfagni, Fabeni, Pazzi, and Mugnai, Phys. Rev. E., 48, 1453 (1993); Mugnai, Ranfagni, and Ronchi, Phys. Lett. A., 247, 281 (199.
• [5] Spielmann, Szipocs, Stingl, and Krausz, Phys. Rev. Lett., 73, 2308 (1994).
• [6] Mojahedi, Schamiloglu, Agi, and Malloy, submitted to Phys. Rev. E.
• [7] Mojahedi and Malloy, to be published.
• [8] Scalora, Dowling, Manka, Bowden, and Haus, Phys. Rev. A., 52, 726 (1995).
• [9] Chiao, Phys. Rev. A., 48, R34 (1993); Chiao, Boyce, and Mitchell, Appl. Phys. B 60, 259 (1995); Chiao, Kozhekin, and Kurizki, Phys. Rev. Lett., 77, 1254 (1996); Morgan and Chiao, Am. J. Phys. 66, 14 (199; Chiao, Population inversion and superluminality, in Amazing Light: a volume dedicated to Charles Hard Townes on his 80th birthday (Springer-Verlag, New York, 1996), p. 91.
• [10] Diener, Phys. Lett. A., 235, 118 (1997).
• [11] Yablonovitch, J. Opt. Soc. Am. B 10, 283 (1993).

regards,