Electromagnetic bubbles that are sealed by themselves. Sounds like ball lighting to me.
Note that mass enters as a relation between the phase and group velocity of a particle via an "internal process". Very understated but dead right.
| Good_Elf.. |
Consider a CW EM Wave propagating along some axis. If I "chop" a segment of this otherwise perfect wave causing it to be finite in time it becomes a packet
Most often, an anti-aliasing filter is a low-pass filter </wiki/Low-pass_filter>. However, this is not a requirement. The Shannon-Nyquist sampling theorem </wiki/Shannon-Nyquist_sampling_theorem> states that the sampling rate must be greater than twice the bandwidth, not maximum frequency, of the signal. For the types of signals that are bandwidth limited, but not centered at zero, a band-pass filter </wiki/Band-pass_filter> would be used as an anti-aliasing filter. For example, this could be done with a single-sideband modulated </wiki/Single-sideband_modulation> or frequency modulated </wiki/Frequency_modulated> signal. If one desired to sample an FM radio </wiki/FM_radio> broadcast on channel 200 </wiki/FM_broadcast_band>, then an appropriate anti-alias filter would be centered on 87.9 MHz </wiki/Megahertz> with 200 kHz bandwidth (or pass-band </wiki/Pass-band> of 87.8 MHz to 88.0 MHz), and the sampling rate would be no less than 400 kHz. (In this case not the audio of the broadcast is sampled, but the actual transmission signal itself , which is not very common.[my emphasis] )
The standard deviation is a measure of the degree of dispersion of the data from the mean value. Stated another way, the standard deviation is simply the "average" or "expected" variation around an average (i.e., square all individual deviations around the average, add these up, divide by N, then take the square root. You then have the root of the mean squared deviation (RMS </wiki/Root_mean_square>, in a very simple sense the average or expected variation around the average). In fact the standard deviation is sometimes called the expected deviation, though this may be confusing as the expected value </wiki/Expected_value> of the deviation is instead the average absolute deviation </wiki/Average_absolute_deviation>.
A large standard deviation indicates that the data points are far from the mean and a small standard deviation indicates that they are clustered closely around the mean.
|The trouble is "reality" is what most people believe they "observe" and sometimes the reality is actually hidden from us by the chaotic "surface" of phenomena and I believe that the surface of that "reality" hides much of what is going on "behind the scenes" .|
Not exactly. It's momentum and/or energy that, as we increase our certainty, will lead to a corresponding uncertainty in position. So really the accuracy of Confused2's statement depends on whether he is talking about rest mass or relativistic mass.
|Edit - GE re (?) I think we have to proceed as though there are no hidden variables (ie not look for them) because we can only hope to deal with that which is 'revealed'.|
|The reason this "ideal water" pooled was because it had some mass which caused the natural depression and all the rest followed due to the "mathematically ideal" properties of this "stiff" but "ideal" membrane.|
|Since it was "perfectly elastic" the total energy of these "packets" remained constant as it spread... just becoming more and more spread|
|The relationship of energy moving around the spiral to its' wavelength (= to 2r) would be ~ pi. Note here a departure on my part from the norm; I am not talking here about a wave packet, or a stream, etc., I am talking about the simple case of a single photon. Because only 1 phase of the wave exists at a time, I use 2r to equal half of the phase. The other half will exist in the next frame, at 1/2 wavelength distance away. So it is a circle cut in 1/2 and separated by time, and connected at the "node" in between the phases.|
|Almost every experiment I can think of takes place in a "medium" that is defined by the "user". This medium, like everything else, has a resonant frequency|
|I like to head Good_Elf off at the pass and I'm too mean to buy the book.|
|I have never heard of Michael Munowitz but no doubt there is a great deal I have not heard. Would you do the honor of explaining his concepts here to not just myself but to all? I am downloading your data and I will have a look into it as well. I do not know how appropriate it is but I am very interested by what the abstract is saying... he he he!|
|Propagation of singularities for Schrödinger equations on the Euclidean space with a scattering metric|
June 6, 2005
Given a scattering metric on the Euclidean space. We consider the Schrödinger equation corresponding to the metric, and study the propagation of singularities for the solution in terms of the homogeneous wavefront set. We also prove that the notion of the homogeneous wavefront set is essentially equivalent to that of the quadratic scattering wavefront set introduced by J. Wunsch . One of the main results in  follows
on the Euclidean space with a weaker, almost optimal condition on the potential.
|Here was I thinking you may be able to assist us all and lo... yours is a jolly "romp" down into a dark and dangerous woods... Damn... should have known... trick or treat. I think I got the "trick".|
|RESULTS AND PROBLEMS IN DECOHERENCE THEORY|
Received on 20 December, 2004
Roland Omnes -- Laboratoire de Physique Th´eorique, Universit´e de Paris-Sud, 91405 Orsay (France)
The main steps in the development of the ideas on decoherence are briefly reviewed, together with their present achievements. Unsolved problems are also pointed out . . .
|General Relativity and Microlocal Analysis |
Last modified August 31, 2005 by Michael Kunzinger.
Due to the inherent nonlinearities of the field equations, studying singularities in general relaivity by means of classical distributional methods soon runs into serious conceptual problems. In order to cope with such problems in a mathematically rigorous fashion one has to resort to some kind of distributional geometry allowing to carry out nonlinear operations with singular objects. As was already mentioned above the development of such a theory is one of the main current projects of our research group.
Together with R. Steinbauer we have studied geodesic and geodesic deviation equations in singular space times. In [J3] a satisfactory solution concept for such equations was developed and applied to the case of pp-Waves (plane fronted waves with parallel rays). For describing such waves Roger Penrose had used a discontinuous coordinate transformation turning the distributional form of the metric into a continuous form. While mathematically ill-defined (involving undefined nonlinear operations on distributions), this procedure provides physically equivalent descriptions of the situation (particle trajectories in both pictures coincide).
The key to understanding this behaviour lies in realizing that the Penrose transformation actually transports points of space time along (discontinuous) geodesics of the original (distributional) metric. By means of a global univalence result of Gale and Nikaido we were able to prove that the transformation is actually the distributional `shadow' of a Colombeau coordinate transformation. This also introduces a possibility of handling `discontinuous diffeomorphisms', see [J4]. The necessary tools for describing such transformations (which furnish an example of manifold-valued generalized functions) are presented in [J12].
Based on regularity theory for algebras of generalized functions (developed by M. Oberguggenberger), the aim of this joint project with G. Hörmann is an analysis of the interaction between nonlinear operations, singularities and differentiation from a microlocal point of view (in particular: propagation of singularities in nonlinear PDEs involving generalized functions). In [J8], microlocal properties of basic operations (multiplication and pullback) in the Colombeau algebra are analyzed. Although multiplication of distributions can be carried out unrestrictedly in the algebra, the wave front set of the product displays high sensitivity to the configuration of the factors' singularity structure. In case the wave front sets of the factors are in favorable position an extension of the classical inclusion relation (in the distributional setting) due to Hörmander is proven. Explicit examples are given showing that the inclusion relation will break down even in the Colombeau algebra if Hörmander's condition is violated.