Wave Particle Duality

This theory of the photon mass was actually proposed by Einstein in about 1905 or 1906. As is well known de Broglie proposed p = h bar kappa in the early twenties. The mass of the photon is regarded in the same way as the mass of any particle. A particle travelling at c must have zero mass, then the relativistic momentum = gamma m v becomes zero divided by zero. This is known as the hyper relativistic limit in the standard physics. It makes no physical sense at all, it is just dogma. In the finite photon mass theory the velocity v of the photon is always less than c. Photons moving at the speed of light have zero mass, not infinite mass, but in any case all that is a thing of the past. In ECE theory the insight is left to geometry, the relativistic momentum is obtained form the tetrad postulate.

In a message dated 24/02/2014 15:39:39 GMT Standard Time writes:

Myron Looks like we are hard up against the Wave /Particle duality paradox. With the Lorentz factor, as I understand, it if a particle moves at the speed of light its mass becomes infinite. So Photons moving at light speed -which they do by definition, should be infinitely massive . Yes?
What we have here is a failure of human imagination.We are lacking some deep insight.Failing that we should simply use equations which tie best to observations from real objects and experiments. Norman

On 2/24/2014 8:42 AM, EMyrone wrote:

The velocity of a photon with mass is defined as if it were any particle with mass, so its relativistic momentum is p = gamma m v where v is the linear velocity and gamma is the Lorentz factor. The structure of the Maxwell Heaviside equations and d’Alembert wave equation is changed to that of the Proca field and wave equations. The existence of these longitudinal solutions imply that the photon mass must be finite, and the photon velocity must be less than c. The latter is considered in photon mass theory as a universal constant defined by agreement in the standards laboratories. So in order to answer the following questions the Beltrami equations associated with the Proca equations must be defined. I will have a think about this for the next note. Some of these questions are addressed in the dielectric ECE papers leading up to UFT49. There is a link between photon mass and vacuum potential and vacuum charge current density. Then there are questions of group and phase velocities. As you know, tachyon theory is highly developed (faster than light propagation), and some of the UFT papers deal with this question. It would be a good thing to make a literatue search through the UFT papers to pick out the relevant papers that deal with these questions. The most important thing is that a Beltrami equation curl B = kappa B always obeys del B = 0. The Helmholtz equation must be generalized to the Proca equation for electromagnetism with finite photon mass.
To start with, it would be important to test the Rodrigues Vaz solution for correctness. If I recall things correctly this solution was claimed to be superluminal, but if it is algebraically incorrect, i.e. does not produce del B = 0, it does not mean anything. Very often we find that grandiose claims of the late twentieth century in theoretical physics are reduced to ashes by careful scholarship. This is part of the renaissance we are going through now, a part of history.

To: EMyrone
Sent: 24/02/2014 12:17:03 GMT Standard Time
Subj: Re: Computer Checks on Two Solutions Reviewed by Reed

What could be considered is that some authors speak of solutions with propagation velocity different from light speed. What happens with the time development? Considering the hydromechanic Beltrami functions, in the Bessel function example the longitudinal part propagates much faster than the circulating transversal parts. But if we take this as a snapshot for electromagnetic fields, the field configuration as a whole is transported, oscillating with a time frequency omega which is coupled to the wavelength appearing in kappa. It could be that there is a dispersion so that the wave form changes over time, for example the field is stretched in Z direction. This would mean that the outer parts move slower than the central part. On the other hand the Beltrami flow is equivalent to solutions of the Helmholtz equation which would indicate a homogeneous propagation speed. Any ideas?
Horst

EMyrone hat am 24. Februar 2014 um 12:39 geschrieben:

Excellent results! These two solutions have already been graphed in stills by Horst, and this example shows that the kappa is in general a function, for example of the Bessel functions. These two solutions are now ready for animation, animations of transverse and longitudinal solutions can be carried out separately, or the complete solutions can be animated. There is never any hurry, we always take sufficient time at AIAS to make sure we are correct. I am sure that Horst will do an excellent job as usual, and the animations can be added to the animation section of www.aias.us. These solutions also give a B(3) type solution as described in UFT257 and in the note send over yesterday. I think that these are sufficient to describe longitudinal vacuum solutions. The Lundquist and Rodrigues Vaz solutions appear to be wrong unless the computer shows that they are divergenceless. As can be seen, Maxima has the facility to compute Bessel functions. This would be extremely laborious by hand.
In a message dated 24/02/2014 09:41:50 GMT Standard Time, writes:

I checked two things:
1. the divergence of the general Beltrami function given by the function psi and constant vector a. The divergence is zero, all o.k.
2. in the Bessel function example the “kappas” of the second and third component are (computed from cylindrical and cartesian coordinates):

So the result is independent of the coordinate system as expected.
The numerical analysis of an example shows that component 2 and 3 give the same kappa, so there must be a theorem with Bessel functions which makes both expressions identical.
I think it is Lemma 2.2 (page 6) of
http://www.math.psu.edu/papikian/Kreh.pdf
The Bessel example therefore is a valid Beltrami equation.
Horst

EMyrone hat am 24. Februar 2014 um 09:37 geschrieben:

I will continue the systematic investigation of the geometrical structure of charge current density. The responsibility of getting correct solutions of the Beltrami equation lay originally with people like Nobel Laureates Alfven and Chandrasekhar, then with protagonists like Marsh and Reed. We are using computer algebra to check for correctness in preparation for animation. The plane wave solutions are simple and easily seen to be correct. There is no reason to doubt the Reed solution, based on that of Chandrasekhar et al., but the solutions by Lundquist and Rodrigues and Vaz don’t look right. The rule with computers is “rubbish in, garbage out”, and I found this out as soon as I started to use them as an undergraduate and post graduate (starting 1970). In other words one has to be sure of the correctness of the equations before animating and one has to understand all details of a theory before coding it up. The computer is only a machine, human imagination is much more powerful than a machine, however useful. Dirac used to say that imagination is paramount, if your solutions are slightly wrong then amend them. In present day physics however there are often wild errors that are covered up very cynically (e. g. UFT225) in an amoral environment dominated by money and power. Any cover up starts as a leak, and quickly becomes a flood.