Re: Propagation of EM waves in a relativistic medium - some mathematical details

From: Bilge (dubious_at_radioactivex.lebesque-al.net)
Date: 07/04/04 

Date: Sun, 04 Jul 2004 08:53:37 -0000

 LEJ Brouwer:
>"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
>>
>> Because there is a fundamental difference between waves in media
>> and ``E&M waves''. Personally, I think the pedagogic value of describing
>> electromagnetic waves in terms of waves in a ripple tank is offset by
>> the inability of people to get rid of that idea once the analogy fails.
>
>It is not merely `pedagogic value'. There are no known examples of waves
>which do not propagate in an underlying medium, which makes EM waves (and
>their cousins) very strange objects indeed if they do not.
 
  I'm sorry, but you've just made my point about not being able to
separate the analogy from the phenomenon due to having the wave analogy
permenantly imprinted.

[...]
>
>In response to those who insist that a new theory make new experimental
>predictions, we have here a situation where there is much to be gained from
>finding a consistent mathematical formulation of the underlying medium in
>that it allows us to throw away the `ad hoc' and nonintuitive concept of
>`field'.

   You haven't done that, either. From your article, I quote:

   ``... where Q is a scalar field describing the charge density
   distribution. W^u = (c\gamma_w, v\gamma_w) is a four-velocity
   vector field describing the motion of the charge and M is a
   scalar field describing the mass density if the charge.''

  In what way have you thrown away the ``ad hoc and nonintuitive concept
of a field''? All you did was add some new fields that weren't necessary
in the formulation that required only one field.

> There is really no need to make different or new predictions - the
 
  Of course there is no _need_. The issue is making ``new predictions''
that are already ruled out existing experiments.

>point is that we gain a more intuitive and appealing understanding of the
>underlying processes. Much of physics research involves trying to explain
>things in a better or simpler way - it is not the sole aim to come up with
>new predictions.
 
  But, your key phrase is ``better or simpler'', neither or which I can
see would apply to your theory. I don't even see why you think it
describes E&M. It's closer to being the description of a superconductor,
that's not really the issue. When you wrote down the wave equation satisfied
by A^u, you simply ignored the conditions you set out in the beginning,
namely, A_+A_+ = A_-A_- = c^2.

  Each of those fields obeys a wave equation of the form:

   d_u F^uv + m^2 A^u = j^u

  You left out the mass terms. Your combined wave equation is therefore,

   box (A^u+ + A^u-) + m^2 (A^u+ + A^u-) - d^u (d_v A^v) = 4\pi j^u

(You can write j^u as QW^u if you want, it doesn't really matter).
Now, to include the interaction,

  (A_u+ + A_u-) box (A^u+ + A^u-) + m^2 (A_u+ + A_u-)(A^u+ + A^u-)
  
            - (A^u+ + A^u-)d^u (d_v A^v) = (4\pi/c) (A^u+ + A^u-) j^u

 Imposing the lorentz condition (your so-called ``continuum gauge''),
which is not an option, eliminates the third term, leaving,

  (A_u+ + A_u-) box (A^u+ + A^u-) + m^2 (A_u+ + A_u-)(A^u+ + A^u-)

               = 4\pi j^u (A^u+ + A^u-)

  The second term is not gauge invariant. You have no freedon to choose
your wave equation to be transverse.

>> A continnuum isn't physically realistic. It also contradicts all the
>> experiments that indicate quantum mechanics is correct.
>
>So perhaps you would like to explain why a `fields' are more realistic than
>a continuum (assuming that they have the same physically observable
>consequences)?
 
  First, because detectors measure field quanta. That's what a gamma ray
counter like a Ge(Li) or HPGe detector are for. I can measure the gamma
ray emitted in a nuclear de-excitation. Second, a continuum, literally
means taking the separations between the constituents of the medium and
the masses of those constituents to literally be zero, but all of those
constituents are located at distinctly different points and each has
some number of degrees of freedom. Any finite volume therefore contains
an infinite number of consituent particles and the entropy is infinite.
 
>I would also appreciate it if you could provide a reference
>to the quantum continuum theory which you are referring to which contradicts
>quantum mechanics? It certainly has nothing to do with my paper as I do not
>even discuss quantum mechanics.

  You don't discuss quantum mechanics, but E&M is inherently quantum
mechanical. If you want to restrict the scope of your theory to one which
physicists in the 19th century would consider plausible, I won't argue
with that.

   As to why quantum theory which conflicts with your theory, just look
at what a continuum means. The force exerted by one constituent in your
medium on another means that the positions and momenta involved are, at
all times, determined to infinite precision.

Relevant Pages

  • Re: Propagation of EM waves in a relativistic medium - some mathematical details
    ... When you wrote down the wave equation satisfied ... Imposing the lorentz condition (your so-called ``continuum gauge''), ... >> experiments that indicate quantum mechanics is correct. ... the masses of those constituents to literally be zero, ...
    (sci.physics.relativity)
  • Re: Epistemology 201: The Science of Science
    ... Observables are Hermitean operators on the ... the terms quantum mechanics and quantum theory are used rather ... subsume Special Theory of Relativity by Dirac and to resolve wave ... which were the particle properties ...
    (sci.math)
  • Re: Epistemology 201: The Science of Science
    ... Observables are Hermitean operators on the ... the terms quantum mechanics and quantum theory are used rather ... subsume Special Theory of Relativity by Dirac and to resolve wave ... which were the particle properties ...
    (sci.cognitive)
  • Re: Epistemology 201: The Science of Science
    ... Observables are Hermitean operators on the ... the terms quantum mechanics and quantum theory are used rather ... subsume Special Theory of Relativity by Dirac and to resolve wave ... which were the particle properties ...
    (sci.physics)
  • Re: Analog or Digital
    ... It's wave mechanics. ... and the wave functions that solve it will have properties ... while quantum mechanics relates momentum to frequency. ... In acoustics if you have some position-space wavefunction like ...
    (sci.physics)