Re: What is luminiferous ether made of?

From: shevek (shevek4_at_yahoo.com)
Date: 09/21/04 

Date: 21 Sep 2004 12:31:48 -0700

dubious@radioactivex.lebesque-al.net (Bilge) wrote in message news:<slrnckui2d.hel.dubious@radioactivex.lebesque-al.net>...
> shevek:
> >dubious@radioactivex.lebesque-al.net (Bilge) wrote:
>
> >> The point is that the wave equation for light is _not_ an approximation,
> >> so it's not legitimate to try and analogize it to the waves in classical
> >> physics which are approximations describing the collective motion of
> >> the particles in a physical media.
> >>
> >
> > I was tempted to immediately respond that of course it is an
> >approximation, like everything else in physics, but I think you have a
> >good point here. In some ways, the wave equation for light is used as
> >a definition, in order to build a space-time coordinate system a la
> >special relativity. In such cases, you are right that it is not an
> >approximation.
>
> Actually my point was a bit stronger. The elastic limit is not simply
> approximate. It's unphysical if one attempts to take that limit
> literally to justify the wave equation for light. If taken literally,
> one has to literally have a continuum, not just small but finite
> particles.
>

Same for sound waves or the ripple waves. If taken literally, one has
to have a continuum. Deriving the wave equation for light does the
same thing, assuming the fields are continuous.

>
> >> Consider the following. You have two sources of radiation, both
> >> propagating in the z-direction. One is plane polarized along x and
> >> the other along y. Assume they have the same frequency. Now, I haven't
> >> given you any information regarding their relative phases, but class-
> >> ically, we can assume that the radiation from source 1 is given by
> >> E_1 = E_0 \exp(ikz - iwt) and from source 2 is E_2 = \exp(ikz' - iwt').
> >>
> >> Do you expect the fields to add coherently or incoherently?
> >> Why?
> >>
> >
> >Easy. E_tot = E_1 + E_2. (vectors all)
>
> Not so fast.
>
> >Of course such sources are impossible to really make, [..]
>
>
> Nowm above you assumed you could just add E1 and E2. But there are
> two ways to add E1 and E2.

Not the way I meant it. At any point in space and time (x,t) find the
total field vector by adding E1(x,t) and E2(x,t). Only one way to do
vector addition.

> In principle, that implies you could
> take two independent sources of linearly polarized radiation and
> just by adjusting the separation distance create a circularly
> polarized wave. But, you can't do that. What you get are two plane
> polarized waves at 90 degrees.
>

Two plane waves propogating together with the same k,w, polarized at
90 degrees with a 90 degree phase shift between them -are- a single
circularly polarized light wave.

> A second example. It's possible to produce an excitation with a
> laser pulse in which two different energy levels are coherently
> excited. Each decays and produces radiation, E1 and E2 as your
> vector model above. However, what you get are four frequencies,
> not two. You get the original energies plus sum and difference
> frequencies. Classically, that can't happen.

You're right, the appearance of beat frequencies, sum and difference
or higher harmonics, is indicative of a nonlinearity of the medium.
That sounds interesting, did you have a specific example in mind?
(i.e. ref please)

> >> Not really. For example, start with a rather general geometry in four
> >> dimensions. There are several choices which give different physics. Your
> >> metric could contain all plus signs (or all minus signs). It could contain
> >> equal numbers of plus and minus signs, or it could be the lorentz metric.
> >> The first two, you can rule out from observation, leaving the lorentz
> >> metric. If you use the lorentz metric, you also get galilean relativity as
> >> a limiting case.
>
> >That is rather general, but still brings preconcieved notions to the
> >table such as coordinates and metric.
>
> I can be more general. You can look at coordinates as an ordered
> n-tuple of numbers rather than employ any preconception about what
> it means. One can also define a meaning for distance that isn't
> obviously geometric. For example, in coding theory, there is a
> such thing as a ``hamming distance''. Picture the alphabet. The
> hamming distance is in some sense the distance between two of
> the symbols (letters), except that the criteria for ordering is
> the relative frequency with which they appear when used to construct
> messages obeying the rules of grammar and spelling. So, basically,
> one can employ some notion of distance for lots of things.
>
> Now, what we call geometry is a particular set of numbers that
> share a common rule for transforming between them, called an
> orthogonal rotation. There is nothing particularly special
> about the choice apart from the being able to use a particular
> array of numbers called an orthogonal matrix to transform one
> set of numbers into another set of numbers in a way that preserves
> the distance between them. We call the rule that defines the
> distance between the numbers the ``metric.''
>
> But that is all the significance there is to geometry. Our perception
> of what ``geometry is'' isn't really relevant apart from making it
> easier to identify a set of parameters that are ``unified'' under some
> rule. You could imagine trying to do this with 3 dimensions and
> electric charge, but the rule wouldn't work out.
>

Unfortunately, the metric you referred to before does not satisfy the
basic rules of a metric as a distance you discuss here.. and is more
properly referred to as a "quasi-metric".

> [...]
> >> The only reason you think anything is more easily visulized is because
> >> you are only trying to visualize light in a very superficial way and not
> >> in the way which is simpler when trying to explain E&M from a fundamental
> >> standpoint. Relativity is about invariance. Using that general idea, it's
> >> possible to derive (1) conservation of energy, momentum and angular
> >> momentum. (2) the electromagnetic field itself along with maxwell's
> >> equations by employing the quantum mechanical replacements for the energy
> >> and momentum and the wave equations obtained from E^2 = p^2 + m^2 to be
> >> guage invariant. That's a lot for very few assumptions.
> >
> >Invariance is very fundamental, I agree. Kind of underlies the
> >concept of truth.
>
> Right. The symmetry is the reality. The rest is a consequence.
>

Which came first, the symmetry or the conserved current?
(rhetorical)

> >Does your dervation (1) include Noether's theorem?
>
> Yes.
>
> >It looks to me like you have assumed a lot more than can be gleened
> >from that one word invariance..
>
> Noether's theorem simply states that for every continuous
> symmetry of the lagrangian, there exists a conserved current.
> Here, lagrangian means anything that can be written as function
> of some independent variables and first derivatives for which
> one can find an extremal path. It's not too restrictive.
>

Without being a little more restrictive, its hard to apply that to
physical reality.

> >although much of what is needed comes preprogrammed in our brains.
>
> Our brains developed in the same universe we are trying to explain.
> One might consider it natural to develop concepts which are
> well suited to describe the environment which produced those brains.
> In different universe with different physics, all of our concepts,
> including the concept of a brain might not even make sense. If the
> universe were 2+1 dimensions, would eyes or ears or food make sense?

Yes, very true. I mean, no, they would not. :)

Cheers -

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