Re: NEC-LIST: Orthogonality under relativistic transformations

Lorentz contraction is more important when modeling how relativistic speeds
affect the perception of a stationary observer. The antenna on a spacecraft
moving at relativistic speed along a direction orthogonal relative to the
source will perceive a doppler shift in the frequency of the radiated
signal, but the Lorentz effect is no more significant than if the source
were moving at relativistic speed in the opposite direction.

For example, we can perceive red-shift or blue-shift in the radiated
energies of start moving at relativistic speeds, but the apparent Lorentz
contraction of a star doesn't generate much of a variation in the model
because distant stars are essentially point-like anyway (IMHO).

In other words, "modes that are local to the antenna" may lose some of the
orthogonality because of apparent frequency shift, as if the antenna were
radiating on another frequency.

I expect that this could be modeled in MATLAB without too much trouble; let
me know if you're interested.

- Mike

----- Original Message -----
From: David Jefferies <d.jefferies_at_surrey.ac.uk>
To: <nec-list_at_gweep.ca>
Sent: Thursday, January 16, 2003 1:58 PM
Subject: NEC-LIST: Orthogonality under relativistic transformations

> Dear List,
>
> I'm wondering whether modes that are local to an antenna,
> and are orthogonal to each other (in the sense that
> the integrated inner product is zero), maintain the
> property of orthogonality when viewed from another
> inertial frame of reference, after all the field
> distributions are Lorentz-transformed. It has always
> appeared odd to me that the antenna properties of interest
> are either "viewed" from a stationary frame, or else from
> one moving outwards at c, the velocity of light,
> in an arbitrary direction. Clearly (to me at any
> rate) any antenna structure, when viewed from any
> outgoing section of the wavefront, must look entirely
> transverse to the line joining it to the wavefront
> section (by Lorentz contraction along the line of sight)
> and therefore, that all outward propagating waves must
> necessarily be transverse for that reason alone.
>
> I understand that the issue of orthogonality of modes
> has application to the arguments in the CHU paper
> about compact antennas.
>
> regards
>
> David.
>
> --
> David Jefferies
> http://www.ee.surrey.ac.uk/Personal/D.Jefferies/
> http://www.eryptick.net/
> fax +44 (0)1483 534139 attn D.Jefferies
> --
> The NEC-List mailing list <nec-list_at_gweep.ca>
> http://www.gweep.ca/mailman/listinfo.cgi/nec-list
>

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