"Neil" <neil_delver@caloricmail.com> wrote in
news:123ojnjmqphjo85@corp.supernews.com:

Let's say I focused light from bright points using a lens with large
N.A. (large sine of half-angle of convergence, maybe 0.5 to 0.8.) That
means the image spots and distinguishable separations are around the
wavelength or so. Suppose an observer (imagined as either an abstract
frame of reference or a little detector screen) moves away from the lens
at 0.98c, to achieve red-shift factor of 10x. (Imagine a hole in the
lens for detector passage if you must.) The velocity transformation of
the intensities of the EM fields should preserve the original
distribution of *relative* amplitudes, including the scale of the
resolution. Yet the new radiation has 10x the wavelength of the
original. Is that a "problem"? It seems odd to me to just *have* an
image available at all, even for a moment, with a scale of intensity
variations at only 0.1 lambda. (It's not a near-field cheat with a
detector close to the sources.) And there is no lower limit in
principle...

I haven't checked yet to see if we can cheat normal resolution limits by
having a lens move towards sources and focus an image based on the
resolution of the wavelength found in the lens frame. The aberration of
the light may prevent that (by changing the angular scale for the
image.) Try your hand if you want.

Even more curious, consider such a transformation for limit-scale
interference fringes produced with a given rest-frame wavelength.

Comments? Precedents, previous intimations, experiments? Is having
something actually there in motion to detect the image, versus a
transformation in principle, relevant? QM issues as well? Students;
try it on your teachers, and teachers; try it on your students!

Neil Bates

I'm no expert by any means, but I think you may be confounding the
problem. Forget the fact that the lens is moving at .98c relative
to the source. All that matters is the light it is collecting. If
it is collecting light at, for conversations sake, 1000nm, the
optics need to be designed for that regime or it won't work right.
It doesn't matter if the source was originally 100nm. What matters
is that the lens sees the 10x redshifted light at 1000nm.

That's why the James Webb Space Telescope to succeed Hubble is
designed to work in the infrared. The light from distant galaxies
is so redshifted that their deep UV emissions are now IR. You design
the detector to the see the IR as it appears at the scope, not the
original light.

As for imaging with the light, now that it is redshifted to longer
wavelengths, the diffraction limits at those wavelengths now apply
and your images are limited to that resolution. So yes, you will
lose resolution. Where you may have been able to resolve the points
before you started receding at .98c, now you won't.
...