Magnification at High Redshift z

Robert Angstrom · 03-28-2006

Since space expands radially in all directions, would evidence of the expansion of light along the z axis indicate an equal expansion along the x and y axes? In other words, should objects having high z values because of their location deep within the Hubble flow appear ‘magnified’ from their original size by the expansion of space? Our best telescopes are unable to resolve the surface dimensions of deep space objects so any anomaly in their apparent size would be undetectable but we should able to detect the effect of magnification by a decline in the object’s luminosity. Any comments?

Qfwfq · 03-29-2006

It takes long enough to see the tangent component of a star's velocity, you're in for a good wait if you want to see the nearest galaxies looking noticably smaller, quasars are call thus because they appear pointlike but aren't stars. Not much hope.

Welcome to Hypography.

Robert Angstrom · 03-29-2006

Quote:

Originally Posted by Qfwfq

It takes long enough to see the tangent component of a star's velocity, you're in for a good wait if you want to see the nearest galaxies looking noticably smaller, quasars are call thus because they appear pointlike but aren't stars. Not much hope.

I am asking if the images of deep space objects should appear visibly larger and dimmer because the expansion of space has magnified their images. I would not expect any apparent enlargement in size to be detectable but, if distant light sources are being magnified, we should be able to detect a decline in their magnitude beyond the anticipated inverse square law. Saul Perlmutter observed an unexpected decline in the magnitude of high z S1a supernovae and I was wondering if ths loss of brightness could be an optical effect that only becomes apparent with objects having high redshifts. For example, an object with a z value of z=1 should appear larger by the same amount of expansion or twice its original size. (1+z when z=1 would be a 2x magnification) A object with a 2x magnification should be one fourth as bright as expected. 1/(1+z)^2

Qfwfq · 03-29-2006

Much the same thing holds, except for the power 2 insead of 1. Try reasoning on the reason for the inverse square law: Assuming constant flux, a given solid angle requires increasing surface, with increasing distance.

Robert Angstrom · 03-30-2006

The inverse square law works in Euclidean space but how would it be different in the non-Euclidean space of the early universe where expansion was a more significant factor than it is today. In Riemann geometry parallel lines meet at infinity and parallel lines are not really ‘straight’ lines but curved geodesics. Infinity, in this case, is the Big Bang singularity where all parallel lines converge at a point so that photons moving in ‘parallel’ are diverging at a non-zero angle from a single point. Our present geometry is essentially flat and Euclidean and photons following parallel lines that may have been divergent in the early universe are now truly parallel in the Euclidean sense. When we view light from distant sources it appears to be moving in parallel lines but we don’t see the curvature of the early universe that caused the parallel lines to be more widely spaced than would be if space had always been so Euclidean. As a result, objects at extreme distances (several billion light years away) should appear larger than they actually were when the light was first emitted. The most extreme example of this magnification is the CMBR which originally may have had a radius of 300,000 light years but it is now appears to be as large as the entire universe. Any objects close to the time of the CMBR should share in the same expansion. We see a similar distortion on flat maps of the Earth where Antarctica is as wide as the equator and any land masses near the poles appear unusually large.

coldcreation · 04-01-2006

Quote:

Originally Posted by Robert Angstrom

Since space expands radially in all directions, would evidence of the expansion of light along the z axis indicate an equal expansion along the x and y axes? In other words, should objects having high z values because of their location deep within the Hubble flow appear ‘magnified’ from their original size by the expansion of space? Our best telescopes are unable to resolve the surface dimensions of deep space objects so any anomaly in their apparent size would be undetectable but we should able to detect the effect of magnification by a decline in the object’s luminosity. Any comments?

.

It seems that spacetime dilation* at great distance would indeed cause objects to appear larger (even though as you correctly imply, it would be quasi-unobservable from Earth).

Would you mind my asking why you are interested in this phenomena?

* (Regarding SNe Ia data. Corrections are made for time dilation. My view is that both space and time are modified (dilated) at high-z from our perspective, not just time. It is ludicrous to imagine time intervals alone being affected by curvature and not spatial increments)

CC

Robert Angstrom · 04-03-2006

Quote:

Originally Posted by coldcreation

.

It seems that spacetime dilation* at great distance would indeed cause objects to appear larger (even though as you correctly imply, it would be quasi-unobservable from Earth).

Would you mind my asking why you are interested in this phenomena?

* (Regarding SNe Ia data. Corrections are made for time dilation. My view is that both space and time are modified (dilated) at high-z from our perspective, not just time. It is ludicrous to imagine time intervals alone being affected by curvature and not spatial increments)

CC

Saul Perlmutter et al have observed an unanticipated decrease in the apparent magnitude of high z supernovae and they explain this loss in magnitude as the result of dark energy accelerating the expansion of the universe. http://www.slac.stanford.edu/econf/C...perlmutter.pdf
I am thinking there has to be a more mundane explanation. The magnification effect I described could be one such explanation or you could also explain the drop in magnitude as an effect of time dilation. These would not be two separate effects but they would instead be a single space-time effect with two different explanations so there would be no need to correct for both explanations. As you correctly stated, you can not separate space from time. Perlmutter’s work corrects for time dilation by shortening the SN light-curve timescales by a factor of 1/1+z. This correction would also re-normalize the redshifts but I don’t see any corresponding upward correction for brightness. An upward correction by the same (1+z) would shift the SN plots out of the part of the Hubble curve that indicates accelerated expansion.

Qfwfq · 04-03-2006

Now I see what you're getting at, but how would you define/measure a decline in the object’s luminosity?

Robert Angstrom · 04-05-2006

Quote:

Originally Posted by Qfwfq

Now I see what you're getting at, but how would you define/measure a decline in the object’s luminosity?

The only decline in luminosity due to magnification that may presently be observable is the decline in the peak brightness of high z supernovae. Stars and galaxies are too dim to be observed at the necessary distances. The article I mentioned describes the details and necessary corrections.
http://www.slac.stanford.edu/econf/C...perlmutter.pdf