Rolando

The omnidirectionally closed universe (analogous to the surface of an inflating balloon) appears to be incompatible with the observations that suggest the universe to be flat. In a flat and open universe, one can talk of two boundaries, both somewhat indistinct. The first one tells how far the matter (the web of galaxies) has expanded. The second one tells how far light and other radiation has propagated. I am not promoting any of these or any other alternative. I just wish to know the reasoning within the frame of standard Big Bang cosmology.

Let me reformulate my question: What happens to light when it moves farther than the material universe has expanded? After the standard Big Bang universe had become transparent - the universe expanded at less than 100 km/s then - what happened to light when it reached the boundary of the universe? Friedman models do not tell this. Instead of matter and radiation, these contain only an abstract fluid, and this is taken to represent the motion of matter. Light moves faster and further in free space. It has sometimes been claimed that the Big Bang universe has no boundary, but this is true only for omnidirectionally closed universes. Our universe is nowadays claimed to be flat and open. Yet I have never seen it explicitly claimed that the universe has a boundary at which light is reflected back. If there is no such boundary, then the material universe is surrounded by a much larger universe that contains only radiation. In order to see the CMBR, one would need to be at the boundary of this larger universe.

This text describes in its first passage how the reasoning goes within Big Bang cosmology: https://ned.ipac.caltech.edu/level5/Glossary/Essay_lss.html The description is intelligible to me. It answers my question and confirms my concern.

Thanks, especially to Strange, for your attempts to answer my question.

We have only moved away a negligible distance from the source of the radiation. It is the radiation front that has moved away very far from us - not its source.

To my understanding, the distance between us and the source of the radiation is now still close to 0 light years, in any case < 1 billion.

If this is the definition of "surface of last scattering", it is a misnomer. The literal meaning of "surface of last scattering" is a surface at which which the photons are no longer scattered by particles, which happens when the temperature of the surface due to its expansion goes below very roughly 3000 K. This surface does not expand. I said it a little less categorically: we have not moved much relative to the sphere where the light originated.

If there was no reflection, why had the light to travel 4 billion light years? Our galaxy has only moved a negligible distance during the past 13.8 billion years.

This sounds reasonable. If the photons we see now started approximately 4 billion years ago (or away) they must have been reflected there if they were originally emitted at the surface of last scattering and have been on their way for 13.8 billion years, but this is not usually told. The text in https://ned.ipac.caltech.edu/level5/March03/Lineweaver/Lineweaver7_2.html lacks this information.

This everywhere was enclosed within a space in which everything was clother than 1 billion light years to everything else – and our galaxy has not moved outside this space. Under these circumstances, in a flat geometry, a ray of light between the source and us can have a length of 13.8 billion light years only if it is reflected on its way. In various non-flat geometries, such a length can be obtained without reflection. I have yet to look at the link you provided in your second response. Thank you.

In standard Big Bang cosmology, the cosmic microwave background radiation (CMBR) originated about 13 billion years ago. Subsequently, it will be visible at a distance of 13 billion light years from its origin. Our own galaxy has only moved a much shorter distance from a place close to this origin since then. My question is how it can be that we, nevertheless, still can see this radiation. Text books assure us that the CMBR is a blackbody radiation that expands with the universe and so becomes more long-waved. This would require either that the universe was (1) infinite or (2) surrounded by a reflecting wall or (3) expanding like the surface of an inflating balloon. Alt. (3) was tenable until it began to be claimed that the geometry of the universe is flat, alt. (2) was always denied and in alt. (1) there is no Big Bang. So, on which additional alternative rests the present doctrine?

This was a waste of time.

How could you fail to see that these descriptions are just the mutually exclusive alternatives under discussion? Each one has to be considered on its own, and the problem is that none of them appears to be acceptable.

In Schwarzschild geometry, it holds that the deeper an atom sits in a gravitational potential well the smaller is the energy difference of atomic levels. This is an effect of space-time geometry and reflected in the frequency of photons observed in a frame of reference in which source and receiver are stationary. This is all that is captured by the usual equations. The problem arises when one tries to locate (ascribe) the effect either to the atoms or to the photons, which needs to be decided in order to illustrate and understand what is going on. Ascribing the effect to the atoms gives rise to the question of why the photons on their way are not affected by the geometry if it is the geometry that gives rise to the effect on atoms. Ascribing the effect to the photons fails to account for observable clock rate differences. Okun et al. reject this alternative with a different motivation. One might also consider Painlevé-Gullstrand coordinates, in which the frequency shifts and clock rate differences under discussion here reflect the same Doppler effect. This may be more transparent.

The first one leaves my question without an answer. The second one denies your claim of what the physics is.