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.

I can agree with this. But if there is such a change and this change is due to geometry, this raises the question of why the photons are not affected by this geometry (in the interpretation advocated by Okun et al. and apparently also by Atkins). In the alternative interpretation, the photons are affected on their way and the atoms cannot be assumed to be affected as well. I am looking for a tenable interpretation.

I thought for a while that I had understood. However, let me quote from Okun, Selivanov & Telegdi (page 7): ”Now we are in a position to explain the redshift in the laboratory frame. According to Eq. (8) or Eq. (10) the energy difference εlab of atomic or nuclear levels in that frame depends on the location of the atom. The deeper atom sits in the gravitational potential the smaller is εlab. For an absorber atom which is located at height h above an identical atom which emits the photon, the relative change in the energy difference is gh/c2, Delta εlab /εlab = gh/c2. (11)” ...”One can say that the energy levels of the absorber atoms are shifted towards the blue in the laboratory frame. Eq. (11) is, of course, nothing but a way to describe the difference in the rates of atomic clocks located at a height h one above the other. On the other hand, the energy (frequency) of the photon is conserved as it propagates in a static gravitational field. This can, for example, be seen from the wave equation of electromagnetic field in the presence of a static gravitational potential or from the equations of motion of a massless (or massive) particle in a static metric. Clearly, in the laboratory system there is no room for the interpretation in which the photon loses its energy when working against the gravitational field.” [This interpretation is alternative (2) in the present discussion.] While the quoted explanation is not made explicit in Atkins’ book, the illustration there is fully in accord with it.

The caption of the figure in Atkin’s book (here) reads: ”In a gravitational filed, an atom emits light with a lower frequency and thus with larger wavelength.” The associated text suggests that the frame of a distant observer is adopted. No confusion so far. It would also be too odd an idea to think that it might hold in the frame of the source itself. (Time can hardly be dilated with respect to itself.) I agree. But if you take a closer look at Atkin’s figure, you will see that frames have been mixed already there (which confirms that I am not the first). The context, as well as the difference between the waves emitted by the two sources, suggests that things are shown in the flat space of a distant observer. However, each wave itself is not shown as it would appear in that space. They are shown as they appear in the curved space in which they propagate. The wavelength remains constant only in this space. If projected onto a flat space, the wavelengths appear shorter close to the attracting body, as they do in the figure here, where the orientation agrees with that in Atkin’s figure. But even this figure is misleading, since it fails to show that the change in wavelength is due to the curvature of space. In order to be clear, it is necessary to show this. Otherwise it is simpler to think of it as Einstein did in 1911.

Conclusions The discussed alternative (1) is illustrated here. The caption says: ”In a gravitational filed, an atom emits light with a lower frequency and thus with larger wavelength.” This alternative is misleading since it evokes the question that I asked. Any attentive student at this level of knowledge might have asked it. I guess that this is the reason for why this alternative has lost popularity. The discussed alternative (2) is illustrated here. This is misleading in a different way, since it can rather be seen as illustrative of how Einstein treated the problem before he came up with GR, i.e., before the idea of gravitational time dilation was born. It is, of course, possible to illustrate GR in a way that is not misleading in any of these ways. Do it, if you are well acquainted with producing such figures, and when you think that it is not misleading in still another way, place it in the Wikipedia. Meanwhile, I have also learnt what is meant by trolling, and I understand that I have been the victim of a troll, who succeeded to some extent. I apologize if this has colored my responses to others as well. I attach significance to the fact that I was urged to talk in mathematical language, although this would in no way have been helpful to answer my question, but just hide it under the carpet. I also attach significance to the fact that the thread with my unspeculative pedagogical question has been moved to a box that is intended for pseudoscientific and speculative threads, which makes it most unlikely for the answer to this question to be noticed by those to whom it might be most relevant.

Thank you MigL. Your answer is to the point. I had failed to not notice that also in alternative (2), the effects can be considered as due to time-dilation, which makes the two alternatives fully equivalent. My mind had become locked on the other possible interpretation of alternative (2), in which the photons loose energy without there beeing any time dilation (as in Einstein’s model of 1911, which I mentioned).

If this thread has been moved to "Speculations", then good by. Thanks to all of you for your contributions.

I am in full agreement with what you say here. This is all stuff that I assumed to be sufficiently well known to all who follow this topic. I cant see what you mean to be wrong. Alternative 1) tells you that you will see the flashes arriving in intervals of two seconds. Alternative 2) tells you that you will see the flashes arriving in intervals of one second. Interpretation only? Same thing from different points of view?

As you can see from my response to Strange, the difference between the descriptions is not just in the interpretation. By telling the year 1911, I ment to tell precicely what you said.

In order to obtain empirical adequacy, the following holds: If you have chosen description (1), where the effect is caused by the atom emitting a different frequency, ... the photons are not affected by the geometry. If you have chosen description (2), where the effect is caused by the photons loosing energy, then ... the clocks are not affected. For ... , you can substitute either 1) then, 2) then it remains a mystery why, 3) then it is necessary to assume that, but you cannot choose 4) then this choice is the explanation for why if you strive for being taken seriously. It is no explanation and not even an acceptable excuse. You can choose one description or the other, not both, but they do not describe the same thing. This is so embarassingly simple to see. Take a clock that flashes in intervals of one second. Place it on a body whose gravitation is strong enough to cause a redshift z = 1 when looked at from your safe distance. Alternative 1) tells you that you will see the flashes arriving in intervals of two seconds. Alternative 2) tells you that you will see the flashes arriving in intervals of one second.