Which spectral lines do we get from far galaxies?

Hi Sofia,

If you google "spectra of distant galaxies", it looks like generally speaking, the spectral lines are the same as for local stellar spectra, but simply more red-shifted.

Without looking into it deeply, I would expect, on the basis of distance and the well-known curve of nuclear stabilities (minimum at Fe, higher at H and heavy elements, corresponding to energy-release potentials of fusion and fission), that as far galaxies are younger (formed sooner after the origin of the U), they will have a little less absorption from the more common heavier elements shortly above lithium (carbon, oxygen etc).

However, I wouldn't like to speculate about the relative frequency of supernovae from stars in younger galaxies, so the consequent formation of heavier elements in supernovae might be greater or lesser than in nearby galaxies, so their contributions to the spectra of far galaxies I leave for someone more expert.

Paul

Sofia,

Thanks for your reply, which makes it much clearer that you're asking about factors affecting the apparent age of remote galaxies, rather than simply the nature of their spectral lines and stellar composition. (I didn't understand the last part of the original question - pls see question at end of this one.)

I have to agree with Remi: As I’m sure you know well, and according to the link below:

"When two observers are in relative uniform motion and uninfluenced by any gravitational mass, the point of view of each will be that the other's (moving) clock is ticking at a slower rate than the local clock."

So the nuclear reactions in stars (and supernova explosions) in remote galaxies appear to us to ‘tick’ more slowly, which appears to slow the stars’ evolution and thus makes the galaxies of which they are composed appear younger than they would if we were local to them.

While the redshift of the combined stars’ spectra indicates a remote galaxy's speed of recession, I don’t see how that would make the galaxy appear even younger still – surely the time dilation has just one overarching effect, and the slowing of the nuclear reactions is one aspect of it?

A remote galaxy that we able to observe (which, scattering apart, must therefore be on our past light-cone, and hence also younger than our local galaxy) is nevertheless youthful in composition because it hasn't had as long to process its primordial elements into heavier elements. But that is only related to its recessional velocity in the sense that the corresponding distance indicates that it's a relatively young galaxy.

And now I have a better idea of your basic question, can you clarify for me why, in particular, you asked “Do we get from the most distant galaxies mostly the spectral lines of heavy elements?”

Thanks for a stimulating question - Paul

Hi Remi,

Thinking a bit more about the preponderance of heavier elements in far distant/young galaxies:

While my intuition is in line with your view, above, that:

"One would probably expect a preponderance of lighter elements in the spectral lines."

...my main uncertainty, as implied in my first reply, relates to whether or not the distribution of star masses of early stars tended towards the heavy end of the range.

In a young universe, on the large scale, matter would surely have been distributed less inhomogeneously than now (fewer stars, galaxies and irregularities to prompt easy proto-star collapse in the interstellar/intergalactic media), resulting in more massive, and thus shorter-lived stars in early young galaxies.

In which case, supernovae might occur sooner than nowadays, and produce relatively more heavy elements.

Regards - Paul

Oh, Remi and Paul!

It was a mistake! I corrected it, please see the text of the question again! Far galaxies are expected to contain lighter elements.

Now, as Remi says,it's a moot whether the red-shift indicates expansion of the universe. I would look into the spectral composition, whether the far galaxies emit lines of heavy elements or not.

If indeed far galaxies recede with velocities close to c, the reaction time should appear to us as lengthened by a factor 1/(1 - v2/c2)1/2. The fact that it takes more time to the light to come to us, indicates that we see the state of the object at a time x/c ago, where x is the distance at which we see it (i.e. where the star was when the beam of light was emitted).

Taking in consideration these two factors seems to me as providing a test to the hypothesis that the universe expands. But I am not sure whether the constant c was always the same in our universe.

Kind regards to both of you !

Adrian Ferent

NASA starts Stealing my Gravitation theory:

“The majority of Ferent matter(Dark matter) is the core of the supermassive black hole” Adrian Ferent(Jan 14, 2015)

NASA --"Primordial Black Holes Formed in 1st Fraction of a Second of the Universe Could Function as Dark Matter" (The Weekend Feature)

October 29, 2016

“Black holes formed in the universe's first fraction of a second -- could work as dark matter." Kashlinsky said (May 24, 2016)

http://www.nasa.gov/feature/goddard/2016/nasa-scientist-suggests-possible-link-between-primordial-black-holes-and-dark-matter

http://www.dailygalaxy.com/my_weblog/2016/10/nasa-goddard-primordial-black-holes-formed-in-1st-fraction-of-a-second-of-the-universe-could-functio.html

Ferent matter is Dark matter – Adrian Ferent (Jan 14, 2015)

https://www.youtube.com/watch?v=taXMgfqKgFQ

please go to the following link

http://www.staff.science.uu.nl/~rutte101/rrweb/rjr-edu/exercises/assignments-spectral-lines/line-usage.pdf

Dear Professor Nihal Ercan,

Thank you for the reference to the interpretation of spectral lines as distance measures.

UPDATE I think I've found the answer I sought (apologies for distracting you)

"“We have studied 10 galaxies in the early Universe and analysed their light spectra. We are observing light from the galaxies that has been on a 10-12 billion year journey to Earth, so we see the galaxies as they were then. Our expectation was that they would be relatively primitive and poor in heavier elements, but we discovered somewhat to our surprise that the gas in some of the galaxies and thus the stars in them had a very high content of heavier elements. The gas was just as enriched as our own Sun,” explains Professor Johan Fynbo from the Dark Cosmology Centre at the Niels Bohr Institute, University of Copenhagen."

As you're considerably more expert in astrophysics than I (a chemist) happen to be, I'd be interested to know if you have a view on whether the composition of the earliest galaxies (by the time they have themselves gone through a few rapid cycles of stellar deaths & subsequent new births) is likely to include less of the heavier elements (as one might at first expect) or more of them: considering my speculation, above, about the possibility of larger early stars and more frequent supernovae, leading perhaps to a possible greater density of heavier elements than in the more recently-formed galaxies comparatively near to our own (?)

Regards - Paul

http://news.ku.dk/all_news/2012/2012.5/baby_galaxies_grew_up_quickly/

Hi Sofia,

My first reaction to your revised question was that distance determinations of remote galaxies depend on the redshift of spectral lines (1st link), rather than whether the lines represent light or heavy elements (tho’ I still have to check through Prof. Nihal Ercan’s link).

However, after seeing that there are other methods of determining distant galaxies (e.g. 2nd link and extract copied in just below), I’m less certain.

"...stars are only a few thousand light years away and are still within our own Milky Way galaxy. Reaching out a million times farther away, the new BOSS measurements probe far beyond our galaxy to map the universe with unprecedented accuracy.

Making a 1 percent measurement at a distance of 6 billion light years is a huge step forward," explained Eisenstein, "and it requires a completely different technique from measurements in the solar system or the Milky Way."

BOSS measures baryon acoustic oscillations (BAO), subtle periodic ripples imprinted in the arrangement of galaxies in the cosmos. These ripples are descendants of pressure waves that moved through the plasma of the early universe, which was so hot and dense that particles of light (photons) were tightly coupled to the protons and neutrons (known collectively as "baryons") that make up the nuclei of atoms. The size of these periodic ripples can be calculated from fundamental physics; by using this standard length as one side of a triangle, astronomers can determine the distance to the clustered galaxies."

Have you any thoughts about just how a variation in composition could affect a distance determination?

Regards – Paul

https://en.wikipedia.org/wiki/List_of_the_most_distant_astronomical_objects

http://news.psu.edu/story/299655/2014/01/08/research/distance-remote-galaxies-can-now-be-measured-1-percent-accuracy

Paul, my friend,

I have first to read the articles that you sent me - thanks a lot for them. The 1% accuracy is, I suppose, in base of some models. So, I have to look carefully.

By the way, let me tell you a bit of history: Asher Peres after having grown tired of the stubborness of the QM in hiding its secrets about entanglements, collapse, and which material the wave-function is made of, decided to return to gravity - he had done his Ph.D. with Nathan Rosen as advisor.

Well, Asher had a very good student, Danny Terno, with whom they discovered that the light velocity could have been different in different epochs of the evolution of the universe.

If you could be interested in that article, please remind me when you finish with those lectures at evening hours (so I understood from your previous letter). I have to seek the article, for the moment I don't know where I stored it.

Now, my question about checking the recession velocity of distant cellestial objects is, of course, naïve, as I don't work in cosmology. Just, somehow, this idea of far objects moving at superluminal velocity, smells somehow not good to me. The relativity shouldn't allow that mass-possessing object exceed the light-velocity.

Best regards,

Sofia

Hi Paul, very shortly i must remind you that the chemical composition , therefore age of the galaxies/clusters of galaxies are mostly related with the type of the supernova core collapse SNcc and/or SNIa happened in their structure then over the galaxy/or clusters of galaxies one can make predictions by looking at their ratio obtained observationally . S,Si, O, Mg, Fe can be common throughout the distribution along the radial distances sometimes making uniform distribution, sometimes showing peaks at certain distances.

let me go through a little bit more about the subject ;

two enrichment scenarios would compete (early-time vs. late-time). In fact, both types of enrichment are not necessarily mutually exclusive. In particular, the typical Fe profile measured out to R_200 in the previous literature suggests that one part of Fe (the uniform distribution seen in the outskirts) was enriched *before* the cluster formation (e,g, Werner et al. 2013, Simionescu et al. 2015), while the other part of Fe (the central peak) could be mostly produced by the stellar population of the central cD galaxy, when the latter was already in place in the centre of the gravitational potential, thus presumably during or shortly *after* the cluster formation (de Grandi et al. 2004, Boehringer et al. 2004). this possible "late-time" enrichment associated with the metal peak may require >~ 5 Gyr of enrichment, which is considerably long. De Grandi et al. (2014) found that the Fe content of a cluster core was already in place at z=1 (7-8 Gyr).the Fe, Si and Mg abundances measured in the outskirts seem to favor an early enrichment. , it would be conceivable that a significant part of the enrichment occured during or shortly *after* the collapse of the cluster, mainly in the central cD galaxy In this respect, Simionescu et al. (2009) measured a peaked O profile in Hydra A, and showed that this central excess of SNcc products could well be explained by SNcc exploding in the cD galaxy. however,it is not clear (yet) whether the central cD galaxy was already in place at z~2-3 (during the cluster formation), i.e. whether the central enrichment is early-time or (slightly) late-time.

Actually, I have not seen a paper clearly claiming/proposing the case of a late-time enrichment, but i could have missed them.

Hi Nihal (if that's appropriate),

Thank you for further clues. I hope to get back to this next week.

Meanwhile, I shall try to make the time to tutor myself via arXiv:1608.03888 [astro-ph.GA], which seems relevant, and look out for indications of variabililty across time.

Paul

https://arxiv.org/pdf/1608.03888v1.pdf

yes Paul ,that one is a very good recent paper! we are working on a similar one at the moment and also collaborate with Francois Mernier at the same time ; our arxiv copy of the recent apper is on top of my publications.

best,

Nihal

Hi Sofia,

Regarding your last remark (final sentence), you might want to look at the link below.

Cheers - Paul

https://en.wikipedia.org/wiki/Metric_expansion_of_space

Hi Nihal,

Many thanks for your explanations.

Now, can you tell us with which velocities recede from us those objects that you mentioned? Not everybody works in cosmology/astrophysics.

With many thanks,

Sofia

https://arxiv.org/abs/astro-ph/0104382

Dear George and Nihal,

You are very kind both of you and thank you. But, let me quote George's statement:

==> "you cannot think of distant objects moving through space, instead think of the gap between us expanding so that light in a distant galaxy is moving through at the usual speed of light relative to the stars it contains, and all matter moves more slowly within it."

Isn't this "la meme Jeanette authement coifee"? (the same Jeanette with another hairstyle - very popular French saying) What is the difference between an object receding from us, and the distance to the object increasing?

Obviously, you both understand more than I in cosmology, astrophysics, and general relativity - these are not my domains at all. But we are told that the most distant galaxies "recede" from us faster than light. To me George's saying - I know that it's not his invention, I heard of that explanation already - seems just wording for justifying faster than light movement that the special relativity forbids. You see, to move faster-than light is forbidden, but to produce the same effect AS IF moving faster than light is permitted. Doesn't that "smell" SUSPECTLY to you?

Of course, I repeat, it's not my domain. Now, Asher Peres and Daniel Terno found, years ago, that the velocity of light could have been different than today in earlier epochs of the universe evolution. Are such things known to you?

Kind regards and thanks to both of you,

Sofia

Dear Sofia,

i have no idea about the velocity of light change, there must be theories alreday mentioned about it but observationally,it is not yet achieved! so, nothing can go faster than light with 300 000 km/s even, light itself. Peres and Terno works which i have no idea et al, but still observayionally there is no way to argue about the early epochs/current epoch of the universe change of speed of light . this may be correct idea/thought but not yet confirmed by observations to my knowledge.

best

Sofia, your question comes up quite often and I could dig around on the web and no doubt find a few pages that explain it, but I feel that maybe putting it in my own words would allow you to question what I say. Do please though have a look around too.

First I have to give a word of caution. "Speed" is a quantity which tell you how coordinates are related, so if an object is moving along the x axis, its speed is the derivative dx/dt. That may sound obvious but in relativity, we recognise that nature doesn't come ready-equipped with coordinates for our pleasure, we have to make up our own. The way I will explain this assume a particular approach to defining coordinates but it is not unique. In particular, you should look into "co-moving coordinates" and "conformal coordinates" which will give different answers. These are covered briefly in the tutorial linked so see below. Note also that the derivative has a specific value at a specific location so the limit only applies locally in relativity.

To start with, you say "to move faster-than light is forbidden" which is valid as derived from relativity, but if we are to use that theory, then you must define it appropriately: "speed in what inertial frame" or "speed relative to what free-falling object"?

For light leaving a star in a distant galaxy, the answer is that it is limited to be measured as not exceeding c relative to nearby inertially moving matter.

Now suppose we imagine light leaving a star within a distant galaxy, and we pick the example of a galaxy so far from us that the gap between it and us is increasing by 3 light years per year. The SR restriction still applies so light emitted away from us will become more distant by 4 light years while that emitted towards us will overall still recede by 2 light years per year.

Matter is similarly constrained to be measured as moving at a speed within the range allowed for light. The limit is described by a geometrical concept called the "light cone", light moves on the surface while matter moves inside it but not on it (I'm sure you know most of this but it makes the story complete).

If you therefore imagine the worldline of a distant galaxy, that is, a plot of its distance as a function of cosmological age, the light cone for it will be wrapped round its path and for light moving directly towards us or away from us, you get a "V" shape which leans away from us. The second link attached is to Prof Ned Wright's introductory tutorial and shows images of this effect. He notes:

Note how the lightcones must tip over along with the worldlines of the galaxies, showing that in these cosmological variables the speed of light is c with respect to local comoving observers.

The red pear-drop shape locus on the next diagram shows how far away light we see now was at earlier times, with distance plotted horizontally and increasing time vertical (we are at the top centre). You can see both how the light cones (the small triangles) lean away and also how light follows the edge of cones everywhere it passes a comoving galaxy.

That link is to page 2, I would strongly advise that you have a look but then go back to page 1 and study the whole tutorial, it's only 4 pages. In particular that simple diagram uses coordinates in which the galaxies move away at constant speed (i.e. straight lines). Lower on the same page he talks about the varying rate of expansion and on page 3 he bring the two together. See the third link for a more realistic spacetime diagram.

Below that on page 3, he covers alternative coordinate schemes where the speed of light becomes constant globally, but remember, all coordinate systems are only invented by us for our own convenience ;-)

SDW: Asher Peres and Daniel Terno found, years ago, that the velocity of light could have been different than today in earlier epochs of the universe evolution. Are such things known to you?

I don't know of their work specifically. There is immediately a problem of defining coordinate in which such a claim would have a physical meaning so I would really need to see what they were saying. I would expect such a change to have an impact on spectral lines so I would ask whether it is tested by the work done on testing variations of the fine structure constant. There are other questions on RG about that so I won't duplicate them here.

https://en.wikipedia.org/wiki/Light_cone

http://www.astro.ucla.edu/~wright/cosmo_02.htm#MD

http://www.astro.ucla.edu/~wright/cosmo_03.htm#MSTD

Dear George,

I looked and looked in the Wikipedia. Now, let me reply:

George: "you must define it appropriately: "speed in what inertial frame"

Here you probably were not so attentive. The speed of light, at least in special relativity, is independent of anr particular inertial frame. As to non-inertial frames, at rest with respect with some accelerated object, at each point P in the space-time in such a frame, we can associate an inertial frame moving with the velocity of the accelerated frame at P.

Of course, this is what I learnt quite a long time ago.

Now, I had a look at the tutorial and I'll read it more deeply. I see that this theory of extenstion of the space-time is needed for fitting diverse astrophysical data. Though, I'll try to find that article of Peres and Terno. There is little chance for me to understand it, but probably, you and Nichal yes would understand.

With kind regards,

Sofia

SDW: The speed of light, at least in special relativity, is independent of anr particular inertial frame.

That is true in SR and locally in GR but does not hold for remote measurements in GR. The answer to your question lies in that distinction.

best regards

George

P.S. I should perhaps point out that while I'm just an amateur, the site linked is by Prof Ned Wright who was one of the chief investigators on the COBE mission and is still heavily involved in research work. He has been teaching cosmology and astrophysics for over 35 years so while you should be sceptical of my very abridged version, the linked tutorial is one you can trust as a good introduction to the current view. My summary should just be a hint on what to look for in that.

http://www.astro.ucla.edu/~wright/intro.html

George, you are very kind, thank you.

I read the tutorial. Of course, there were things that I didn't understand as I am not professional in the topic. But I saw that this hypothesis of extension of the space-time was emitted because astrophysics data required so.

With kind regards,

Sofia

Dear friends,

By the way, I saw a diagram named "Nature timeline" in Wikipedia, at the site

https://en.wikipedia.org/wiki/Metric_expansion_of_space

that Paul recommended me (and thanks!).

If one looks attentively, one sees beginning from the bottom of that diagram upwards: Earliest universe (13.8 billions of years) and Earliest Gravity, then Earliest Galaxy and Earliest light, then Earliest Quasar, etc.

So, it seems that photons didn't exist at the Big-Bang time. But what about matter with rest-mass? Is it known what type of matter existed?

The diagram shows the earliest light we can see (the CMB from ~378 thousand years age) but that is only because the universe was previously opaque. The energy density of light was about the same as that of matter when the universe was about 50,000 years old and dominated before that. Have a look at this link too.

https://en.wikipedia.org/wiki/Scale_factor_(cosmology)#Chronology

Thanks George,

I read the reference. But there is one thing that seems strange to me. Please see, the photon is a stable particle. It does not disintegrate into an electron and positron unless forced into a cavity of linear dimension less than the photon wavelength. How the matter appeared in a universe in which there were only photons and neutrinos? And mainly how the protons appeared? I quote:

"After Inflation, and until about 47,000 years after the Big Bang, the dynamics of the early universe were set by radiation (referring generally to the constituents of the universe which moved relativistically, principally photons and neutrinos)."

"Between about 47,000 years and 9.8 billion years after the Big Bang,[11] the energy density of matter exceeded both the energy density of radiation and the vacuum energy density."

The origin of matter is still a bit vague. The current idea is that there was a period of inflation driven by some field. When that stopped, the energy that was driving inflation coupled through weak interactions (I think) to produce a surge of particles. Anyway, there's a graph on page 23 of the first link, the TASI lecture on inflation which shows where particles would be created in the phase called "reheating" after the flat slow-roll inflation period.

The bulk of those would be photons but every other possible particle would be created too, up to some mass limit. There would be dynamic equilibrium for a while with particles annihilating with anti-particles to create photons and photons colliding to make new particles. Remember if two particles annihilate to create photons, then the process is reversible if the photons have more energy than the mass of the particle pair.

Eventually everything cooled enough that new matter could no longer be created, the photon energy fell below the minimum particle mass but annihilation continued until all the anti-matter was used up, but oddly there was a smidgeon of normal matter left. For every billion anti-matter particles, there were about a billion and one particles of normal matter so after annihilation, that left two billion photons for every normal particle and no anti-matter.

As the universe expands, matter density decreases by the cube of the scale factor but radiation decreases as the fourth power so the density falls faster. The density of vacuum (dark) energy is constant so there are separate periods of dominance. The relative densities of radiation, matter and dark energy are shown on the third page of the second link which is an addendum to a lecture. The radiation density dropped below matter at around 47 thousand years and that of matter fell below dark energy at about 9.8 billion years.

A chart of the formation of hydrogen, helium, etc. are described briefly in the third link in case you're interested. The image is from another overview that might be of interest, and in particular it has a useful timeline that mentions when protons would have been created.

https://arxiv.org/abs/0902.1529

http://www.nicadd.niu.edu/~bterzic/PHYS652/Appendix_09.pdf

https://universe-review.ca/I02-09-nucleosynthesis2.jpg

https://universe-review.ca/F02-cosmicbg01.htm

You are very, very kind George,

I'll read all the links.

Also, you pointed to a odd property of our universe. It's a universe of matter, the amount of anti-matter is by far much smaller.

With appreciation for your help,

Sofia

Yes, that's not understood. Some asymmetries have been found, just not quite big enough to explain the observed photon/baryon ratio which is reasonably well constrained.

Dear George,

Are you good at relativistic quantum mechanics? I am affraid that it is not exactly your domain. Though, I hope that I am wrong. In the Dirac equation, particles and antiparticles are treated on equal footing. But it seems that our universe does not "consider" in the same way. Otherwise, the amount of matter and anti-matter would be equal. Well, it's just a thought.

You say that "some asymmetries have been found". Can you indicate reference, or can you explain a bit?

SDW: Are you good at relativistic quantum mechanics?

No, I haven't touched it in over 40 years.

SDW: You say that "some asymmetries have been found". Can you indicate reference, or can you explain a bit?

I would suggest starting with what we know from the experimental evidence which you can get from the references section on the linked page. The second link discusses the connection to baryon asymmetry.

"The Standard Model contains at least three sources of CP violation. The first of these, involving the Cabibbo–Kobayashi–Maskawa matrix in the quark sector, has been observed experimentally and can only account for a small portion of the CP violation required to explain the matter-antimatter asymmetry. The strong interaction should also violate CP, in principle, but the failure to observe the electric dipole moment of the neutron in experiments suggests that any CP violation in the strong sector is also too small to account for the necessary CP violation in the early universe. The third source of CP violation is the Pontecorvo–Maki–Nakagawa–Sakata matrix in the lepton sector. Current neutrino experiments are not yet sensitive enough to allow experimental observation of CP violation in the lepton sector, ... If neutrinos are Majorana fermions, the PMNS matrix could have two independent CP violating phases leading to a fourth source of CP violation within the Standard Model."

https://en.wikipedia.org/wiki/CP_violation#Experimental_status

https://en.wikipedia.org/wiki/CP_violation#CP_violation_and_the_matter.E2.80.93antimatter_imbalance

George,

Thank you for your informative and useful summary of the experimental evidence relating to the apparent matter-antimatter asymmetry in the universe.

From the theoretical perspective, having some bearing on the OP’s main question about cosmic distance and later questions about antimatter, one can consider an alternative, cosmological explanation for antimatter’s large-scale absence in the observable cosmos, consistent with the conservation rules that dictate symmetry in its production and annihilation.

Could it be that the origin of the universe involved an almost immediate separation of matter and antimatter in time resulting in a time-symmetric matter-antimatter cosmology?

This type of model involves a ‘mirror universe’ of antimatter, co-spatial with the one we experience but separated temporally from us by twice the age we attribute to the universe we inhabit. (It’s consistent with the Feynman–Stueckelberg interpretation: that antimatter and antiparticles are regular particles traveling backward in time [1] , and also [though I'm not sure I'd agree] with Villata’s consequent argument that “the assumption of antimatter as CPT-transformed matter would imply that the gravitational interaction between matter and antimatter is repulsive” [2]).

This cosmological model has been conceived more than once. As far as I’m aware it was the now-eminent Princeton professor, J Richard Gott III, who first published it in a peer-reviewed journal, ApJ [3], while he was at CalTech (co-temporally with Feynman!) Since then the idea has also been attributed to others, including the particle physicist Victor Stenger, and another, as mentioned in a brief 2009 letter published by New Scientist [4].

Regards - Paul

Footnote: If it’s not too off-topic, I’d like to add an historical footnote: Just prior to the appearance of Richard Gott’s paper (1974), Henry Margenau, then editor of Foundations of Physics, requested a revise & resubmit for a paper involving the same basic cosmology.

Gott’s essentially mathematical paper sought “the most general solutions to Einstein’s field equations with symmetries about an event singularity”. Mine, in contrast and with falsifiable observational consequences, was an early attempt to explain quasars: observed by us, but assuming the mirror-universe's existence, then in either of the two universes quasars could appear as ‘white holes’ ejecting mass-energy that had transited via wormholes, after having fallen into co-spatial black holes in the ‘other’ universe. Jacob Bekenstein, approving the physical insight, advised me to make the paper more quantitative, which, had I had the maths, should have turned out to be the same model as Gott’s.

https://arxiv.org/pdf/1204.4186

http://iopscience.iop.org/article/10.1209/0295-5075/94/20001/meta

http://adsabs.harvard.edu/abs/1974ApJ...187....1G

https://www.newscientist.com/letter/mg20327160-600-antimatters/

Dear Paul and George,

You are both very wise and very kind.

Now, from the article https://arxiv.org/pdf/1204.4186 (thanks Paul!) I understand that the huge asymmetry between the amount of matter and anti-matter in the present universe, is due to only a small fluctuation, a small amount of matter exceeding the amount of anti-matter. Then, the equal amounts of matter and anti-matter annihilated with production of photons, and only the excess remained.

If indeed, the ratio between the matter and electromagnetic radiation in the universe is so tiny, then the explanation seems acceptable. I understand that everything could have been vice-versa, i.e. an excess of anti-matter in the beginning.

As to the " CP violation " in Wikipedia (thanks George!) it is very interesting. So, there are laws of the universe which treat a particle and its anti-particle in a non-symmetrical way. Dirac's equation doesn't show this asymmetry.

Many thanks to both of you!