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Author Topic:   The accelerating expanding universe
Alfred Maddenstein
Member (Idle past 3989 days)
Posts: 565
Joined: 04-01-2011


Message 101 of 149 (611303)
04-07-2011 8:14 AM
Reply to: Message 48 by Percy
04-01-2011 5:10 PM


Re: Relative Space in Linear, Flat and Absolute Time
Thank you, Percy for recommending Viv Pope to me. He is definitely a very sensible fellow and his book "In the eye of the observers" deserves to be read. What he advocates is return to simplicity in the natural science taking his relativism straight from the horse's mouth of Ernst Mach.
His idea of space, time and light being strict relative measures of one another with the triad forming the tightest knot in nature is precisely what I am saying.
The relations between the sides of a triangle are strict geometry: space, time and light are to be studied as a triangle and the relations between them are be taken accordingly and can be violated only inside the head of a modern theorist and that simple consideration alone should put paid to all the expanding universe fantasies where space behaves like a magic carpet and the galaxies are accelerating like a bunch of scared pigeons.

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Alfred Maddenstein
Member (Idle past 3989 days)
Posts: 565
Joined: 04-01-2011


Message 102 of 149 (611306)
04-07-2011 9:00 AM
Reply to: Message 52 by cavediver
04-01-2011 6:26 PM


Re: Relative Space in Linear, Flat and Absolute Time
Well, Crankdriver you call Luis Savain an idiot failing to demonstrate him as such. He might not have any real solutions but he points out to the real contradictions in relativity.
At least he thinks for himself. His crankship is in a minority so his concepts are mocked as fantastic. They may well be such.
You reckon that if your black holes, dark energy, matter and inflation the rest is a widely accepted, deeply revered and peer-reviewed lunacy that gives you a good reason to be so smug and condescending towards Luis?
Think again. We are all equally mad to a hypothetical sane observer. Only all the madmen are of two types.
The brave mad and the cowardly raving. The courageously mad are not scared to be mad alone and in their own way and but the cowardly insane need all their pathetic lunacy to be fed to them with a spoon first, they need all the peer approval before they dare to rave a little.

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 Message 52 by cavediver, posted 04-01-2011 6:26 PM cavediver has not replied

  
Alfred Maddenstein
Member (Idle past 3989 days)
Posts: 565
Joined: 04-01-2011


(1)
Message 103 of 149 (611310)
04-07-2011 9:54 AM
Reply to: Message 93 by cavediver
04-06-2011 5:56 PM


Re: A general question for anyone
Well, Crankdriver, your sophistry is lame. What your friend's mother may be doubting is just the factualness of the NASA claim to have landed men on the moon. Both scenarios are perfectly possible. I don't hold it as very likely that NASA went to such great lengths to put up a mere show of the landing, on the other hand that cannot be ruled out completely.
Neither in the possibility that they did not deceive anybody in the present case but the events had actually taken place as claimed is anything that may violate the first law of thermodynamics.
Whereas if I say that no expansion of the universe is taking place other than deep inside of your theoretical head that is because any expansion would break the law of conservation of motion and rest and the law of the preservation of the parity between matter and void making that motion and rest possible.
And your suggestion you keep on patronising me for doubting breaks that law with a vengeance.
That I hold to be physically impossible unless you show me otherwise in a reasonable manner which you cannot.
As I said expansion is gaining volume by definition. The universe is all that exist and is therefore surrounded by all that does not exist which is called nothing pure and simple. So it is one and only universe necessarily.
Nothing is all that does not exists and what does not exist may take no place to exist and what take no place to exist may need no volume to succeed in being perfectly absent.
Thus to be expanding into nothing as your fairy-tale of a theory claims in the physical and measurable terms may mean to be gaining all the volume nothing may be losing to it in the process.
The volume that is possible to gain from nothing is no volume the nothing is capable of possessing. That volume may equal zero necessarily. A zero increase in volume possible for the universe translated in plain English is the retention of the same size and volume as ever.
That is logic, my friend, and no seven million peer reviews you may need to ignore it can change a letter of it. That's Aristotle for you. You may choose to be smug towards the man but that won't last long unless your peer-reviewers discover a magic trick of accelerating their expanding angular momentum.
Their concepts brave and porous
they all dare rave in chorus
Edited by Alfred Maddenstein, : Grammar

This message is a reply to:
 Message 93 by cavediver, posted 04-06-2011 5:56 PM cavediver has not replied

Replies to this message:
 Message 104 by jar, posted 04-07-2011 10:02 AM Alfred Maddenstein has replied

  
Alfred Maddenstein
Member (Idle past 3989 days)
Posts: 565
Joined: 04-01-2011


(1)
Message 105 of 149 (611318)
04-07-2011 11:21 AM
Reply to: Message 104 by jar
04-07-2011 10:02 AM


Re: A general question for anyone
Reality trumps logic every time.
No. Reality may be a paradox yet even as a paradox it is consistent. Not just anything goes like you are trying to make me believe. So, no. You may get the cat that either dead or alive but no squeaking pig or flying dog may pop out of the hat if it was a cat that went first into your magic hat.
So, from nothing only nothing comes. Something comes from something only. Motion is not created by magic and the laws of motion do not break in a singularity. They all hold with good logic and it is any singularity that breaks before it when properly examined by it.

This message is a reply to:
 Message 104 by jar, posted 04-07-2011 10:02 AM jar has replied

Replies to this message:
 Message 107 by jar, posted 04-07-2011 11:24 AM Alfred Maddenstein has replied

  
Alfred Maddenstein
Member (Idle past 3989 days)
Posts: 565
Joined: 04-01-2011


(1)
Message 108 of 149 (611326)
04-07-2011 12:01 PM
Reply to: Message 107 by jar
04-07-2011 11:24 AM


Re: A general question for anyone
I am afraid, my friend, you have to try much better than that. You say that my statement was a word salad.
That declaration is as empty of meaning as would be my claiming that what you have replied with was a syllable hodgepodge.
Reality trumps logic every time may be remaining another vacuous assertion of yours, unless you bring me concrete examples. Say, give me a list of the alleged trumpings of logic by reality that you have observed to-day.
Then we may examine the occurrences and establish whether such was the case.
Catch my drift?

This message is a reply to:
 Message 107 by jar, posted 04-07-2011 11:24 AM jar has replied

Replies to this message:
 Message 109 by jar, posted 04-07-2011 12:28 PM Alfred Maddenstein has not replied
 Message 110 by fearandloathing, posted 04-07-2011 12:29 PM Alfred Maddenstein has not replied
 Message 117 by Buzsaw, posted 04-08-2011 9:14 PM Alfred Maddenstein has replied

  
Alfred Maddenstein
Member (Idle past 3989 days)
Posts: 565
Joined: 04-01-2011


Message 111 of 149 (611342)
04-07-2011 1:58 PM
Reply to: Message 106 by Son Goku
04-07-2011 11:24 AM


Re: Relativity
Yes, that is correct. I do indeed find the theory of relativity to be reasonable but the solutions from which the flat universal clock rate is derived seem to me contrived and patched upon it arbitrarily and it appears that they were simply needed in order to fit the theory to the assumption of the universal uniform expansion from a single dot of spacetime.
One of the reasons why I call the speed of light the speed of time itself is clear if you remember that that aspect of time which is measured by a clock rate is irrelevant at that speed. They say time stops at the speed of light. What I say is but a different manner to express the same.
Anyway, the concept developed by that chap Alexander Franklin Mayer strikes me as much, much more reasonable.
He takes the ideas straight from Minkowski and Feynman and the logic in his treatment is sound and compelling.
Just a little passage:
First he cites Feynman
"A difference between a space measurement and a time measurement produces a new time measurement.
In other words, in the space measurements of one man there is mixed in a little time, as seen by the other.
Now in Lorentz transformation and the Minkowski metric the nature is telling us that time and space are equivalent; TIME BECOMES SPACE; they should be measured in the same units."
Now Mayer gives his own development of the above restoring the Copernican principle back to its glory or rather restoring the temporal side of the coin:
"If we understand Minkowski's contribution to imply that time is to be treated mathematically and therefore conceptually in the context of geometry, it then makes perfect sense to interpret temporal effects in special relativity as an equivalent relative change in the length of the reference time unit, rather than the relative rate of clocks. A shift in thinking from the algebra of relative clock rates in one dimension (i.e.., the real numbers) to the geometry of relative time lengths in 'complex' 4-dimensional spacetime (naturally measured in meters in the context of geometry) allows the inherent symmetries of physical measurements to be modelled with unprecedented clarity. The geometric nature of relativistic time revealed by Minkowski implies an infinite number of distinct cosmological time-lines rather than one, and distinct time-lines associated with distinct cosmic regions cannot be parallel."

This message is a reply to:
 Message 106 by Son Goku, posted 04-07-2011 11:24 AM Son Goku has replied

Replies to this message:
 Message 112 by Oli, posted 04-08-2011 10:40 AM Alfred Maddenstein has replied
 Message 124 by Son Goku, posted 04-13-2011 9:38 AM Alfred Maddenstein has replied

  
Alfred Maddenstein
Member (Idle past 3989 days)
Posts: 565
Joined: 04-01-2011


Message 114 of 149 (611517)
04-08-2011 1:17 PM
Reply to: Message 113 by cavediver
04-08-2011 12:17 PM


Re: Relativity
Yes, and from this assumption Mayer derives a different explanation to the red-shift phenomenon. Dropping the presumption of physical impossibility of space expanding at superluminal velocities led him to recalculate the distances, redraw the map of cosmos and in this view the red-shift is due rather to the ubiquitous time-dilation.
The earth is seen as the miniature model of cosmos, space-time a mental reflection of the earth on the universal scale with time-lines rotating slowly instead of the gravity vectors as is the case with the terrestrial sphere.
It is a beautiful model and unless it is conclusively shown incorrect when tested against observational data, I am very pleased to support it.

This message is a reply to:
 Message 113 by cavediver, posted 04-08-2011 12:17 PM cavediver has not replied

  
Alfred Maddenstein
Member (Idle past 3989 days)
Posts: 565
Joined: 04-01-2011


(1)
Message 118 of 149 (611599)
04-08-2011 10:52 PM
Reply to: Message 117 by Buzsaw
04-08-2011 9:14 PM


Re: Welcome, Alfred!
Thank you for your welcome, Buzsaw!
Your signature beautifully expresses my own view on time.
I don't mind being in a minority, as being surrounded by a strong opposition keeps my mind on its toes.
To mark the occasion I added another couplet to the one in an earlier post:
their concepts brave and porous
they all dare rave in chorus
when it comes to rave alone
they are silent as a stone

This message is a reply to:
 Message 117 by Buzsaw, posted 04-08-2011 9:14 PM Buzsaw has replied

Replies to this message:
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Alfred Maddenstein
Member (Idle past 3989 days)
Posts: 565
Joined: 04-01-2011


Message 120 of 149 (611660)
04-09-2011 6:37 PM
Reply to: Message 112 by Oli
04-08-2011 10:40 AM


Re: Relativity
Oli, the best way to familiarise yourself with Mayer's logic is to hear the description of the model from the horse's mouth in all the details. The logic moves with the force of a steam-roller. It's hard to kick against the time-lines on the circle of the space-time globe drawn by it. All is solid maths and geometry that speak for the themselves and all the analogies that should help to visualise the new concepts introduced are right under every one's nose. A sphere with altitudes, latitudes and longitudes unlike the dark energy and matter, is something that is readily observable and graspable by any child.
Think about time directions of the space-time globe as altitudes or gravity vectors of the terrestrial spheroid. The gradient of the circle in spatial terms is the gradient of time dilation on the cosmic scale which corresponds to the the relativistic change in the rate of clocks that is caused by the relative motion. Therefore the distance itself is demonstrated to produce precisely the same effect as the relative motion does with the red-shift explained without any fantastic and physically impossible stretching of space postulated by the standard model.
He recalculates then all the distances to be less by a few orders of magnitude with the corresponding changes to the presumed luminosities to draw an elegant map of the cosmos with an visible horizon corresponding to the familiar terrestrial equator. What is presumed to be the Big Bang is just the region immediately beyond the cosmic visible horizon or equator. Unlike the terrestrial equator the cosmic one may not have a fixed physical meaning and location as it is relative to the position of the observer. On the map the cosmic equator is determined by the positioning of the Milky Way right at the pole.
A couple of days ago I've found his older Stanford lecture entitled The Many Directions in Time where the exposition is more compact than in the later dissertation so perhaps it would be a good idea to start from that.

This message is a reply to:
 Message 112 by Oli, posted 04-08-2011 10:40 AM Oli has not replied

  
Alfred Maddenstein
Member (Idle past 3989 days)
Posts: 565
Joined: 04-01-2011


Message 121 of 149 (611661)
04-09-2011 6:37 PM
Reply to: Message 112 by Oli
04-08-2011 10:40 AM


Re: Relativity
Oli, the best way to familiarise yourself with Mayer's logic is to hear the description of the model from the horse's mouth in all the details. The logic moves with the force of a steam-roller. It's hard to kick against the time-lines on the circle of the space-time globe drawn by it. All is solid maths and geometry that speak for the themselves and all the analogies that should help to visualise the new concepts introduced are right under every one's nose. A sphere with altitudes, latitudes and longitudes unlike the dark energy and matter, is something that is readily observable and graspable by any child.
Think about time directions of the space-time globe as altitudes or gravity vectors of the terrestrial spheroid. The gradient of the circle in spatial terms is the gradient of time dilation on the cosmic scale which corresponds to the the relativistic change in the rate of clocks that is caused by the relative motion. Therefore the distance itself is demonstrated to produce precisely the same effect as the relative motion does with the red-shift explained without any fantastic and physically impossible stretching of space postulated by the standard model.
He recalculates then all the distances to be less by a few orders of magnitude with the corresponding changes to the presumed luminosities to draw an elegant map of the cosmos with an visible horizon corresponding to the familiar terrestrial equator. What is presumed to be the Big Bang is just the region immediately beyond the cosmic visible horizon or equator. Unlike the terrestrial equator the cosmic one may not have a fixed physical meaning and location as it is relative to the position of the observer. On the map the cosmic equator is determined by the positioning of the Milky Way right at the pole.
A couple of days ago I've found his older Stanford lecture entitled The Many Directions in Time where the exposition is more compact than in the later dissertation so perhaps it would be a good idea to start from that.

This message is a reply to:
 Message 112 by Oli, posted 04-08-2011 10:40 AM Oli has replied

Replies to this message:
 Message 125 by Oli, posted 04-24-2011 12:24 PM Alfred Maddenstein has replied

  
Alfred Maddenstein
Member (Idle past 3989 days)
Posts: 565
Joined: 04-01-2011


Message 127 of 149 (613289)
04-24-2011 2:04 PM
Reply to: Message 125 by Oli
04-24-2011 12:24 PM


Re: Relativity
Oli writes:
Alfred Maddenstein writes:
All is solid maths and geometry that speak for the themselves and all the analogies that should help to visualise the new concepts introduced are right under every one's nose.
Alfred, I have read through Mayer's text. The problem is that he lacks a mathematical framework for his ideas, without which he will never be taken seriously by physicists.
He says that the book is meant to be understood by people of all disciplines, but I can't find anywhere that he has published any of the maths to back up his claims. His only published paper (in the IoP conference series) is on a different subject.
Oli
How do you mean it lacks maths? Do you mean it in a relative or absolute sense? Have you read "A Brief History of Time"? There is only one equation in the whole book. The book is taken seriously by physicists and laymen alike yet if that should be taken as any standard, then in a comparative and relative sense Mayer's "On the geometry of time in physics and cosmology" is overburdened by equations.
I mean, come on, there is a row of figures there leading to one formula expressing the relation of red-shift and cosmological distance. That is either correct or it is wrong. If it is wrong, both logically and mathematically you are more than welcome to tell why it is so wrong and where is the error exactly.
Otherwise, he is taken very seriously by me and my cat who is a very learned Cheshire feline with a true angular momentum to the grin he meets all empty assertions with.
What you say translated in a plainer English may mean that anybody could claim anything at all but given a sufficient mathematical formalism my cat's claim to be persecuted by the mice loving pink unicorns must be taken seriously by the physicists.
There are more papers in different places, still if the one you mention is correct, maths and all, thousands of textbooks may need to be rewritten.
Then again, if you remember, what he says at the end of it is that everything looks very compelling on paper but the last word is the testing it all experimentally.
Anyway, that paper on waves and particles is related to Einstein's remark about God's aversion to gambling:
Since God refused to throw dice
The Devil's due to throw twice;
Each die stops by God's hand to load;
The load rolls down Devil's road

This message is a reply to:
 Message 125 by Oli, posted 04-24-2011 12:24 PM Oli has replied

Replies to this message:
 Message 129 by DrJones*, posted 04-24-2011 4:34 PM Alfred Maddenstein has replied
 Message 133 by Oli, posted 04-25-2011 10:27 AM Alfred Maddenstein has replied

  
Alfred Maddenstein
Member (Idle past 3989 days)
Posts: 565
Joined: 04-01-2011


Message 130 of 149 (613403)
04-25-2011 12:53 AM
Reply to: Message 129 by DrJones*
04-24-2011 4:34 PM


Re: Relativity
DrJones* writes:
Do you mean it in a relative or absolute sense? Have you read "A Brief History of Time"? There is only one equation in the whole book. The book is taken seriously by physicists and laymen alike yet if that should be taken as any standard, then in a comparative and relative sense Mayer's "On the geometry of time in physics and cosmology" is overburdened by equations.
A Brief History of Time is a popular science book, Hawking has years of academic research behind him, you can find many many equations in his scientific papers.
Granted, comparing the two researchers- Hawking and Mayer, Hawking has got many, many more rows of figures in many, many more scientific papers published along many more years of academic research under his belt. Is that the question here though?
These two people got two opposing views on the nature of time and the issue we are debating here is which of these two views the nature itself is in agreement.
The issue is not decided by the quantity of maths or papers to support each respective point of view. Or is it?
Somebody said that there is no point in being precise if you don't know what you are talking about.
Mind you, I have got no stake in academia and its consensus so bringing anything to do with that to support a view sounds perfectly irrelevant to me. All I care about is one on one consensus with nature only.
Now if the logic behind any equations is fatally flawed to begin with, no number of citations of the papers may removed the error.
Hawking's view on time is that it had a certain point of beginning that he compares to the North Pole. Time at the North Pole according to that view was t0 so asking what was before that is like asking what is north of the North Pole.
First of all, physically there is no barrier at the North Pole. So north of the North all the way down South lies for the traveller to proceed unimpeded.
Also to the opposing view, the point of such reference is relative, and could be chosen arbitrarily since every point on the surface of the hypersphere is a temporal pole.
The question here is again which view is the correct one and not which set of the supporting equations is more sophisticated irrespective of whether the logic behind the maths is being true to nature or is flouting it in its face.

This message is a reply to:
 Message 129 by DrJones*, posted 04-24-2011 4:34 PM DrJones* has not replied

  
Alfred Maddenstein
Member (Idle past 3989 days)
Posts: 565
Joined: 04-01-2011


Message 131 of 149 (613417)
04-25-2011 3:59 AM
Reply to: Message 124 by Son Goku
04-13-2011 9:38 AM


Re: Relativity
Son Goku writes:
quote:
Yes, that is correct. I do indeed find the theory of relativity to be reasonable but the solutions from which the flat universal clock rate is derived seem to me contrived and patched upon it arbitrarily
They are not patched upon it arbitrarily, the follow from it directly if you use a homogeneous matter source
quote:
and it appears that they were simply needed in order to fit the theory to the assumption of the universal uniform expansion from a single dot of spacetime.
You have it the wrong way around. Roughly homogeneous matter was observed already, so it was put into Einstein's field equations to see what the predicted spacetime would be from the observed matter. The result was the cosmological expansion spacetime.
Hence the actual chain of thought is:
Observe homogeneous matter => Use homogeneous matter in Einstein's field equations => Field equations predict cosmological expansion.
I would not be sure about that. As far as I know that is only one of the possible solutions while all the solutions may look very good on paper. That means that a solution implying something physically impossible happening may have a proof that is mathematically as valid as the proof reflecting what is actually taking place.
Now there is another solution to the whole thing. If the local scale phenomenon of the acceleration resulting in time is paralleled by the effect the distance itself on the cosmic scale is producing the difference in the time dilation observed at such a distance reflects the difference in scale. That is only logical as velocity is strictly related to distance anyway so there is no reason why the distance itself must not be producing the same effect without any contribution from the relative motion given that the distance is great enough and it may explain the red-shift without any recourse to the hypothesis of the physically impossible expansion of nothing into nowhere.
In other words what is intrinsically or locally measured at some point in the universe as ten billion years given a sufficient distance may appear as just one billion. That difference between the intrinsic age of a cosmic object and that apparent from a distance may vary as a function of the distance itself.
Why is it so difficult to consider such an elegant scenario? What are the explanatory advantages of the expansion idea? I don't see any at all, so the reluctance to consider the unorthodox view must be due to the cultural habits of thinking only.
Preaching all that to you, I feel like Dawkins would be feeling if he landed smack-dab in the middle of a catholic symposium.

This message is a reply to:
 Message 124 by Son Goku, posted 04-13-2011 9:38 AM Son Goku has replied

Replies to this message:
 Message 132 by Son Goku, posted 04-25-2011 8:51 AM Alfred Maddenstein has replied

  
Alfred Maddenstein
Member (Idle past 3989 days)
Posts: 565
Joined: 04-01-2011


Message 134 of 149 (613448)
04-25-2011 1:08 PM
Reply to: Message 133 by Oli
04-25-2011 10:27 AM


Re: Relativity
Oli writes:
DrJones writes:
A Brief History of Time is a popular science book, Hawking has years of academic research behind him, you can find many equations in his scientific papers.
True.
Alfred Maddenstein writes:
What you say translated in a plainer English may mean that anybody could claim anything at all but given a sufficient mathematical formalism my cat's claim to be persecuted by the mice loving pink unicorns must be taken seriously by the physicists.
Yes, but the maths then allows experiments to be devised to check your cat's claim against the unicorns with some precision.
Alfred Maddenstein writes:
there is a row of figures there leading to one formula expressing the relation of red-shift and cosmological distance.
I don't find it clear how he gets to this prediction from his theories. It's true that there are lots of equations, but I don't see how they fit together.
Oli
Well, his starting points are the invariance of the speed of light in vacuum and the equivalence of space and time as measures of existence. That comes straight from Minkowski. Basically he reduced the whole thing to two dimensions only and these two dimensions are treated as strictly orthogonal to each other with an infinity of possible vectors. That's the first principles from which all else ensues. You say that you don't get how the rest follows from that, but I'd rather you be more specific pointing out exactly the links in the logical chain that appear to you to be missing or broken. On his site he welcomes all the criticism if that is constructive.
Since I have no stake in the existing paradigm and academic consensus, the only criteria for the validity of a theory is the logical beauty which that one seems to satisfy. I am though a sceptical cat and could never be quite sure of anything so would always appreciate a logical inconsistency I might miss somehow pointed out to me. So far, in this particular case, all I manage to get is but empty assertions, prevarications and vague appeals to authorities.
Just saying that you do not see how anything fits together is not good at all, I am afraid.

This message is a reply to:
 Message 133 by Oli, posted 04-25-2011 10:27 AM Oli has replied

Replies to this message:
 Message 136 by Oli, posted 04-27-2011 9:37 AM Alfred Maddenstein has replied

  
Alfred Maddenstein
Member (Idle past 3989 days)
Posts: 565
Joined: 04-01-2011


Message 135 of 149 (613540)
04-26-2011 1:10 AM
Reply to: Message 132 by Son Goku
04-25-2011 8:51 AM


Re: Relativity
Son Goku writes:
quote:
I would not be sure about that.
Well, you don't have to be, that is what occurred historically. It was the chain of logic.
quote:
As far as I know that is only one of the possible solutions while all the solutions may look very good on paper.
That is incorrect. With homogeneous matter that is the only solution to Einstein's field equations.
quote:
Why is it so difficult to consider such an elegant scenario? What are the explanatory advantages of the expansion idea? I don't see any at all, so the reluctance to consider the unorthodox view must be due to the cultural habits of thinking only.
The explanatory advantages of the expansion scenario are obvious:
1) It is a natural consequence of a theory that already correctly describes gravity on solar system scales, predicts the orbits around hyper dense objects, etc
and
2) It matches the evidence.
Deriving the jerky inflation of sameness from the fact that sameness exist is a non sequitur.
1) How do you mean? As I understand it, the theory clashes with the description of gravity on the solar scales as according to it most of the matter in the solar system is of the cold, dark and undetectable kind. Or is the Solar System an exception to the homogeneousness rule so unlike anywhere else the dark matter is absent in it? Or maybe the Milky Way is an exception?
2) If you check all the links in Mayer's book, you will find those leading to the Big Bang theory predictions on the one hand, and to the databases on the other. With a glaring mismatch between the two. How do you explain that evidence?

This message is a reply to:
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Replies to this message:
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