The accelerating expanding universe

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.

I guess this is obvious, since the scale factor changes the length of the three 'space' dimensions relative to the time one. When I was just considering the geometry of the hypersurface the scale factors cancelled. I think my main problem is defining 'parallel'... In the case of red-shift between two comoving observers, do we just see the cosmological red-shift though?Oli

Well, you have a (metric-based) connection, so parallel transport is not a problem... and thus you can drag your light cones around and compare them. Yes, but essentially by definition.

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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

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They are not patched upon it arbitrarily, the follow from it directly if you use a homogeneous matter source

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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.

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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.

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

Thanks for the help! I've just finished an undergraduate course in GR, and thinking about this has helped me start to get an intuition for the subject. I think I'm only just realising how rich it is though

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

Cool - where are you studying? Are you going on to postgrad?

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.

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It's not enough to bash in heads, you've got to bash in minds
soon I discovered that this rock thing was true
Jerry Lee Lewis was the devil
Jesus was an architect previous to his career as a prophet
All of a sudden i found myself in love with the world
And so there was only one thing I could do
Was ding a ding dang my dang along ling long - Jesus Built my Hotrod Ministry
Live every week like it's Shark Week! - Tracey Jordan
Just a monkey in a long line of kings. - Matthew Good
If "elitist" just means "not the dumbest motherfucker in the room", I'll be an elitist! - Get Your War On
*not an actual doctor

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.

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.

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I would not be sure about that.

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Well, you don't have to be, that is what occurred historically. It was the chain of logic.

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As far as I know that is only one of the possible solutions while all the solutions may look very good on paper.

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That is incorrect. With homogeneous matter that is the only solution to Einstein's field equations.

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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.

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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, etcand2) It matches the evidence.

True. Yes, but the maths then allows experiments to be devised to check your cat's claim against the unicorns with some precision. 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.

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?