The accelerating expanding universe

Hi there, this is my first post!I have looked through the book by Alexander Franklin Mayer you referred to earlier. It can be found here:
http://jaypritzker.org/pages/book.htmlAlthough I don’t claim to have followed all of the text, the main thrust of the argument seems to be that Einstein did not understand the geometric meaning of Minkowski spacetime as intrinsically four dimensional when he derived General Relativity, and by extension the big bang model doesn’t include time correctly.The author uses the big bang timeline to apply his point of view to the universe. He claims that, as special relativity means there is no absolute universal time (since observers moving at different speeds experience time differently relative to each other), there should be no universal time axis from which to construct the timeline.However, in the derivation of the FRW metric (as I understand it) we observe that the universe is isotropic and homogeneous on large scales. Then the galaxies or superclusters make up a ‘cosmological fluid’ filling the universe. The proper time for ‘Fundamental Observers’ at rest in this cosmological fluid can be used to define a universal time. Spacetime is sliced up into spacelike hypersurfaces, each labelled by a constant time coordinate, so that the worldlines of the fundamental observers are orthogonal to the surfaces.So although the big bang model does include a form of absolute time, this does not mean spacetime is not intrinsically four-dimensional.Oli

Alfred,Firstly, when you say:...since there are three spatial dimensions and the motion in any of them is measured by and is convertible into time, the time dimension is orthogonal to each three of them...I believe you mean the same as the book which says:It is based on the understanding that since there are three spatial dimensions and the motion in any of them is measured by and is convertible into time, the time dimension is orthogonal to each three of them.This correctly implies that Minkowski’s spacetime is a four dimensional ‘combination’ of three space and one time dimension.Secondly, I apologise for using specialist language, not that I claim to be a specialist in any way. The ‘Fundamental Observers’ and hypersurfaces are just a way of defining a coordinate system in the universe. There are an infinite number of ways to do this, just as there are an infinite number of ways to specify a location on the Earth’s surface. For example, we could give the position of London by its longitude and latitude, by a number of miles and direction from Paris.Just as any of these methods is equally valid on Earth, we are free to choose any coordinate system to specify positions in space and time in General Relativity. The fundamental observers are then hypothetical ‘beings’ who are at rest with respect to all the ‘stuff’ in the universe: the ‘cosmological fluid’. To simplify the maths, the FRW space-time is commonly expressed using the proper time of the Fundamental Observers as a time coordinate.I hope this clears things up, but I don’t find it easy to explain.Oli

Alfred, I agree with most of the quote from Mayer’s book. He has a grasp of special relativity (as I understand it) and how measurements made by observers moving at different velocities in Minkowski space are related by the geometry of that space; i.e. rotations of the coordinate axes.However, as has been said before in this thread, I don’t agree that: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.There is no absolute time-line in general relativity, so there are indeed an infinite number of possible time-lines we could define which would correspond to different observers moving through the universe. However, in a homogenous isotropic universe we can CHOOSE a convenient set of coordinates with a time axis parallel to that experienced by observers at rest with respect to the cosmological fluid (the galaxies). This choice does not affect the answer since it is the geometry that describes the physics, not the coordinates we choose to describe it.In this coordinate system, the time axis is a natural way to describe the universe’s time-line, since events measured as simultaneous by an observer sat on one galaxy are simultaneous as measured from another. General relativity doesn’t give us a universal clock rate, the universe does.I would be interested to hear your description of the logic Mayer uses to go from this to a new model of cosmology.Oli

Hmm ok, but was what I said about being able to define a universal time correct?In one form of the FRW metric there is a scale factor ‘R’ and a constant ‘k’ representing the curvature of the space-like surfaces at constant t. If k is -1 or 1 then I can see that the ‘time’ axis changes direction throughout the 3-space, but if k is 0 I think they are Euclidean. In that case are the four-velocities of observers parallel?However, I may not be thinking about this right because the cosmological redshift depends on the ratio of scale factors at the emitter and receiver. That would mean that we would get redshift without non-parallel time axes for k=0.Thanks,
Oli

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

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

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

Indeed, apologies.From what I’ve read, Mayer's logic goes something like this:
1) Einstein did not properly understand Minkowski's idea of time in special relativity as a geometric effect.
2) So when Einstein worked out general relativity he didn't properly take these ideas into account. Mayer writes: A fundamental conceptual error occurred at the beginning of his quest to unify special relativity with accelerated reference frames.
3) Cosmological models based on GR are therefore flawed.
4) Mayer introduces cosmological latitude Ϛ: an angular parameter relative to any arbitrary point of observation in the Cosmos. The different values of Ϛ map out a circle, with the time directions everywhere perpendicular to it.
5) Comparing the rates of clocks at different values of Ϛ gives the cosmological redshift for light travelling between them.My first problem is that 2 is just not true. As I understand it, the equivalence principle from which Einstein derived GR says that in a freely-falling laboratory in a small part of spacetime the laws of physics are those of special relativity. Mathematically, this means that in a small region around every point the geometry can be described exactly as in 1 (in an appropriate coordinate system). Minkowski’s spacetime is the foundation of GR.Also, the quote in 2 reveals Mayer’s lack of understanding since special relativity has no problem dealing with accelerated reference frames.Secondly, it is not made clear how 2 leads to 4, although I guess this kind of leap is ok if the conclusion is supported by experiment.However, the book doesn’t give a metric for the proposed four dimensional spacetime in 4, or a lot of mathematical details about how this comes about. Only two dimensions are described. Also, it doesn’t reference the matter in the universe and how that justifies the chosen geometry. GR says that the matter and energy distribution of the universe results in curvature of spacetime. How does Mayer explain gravity if he’s not taking general relativity into account?Oli