The accelerating expanding universe

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Thank you, for your very reasonable exposition of General Relativity. Unfortunately I do not see how from anything either Einstein or yourself stated may follow anything that would require violating the necessity of the Copernican mediocrity principle being applied temporally. As it is the principle is spatially honoured by the contemporary cosmological model. Given the unity of space and time this situation strikes me as a contradiction.
All that you said about the free falling bodies constituting the inertial frames is correct. The universal flat calendar hardly follows from any of that.

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cavediver has mentioned this already, but you are mixing up the theory with a solution. General Relativity is a theory which describes the spacetime generated by any arrangement of matter. If the matter is homogeneous, the spacetime will be homogeneous.Maxwell's electromagnetism does not imply that electric fields are rotating, however if the electric matter is rotating then it does predict that electric field will rotate.Maxwell's equations and General Relativity are both theories which predict what fields will be created by what arrangement of matter. The field will be different for different arrangements of matter and for homogeneous matter you will get a homogeneous field, but that's not a direct implication of General Relativity.An everyday example would be the "rules" of a car insurance company. The rules in abstract don't imply that you pay the maximum price. They apply differently to different drivers. However when applied to an extremely dangerous driver they do imply the maximum price.

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What it may imply philosophically in terms of motion is only that the speed of light is the speed of time itself.

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It does not imply that. Speed is the amount of distance covered in a given time, hence light has a speed. Time does not cover a distance, hence there is no concept of the speed of time. The closest thing to a speed of time would be in relativity where you can compare the rate of change of one observer's time to another observer's time. Edited by Son Goku, : No reason given.

I'm sorry but that is simply word salad.Reality does trump logic every time. In addition, absolutely NOTHING in that post is related to the topic or even related to logic.

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Anyone so limited that they can only spell a word one way is severely handicapped!

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?

Nope, don't catch your drift and unlike Alice, don't follow white rabbits.The topic, in case you missed it, is "The accelerating expanding universe ".That cannot be determined through logic, it is a matter of reality, of observation, of measurement.When you have something more than logic, please present it. Until then I suggest that like the Dormouse you should avoid having your head put in the teapot.

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`You might just as well say,' added the Dormouse, who seemed to be talking in his sleep, `that "I breathe when I sleep" is the same thing as "I sleep when I breathe"!'

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Anyone so limited that they can only spell a word one way is severely handicapped!

Well this is an off-topic question/response, although I cant help but to think of this...If you had a perfectly level field and fired a gun at say 5 feet off the ground, perfectly level, and dropped a bullet of the same weight at the same time as the one leaves the barrel from 5 feet also, which one will hit the ground first?? No wind or any other atmospheric conditions are affecting either bullet.Ask 10 people, you might be surprised as the answers you get. My point being that sometimes peoples logic can be flawed, but the truth is still the truth.Edited by fearandloathing, : No reason given.

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"I hate to advocate the use of drugs, alcohol, violence, or insanity to anyone, but they always worked for me." - Hunter S. ThompsonAd astra per aspera

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."

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

Actually, I don't find anything in that statement objectionable. The time directions in distinct cosmic regions are certainly not parallel - it is precisely this fact which gives rise to cosmological red-shift.

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.

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

Yes, it was a good description. No. The k=0 solution, the "flat" solution, is only flat in the hypersurfaces - i.e. intrinsic 3-curavture is zero, but extrinsic 4-curvature is non-zero. This is a very common misconception. Exactly. The red-shift is simply given by the angle between the light-cones at emission and reception - this angle is generated by both curvature (cosmological red-shift, light-cone tipping) and motion (doppler, Lorentz transformation).

Hi Alfred. A hearty welcome to EvC. I surely hope you will stay with us. Though I just happened to notice this thread and have not read and assimilated all that you are saying, I've seen enough that I agree with at least much of it.I've argued the logic of an unbounded space universe and property problems with the concept of expanding space in past threads. I see that you are studied and able to articulate your science arguments much better than I. That's why I hope you will not become discouraged, having the minority POV and leave off posting.

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BUZSAW B 4 U 2 C Y BUZ SAW.
The Immeasurable Present Eternally Extends the Infinite Past And Infinitely Consumes The Eternal Future.

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

Very good, Alfred. Science peers sanction songs sung suitably.

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BUZSAW B 4 U 2 C Y BUZ SAW.
The Immeasurable Present Eternally Extends the Infinite Past And Infinitely Consumes The Eternal Future.

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.