## Faradave's 3-Ring Circus Model of Spacetime

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### Faradave's 3-Ring Circus Model of Spacetime

Mod Edit: This new thread by Faradave was split off from Watson's old thread "Is the Universe rotating?" by agreement. I think it contains interesting ideas, although it may perhaps not pass muster as a viable scientific theory. Happy New Year to all, Jorrie

Lincoln wrote:ALL space points, including where you're sitting right now, is the center of the universe. That's the only explanation that is consistent with the uniformity of the 3K background radiation. ...
In order for the universe to be rotating, there would have to be a preferred reference frame. This isn't impossible...after all relativity is merely a theory, to be trumped by a new observation. But the 3K uniformity is hard to argue against.

It's been suggested that a frame at rest wrt to the 3K background makes a very tempting candidate for a "preferred frame". It's universally accessible and Relativity would seem to grant its uniqueness as the oldest of frames (none suggesting an older age to the universe).

Lincoln wrote:To the best of our knowledge the universe is uniform as far away as we can see. Further, we have no known methodology for accessing any possible (but unproven) higher dimensions.

A higher dimension does not have to exist to be useful. A Flatlander could rotate in its plane of existence about a 3rd dimensional axis, even if a 3rd dimension didn’t exist. An extra, imagined dimension also provides a helpful perspective from which to "observe" those dimensions which are known to exist.

Lincoln wrote:BTW an ant on a rotating pizza would be able to determine that the pizza was, indeed, rotating. It would not be much different than the observed coriolis force here on Earth.

Agreed. My impression is that while the Coriolis and centrifugal forces will impact objects moving in the plane of a rotating disk, for particles confined to a circumference, only centrifugal force will be experienced. A circumference is defined relative to a center, so the dimensionality of the center (and that of a rotation axis through it) is important.

Consider two distinct modes of ring rotation. The first employs a polar axis, resulting in a gradient of outward forces on the ring, increasing from zero at the poles to maximum at the equator.
If the axis of rotation is a diameter, ring forces maximize at the equator.

Another mode employs an external axis of rotation perpendicular to the center of the disc it encloses and not intersecting the ring. In this case, the forces are uniform at every point on the ring. If the ring was rubber it would expand. An external axis need not be real. For example, a 2D image can rotate on your display about an imagined axis through it.
A 1D circumference (ring) encloses a 2D area (disk) rotating about a 3rd dimensional axis and resulting in uniform outward forces.

Imaginary inhabitants within the ring would not be aware of constant angular velocity, but all would be subject to the outward force. This is experienced on spinning carnival rides.

Going up a dimension, a sphere rotating about a polar axis again produces a gradient of forces increasing from zero at the poles to a maximum at the equator. Thus, objects weigh slightly less on earth’s equator than at its poles.
Polar axis rotation produces the same force gradient on a sphere as on a ring.

However, when a sphere is represented more compactly, as a "2-ring", the second mode of rotation presents itself. A 2-ring encloses a 3-disk (just another way of saying a sphere contains a volume). This compact depiction allows us to see that it can rotate about a 4th dimensional axis, perpendicular to the center of its 3-disk. That produces a uniform force distribution to all locations on the 2-ring (i.e. at all locations of the sphere). Uniform expansion of a sphere and its rotation about a 4th dimensional axis entail identical fields!*
A 2-ring representation of a sphere reveals that inflating a balloon involves the same field of expansion forces as rotating it about an extra-dimensional axis. Centrifugal force is inflationary, regardless of dimension.

Progressing one more step, three dimensions can similarly be assigned to a "3-ring" curved in a 4-plane. If the 3-ring rotates about an imagined external, 5th dimensional axis, uniform outward forces will occur at all locations on the ring.
With space represented by the 3-ring, time is radial, coinciding with the outward expansion forces. The axis of rotation is perpendicular to the spacetime 4-plane.

Allow the 3-ring to represent our three compacted spatial dimensions with radial time comprising its 4-disk (and occurring perpendicular to space at every intersection). The rotation provides outward forces which give an arrow to time. The natural divergence of the radii correlates to "dark energy" and yields spatial expansion as time progresses.

Why should the 3-ring be rotating? Why not? Do we know of anything that isn’t? The 3-ring represents a spatial simultaneity with respect to the Big Bang event. The imaginary axis of rotation is perpendicular to the spacetime 4-plane.

Of course there are other influences to the expansion. For example, when the ring was very, very small, particles inhabiting it would have been within range of the strong force, producing a great deal of "surface tension" in the ring. Once, expansion reduced particle density beyond that, there would have been a rapid expansion to a new steady state. From that stage, while gravitation exerts local tension, at larger scales, I believe gravitational expansion relating to the ring structure, does the opposite.

*Don't underestimate the value of this. Rotation about a 4th dimensional axis creates a radial 3D field. If you can grasp that simple concept, your understanding of field theory will exceed that of current physics. It won’t mean you know more, it'll mean you know better. So yes, you should reread it a few more times. When the question occurs, "What 4th dimensional axis?", you’re almost there.** When the answer yanks you bolt upright from sleep, in a cold sweat, you’ve got it! (or menopause). Quickly, write it in your own words. You do keep a notepad and pen by the bedside, don’t you?
Last edited by BurtJordaan on January 1st, 2015, 2:34 am, edited 1 time in total.

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### Re: Clarification

My use of the term "external axis" above might be confusing as it occurs through a center within the n-rings (circle, sphere, hypersphere) I referred to.* What I meant by external axis of rotation was one not intersecting the n-ring, in contrast to a polar axis (i.e. a diameter as axis). More specifically, my "external" refers to an axis perpendicular to every diameter of the n-ring. I wanted to call it an "orthodiametric axis" but I could swear your eyes just started to glaze even at that single mention of it. Besides, I already make up too many terms.

Just as Flatlanders would have a hard time imagining an axis perpendicular to all the diameters of a circle in their realm, we can hardly picture such an axis perpendicular to the diameters of a sphere in space or a hypersphere in spacetime. They are nonetheless functionally available, at least one dimension up from the known dimensions.

*In astronomy, "external axis" typically means entirely outside the structure, in association with orbital rotations. For example, a GPS satellite orbits an axis well outside itself, through earth’s center.

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### Re: Is the Universe rotating?

I get it and a great concept Dave. A rotation on the Temporal Axis seems like a neat explanation for Dark Energy that effectively causes the 3D Universe to Stretch on all 3 Axis.

If we think of Reality as being all Fields then those Fields will be Stretched in all directions from any focal point in 3D. Since light stretches when leaving a Gravitational Field (Red Shifts) and reconstitutes when entering another Gravitational Field (Blue Shifts) then on the average it's a push (self canceling given equal fields) but light that has been in transit for a longer period can't be reconstituted (compressed) as that would require transit through an area of prolonged compression (opposite of the stretching effect). Thus.. the longer light has traveled, the greater the average Red Shift.

Also, unlike a localized Gravitational Field (Gravitational Lensing), we get the opposite effect of Luminary Dispersion, which would be observed as a dimming effect on Standard Candle Stars.. depending on true distance across any given void the light has traveled through. Somebody published last year on such but I don't have my notes at my fingertips at this time as I am at home on vacation. I'm a fan of a Stretching Universe (not Expanding by adding new Space-Time) and your idea rings true to me. (for what it's worth..lol)

So.. while I didn't bolt up in bed and shout "Eureka", your idea does seem like a reasonable explanation for Dark Energy, which is something I've been looking for. Bravo!

Best wishes,
Dave :^)

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### Re:

Lincoln » Wed Apr 29, 2009 8:48 am wrote:Keep in mind if the universe is rotating, this presupposes an axis, which breaks the symmetry of all points being equivalent.

Were the universe rotating around some axis, it would revolutionize our model of the universe. So a definitive answer to the question is a big deal.

On the other hand, I'm not holding my breath.

People might like to check out a rotating solution to Einstein GR equation that Kurt Gödel came up with in 1949.
http://en.wikipedia.org/wiki/Goedel_met ... rpretation

The so-called "Goedel rotating universe" does not have distance expansion. So in that sense it is unrealistic (our universe expands, Goedel's rotating model does not. But I don't see why that precludes the possibility of other rotating solutions to GR that are LIKE Goedel's in some respects, but which also have expansion.

In any case it might be interesting to see how Gödel achieved a rotating spacetime geometry.

BTW Gödel and Einstein were good friends and used to take walks together while they were both at Princeton IAS. Gödel is famous in part because of that popular book by Doug Hofstadter titled "Gödel Escher Bach"
http://en.wikipedia.org/wiki/Kurt_Godel ... itizenship
==quote==
...Albert Einstein was also living at Princeton during this time. Gödel and Einstein developed a strong friendship, and were known to take long walks together to and from the Institute for Advanced Study. The nature of their conversations was a mystery to the other Institute members. Economist Oskar Morgenstern recounts that toward the end of his life Einstein confided that his "own work no longer meant much, that he came to the Institute merely ... to have the privilege of walking home with Gödel".[13]...
==endquote==
Marshall

### Re: Is the Universe rotating?

A couple of points come to mind....

If the spatial dimension of the universe is 3, then there will be an issue relative to transforming left hands to right hands, and vice-versa. Given that life itself is able to develop a whole host of structures, is there evidence that life has concocted a way to convert a left to a right hand, or does the evidence point merely to (mirror) symmetry at the origin of each? (Note that I'm not assuming actual hands -- merely handedness.)

Now, were the dimension of the universe 4, such transformations would be no different than in the case of transformations of 2-structures within 3-space and life might have the ability to take advantage of that higher dimension.

Now, if 3-space is turning on some axis, there will be a differential direction toward or away from the axis. And unless the rotation is unnoticeably slow, it would seem as if it could be detected by an evolution that has within its sphere of influence the background cosmic radiation, perhaps causing a bias in the possible structural adaptations.
owleye

Re: Easy Rider (carousel edition)

Lincoln wrote:Keep in mind if the universe is rotating, this presupposes an axis, which breaks the symmetry of all points being equivalent.

Symmetry breaking is dependent upon on the axis of rotation and the region being observed. There IS symmetry in centrifugal force about the equator when the axis of rotation is perpendicular to the equatorial plane.

Lincoln wrote:No, no, no....There is a horrible assumption tacit in many people's posts...that there was a spot in space at which the big bang occurred. This is simply not correct...

Agreed. The Big Bang (BB), as an event, is located in spacetime, not space. At least, not any spatial simultaneity since the actual, t=0 bang.

Lincoln wrote:In order for the universe to be rotating, there would have to be a preferred reference frame.

There is one frame, at rest wrt the BB (i.e at rest wrt the cosmic background radiation). It's not "preferred" by nature in terms of any physical laws but it is unique and universally available as a reference.

Thanks for the Gödel reference Marshall.

Gödel’s rotating solution to Einstein's Field Equation was to have invoked closed timelike curves among other indications that he presupposed an axis of rotation within space. He went to his grave asking, "Is the universe rotating yet?" He was looking for data consistent with such an internal axis none have been observed.

Dave_O, Thanks, enjoy the rest of your vacation.

Owleye wrote:Now, if 3-space is turning on some axis, there will be a differential direction toward or away from the axis.

As usual, you have put your finger on the key point. I have, by contrast, modeled a 4-space turning on an axis which defines a center. (Like saying the BB had an original spin. Why not?) The forces correspond to the observed direction of time and thus may serve to model a source of time's unavoidable motivation.

I’m concerned that I didn’t properly convey the elegance and utility of the 5th dimensional axis. If you expect a 5th D axis of rotation to be difficult, you’ll miss it. It’s as simple as the sums:
1 + 2 = 3,
2 + 2 = 4 and
3 + 2 = 5
Try to relax and let the concept slide right in.

We’re looking for a uniform expansion force attributed to dark energy. That’s exactly what we get at the equator of a sphere rotating about a polar axis. The equator is a one dimensional (1D) line curved into a great circle, midway between the poles. The equator encloses a two dimensional (2D) great disk. The polar axis of rotation is perpendicular to that disk and corresponds to a third dimension (3rd D).
A great disk bisects a sphere (not shown) at its equator. With rotation about a polar axis, outward radial forces occur uniformly at all locations on the equator.

Now all we have to do is up the dimensionality of the equator, disk and axis by 2. That’s it! Rotation of a 4-disk about a central axis causes all locations at a given radius to experience uniform expansion forces.
Adding two dimensions, a ring becomes a 3-ring, a disk becomes a 4-disk, and its perpendicular axis would entail a 5th dimension. Rotation tends to expand the 3-ring (space) uniformly.

In this case, time is radial and the 3-ring is a spatial simultaneity (all three dimensions of space at a given time) with respect to the center. This model of spacetime contains a center (the BB), which lies apart from space (the ring). Other models of spacetime exist but they require a novel primary expansion force.

If the 5th dimensional axis is distracting, let’s get rid of it. Ask yourself, how long does that axis have to be? The only point on it that matters is the one that intersects the BB. Keep the BB and the rotation but lose the axis.
Another version of the last diagram replaces the axis of rotation with the Big Bang event. Time is a radial 4D field corresponding the centrifugal forces experienced uniformly by all spatial locations at a given radius (time=now), resulting from the rotation.

Rotation is not to be interpreted as that of the 3-ring within its 4-plane. The entire 4-plane rotates. There is a unique reference frame at rest with the BB from which observers in space see uniform red shift (cosmic background radiation) in the direction of the BB (i.e. at every spatial direction, looking back in time).

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### Re: Top Down Approach

Another way to arrive at what I’ve called the "3-Ring Circus" model of the universe is to start with a five-dimensional ball (5-ball). Can’t picture that? Neither can I. Not to worry. Just picture an ordinary ball and assign five dimensions to it. Like any ball, it is enclosed by a sphere entailing one less dimension. An ordinary 3D ball is enclosed by a 2D sphere and a 5-ball is enclosed by a 4-sphere.[1]

More relevant is that the equator of a ball is two dimensions less than the ball. As the equator of an ordinary 3D ball is 1D (a curved line), the equator of a 5-ball is 3D (a 3-ring). And if the 5-ball rotates on a polar axis, uniform expansion forces occur at all locations on that 3-ring equator.
A 5-ball enclosed by a 4-sphere has a 3-ring equator. Rotation about a polar axis produces uniform outward force at all equatorial locations. The great disk of the equator models a 4D spacetime with a radial temporal field.
A cross section of a 5-ball, at the equator reveals a 4 disk. With three dimensions of space occurring as a 3-ring at any given radius, the 4th dimension occurs radially, always normal to its intersection of a 3-ring. This corresponds to the centrifugal forces emanating through the great disk and to the dimension we call time. If the concept of a radial temporal field seems too unconventional, here's an illustration (with caption) used by noted author Sean Carroll in the guidebook accompanying his course, The Mysteries of Modern Physics: Time.

Professor Carroll did not use the term "temporal field" but I can’t ignore the implication of his analogy to a gravitational field. One might ask, where is space in the right diagram? The general answer is everywhere, but we can be more specific by asking, where are spatial simultaneities in the depicted frame?

The answer can be drawn as any arc at constant radius (time) from the Big Bang. I would not characterize space as an independent object, which expands but instead a dependent feature of a divergent temporal field. World lines of particles at rest in this frame advance from smaller spatial simultaneities outward to larger, expanded ones, as the particles are found to age. The vastness of these arcs makes them seem quite flat, locally.
A particle at rest has a radial world line, which encounters concentric, progressively expanded, spatial 3-arcs. Time increases from simultaneity t1 to simultaneity t2.

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### Re: Is the Universe rotating?

I am sorta getting this, but wondering how coriolis force would play out along the 4-surface of the 5-sphere?

The account of dark energy this offers is as good as anything I've seen. Where does the spin originate when the 5-sphere is a primordial point? It's just inherent, right?

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### Re: Going Flat Out

BiV wrote:I am...wondering how Coriolis force would play out along the 4-surface

One round flatlander doesn’t seem flat to another. They perceive each other as substantial only from a perspective within their plane. We, in seeing from an additional dimension, see flatlanders as flat.

In the same way, though you and I seem mutually substantial within our space, we are nonetheless quite flat from time's perspective. Every particle in your body ages at the same rate (absent nonuniform accelerations). That’s because those particles all proceed "side-by-side" outward along time.

Why the emphasis on flatness? Coriolis effect requires some physical extent on the surface of rotation and 3D objects don’t have that in any given simultaneity. Consider a pan holding a thin film of milk with a cereal flake floating at the 12 o'clock position. If an astronaut holds the saucer in the plane of a rotation of his space station, the milk and cereal will appear to rotate, opposite to the direction of the station. Actually, the milk is remaining at rest, while the pan turns relative to it. (In a longer time frame, the cereal would also respond to the centrifugal force.)
Liquid in a pan occupying the station’s plane will appear to rotate counter to the rotation of the space station. Compare cereal at rest in the "plane pan" to the pan's handle at four different locations. A pan facing inward from a floor will experience only the intended artificial gravity, owing to centrifugal force (unless the angular velocity changes).

On the other hand, if he sets the pan on a "floor" of the space station, so that it's facing the center of rotation, the only force it will feel is outward. No rotation of the milk is observed. This is the flat orientation you have, relative to time. Regardless which direction we gaze in space, we find ourselves facing the Big Bang 4-center (seen as cosmic background radiation). The "spokes" of our spacetime 4-disk are temporal, not spatial, so there is no way for a 3D object to have a planar orientation.
BiV wrote:Where does the spin originate when the [5-ball] is a primordial point? It's just inherent, right?

Yes. The 5-ball does not even have to exist. The plane of its great disk is, by itself, sufficient to model of our spacetime. You can think of its angular velocity as like that of a common flat spiral galaxy. There are a lot more ways to spin than to not spin. One might suggest that only a universe with spin provides a centrifugal motivation to time's advance. If you lean toward a "Big Bounce" model, then whatever previously contracted into the Big Bang (our t0) already had spin when it did.

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### Re: Is the Universe rotating?

Faradave, as one of the protectors of the canon around here, I have to point out that your "5-ball" and "4-plane" are not new concepts, because mathematically we can go for any number of dimensions. That's not the problem, but I still detect the issue of your time dimension as an "expansion direction" and now even with some form of rotational mechanism that causes that "expansion".

I agree that it is interesting reading, controversial and pictorially appealing, all factors which forums like SPCF thrive on. It does not necessarily make for good science, though. A few (incomplete) comments pertaining to this.

(i) The consistent view is that since the BB happened everywhere, we are sitting where the BB happened, spatially at the 'center' of our observable universe and we are looking outwards. Where was 't0'? Far away in every direction, in terms of space and of time. To picture t0 as at the center of some or other spatial dimension may create false impressions.

(ii) For any rotation of the whole to be causing spatial expansion is equally problematic. Rotation is an absolutely measurable quantity - we can just look at light paths over long distances and rule it out (or confirm it, for that matter). We can see that individual parts of the universe are rotating, but when we look at large enough scale, we see nothing of that nature. There is also no surviving cosmic theory that predicts universal rotation.

(iii) Sean Carrol's diagrams made a point about "why time has a direction" and I do not think it has anything to do with expansion. The universe can also contract (and probably has contracted in the past), but time will still go in the same direction.

All this said, if we are careful with jumping to conclusions from mental aids and pictures, they can be useful in getting a consistent picture together. For example, the balloon analogy is very useful in explaining certain cosmology concepts, but to think of the dimension going 90 degrees to the skin of the balloon as time will lead you up the garden path.

Is this why you are contemplating a 5th dimension (for time), Faradave?

--
Regards
Jorrie

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### Re: Is the Universe rotating?

BurtJordaan » Tue Dec 30, 2014 10:31 pm wrote:...
I agree that it is interesting reading, controversial and pictorially appealing, all factors which forums like SPCF thrive on. It does not necessarily make for good science, though. A few (incomplete) comments pertaining to this.
...

One of the best examples of science forum moderation I can remember seeing.
I don't think I can come up with any comments that are as understanding, simpatico, helpful, so reason tells me to just be quiet and let FD and Jorrie calmly resolve. I might only distract and muddy the waters. But out of sheer sociability I want to add a remark.

I think it is one of the defining characteristics of a rotation is that it have closed 1D orbits
If you pick an arbitrary point and apply the rotation you get a 1D submanifold that is topologically just a circle.
The point goes on a circumnavigation journey and comes back to the same place.

This is regardless of the number of dimensions.

One doesn't want to confuse that with some "equatorial region" of a D-sphere which is thought of as a D-1 sub manifold by analogy with the equator ring around a 2-sphere.

A 2-sphere (the surface of a conventional globe) has a D-1 = 1 dimensional ring for equator, we can all pictures that. OK. And a 3-sphere might have a 2D equatorial region. And a 4-sphere (embedded in 5D space) might have a 3D equatorial region. But these regions are obviously not orbits.

I want to draw that distinction, in case it might help clarify.

In the conventional 2-sphere case we can imagine motion along the equatorial orbit involving centripetal acceleration, and that acceleration constituting an outwards pseudo force, which acts like it uniformly STRETCH the circular orbit. There are only two directions along the orbit and the stretch is the same in either. so it resembles the expansion of the universe in the simple sense of no preferred direction. Neither direction (neither clockwise nor anti :^)) is preferred. Now you have to show something analogous in higher dimension.

Consider a 3-sphere t2+x2+y2+z2 = 1

The equatorial region is {(0,x,y,z) with x2+y2+z2 = 1}

It seems to me you have to show that for whatever point you pick in the region, if you go along its orbit the centripetal acceleraton is towards the center of the sphere, and of the same magnitude, so that the imagined effect is uniform stretching with no preferred direction in the equatorial region.

It's possible...

But even if you can show that, I'm highly doubtful that nature works like that :^)
So I agree with the viewpoint that Jorrie expressed.
Marshall

### Re: 5-balls vs. Canon balls

Jorrie wrote:...as one of the protectors of the canon around here..."5-ball" and "4-plane" are not...the problem, but...your time dimension as an "expansion direction" and now even with some form of rotational mechanism that causes that "expansion".

As this was not my thread, I’m appreciative of any readership at all and especially honored by our fine moderators (a Happy New Year! to them all).

Let’s be clear. 3-Ring Circus (3RC) is a personal model, which I like and ask others to consider. It should recover present observations and hopefully offer some advantage in doing so. Simplicity is high on my list of advantages.

Time is unidirectional but it's one thing to have unidirectional freedom, it's another to be compelled to use it. I’m identifying both unidirectionality and motivation as inherent to time. The concept of 4-velocity acknowledges but does not give a mechanism for the temporal velocity of a spatially "at rest" object. There is need for a model which does and 3RC provides this.

The idea of a rotating universe, as Marshall has noted (e.g. Gödel’s model) is not new. The idea of a radial temporal field is also illustrated in Carroll’s course. 3RC simply combines these and I consider it a credible answer to the OP. If it seems too unconventional and you want to move this part of the thread, to Personal Theories, its fine with me. Perhaps a split here, with a note pointing to the new location. The new thread might be named "3-Ring Circus Model of Spacetime".

Jorrie wrote:(i) The consistent view is that since the BB happened everywhere,

Agreed. "happened" is past tense. Every current location in space (x,y,z) maps onto the BB but has a different temporal coordinate (tnow). By "different" we mean different from the t0 of the BB. This is consistent with any model suggesting an "age of the universe", including 3RC.

Jorrie wrote:(i)... we are sitting...spatially at the 'center' of our observable universe and we are looking outwards.

Agreed. To be clear, our telescopes look outward spatially (from earth). However, all light received comes from the past. In spacetime we gaze only toward the BB (inward in 3RC) and indeed, the BB is what we always see (barring obstruction), as cosmic background radiation.

Jorrie wrote:To picture t0 as at the a center of some or other spatial dimension may create false impressions.

Agreed. As I wrote above, "spacetime contains a center". 3RC places the BB at the center of spacetime, not space. Specifically, it's the single event of (x,y,z,0). Like a pole of the earth, the BB is one of those locations, in a non-Euclidean geometry, where many (even infinite) coordinate designations map to the same location. I believe Professor Carroll would place it as t0 below, the event from which temporal field lines radiate in 4D.

Jorrie wrote:(iii) Sean Carroll's diagrams made a point about "why time has a direction" and I do not think it has anything to do with expansion.

Please, think again. I would invite anyone, including professor Carroll, to answer this question. Where do spatial simultaneities (foliations) occur in his diagram? I believe he would place two of them as my superimposed dashed arcs indicate. Wouldn’t you? I’m considering writing to ask him, but my response rate on such correspondence is < 20%.

Jorrie wrote:(iii)...The universe can also contract (and probably has contracted in the past), but time will still go in the same direction.

The physics of such a phenomenon (e.g. reversal of 2nd Law of thermodynamics, so entropy decreases over time) seems inapplicable to this existence. 3RC does not attempt to accommodate or exclude a bounce.

Jorrie wrote:(ii)...Rotation is an absolutely measurable quantity

Agreed. Centrifugal force is one of the ways it is detected. World lines aim forward in time to outer, larger spatial foliations. 3RC models centrifugal motivation force. An individual foliation does not need to expand, rather concentric foliations are part of the continuum.

Jorrie wrote:(ii)...we can just look at light paths over long distances and rule [rotation] out (or confirm it, for that matter). We can see that individual parts of the universe are rotating, but when we look at large enough scale, we see nothing of that nature. There is also no surviving cosmic theory that predicts universal rotation.

Two reasons previous rotation theories have failed. First, they have failed to employ an axis of rotation through the center of the temporal field. That axis does not intersect the concentric spatial foliations anywhere (except at the central BB event of t0). This is in the same way that a central z-axis does not intersect a circle in an xy-plane.

Second, they have failed to rotate the entire 4-plane. Particle A, embedded in the 3-ring below, does not slide along the ring. It rotates with the ring and with the entire 4-plane. The particle thus, does not change its spatial coordinates nor its orientation wrt to those coordinates. The particle does not accelerate classically, due to this universe rotation. The only direction an object found to be "at rest" moves is temporally (radially in 3RC).

By contrast Gödel had space slipping past its temporal field and thus predicted light cones tilted as a function of radius. Time needs to move with space, like the spokes of a wheel move with the rim.

Jorrie wrote:...the balloon analogy is very useful in explaining certain cosmology concepts, but to think of the dimension going 90o to the skin of the balloon as time will lead you up the garden path.

Is there any better way to read Carroll’s diagram? It should be seen as an expression of the balloon analogy, where time is a radial field and the balloon skin, at increasing times, is concentrically expanded space. His timelines are normal to the spatial foliations at every intersection. I’m not saying this is the only model, but as you note, it is a convenient one.

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### Re: Faradave's 3-Ring Circus Model of Spacetime

The problem with most of the theories/models offered in this section of SPCF is that it is difficult to know and show that they "recover prior art". Very few of us around here know the "art" well enough to be 'expert' and it takes a lot of time to work through the proposals to find any flaws.

Some proponents of own theories quickly demonstrate that they know far too little to achieve what they set out to do. FD is one not one of them; he knows a good chunk of standard theory, so it is even more time consuming to find flaws (if any), especially since pictures and prose without math are very imprecise.

My compromise is normally to read what a person says about the 'standard theory' and then point out any apparent misunderstanding and/or misconception about the standard theory. This mostly leads to lengthy discussion, which does not always result in a resolution. But as long as everyone (including us moderators) have learned something, I think it is good for the Forum.

Occasionally, a personally theory like rlloydbowen's "Space Production Model of Gravity" comes along, which is so close to 'the standard' that it warrants considerable effort. As it turned out, after a few pages of comments, the originator decided to study the standard theory in more depth, which is good. I'm not saying this to promote my eBook (which was written in the previous century for engineers and is a little outdated by now), but he said he is busy reading it with some other stuff.

Faradave, I'm pretty sure you have also studied the modern standard theory and I have some idea of what your objectives are. It seems to me that you are searching for 'holes' in the standard theory, especially its apparent lack of answering many of the how's and all of the why's of gravity and cosmology. Are you hoping to get some of those holes plugged by your '3-Ring Circus Model'?

Since it's New Year's Day, I do not have the inclination now to deal with some statements in your prior post that will need rectification or clarification. I will do that in some future reply.

Enjoy the day. :)

Jorrie

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### Re: Faradave's 3-Ring Circus Model of Spacetime

Around 1980 some astronomers discovered that the CMBR was polarized if you look at it in different directions and they took this as possible evidence that the universe was rotating. No one else was able to repeat their observation and it was later determined to be in error. This makes me wonder if the CMBR in a rotating universe should be polarized or if the lack of polarization may be evidence that the universe is not rotating.

Also, an excellent model of the universe as a rotating 4-D hypersphere can be found in “Geometry, Relativity and the Fourth Dimension” by Rudolf Rucker. See Chapter 7 “The Shape of Space-Time.”
In Rucker's model, our universe is one rotation in a continuous cycle of creation and destruction.
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### Re: Faradave's 3-Ring Circus Model of Spacetime

I located the book on openlibrary: https://openlibrary.org/books/OL4890320M/Geometry_relativity_and_the_fourth_dimension.

I did not see anything on a rotating hyperspherical universe, just the more or less standard cyclic model. Did you see it in one of his references?

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Re: Orbituary
Marshall wrote:I think it is one of the defining characteristics of a rotation is that it have closed 1D orbits

How fascinating that you have taken this approach! I had debated presenting an orbital progression in support of 3-Ring Circus (3RC) but thought it might be too much of a conceptual leap. Apparently, I was wrong.
Marshall wrote:If you pick an arbitrary point and apply the rotation you get a 1D ... circle. The point goes on a circumnavigation journey and comes back to the same place. This is regardless of the number of dimensions. One doesn't want to confuse that with some "equatorial region" of a D-sphere which is thought of as a D-1 sub manifold by analogy with the equator ring around a 2-sphere.

You make the interesting suggestion that orbits, being 1D, correspond to 1D equators, regardless of ball dimension. Using Wikipedia terms (their "n" is your "D"), an n-ball is enclosed by an (n-1)-sphere.

Let’s start the progression as small as we can, dimensionally speaking. A 1-ball is a line segment having a center and enclosed by a 0-sphere (its two endpoints), which is also the equator. I must assert that a 0-equator can only support a 0-orbit. The only available continuous path, including both endpoints, oscillates through the 1-ball, as if continuously accelerating toward its center. A satellite dropped in a tunnel along a diameter of the earth would exhibit this simple harmonic motion, "orbiting" only two surface locations.

Marshall wrote:A 2-sphere (the surface of a conventional globe) has a D-1 = 1 dimensional ring for equator, we can all picture that.

Yes. A typical earth orbiting satellite can illustrate this, combining two perpendicular oscillations at once. With the same center, frequency and amplitude a circular 1-orbit (a 1D sub manifold) is achieved.

Marshall wrote:[flagrantly edited] Now you have to show something analogous in higher dimension...a 3-sphere might have a 2D equatorial region. And a 4-sphere (embedded in 5D space) might have a 3D equatorial region. But these regions are obviously not orbits... even if you can show that, I'm highly doubtful that nature works like that :^)

This is where things get interesting! The term "orbit" understandably invokes a planetary perspective but I’m going to ask that we look microscopically for this answer. You’re correct. They’re not called "orbits". They’re called "orbitals"! Though wave mechanics complicate the math, the simplest S-orbitals have approximately spherical solutions. They’re all >1-orbits.

"The electrons do not orbit the nucleus in the sense of a planet orbiting the sun, but instead exist as standing waves. The lowest possible energy an electron can take is therefore analogous to the fundamental frequency of a wave on a string. Higher energy states are then similar to harmonics of the fundamental frequency.
...atomic orbitals do not closely resemble a planet's elliptical path in ordinary atoms. A more accurate analogy might be that of a large and often oddly shaped "atmosphere" (the electron),...
... tends toward a generally spherical zone of probability describing where the atom’s electrons will be found.
"

The shapes of the first five atomic orbitals: 1s, 2s, 2px, 2py, and 2pz. The colors show the wave function phase. These are graphs of ψ(x, y, z) functions which depend on the coordinates of one electron.

A progression of orbits from 0 to 1 to 2+ suggests that the progression continues to higher dimensions and that the forces entailed are equally available in those dimensions.

Marshall once convincingly argued that the formula for circumference of an n-sphere is the same (c=pi2r), regardless of dimension. The question is then, how many orthogonal circumferences (along with all the n-surface they entail) can be equally rotated about a 5th dimensional axis? I maintain that the answer is three.

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### Re: Faradave's 3-Ring Circus Model of Spacetime

BurtJordaan » January 2nd, 2015, 3:44 am wrote:I located the book on openlibrary: https://openlibrary.org/books/OL4890320M/Geometry_relativity_and_the_fourth_dimension.

I did not see anything on a rotating hyperspherical universe, just the more or less standard cyclic model. Did you see it in one of his references?

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Rucker's model with a 4-D space-time manifold is in the main text but I should have been more specific with my description.

A 4-D sphere is impossible to imagine so Rucker expanded his 4-D sphere into 3-D space-time for purposes of explanation and a 4-D sphere expanded into 3-D space is a torus. Rucker calls this his “Torus” model. See Fig. 123.
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### Re: Faradave's 3-Ring Circus Model of Spacetime

bangstrom » 02 Jan 2015, 19:17 wrote:A 4-D sphere is impossible to imagine so Rucker expanded his 4-D sphere into 3-D space-time for purposes of explanation and a 4-D sphere expanded into 3-D space is a torus. Rucker calls this his “Torus” model. See Fig. 123.

Yes, I've seen that, but AFICS it is a cyclic model, not a rotating model in the sense that Faradave implies in this thread. What am I missing?

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### Re: 5-balls vs. Canon balls

I have indicated that I will reply to (IMO) some questionable statements that FD made in this thread.
Faradave » 01 Jan 2015, 07:58 wrote: \In spacetime we gaze only toward the BB (inward in 3RC) and indeed, the BB is what we always see (barring obstruction), as cosmic background radiation.

This is approximately so. The CMB photons came from some 370,000 years after t0. We hope to one day "see" farther back by means of other particles and radiation (neutrinos and gravitational waves).

Agreed. As I wrote above, "spacetime contains a center". 3RC places the BB at the center of spacetime, not space.

Since time as we define it may stretch from minus to plus infinity, it may not have a center in the sense that any time is as good as another time as 'a center'. All we can say for sure is that there was a time in the past that naive extrapolation of our definition gives a "time zero" and there was probably (negative) time before that.

The physics of such a phenomenon (e.g. reversal of 2nd Law of thermodynamics, so entropy decreases over time) seems inapplicable to this existence. 3RC does not attempt to accommodate or exclude a bounce.

Modern bounce cosmologies do not suffer from this problem. The area of (empty) space eventually collapsing and producing a new cycle has extremely low entropy because of the accelerated expansion. There is no "reversal of 2nd Law of thermodynamics".

Is there any better way to read Carroll’s diagram? It should be seen as an expression of the balloon analogy, where time is a radial field and the balloon skin, at increasing times, is concentrically expanded space. His timelines are normal to the spatial foliations at every intersection.

Firstly, Carrol's diagram is just a tool for illustrating a specific point to novices. It does not represent the 'balloon analogy' in any way. Secondly, the latter has no time direction indicated, the radial direction being fictitious 'hyper-space', which plays an important role in understanding the analogy to the real cosmos.

The usual way to include time is to show a 'trumpet-like' picture, with time progressing along the length of the trumpet, e.g http://upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Dark_Energy.jpg/524px-Dark_Energy.jpg:

Here the observable space balloon surface is replaced by a disc (representing a time slice) and the circumference of this disc is representing the hyperspace radius. Note that 'bounce-cosmologies' would have a mirror image below the "Big Bang", still with time running 'upwards' in the diagram.

You are apparently adding another dimension to the picture an hence have an "axis of rotation" that I fail to understand. In modern 'brane-cosmology', the 5th dimension represents 'the bulk' in which extra 4-D branes can live.

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### Re: Internal axis

bangstrom wrote:Around 1980 some astronomers discovered that the CMBR was polarized if you look at it in different directions

Watson posted this article link, which indicates that the polarization you mentioned is undergoing further study. Allowing that some slight rotation is detected, I believe it would be about an identifiable spatial axis as with a galaxy. That would yield direction dependent polarization, as you mentioned. If so, it would not be the same type of rotation I use in 3RC and associate with dark energy. Interesting nonetheless.

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### Re: Internal axis

Faradave » 05 Jan 2015, 04:14 wrote:Watson posted this article link, which indicates that the polarization you mentioned is undergoing further study. Allowing that some slight rotation is detected, I believe it would be about an identifiable spatial axis as with a galaxy.

CMB polarizations seem to have nothing to do with cosmic rotation, but rather with local ripples in spacetime.

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### Re: Empty Balloon Analogy

Jorrie wrote:Are you hoping to get some of those holes [in standard theory] plugged by your '3-Ring Circus Model' [3RC]?

Yes, you’ve nailed it! 3RC should be considered part of my personal paradigm, Phyxed (physics-fixed, better than real). It is essentially my onion model but dimensionally compressed to flatness in order to illustrate rotation as a potential motivation for expansion (an alternative to dark energy).

Space is not an object which must expand in this model. Rather, the spacetime of 3RC entails concentric 3-rings of space corresponding to all past, present and future instances wrt to radial time. An outer, spatial 3-ring is already larger (more "expansive") than an inner one, where an observer’s worldline crosses it.

Since time as we define it may stretch from minus to plus infinity, it may not have a center in the sense that any time is as good as another time as 'a center'. All we can say for sure is that there was a time in the past that naive extrapolation of our definition gives a "time zero" and there was probably (negative) time before that.

So long as we are to accept convergence to an essentially zero space s0 in the past, I don’t consider it "naïve" but intuitive and convenient to label that time t0. Here’s how Carroll put it:
"In conventional cosmology, the actual size of the observable universe when the universe started is about 1 centimeter. In inflation, if we trace our currently observable universe backward in time, it can start with a region that’s about 10-30 centimeters across, and it’s much more plausible to particle physicists that the universe started in exactly that state."

Granted the singularity prevents us from knowing exactly what there was before t0 but that’s all the more reason to ignore vast durations of (negative) time before then. Typically, those explorations are aimed at explaining how we got such a low-entropy Big Bang to begin with. 3RC can provide a different mechanism for that.

Carrol's diagram is just a tool for illustrating a specific point to novices. It does not represent the 'balloon analogy' in any way...the latter has no time direction indicated, the radial direction being fictitious 'hyper-space', which plays an important role in understanding the analogy to the real cosmos.

To the extent that the balloon analogy is used to represent the Metric Expansion of space, I must reluctantly agree with you, as Wikipedia does:
"The expansion of space is often illustrated with conceptual models which show only the size of space at a particular time, leaving the dimension of time implicit. This analogy is potentially confusing since it wrongly suggests that the big bang took place at the center of the balloon. In fact points off the surface of the balloon have no meaning, even if they were occupied by the balloon at an earlier time."

That's a glaring deficiency of the balloon analogy! People will always ask, isn’t the past inside the balloon and the future outside, to which the answer will be affirmative. And yet, we’re somehow not to draw worldlines connecting corresponding points of successive instances of the balloon. I can’t think of a single kind thing to say about that.

No matter! 3RC does have radial time along with curved space.

Perhaps Carroll was intuiting 3RC with his drawing of a radial temporal field? He certainly could have drawn it flat. His analogy was earth's gravitational field but he could have used Einstein’s elevator, if he wanted to illustrate a non-divergent temporal field. And his Big Bang proceeds from small, hot, dense origins to what we have now.

The usual way to include time is to show a 'trumpet-like' picture, with time progressing along the length of the Here...a disc (representing a time slice) and the circumference of this disc is representing the hyperspace radius.

.
Though I like this better than an empty balloon, the trumpet's edges provoke questions about what it is embedded in. I appreciate that time is represented generally in the vertical. However, more precise representations will have time follow the contours of the trumpet’s sides. (Perhaps it would be better to think of the vertical as a(t), the scale factor.)

With just x- (purple) and t- (blue) grid lines shown, yellow and brown are object worldlines. These objects are at rest but have varying separation velocities attributable to expansion. Red and orange are light paths not relevant to this discussion.

3RC accommodates diverging timelines by curving space. It accommodates a(t) by varying the packing density of concentric simultaneities.

There is no "reversal of 2nd Law of thermodynamics"...Note that 'bounce-cosmologies' would have a mirror image below the "Big Bang", still with time running 'upwards' in the diagram.

This is where I get the impression that 2nd law of thermodynamics is violated. If we agree that the Big Bang represents low entropy, then timelines converging into it, from negative times and a higher entropy past, would seem to be unscrambling eggs.

You are apparently adding another dimension to the picture an hence have an "axis of rotation" that I fail to understand.

My use of 5th dimension is only for a perspective from which to view the spacetime 4-plane, in which spatial 3-rings exist. The 5th dimensional axis does not have to exist in order to function. A flatlander can turn an about face in his 2-plane, even if that's all the space that exists. Yet in doing so, it turns about an imaginary 3rd dimensional axis. In fact, the entire 2-plane may rotate that way. The same rotation is what I describe for the 4-plane of 3RC.

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### Re: Faradave's 3-Ring Circus Model of Spacetime

I admit that it's a bit confusing to posit a 5-d axis that doesn't really exist, in any ontological sense, but somehow functions as a pivot point. The about-face Flatlander is helpful somewhat, at least in underscoring that the higher-D axis is imaginary (or rather, imaginary, if Flatland were really how the universe was). Yet how can any rotation really be said to happen, if the axis is imaginary? Seems like we are rotating math in our heads, and nothing substantial.

Sorry if this all sounds a bit dense. On higher-D matters, I AM dense.

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### Re: Spinning Wheels

Braininvat wrote:Yet how can any rotation really be said to happen, if the axis is imaginary?

That's the point really. It can be "said to happen" if we observe an expansion force consistent with the rotation. In our case that force is uniform at all spatial locations, toward the future and an expanded spatial simultaneity (3-ring).

An axis is a bit like an axle. Wheels have them, Freebee's don't but both spin quite nicely. Drops of water will fly off radially in either case.
Last edited by Faradave on January 7th, 2015, 3:55 pm, edited 1 time in total.

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### Re: Empty Balloon Analogy

Again, I will only comment on problems regarding your representation of the standard model.

Faradave » 07 Jan 2015, 20:27 wrote:
Jorrie wrote:.
Though I like this better than an empty balloon, the trumpet's edges provoke questions about what it is embedded in. I appreciate that time is represented generally in the vertical. However, more precise representations will have time follow the contours of the trumpet’s sides. (Perhaps it would be better to think of the vertical as a(t), the scale factor.)

No, this would be confusing to everybody here, because the horizontal actually depicts the scale factor (or rather the expansion factor) a(t). Since the vertical is t, the slope of the trumpet's side gives da/dt and the change in slope represents the second derivative d2a/dt2, in other words the acceleration of the expansion factor. Lines up the sides of the trumpet represent world-lines, not time.

This is where I get the impression that 2nd law of thermodynamics is violated. If we agree that the Big Bang represents low entropy, then timelines converging into it, from negative times and a higher entropy past, would seem to be unscrambling eggs.

I think our impression is incorrect, because modern bounce cosmologies start way back with a low entropy. The observable universe eventually becomes empty of matter and radiation, in other words a 'true vacuum', with no eggs to unscramble. Quantum fluctuations can readily 'pinch off' a region with low entropy and let it contract from this low entropy state to a bounce with low entropy.

More classically viewed, Einstein's original static model being 'propped up' from collapse by the cosmological constant would have been unstable to tiny deviations and would either expand or contract with equal probability. An empty universe with a constant Hubble radius would suffer the same consequences.

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Jorrie wrote:Since the vertical is t, the slope of the trumpet's side gives da/dt and the change in slope represents the second derivative d2a/dt2, in other words the acceleration of the expansion factor.

Yes, that makes sense. Thanks.

Lines up the sides of the trumpet represent world-lines, not time.

Agreed. But for objects "at rest" (say, wrt to CBR or BB) world-lines may be considered timelines? Vertical timelines seem to present a problem when we drop them down from the outer rim of the trumpet. We'd be creating a false "history" for those locations in doing so. It would look as if they arose from outside the BB!

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### Re: Faradave's 3-Ring Circus Model of Spacetime

Hi Everyone,

Just a quick drop by here. In regards to Flat-Land, a denizen of such a place understands a circle. If a Flatlander places a circle on an inclined plane.. it rolls downward. They understand the circle to be a solid and that the circle has a center. But these folks have no concept of axle rotation. Any line drawn though a circle can not be rotated around that line without leaving the 2D surface.

If their version of Einstein derived Relativity, he might suggest that an Axis exists 90' from the flat plane of Existence. That they are used to thinking in terms of X and Y coordinates, but a Z coordinate? That's silly and must be an imaginary axis for a circle to call as a rotational axis. It obviously can't exist in Real Flat Space.

But this Einstein has shown in his Relativity, that the "Z" Axis is real and is called "Time". That the Axis of rotation for a Circle points towards the Past and Future. This implies a 3D reality with "Time" as a Spatial Axis or (X, Y, cT).

Does this sound familiar to anyone? (lol)

And of course, it's not just the Matter in such a 2D volume that is moving around such an imaginary Axis, but the whole Flat Universe is in rotation.. Vacuum included (Space-Time). And they have a real problem representing such an Image in Flatland, as it would look like the 3D Trumpet image we are accustomed to seeing in 4D land. But we can't see rotation on a Temporal Axis, so it must be imaginary.. right?

Anyway, just my two cents as always.

Best wishes,
Dave :^)

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Faradave » 07 Jan 2015, 22:14 wrote:Agreed. But for objects "at rest" (say, wrt to CBR or BB) world-lines may be considered timelines? Vertical timelines seem to present a problem when we drop them down from the outer rim of the trumpet. We'd be creating a false "history" for those locations in doing so. It would look as if they arose from outside the BB!

Yes, but cosmic time and wordlines are not the same thing, but these things are coordinate dependent and one can choose all sorts of weird coordinate systems. It is dangerous to make physical interpretations from coordinate choices.

All said, I have not really criticized your idea, because it is perhaps no more mysterious than many a dark energy idea. If I use Einstein's cosmological constant and view it as a 'mysterious force' caused by the negative pressure of the vacuum and you view it as a rotation about some 'mysterious axis' and we get the same quantitative result, what does it matter. The question is: do we get the same result or prediction?

Interestingly, the increase in the recession speed of a particular galaxay at CMB-rest (and not bound into an orbit) grows linearly with proper distance; it is presently of the order one pico-g per billion light years (equation $a=D H_0^2 (\Omega_\Lambda - \Omega_m/2)$). Now, this is the same 'law' that one would expect for a system that is rotating at a constant angular rate ($\omega$), i.e. centrifugal acceleration increasing linearly with radius ($a = r\omega$).

With this I'm not saying I'm buying into your idea, but it may not be that far-fetched if that axis is 'hidden' so that we cannot notice any rotation! Also provided it can also give the right acceleration profile over cosmic time: first decelerating, then practically coasting for a while, before gradually going over to accelerating expansion.

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BurtJordaan » 07 Jan 2015, 23:09 wrote:Interestingly, the increase in the recession speed of a particular galaxy at CMB-rest (and not bound into an orbit) grows linearly with proper distance; it is presently of the order one pico-g per billion light years (equation $a=D H_0^2 (\Omega_\Lambda - \Omega_m/2)$).

I should not have used $a$ for acceleration, since it normally means expansion (or scale-) factor in cosmology. Should have written $d^2D/dt^2=D H_0^2 (\Omega_\Lambda - \Omega_m/2)$, where $D$ is the proper distance to the galaxy.

Also, the equation gives the "instantaneous" change in the recession rate of a particular galaxy, but if observed over a period of time, the "constants" H_0 and the Omegas also change, albeit very, very slowly. The general equation for the acceleration/deceleration of the expanding distance is $d^2D/dt^2 = D H^2 (\Omega_\Lambda - \Omega_m/2a^3) - \Omega_r/a^4)$, with $a$ the expansion factor and $\Omega_r$the radiation energy density parameter of today. The variable Hubble parameter scaled similarly as: $H^2 = H_0^2 (\Omega_\Lambda + \Omega_m/a^3) + \Omega_r/a^4)$.

Before the late $\Omega_\Lambda$ domination, the acceleration was negative, i.e. a deceleration, because the gravitational 'pull' of matter and radiation dominated. The contribution of $\Omega_\Lambda$ still scaled linearly with proper distance, but its influence was insignificant.

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### Re: Circus Act

Thanks, I appreciate the interesting and encouraging recession rate equations.
Jorrie wrote:If...we get the same quantitative result, what does it matter? The question is...prediction?

It seems unique to 3-Ring Circus (3RC) that it predicts a universal speed limit relating to its curved space, radial time structure. Consider the indicated "region of interest" on the spacetime 4-plane. It shows corresponding arcs from two concentric spatial 3-rings at t1 and t2. It will suffice to consider just the x dimension of each.

The path of an object at rest is indicated by the worldline v0, overlying the timeline connecting event A on t1 to future event B on t2. A worldline having velocity v1 is shown at an angle with respect to the timeline, while the worldline of greater velocity v2 makes a greater angle. However, the unidirectionality of time prevents any worldline from exceeding the tangent at A, perpendicular to its timeline and shown as vmax.

Interestingly, the trajectory of vmax, has no component on ∆t, suggesting it avoids aging as it proceeds to future location C, spatially displaced by ∆x = BC. Given local flatness, arc BC is essentially the hypotenuse of right triangle ABC and separation AC is an interval, ∆d. From Pythagoras: AB2 + AC2 = BC2, which naturally yields the interval formula: ∆d2 = ∆x2 - ∆t2.

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