Relativity and Cosmology

Jorrie,

If the universe was spherical in 4 dimensions, would those red blocks be perfectly lined up along a set of blue bars, or would they be ever so imperceptibly out of alignment?

Hi Guest,

The red blocks would remain perfectly lined up as far as we can tell, because light would follow whatever (4-d) curvature there is. Light cannot "wander off" into hyperspace any more than what we can!

One way of detecting 4-d curvature is to "put" an astronomer on each of three red cubes forming a very large triangle. If each of them measure the angle between the other two astronomer's cubes (galaxies) and they exchange data, they will find that the three angles of the triangle add up to more than pi/2 radians.

However, with us bound to just one vantage point inside the lattice, we have great difficulty doing just that and so far, we were unable to detect any local curvature. This may mean there is no space curvature, or it is too small for us to detect with present technology.

-J

Hi Jorrie,

Great post. I think I found a couple of typos: "...insignificant spec in an infinite "sea" if space and matter-energy! (should be of?). "...but in reality having the same curvature than the universe at large." (should be as?). Hope you don't mind my nick-picking.

S

Thanks S, I'll fix those.

Did the final edit in the small hours of the morning!

-J

Hi StandardsGuy,

You are definitely nick-picking Jorrie. Hope you don't become like Mikerho who really is a prick. I didn't like his comments he made about a post Ashman posted 2 days ago about "Yet another gravitational conundrum"

I rarely post comments on CR4, but love to read interesting posts especially from Jorrie, even loved your post on the "The State of the big bang theory", can't what to read the replies.

I am not as highly educated as you guys but really enjoy reading about the Universe & stuff. I know that Jorrie probably does not mind (or see you as nick-picking) the modest guy that he is. The flaws/mistakes you guys make when typing or expressing yourselves really reminds me that you are humans (and some intellectual god), and your views and ideas can change over time.

Also, the reason for posting is that I got to stand up for my fellow countryman Jorrie.

I know that I made a few mistakes in this post, but who cares.

Hi Raakwys, thanks for coming up for me, but I really don't mind being corrected, especially in Blog title posts, which have a much higher visibility on the web than general posts.

BTW, English is not my mother tongue, but a "true African one" is. I suspect so is yours, looking at your pseudo-name.

-J

Excuse my relative ignorance, but to me it doesn't seem so intuitive once realized: that an expanding...entity must, by intuition, (at least seem to) have a static point (focus of expansion); and the hopelessness of finding any such body or point that is concurrently static both in location and in time. But, what am I missing that clouds from consternation?

Jorrie,

Great post. This is not my field but you make it very interesting.Thanks

PS: The spelling & grammer errors do NOT take away from the content, at least for me.

I got one for you. where is the center of the Universe ???

Guest asked: "I got one for you. where is the center of the Universe ???"

You are at the exact center of your personal observable universe. The Universe at large has no center.

-J

Though there may be no object in the center of the universe, I think it is a "definate maybe" that the universe has a center, that is, if one believes that it began at a single point

Hi SmithsEng

If the universe is infinite as often postulated, then the term center would be meaninless since no matter where you were you would always be that same distance from infinity.

This may or may not have been a lucid moment for me ..Thank You

Hi Yani, you wrote: "If the universe is infinite as often postulated, then the term center would be meaningless since no matter where you were you would always be that same distance from infinity."

A perfect (partial) answer!

If the Universe is finite, yet unbounded, as I speculated in the opening post, it has a center in four dimensions, but not in three. Just like Earth has a center in three dimensions, but not in two - where's the center of Earth's surface?

-J

Thaks Jorrie,

That post made things much clearer. Some concepts are, by their very nature, difficult to comprehend and such examples are really a big help.

Keep up the good work,

John

If the Universe has no center then how could it have any shape ?

Guest asked: "If the Universe has no center then how could it have any shape ?"

Recall what I wrote in the OP: "Like the total ocean, the Universe at large may have any of a number of different shapes, with the distinction that the Universe may even be infinite, in which case it has no shape at all".

However, if it is closed in 4 dimensions, it has a 4-d shape, forming a hypersphere in 4 dimensions. As also stated in the OP, this makes little difference to man and beast, because we can never detect the center or an edge or circumnavigate this hypersphere.

Final analysis: it does not matter!

-J

Where is the centre of a ring doughnut? (torroid)

I mean if the universe is torroidal you cant say the centre in in the hole in the middle.

Who cares anyway, why bother our heads with these questions while the world go's to hell in a handcart! Spencer.

Some day, hopefully before the suns expansion fries our world, we will become an intergalactic race of nomads, where if we go to various planets in other systems, we can spend generations adapting to the conditions we will face on arrival. I'm sure in a hundred or 2 generations, we could adapt to pressures of maybe 0.2 or 20 bar, and temperatures of 220 to 350 K and gravities of 0.1 to perhaps 10G while en route, if we know what we are going to.

Wherever we go, we can carry Darwin with us, and count on the adaption being directable, and planned. Wherever we go, whatever we do, we always will do it together, with Darwin.

RichH

Darwin is dead & Darwinism is under attack! Intelligent Design is the new Paridigm.

Intelligent design, now there's one of the all time great evolutionary dead ends.

Per chance, would you be pushing for an horary mention in the 2008 Darwin Awards?

Sub: Shape of the Universe and Center of the Universe

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IV.HEART OF uNIVERSE TO DYNAMIC FUNCTION -COSMOS YOGA VISION SERIES IV (DEC 2007)
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Hi,

Is it true that every time the sensitivity and the exposure time of telescopes have been increased, new objects were found in the (seemingly) empty gaps of space? If so, does that mean that the only evidence of the universe expanding is the backround radiation?

Thanks!

Guest asked: "... If so, does that mean that the only evidence of the universe expanding is the background radiation?"

Farther and fainter galaxies are observed as the technology improves, yes. The cosmic expansion is deduced from the redshifts of galaxies that are larger for more distant galaxies, following Hubble's law. The background radiation (CMB) is just one point of a set of data, showing a consistent distance/redshift ratio.

-J

Would not the 'universe have no shape as it has no bounderies? Or are we talking of just the 'space' that the galaxies currently occupy? If it is just the 'space' 'area' that the galaxies currently are in. What is the area called that lies outside of the 'area' occupied by the galaxies? I ask because a few months ago I read the universe is 'flat' or flattened on the 'top' and 'bottom' but expanding outward. When I read items like this what is never addressed is what is the 'space' 'area' called that the universe is expanding into?

Let me give this a wack. If the universe is a infinite "container" then expansion within the "Container" is only relative to items in the "container". There fore the space between (or Time between) galaxies may be growing but only in relation to each other. The infinite part remains constant at infinite.

Although I sometimes have dificullty grasping the meaning of infinite. I understood it in the sense of a "Limit" in Math but as a Universe it becomes foggy.

I shall return to my nap.

You need to add a class to your infinities.

1. points on a line ∞

2. points on a plane ∞ ²

3. points in space ∞ ³

4. points in space/time ∞ ⁴

And for how many dimensions suggested by qt?

Or, maybe the time dimension has a limit, either a starting or end point? A closed universe?

RichH

Hi Rich,

Yea, I sincerely hope the Universe is a finite, unbounded, 4-d hypersphere that avoids all those infinities on the large scale!

But, as I hinted in the OP, if expansion is accelerating, no photon can ever circumnavigate the hypersphere. So, how the heck does this differ from an infinite universe?

-J

If we have a soul, perhaps someday you and I can travel across that 4th dimension, limited or not, and discover the ends of time, if there are, from the vantage of a cosmic conscience.

If we don't have a soul, i guess we will find our own end of time. From the funerals I've attended, the deceased seems to lack a dimension, but you can hardly call that evidence.

RichH

I hope we can then travel at superluminal velocity, otherwise it will take an "infinity" to the ends of time... Maybe not such a bad prospect!

-J

I know a shortcut between the 5th and 6th dimrnsions. We'll be there in 10 minutes.

If the universe is closed in another dimension, that would mean that only a part of that dimension's range would be available, with more "unused" range which we are closed out of. If an open universe, be it time or something so far from our feeble imaginations that we'll never conceive of it, we can never see the ends, as they wouldn't exist, except in our vision.

if the asymptote to the hyperbolic is the end of our time, the slope will never lead us there. The usual image shown for a hyperbolic paraboloid is with the focus of the parabola opposite the hyperbolic curve (A classic saddle-shaped open universe).

Tell me, if both the hyperbola and the parabola are curved in the same direction, would not all of our measurements show a closed universe, and really be just as open as the opposing curves?

We'll have to look some day. No rush.

RichH

Any discussion of the shape of the Universe is essentially meaningless.

Here's why: One essential feature that spheres, ellipsoids, and even Christie Brinkley's celestial body all share in common is a surface. In each case, the surface serves the essential purpose of dividing the interior from the exterior. In the current context, this surface would, of course, curve in four dimensions - if, in fact, the Universe has a surface. The problem with any discussion of shape in the context the Universe arises when one considers that the Universe has no exterior. There is no Outside, no Something Beyond, No Anything Beyond the Universe from which a hypothetical surface might partition the interior. And since there is no exterior, the whole concept of an interior is meaningless as well.

Allow me to point out that the concept of an interior is meaningful only in the context of an exterior and an intervening surface. As neither of these requirements are met in the case of our own Universe, the concept of an interior exists in a complete vacuum (you decide if this is a pun or not).

One might speculate that there is a Something Out There Beyond The Universe (deities aside) in which the Universe is embedded somehow, but allow me to point out, however, that such a Something must either extend the Universe - in which case we're back in the same boat as before - or the Something's topological properties must be so completely distinct from our own four dimensional spacetime as to be utterly alien. This latter requirement is necessary, again, if any distinction is to be made between the Universe and What Lies Beyond. If it is not, then it becomes merely an extension once again of our four-dimensional Universe - and we find ourselves once again bailing water.

Finally, assuming the latter scenario is true, this Something must not be so distinctly distinct from the topological properties of our own Universe that the concept of shape - or even the concept of embeddedness itself - has no meaning. We seem to be in something of a quandry!

I submit, therefore, that the Universe has no shape. Not only does it not have a shape, but the whole idea of 'shape,' itself, in this context, has no meaning whatsoever.

Sorry, Christie. Maybe next time.

Hi Ace, you wrote: "As neither of these requirements are met in the case of our own Universe, the concept of an interior exists in a complete vacuum ..."

I can't help it, but I've got this strong feeling that somehow I'm on the interior side of or own Universe!

-J

Hi Ace,

In each case, the surface serves the essential purpose of dividing the interior from the exterior....if, in fact, the Universe has a surface.

Don't forget the mobius strip where 2 dimensions appear to fold into 1!

According to super string theory, 4 dimensions just simply are not enough. Six more dimensions are essential to explain the various particles that make up our universe.

Check out this site: http://www.columbia.edu/cu/record/23/18/14.html

Here is an excerpt from the website by Professor Brian Greene:

"Space and time themselves may be the result of an enormous number of little vibrating strings all coalescing together and vibrating in a particular coherent pattern.

"If so, you can imagine a state of the universe when the strings have not coalesced in that manner, and space and time have not yet been formed. And it is possible that the universe could return to that state."

Could strings also coalesce into another kind of universe?

"In principle," said Greene, "it is possible."

So our discussion obviously comes down to a certain degree of speculation. Since our universe, the observable universe, supposedly began with the "big bang" which is where time and space began (for us, in our universe anyway). Consider a universe of universes in which ours began with the explosion of a supermassive black hole some 14 billion years ago. Our universe, then has progressed to the point where it contains innumerable stars, black holes, etc. all expanding away from each other to the extent of red-shifting which is where our observable universe ends.

Then lets say that this entity that we call our universe (unbounded as it may be, to us) is, in fact, bounded by, lets say, the cosmic microwave background. Now lets call this entity, for example, a "galactic universe". In a bigger universe, there may be other "galactic universes" of which ours is only one among an uncountable number of similar entities. Just more food for thought.

Cheers,

John

P.S. I'd like to also hear what Jorrie has to say on this.

Addendum to post #30,

"Don't forget the mobius strip where 2 dimensions appear to fold into 1! "

At least the mobius strip gets rid of the idea of inner and outer surface.

In addition,

"The problem with any discussion of shape in the context the Universe arises when one considers that the Universe has no exterior. There is no Outside, no Something Beyond, No Anything Beyond the Universe from which a hypothetical surface might partition the interior. And since there is no exterior, the whole concept of an interior is meaningless as well."

You are correct Ace in that there is "no exterior" but that's from our perspective, the inhabitants of our universe. The term "no exterior" is a very subjective term here. But you're right. From the standpoint of our current knowledge base, there is no Outside, no Something Beyond other than what our fertile imaginations can project as I said in my previous post.

Who knows! If we can develop time travel we may just be able to go back in time to some earlier point. I realize there's a host of well- known problems associated with backward time travel as opposed to traveling ahead in time. But, just but, if we let our imaginations soar for a moment and somehow overcome these annoyances why couldn't we go back far enough to go beyond the "big bang"? Think about it! If we went beyond the "big bang" which is where time began (for us) we would not then be doing time travel because we went beyond time itself. Wow! What a concept.

Then, theoretically, we would be in that "bigger" universe to which I earlier referred. It seems only logical that "that" universe would somehow have a time reference of some sort although it may not be anything like the time that we're accustomed to. Anyway, if we landed in that larger universe we just might be able to catch a glimpse of many "galactic universes" that had already been spawned. And even that larger universe might just be a drop in the bucket, just another everyday universe in a larger one still.

One things for sure. Regardless of how you conceptualize it, the Creator sure does things on a more grandiose scale than anything we can conceive of (other than with our wildly rampant imaginations).

John

I think that the mobius takes two surfaces (Interior and Exterior, if you will) and closes them into a single surface. It's still a 2 dimensional surface, but with only a single surface. An ant crawling along would never find an end in one direction, making it seem of ∞ length, from his locked-to-the-surface viewpoint. The twist is in a third, unapparent dimension.

Imagine a piece of paper, which when you turned it over, wasn't. It only has a single surface. Would you see it in a mirror? Only after you turned it away from your real world.

Kinda like that.

RichH

Hey NoSciFi,

"Imagine a piece of paper, which when you turned it over, wasn't. It only has a single surface. Would you see it in a mirror? Only after you turned it away from your real world."

Huh?

"from his locked-to-the-surface viewpoint"

Sometimes I think many of us have such a viewpoint! We may very well be locked-to-the-surface of that hyperbolic saddle that you mentioned earlier.

HEP (high energy physics) takes us a long way but when one attempts to reach out beyond the observable universe we are, when you come right down to it, pretty much left with speculation and imagination.

I tried the shortcut between the 5th and 6th but there was a detour sign. It led me to fold the 5th over onto the 4th. It was weird man! It took me 3 hours to make that little 10 minute trip. You had already gone by the time I got there. Oh well, maybe Roads & Drainage will get the problem resolved soon and I can get back to my comfortable "surface". Meanwhile I'll just hang out in this... whatever this is that I'm in.

John

Were the signs still yellow and orange, which I believe is one of the few constants available to use throughout tine and distance/dimension.

RichH

John,

We seem to share the conviction that time and space can be infinite in all dimensions. From this I draw the conclusion that we are insignificant. I decline to attempt the persuasion toward my opinion of any persons believing themselves to be the center of the universe.

Cheers;)

Well said Ace!

Many of us just don't appreciate being insignificant. Personally, I'm happy being just who I am.

Take care,

John

By the way, John, a lifetime IS forever, if you live it right.

RichH

Rich,

Ace said "A lifetime is not a long time", not me.

John

Mea culpa. Sorry about that. i'll take care of it on the return trip.

RichH

"The problem with any discussion of shape in the context the Universe arises when one considers that the Universe has no exterior. There is no Outside, no Something Beyond, No Anything Beyond the Universe from which a hypothetical surface might partition the interior. And since there is no exterior, the whole concept of an interior is meaningless as well."

-----

I do believe this is the first time I've been seriously cited on this forum! (sans credit, but what the hell)

-e

I still maintain the Universe is shaped like Christie Brinkley. Btw, whatever happened to the ellipsoidal-universe business we discussed last fall? Have the gods reinterpreted the CMB? (yet again?)

We each have our own tools to imagine the added dimensions a universe has that we are not privy to. Some are better than others.

RichH

Before taking a guess I will first recap the little I know.

We live on the 3^rd rock from the sun. We call it earth and it is of the class planet. It is similar but different from other planets. We have a moon which is also similar but different from other moons. And also very similar to earth.

The whole merry lot rotates about a star we call sun.

The star is similar but different to other stars. Some of the other stars may have planets and moons similar to our solar system..

A lot of stars including our sun are circling something. We cannot see it because the view is obscured. It huge blob or a black hole or whatever.

The rotating thing we call a galaxy. The galaxy must be similar or different to other galaxies visible in the sky. Therefore most probably of the class spiral galaxy.

The galaxies seems to be placed randomly but if the same pattern of objects in orbit around a centre is assumed the universe may also be galaxies circling a point or larger object.. It is also evident that for two galaxies to collide that the cloud of galaxies may actually circling the centre in the form of a ball. Alternatively the offending galaxy may actually be a comexy.

My guess for the shape of the universe is therefore a spiral disc (or sphere).

Can there be more universes? Most probably. The shape of the Maxiverse may be a lot of universes circling a bigger object in a disc or round system. Etc. etc. etc.

The next step is to visualize the universe in the 4^th or higher dimension.

The possibilities are endless. The concept of matter being here, there. not here or not all there are to much for me. My guess to the shape of the Maxiverse is "kiss me if I know"

It is in any case time for my beauty sleep. (it didn't help for the past 60+ years but there is no harm in trying)

And as you look the other way, you see how ignorant we are of our position on the ladder of things. That even though we each feel that the universe revolves around ourselves, we can look through the other end of your glass, and see that the concept of motion circulating around a mass goes downward, too.

The lowly electron revolves around the mass of a proton inside of the hydrogen atom, and all of it's kin. We've done our best to disect that proton into its pieces, and perhaps those pieces orbit some sub-quark. We've looked for God in whatever "dimension" was just outside our understanding, in the volcanoes, mountains, the heavens, and now the search for a god particle just beyond our reach in that direction. I wonder how many giga-magnitudes we will eventually extend ourselves to, in both directions.

And you forgot the galactic clusters, of which ours appears to be perhaps larger than normal.

Kind of makes one understand insignificance.

RichH

Hendrick,

Just maybe we are the maxiverse to some other much smaller groups universe! Think about it. If what we we call our universe existed somewhere amongst the quarks, bosons, axions, etc. we could not conceive, except in our imaginations, that physicists, and others, were doing their best to look closer and closer at us. From their perspective, our universe lies at the very heart of matter but, from our perspective, they are beyond the observable universe. Thus the maxiverse always has the advantage.

Anyway, I enjoyed your dissertation and your perspective. Have you tried "Oil of Olay" for your beauty?

John

I'd rather try it on Christie Brinkley. With what that would do to my imagination, I could reach right out and shake the hand of those "outside observers"

The on-line maps and pics all have that zoom bar. A thousand orders of magnitude each way, and we might still be stumbling over what we have always been sure is the limit.

RichH

View the Milky Way at 10 million light years from the Earth. Then move through space towards the Earth in successive orders of magnitude until you reach a tall oak tree just outside the buildings of the National High Magnetic Field Laboratory in Tallahassee, Florida. After that, begin to move from the actual size of a leaf into a microscopic world that reveals leaf cell walls, the cell nucleus, chromatin, DNA and finally, into the subatomic universe of electrons and protons.

http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/

Excellent Ace!

You found us down here. We were waiting for you.

That site is really cool!

John

only 39 orders of magnitude. We know of at least 3 more up. That 3rd one takes us to 13.8 billion years ago, and appear to be retreating at about 0.85 c. If the new scopes can get another billion, (if it exists) maybe we'll see the muons and quarks before condensation. Maybe we'll find God ( the particle) out there in the heavens before we find God (the particle), in the next generation or 2 of particle accelerators.

What kind of EMR would we look for to find it?

Rich

Hi Rich,

You make my mind hurt! However,

You wrote: "Maybe we'll find God ( the particle) out there in the heavens before we find God (the particle), in the next generation or 2 of particle accelerators."

Nope! Ain't gonna happen. If the God particle is "out there" it absolutely has to be in a "maxiverse", and thus totally unobservable by us n's. The "maxiverse" (have we actually coined a new word?) by definition must lie beyond the CMB. Even if we get another billion as you say, or even more, somewhere along the line we'll approach a "divide by zero" point as we get REAL close to the big bang (just can't seem to go past the beginning of time). The beginning for us, of course.

However, as I said earlier, an observer in a "maxiverse" always has the advantage so let's look the other way where we do have it. Just maybe when the Large Hadron Collider starts running at full strength (2008?), "it may produce the elusive Higgs boson particle — often dubbed the God Particle —" (from Wiki).

Who knows? Time, if it exists, will tell the story. I still say "any sufficiently advanced technology is indistinguishable from magic".

Regards,

John

Ah, the elusive Higgs, with a mass worth its weight in gold. Or something close. Those distant galaxies, at 13. is it 8? billion light years away. Formed when the Universe (of ours) was less than a half billion years old.

That would mean that if we can see back a billion or so more, what would there be to see?

Along the way, early in the condensation into matter. one of the first bits of matter to form, after the universe started cooling by shedding radiation still scattered around the universe, would have been the Higgs. May not have lasted long, but if that were all that existed in the Uiverse, what would it have looked like? What form of radiation would it have emitted on its way to quarks?

That's where we maybe we would see god out there, about 42 orders of magnitude from the femto world we're looking for it in.

I'm not sure if it's the farther we get the closer we are, or the closer we get the farther we are.

RichH

Rich,

You wrote:

I'm not sure if it's the farther we get the closer we are, or the closer we get the farther we are.

That pretty well sums it all up.

John

Hi NoSciFi, you wrote: "Those distant galaxies, at 13. is it 8? billion light years away. Formed when the Universe (of ours) was less than a half billion years old."

Your 13.? billion years away is quite close. In pure light travel time it took the the light from the most distant galaxies observed so far (redshift just over 6) about 13 billion years to reach us. The CMB's light took about 13.7 billion years, roughly the age of the universe.

However, this is misleading, because those galaxies are over 40 billion years from us today! While the light was on its way to us, they just kept on moving farther.

-J

Hi Jorrie,

This is fascinating. I am however, even more confused now.

You said:

"The CMB's light took about 13.7 billion years, roughly the age of the universe.

However, this is misleading, because those galaxies are over 40 billion years from us today! While the light was on its way to us, they just kept on moving farther."

If the universe is about 13.7 years old, then how can anything possibly be 40 billion years from us? Even if, as you say, the galaxies are moving away all the while light is traveling toward us, that makes it seem like those galaxies are, in fact, older than the big bang. Can this be?

Please explain.

Cheers,

John

Hi John, you wrote: "If the universe is about 13.7 years old, then how can anything possibly be 40 billion years from us?"

The secret lurks in the expanding space between us and the galaxies. During the first 2 billion years or so after the big-bang, space expanded so fast that light coming from those most distant galaxies made no headway towards us - the photons were dragged away faster by the expansion of space than what they could move (at c through their local space).

From some 2 billion years onwards, the photons started to make headway slowly, meaning he photons got closer to us, still moving at c, but part of their movement being cancelled by the fact that the very space that they were moving through moved away from us.

The illusion that you stated: "... that makes it seem like those galaxies are, in fact, older than the big bang. Can this be?" is solved by the fact that the range to the most distant objects once increased at a rate exceeding c, while they were actually rather stationary in this expanding space.

I hope this makes some sense!

-J

Hi, Jorrie

I think I understand that quite readily. What I was trying to say, is that if we can see far enough to look back another quarter billion years or more, to perhaps the first 100,000 years of our universe, we would reach the point where the only "thing" existing was the freshly condensing matter, which would be the point in time, when the Higgs Bosun was the preponderant matter, and what would we see? What would be the spectral lines of the soup clumps starting to form atoms of mostly H¹ and a little H² and even lesser amounts of H^₃ ? What will we be finding? Will we see to a point that, prior to condensation, there was only energy?

Those are the point in time that we should see perhaps god in the heavens, possibly before we find Higgs Bosun at CERN.

Just a random thought, bringing the two ends of the spectrum back to the same god particle.

Or will we just not see anything else in the space the universe was about to take over?

RichH

"Time, if it exists, will tell the story." (emphasis mine)

-----

???

Hi europium,

You wrote (quoting me):

' "Time, if it exists, will tell the story." (emphasis mine) '

Take a look at this month's Discover magazine (June 2007), page 78.

John

The question is similar to "How will an electron in a drop of oil on Christie describe the shape he happens to be on" With my luck I would land on some or other desserted location.

Fortunately (for you), Christie's body - from an electrical standpoint - is a bag of lossy electrolyte having a fairly conductive surface. Uncomplimentary visual imagery aside, this means that, as an electron, you're rather mobile. Consequently, you can not only move about quite freely, but you can do so with blazing speed. So, if you don't happen to like (or fully appreciate) your location on Christie's body, simply wait a few microseconds. You will.

Let's assume that anything that has a shape has to have a boundary between inside and outside.

Any observer inside the Universe would not be able to find the boundary between inside and outside, as to do so (s)he would have to travel faster than the boundary is receding. Upon reaching the boundary and still travelling, the Universe changes shape by definition to contain the observer at the new location. So the shape is undefined, as by being there to assess it, the observer changes it [PWSlack's Uncertainty Principle].

An observer outside the Universe would not be a part of it and, as the boundary wouldn't have reached this observer, would simply not be aware of it.

So the Universe has no shape, by definition. So there. With knobs on.

There's some logic here that is uncomfortable. It made the brain hurt a lot and that dark, quiet room looks very inviting at the moment....

Hi PWSlack, you wrote: "So the Universe has no shape, by definition. So there. With knobs on."

Very well stated!

This "question" that I asked in the OP has no sensible answer, so knobs or no knobs, this is as good as it gets!

-J