# The Patterns of Spacetime

Lately, my head has been up in space–well, not literally, but I’ve been thinking of space–spacetime, that is.

I’m thinking of all the ways in which it can bend, warp, curve, distort, and even fission (sometimes there can even be “rips” in the spacetime continuum–or wormholes! Or blackholes! [size=85]Or asshole… well no.[/size]). In essence, space isn’t just “flat”–it’s more dynamic than that. (see Einstein and company for proof.)

So this got me thinking: what kinds of patterns are possible in the fabric of spacetime? I mean, if it’s not just flat, what other patterns could it take?

To be sure, the only alternative patterns to a flat spacetime that Einstein offered for the universe were: a 4D sphere or a saddle-shaped plane (or surface–I’m not sure, but I think a “plane” is technically defined as flat).

But I think we can be more creative than that.

I forget who proposed it, but I remember once reading Brian Green’s The Elegant Universe and he referenced a geometrical model of the universe made famous by a thinker who’s name escapes me now. It features an actual finite limit to a 3 dimensional space (such that the “edge of space,” as it were, is a finite distance away), but that as one approaches this outer limit, space becomes more “dense” or “thick”–that is, if you were to map a geodesic of space from you (at a specific point in time as you travelled towards the edge of space) to the actual edge of space, the distance between the tick-marks on that geodesic (as if it were a ruler) would have to be drawn more closely together the closer you got to the edge of space. The end result would be that, though you always approach ever closer to the edge of space, your speed slows down… and you never really reach the end of space–it’s an “infinite” distance away for all practical purposes.

Now, that’s just one pattern.

There are others: wormholes present a pattern whereby the universe might conceivably feature parallel planes linked together by a wormhole (looking like an apple core). Of course, these “planes” would really be 3 dimensional, and the wormholes would project out into a fourth dimension of which we have no way of experiencing (hey, this is all Einstein, not me). Then there are blackholes, points in space towards which spacetime converges–but kind of in the opposite way from the model I relayed above (the one whereby space becomes more “dense” the further out you go). In this pattern, you get space getting “thinner” the closer you get to the center of the blackhole, and thus things travelling towards it accelerate.

But the thoughts that I’ve been having lately have been more along the lines of repeating patterns.

To be fair, there are models of spacetime geometry that feature complex detail–as opposed to smooth and simple patterns only interesting when seen at a cosmological level–and I’m reminded of what they call “quantum foam”. Quantum foam, if I understand it correctly, is a model of spacetime in which, way down at the subatomic level (at the “quantum” level, as they say), spacetime is really bumpy–it isn’t smooth as we experience it here at the macro-level–instead it’s more like “foam”–twisting and winding geodesics, all intersecting, merging, bending, blending, splitting, splicing, separating, connecting, rising, falling, growing, shrinking, etc., etc., etc.–basically like a fur ball a cat coughed up (except the strands of fur are infinitely long).

Interesting pattern.

But still, there is no repetition. What if spacetime were more like a checker board–you can even imagine it as a 3D checker board–with cubes instead of squares–like Q-bert!

Each cube-like section of spacetime would be characterized by either of two features, and those two features can be anything you like. For example, say all the odd squares had “thin” space, and all the even squares had “thick” space. That’s it–there you go–the cosmic checkerboard!

But, you say, wouldn’t we notice differences as we pass in and out of these two kinds of spacetime cubes? Wouldn’t things behave differently somehow as they passed in and out of these cubes? Well, that depends–how subtle is the difference? Remember, I only said the odd cubes were “thin” and the even cubes “thick”–I never said drastically thin or thick. The degree to which they differ may be so unnoticeable that it’s several magnitudes smaller than the Plank scale. Or how about this: the difference may be great, it may be staggering, but the cubes are absolutely, extraordinarily, utterly tiny–smaller than the Plank scale–that not even the electrons and quarks that make up our bodies undergo a disturbance as they pass through them.

How about a pattern like a Persian rug? How about a complex computer circuit? How about a fractal?

[size=150]Solution to the Problem of the “Eternal Faller”[/size]

I don’t know why, but I’m having plenty of thoughts about spacetime. Here’s a few on blackholes:

The “eternal faller,” as I call him, is the hypothetical character in the well-known physics thought experiment that features a person falling into a blackhole and we, as observers watching him a safe distance away, never actually seeing him touch the event horizon.

Just for those of you who don’t know, the “event horizon” of a blackhole is the surface of the blackhole itself–the surface of that black sphere that is depicted in most diagrams of blackholes. They say that as one falls towards a blackhole (which is nothing more than an incredibly massive sun that collapsed on itself under the weight of its own gravity–enough gravity to pull anything in, even light), time slows down for him relative to an observer a safe distance away (say 6 billion light-years away). It slows down so much, in fact, that it ends up, from the point of view of the observer, taking an eternity for the faller to actually hit the event horizon. Thus, the eternal faller.

From the faller’s point of view, however, the fall is definitely ternal (like “finite”). The closer he gets, the faster he travels, and he most definitely hits the event horizon within his own life time (not that he would still be alive at that point but…).

Now, I’ve always thought of this as a problem–indeed, a paradox: how can an event which the laws of physics demand happen given the right pre-conditions (i.e. a man falls into a blackhole) also demand that this event never actually happen for observers a safe distance away?

Last night, I came up with a solution: we’re all going to end in a Big Crunch.

In what other way can one logically reconcile an event that is to happen and never to happen in the same universe? The solution is that the event will happen–for everyone–it’s just that for the faller, it will happen very soon, but for the rest of us, we have another several billion years to go–for when that happens, we’d be in the same reference frame as the faller, and therefore he wouldn’t have to take an eternity, relative to us, to hit the event horizon.

Now there is the Universal Heat Death that most physicists are predicting (I’ll call it the UHD for short)–which is a scenario in which all matter and energy are fated to float away into the distant cold darkness of space forever–as we expand ever farther apart (some even say we are accelerating further apart). Yet, I don’t think it’s quite proven that a Big Crunch is absolutely impossible (someone will have to correct me on that if I’m wrong, but I don’t think I am). I think there are certain plausible scenarios for the fate of the universe in which we all end in a Big Crunch–in all matter and energy pulling itself back together under the influence of its own gravity, eventually overcoming the forces of expansion.

If this indeed happens, then we are all fated to fall into a blackhole sooner or later (probably later). A Big Crunch would result in the ultimate blackhole–the biggest, most humungous, most monolith concentration of matter and energy–exerting the most powerful gravitational field physically possible. The original blackhole that the faller was falling into would, of course, be a part of this ultimate blackhole, and so his hitting the event horizon would still occur.

Einstein’s deepest insight, as far as I’m concerned, is the relativity of simultaneity–the realization that whether or not two events happen at the same time is relative–that is, two events may happen simultaneously for you, but not necessarily to another observer–and there is no fact of the matter whether they really did happen simultaneously or not. Thus, even though it doesn’t seem like it from our current understanding (given the eternal ongoing fate of the universe according to the UHD theory), we actually will be around to observer the faller hit the event horizon, it’s just that we’ll be hitting it with him.

[size=150]The Edge of Space[/size]

Here’s yet another thought:

This one I’ve actually had for a long time–I wonder if the event horizon of a blackhole is literally the edge of space–as in, there is literally nothing beyond the event horizon.

The relativity of spacetime has me wondering if the size of geometric points can be relative. Could you have a gigantic, humungous geometric point spanning several million miles across? How could that be? Isn’t a geometric point defined as having 0 extension in any dimension? Yes, but if you think of a blackhole–the region inside the event horizon–as simply not there, with not even spacetime being there (the edge of space), then there really isn’t any extension, no amount of space, from one end of the blackhole to the other. This could be considered keeping with the definition of a “geometric point.” And geometric points are, after all, a construct of spacetime, and if spacetime is malleable, as suggested by Einstein’s theories, then why not in terms of size as well? Size, after all, is just a certain amount of spatial volume, which in turn is made up of a certain amount of each of the 3 dimensions of space we know about. If the 3 dimensions of space are malleable, then so too should be volume and size. A block of space may be only a few cubic inches in volume relative to one observer, but miles across relative to another. Granting this, why not for a geometric point? All a geometric point is, after all, is the smallest conceivable volume of space–so if the size of spatial volumes are relative, so is the “size” of a geometric point. There would be nothing “inside” a blown up geometric point as you still couldn’t have smaller volumes of space within its limits, but why should the space just outside those limits be considered adjacent–that is, as “touching”–for it would be a rip, a hole, in the spacetime continuum.

But the event horizon, you say, can’t be the edge of space, not if the original matter that became the blackhole was sucked up by it in the process. Where did that original matter go? Well perhaps what happens to matter once it gets sucked out of existence by the force of its own gravity is that it’s opposite–nothingness–takes its place: somethingness gets traded in for nothingness. You will notice they behave in exactly the opposite way. Whereas somethingness (matter) gets pulled in by its own gravitational pressure, nothingness grows outward, becoming bigger, in response to gravity. A great shrinking ball of something gets exchanged for a great expanding ball of nothing.

This, of course, implies that spacetime itself is the “happy medium”–the neutral middle ground between somethingness and nothingness, between actual stuff and real emptiness. That spacetime can be molded according to Einstein’s theories have physicists now-a-days conceding that it really isn’t pure nothingness, even though it isn’t as much “there” as matter.

And we are still being consistent with the principle that the “edge of space” shouldn’t actually be reachable in a finite amount of time. Even though someone falling into a blackhole streams ever faster towards the edge of space, his time does slow down relative to observers a safe distance away. So we never actually get to see him hit the event horizon, so it is like he is on an eternal voyage to the edge of space. As for the experience of the falling victim himself, well, it’s hard to take seriously the thought that he actually experiences hitting the event horizon, for he is surely to be torn into a long strand of bloody spaghetti before he can “experience” anything beyond that point. So reaching the edge of space remains inexperienceable.

Two questions;

1) Is that an exclusive brand you are smoking?

and

2) Are you sure that you really want to argue that point with Me?

Did you want some?

I know how you feel about Einstein.

I doubt that. I believe him to have been an honest man. And his famous paper concerning the idea of the relativity of simultaneity was a good thought for the college student that he was at the time. His theory just happened to have been provably wrong, even back in those days. And from then til now it has become nothing but religious, distractive propaganda, although not nearly as fanciful as quantum phantasy physics. So of course, everyone is supposed to believe in relativity. It is PC and mainstream.

Of course with you, the truth is whatever you want to believe.

The problem is that this statement;

…happens to be incorrect. And even if it was correct, it would not make the theory correct.

Einstein in college proposed that no one could tell who was right about a simultaneous event, that all observers have equal standing. Thus we can ignore objective reality, arbitrarily claim subjective truth, and know that no one can claim foul (known as “plausible deniability” and “scapegoating”). There happens to be some religious ties to that notion. But for physics, it happens to be a false notion.

The theory was typically naive. It proposed that if one person saw an event occur simultaneous to another and another person saw the same events, but saw them as not simultaneous, there could be no means to know who was right. But what if there was a way? What if they were not so naive as to merely presume from their immediate impressions? What if they were thinking people?

If a detective wants to know the truth after hearing contrary witness accounts, he seeks out other evidence. And although there are many times when other confirming evidence can’t be found to support which witness was accurate, quite often there is such evidence readily available. Thus a theory that says that reality itself is entirely subjective, is necessarily going to be found to be false. And so it is with Relativity.

PC and mainstream? Well, in that case, of course we ought to disbelieve it. We’re also taught by the mainstream that the Earth revolves around the sun, that species evolve, that matter is made of atoms, and other “PC” stuff… I guess rational thinkers should therefore recognize how false these claims are.

Oh, how life would be grand if that were true.

This has got to be the shallowest reading of Einstein’s idea I have ever heard.

This is not about how things look to a particular observer, it has to do with the nature of light, specifically its absolute speed irrespective of the observer.

If two supernovae explode at the same time, and one is a light year away from Earth and the other is two light years away, it’s true that we will see the closer one explode one year before the other one, but this is not the basis on which Einstein claimed the simultaneity of the two events is relative. It has to do with the fact that light travels at c regardless of how fast you as an observer are traveling. If you and a friend stand right next to each other and switch on a flash light, and your friend immediately begins chasing the light beam at, let’s say, c/2 the speed of light, both you and your friend will observe the light beam as traveling ahead at c relative to yourselves.

Take those principles and let the following video explain the rest:

So you’re saying that you don’t actually even know the theory that you are admiring?
… not surprised.

No, you’re right. It isn’t. So why did you bring it up?

…Presuming that one could “observe a light beam”. And you are now speaking of Special Relativity (not simultaneity).

Emmm… no.

You want to claim the theory to be great and good, you need to be the one explaining it, else you are just proselytizing, not philosophizing. I am not going to argue with a video or a book.

Huh? I explain the absolute speed of light as what’s at the heart of Einstein’s theory, and you say I don’t know the theory I’m talking about?

To correct your misconception. You’re the one who said that Einstein’s theory is all about the subjectivity of what each observer experiences, and how that implies that there is no objective fact of the matter–when in fact this is not what Einstein’s theory is about. It’s all about light. Understand that, and everything else follows.

Silly James, the relativity of simultaneity is part of SR. You need to understand this crap if you’re going to understand the relativity of simultaneity.

Yes, that’s exactly what I want–to boast about the greatness of the theory–not it’s truth, not that I can back up my own points with it, just how frickin’ awesome it is.

I’m sorry to hear you don’t like reading books or watching educational videos, but I don’t “need” to explain anything if there’s a video or other resource I can point to to do the explaining for me. That’s the beauty of references. How this becomes “proselytizing,” I have no idea.

Actually, you are the one who said there is no [objective] fact of the matter. And SR is entirely about what the observer reports/observes (“subjectivity”) and thus deduces to be fact. Perhaps read the paper?

Actually, although the simultaneity issue was proposed along with SR, it is a separate issue. And it is proven to be incorrect by a different means. The consistency of the observed speed of light is not terribly relevant (until proving it to be incorrect).

Gib, this is one of those “almost before you were born” things. You have no idea what you have blindly jumped into.

It was an easy guess. The only thing you know of it is hearsay. Perhaps you should study those videos yourself before you take on challenges to them.

Yes I did, and I stand by that. I wasn’t saying that you said that, I was saying that you think that this part of SR is based on the subjective perceptions of observers. Read it again and see if you can get that interpretation:

“You’re the one who said that Einstein’s theory is all about the subjectivity of what each observer experiences, and how that implies that there is no objective fact of the matter…”

What can I say, James? I can’t really argue with someone who just spews out misconceptions and plane lies. It’s like arguing with someone who thinks evolution theory is all about how we are descendent from aliens. ← What do you say to that?

You’re gonna have to explain to me where you get your “facts” from.

What the hell are you talking about? If this is some huge mistake on my part, why don’t you just let me have it already. What embarrassing mistake did I fumble over that’s just waiting to make a fool of me?

I see sarcasm is lost on you.

I take it that you are not going to actually read his paper.

So tell me, Gib, do you know anything about physics at all? Like the simple stuff, “F=ma” and what it means?

Again? I already did a long time ago, along with a whole bunch of other sources concurring with what I’m saying and not you.

I know a lot about empirical science, but I realize that to you, as a rationalist, that’s all wrong.

Yeah well. A lot of people read the Quran too. Or at least they interpreted it to mean as they were told.

Well good (not that I believe you, but…). And btw, rationalists support actual Science more than anyone.

So you know, for instance, that if such a formula as “F=MA” applies to one train, it applies to all trains, assuming all else to be equal. Right?

And if one applies force “F1” to a previously stationary train of mass “M1”, it will accelerate across a distance determined by “A1”. Right?

And that if one were to do also apply force “F2” to a second previously stationary train of mass “M2”, it will accelerate across a distance determined by “A2”. Right?

And if it happened that F1=F2 and M1=M2, then it is necessarily true that A1=A2 and both trains would travel the exact same distance (all else being equal). Right?

Thus if the two trains were 20 meters apart on the same track when they were stationary, throughout their entire acceleration, they should remain exactly 20 meters apart. Right?

Thus the distance between them couldn’t change from such acceleration.

What does SP say about that?

You mean, SR? Not much, only that the trains remain stationary relative to each other.

Yes sorry, “SR”.

So an observer watching all of this won’t see any length contraction between the trains?

He’ll probably see a minute amount.

What is that supposed to mean? Does the theory say there will be length contraction or not?

Just to give it some numbers, let’s say the trains get up to 0.5c. What length contraction would be observed, if any?

The theory does say there will be length contraction. The trains will be half their resting length.

Well, I am not talking about the length of the trains. I am talking about the distance between the trains, between their centers.