Infinite Universe = Impossible

[shynung]

Exactly, and just because that person says, "There is nothing that exists outside these walls" does not make it fact.

It matters not whether he is wrong. What matters is that he'll never know for sure whether his hypotheses about the 'outside world' is correct, since he has no way of confirming it.

It's easy for us to falsify his assumptions due to our experiences concerning the 'outside world', but what about him?

[rtxoff]

distrust the actual

expect the impossible

embrace the unknown

Only then flat earth becomes a ball of dust.

Only then earth will not be the centre of the universe.

Only then planes begin to fly.

And only then we might gain the knowledge to finally conquer the stars.

[EdFred]

It matters not whether he is wrong. What matters is that he'll never know for sure whether his hypotheses about the 'outside world' is correct, since he has no way of confirming it.

It's easy for us to falsify his assumptions due to our experiences concerning the 'outside world', but what about him?

It is his truth. But truth != fact.

- - - Updated - - -

Sure. But this is the actual theory, instead of the foolishness people throw around about space having once been a single point

That depends on your POV. If space was compressed as they said in the video and it could be observed from an outside perspective, (5th dimension or higher) it may actually appear as a single point. Just like being on the surface of an uninflated/compressed balloon. To every habitat of balloon land it's always the same grid spacing to another coordinate on the surface. But from our point of view, not living on the balloon's surface we see it grow from a single point (ok, we can't compress them that small, but you get my point) into a large sphere.

I am not saying that is it fact that you can observe our universe from the outside, but I think it not only possible, but probable. It just takes a completely different set of physics to do so, and as residents of this universe we probably can't leave it. But that doesn't mean that everything ends at the 'edge' of our universe. For us, our truth is the universe contains everything, but as I said above, truth != fact.

Edited January 20, 2015 by EdFred

[Technical Ben]

Simple example. Surface of a sphere is a 2d manifold that can be embedded in 3d space. Locally, it behaves like a 2d surface, but if you want to picture it as a complete shape in flat space, you need at least one extra dimension.

GR space-time is a 4d manifold. Some special cases can be embedded. You might have seen a picture of a funnel that represents curvature of space around a black hole. Of course, these representations are somewhat limited, since it is hard for us to picture more than 3 dimensions at the same time. But they exist, nonetheless.

Well, an interesting result in GR is that a general solution to Einstein's Field Equations cannot be embedded. In other words, for any finite number of dimensions, there exists a mass arrangement that results in a space-time shape that cannot fit into that number of dimensions. Therefore, our space-time is not embedded. If it was, there would be significant and measureable differences in how gravity works.

Sort of can. As mentioned above, ebedding is not an option. Some flavors of String Theory work with a bulk, but they also make predictions that do not pan out based on it. So bulk seems unlikely. Locally, topology is fixed, so there cannot be a connection to an outside of any sort. That leaves edges, but we observe a very uniform universe. So unless we are dead center of a huge, much larger than observable, but still finite universe, it does not look good for edges either. If you have some other definition of outside, please, bring it forward. As it is, I can claim lack of outside as a scientific fact. If you need a greater absolute, then yes, I cannot help you, being a mere mortal and all. But you'd have better luck looking for unicorns than an "outside" of our universe.

That is entirely new to me. I've not heard anyone claim that before. In fact I was under the impression such "embedded systems" are exactly what some are looking for to use in calculations.

(It matters not to me either way which is true or false, as long as it matches observation. But as said, I've not heard of such observations being made before.)

As a final example, how can "Well, an interesting result in GR is that a general solution to Einstein's Field Equations cannot be embedded" be true, if we can write down those equations. Is that not also a definition of "embedding" them.. just in this case on paper?

"Point me to some line that you have to cross to be outside."

This is where you loose me. A 2d universe cannot by definition point to the 3d universe as "a direction". It can though presume/theorise on one, though never truly "detect" it (it can comprehend, but all interpretation would have to be assumed true, it could not "prove" it one way or the other AFAIK).

Likewise, what stops there being additional dimensions we have not <i>yet</i> detected? While the definition of "universe" means everything, we constantly learn of new things to add to it!

Edited January 20, 2015 by Technical Ben

[Sirrobert]

That depends on your POV. If space was compressed as they said in the video and it could be observed from an outside perspective, (5th dimension or higher) it may actually appear as a single point. Just like being on the surface of an uninflated/compressed balloon. To every habitat of balloon land it's always the same grid spacing to another coordinate on the surface. But from our point of view, not living on the balloon's surface we see it grow from a single point (ok, we can't compress them that small, but you get my point) into a large sphere.

I am not saying that is it fact that you can observe our universe from the outside, but I think it not only possible, but probable. It just takes a completely different set of physics to do so, and as residents of this universe we probably can't leave it. But that doesn't mean that everything ends at the 'edge' of our universe. For us, our truth is the universe contains everything, but as I said above, truth != fact.

That is true, but let's not confuse the discussion about clarifying a theory further by adding dimensions.

Though to respond, I have no doubt that, for beings that can observe other dimensions that we can, it might look completely different. If we asume that time (4th dimension) is finite, than a being observing a balloon made of those 4 dimensions should indeed see a finite thing.

A theory I once saw on youtube science stuf (1 hour long video, very interesting) actually suggest that that is exactly how the Universe works. The Universe is basicly a balloon made up of the 4 dimensions that we have. And with string(?) theory saying there are 12(?) dimensions, there are also other Universes made up of a different combination of dimensions.

It also suggested that, instead of stretching out infinitly, it indeed stretched like a balloon. So if you went constantly in 1 direction, you'd eventually reach your starting point again. Though the distance you have to travel would keep growing, because the balloon is still stretching (blowing up)

[ZetaX]

That is entirely new to me. I've not heard anyone claim that before. In fact I was under the impression such "embedded systems" are exactly what some are looking for to use in calculations.

(It matters not to me either way which is true or false, as long as it matches observation. But as said, I've not heard of such observations being made before.)

That's not an observation but a theorem: a conclusion that follows from the assumptions (GR) by purely logical means.

As a final example, how can "Well, an interesting result in GR is that a general solution to Einstein's Field Equations cannot be embedded" be true, if we can write down those equations. Is that not also a definition of "embedding" them.. just in this case on paper?

I am not sure if you are serious about this part, so just a short answer: that's not the definition of "embedding" that is used in the statement.

"Point me to some line that you have to cross to be outside."

This is where you loose me. A 2d universe cannot by definition point to the 3d universe as "a direction". It can though presume/theorise on one, though never truly "detect" it (it can comprehend, but all interpretation would have to be assumed true, it could not "prove" it one way or the other AFAIK).

If that other dimension has neither an observable effect on the universe nor gives any advantage when doing computations and such, then there is no reason to even talk about it. If using it actually gives an advantage or is the best way to explain some phenomena, then it will be used; GR is an archetypical example where only considering space fails while considering space-time as a whole gives a nice theory.

Likewise, what stops there being additional dimensions we have not <i>yet</i> detected? While the definition of "universe" means everything, we constantly learn of new things to add to it!

Nothing, but unless you have at least some observation or other reason to assume so, you should not assume it. That does not mean you should not look for one, though.

[K^2]

I was under the impression such "embedded systems" are exactly what some are looking for to use in calculations.

They do. For some special cases. Because it makes computations a hell of a lot easier. When you want to consider gravity just in the neighborhood of a black hole, or when you are working out a design of a theoretical warp drive, you can use embedded manifolds to simplify a lot of the math both computationally and conceptually. It's a great tool. But that's kind of like reducing orbital mechanics problem to 2D. It works in a simple case. It does not solve general problems.

This is where you loose me. A 2d universe cannot by definition point to the 3d universe as "a direction". It can though presume/theorise on one, though never truly "detect" it (it can comprehend, but all interpretation would have to be assumed true, it could not "prove" it one way or the other AFAIK).

That's why I've mentioned superstrings and bulk. We can't detect these things directly, but we can ask what would be different if these dimensions existed in some way that's topologically relevant. We get some variation of String Theory. Well, String Theory makes predictions. We've been testing these predictions for over two decades on larger and larger accelerators. By now, String Theory has a standing of, "An interesting idea which shed some light on particle physics, but has no direct practical applications." We simply don't live in a universe where String Theory applies. There are still some people who are trying to work out some variation that might work, but essentially, if you need proof that there are no higher dimensions, accelerator facilities at RHIC and LHC have provided it.

[EdFred]

That is true, but let's not confuse the discussion about clarifying a theory further by adding dimensions.

Though to respond, I have no doubt that, for beings that can observe other dimensions that we can, it might look completely different. If we asume that time (4th dimension) is finite, than a being observing a balloon made of those 4 dimensions should indeed see a finite thing.

A theory I once saw on youtube science stuf (1 hour long video, very interesting) actually suggest that that is exactly how the Universe works. The Universe is basicly a balloon made up of the 4 dimensions that we have. And with string(?) theory saying there are 12(?) dimensions, there are also other Universes made up of a different combination of dimensions.

It also suggested that, instead of stretching out infinitly, it indeed stretched like a balloon. So if you went constantly in 1 direction, you'd eventually reach your starting point again. Though the distance you have to travel would keep growing, because the balloon is still stretching (blowing up)

I think what it comes down to and we probably agree. For our 4 dimensions, x, y, z, t our universe all there is. However, I like to think (though I have no math to back me up) that all the dark energy/matter in our universe is 'bleedover' from dimensions 5 and up. For whatever reason we are detecting the mass from the other dimensions, that's bleeding through to our 4 dimensions. Which is why I think there is something beyond our universe. Not that we are a 4D universe inside a 4D superverse where if we rip space-time we see a bunch of other 4D balloons, but that we would see (though we couldn't see it because we are 4D creatures) a 5-8D mesh which may be inside a 9-12D mesh. Or Brane, or whatever you want to call it.

[Bill Phil]

You know, Dark Matter could be 5D intersections. Intersections of dimensions are always one dimension below it.

Lines intersect at points.

Planes intersect at lines.

3D plane intersects at 2d planes.

4d intersects at 3d.

and so on and so on.

So, maybe Dark Matter/Energy is the intersections?

[ZetaX]

You know, Dark Matter could be 5D intersections. Intersections of dimensions are always one dimension below it.

Lines intersect at points.

Planes intersect at lines.

3D plane intersects at 2d planes.

4d intersects at 3d.

That's not true. Two lines in 3-space normally don't intersact at all. Similiarily, two planes in 4-space intersect at a point unless they are in a special arrangement.

A correct version is: two n-dimensional subspaces of (n+1)-space which are in generic position intersect in a (n-1)-dimensional space.

More generally, codimension (the difference between the dimension of a subspace and the full space considered; for example a plane in 3-space has codimension 1, while a line would have codimension 2) is additive when intersecting spaces in generic position.

[Bill Phil]

That's not true. Two lines in 3-space normally don't intersact at all. Similiarily, two planes in 4-space intersect at a point unless they are in a special arrangement.

A correct version is: two n-dimensional subspaces of (n+1)-space which are in generic position intersect in a (n-1)-dimensional space.

More generally, codimension (the difference between the dimension of a subspace and the full space considered; for example a plane in 3-space has codimension 1, while a line would have codimension 2) is additive when intersecting spaces in generic position.

Okay, then. Enlighten me.

I said that lines intersect at points. You said most lines don't intersect at all. That's not a counter-argument.

And what do you mean "subspace"?

.

[K^2]

ZetaX, he got you there. Two lines don't have to intersect in 3D, in fact, any two random ones are guaranteed not to, but if you chose two lines that do intersect, they do still intersect at a point in any number of dimensions.

You know, Dark Matter could be 5D intersections.

For the third time in this thread, that's what they've been trying to do with bulk in String Theory. This assumption makes predictions that don't check out. And we don't need to invent explanations for dark energy. We already know what it is. We simply don't know if it has other properties or be able to actually detect it directly.

[Bill Phil]

True. It was really an explanation as to what causes dark matter to be where it is, and not somewhere else. But I don't know that stuff. I'm no particle or theoretical physicist.

[EdFred]

ZetaX, he got you there. Two lines don't have to intersect in 3D, in fact, any two random ones are guaranteed not to, but if you chose two lines that do intersect, they do still intersect at a point in any number of dimensions.

For the third time in this thread, that's what they've been trying to do with bulk in String Theory. This assumption makes predictions that don't check out. And we don't need to invent explanations for dark energy. We already know what it is. We simply don't know if it has other properties or be able to actually detect it directly.

Since when? Everything I've read seems to still be a hypothesis, not a definitive answer.

[ZetaX]

K^2: I don't think he got me there. The existence of counterexamples is why I said "normally", "unless in a special configuration" and "in generic position" (for most other readers: the latter is the formal term used for this).

Okay, then. Enlighten me.

I said that lines intersect at points. You said most lines don't intersect at all. That's not a counter-argument.

And what do you mean "subspace"?

.

Why is that not a counter-argument¿ I could have given an actual example, but it's quite simple to find one yourself (any random one does, as already mentioned). Anyway, see http://en.wikipedia.org/wiki/Skew_lines .

I also mentioned the 4-space one with planes in case you actually want subspaces (i.e. containing 0) instead. If you want the example for that: coordinates w,x,y,z, planes w=x=0 and y=z=0.

- - - Updated - - -

A little addition to my previous two posts: the formal meaning of "generic" or "random" would probably be a bit too mathy. If you truly want to know, then I (or K^2) should be able to explain, but expect it to contain at least some math and the term "parameter space".

Since when? Everything I've read seems to still be a hypothesis, not a definitive answer.

I think, but wait for his own answer, too, that K^2 and you have a very different understanding on what the answer to "what is dark energy" looks like. To you, it is some kind of explanation where it comes from and why it is there, but to him it probably is a full description of what it does. In the end, everything we can research will likely turn down to "how does it behave" instead of "why does it behave that way". The good old example of gravity strikes again: one could say that mass bends spacetime and thus all the conclusions from general relativity; but in the end, you only moved the goal post to "why does mass bend spacetimee¿". Instead, the pragmatic way is to just find all the formulas and such describing its properties and I think that's what K^2 is talking about here.

Edited January 21, 2015 by ZetaX

[Bill Phil]

It's not a counterexample because you aren't speaking about the same topic. You said that most lines don't intersect. I said that when they do, they intersect at points. I don't see how saying that most do not intersect is a counter example to my statement.

[ZetaX]

It's not a counterexample because you aren't speaking about the same topic. You said that most lines don't intersect. I said that when they do, they intersect at points. I don't see how saying that most do not intersect is a counter example to my statement.

You said: "Intersections of dimensions are always one dimension below it. Lines intersect at points.".

I answered that in general, they don't intersect at all (i.e. their intersection is empty). If you consider your phrase to automatically assume that they intersect at all (which with the usual mathematical meaning it won't, but I can accept your version for now) then my 4-space example still shows that your statement is wrong.

Edited January 21, 2015 by ZetaX

[Bill Phil]

Again, what?

Points have no dimensional value. They can be labeled as the Zeroth dimension as they have zero size. It's really just a name, though.

And, are you saying lines don't intersect? Because that's a very basic concept...

And I don't understand your "4-space" example. Explain it in clearer terms, please.

(I'm starting to think you're talking buzzwords/gibberish, please make it simpler)

[ZetaX]

Again, what?

Points have no dimensional value. They can be labeled as the Zeroth dimension as they have zero size. It's really just a name, though.

Yes, points have dimension 0 and that's not just a name. Everything works better that way in mathematics and there really is no reason whatsoever to not use that. The dimension of the empty set is a different matter, though (-1 or -infinity are common).

And, are you saying lines don't intersect? Because that's a very basic concept...

You know, I gave you a link to Wikipedia's article on skew lines. At the very least read it before acting like I am too dumb to know your (wrong) statement that "lines always intersect".

And I don't understand your "4-space" example. Explain it in clearer terms, please.

It's a bit difficult to just explain 4-space intersections in a couple of lines in a forum. You could try some 4D stuff to get a better grasp (I recommend the 4D version of rubik's cube) of this. Apart from that, defining subspaces by equations is a good way of dealing with this without the requirement for that, and that's what I did there. Longer version:

Let your 4-space have coordinates w,x,y and z; in other words, every point is given by its four coordinates, e.g. the point with coordinates w=1, x=-5, y=pi and z=0 (like 3-space has three axes you may call x,y,z and a position is given by three numbers). Then we consider the plane A where the first two coordinates are zero, and the plane B where the last two coordinates are zero (both are really 2-dimensional planes). The only common point is the one where all four coordinates are zero; thus they intersect in a point.

You will have to believe me that this is the "usual" case, not a special one like parallel lines in the plane, though.

(I'm starting to think you're talking buzzwords/gibberish, please make it simpler)

Actual (yet still correct) use of buzzwords to demonstrate that I am pretty nice so far : a possible definition of "in generic position" is given by "the corresponding subset of parameter space contains an open and dense subset of the Zariski topology"

More seriously, I am trying (see the part on 4-space). But properly dealing with 4-space or even GR is not something to fully explain in a couple of lines in a forum post.

Edited January 21, 2015 by ZetaX

[Bill Phil]

By 4-space you mean 4D?

Where did you get the Lines Always Intersect Part? Because that's obviously not true. I said that lines intersect at points. That lines ALWAYS intersect AT POINTS. The "when they do intersect" part was kind of implied.

So, lines always intersect at points. Not saying lines always intersect. I'm saying they intersect at points in all circumstances.

EDIT:

In your coordinate example, you're talking about plane segments that reside on the same infinite plane. So, two planes aren't intersecting. It's really the line segments of the plane segment.

Edited January 21, 2015 by Bill Phil

[Steellwaters]

I don't buy Dark Matter/Energy. IF your empirical evidence contradicts your mathematical theory then you rework the theory to fit the evidence.

Instead they have invented matter and energy to account for the discrepancy. to my knowledge the only evidence for dark matter and Dark Energy is that the predicted result doesn't match the observed result. that just means the equations we have created to model the properties of Gravity are missing a term. No model will ever be 100% perfect and the more correct the the model the more extreme the measurement needed to notice the discrepancy.

So until somebody has some is a jar I see no reason to believe in dark matter/energy.

I think this is off topic but I just wanted to give my 2 cents.

[ZetaX]

By 4-space you mean 4D?

Yes.

Where did you get the Lines Always Intersect Part? Because that's obviously not true. I said that lines intersect at points. That lines ALWAYS intersect AT POINTS. The "when they do intersect" part was kind of implied.

So, lines always intersect at points. Not saying lines always intersect. I'm saying they intersect at points in all circumstances.

You also want to exclude the case of both lines actually being the very same one, because then their intersection is a line (nitpicking indeed, but you said "in all circumstances"). But apart from that: yes, intersecting lines will always intersect in a point when not being identical.

But you also made a statement about higher dimensional versions (planes always intersecting in a line) and those are still wrong. You already missed or did not mention two special cases when intersecting lines (no intersection and they being identical) by not being well-aquainted to working with these on the formal level (the one where you have very concise and strict definitions and rules); planes in 4D are even more complicated.

[Bill Phil]

If the line/plane is the same, it's not an intersection.

[ZetaX]

If the line/plane is the same, it's not an intersection.

Well, it actually is in the formal meaning. You are putting too many unspoken assumptions into your statements. It would be better to state them (I already did that for you, so this is more of an advice for the future).

Anyway, my main point is not being nitpicky about lines, but the 4D example. I don't think the latter has such simple excuses.

[shynung]

It is his truth. But truth != fact.

Again, you've missed the point. It is easy to understand how his 'truth' would stand under our scrutiny, because we've seen what he has not. Assuming a lack of communication, he'll never know the real 'truth', and have to live with what he knows for the rest of his life.

Right now, we're in his position. We've seen the universe around us contain everything, and we see no obvious 'windows' or 'doors' to to it. We cannot observe or travel to the 'outside' of the universe, at least not now. We are the man who is locked in the house. How is it not logical for one of us to conclude that there are no other universes besides our own?

You may argue that this may not be true. And you may point out that someone better informed in the future could make a better conclusion than what we have. But for now, we have no evidence about the existence of the 'outside' of the universe. While absence of evidence may not mean evidence of absence, in this case, the existence (or lack thereof) of another universe have little visible effect on the workings and mechanisms of our universe, at least as far as one can predict from here, so it is convenient to simplify the hypothesis by stating that there are no other universes out there.