In the balloon analogy, you have to think in terms of a 2D world, so from that perspective it is not expanding into any space. Plus. the Big Bang created space. Think: if there is a single point, how do you define space anyhow?
Sure the Big Bang is a terrible term - but remember it was coined by an opponent of the theory, and caught on anyway. Not surprising it is inaccurate.
While space is indeed expanding, gravity means that a galaxy, for instance, is not getting any bigger, let alone something like a planet. So your analogy would have to be modified to keep a set of selected objects constant in size while growing the rest of the picture. I don’t know that Photoshop has that feature - but I don’t know 99% of the features of Photoshop.
Yeah, that’s what I was trying to get at, but I didn’t explain it very well. AutoCAD uses vector graphics, so a point is a point, no matter how much you scale it. Photoshop and the like use bitmap images, so the dots would scale too. That’s why I said the effect would be lessened in Photoshop and similar.
I figure on the scale of the universe, even a galaxy is just a point.
Ok. I’ll buy the shaving foam description or the vector graphics explanation.
But for every enlargement there is an invariant point – the centre of enlargement. We are constantly told that there is no such animal for the big bang.
I don’t follow your reasoning, there simply isn’t one.
The starting assumption of big bang comsology is the Copernican cosmological principle, which in this context is the assumption that there exists a global frame which can be constructed (homogenously and isotropically) in which the universe appears to be completely homogenous and isotropic.
Any ‘centre of expansions’ would break the symmetry induced by this assumption and there’s no mechanism for this symmetry to be broken. If such a centre appear in a model you know that you’ve made a mistake somewhere.
Infact the universe isn’t completely isotropic and homogenous so infact it’s assumed that the actual general relativstic description of the universe is some small peturbation of the big bang model. So infact you may well find that there exist local centres of expansion, but we needn’t worry about these.
I start with a triangle ABC. Some time later it has enlarged to A’B’C’. The lines AA’, BB’ and CC’ intersect at a point that is invariant under that transformation. That point may be within ABC or outside of it, but it exists. In my corner of the world it is known as the centre of enlargement – a focal point from which expansion takes place.
Expanding shaving foam or enlarging an autocad diagram will do exactly the same thing. But I am told that no such centre exists for big bang expansion.
Therefore, like the balloon analogy, these two descriptions are inadequate.
The universe’s geometry is not Euclidian. Euclidian geometry applies to a 2D flat surface. The surface of the Earth is curved and non-Euclidian (the shortest distance between two points on the earth is a curve, not a straight line). The universe’s geometry is at a minimum 4D, and is “curved” (analogous word) by the presence of mass and energy in those dimensions.
All you’re saying though, is that the center of a group of points is defined as being equidistant from all points. If we apply that to the observable universe, the center is… us (or very near to). The conclusion would have to be that the big bang occurred at our current location in space, because all of our observable universe exists in a uniform sphere around us, with a fairly even distribution of matter in all directions. Further - it would always and forever have appeared this way to anyone looking.
The thing is, someone in another galaxy would conclude the same thing - that THEY are the equidistant point of their observable universe, because their observable universe centers around them. This is why people say “the big bang started everywhere”.
So, is there an equidistant point in the non-observable universe? The thing is, it’s impossible to ever know, and there’s no good evidence to believe one should exist. I’ll leave it to the actual cosmologists to explain it better though.
As far as analogies go, this is why the “stretching an infinite rubber sheet” is probably better than the balloon one, except that anything where you have to imagine infinity kind of ruins the neatness of having an analogy in the first place.
No I am not.
If I am not mistaken, standard 3D geometry can be considered Euclidian as well.
I am quite aware that space-time is considered four dimensional. What we are considering here is the relative positions of points in 3-D space as time changes.
And I know that relativistic principles apply and that space can be considered bent in the presence of mass. However, at present space is fairly sparse and Euclid will do as a first approximation. These are my own pants implied that such inhomogeneities can be ignored.
So, my two questions still stand.
- What is the technical difference between two points moving further apart and the distance between them increasing? In the absence of any absolute reference frame and without objects to stand as placeholders there doesn’t appear to be any concrete way of distinguishing between these two constructs.
- And I will rephrase this question in the light of what has been posted: What kind of expansion is possible if (a) there is no centre of expansion and (b) the universe is not topologically a sphere with the property that a straight line becomes a loop.
Every point can be taken to be the focal point of the universe’s expansion. In the triangle example, you can picture yourself standing at the center of the triangle, observing ABC getting mapped into A’B’C’ – everything expands away from you. Or, you can imagine yourself sitting at A, such that A gets mapped into itself, and B and C get mapped to B’’ and C’’, and again, everything expands away from you – but A’B’C’ and AB’‘C’’ are the same triangle, merely translated along A’A. Perhaps what’s tripping you up is that with raisin dough, shaving cream, and balloon, you have an outside view, but with the universe, there isn’t one, it’s all there is.
As for your first question, I’m not sure I get what you mean. Where is this difference typically made? All I can come up with is that one could misinterpret expansion to imply that everything gets uniformly bigger, which you would not notice – the distance between two points gets doubled, but all your measuring rods double in length, as well, so one inch would still be one inch, it would just be a ‘bigger’ inch. To avoid this confusion, one could perhaps point that the two points move actually further apart.
I think there’s several ways of tackling your objection. Let’s say we have an imaginary triangle in space expanding under the influence of Hubble expansion. Let’s assume space is flat (as it is obsevred to be on a large scale).
Mathematically speaking we’re mapping the points in a triangle on one submainfold of a FLRW (Friedmann-Lemaitre-Robertson-Walker) spacetime onto the points in another triangle on a different submanifold of the same FLRW spacetime. I.e. the lines AA’, BB’and CC’ don’t lie on either submanifold (if we view A,B,C,A’,B’and C’ as events these lines intersect at the big bang).
Several in this thread have mentioned that space itself is expanding and that it is difficult to comprehend there being nothing for it to expand into.
[quote = ECG]
There was no already existing space. Space itself started as a single point, and expanded outward. It is still expanding. If you were to magically pick a point in space (let’s call it X) and another point in space a thousand miles away from it (let’s call that Y) and you could magically put markers on those points that never, ever moved, they would still move away from each other, not because they are moving (they aren’t) but because the space between them is expanding. The more you move forward through time, the more the space in between those points will expand, moving those points farther and farther apart from each other.
[/quote]
emphasis added.
You (HMHW) seem to be implying that if two points are an inch apart and the universe expands they remain an inch apart, only that inch is bigger and the ruler to measure it is bigger. In which case, what does the expansion of the universe mean at all? This notion seems rather circular to me and at odds with what others are saying.
FLRW?
You want to translate?
I said that to interpret things this way would be a misunderstanding.
Apologies. I misread.
As I said FLRW stands for Friedmann-Lemaitre-Robertson-Walker, as in FLRW spacetime which I just use as a generic term for spacetime where the Copernican cosmological principle is true.
FLRW coordinates provide a natural way of mapping a triangle at one point in time to a triangle at another point in time, but space at each point in time is distinct from space at another point in time. This is as space at each point in time is represented by different submanifolds (the manifold of which they are submaniflds of being FLRW spacetime).
Or in other,slightly less technical, words: in your triangle example you can compare the original triangle and the enlarged triangle because they lie in the same 2-D plane. However when a triangle is expanding under Hubble expansion the triangles at different times don’t lie in the same 2-D plane (or even 3-D space). Though we may map the plane in which the original triangle lies in to the plane that the enlarged triangle lies in, the mapping is the same one which enlarges the triangle (or alternatively if we were to use another mapping taht preserves distance it would be arbitary).
If space is infinite now, it always has, and always will be, infinite. So, no, if it’s not infinite now it never will be.
Let’s extend the balloon/sphere analogy so that the radius of the sphere is time. The present moment is the surface of the sphere. Every past moment is some smaller sphere, going back to the Big Bang, which is at zero radius, at the sphere’s center.
So now, in that context, ask the question “Where is the center of the universe?” A (the only?) reasonable answer is “at the Big Bang.” If you ask "Where is the center of the universe right now, it doesn’t have a well-defined answer. No more than if you asked “Where on the surface of the Earth is the center of Earth?” or “Where on the surface of the Earth is the center of the surface of the Earth?”
Take four pencils. Hold up one pencil, and align the second so it’s at right angles to the first. Now take the third pencil, and align it so it’s at right angles to both the first and second pencil. Now comes the difficult bit: take the fourth pencil, and align it so it’s at right angles to all of the first three. Once you’ve done that, the fourth pencil will now point along the direction that the universe is expanding.
But you’ll have to figure out yourself whether the tip of the fourth pencil is pointing in towards the centre of the universe or not, it depends on which way you’re holding the pencil. (if you’re holding the pencil correctly, this should be obvious)
Hope this helps. 