Hokulele
Deleterious Slab of Damnation
Do you accept time as a dimension at all? Would you agree that the universe is getting older?
If so, why should time be any different from any other dimension?
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Stationary Centre of Universe Defined?
- Thread starter ynot
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Do you accept time as a dimension at all? Would you agree that the universe is getting older?
If so, why should time be any different from any other dimension?
I agree, and will make every effort to read even if I can't post.No worries, this is an interesting thread with or without you.
I’m only imagining a larger size relative to a former size. Nothing external.
Everyone is at least the centre of their own experience of the Universe.To explain this using a non-spatial dimension, if you were approaching a black hole and I was sitting here watching you, to me, it would appear that you are essentially slowing down. In other words, I would find myself aging at the normal pace (*sigh*), but you wouldn't be. To you, time appears to be running at the same pace it always has. Which is the "correct" time?
In other words, there is no linear universal spatial center, just as there is no linear universal time. It is all relative to your frame of reference. If you do not believe my words, take a look at how GPS receivers work as this time dilation effect is pretty much built into them. There really is some solid evidence to support my claim.
On a positive note, it would be correct to state that you are the center of the universe. As am I.
AntiTelharsic
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Neither do physicists. The model distinguishes very clearly between time and space dimensions, but it does treat them as part of the same "manifold".
Yes.
The universe is no longer a singularity.
I don’t have an issue with time being called a dimension as long as it’s made clear that it’s not a spatial dimension. Time is different from a spatial dimension because it isn’t one.
Depends what you mean by “time” and “older“.
AntiTelharsic
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Imagine a line segment -- just some finite piece of a line. To each and every point in that line, you can associate a real number between 0 and 1. If you stretch the line segment so as to double its length, you still have the same number of points; no new points need to be introduced, and all previous points are still accounted for; the line still has an association with the real interval from 0 to 1. Similarly if you contract the line segment. If you contract it all the way down to zero length, then you have done something analogous to rewinding the universe back to the singularity. At every time prior to complete contraction, you still have an entire [0,1] interval's worth of points, even though the length of your line segment is much smaller than it originally was, and when it's completely contracted, you view all those points as occupying the same place.
Do the same thing with the outline of a circle, as suggested in my earlier post. As you contract the circle, say, about an imaginary point at its center, you aren't removing any points -- in fact, you can identify a point in the circle at one stage of the contraction with a point at any other stage by drawing a line from the first point through the imaginary center point. At all times during the contraction (reverse expansion), all your points are present; when you contract completely down to a point, all your original points can be thought of as being located at that single point (singularity).
The universe works the same way. In these analogies the universe -- by which I mean the entirety of both space and time -- corresponds to the line segment or the circle. The analogy breaks down because there is no outside space in which the universe is embedded, and there's no imaginary point toward which it contracts. The essential point of the argument is to be seen by thinking about only those points within the line segment or the circle, and thinking about what happens to them.
Do the same thing with the outline of a circle, as suggested in my earlier post. As you contract the circle, say, about an imaginary point at its center, you aren't removing any points -- in fact, you can identify a point in the circle at one stage of the contraction with a point at any other stage by drawing a line from the first point through the imaginary center point. At all times during the contraction (reverse expansion), all your points are present; when you contract completely down to a point, all your original points can be thought of as being located at that single point (singularity).
The universe works the same way. In these analogies the universe -- by which I mean the entirety of both space and time -- corresponds to the line segment or the circle. The analogy breaks down because there is no outside space in which the universe is embedded, and there's no imaginary point toward which it contracts. The essential point of the argument is to be seen by thinking about only those points within the line segment or the circle, and thinking about what happens to them.
If the Universe uniformly expanded from the point of the singularity then surely it follows that the expanded Universe is concentric to that point.
AntiTelharsic
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Indeed. But you can model the universe using a geometry that incorporates both space and time into a single object, while treating them both differently, and doing so explains and predicts enough phenomena that the model can be said to have been experimentally well-verified.
AntiTelharsic
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I snuck a post in above this reply -- have a look at that.
Would love to continue but really gotta go. Thanks for your posts.
You are going stubbonly refusing to listen to and learn from posters who know what they are talking about. Good work.
Very quickly . . .
But the points on the line that were previously 1 inch apart will now be 2 inches apart. Every point will have a different spatial position relative to every other point. Same thing with a contraction of the line.
Not sure what you mean by “real interval”.
SezMe
post-pre-born
And therein lies your problem. You're stubbornly using your 3D concepts in an attempt to understand the universe which is decidedly NOT 3D. Think of the Flatlanders mentioned earlier. They ONLY know 2D; 3D is simply outside their ken...except mathematically. Now, you are like the stubborn 2Der who refuses to think beyond 2D and rejects 3D mathematics. That's fine as long as you don't want to understand 3D.
Similarly, if you want to understand a 4D universe but refuse to go beyond 3D concepts, fine. But don't expect to get anywhere.
You think a 2D Flatland and 2Der’s actually exist independently of a 3D Universe?
I will be happy to go beyond a spatially 3D Universe when someone provides credible evidence that a fourth spatial dimension actually exists.
godless dave
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Concentric to that point in time, but not in space.
If things have uniformly expanded from a point then that point is always spatially the centre point of that expansion.
No it's not. Again, you have ignored explanations of this.
AntiTelharsic
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Yep. But "spatial" here means nothing more than "inside the line". The point of intrinsic geometry is that there's no outside. So as the line contracts, all the points in it get closer and closer until finally, when the line has contracted to a single point, all those points are one.
Just talking about the identification between points in the line (our "space") and real numbers in the interval from 0 to 1 -- it's a coordinate system in the line intended to assist visualization.
There's nothing wrong with considering a purely 2D universe without a 3D universe to put it in. Similarly, there's nothing wrong with considering a 4D universe (spacetime) without a higher-dimensional universe to put it in.
If we model the universe as a 4D object with three space dimensions and one time dimension, then that model implies that we will observe certain phenomena in the real universe. So we look for those phenomena, and we find them. This is evidence (but not proof) that the model is accurate, at least in the sense that we can say that as far as we can tell it is a reasonable approximation to whatever the universe actually might be. The model may end up being revised in light of new observations, and the picture may change (or we may find that the current picture is just a subset of a larger picture, as happened with Newton's physics when Einstein came along), but in the meantime the 4D spacetime you're arguing against gives the best description we've ever had of the observable large-scale universe. Einstein's model has a vast amount of evidence in support of it.
Not accepting or understanding is different from ignoring.
AntiTelharsic
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When mathematicians talk of a "space" they generally refer to a set of "points" (which can be abstract entities, and not geometric points like you're familiar with) and some properties of that set which give it some kind of structure. For our purposes, a space is a set of points along with a function, called a "metric" -- think "distance function" -- which lets us define distances and angles between points. We also want our space to be "smooth"; basically we'd like it to appear flat everywhere, if you look at it closely enough, just as the Earth appears flat when you're standing on it, though it may be curved at different scales.
In normal (Euclidean) 2-space, i.e., the plane, the usual (but by no means unique) metric is a function which takes two points and gives you the regular distance between them which you'll be familiar with from high school geometry. But there are all kinds of distance functions you could use instead (they merely have to satisfy a few special conditions), and you'd still be able to do interesting and useful geometry.
You can even create a distance function for the plane which makes it behave as though it were curved in three dimensions. But the important thing here is that you don't need three dimensions in order to do so. You can proceed just from a two-dimensional space, defining a suitable distance function on it, and get something which as far as any Flatlander living in it would be able to tell might as well be curved in three dimensions.
And this is what we have with 4D spacetime. We have a geometrically four-dimensional "space" ("space" in the abstract mathematical sense), with three of the dimensions corresponding to regular 3-space, and one dimension corresponding to time. Points in this spacetime have four coordinates: three spatial and one time. We define a metric on this object, a distance function, so that we can do geometry with these points inside it. This distance function treats the time coordinate slightly differently from how it treats the spatial coordinates, but the general operation is a very close analogue of what you would do with a purely spatial four-space. The metric we use to model the universe changes in the presence of mass, and overall gives us a geometry which, living inside this object, we perceive as global curvature in the same way that a Flatlander above perceives his 2D space with its special distance function as being curved. The local changes of internal geometry in the presence of mass are what gives us gravity, and the global changes, as you move across very long distance, are what give us the large-scale curvature which is being discussed in this thread.
It doesn't have to be a big thing which is actually curved around some imaginary point in a higher-dimensional space -- it's simply that it is stretchy and twisty and our measurements of angles and distances inside it are such that it might as well be. There's no outside -- you can expand it and compress it all you want, and all that means is that you're playing with the internal notion of angle and distance. You can even compress it more and more tightly, so that the points all get closer and closer together, until they all occupy the same position (as in the singularity), and then blow it back up again (as in the big bang) -- all you're talking about is internal changes in geometry, without reference to any exterior points.
The evidence is, as I've mentioned, in the model's ability to account for observed phenomena and the experimental confirmation of its predictions. We can see how geometry changes in the presence of mass by watching what happens to light as it passes near massive objects, and it does so in precisely the manner you would expect if the universe was exactly as Einstein described -- a four-dimensional, curved spacetime with particular metric properties. It's one of the most spectacularly successful models we've ever come up with.
This is a lot to try to come to terms with. It would probably fill a couple courses in Functional Analysis and Differential Geometry at least, and I've had to try to explain all this math in as non-mathematical terms as possible, which brings its own problems. But I hope you at least try to have a think about it, and maybe find it a little bit useful.
In normal (Euclidean) 2-space, i.e., the plane, the usual (but by no means unique) metric is a function which takes two points and gives you the regular distance between them which you'll be familiar with from high school geometry. But there are all kinds of distance functions you could use instead (they merely have to satisfy a few special conditions), and you'd still be able to do interesting and useful geometry.
You can even create a distance function for the plane which makes it behave as though it were curved in three dimensions. But the important thing here is that you don't need three dimensions in order to do so. You can proceed just from a two-dimensional space, defining a suitable distance function on it, and get something which as far as any Flatlander living in it would be able to tell might as well be curved in three dimensions.
And this is what we have with 4D spacetime. We have a geometrically four-dimensional "space" ("space" in the abstract mathematical sense), with three of the dimensions corresponding to regular 3-space, and one dimension corresponding to time. Points in this spacetime have four coordinates: three spatial and one time. We define a metric on this object, a distance function, so that we can do geometry with these points inside it. This distance function treats the time coordinate slightly differently from how it treats the spatial coordinates, but the general operation is a very close analogue of what you would do with a purely spatial four-space. The metric we use to model the universe changes in the presence of mass, and overall gives us a geometry which, living inside this object, we perceive as global curvature in the same way that a Flatlander above perceives his 2D space with its special distance function as being curved. The local changes of internal geometry in the presence of mass are what gives us gravity, and the global changes, as you move across very long distance, are what give us the large-scale curvature which is being discussed in this thread.
It doesn't have to be a big thing which is actually curved around some imaginary point in a higher-dimensional space -- it's simply that it is stretchy and twisty and our measurements of angles and distances inside it are such that it might as well be. There's no outside -- you can expand it and compress it all you want, and all that means is that you're playing with the internal notion of angle and distance. You can even compress it more and more tightly, so that the points all get closer and closer together, until they all occupy the same position (as in the singularity), and then blow it back up again (as in the big bang) -- all you're talking about is internal changes in geometry, without reference to any exterior points.
The evidence is, as I've mentioned, in the model's ability to account for observed phenomena and the experimental confirmation of its predictions. We can see how geometry changes in the presence of mass by watching what happens to light as it passes near massive objects, and it does so in precisely the manner you would expect if the universe was exactly as Einstein described -- a four-dimensional, curved spacetime with particular metric properties. It's one of the most spectacularly successful models we've ever come up with.
This is a lot to try to come to terms with. It would probably fill a couple courses in Functional Analysis and Differential Geometry at least, and I've had to try to explain all this math in as non-mathematical terms as possible, which brings its own problems. But I hope you at least try to have a think about it, and maybe find it a little bit useful.
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SezMe
post-pre-born
ANALOGY, ynot.You think a 2D Flatland and 2Der’s actually exist independently of a 3D Universe?
This is just stubborn refusal to listen and learn. I'm back outta here.