Singularity, Infinity, Edge, Expansion

[salvestrom]

Good luck with that. It at least has the advantage that it MIGHT be right.


I see that you adamantly refuse to learn the maths of infinity. Good luck with that as well.

Maths proved that 1=2. The argument against it is that the operation of dividing or multiplying anything by 0 is not a viable one. I see no difference with your example. You can suggest it as a concept but turning it into a reality is impossible. Both of your lines are polite insults. I could accuse you of refusing to accept the practicalities of reality.

For the life of me, I can't find the 1=2 article to use the word they used instead of 'viable'.

Anyway, final point. Doesn't physics strive to remove infinity from its equations whenever it pops up? I've heard it said it is a good indication you're done something wrong.

Just to stress, I'm fine with debating a concept. I just don't think inifinity actually exists anywhere in the realworld.

 

[Chronos]

I sypathize with infinity bashers. Scientists are working dilignently to do away with the infinity in the center of a black hole. Renormalization was developed to do away with the infinites that routinely arise in quantum calculations. Can we do away with the apparent infinity of the universe? It's not for lack of effort. We still search for tell tale signs of a wrap around effect. One of the first I recall was an article titled 'Circles in the Sky'. They didn't find any, but, we haven't stopped trying. They did manage, however, to constrain the minimum size of the universe [which turns out to be gimongous]. The effort is still ongoing. An infinite universe that is causally connected would invoke issues that are at least as mind bending as the idea of a finite, but, unbounded universe - like how can something spatially infinite be temporally finite?

 

[Simon Bridge]

This doesn't leave me with very much choice other than to side with Aristotle and take the finite, unbound view of our universe.

You are in good company.

Everyone has their favorites, but we should bear in mind that there are other good ideas around too. The best we can do is to see if we can find an upper bound for the very-large-scale curvature of space-time. Ah - that reminds me ...
https://www.physicsforums.com/showthread.php?t=298279
... a thread on PF discussing an artistic representation of the Universe.
You'll like it - it shows my 1D loops expanding through the different stages in a simple-ish big-bang model.

Stretching B to twice A's length requires A to have an end that can be surpased.

But that's not what I did - I didn't change the length of A at all :) What I did was change it's coordinate density.

If each of the numbers on the line were masses, you'd be quite happy with halving the density of A wrt B ... but if you counted the masses, there would not only be an infinite amount in both but there is a 1-1 mapping from one set of masses to the other.

Infinite sets require a special language to cope with.
For instance, A and B have the same number of elements, so you'd think that A + B combined would have twice as many elements as A wouldn't you?

Aside from this, performing the action on anything other than a finite line seems to serve no practical purpose in reality.

And yet differential calculus and geometric sums do just that.

Your second example seems to tie in with concepts of the expansion of space. Although in that case the distances are always finite.

Both of them do - the first one expands space, the second adds an extra bit of space between two coordinates. The first one is a closer representation of expansion.

You'll probably be most comfy with the ideas of quantized space-time, which does away with infinities in every direction. I'd say this is good enough for now - it is a very big subject and we are in a small website. Have fun exploring.

 

[salvestrom]

Well, you said stretch B twice. Not sure how else that can be taken. But on to way more interesting things...

Space!

I did realize that the first example is also a type of spatial expansion. The reason I didn't edit to say so was because that idea of space expansion was shot down in another thread of mine, and I got the distinct impression that expansion type 2 - where new space is created/added - was actually the accepted view.

The model you show does have inconsistancies that I've never really dwelled on. The galaxy end can, if you squint, be viewed as if the galaxies are attached to the cylinder, with the surface, the hoops, representing x in space while the horizontal lines are t. But it doesn't work all the way down the tube. But then, one picture is not a thing to base ones knowledge of the universe on. If it were, I'd draw a quilt, call it quantised 2D space and never come here again to see how real scientists are doing.

Oh, thanks for percivering. I'm stubborn as hell. Tauren.

 

[Simon Bridge]

If the Universe did not expand of contract, the picture would be a cylinder - that is correct. If the expansion was a constant, it would be a cone ... providing the singularity at the point that we talked about getting rid of earlier.

To avoid the point, the geometry requires the time axis to curl around so the space-time picture resembles a hemisphere. In the picture, there are a few extra tweaks to account for quantum effects in the very early universe - the hemisphere looks like a nipple in the bit labelled "quantum fluctuations".

In the other direction, there is a trumpet-like flaring ... this is due to the currently observed acceleration in the expansion.
The artist has drawn that end open because any ideas about how the Universe ends up is pure speculation at this stage.

I have a post in that thread talking about the bits I see as misleading in that picture.
Anything we do like this can only be an analogy - and all analogies have limitations.