Infinity and mathematical phyisics

[Pjpic]

If the bulk universe is infinite (IF it is), would mathematical physics have trouble describing it because infinity is not a number?

 

[jedishrfu]

It doesn't matter that infinity is not a number as to whether the universe is finite or infinite. The current view is that the universe is relatively flat and it goes on forever and that we can only see a portion of it 13 billion light years out. We simply can't say if its finite or infinite

http://en.wikipedia.org/wiki/Infinity

 

[Chalnoth]

Even if infinity is not a number, it is a very specific mathematical concept (well, actually a class of concepts, but no need to go into too much detail). So the answer is no.

 

[Pjpic]

Even if infinity is not a number, it is a very specific mathematical concept (well, actually a class of concepts, but no need to go into too much detail). So the answer is no.

- So, there's no problem with actual infinity like the one you get with division by zero.

 

[Chalnoth]

- So, there's no problem with actual infinity like the one you get with division by zero.

There are actually ways to normalize some divisions by zero in sensible ways. For example, there's a theorem in complex analysis that states that the value of an integral along a closed contour in complex space is equal to the sum of the "residues" at the function's singularities (places where a division by zero occurs) that fall within said contour. See here for some more detail:
http://en.wikipedia.org/wiki/Residue_(complex_analysis )

Basically, you can't ever actually divide by zero and get a sensible result. But you can take an equation that does divide by zero for some values of the variables and still extract useful information. In fact, sometimes the very fact that there are some values where a division by zero occurs is critical in producing a solution. The way you get at this in practice is to never actually divide by zero, but instead take limits and show that the value you're looking for converges to a specific result no matter how close to zero you actually get.

It's more or less the same with infinities: you can deal with infinities just fine as long as you just deal with limits.

Now, that said, it turns out that if you take the universe to be infinite, it becomes impossible to sensibly answer certain questions (e.g. how probable is event X compared to event Y?). If you want to look into this issue in more detail, it's known as the measure problem. This may be a hint that an infinite universe can't exist, but it isn't clear.

 

[0zyzzyz0]

Chalnoth, The 'measure problem' you mention interests me. It seems, as I first entertain this thought, that whether or not we can make a probability comparison this does not bare on the question of whether the universe is finite or infinte. It would specifically rule out that particular kind of comparison, frustratingly maybe, but not the the possibility of actual infinity.
I will look more into the 'measure problem', taking responsibility for doing my own homework, but can you tell me if you are aware of any other ways in which this problem might weigh on the question of whether 'the universe' or 'all of reality' or 'the omniverse' or whatever is finite or infinite? That's the question I am digging into.

 

[Chalnoth]

It seems, as I first entertain this thought, that whether or not we can make a probability comparison this does not bare on the question of whether the universe is finite or infinte. It would specifically rule out that particular kind of comparison, frustratingly maybe, but not the the possibility of actual infinity.

Well, not quite. Consider two different models of the universe, A and B. Model A happens to be finite, while B is infinite. In model B, some questions just can't be answered. In model A, they can be answered, but they might be wrong.

This does make model A potentially more interesting, depending upon your biases. I don't think there's any a priori reason to prefer the finite model, but it can be investigated more easily. Does this make it more likely to be correct? I don't think there's a way of answering that, except by demonstrating that one specific model is likely to be the correct one.