Actual Infinity in Reality?

[polymath257]

Professional astronomers don't have a problem with space being an actual infinite:



What is the universe expanding into? (Intermediate)

I just wanted your perspective on this question.

From a University of Cambridge conference series on the Philosophy of Cosmology, on the topic of "Do Infinities Exist in Nature" we get the conclusion at the end of the article:

And opinions are indeed divided. Both Barrow and Aguirre are happy with mathematical infinities and don't shut the door on physical ones either. "I think it's certainly true that we can develop theories that have infinity in them that can be perfectly useful," says Aguirre. "It's certainly true that as finite beings we can only experience a finite part of [the Universe], but I can't see any reason to place limits on whether the Universe can be finite or infinite in principle."

Ellis, on the other hand, does not believe that physical infinities exist and points to potential problems with using infinity in mathematical arguments pertaining to physics. He refers to a famous thought experiment due to the mathematician David Hilbert. Suppose you have a hotel with an infinite number of rooms, and suppose that the hotel is full. The paradox is that you can still fit a new person in; you simply move every person in the hotel one room along, so the person from room 1 goes into room 2, the person in room 2 goes into room 3, and so on. Since there isn't a largest number, you can do this without making anyone homeless and then you can fit the new person into room one.

Because of paradoxes like this one, Ellis thinks that you have to be very careful when you use infinities in a physical context. "I'll make a distinction; there are some times when people talk about infinity when all they really mean is a very large number, and they're just using infinity as a code word for a large number. In that case, I think it's more informative to make a guess what that large number is and to talk about that large number, not infinity. There are some cases where people use infinity in its deep sense; in the paradoxical sense. The paradoxical sense is, for instance, Hilbert's hotel. In my opinion, if a physics argument or any other argument depends on those paradoxical arguments, then this is a false argument and it should be replaced by something else."

In summary there is as yet no consensus as to whether infinities exist in the physical world. In the absence of concrete scientific answers it makes sense to turn to philosophers. "I think it's very important to get physicists and philosophers together," says Aguirre. "I think there's a reaction that a lot of my physics colleagues have about philosophers which is that they don't know any physics. They're just saying things about physics and they don't really know what they're talking about, and criticising physics but they don't really understand it. I think there may once have been some truth to that and I'm sure that there is now, but the philosophers that I talk to all know lots of physics. I see them as being specialists in thinking about the intellectual foundations of those questions, looking at them from a slightly bigger and different point of view than a more empirically or pragmatically engaged physicist would. I think that's incredibly valuable."

Emphasis added

The whole article is very interesting. Also distinguishes early on between actual infinities and potential infinities.

And again, the Hilbert Hotel is a *paradox* and not an actual logical problem. But let's face it, physics alone has many paradoxical issues: paradoxes concerning rapidly rotating objects, the twin paradox, paradoxes concerning entropy, paradoxes concerning the relationship between quantum theory and gravity, etc. To have a paradox just means our initial intuition is incorrect and needs to be corrected. it is an opportunity to learn.

From my experience, philosophers know a fair amount about *popularizations* of physics, but very little *actual* physics. Most would not be able to compute a quantum probability in any way. Most cannot solve a differential equation. And, I am sorry, but unless you can do both of those with some fluency, you simply do NOT understand the physics. And I certainly do NOT consider philosophers as any sort of experts on infinity. For that, you should go to mathematicians.