Is the physical universe infinite? What is the physics-related reason behind the fact that physicists use this term in their theories?
Let’s deal with these two questions one at a time.
Is the physical universe infinite?
This is one question that strikes most people some time in childhood, certainly at least by the time they are into high-school. (By high-school, I mean: standards V through X, both included.) They may not yet know a concept like infinity. But they do wonder about where it all ends.
A naive expectation kept in those years is that as one grows up and learns more, one sure would gain enough knowledge to know a definite answer to that question.
Then, people certainly grow up, and possibly continue learning more, and sometimes even get a PhD in one of the STEM fields. Yet, somewhat oddly, people are found still continuing to think that one day they (or someone else) would be able to at least deal with this question right. If the nature of opinions expressed in the history of science is any indication, for most of them, such a day never comes. So, the quest goes on to continue even further, well after their PhD and all. At least for some of them.
At least, to me, it did. And, I found that there also were at least a few others who had continued attempting an answer. A couple of notable names here would be (in the chronological order in which I ran into their writings): Eric Dennis, and Ron Pisaturo. But of course, their writings was not the first time any clarification had at all arrived; it was Ayn Rand’s ITOE, second edition, in the winter of 1990. In fact, both the former writings were done only in reference to Ayn Rand’s clarifications. (Comparatively very recently, Roger Schlafly’s casual aside threw the matter up once again for me. More on his remark, later.)
Ayn Rand said that the infinity is a concept of method, that it is a concept of mathematics, and that infinity cannot metaphysically exist. Check out at least the Lexicon entry on infinity, here [^].
A wonderful answer, and a wonderful food for some further thought!
The question to deal with, then, immediately becomes this one: If everything that metaphysically exists is finite, including the physical universe, then it is obvious that the physical universe would have to be finite. For physical entities, and therefore for the physical universe, definiteness includes: the definiteness of extension.
If so, what happens when you reach the (or an) end of it? What do you see from that vantage point of view, and looking outward? In fact, Dennis (in a blogsome essay on a Web page he used to maintain as a PhD student—the page is I guess long gone) and Pisaturo (in an essay) have attempted precisely this question.
Guess you have noticed the difficult spot: Seeing is a form of perception, and before you can perceive anything, it must first exist. If the entirety of the universe itself has been exhausted by getting to its edge, and since there is literally nothing left to see on the other side of it, you couldn’t possibly see anything. The imagery of the cliff (complete with that Hollywood/Bollywood sort of a smoke gently flowing out into the abyss at that edge) cannot apply. In principle.
“But why not?” The child in you cries out. “I want to see what is there,” it tugs at your heart with a wistful intensity. (In comparison, even the Calvin would be more reasonable—not just with the Hobbes but also with the Susie. (Yes, I think, the use of the the is right, here.))
The answers devised by Pisaturo and Dennis (and I now recollect that the matter was also discussed at the HBL), are worth going through.
I myself had written something similar, and at length (though it must have gone in my recent HDD crash). In fact, many of my positions were quite similar to Pisaturo’s. I, however, never completed writing it; something else caught my attention and the issue somehow fizzled out. See my incomplete series on the nature of space, for an indication of my positions, starting here [^], and going over the next four posts.
The question grabbed my attention once again, in the recent past.
This time round, I decided to attack it from a different angle: with even more of an emphasis on the physics side of the mathematical vs. physical distinction.
In particular, I thought: If the concept is valid only mathematically and not valid metaphysically (in the sense: infinity does not metaphysically exist), and thus, if it was invalid also physically, then why do physicists use it, in their theories?
Note, my question is not how the physicists use the term “infinity;” it is: why.
It is perfectly fine to pursue the how, but only inasmuch as this pursuit helps clarify anything regarding the why.
I intend to address this question, in the next post. I sure will. It’s just that I want to give your independent thinking a chance. I just want to see if in thinking about it independently, some neat/novel points come up or not.
A little bit of suspense is good, you know… Not too much of it, but just a little bit of it…
A Song I Like:
(Hindi) “saare sapane kahin kho gaye…”
Lyrics: Javed Akhtar
Singer: Alka Yagnik
Music: Raju Singh