The thread about extra light in our universe and the comment on a closed topology got me thinking. Is there anything in our universe that is either known or could possibly be infinite in quantity? My knowledge comes from taking freshman and sophomore level physics, so I’m not an expert. As far as I know, we don’t have anything that gets to infinite, either small or large. We can’t reach absolute zero. The Big Bang doesn’t go all the way back to exactly zero seconds. Things measured at smaller distances than the Planck length don’t have any meaning in reality. It’s harder to say one way or the other on the large size, but AFAIK the universe is not thought to be infinitely large or to have an infinite amount of matter / energy. Am I wrong about any of these things? Are there any hypothesis that at least suggest some fundamental quantity or another could be infinite?
It’s possible the universe has infinite size.
There are infinite numbers.
But I think the OP is asking about tangible objects.
The only thing that it makes sense to talk about is the size of the universe. It is possibly infinite. If it is infinite and we don’t live in an unusual part and the rest of that infinite universe doesn’t have matter, the universe also has infinite matter and energy.
And absolute zero and zero time are not infinities, and their unattainableness are radically different.
Absolute zero is unachievable because there is always some energy left in a system.
“Zero time” is just a reference point in the Big Bang Theory and a point the theory will likely never move past because we don’t have enough evidence available to test hypotheses for what happened before the Big Bang. It’s a “we can’t know”, rather than a “it can’t be”.
I don’t think there is any conceivable way to answer the OP.
As far as time 0 being an infinity, I like to think of time since the big bang as logarithmic and the log of 0 is -infinity. The reason I think of it that way is that I got the impression from Steven Weinberg’s “The first three minutes” that as much changed between 10^{-43) seconds and 10^{-42} seconds as between then and 10^{-41} and so on.
Perhaps some aspects of a black hole would qualify as things may fall forever, and has the original matter and matter that has since fallen scattered from the event horizon all the way to the zero which one can never reach, but could be there from it’s creation.
Infinity is not a number - you cannot have an infinity of marbles in a bag. Infinity is a description of the behavior of a process. If you try to count up to the largest integer, you will not finish up having counted an infinity of numbers; you’ll just never finish. If you try to slice something in half over and over (ignoring physical considerations) you will not end up with an infinite number of slices which are all infinitely small; you will just never finish. And despite the fact that you will never finish, you will never find that you have been counting or slicing for an infinite amount of time, having experienced an infinite number of birthdays some of which had cakes with an infinite number of candles on them. Your age will always be a finite number, with a finite number of candles, forever.
So yeah - there is no such thing as an actualized infinity, and there can never be. The universe is not infinitely old, and it’s not infinitely large. The closest you could get to infinity would be for it not to have a size - there could be direction where there is no edge that you could hit, where there is no pair of opposing edges that you can measure from one edge to the other. In that case you could travel in the open direction ‘infinitely’ - though at any given time you will only have traveled a finite distance.
This is a valid point of view, but it is not the only point of view. One could argue that infinity is a number. Specifically, it is the reciprocal of zero,
By identical argument, NaN is a number, as is ERR.
Maybe in some math systems, but not in the one we usually use.
It depends on the number system you’re using.
If you’re using the real numbers or the complex numbers, then zero has no reciprocal. In other words, 1/0 is an undefined expression. Also, in these systems, there’s no such number as infinity. In other words, ∞ is an undefined symbol.
If you’re using the projectively extended real line or the Riemann sphere, then the reciprocal of zero is infinity, and the reciprocal of infinity is zero. In other words, 1/0=∞ and 1/∞=0. (Note that the reciprocal of infinity is exactly zero, not infinitesimal. None of these four number systems contain any infinitesimal numbers.)
Out of these four number systems, the first two (the real numbers and the complex numbers) are much more commonly used than the last two (the projectively extended real line and the Riemann sphere). So much so, in fact, that we usually say “division by 0 is undefined” and “infinity is not a number” without clarifying which system we’re using.
I suppose my last post was too flip. Infinity get written in in a lot of places where you would normally expect to find a number; one obvious example is it’s often the result of limits. But even when it appears as the answer to an equation, it functions as more of an informational error value - it’s saying that your equation doesn’t calculate to a number, but rather keeps shooting off in some direction without ever resolving.
I’m far too (something) to learn new number systems at this point, but in these systems is “∞+1” different from “∞” or “∞+5” in any sensible way? (You know like actual numbers are.)
How do you know? Human intuition has not proved at all reliable with (say) Quantum Mechanics. We have no good answer to “why is there something rather than nothing” in the deepest sense. I don’t mean in Krauss’s relatively trivial sense of something arising in a vacuum according to a set of physical laws that apply in a given universe or multiverse. I mean in the deeper sense of why such laws or anything else would ever arise in the first place. I have no explanation of how or why there is something rather than nothing, but It seems more natural to accept that since we certainly know there is something here and now, that implies that the presence of something rather than nothing must be unbounded.
Infinity is a concept of something without measurement, without end, whose size cannot be determined, ever. No value can ever be determined for something that is infinite.
The size or any measurement of an infinite quality of anything cannot be determined. And by following, we cannot even determine IF some measurement is infinite.
We can say that the size of the universe is infinite, but we cannot know that, only that we currently cannot measure that value. Infinity is used as a concept of something that we do not know, or cannot know the value of. That does not mean that an absolute value does not exit, just that we currently do not know what it is.
Anyone who says that there are infinities of various sizes has been listening to Joe Rogan and Neil deGrasse Tyson when they have smoked too much pot.
This is what I’m trying to get at. As far as we know, is there any quantity that we can keep slicing over and over (or doubling over and over) while NOT ignoring the physical considerations.
Math is neat. The whole frikking thing is man-made and clearly defined. What a number is, and how a number works, is defined.
Also defined is the word and concept of “infinity”. And it’s defined in such a way that it can never be actualized in the way a number can, because however many of something you actually have, that’s less than infinity. However old you are, however many birthdays you’ve had, that’s less than infinity. However wide you are, that’s less than infinity. Because however big something is, it has a size. And if you have a size, or an age, or a count, then by definition, that size/age/count isn’t infinity.
Even supposing this to be true (as others have mentioned, it’s not exactly wrong, but does correspond to a specific point of view), it does not mean there’s no actualized infinity in the universe.
Suppose we somehow show that before the Big Bang was a big crunch of another universe. And before that was another big bang, and another big crunch, and so on. This is a process, of sorts: for any precursor universe, we can identify one that came before that, just as every integer has a successor. So were that the case, we could say that time goes infinitely far back, even if we can’t identify a particular universe that’s infinitely long ago.
More concisely, something infinite is unbounded. But you have just stated the definition, you have not shown that everything must be bounded. You just think it’s a weird notion for something to be unbounded, that we don’t know intuitively what to make of that.
The exact same kind of arguments from incredulity and intuition that you’re making can be used to show that Quantum Mechanics is so preposterous that it cannot possibly be true.
I don’t think arguments from incredulity count for anything at all in the deeper aspects of existence.
It’s actually an argument from definition. (Which happens to also prove that there cannot have been an infinity-long chain of explosions all the way forever. If every bang requires a preceding big bang, that’s actually a proof of either time travel or that there are no big bangs.)
Speaking of incredulity, I’m also incredulous that quantum mechanics includes actualized infinities. In fact I was under the vague impression that lots of stuff in quantum mechanics barely exits beyond the potential and statistically-possible, though I concede my knowledge on this front is close to negligible.
This is exactly my point. We don’t know why there’s something rather than nothing; but given that we know there is something here and now, I think the most natural assumption is that there is/was always, in some manifestation, something rather than nothing. The notion that there is some kind of bound, beyond with there is/was nothing rather than something, makes even less sense to me than the (admittedly bizarre) notion of it being unbounded.