Last I heard, the answer to “Why is there something rather than nothing” is “We don’t know.”
Philosophy claims to have the answers (to this and everything else), but I don’t trust 'em.
And I’m not claiming to have the answer to “why”. But what is indisputable is that there is something rather than nothing here and now. I’m then asserting that it’s reasonable to expect that if we track back to the origins of our current configuration of something, some other configuration of something gave rise to it (albeit “outside” of our universe, perhaps outside of the usual notion of the flow of time and space, but we have no other vocabulary). And even if we haven’t the faintest idea just what the rules are, the argument still seems sensible when applied to any “preceding” configuration of something. The notion of “infinity” only arises from iteration, it’s just another way of saying that it’s hard to see how the rule could ever not apply. If there’s a bound, that means in some sense a transition from nothing rather than something to something rather than nothing. I find the notion of that transition more troubling than infinite regress.
Whereas I find infinite histories to be logically impossible, and “something from nothing” to be no trouble at all. Perhaps hearing about the big bang for most of my life conditioned me to accept it? (Though even theoretically I don’t see what’s troubling about it.)
Perhaps “troubling” was the wrong word. It just seems to me that you offer no explanation. In principle, I can explain any step you point to in the infinite regress.
Step 1: “An infinite regress appears!”
There’s no appreciable difference between an infinite regress of discrete things and one single thing that’s lived forever - the classic example being an eternal god. But nobody seems to be able to answer “Why is there a god?”
Does God need a “why”?
Technically no - but if he doesn’t, neither does the universe nor the bottom turtle.
(And this does not mean I’m granting either God or the universe infinitely long histories. I’m just saying that there’s nothing about the god character that gives him special exceptions.)
My understanding of today’s quantum mechanics is that it says that “nothing” is an impossible condition. Virtual particles emerge from vacuum energy and a universe could spontaneously do so as well, something different only in scale and so within the possibilities given enough time.
Humans seem to have a conceptual difficulty with nothingness. Our perception is limited to somethings; we can’t grasp what nothing might be so we want to keep populating it with stuff. If QM provides that stuff, then maybe it makes the whole futile argument of something from nothing moot and we can get on with actual science.
All infinities must be the same size, unknown and possibly actually infinite. once a measurement is made it is no longer infinite.
That there could be an infinite number of infinites of various sizes remains wrong…
Have they actually taken quantum-type measurements from outside the universe? Can they determine that things like vacuum energy and such are not a product/property of the universe’s space-time which came into observable existence around the time of the big bang?
Actually humans in general are fine with the concept of nothing. “What in that box?” “Nothing.” “Actually there’s air in there.” “Shut up.”
The problem is that scientists keep taking closer and closer looks at things and finding something where we’d thought there was nothing - everywhere we’ve looked so far.
Nah, there are lots of different scales of infinities. It’s very much a math thing though, and you have to start doing math stuff to tell them apart.
Can you describe which part of Cantor’s diagonalization argument you find unconvincing?
Ah, how I miss crank.net! They used to bring us links to all sorts of cranks and crackpots, and math cranks were well represented. You could (and I’m sure still can) find elegantly crafted websites with detailed explanations of why Cantor was wrong. Also Einstein, Darwin, Newton, Galileo…
The weird part about this one, though, is that it doesn’t require any kind of external knowledge, and the argument is pretty simple. A bright grade-schooler can understand it. Evolution denialists and flat-earthers can simply claim that the scientific evidence was fabricated, but the Cantor proof doesn’t need any of that. And the proof is even more obvious and convincing than The Math Result Involving The Number Nine Which Shall Not Be Named.
Here is a very easy to understand example:
- There is an infinite number of even positive integers
- For every even positive integers there are two positive integers.
- Therefore, the set of positive integers is an infinity twice as large the infinity of even positive integers.
It this doesn’t make sense, think of this:
- The sum of all positive even integers subtracted from the sum of every positive even integer is zero, because every term of will cancel out.
- But the sum of every positive integer minus the sum of every positive even integer still leaves the sum of every positive odd integer, which is infinity.
- So the sum of every even positive integer is infinity less than the sum of every positive integer
No, those two are the same size. But the number of decimal numbers is greater than the number of integers.
You have to go back to basics when comparing infinite sets. Say you could not count past the number 1. How would you compare a basket of apples with a basket of bananas? Well, one approach would be to take out an apple and banana at the same time, and going until one or both baskets is empty. If they become empty at the same time, then the counts are equal. Otherwise, the one that ran out first is smaller.
With infinite sets, you must come up with a pairing rule. If we can come up with any pairing rule that matches up one set with another, then they must be equal in size. With all integers vs. even integers, the pairing rule is that you match up N with 2*N. Then, every integer matches up with exactly one even integer, with no leftovers.
Sure, we could come up with some bad pairing rules, like matching N to N, which means there will be some leftovers in the integers. But we can have leftovers in the other direction too, like if we matched up N with 4*N. We cover every number in the full set of integers but miss half the elements in the set of even numbers.
If we can’t find any pairing rule, though (and prove that no such pairing rule exists), then the sets must be a different size. That’s what Cantor’s diagonalization argument does, and shows that there are more decimal numbers than integers.
Right, it would take an infinite amount of time to count all the integers.
But with reals, it would take an infinite amount of time just to count to 1, or to .1, or to .01, or to .001, and so on.
You can pair integers to even integers, but you can’t pair integers to reals.
Quibble with the phrasing, not the intent. There is no way to “count to” anything in the reals, by the normal definition of “count to”. If you start at 0, what is the next number? If you pick one, you’ve gone past an infinity of smaller ones.
True, I was pointing out the futility of even trying to count the reals. With integers, you will give up before you get done. With reals, there’s not even a place to start.
Though your phrasing conveys that better.
I don’t believe that there can be physical infinities in the knowable universe, but there are tantalizing hints that there may be in unknowable ones. I’m not sure if this is a good definition of “infinity”, but one such hint is suggested by the Hartle-Hawking no-boundary proposal (below), and I thought it might be an interesting case. It describes a model in which spacetime is Euclidian, using a mathematical concept that Hawking describes as “imaginary time” but which he asserts may be more real than our mere illusory perception of the arrow of time.
The no-boundary proposal doesn’t imply a universe of infinite size, but simply one that is unbounded in the same sense as the surface of a sphere. But in Euclidian spacetime, time itself comprises the physical geometry of this surface. In this model there is no paradox of what happened “before” the Big Bang, because it becomes merely a coordinate on this unbounded but finite surface. The universe is not infinite in physical extent in this model, but it’s infinite from our perspective of temporal extent – it has no beginning in time and no end. If you could somehow travel back in time, further and further until you arrived at the Big Bang, what would happen if you tried to travel further? You wouldn’t – everything from that point is the future. From our perspective as mere mortals doomed to live with the arrow of time, such a universe is eternal.