With math there isn’t a place to start. Although I admit I don’t know near enough about it to say for sure, my understanding of quantum physics is that it is possible to start at a certain point in the real world. If we’re dealing with time, I think it’s possible to start at 5.39 x 10^-44 seconds. The next number would be 2x that and so on. That’s part of what I’m asking. Does it make any kind of sense, in the real world, to speak of a smaller amount of time?
Not given physics as we know them.
Which may only mean that we don’t know them well enough.
There isn’t any reason why something can’t happen in a time shorter than the plank time, it’s just that anything shorter than that is not meaningful in a way that we can understand. Virtual particles can pop up and exist for any amount of time, though the longer they persist, the rarer they are. That would indicate that as you approach shorter measures of time, there are actually more virtual particles and virtual particle interactions.
Either something happened at 10^-45 seconds, as well as 10^-46 and 10^-47 and so on, and we asymptotically approach t=0, or we go straight from one plank time to zero, and that implies a singularity.
We cannot, even in principle (by our current understanding of physics) measure any increments shorter than a plank time, but that doesn’t mean that there is has to be a granularity to time.
By this approach a hula hoop is infinite. (And thus a handy disproof of my assertion that you can’t have actualized infinities.)
Two things:
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That’s not the central point of the no-boundary proposal at all. The bit you quoted was just a preamble. The real point of the Hartle-Hawking model is the idea of Euclidian spacetime. The infinity that this suggests to me arises from the discrepancy between our perception of the arrow of time, and what may be the actual Euclidian “imaginary time” dimension hypothesized by the model.
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The second thing is that I already acknowledged that infinities are probably not possible in the knowable universe.
So, presuming that the six paragraphs on wikipedia are a complete and accurate summary of the theory (which seems like a reasonable enough assumption to me), if you were to scan backwards through the timeline, you would eventually roll back to a point where “time gives way to space such that at first there is only space and no time.”
Sounds to me like that would be the start of time. More specifically, it sounds to me the process of ‘banging’ initiated both the physical existence of observable space, and also the timeline that we’re experiencing while we observe that space.
ETA: I think when they say the universe has no origin, they mean that it didn’t come from anything else. No turtles all the way down.
This is getting off the topic of infinities so I don’t want to belabor it, but you’re still not quite getting the point. The Wikipedia description may be more or less accurate but it completely fails to describe Hawking’s Euclidian spacetime model and the “imaginary time” concept from which it originates. The article I linked describes some of the concepts better, but better still are Hawking’s own writings on the subject, though they may reflect his own biases (or my understanding of them). Our differences here are that what you describe is how we perceive time, whereas Hawking’s model implies that “imaginary time” is what describes the real universe, and it’s equivalent to a spatial dimension, and is equally finite but unbounded. In such a model, the question of the origin of the Big Bang becomes moot, because in that description it’s not a singularity at all and has no more special status than any other coordinate in spacetime.
I make a habit of perceiving time as a spatial dimension, actually.
if we simply all the other dimensions down to a single one, spacetime is a sheet of paper. The ‘beginning of time’ is the top of the sheet. The bottom of the sheet is either the end of time, or the present time, depending upon whether we’re just working our way through a static timeline to its conclusion, or whether it’s a timeline that is expanding indefinitely with us riding its crest.
So: the paper certainly has a beginning of time: the top of the page.
On the other hand, that says nothing about where the paper itself came from. It may exist within its own ‘ubertime’, but we don’t even have terms to contextualize that because our terms regarding ‘when’ or ‘where’ something happened are all relative to locations on the sheet of paper itself.
Sez you.
There are two questions here. Is there any actual infinity in the real world? And is there a mathematical infinity?
For the first, the jury is out and likely will forever be. For the second, there are many mathematical models of infinity. And in some of them ∞ + 1 = ∞ and in some it isn’t.
In set theoretic infinity ∞ + 1 = ∞, while in extended real number infinity, they are different. And there are many many models of each, but I won’t go into the details here.
“Forever?” (Grin!) This juror votes no: there is no such thing as “infinity,” for the reasons given above. Infinity “isn’t a thing.” It’s like the joke in The Phantom Tollbooth: you go in that direction forever and then turn left.
For any given real-world purpose, there is a finite number, N, which cannot be constructed, counted, or put into a one-to-one correspondence with any real thing. That is to say, not only is there no such thing as “infinite galaxies,” there isn’t even “Googleplex galaxies.”
That’s maybe true for things that have a beginning, a point where you can start counting, but it’s false for anything actually infinitely old. If the universe is infinitely old, there still isn’t any infinite timespan, because there’s no two points in time such that there is an infinite amount of time between them. It’s the same with the infinite real line: there are no two points on the line such that the distance between them is infinite, but nevertheless, there is no finite maximum distance.
There are an infinite number of energy levels for any free particle—in fact, there are infinitely many energy levels between any two energy levels for a free particle: its spectrum is continuous.
This whole ‘virtual particles pop in and out of existence’ is a bit of a problematic popularization, like the ‘rubber sheet’ analogy of general relativity. Yes, within limits, it has its uses as illustration, but when stretched beyond these limits, one gets nonsensical answers (as in the rubber sheet analogy: what, after all, is causing the planets to make dents in the sheet, if not gravity? Hence GR must be circular!!).
It makes arguably more sense to think of quantum field theory in terms of a fundamental ontology of fields, rather than particles, with particles just being an approximate notion, and the precise value of the fields ‘fluctuating’ across small scales (or perhaps even more appropriately being ill-defined). But then, the question just becomes, where do those fields come from? Why those fields? And indeed, why quantum mechanics (or field theory) at all?
You do realize that you’re quoting from an argument that, in my opinion, does a very effective job of demonstrating why nothing can be infinitely old? So you’re basically saying ‘your argument would be wrong if your argument was wrong.’
Once again this is rather explicitly not an actualized infinity - in fact every single emitted particle only has a single energy level. There are not an infinite number of particles being emitted, so there are not an infinite number of actualized energy levels.
This is actually a really good demonstration of how infinities relate to the real world. Infinities appear as instances where there is unlimited potential. Numbers can potentially get as large as you want - but no number is ‘infinitely large’. The universe could perhaps expand infinitely far - but at all times it is a finite size. There may be an infinite number of different energy levels that a particle could have, but it only will have one.
No, I’m pointing out that it hinges on a false premise: that for anything to be infinitely old, it must’ve had an infinite number of birthdays. But that’s not the case: an infinitely old universe, which is a perfectly consistent logical option, would’ve always been infinitely old; it would never have been, say, one year old, only to then age to infinity. That may indeed be impossible.
Or, take infinite extent in space: an infinitely large universe just pops into existence. There’s nothing logically troubling with that: nothing needs to traverse an infinite distance. But since, per your claim, you’re quite apt to think of time as spatial, as well, just take one of that infinite universe’s dimensions to be time: and you’ve got yourself an infinitely old universe, in which, however, no infinite timespan has ever elapsed. And your argument only attacks that possibility; hence, pointing out that this possibility doesn’t obtain in an infinite universe just points out that your argument doesn’t apply to an infinite universe. It would apply if the universe had to get infinitely old—if it had been born at some t=0, to then age infinitely. But that’s just a mistaken assumption.
No. In standard quantum mechanics, a particle typically won’t have a single energy level, but will be in a continuous superposition of all possible energy levels it could attain. Only in very specific circumstances will that collapse to a single value for the energy (and in fact, even there, the value will typically not be infinitely sharp, but there will be some continuous spread across an infinite range of possibilities).
It is the case that for anything to be infinitely old, it must indeed have had an infinite number of birthdays. That’s unavoidable - birthdays are the marks on the ruler. If you have an infinite ruler, it has an infinite number of marks. If you think that’s impossible, then your position is impossible.
If your position is not impossible, what will happen is that your universe will have had an infinite number of birthdays - none of which are numbered. Because it never had an age and never will. And any deity that popped into existence with an infinite past scrawled into their backstory will only be able to articulate intelligently from a time 0 of its own making. For example, if you ask it what its first word was, it will either remember - meaning that prior to that point, there was an infinite expanse of no words, or it will not, because words are scattered about across its entire prior existence with no beginning that can be recalled. Everything will be like that - there will be a set of things that it actually remembers as distinct events starting from a point (and the things need not all use the same point) or it will be “events” that are really just a random or repeating part of the terrain - the grain on the wood of the ruler.as it extends in no notable way into the infinite past. (Birthdays would be an example of the latter type of thing.)
Let’s try and be precise. Your argument, if sound, establishes that there are no infinite timespans—no infinite durations. Nothing can endure an infinite time passing. You claim that this then disproves a temporally infinite universe. This necessitates a commitment to the thesis that every temporally infinite universe necessarily includes infinite timespans.
A timespan is the time elapsing between two moments, t1 and t2. Then, a universe that is temporally infinite and whose temporal axis has the ordinal structure of the real line doesn’t include infinite timespans: for all t1 and t2, |t1 - t2| < ∞. Hence, it’s not the case that a temporally infinite universe includes infinite timespans—nothing ever sat around waiting for an infinite time to pass; no clock ever has ticked away an infinite number of seconds. There is no moment t1 in the past such that between then and now, an infinite amount of time has passed. This is the same as how, for a spatially infinite universe, there are no points x1 and x2 such that they are infinity kilometers apart.
Hence, the premise that every temporally infinite universe must contain an infinite timespan isn’t correct. There are conceivable universes where that is the case, whose temporal axis has a different ordinal structure, but it’s not true in general. Hence, your argument doesn’t establish that a temporally infinite universe is impossible.
You confuse yourself by thinking about ‘first’ somethings. You imagine that the universe must’ve come into being at some point, and if it’s infinitely old, an infinite amount of time must’ve passed since then. But a temporally infinite universe has no first moment: that’s what it means to be temporally infinite. There is no point such that an infinite amount of time must’ve passed since then, and without that, your argument just fails to apply, even if in itself it might be perfectly sound.
I find “Time just appeared out of nowhere 14 billion years ago” to be just as illogical as “time’s been going on forever”.
“Something of infinite age must have had an infinite number of ‘birthdays’, which is impossible, so nothing is of infinite age” is not only circular logic, it is also contradicts a just as circular argument for the infinite age “Anything with an age was preceded by something else with an age. So existence is infinitely old.”
But time is relative. It all depends on your definition of time.
The most accurate models thus far seem to imply that even black holes evaporate, eventually. And some physicists think that even subatomic particles have a half-life. If that’s the case, as the universe expands, and black holes evaporate, and matter decays away, and everything flies apart faster and faster, eventually you reach the heat death of the universe. Maximum entropy.
At that point, is time continuing infinitely onwards? If time is relative, and there is nothing, how do we measure time? Time relative to WHAT?
And by that same logic, rewind the universe until you’re back at the singularity that led to the big bang. All matter and energy in one arbitrarily small point. Again, there is no change here, no energy gradient. The entire universe is static: full to absolute capacity with energy. How does time exist here?
When the big bang happens, the universe expands. Energy and matter change forms, move around the universe. Change is happening. Now we can meaningfully speak of “time”.
Actually I confused myself by entertaining your thesis. You yourself have made half of my upcoming argument for me, though, so I should be able to make myself clear here.
Yes, a universe with an infinite past can in theory be handwaved into existence. But, as you note, there is nothing that has experienced the infinite past. Everything that exists, everything that has been instantiated (which is a word I have been repeatedly saying for a reason) has a defined start point at which it started experiencing time ‘our way’.
And the universe as we know it qualifies as a thing that exists. The whole ‘infinite past’ thing is actually just a giant sea of nothingness within which instantiated objects can appear, experience time, and then cease to experience time. (Or continue to exist indefinitely.)
But wait! Hope is not lost! Because:
This is actaually wrong. It is true (and non-circular) that nothing has experienced an infinite number of birthdays - everything that is experiencing time in the left-to-right manner we are has been doing so for a finite amount of time with a definitive start. However this does not mean that there is some ‘start of time’ before which there must necessary have been nothing at all. That infinite expanse of ‘before time’ doesn’t have to be unvaried; the infinite ‘nothing’ can have ‘terrain’. Each rock and pebble floating scattered across the landscape of the infinite past must itself have experienced only a bounded, finite existence, but there could be an infinite repeating (or random, or patterned) sea of such objects.
For an example, let us presume that the terrain of history includes a bunch of Solomon Grundys. Each Solomon Grundy is born on a Monday, christened on Tuesday, married on Wednesday, takes ill on Thursday, grows worse on Friday, dies on Saturday, and is buried on Sunday - and that’s the end of that Solomon Grundy. However just as Solomon Grundy always experiences a week, in this universe every week always experiences a Solomon Grundy. All the way back into the infinite past which day of the week it is can be calculated, resulting in an infinite number of Sundays, and a correspondingly infinite number of Grundys that came into existence, lived, and died. No single Grundy experiences infinite time, since that’s impossible, but Grundys are a feature of reality and there has always been a Grundy, all the way back through time. (Well, except on the saturdays.)
If an eternal chain of Grundys doesn’t do much for you, you could swap them out for universes. There could always have been a universe - not a single infinitely old universe, but an endless series of them, extending back through time with each big bang preceded by a previous universe’s big crunch.
Or, to put in in a TL;DR way, the following thing I said earlier:
This was wrong. There is a very appreciable difference between an infinite regress of discrete things and a single thing that’s lived forever: the former is theoretically possible, but the latter is nonsense.
There cannot possibly be an eternal god that has existed forever. (Which is why when you try for it you get a bunch of contradictory conclusions like having had birthdays without age.) However a series of discrete things is theoretically possible - foliage on the terrain of history. Eternal gods are impossible, but there could be turtles all the way down.
This whole discussion demonstrates what I said above. We don’t know if either time or space is infinite and likely never will.
One thing to note is that the so-called entropy death of the universe is only an asymptotic phenomenon that can never be reached. There will always be some free energy. There could even be life forms that continue to exist. They would be very very large and, by our standards, very very slow. It is known that there is no minimal energy needed for a computation. Non-zero, but no lower bound.
Yeah, no. You were right the first time and have just shown that your argument against an infinitely old existence of existence is nonsense.
I don’t understand what’s wrong with me saying “an infinite amount of time shall pass after this very second”. I have always operated under the fundamental assumption that time always advances. There may be disagreements about how far backwards time goes, but I am not aware of any theory whereby time is limited in the future.
~Max