It doesn’t follow. There is still only one direction where entropy increases. If entropy stops increasing (assuming that for the sake of arguement), that does not change the fact that there is only one direction where entropy ever increased.
~Max
I didn’t say time would loop, I said the state of the system might loop over time.
~Max
Time is a part of the system. For the system to loop “over time” implies that time is somehow apart from the system and measures its states. But that’s not how time works under general relativity.
There’s a good chance I don’t properly understand general relativity. I believe you wouldn’t use time as an absolute reference to the state of the system, but spacetime. So you could say the state at (x,y,z,t=0) is identical to the state at (x,y,z,t=5), or t=10, 15, 20, etc for constant x,y,z.
~Max, no longer confident he knows what he’s talking about
Unless I’m way off-base, it doesn’t make sense to say time loops because t would be from the frame of reference, which is apart from the system being measured. So yes, time still advances, and it’s still infinite.
~Max
Imagine a tiny universe with a small handful of particles and different laws of physics that mean a closed system can perfectly retain energy rather than lose it over time.
You have 5 particles orbiting each other in a complex system. None of them change over time in our pocket universe.
The five particles go through their orbits. Each starts at a set of x,y,z coordinates at t=0.
Now, imagine that the orbits of the particles take them on a closed loop. Remember, this universe has slightly different physics, so there is no loss of energy here.
At t=100, every particles is back where it started at t=0. At t=101, the particles follow the same path that they did at t=1, looping again at t=200.
From within this universe, I would argue that there is no meaningful difference between t=1 and t=101. You may as well say that t is back to 0. Even if some hyperdimensional aliens are looking at our pocket universe and their hypertime keeps incrementing up, time within the pocket universe loops.
The difference is that in our universe there are a lot more than 5 particles, and because the total energy in the system decreases as t increases, we can never have all particles return to their prior state. So a time loop is impossible.
That’s an assumption that doesn’t need to be true. Objects within an infinite universe could just as well be temporally infinite. Only objects that came into being at some particular point in time can’t have experienced an infinite time since then, as there’s no point in time since when they could’ve experienced that infinite amount of time. But temporally infinite objects don’t come into being at any particular point in time—that’s the whole business of being ‘temporally infinite’. Instead, at any point in time, they’ve already always been around. So the fundamental particles in an infinite universe, i. e. those particles that can’t decay into others, could just as well be infinitely old—which doesn’t mean that they’ve experienced an infinite amount of time passing.
So, in that universe, there’s an actualized infinity of Solomon Grundys, no?
No; such an entity would simply always (that is, at any given point in time) have been infinitely old—which does not imply that it has experienced two moments in time such that between these two points, an infinite amount of time has passed.
Again, that’s just false. There can’t have been (we stipulate) an infinite amount of time between any two moments; but that’s not enough to entail that ‘the entire instantiated timeline is finite’. It means that any entity that comes into being (at some point in time) only experiences a finite amount of time up to any given point, but that’s a very different thing, and in particular, doesn’t exclude entities that have always existed, as those necessarily don’t come into being at any particular point in time.
Nope. Keep in mind that we’re talking about entities that are interacting with time as we do - one moment after the next after the next. This means that to get to the present time they will have to have counted up through time, experiencing all that time, counting up to and reaching infinity in order to have lived through all the prior time and ‘caught up’ to the present moment. This is impossible, so entities that have experienced infinite time are impossible.
Yes - though not all at once, of course. (And for a rather fuzzy definition of “universe”, since the universe-as-we-know-it is experiencing time, and thus started at a finite point in the past - a time near the big bang, specifically. The scope of time that includes all the Grundys extends into the arbitrarily-defined infinite past.)
As noted, I see convincing argument that this is impossible. (The fact that you’re literally talking about an entity that doesn’t get older as it ages is a hint of this.)
In that post I was literally just talking about time in our universe, as I made clear with my mention of the big bang.
Max_S and I were discussing time going forward indefinitely. Whether or not there is also a timeline extending infinitely into the past too was largely irrelevant to the discussion and would muddy the terms, so I avoided the possibility there.
back to the OP, would the density of a black hole count as infinite?
Unless I misunderstand you, you describe a system in equillibrium. In such a system the concept of time is undefined; entropy never changes and all measurements of state are the same.
Distinguishing between “hypertime” and time is just a semantic trick. Hyper-dimensional aliens (that is, you and I) will describe the pocket universe using what you call hypertime, which is just normal time in their frame of reference.
~Max
And it is possible that there existed life, civilizations, and intelligence in the 10^-45 seconds range after the big bang. They would look forward in time, and see that it would soon be an empty featureless void, exactly the universe we call home today.
In any case, there are schools of thought that declare that the nothingness of the heat death would be unstable itself. If we reached a point where a patch of space no longer contained anything in it, then it would eventually spontaneously undergo inflation and start up a new universe.
So, to bring this to the thread, if this school of thought were to be validated, if we were able to prove that this universe sprang from the ashes of a prior one, and that a new one will come along once ours is used up, how could anyone say when it began, a sequence like this could not have a beginning.
If this version of conformal cyclic cosmology is the nature of the universe is correct, then time is in fact infinite, in both directions. And of course, if the universe has been expanding for an infinite amount of time, then it is also infinite.
Entropy doesn’t change, but if you come back to the system at t=1, t=45, and t=99 you will find different states. You can look at an image of the system and figure out what t it was taken at (between 1 and 100) but not which cycle it is on. So I think time must have some meaning, no?
If the universe is expanding, it can’t be infinite because, as far as I know, something can’t get larger than “infinite”. On the other hand, if it is contracting, something getting smaller by the moment can’t be infinite, either.
I don’t believe black holes have infinite density by definition, only that they are predicted to eventually reach that density. So you can actually calculate the “density” by taking the mass and dividing it by 4 * pi * r_s^3 / 3, where r_s is the Schwarzschild radius and the divisor is just the volume of a sphere.
~Max
I can’t be sure I’m using the word the same as everyone else, but when I speak of hypertime I’m speaking of something completely separate and independent of normal time. It’s certainly more than a semantic difference.
Hypertime relates to our time like we relate to the timeline of a movie on videocassette. To us the entirety of the movie’s timeline exists at once; we can look at all the moments of the movie at once or in any order. We can rewind it, fastforward it, jump around in it; whatever.
When we speak of a timeline growing in hypertime, that’s analogous to somebody splicing additional footage onto the end of the tape. It takes time in the outer world, but in the world of the movie the new time is just suddenly there.
Unless it started out as infinite in the first place.
We only know what little bit of the universe we can see. Based on what we can see, we know that the actual universe is many orders of magnitude larger than the observable universe. Whether it is infinite or not, we are not sure, but there is no reason to believe that it ever had a boundary in the first place.
It would if one of the two quantities in density were infinite for a black hole. But do we know that black holes are infinitely small? I’m guessing that that they are known to not be infinitely massive.
But the Schwarzschild radius isn’t the black hole, it’s the shroud that surrounds it, the point of no return. We really don’t know what is going on inside it down at the center, because our standard laws of physics sort break down. It is possible that the singularity is really singular or maybe it isn’t. But given that the OP allowed for “possibly infinite” I think that this would qualify. (unless Chornos steps in and says I’m full of it.)
I think the difference between time looping or continuing forever under Poincaré recurrence is one without distinction. Simple division can be used to obtain a value within range; even if time itself does not properly increment forever, all calculations and theorems will work if you use a number out of range. It can even be said that recurrence is itself never ending and therefore infinite. So I think I win this argument either way. 
~Max
Well that’s my point though. There is no time independent from space. So if your spacetime universe fully cycles around such that all particles are back where they started in space,
So - if a looping universe returns to the same time, effectively - a static universe at either the big bang end (all matter and all energy is in one singularity) or the heat death end (no energy or matter anywhere in the observable universe - or a big rip scenario where each subatomic particle is on its own, every other particle having slipped over the event horizon of the observable universe) has no time at all, because there is no change of any kind to measure the time relative to.