Never ending outer space..... Outer space is never ending and infinite in size. At least that's what I assume. The confluence of events that it took to create earth the way that it is and the galaxy that it is in was like a 1 in a centillion to the centillionth power event. Being that outer space is infinite and never ending, that would mean that earths, EXACTLY like the one that we are living on, have been created an infinite amount of times. Because there are an infinite amount of centillion to the centillionth powers in infinity. Is this logic correct??
Re: Never ending outer space..... Welcome to PF, We don't know this for sure. Some versions of the standard cosmological model (those said to have"flat" or "open" geometries) are spatially infinite, whereas others (said to have "closed" geometries) are finite in spatial extent. EDIT: I should say that the best observational evidence to date points to the universe being very very close to having a flat (Euclidean) geometry. Are you just guessing??? :tongue: You do realize, that in order to calculate this probability (EDIT: assuming it is even possible), one would have to apply a great deal of rigourous thought and physical principles? Furthermore, the calculation would probably require input information that astronomers still don't entirely know, or are just starting to get a handle on, such as how frequent planetary systems are, and how frequently Earth-like planets form within such systems. If you just picked an arbitrarily large number out of the air in order to make the point that this probability is vanishingly small, then I whole-heartedly agree. Especially when you factor in the part about the planet being "exactly" the same, right down to the development of life and history of events. Abuse of concepts like "infinity" aside, I think you're forgetting that the universe has a finite age. Given an infinite amount of time as well as of space, then it is conceivable that a duplicate Earth (or infinitely many of them) could emerge. However, I assert with some confidence that over the age of the universe so far, the number of planets to emerge that are exactly like Earth in every way is ZERO.
Re: Never ending outer space..... Now that I think about it some more, given that we don't even know if the problem is well-defined (i.e. whether it is possible to define/compute the probability of said event), I am not sure if I can assert anything with confidence, nor am I sure whether both an infinite amount of time and an infinite amount of space are required, or whether simply having an infinite amount of space is sufficient. Assuming that we can define the probability of what you describe, and assuming that it is non-zero, then that would lead me to be believe that we could compute the expected number of such identical planets that would occur per Hubble time (age of universe, essentially) and per Hubble volume (i.e. volume of the *observable universe* -- the part of it that we've had enough time to be able to see so far). Since this number is (speaking in the hypothetical) non-zero, and if there are infinitely-many Hubble volumes in the universe, then naively I WOULD expect there to be an infinite number of extant duplicate Earths. So I may have spoken too hastily before. I don't know the answer, or whether there is even a well-defined answer.
Re: Never ending outer space..... I'm hypothesizing a "flat" or "open" geometry. Yes, I am guessing. Um, isn't that what most of this is????? LOL!....the number "1 in a centillion to the centillionth power" is just meant to show that Earths creation and its development and sustainability of life as we know it happened against EXTREMELY long odds (to say the least). The frequency of how often planetary systems like Earth are created is mute when you are considering infinity (or the abuse there of). I am not purely discussing OUR universe here, and I am aware that OUR universe has a finite age. I'm am discussing the vast expanse, known in laymen terms, as outer space. Which, as I mentioned in the 1st sentence, is infinite for the purposes of this discussion :)
Re: Never ending outer space..... Fine. I didn't realize we were dealing with a purely philosophical discussion here. But even given your starting premise(s)/assumptions, I don't know what the answer is. As I outlined in my second post, naively, I think, yes, there would be infinitely many Earths after a Hubble time. But I could be wrong...
Re: Never ending outer space..... I don't think "time" is relevant for the purposes of this discussion. Given an infinite amount of space and the smallest odds of something happening simultaneously in that infinite amount of space, time is irrelevant, in more ways than one.
Re: Never ending outer space..... this is going to sound stupid........and make fun of it if you so desire......but if I give you every possible ticket for the lottery today, you're going to win, no matter what the odds are, they become irrelevant...........if I give you every possible combination and ticket again the next day, you're going to win again. And this is a stupid small example of how I think of infinite space. It's never ending (for the purposes of this discussion). So, (for the purposes of this discussion) this Earth has happened an infinite amount of times and at the same "now" that this Earth is currently existing, albeit, infinities away from here :)
Re: Never ending outer space..... and I am aware that "infinities" is not a viable concept....lol.......it was just a bit of hyperbole on my part :) :)
Re: Never ending outer space..... I was just trying to use some careful reasoning to arrive at the conclusion that you take to be obvious. My reasoning was as follows: if the probability of forming a planet exactly like Earth is vanishingly small but non-zero, then the expectation value for the number of Earths that would occur per Hubble volume and per Hubble time is probably non-zero. Therefore, naively (i.e. taking that result at face value), given that there are infinitely many Hubble volumes in our hypothetical universe, I would expect there to be infinitely-many Earths. I don't think time is totally irrelevant to the discussion. You can't form an Earth when it's so early that the universe is so hot and dense that stable atoms don't even exist. You can't even form an Earth after the universe has cooled somewhat, but just consists of a mostly smooth/homogeneous distribution of neutral hydrogen gas with only a few small density fluctuations that haven't grown yet under their own gravity to produce structures. You still can't even form an Earth after the first luminous, self-gravitating objects (e.g. stars) have formed, but not enough time has passed for them to produce heavy elements (that planets are made out of) and to die and spread those elements throughout space. My point? There is some earliest time before which a planet cannot exist, let alone one that is exactly like the one we're sitting on now. So I imagine that the probability is a function of time, and if we were somehow having this conversation at some other epoch, the answer would be different. You may have an infinite amount of space, but it matters when.
Re: Never ending outer space..... The things you mention here like "smooth/homogeneous distribution of neutral hydrogen gas" and "first luminous, self-gravitating objects" are all things that happen simultaneously in infinitesimal probabilities.....I understand that......but in an infinite amount of space the infinitesimal probability does not matter.......meaning that they can happen an infinite amount of times ,at the same "time", simultaneously.
Re: Never ending outer space..... I once attended a lecture by Dr. Ken Krane, he used a very similar argument about an infinite universe to show that a traveler could not tell if he has arrived at the identical world which must exist in a infinite universe or returned home in a closed universe. The question being, of course, is the universe open or closed.
I am sorry but I do not understand what you are saying here at all. Integral -- good to know that smart people who've actually thought about this somewhat confirm our naive view
Re: Never ending outer space..... Although that's interesting, becuase I guess Crane's scenario for the infinite universe involves happening upon an exact copy of our entire local universe including clusters, the local group, the milky way, the solar system etc. How else would one be fooled?
Re: Never ending outer space..... Infinites invite paradoxes. Let's start with what we do know. We can say with some confidence the universe has a finite age. The spatial part is unclear. It might be finite and unbounded, or, it might be infinite - with nearly all of it forever beyond our observational reach. I have issues with that. How can a spatially infinite universe be temporally finite? And if it is spatially infinite, what observable effects might that have on our comfortable little patch?
Re: Never ending outer space..... I think we have to take "identical" literally. So if the sky were different it would not be a identical copy of earth.
Re: Never ending outer space..... Hey Guys, I have given this a fair bit of thought so here goes: In order to have an EXACT duplicate of Earth, and when I say exact I infer identicality down to the configuration of individual atoms. That being said the Earth is being constantly bombarded by photons from our own hubble volume (in various EM wavelengths.) That being the case an identical Earth2 would need to exist in an identical hubble volume for Earth2 to be identical to Earth, within an identical Milkyway2. An exact duplicate of Earth cannot exist unless it exists in an exact duplicate of Milkyway.. ad infinitum until we are at the hubble volume size and causal disconnection takes effect. EDIT: Saw Cepheids post outlining this above after my post. (Post 13) It is possible to take a small amount of finite states and give an infinite amount of time and never repeat the same initial states so equally possible that an infinite amount of initial states over a finite time do not repeat the same configurations. The whole idea of another world with another me and everything the same... for some reason I just cannot accept that even an infinite Universe would repeat the same configuration exactly., although in fairness the Universe does not require my acceptance.
Re: Never ending outer space..... Yes I think "identical" by definition would need to include the entire OU for everything to be an exact duplicate.
Re: Never ending outer space..... Actually that seems to make sense to me. If you say that by duplicate you mean duplicated right down to every single last detail, everyones thoughts and actions and everything, even random events, then that would "seem" to require that everything observable at each point in time is identical in every way as well. But what do I know...I'm just a wikipedia scientist.
Re: Never ending outer space..... This is exactly as I understand it, the entire cosmos we see would need to be duplicate or earth would - eventually deviate from identical. Thoughts and actions and even quantum randomness would need to be the same, EVERYTHING. I just think it extremely unlikely to have an EXACT earth copy, primarily because I think it would require an identical hubble volume. Then consider this; a galaxy on the ege of our Observable Universe would need to exist within an identical OU of its own to the one that exists within earth2 observable Universe, because if that galaxy had a different OU then the galaxy evolution would be different and have a knock on effect on everything else. As I mentioned earlier it is mathematically simple to show a finite value set with an infinite time set and never repeat initial configuration but when the value set could be infinite then who knows!
Re: Never ending outer space..... There is no need to have an infinite universe in order to find a duplicate hubble volume. Since the entropy of the universe is less than 10^{121} (the Bekenstein bound, the actual entropy one can account for is considerably less) there are at most ~10^(5*10^121) available microstates. So, one would expect to find at least one out of 10^(5*10^121) hubble volumes in the universe is exactly like ours, all the way down to the atomic scale everywhere within it. Since we live in a three dimensional space, one should expect that the nearest duplicate hubble volume is no more than ~10^(1.7*10^121) hubble radii away (though it is essentially the same number in meters, units don't matter much when the uncertainty in the exponent is this large (for reasonable unit choices)). On the other hand, the universe is not known to be flat enough to be so large.