Can an infinite universe with infinitesimal detail be nonrepeating?
... since it's infinite, it doesn't have to repeat itself right? (... umm...is this an astronomy question?... -.-)
a single infinite universe might not repeat if complexity and novelty increases without limit- but there are only a small number of elementary particles and just 92 natural elements- if the actual nature and parameters of spacetime change over vast regions and there is no limit to these variations- then uniqueness might be possible [but probably not]-when you start to consider the kind of nested transinfinities you get with an infinite/eternal multiverse would require infinite repetition of any possible finite form/pattern-
ultimately I don't think you can avoid having an infinite number of yous-
What does the large but finite number of distinct particles relate as to the possible infinitude of the universe?
Since the universe has a particle horizon, the question is not physically meaningful.
How does the universe impose a virtual particle horizon (and thus limit the possibility of actual particles approaching infinity) if the general consensus is that the physical universe is unbounded?
The universe is observationally finite - about 13.7 billion light years. That does not mean it has a physically meaningful boundary.
What kind of distance are you employing? I usually like to use the comoving radial distance. In this kind of distance, the radius of the observable universe is about 47 billion light years. The formula for the comoving distance to the particle horizon at a particular cosmic time t is:
D = c \int_0^t dt/R(t)
A teaspoonful of Infinity, please.
I have come to think of "Infinite" as meaning unfinished, having no end, so no limit, no boundary. But one must be more descriptive. Objects commonly can be unbounded in some dimensions, bounded in others. I suppose we may consider the universe as an object.
For example the surface of a sphere, if very large and considered very locally, may be described by only two dimensions, say x and y, altho on earth we use North and East. We could say that the surface of the earth, as far as we are concerned, has no boundary in x and y, but actually this is a convenient lie.
x and y are actually tangential to the curved surface, so we have to correct every so often. Either we have to apply a curve in the z direction (up and down for earthlings) or we have to put some kinks into the lines. Ever look at a geodesic survey map and find places where the longitude lines take a break, ending in one place and starting again over to the east or west a little bit?
It seems to me that I have seen a place on a map of the great plains states where a road following a section line north-south has to take a pair of close right angle turns to stay between adjacent properties.....
Anyway, a closed surface such as a sphere can be infinite and unbounded. Think of a fractal line, like a coastline. Just exactly how long is the coastline of England, for example? If you are very careful and pace it off you will get an answer, but if you are less careful and just measure it with a portage rod, (16 feet long) you will get a different answer. Is one answer right and the other answer wrong? Well, if you measure it with a centimeter stick you will get a different answer again. The answers don't even have to be close!
Think about measuring the coastline in say, Angstroms. How many atom widths are there in the coastline of England? Well now we have to measure every nook and crannie, every variation in every pebble. Since the coastline is changing all the time as waves go up and down and rearrange things, we really find that at small scales the answer is statistical. You can't just measure it once and get an answer. Next time you measure it, there is a different answer. So you have to measure it a lot of times and average to get a reasonable approximation.
So the length of the coastline is longer in inches than in miles. If you measure it in miles, you can skip a lot of fine features. If you measure it in inches you end up going around a lot more little stuff like boulders and sunbathers. A fractal line, such as a coastline, can be infinitely long and unbounded on the surface of a sphere, such as the earth.
Now the really interesting question is, if you measure once around from Greenwich to Greenwich, do you arrive back at the same Greenwich where you started out? Well, no, it is not exactly the same Greenwich, is it? Greenwich is moving. England is moving slowly away from France, the planet is rotating on its axis, the axis is orbiting the sun, the sun is orbiting the galaxy, the galaxy is drifting toward the Great Attracter, and the Great Attracter is just a little bump on the wall of a huge expanding bubble. Urp.
And you wanted to ask about infinities. Huh. Better not ask. If you think about it too long, it will give you indigestion.
Better question, maybe, is an infinitely long line open or closed? Hmmmmmm....
Loren: if this is truly your question, it's in the wrong place; IMHO it's a philosophy question. Why? Think science; how - in your wildest dreams - could you imagine this may be amenable to observational or experimental testing?
Wow! And would you like chocolate sprinkles on top?
Loren, it's so theory-laden it makes no sense. Or, it's just a question of what 'the possible infinitude of the universe' means within GR+QFT. I'll happily copy your post into the SR&GR section (also the QM section) if this is what you are asking.
In terms of Loren's question, this is no different from Chronos' answer; a large (finite) number is trivial wrt 'an infinitude'.
nightcleaner: interesting speculation. Without wishing to be too rude, what does this have to do with the science of cosmology?
Thanks to you for your offer, Nereid - copy this thread wherever you think it would be best received. My post is based on the Scientific American article by Max Tegmark, "Parallel Universes," May 2003. Skim over that essay when you have the chance, with my original assertion in mind:
Can an infinite universe with infinitesimal detail be nonrepeating?
(See also Max's website at http://www.hep.upenn.edu/~max/multiverse1.html.)
I am familiar with that article and hold Tegmark in high regard. But he is being philosophical, not scientific, in that article. That is all Nereid, meteor, and I were addressing. It does not matter how 'big' the universe is in 'reality'. The only thing that matters, wrt science, is the portion of it we can actually observe and use to validate [or invalidate] our notions of reality. That is the scientific method. I have no objection to speculations. I even have a few of my own. I try not to confuse one with the other.
Possibly I shouldn't be tresspassing in cosmology, and I apologise, for my sparks often go off in unexpected directions. I mean no harm and try not to burn anyone's house down.
Anyway, I commented because I thought I detected a misunderstanding of the idea of what infinity is. Many people think infinity is someplace far away, like the end of the universe or something like that. I wished to help Loren with his question by pointing out that infinity can be held in the palm of one's hand.
As you have already noted, the question is really more philosophical, or perhaps mathematical, than it is cosmological, or even scientific. Infinity and zero are both inconvenient numbers in science, which is more interested in things which are countable.
But ok, since you ask, let us suppose for a moment that the universe, whatever that means, goes on out to infinity (and beyond! to quote Buzz Lightyear.) Does this mean that any sequence we encounter in the universe (say the sequence we encounter in this solar system, for example) has to be repeated, in infinity, an infinite number of times? Well the answer is yes, sort of.
If you set out in your lightspeed ship and set your sensors to alert you so you can stop the next time you encounter a planet exactly like Earth, how will you know if you have found a repeat of Earth or if you have gone all the way around the cosmos and just come back to the same old Earth as the one you left? If they are identical, you can't know, can you?
Perhaps you will object, and I believe rightly so, that it is unreasonable to expect to actually find a repetition of this sort even if you do have a lightspeed ship. But what if we imagine infinity in a teacup? Should there not be repetitions of some sort there that we can actually hope to observe? Well at least we don't have to deal with the problems of a lightspeed ship.
And, in theory, we do see repetitions of various kinds in a teacup. After all, it is all tea, isn't it? If you look on one side of the cup, it is tea. Other side, still tea. You can take a milliliter from one side of the cup and exchange it for a milliter on the other side of the cup, and it is still the same cup of tea, isn't it.
On a finer scale, there are electrons and then there are....electrons. One electron is not much different from another electron. Do we really know we are looking at a lot of different electrons, and not just the same electron, over and over again? Well it is the repetition of infinity problem again, isn't it?
Really, the question is, what exactly do you mean when you say it is the same? What qualities must an object have to ensure that we will all agree it is the same object as it was in a previous time frame? The pool ball you strike with the cue is the same pool ball that falls in the corner pocket, right? Well it is when I am playing pool anyway. But never mind that, let's say that we follow the pool ball closely and watch it every instant and as it crosses the table it never once gets crushed by a passing meteorite or even experiences so much as a single beta decay of a proton. Are we justified in saying that it is the same pool ball on falling in the pocket as it was struck by the cue?
Statistically, yes, it is the same. Explicitly, in terms of all of its parts, no, it clearly is not and cannot be the same. Photons and electrons and other sorts of stuff are jumping around all over inside of that little ball. It is only the same ball grossly, if you don't look too close from one instant to the next. Meanwhile the changes it has undertaken are immense, perhaps infinite, certainly uncountable. But we ignore all of that when playing pool.
Now in cosmology, and I am sure you know more about this than I do, but I will risk sticking my neck out here anyway, since you have been so kind to smile on my little speculations, in cosmology, I say, there is a problem called the horizon problem, which has to do with why the universe is so self consistant. You look in one direction, and it is pretty much the same as if you look in the other direction.
Maybe we look forty-four billion years back in one direction, and forty-four billion years back in the other direction, and we notice that the two sides are pretty much the same, even though the universe itself is only thirteen point seven billion years old, and we get rather excited by this and ask how it can be that they can even exist that far apart, much less how they can be so much the same. There can have been no exchange of information, no thermal equalization, no cosmic teaspoon to stir the cup. Those two horizons have no way to know what the other one looks like, no time to make themselves up to look the same. You might be as surprised if all the glamor stars showed up at the awards ceremony one night wearing the same gown! Never mind how we know it is the same gown, or how we can assert that all of them will fit in there. It happens. We are surprised.
I love the stars, although I will admit that I once ran into the house because I was suddenly afraid that Gemini was going to get me. But how do we know how many of them there are? How do we know that, when we look at a galaxy in Alpha quadrent that it is really a different galaxy than one we see when we look over there at in Gamma? Couldn't the light have gone all the way around the cosmos and come back to us, like G_d looking at the back of his/her own head?
Now don't tell me that there hasn't been enough time for light to go all the way around the cosmos until after you explain how there has been enough time for the cosmos to outgrow it's Buzz Lightyear pajamas. How did the cosmos get to be forty-four billion light years in radius in only thirteen point seven billion years?
Call it inflation. Call it a teacup. The truth is we don't know what is going on, for all of our science and love of the stars. Dark matter and dark energy. What a load of speculation. These are not answers. They are only more distant questions. Sometimes, although I love to think about these things, I finally have to conclude that we would be better off growing corn.
Thanks, and by the way, it didn't do any good to go in the house. Gemini got me anyway!
While Wikipedia is not a rigorously scientific and peer reviewed source, it offers a sensible answer to the fundamental question:
The reader should be warned that both popular and professional research articles in cosmology often use the term "Universe" when they really mean "observable universe". This is because unobservable physical phenomena are scientifically irrelevant (i.e., they cannot affect any events that we can perceive, and therefore effectively do not exist.
the problem I have with your view- Chronos- is that any discussion of the origin of the Universe/Multiverse or of Infinity is necessarily an Ontological discussion- and Empirical Science is a part of Ontology but not the whole of it- since Physics by it's very nature cannot access absolute fundamental and self-evident aspects of existence- one must turn to various logics when dealing with the basic questions of the nature of existence and the nature of Infinity and Finity and of Being/Motion- once one determines some feasible logical framework- only then can science be used as a tool to determine the physical processes that emerge from that fundamental structure [which is why ontological discourse is not "scientifically irrelevant" as you say- for the fundamental structures of existence determine what cosmologies can actually exist and science must build models which predict the nature of the reality that emerges from the fundamental absolutes]
so then- Chronos- you attempt to constrain and define the fundamental absolutes of existential structure of the universe by trying to limit yourself to the method of strictly empirical science which cannot by DEFINITION deal with these existential/ontological absolutes and axiomatic logic structures- such a limited approach by others in physics is the heart of why the Anthropic Principle still confounds so many otherwise intelligent people-
and this notion that "unobservables=non existence" works only for controlled experiments on closed systems! you cannot apply this to the origins of Existence! before the discovery of optics and the invention of lenses- Science would have to say that anything too small to see with the human eye was "unobservable- and so scientifically irrelevant and thus non-existant"- but the plagues didn't care and killed us anyway- to say that our very primitive and incomplete scientific models of the universe can now tell us what is and isn't observable or will physically affect us is absurd and hubristic-
these issues are at the heart of why theoretical computer science and mathematics are out-pacing theoretical physics in answering and dealing with the fundamentals of existence
That which is unobserved is not the same as that which is unobservable.
If there are branching universes then they are in theory observable at the point of branching, and maybe for an instant or two or three beyond that point.
This kind of observation would not be like peering into another room through a tiny hole. During the instants of separation the two universes would be intimately connected in every part. One would see the other growing very large, or becoming very small, or dropping over some other kind of horizon.
And what about the past? You cannot observe Napoleon at Waterloo, or Plato in his cave, or even re-witness your own birth, but surely, I hope, you are not one of those who deny history.
And what about the present? We observe continuity in motion all around us, but Zeno taught us there is something rather mysterious about our observations. And tell me, where is Andromeda this instant, when we will not see her light for some sets of hundreds of thousands of years? You and I will never see her light right now at all. Shall we deny that Andromeda has any existance in our universe in the sense of Now? Hardly worth setting out for the grocery story around the corner for a loaf of supposed bread if we reduce that argument to absurdity. Where is it now? Oh, well, we cannot observe it now so it cannot exist so there is hardly any point in going out to get it. Try telling that to your hungry kids.
I would not deny that there is effectiveness in the scientific viewpoint that the unobservable is irrelevant. It allows us to focus our thoughts on what we can do rather than worry about what we cannot do. But let's not blunt Occam's razor by claiming there is no other half.
BTW, if there are branching universes, should we not conclude that there may be converging ones also? nc
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