January 25, 2013 report
You don't exist in an infinite number of places, say scientists
Francisco José Soler Gil at the University of Sevilla and Manuel Alfonseca at the Autonomous University of Madrid have looked at two different proposals – one based on classical cosmology and the other on quantum mechanics – that contend that we live in an infinite universe in which history is repeated an infinite number of times in space. They have picked apart both proposals and argue that both are highly speculative, despite often being presented as plausible ideas. Moreover, they argue that we really don't know whether we live in an infinite universe, as a finite one seems equally likely.
The basic idea of the infinite repetition of histories in space is that, if you take yourself right now and change one thing (say make your red shirt a blue one), then there's another you somewhere who is exactly the same except for that one difference. Change your shirt to purple, and that's a third you. Change the drink in your hand from soda to tea, and there's another one. Plus, there are copies of all of these universes – an infinite number of copies. In their paper, Soler Gil and Alfonseca quote the popular science book "The Music of the Big Bang, The Cosmic Microwave Background, and the New Cosmology" by Amedeo Balbi: "In an infinite universe, every possible event does happen. Not just that: it happens an infinite number of times."
This infinite repetition idea can be found in early philosophy, ancient mythology, and today's sci-fi literature. But can it be derived from physical theories about the universe, and does it have a place in science?
In the first proposal that Soler Gil and Alfonseca analyze, Ellis and Brundrit argue that infinite repetition logically arises from classic relativistic physics. A more detailed summary can be found in the arXiv paper, but the general argument is as follows. If the universe, the number of planets and galaxies, and the number of possible histories (the one we're familiar with is our 13.7-billion-year history) are all infinite; and if the probability of DNA-based life is greater than zero; and if the number of types of DNA-based living things is finite (because the size of the DNA molecules cannot be arbitrarily large); then an infinite universe must contain an infinite number of copies of the finite number of DNA-based living things, and some of these living things will follow very similar and even identical history lines. In other words, infinite histories plus finite types of living things means that those living things' histories are infinitely repeated.
Soler Gil and Alfonseca take issue with several of these assumptions. One of their main counterarguments at first seems odd: they say that we can't be sure that the probability of DNA-based life is greater than zero. Neither our existence nor our discovery of a finite number of cases of life on other planets can, at least in the logical sense, be used to deduce that the probability is greater than zero. As a result, the infinity of histories is larger than the infinity of living individuals, so each planet compatible with life could have its own unique history.
"If there is an infinite number of possible histories, the fact that there is a given history (or a finite number) leading to life does not make that history probable: its probability would be 1 divided by infinity, which is zero," Alfonseca explained to Phys.org. "To have a greater-than-zero probability, you need an infinite number of approaches. But in any case, with this scenario, the number of histories would always be larger than the number of beings, so the same beings infinitely repeated would still have different histories."
The second proposal, by Garriga and Vilenkin, does involve a finite number of histories, but is rooted on the idea in quantum theory that discrete regions of space have finite amounts of energy. In the decoherent histories (DH) interpretation of quantum mechanics, the infinite universe can be divided into an infinite number of regions that cannot influence one another (i.e., they're causally disconnected) because they are separated by event horizons. Then Garriga and Vilenkin deduce that the number of possible histories in each region is finite because the energy in each region is finite and, according to quantum mechanics, energy is quantified. To put it briefly, an infinite number of regions plus a finite number of possible histories in each region means that every history must be repeated an infinite number of times.
Soler Gil and Alfonseca criticize almost all of the assumptions in this proposal, starting with the application of quantum theory to cosmology, which is currently mere conjecture without evidence. Other problems arise when considering the gravitational effects of black holes and the expansion of the universe, which can potentially increase the number of possible histories indefinitely, preventing repetitions.
But the scientists' biggest criticism of the idea of infinite repetition in both proposals is the assumption that the universe is infinite. Whether the universe is infinite or finite is a big open-ended question in cosmology that scientists may never answer. Soler Gil and Alfonseca note that, looking back at the history of physics, situations emerged where infinities seemed impossible to avoid, yet improved theories eliminated the infinities. Currently the two basic theories in physics, general relativity and quantum theory, both predict infinities. In relativity, it's gravity singularities in black holes and the big bang. In quantum theory, it's vacuum energy and certain parts of quantum field theory. Perhaps both theories are simple approximations of a third more general theory without infinities. Soler Gil and Alfonseca also note that, Paul Dirac once stated that the most important challenge in physics was "to get rid of infinity."
While Soler Gil and Alfonseca can't disprove the proposals of infinite repetition, they emphasize that the point of their critique is to show that the idea remains in the realm of philosophy, mythology, and sci-fi tales, not modern cosmology. They call the speculation "ironic science," a term used by science journalist John Horgan to describe options that do not converge on truth but are at best "interesting." Despite the accounts of many popular science books, the idea that our lives are being repeated an infinite number of times somewhere out in the universe is in no way certain and far from either probable or plausible.
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User comments
Example, pi is an irrational number, and the computation of that number carries out infinite places, it never ends. Even so, no matter how far you looked, you would never find the numeral 1 repeated a trillion times, never.
Perhaps there are endless numbers of universes, and some might have similar physical laws. But never would you find the mega godzillion particles assuming the exact same configuration some billions of years after the universe began expanding. Can't happen.
I'm pretty sure thinking of time and reality as a forward "flow", with alternative paralleled universe "flows", is the old paradigm, and new sciences show that what appears to be reality is not really reality as we intuitively seem to grasp it eh
I'm not sure this can be applied to the case.
The mathematical reasoning is that between every real number there must be an infinite amount of numbers, and since between 1/inf and 0 there is no other number, then both must be the same number.
But when applied to real things that come in integer amounts, that's like saying that since there isn't a house between my house and my neighbor's house, then our houses must be one and the same.
The mathematical axiom that leads to this conclusion causes obvious paradoxes when you apply it to things like the probability of life, because if you claim that the probability of something happening, even in infinity, is zero, then there must be no cases of that.
Perhaps this is what they mean by being constrained by classical thinking. Maybe there is a house between my house and my neighbor's - in some weird quantum sense - that must be there for both to exist apart.
An open question in (e.g. quasiclassical) cosmology is as to whether the universe is infinite or finite. As the author's acknowledge, this problem is currently unsolved. So everyone, both critics and supporters of the infinite classical spacetime hypothesis, is in the same boat: we don't know. It seems strange, therefore to pitch a critique at the level of this uncertainty. Since the argument for the infinite 'repetition' of finite physical systems throughout putatively infinite classical spacetime is essentially an IF-THEN conditional, an appropriate critique must also adopt this format. I.e., the critique must take the form of IF infinite classical spacetime, THEN 'infinite repetition of finite physical system's' doesn't occur, for some reason.
PS don't see what's so ironic about any of this!
Because either one has to give: either you stop requiring that real numbers have other real numbers in between them, which would mean that there's a finite number of fractions between 1 and 0, or you admit that 1/inf is not a number and therefore the argument they propose is flawed.
But this dichotomy depends on the definition of a number. Since the occurence of life comes in integer amounts - it either occurs or it doesn't - the same concept of a number doesn't apply and the same concept of infinity doesn't apply, and therefore it is not given that 1/inf = 0 even if we consider inf to be a number.
Since life either occurs, or doesn't occur, it doesn't come in half measures. We're dealing in positive whole numbers, where the rule of every number having other numbers in between them does not apply. Otherwise we would have to conclude that 1=0 since there isn't a positive whole number in between them.
Therefore we must conclude that in this case 1/inf is either not a number, or it is not zero.
If it is not zero, then it must be one since the occurence of life does not come in half measures. In other words, if life occurs in one permutation of history, it must occur in all of them, and if there are infinite permutations of history then there is infinite permutations of life.
If 1/inf is not a number, then we are none the wiser about the probability of life in each permutation of history.
Assuming it is a number for the time being, what is the justification for considering this number a probability?
Oh, the irony.
BTW Is the idea "we exist in an infinite number of places" equivalent the concept of "infinite repetition, the idea that planets and living beings must be repeated an infinite number of times"? I'm missing the logics even in the article title.
Theoretical Cosmology needs to start thinking WAY outside the box, and try to find patterns in the micro and the macro. Just as the branches of a tree look like a tree, so do atoms look like solar systems. The answer is in the patterns....
I think these are two guys imagining themselves to be as intelligent as Einstein, you know, newcomer wannabees who have finally figured out "entropy" cannot occur in an infinite Universe. Maybe I should have them send me their resumes, we're always looking for good people who innately understand Conservation of Energy principles cannot function in an infinite unbounded Universe.
Because infinity in a physical theory means "you need to work on this part."
The McDonalds McRib thing is funny but not valid because only finitely possible things will happen an infinite number of times. And a planet mass of McRib sandwiches, configured into a planet formation, will compress into... a planet. Potentially a very nice smelling planet with weird BBQ slicks on it's surface. But not a ball of McRibs going all the way down. :)
If Space and time are quantized in some fashion then the concept of the very small becomes just a mathematical quirk with no basis in reality.
I seem to think that infinities have no place in the universe, how one proves it is another matter.
Le's not forget the bun, coke and fries....
How you prove it is by studying "ENTROPY". Then you will discover that if the Universe really were "infinite", the amount of usable energy available for "work" would have been exhausted within a few centuries after the occurance of the Big Bang.
These guys are unwittingly giving Einstein credibility in Sect 30-Part 3: "Considerations on the Universe as a Whole", "The Structure of Space According to the General Theory of Relativity". This is interesting reading if you've never done it.
The point here is that the existence of life in the infinite universe IS quantized. It either exists or it doesn't exist. There's no in-between states.
Which means that fractional probabilities of life are non-sensical regardless of the size of the universe. If there's two separate cases of life, then the probability is 2, and so on.
The probability of life in the universe is always a positive integer, and with positive integers there is no 1/x because there are no fractions smaller than one. That's why there exists no 1/inf either. The only case when it is defined is when x=1.
That's why it's not technically infinite either, since approaching zero from the positive or negative side gives you two different infinities, positive and negative respectively. The same number would be two completely opposite numbers, which makes no sense.
Only |1/x| is infinite when x=0
@krundloss
To be technical, 1/inf = 0 is really a shorthand notation for the following:
Lim 1/x = 0
x->inf
This is the concept of a limiting value. The statement says that the quantity 1/x approaches 0 as x approaches infinity. While 1/x cannot ever be exactly 0, given any value you choose arbitrarily close to 0, I can choose a value for x in which 1/x is closer to 0 than your value. Thus, 0 is the limiting value of 1/x. Limits are the central concept in calculus and it is shorter to state 1/inf = 0 than it is to go through the verbose statement of the problem in terms of limits.
Why ponder the "infinite universe" when we can reduce our pondering to something more manageable,,,, planet Earth.
The probability of life in the universe is unity,,, ONE. Assuming that I (a real living organism) am responding to you.
The reason 0 is undefined, is because any fractional part of something must be, by definition, more than zero. You can not divide something into 0 parts, it can be the whole or some part of the whole. Dividing by 0 the same as dividing infinity by infinity. It's why we do everything we can to eliminate infinity from practical science. It is in the realm of philosophy not science.
If we live in a multiverse of infinite universes then YES you EXACTLY as you are now exist in infinitude. This is the definition of infinity, it's endless. This is a philosophical construct, not a mathematical one.
If you're asking if you can win the lottery by going back in time with the numbers then yes you can...it's just going to take you a loooooooooooong time and a LOT of iterations :)
It all depends on how you parse the situation.
Probabilities are never greater than 1 (ONE), they can infinitesimally small, but never greater than 1 (ONE).
Wait a minute here!!! Do you mean to tell me that the Inquisition did in fact happen? Are you sure? Who would have thunk it was a real thing?
Why not? On the averages each trillion-digit sequence happening once in each 10-to-the-trillion digits. 63.4% of all possible trillion-digit sequences will occur at least once in the FIRST 10-to-the-trillion digits.
There is a 69.4 (1 - 1/e = 0.694) percent chance that a trillion ones in a row occurs in ANY 10-to-the-trillion digits of ANY irrational number.
The odds are only ~ 1 in ten trillion of a trillion ones in a row NOT happening in the first ten-to-the-(one trillion + 30) digits.
For all their attempts to find a 'unified' theory of everything; they still insist on using Occam's Razor to continually divide it into finer and finer portions...
It's also the same as multiplying Zero by Infinity.
But, if you ascribe to the Big Bang theory; then you believe in the something from nothing concept. Before the Big Bang, they would have us believe there was nothing; then after, everything. From Zero to Infinity in one absurd theory.
If it is not happening in this reality, it must be happening in another.
We were right all along.
For: f(x)=1/x, where x approaches infinity, f(x) approaches zero.
For: f(x)=1/x, where x approaches zero, f(x) approaches infinity.
1/0 does not have an answer. One divided zero times is absolutely meaningless.
If you have 2 kids and 20 candies, 20/2, each kid gets 10. In a morbid case, if you have half a kid, a whole kid, 20/(1/2), gets 40 candies. If you have zero kids, 20/0, WTF are you calculating? Division by zero is absolutely meaningless. An infinite number of kids, this one is tricky, the ability to divide the candy stops at the sugar molecule, in an infinitely fractal universe each kid would get an infinitesimally small piece of candy (but not zero), this doesn't work in reality so we have to normalize the situation, breaking 20 candies beyond the sugar molecule level destroys the sweet, we eventually get atoms and ultimately we're left with quanta. Normalized 20 candy/infinite kids is 0 candy parts
I do in fact ascribe to the so-called "Big Bang theory". Though I think the term "Big Bang" is unfortunate. I would call it the "Standard model with cold inflation", but they didn't ask me, so the name is what it is.....
But this model by what ever name, doesn't assume a priori that everything came from nothing,,,, quite the contrary,,, the theory stops at the so-called "Planck-time", when everything that is here was already there, before that it makes no predictions.
Many people speculate on what existed, or if anything existed before the Planck-Time, but those speculations are not part of the standard "Big Bang w/inflation" model. The only ones who claim it is are the detractors of the "Big Bang" model.
Or in one sense, the 'infinity' problem arisen because both the theories' main theme is mathematic –not physics! They are no philosophy background which explain what mechanism hidden behind and how it works. Maybe this physics oriented theory could solve the problem.
http://www.vacuum...=9〈=en
Therefore the statement "In an infinite universe, every possible event does happen. Not just that: it happens an infinite number of times." is false. The universe would have to have a finite spatial extension and infinite temporal extension for all event to be repeated.
And they are made from Candyfloss.
What the dense aether model says about it? The Universe is filled with foamy density fluctuations (dark matter streaks) which may act like reflecting barriers for low-energy light (the interior of black holes is behaving like mirror in AWT). Which means, that some CMBR structures may be really reflected in the infrared light from the inner cells of our portion of Universe. Therefore some very subtle structures may exist at the multiple places of Universe or at least being observable so. The more dense structures are indeed quite random and as such unrepeatable. This may serve as an example of proverbs "There's a bit of truth in every gossip. There's no smoke without fire".
Dang... VD strikes gold again...
The white rabbit must die...
My only answer is - without a little humour and the subsequent appreciation of it - we might as well just end it all.
It's Friday... relax and have a little fun...:-)
Another stupid comment. I won't read it. I did, fuck! Another me
Another stupid comment. I won't read it. I did, fuck! Another me
Another stupid comment. I won't read it. I did, fuck! Another me
Another stupid comment. I won't read it. I did, fuck! Another me...
If PI is a uniformly distributed random number (and although it hasn't been formally proven, it's generally considered a 'normal' number, with digits uniformly distributed in every base), then it must contain any finite sequence of digits -- including '1' a trillion times. Infinity is difficult to conceptualize, hence the endless back-and-forth about its precise ontological status. But it is clear from the definitions of uniform randomicity and inifinity as 'that which is as large as you want it to be' that every finite sequence must occur within an infinite string.
This is about as close to the truth as we can possibly get.
We can make the provable observation that Time is the ONE thing that everything else is related to on one level or another. Yet - somehow - that fact gets obfuscated by the rush of all the other stuff we're observing...
Dang... Why can't I get this damn white rabbit out of my head?
Another problem is their lack of understanding of physics. For example, it is an open question if the initial inflation in standard cosmology runs into singularities if you go backward in time. Planck scale potentially, but we know from cosmological supernova photons that physics happens on a smooth manifold even below that scale.
Mostly, the generic argument for repeats, not of history necessarily but of the exact same events, is that the observable universes is finite and have a finite number of particles. So you have to happen on the same configurations elsewhere. (Cf Tegmark's multiverse.) And the simplest standard cosmological universe is infinite.
Infinity, no matter how much we are seduced into thinking we can grasp it, always remains an "I don't know what." Infinity is always an undefined. When infinity shows up as the result either in mathematics or in physical theory it points to a something that lies outside the calculational or descriptive power of whatever mathematical or physics model one is using.
IF you watch the Universe series on History & Science channels, nearly all the Asro-Physicists & Astronomers conclude with you that the Universe is finite. These are people who fully understand the greatest & most far reaching concepts of Conservation of Energy & Einstein's Theory of General Relativity which does not allow for "infinity".
It may very well be that the Universe we live in may be a "stellar island", & beyond the domains of this stellar island may very well be other stellar islands, but a Conservation of Energy principle we call "entropy" will prevent us from ever viewing through or crossing that barrier.
"For example, it is an open question if the initial inflation in standard cosmology runs into singularities if you go backward in time." - Torbjorn
It makes much more sense to me to simply have matter manifest itself from nothing through the entire volume of the space/time manifold.
Whose we are you calling yourself? I ask because WE call "conservation of energy" the 1st Law of Thermodynamics. And WE associate "entropy" with the 2nd Law of Thermodynamics.....
Oh yeah,,,, yes I took several course devoted to thermodynamics. And made very good grades in them.
In L-CDM theory the geometry of Universe is described with FRLW metric, which is essentially the black hole geometry inverted. But we aren't traveling against time, when we are falling into black hole, so I don't understand, why the traveling into distance within cosmic space isn't interpreted in the same way. For me the whole the idea of space-time expansion has absolutely no sense. The Universe beginning just brings another questions, so it doesn't solve anything anyway-it's causally redundant hypothesis.
Entertainment - which is why we all are here in the first place...
Perceptions need to cross-over to Cosmic Vision development.
ignore the origins-you will end up no-where
Does it boil down to psychology of Human perception ?
Apparently there's been some inbreeding in the royal family of Bosnia.
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With the possibility of infinite arrangements, just slightly out-of-phase and thus shifted so that from the view of seeing all potential shifts there are an infinite number of houses between both homes in your singular view.
The sheer number of the competing theories on quantum mechanics and cosmology shows this.
I wish more time would be used to finding unrepairable holes in existing theories, instead of everybody building their own.
Unfortunately - we can't. Not the way our (quantum) brains work...
It is just a pop-science thing. The FLRW metric is based on GR which is classical so if you extrapolate to t=0, you get a scale factor a(t) which is also zero, and many parameters such as energy density become a division by zero, a singularity in the maths.
If you take a cosmology course, the real science stops at a time expected to be of the order of the Planck Time. To project before that we need a quantum theory of gravity which as yet doesn't exist.
Only approaching from the right. If you approach from the left, the limit approaches -inf. That is why 1/0 is undefined.
The limit is the same regardless of which side you approach it from. The limit is 0. The 1/X is what is approaching 0. NOT the denominator,,,,, that is going farther and farther AWAY from 0.
Dividing 1 by infinity or negative infinity is completely equal, they approach each other to the point where they are the same point,, They converge at 0
f(1/infinity) or f(1/neg infinity) both have ZERO as a limit.
There is no 0 in the denominator, the denominator is increasing without out limit yielding a function whose limit is zero.
You guys are mixing up the concept of dividing by zero, and dividing by infinity. Dividing by zero is undefined. Dividing by infinity is NOT undefined.
"Survey shows physicists can't agree on fundamental questions about quantum mechanics"
http://phys.org/n...firstCmt
Then again Einstein thought nature would "protect" us from singularities, even though he agreed with Schwarzschild's math...
You shouldn't try to comment on things you don't understand. GR describes the gravity that holds you onto the Earth, not just cosmology while QED describes the interactions that hold the atoms of your body together. Normally we can use then separately by treating one or the other as negligible, a merged theory would provide a tool to analyse situations where neither can be ignored.
Why do we need "gravity" at all, it was just "invented" to explain observed phenomena? There is no actual evidence for multiple universes either, so why "invent" them? I would dearly like to see a logical refutation of Reg Mundy's "simple" theory of how the universe works.
The whole of science exists to provide mathematical tools by which we can model observed behaviour. Those are the tools that allow us to engineer solutions to real-world problems. Modeling gravity in particular has allowed us to send craft to other planets, put GPS satellites into accurately known orbits and correct for the relativistic effects that affect the signals from those satellites and their on-board clocks. Next time you use a satnav, realise it wouldn't work without Einstein's understanding of gravity.
I think you have made my point beautifully, gravity is just a "mathematical tool" invented to explain reality - but it doesn't, it stops working in extreme situations. I know of no proof of its existence, do you? Someone once said "The objective of science is to remove infinity from all equations/theories". Gravity should be removed as well.
General Relativity is the tool we invented to model "gravity" which is an effect in the real world. Gravity doesn't stop working, only GR is limited.
The proof of the existence of GR is that you can find it in many textbooks.
The proof of the existence of gravity is that you don't hurtle off into space even though our planet is rotating.
If you find a way to cancel gravity, good luck surviving in deep space.
Your "proof" of gravity seems to be that "you can find it in many textbooks"! I expect that a few centuries ago you could find that the Earth was flat "in many text books", and that the atom was indivisible. And there are several explanations as to why we don't "hurtle off into space", try reading "The Situation of Gravity" for one.
Nope: http://en.wikiped...at_Earth
Perhaps, scientifically it was and still is the smallest division of matter that retains the behaviour of the bulk element.
Alternative explanations aren't the same as gravity not existing thus needing no explanation.
ROFL, no thanks, plugging your book under a sock puppet account won't increase your sales. If you want me to comment on the idea, summarise it here. If it is new and credible, that will get you your sales ;-)
And of course the atom is divisible, whether you like it or not, no matter how you play with semantics, and that was stated "in many textbooks".
Finally, although it is not my book, I wouldn't ask you to comment on it as you seem to have a closed mind on the subject and have failed to justify your viewpoint with a single logical argument. If you know of one proof of the existence of gravity, kindly tell me about it.
And my point is that you CANNOT find it in ANY text books, it was a myth created long after the time when people were supposed to have believed it.
No I didn't, sloppy reading Jack. If you look at my post, I said that its presence in textbooks showed that the equations know as General Relativity exists, not gravity. You seem to be incapable of telling the difference.
I already have, unless you are now flying away from the Earth at approx 1000mph. Explain it any way you like and model it with any maths you like to whatever accuracy you want, the effect certainly exists or you wouldn't be on the planet.
And as for flying off the planet, you are once again quoting an "effect" not a proof, which can be explained in several ways without inventing "Gravity".
Finally, while I must say I have enjoyed our little "tete a tete", we must call it a day before we bore the rest of the phys.org readers to death. Please, have a final rant if you must, but I'm finished - you can pretend I've been hurtled off into space if you like....
ROFL, we were talking of scientific textbooks, not religious scripture.
The "effect" is what is called "gravity", you just need to learn the jargon.
No thanks, you're doing fine by yourself.
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