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The idea of an infinite ensemble of universes has arisen in many different contexts in physics, from quantum mechanics (the many worlds interpretation) to certain cosmological models (eternal inflation models).
In a purely instrumental approach (accept only that what you can in principle measure in experiments), one should always replace a multiverse theory by a single universe theory. However, this may not be a very natural thing to do.
Another motivation for the multiverse is this: Physics, as it is practiced now, is necessarily incomplete. A fundamental theory needs to postulate certain fundamental physical quantities like the physical universe, spacetime, fields (or strings) etc. and fundamental laws of physics. These quantities are themselves beyond the realm of explanation. If they can be explained then that would only mean that there exists a more fundamental theory, with less fundamental quantities.
Clearly, the only possible way in which everything can (in principle) be explained is if there are no fundamental physical quantities at all. Suppose that there doesn't exist a physical universe. It could be that only mathematical worlds exist. That would mean that all possible mathematical worlds are ''as real'' as this one.




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Another motivation for the multiverse is this: Ibliss:"Physics, as it is practiced now, is necessarily incomplete. A fundamental theory needs to postulate certain fundamental physical quantities like the physical universe, spacetime, fields (or strings) etc. and fundamental laws of physics. These quantities are themselves beyond the realm of explanation. If they can be explained then that would only mean that there exists a more fundamental theory, with less fundamental quantities." I do not agree with your statement below, for two reasons. a) If indeed "fundamentality" is characterized by the number of basic concepts/quantities, such that thew more fundamental the theory the fewer such concepts/quantities, it is not necesarily that a more fundamental theory cannot make use of already explained concepts/quantities. Even if such a series of fundamental theories convrges in the sense that in the end there may be a theory with no unexplained quantities, this does not mean that such a theory does not have fundamental concepts. b)Practical experience, so to speak, shows exactly the opposite of your statement. the more fundamental the theory, the larger the number of such necessary concepts. Think about statistics and quantum mechanic, or even better, about Newtonian mechanics and general realtivity. In classical mechanics, geometry is a given, while in general relativity it becomes one of what you call fundamental quantities. So for (at least) the time being, the trend appears to be opposite to what you state. Ibliss: "Clearly, the only possible way in which everything can (in principle) be explained is if there are no fundamental physical quantities at all." I am not so sure about that, say for the reasons above. ES:"Suppose that there doesn't exist a physical universe. It could be that only mathematical worlds exist. That would mean that all possible mathematical worlds are ''as real'' as this one." Why this kantian aproach? Besides the fact that it is far fetched principially, what does such a concept bring as useful knowledge? If I were to follow Kant's conclusions, in the end each of us is a walking asylum, so to speak, and what matters is only what one believes it matters. In the case of your example, you end up with a sort of mathematical mysticism, where only what one believes matters, and there is no "objective" (that is experimental) way of testing one's belief. How exactly would this help with our knowledge? I am trying to imagine now, in our present "asylum", what would happen if what you say were right. Well, you would have instead of human beings some sort of kabalists making more or less preposterous claims, and worse even, fighting for the power of imposing their system of beliefs. Hm, this sounds very familiar, so maybe I am not imagining it and you are right




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I do not agree with your statement below, for two reasons. a) If indeed "fundamentality" is characterized by the number of basic concepts/quantities, such that thew more fundamental the theory the fewer such concepts/quantities, it is not necesarily that a more fundamental theory cannot make use of already explained concepts/quantities. Even if such a series of fundamental theories convrges in the sense that in the end there may be a theory with no unexplained quantities, this does not mean that such a theory does not have fundamental concepts. b)Practical experience, so to speak, shows exactly the opposite of your statement. the more fundamental the theory, the larger the number of such necessary concepts. Think about statistics and quantum mechanic, or even better, about Newtonian mechanics and general realtivity. In classical mechanics, geometry is a given, while in general relativity it becomes one of what you call fundamental quantities. So for (at least) the time being, the trend appears to be opposite to what you state. A new theory could lead to new concepts because new, previously unknown, phenomena are discovered. So, I was considering just the known phenomena. Also, I would say that old concepts are in fact used in newer theories, even if they are strictly speaking redundant. E.g. mass and energy where two completely different concepts that have turned out to be the same thing (although when I was a first year physics student, the physics professor and his teaching assistant didn't agree on this). Now, I don't really see how general relativity contains more fundamental concepts than classical mechnics. Space and time did exist for Newton! They are just fixed quantities, but still fundamental (unexplainable) within classical mechanics. Moreover you have gravitational mass and inertial mass in classical mechanics. I already mentioned energy and mass above. Of course, in GR you have to deal with a more complicated spacetime... Also you could say that particles have all sorts of charges, hypercharges etc. which were not present in classical mechanics. But then classical mechanics doesn't say anything about particles. Every particle could have a different mass, charge etc. We know now that every electron has the same mass and charge. So you have far less free parameters. Why this kantian aproach? Besides the fact that it is far fetched principially, what does such a concept bring as useful knowledge? It could explain why we find ourselves in this particular universe, rather than in some other. Of course, you need to define a measure over the set of all possible universes first. This measure is the nontrivial physical content on the theory. once this is specified, everything is fixed. The fact that we seem to live in a ''regular'' universe, suggests that universes that can be specified with less parameters have a larger measure. In fact, one can argue on purely physical grounds that the measure of a universe has to decay at least exponentially with the size of the algorithm that specifies it. The probability that you exist somewhere in a universe is proportional to its measure and the number of times you are present inside it. But for any algorithm you can invent another one that just runs the algorithm N times. To get a normalizable probability distribution the measure of that universe has to be N times less. Now, the algorithm has to specify the number N, and that takes Log_2(N) bits. So you see that if the measure depends on the size of the algorithm it will have to decay at least exponetially with the size.




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quote: "It could explain why we find ourselves in this particular universe, rather than in some other."
There is no valid reason for even asking the question any more than asking the question "Why wasn't I born into a different family" or "What if different people see the color green differently". It is all philosophical nonsense. At least from the standpoint of science.
We are here because we are here. End of question.
That said ... one should never draw conclusions from what is unknown but rather from what is known. And in that regard we have every reason to believe that single universe or multiverse it will all come down to a single set of fundamental facts: And the fewer the better.
DA Morgan




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''There is no valid reason for even asking the question any more than asking the question "Why wasn't I born into a different family" or "What if different people see the color green differently". It is all philosophical nonsense. At least from the standpoint of science.
We are here because we are here. End of question.''
Well, whether questions have meaning or not also depends on the circumstances. If there exists only a single universe, then you are right. If a whole ensemble of universes exists then the question why we live in this particular universe with the particular laws of physics does have meaning (you could rule out ensemble theories which predict the wrong laws of physics).




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Ibliss: ?A new theory could lead to new concepts because new, previously unknown, phenomena are discovered. So, I was considering just the known phenomena.?
I am not so sure that you can do that. But in a way, you are supporting my view that the more fundamental the theory, the more the complexity increases.
Ibliss: ?Also, I would say that old concepts are in fact used in newer theories, even if they are strictly speaking redundant. E.g. mass and energy where two completely different concepts that have turned out to be the same thing (although when I was a first year physics student, the physics professor and his teaching assistant didn't agree on this).?
One more argument in support of the ?more fundamental means more complex?, i.e. more basic concepts/quantities. The redundancy, while it exists sometime, does not reduce significantly the number of concepts. Principially, redundancy can at the very best make a more fundamental theory have the same complexity with a less fundamental theory, and we already know this is not the case in fact. Also, you may want to think about say, topological field theory, there depending on the topology of the manifolds you end up with different sets of topological invariant quantities that you need to specify your system. But I think that we can solve this issue of fundamentality/complexity for the theories we know by simply establishing a hierarchy of such theories, something like classical mechanics>quantum mechanics>quantum field theory, or classical mechanics>special relativity>general relativity>quantum gravitation, and then simply count the fundamental concepts involved.
As for the example you gave regarding mass and energy, personally I am more inclined to agree with the one saying that in fact they are not the same (I guess this would be the physics professor). Mass is still a measure of inertia (you cannot disregard the marticles with rest mass), while energy is significant in conservation laws. Sure, there is a definite relation between them, but they are principially not the same, in my oppinion. They describe different concepts, in spite of the traditional ?equivalence between mass and energy.
Iblisss: ?Now, I don't really see how general relativity contains more fundamental concepts than classical mechnics. Space and time did exist for Newton! They are just fixed quantities, but still fundamental (unexplainable) within classical mechanics. Moreover you have gravitational mass and inertial mass in classical mechanics. I already mentioned energy and mass above.?
I guess we disagree here. Sure, the concepts exist in Newtonian theory, as fundamental concepts, though I would not put it quite this way. In newtonian theory, geometry is just a background, and the fundamental concepts are related to absolute and relative postions and times. It is not part of the dynamics. In GR, while it retains space and time as fundamental issues, geometry itself becomes a dynamical variable . Sure, you can have GR on a fixed background, but you can also view GR as a background independent theory.
Ibliss: ?Also you could say that particles have all sorts of charges, hypercharges etc. which were not present in classical mechanics. But then classical mechanics doesn't say anything about particles. Every particle could have a different mass, charge etc. We know now that every electron has the same mass and charge. So you have far less free parameters.?
True, but in he more complex theory there are also more particles so to speak. And while in the more complex theory quantities as hypercharge, etc. occur naturally, in the less complex theory they don?t. Sure, you can introduce them adhoc in the less complex theory, but they don?t have any meaning. And you cget back to the old issue of superimposing theories (mechanics and say electromagnetism) versus unified theories.
Ibliss: ?It could explain why we find ourselves in this particular universe, rather than in some other.?
I don?t think that you are asking the right question at this time. In a sense I agree with Dan, although for slightly different reasons. At this moment in our history we know very little about the underlying complexity of our universe. The fact that we can describe mathematically in a more or less cumbersome manner the interaction between two very odd particles is only one face of the issue. Heck, at this time we are only toying with a form of inorganic chemistry so to speak. And I think we are eons away from having a consistent model describing say, the amoeba as a living organism. And by this I don?t just mean a that we need to extend physics in the realm of biology. What I also imply is that at this time in history we are not even able to construct a living cell from ?spare parts? although we know what they are, and although we have started to actually play a bit with modifying such parts in a living cell. But we still cannot ?frankenstein? to life a living cell. And by this argument, we are not privy to a lot of the ?surrounding? complexity that could beused somehow to answer your question.
Of course, we can use what we have as partial arguments for partial conclusions, but in my opinion at least, our partial knowledge at this time is far to puny to develop any significant conclusions. And for the time being, and even though this does not give me any pleasure, the anthropic principle is the best we have, even if we may or may not agree with it.
Ibliss: ?? you need to define a measure over the set of all possible universes first?.In fact, one can argue on purely physical grounds that the measure of a universe has to decay at least exponentially with the size of the algorithm that specifies it??
You have lost me here, I am simply not familiar with the measure arguments. So before I am able to give a more or less cogent answer, I would appreciate if you could provide me with some refs.




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With respect to the why are were here versus there question it basically comes down to the fact that we are where we are and we are not where we are not.
Now if you wish to postulate that there are an infinite number of "you" that is philosophical mumbo jumbo because you^1 thorugh you^n are not in contact with each other by any means known or theoretical.
In fact before you could even postulate that the different you's were "you" you would need to define exactly what "you" is (or is it are?).
With respect to simplicity versus complexity as things become more fundamental ... I would suggest that consideration be given to the fact that so far as I know no part of physics can not be correlated with information theory. And I have no reason to believe that the entire universe, as we see it, can not be constructed from zeros and ones. Remember fractals create infinite complexity in finite space. The complexity to which you refer may only be obfuscation. The complexity of all of chemistry comes down to just a handful of very simple statements of fact.
DA Morgan




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DAM: "With respect to the why are were here versus there question it basically comes down to the fact that we are where we are and we are not where we are not."
Dan, you can say the same about the pressure in a vessel. It is in a way the principial difference between thermodynamics and statistics. The pressure is the one that is and not the one that isn't. And yet you can find a more "fundamental" explanation of why that is indeed so.
DAM: "Now if you wish to postulate that there are an infinite number of "you" that is philosophical mumbo jumbo because you^1 thorugh you^n are not in contact with each other by any means known or theoretical."
True, but that is beyond the point of this modelling.
DAM: "In fact before you could even postulate that the different you's were "you" you would need to define exactly what "you" is (or is it are?)."
Well, Dan, I kind of did define that, if you look closely. The problem is that at this time we don't exactly know what that means.
DAM: "With respect to simplicity versus complexity as things become more fundamental ... I would suggest that consideration be given to the fact that so far as I know no part of physics can not be correlated with information theory. And I have no reason to believe that the entire universe, as we see it, can not be constructed from zeros and ones. Remember fractals create infinite complexity in finite space. The complexity to which you refer may only be obfuscation.The complexity of all of chemistry comes down to just a handful of very simple statements of fact."
Dan, this is what I tried to say, if you look closer. We have certain building blocks (fundamental/complexity refers only to the buiding blocks, not to the ensuing structure  I haven't even begun to address the issue of structure, although Ibliss did so), but we don't have them all. In fact we have so few that we may not be able to draw even partial conclusion that could withstand even a slight change into the underluing assumptions. I was trying to make the comparison between inorganic chemistry and biology, but it misfired.




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Pasti wrote: The fact that we can describe mathematically in a more or less cumbersome manner the interaction between two very odd particles is only one face of the issue. Heck, at this time we are only toying with a form of inorganic chemistry so to speak. And I think we are eons away from having a consistent model describing say, the amoeba as a living organism. And by this I don't just mean a that we need to extend physics in the realm of biology. What I also imply is that at this time in history we are not even able to construct a living cell from “spare parts” although we know what they are, and although we have started to actually play a bit with modifying such parts in a living cell. I agree that this is a serious problem for practically implementing the idea I'm in favor of. It is not possible in practice to program fundamental laws of physics in your computer and then see humans discussing physics on your computer screen. However, in single unverse theories the question of why we live in this unverse doesn't even make sense (as DA Morgan wrote), while in ensemble theories it is a valid question (but perhaps not answerable in practice). I will write about the ''measure'' later.




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With respect to the why are were here versus there question it basically comes down to the fact that we are where we are and we are not where we are not. That's right, but this statement has different implications in single or multiple universe theories (even in a single infinite unverse). In a multiple universe setting all the information you have about yourself and your surroundings doesn't pin you down at one place. There would still be an infinite number copies (who are exactly ''you''). I agree that the different versions of you cannot contact each other but within some theories that predict an infinite universe it would be unnatural to ''cut them away'' by pretending that the predicted infinite universe somehow isn't real far away from here. In fact before you could even postulate that the different you's were "you" you would need to define exactly what "you" is (or is it are?). Well, most scientists believe that we are just a combination of the right chemicals and do not invoke supernatural things. So you are a certain combination of atoms. Now certain theories predict that every allowed combination of atoms occurs infinitely often. In fact Vilenkin et al. have shown that the exact history of the entire universe shoud occur infinitely often in his ''eternal inflation theory''. With respect to simplicity versus complexity as things become more fundamental ... I would suggest that consideration be given to the fact that so far as I know no part of physics can not be correlated with information theory. And I have no reason to believe that the entire universe, as we see it, can not be constructed from zeros and ones. Remember fractals create infinite complexity in finite space. The complexity to which you refer may only be obfuscation. The complexity of all of chemistry comes down to just a handful of very simple statements of fact. I agree.




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Pasti: ''As for the example you gave regarding mass and energy, personally I am more inclined to agree with the one saying that in fact they are not the same (I guess this would be the physics professor). Mass is still a measure of inertia (you cannot disregard the marticles with rest mass), while energy is significant in conservation laws. Sure, there is a definite relation between them, but they are principially not the same, in my oppinion. They describe different concepts, in spite of the traditional “equivalence between mass and energy.'' Well, this reminds me of heat and energy: http://sci.techarchive.net/Archive/sci.physics.research/200408/0314.html




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Ibliss: "...Well, this reminds me of heat and energy..."
Well, Ibliss, you might be laughing, but there is a "similar" distinction between energy and heat also (and work). Doing thermodynamics a la Karatheodory, energy is a quantity describing both states and processes, while heat and work only describe processes (i.e. changes of the state of the system). But then one can always claim context, and sometimes with good reasons.
How about those refs?




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Pasti: Ok. Let's start with the idea that universes are just algorithms. Although that's too speculative for most physicists, it at least makes the problem mathematically well defined. J?rgen Schmidhuber has done some recent work on this idea. He gives references and some explanations here. I actually don't agree with most of what Schmidhuber writes there. First of all if you are considering completely general algorithms there is no need to worry about quantum mechanics not being explainable as a local deterministic theory. Also I disagree with the remarks about the Anthropic Principle. In fact he totally ignores an ''anthropic factor'' in the measures he proposes in his papers. For him this is a one or zero thing. Schmidhuber says that you exist or you don't exist in a universe. He considers two universes with equal ''intrinsic'' measure equally likely even if you occur a million times more often in one of them. That's convenient, because then he then doesn't have to worry about how to define a (human) observer inside an algorithm and how to count them! To understand why it is necessary to include the anthropic factor in the measure we have to look at how the Doomday Argument was resolved (although some people still don't agree with this). Ken Olum has done some recent work on such problems. He explains here why it is necessary to treat ''possible observers'' in the same way as ''actual observers''. In a multiverse setting this implies that you should include the anthropic factor in the measure. On page 15 of the article he actually gives a simple argument why (once one accepts the anthropic factor), the measure of a universe should decay exponentially with the amount of information needed to specify it. This feature seems to be universal, as it is also present in the formulas given in Schmidhuber's papers. Also, you can consider the argument about running an algorithm N times as wrote earlier. Also, note that many physicists do have an implicit notion of measure. E.g. most physicists find the occurrence of an incredibly small but nonzero cosmological constant troubling...




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Pasti:
I've been out of town so this in response to your response to me. (which is what I dislike most about this forum ... the inability to branch.
We are in complete agreeement ... my commens were not aimed your way. I don't believe any final theory is anywhere in sight until we understand, at a pretty deep level, that which composes the vast majority of the energy and mass in this universe. Trying to understand the universe based on quarks and electrons is like trying to understand the nature of a diamond from its inclusions.
DA Morgan




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DAM: "Trying to understand the universe based on quarks and electrons is like trying to understand the nature of a diamond from its inclusions." Well, I would have to say maybe or maybe not. But what I can definitely say that we will only know the answer to this issue after we become privy to the rest of the complextity that we know nothing about now




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Ibliss, I downloaded some of the refs you gave me. I will need a few days though to get through them, mostly because I hate it to read articles off the screen, so I need to print them. I managed to browse a few of them, but for the time being I cannot escape the impression that I am one of Asimov's Foundation characters reading the trilogy from the "inside". As for Schmidhuber's use of the anthropic principle, for the timeing it seems reasonable enough, since I cannot see any good way to calculate this anthropic factor (at leat the way I understand it should be calculated). So considering a "bitlike" set of values does not seem farfetched (or mre farfetched than the entire line of reasoning). But as I said, give me a few days to get used to the topic, so to speak. I am constantly fighting the urge of asking for some observational evidence that would justify this approach.




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And one more thing that sort of "puzzles" me. It is this "computability" aspect of the universes. I do not agree very much with Zuse's ideas of computability, when it comes to universes.
While it would be rather easy to compute rather idiotic spacetimes like I don't know, a Schwarzschield spacetime, or something simple like that, I don't see how once could do so with complex spacetimes where you have a natural loss of information during the history(ies). Aside from the fact that this is a huge analitical problem, how can you algorithmize an universe with changing laws, or with emerging new laws if the hystory becomes incomplete due to the natural loss of info.
Ibliss, do you know of any implementation of such algorithms, besides the regular cosmologicalsimulations?




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Hello Pasti,
Well, I don't know much about modeling spacetimes (not my subject). However, the question is if it can be done in principle. If you can formally describe what is going on then that's enough.
Another way to approch this is from the perspective of information theory. I think that Seth Lloyd has done some recent work on that. You could say that assuming the universe is algorithmic in some sense (Seth Lloyd doesn't make such assumptions) then that poses limits on the performance of a computer you can build (you can't compute faster than the universe itself).
It is known that classical mechanics allows for ceretain noncomputational phenomena. In a purely Newtonial world you could build a socalled ''Rapidly Accelerating Computer'', that could perform an infinite number of computations in a finite time.
So, according to what we know about the universe, we could be living inside an algorithm.




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Ibliss: "Well, I don't know much about modeling spacetimes (not my subject). However, the question is if it can be done in principle. If you can formally describe what is going on then that's enough."
Well, I do know something about modeling spacetimes, I did some modeling some years ago. The main issue related to modeling is that you must know all before you model something. Modeling does not bring you any fundamental information. So the question of principle as I see it is something like that: what additional knowledge do I get from having a computable universe? Computability means necesarily the existence of an analytical model, and once I have such a model, computability remains just a tool of the detail.
Ibliss: "Another way to approch this is from the perspective of information theory. I think that Seth Lloyd has done some recent work on that. You could say that assuming the universe is algorithmic in some sense (Seth Lloyd doesn't make such assumptions) then that poses limits on the performance of a computer you can build (you can't compute faster than the universe itself)."
OK, so? I have bounds on computational speed for a computer, which is fine, and it is also something to be expected (simply because interactions propagate with finite speed). While this is important in CS, what does this bring new to gravitation, quantum gravitation and cosmology? Maybe something related to the "speed of evolution" of a universe. Do you know any refs on this issue? This would be interesting.
Ibliss: "It is known that classical mechanics allows for ceretain noncomputational phenomena. In a purely Newtonial world you could build a socalled ''Rapidly Accelerating Computer'', that could perform an infinite number of computations in a finite time."
So? Even the worst computers cannot be described by a purely newtonian model (abacus and slide ruler excluded).
Ibliss: "So, according to what we know about the universe, we could be living inside an algorithm."
Hm, this is the same as saying that we live inside a model of reality. Which is an ideea that I do not particularly subscribe to. There is also the possibility that we make models to understand the reality as we perceive it, and this reality exists beyond observers. And medical cases excluded, this seems to be for the time being the case.This is why I am rather unhappy with Penrose's combinatorial approach to "reality".




