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.

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

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 space-time...

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.

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.

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.

''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).

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 ad-hoc 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.

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.

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.

Pasti wrote: 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.

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.


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''.

I agree.

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.tech-archive.net/Archive/sci.physics.research/2004-08/0314.html

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?

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...

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.

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

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.

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?

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 non-computational phenomena. In a purely Newtonial world you could build a so-called ''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.

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 non-computational phenomena. In a purely Newtonial world you could build a so-called ''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".

Pasti:''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.''

That's right.


Pasti:''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.''

It may be that the fundamental laws are a consequence of deeper principles in which the concept of information plays a more important role. In the modles proposed by schmidhuber this is quite obvious, although it is not clear to me that his models are consistent with the known laws of physics.

I'll try to find the articles by Seth Lloyd.


''Ibliss: "It is known that classical mechanics allows for ceretain non-computational phenomena. In a purely Newtonial world you could build a so-called ''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).''

Well, in a Newtonial world you could build a machine that cannot be simulated on a Turing machine. So, if you only consider computable universes in your ensemble, then such a classical world is 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".''

Yes, the idea being that reality is the model itself. So, you eliminate the question: ''what is physical reality?''. You just postulate that it is precisely the (unknown) mathematical model in which we live.

The fact that science works at all is evidence such a scenario. For our macroscopic world to exist you only need gravity and the standard model. Otherwise, there would be no reason why there couldn't be non-renormalizable terms in the Lagrangian. Where does the preference for simple elegant theories which contain only a few coupling constants come from?

2 questions - 1: Can any of you demonstrate a time event that is NOT a kinetic energy event? 2: Can any of you DEMONSTRATE infinity? This is the beginning of understanding...

Timer, you should have been more explicit in stating your question, since the meaning is rather equivocal. So I will answer you in the same manner. If you really want to discuss that, we'll srt it out later.

Timer: "1: Can any of you demonstrate a time event that is NOT a kinetic energy event?"

Any pure timelike event. It EXISTS by construction.

Timer "2: Can any of you DEMONSTRATE infinity?"

The accumulation point of any monotonical and unbound say, real function. Once again, it EXISTS by construuction.

How are these questions relevant to the current topic?

A failure in the logic circuit...like most<if not ALL>people, you think of time and energy as two different things, as the phrase : "don't waste your time AND energy" is quite common. Yes, I know, it seems to be a minor point<t=dKE>but such are the subtle forks in the road between truth and falsehood, right and wrong. You now stand at that fork : define, precisely, the difference between time and kinetic energy.

Timer: "...t=dKE..."

And this stands exactly for what?

Timer: "A failure in the logic circuit...like most <if not ALL>people, you think of time and energy as two different things, as the phrase : "don't waste your time AND energy" is quite common..."

Error #1: You have no clue what I think, for starters.

Timer:"...Yes, I know, it seems to be a minor point <t=dKE>, but such are the subtle forks in the road between truth and falsehood, right and wrong..."

Yeah, yeah, yeah...Cut this mystico-scientological rambling and get to the point. YOU should spend more TIME AND ENERGY in trying to make your points clearer.

Timer:"...You now stand at that fork : define, precisely, the difference between time and kinetic energy."

As for the definition you want, this is rather trivial. Yu can define a time variable without having to involve the concept of kinetic energy (see the pure timelike event I mentioned previously).

10-4

Hi Ibliss,

Sorry for the delay in continuing this thread. Before continuing the discussion, and taking into account the direction this thread is going, please tell me that you have no hidden "intelligent design" agenda, because I wouldn't like to waste my time under such circumstances. I highly doubt this is the case, but one can never know. I would appreciate a honest answer to this issue.

Ibliss: "It may be that the fundamental laws are a consequence of deeper principles in which the concept of information plays a more important role. In the modles proposed by schmidhuber this is quite obvious, although it is not clear to me that his models are consistent with the known laws of physics."

Somehow, as much as this idea sounds appealing, I don't think this is the case. Information is lost and created at every moment in time. Unless you have a set of "fundamental bits" that are eternal and indestructible, or unless you account somehow "informationally" for the principle of general invariance, I don't see how this is possible, beyond some simple and unrealistic cosmological models(like Schmidhuber's models).

Ibliss: "I'll try to find the articles by Seth Lloyd."

Would be interesting.

Ibliss: "Well, in a Newtonial world you could build a machine that cannot be simulated on a Turing machine. So, if you only consider computable universes in your ensemble, then such a classical world is excluded."

And? If a newtonian world (which is not exactly a realistic one for our purposes) cannot be computationally representable, why would I even bother to try a computational representation of a quantum universe? As I said before, I do not entirely agree with the combinatorial view of the quantum world conjectured by Penrose. While for simple geometries and topologies it is true that a quantum theory can be purely combinatoric, I personally doubt that such combinatorial properties are preserved in a realistic quantum cosmological model. Think about it.

Ibliss: "Yes, the idea being that reality is the model itself. So, you eliminate the question: ''what is physical reality?''. You just postulate that it is precisely the (unknown) mathematical model in which we live."

Oh, come on Ibliss. In this form, this is a very cheap version of Kantian philosophy, and much worse, it is principially at odds with the scientific approach. The Newtonian model was solved long before the beginning of the last century, and yet people have continued to try and look beyond the (known) Newtonian model, towards new phenomenology, newer "models" and so on and so forth, you know the drill. You cannot eliminate the question of what is physical reality, because then you loose the consistency of description. In other words, everyone becomes a mental case with his own perception, no matter what the perception of others is.

Ibliss: "The fact that science works at all is evidence such a scenario."

I am not so sure that the fact that "science works at all" is evidence of anything of the sort you mention. It should "damn well work", so to speak, because it ia based on the observation of the physical reality. And while mathematical models are necessary for "manipulating" different aspects, you do not always need math/models to describe the different levels of "reality".

Hello Pasti, I had some problems posting here (I could no longer login and had to register again).

I have no hidden agenda. My agenda is nothing more than trying to show that the notion of a physical universe is flawed (like the notion of a God).


About information you wrote: ''Somehow, as much as this idea sounds appealing, I don't think this is the case. Information is lost and created at every moment in time. Unless you have a set of "fundamental bits" that are eternal and indestructible, or unless you account somehow "informationally" for the principle of general invariance, I don't see how this is possible, beyond some simple and unrealistic cosmological models(like Schmidhuber's models).''

I don't see how information is created according to any of the known or proposed laws of physics. Hawking radiation wouldn't have been a big deal if physicists really believed this.

No experiment has ever observed a nonunitary time evolution of an isolated system.

I still have to look up the articles by Lloyd. I don't know enough about Quantum Cosmology to say that Penrose's models are realistic. However, let's not forget that in mathematics only systems that use first order logic are 100% well defined.

It is more convenient in practise to use higher order logical systems, but one cannot argue that just because we use, say, the uncountable reals, that space-time is necessarily uncountable. A trivial counterexample:

In principle, I could have simulated a physicists making this assertion inside a finite state machine!


I didn't understand this comment:

''You cannot eliminate the question of what is physical reality, because then you loose the consistency of description. In other words, everyone becomes a mental case with his own perception, no matter what the perception of others is.''

The world in which we live would simply be purely mathematical in nature. It doesn't mean that I cannot do physics anymore. What is true is that the question of why the scientific method works becomes relevant and now has to be explained (maybe that is what you meant)


Pasti:''I am not so sure that the fact that "science works at all" is evidence of anything of the sort you mention. It should "damn well work", so to speak, because it ia based on the observation of the physical reality.''

I don't see this. There is no reason why today the universe works according to the same laws as yesterday. You have to postulate the existence of fundamental laws first. You cannot invoke the AP, because our existence is compatible with, say, changing the masses of electrons by tiny but measurable amounts.

Note that I want to explain the observation of physical reality that these things do not happen. Saying that it doesn't because we don't observe it doesn't explain it. Newton could have said that apples fall toward the ground because he opbserved it. True, but that doesn't explain his observation.

Similarly, I want to know why the scientific method works.

Ibliss: "Hello Pasti, I had some problems posting here (I could no longer login and had to register again)."

Send an email to Kate, she should be able to fix this problem.

Ibliss: "I have no hidden agenda."

I am more than happy to hear this. So let's continue the discussion.

Ibliss: "My agenda is nothing more than trying to show that the notion of a physical universe is flawed (like the notion of a God)."

Why would you need that?Why does the existence of the concept of physical reality bother you so much? Alternatively, why does the principles of general covariance/invariance bother you? You consider them incorrect?


Ibliss: "I don't see how information is created according to any of the known or proposed laws of physics. Hawking radiation wouldn't have been a big deal if physicists really believed this."

Let me see. I just destroyed 25 of the 50 pages I wrote for my paper,so I created info, and I destroyed some, and the net balance is that I actually created info.

As for the Hawking radiation, do net get too excited, since in the context of information creation/annihilation the BH is not a very relavant example, in the sense that the system is much too simple, and does not reflect the overall physical reality (see above childish example). If I look to the attempts made today in the context of quantum gravity to characterize information contained in the horizon of the black hole, it reminds me of the Fall of the Constantinopole, when with the turks at their gates the church could find nothing better to do that debate hom many angels can exist on the tip of a needle!

Ibliss: "No experiment has ever observed a nonunitary time evolution of an isolated system."

Once again, the systems investigated are rather simple, and isolated systems are in truth only abstractions. I think calorimetry illustrates this point very well.

Ibliss: "I still have to look up the articles by Lloyd. I don't know enough about Quantum Cosmology to say that Penrose's models are realistic."

Well, for the Penrose ideeas, if you want I can dig up some refs. It is called combinatorial quantization, and sme people, Penrose included are or have been very excited about it.

Ibliss: "However, let's not forget that in mathematics only systems that use first order logic are 100% well defined."

I am not familiar with what first order logic means, but since when are all physical systems well defined? Think of QED and renormalization.

Ibliss: "It is more convenient in practice to use higher order logical systems, but one cannot argue that just because we use, say, the uncountable reals, that space-time is necessarily uncountable. A trivial counterexample:In principle, I could have simulated a physicists making this assertion inside a finite state machine!"

I agree with you, regarding the countability argument. But on the other hand one cannot impose countability as a principle just because for a few simple models indeed the quantization is purely combinatorial.


Ibliss: "I didn't understand this comment:''You cannot eliminate the question of what is physical reality, because then you loose the consistency of description. In other words, everyone becomes a mental case with his own perception, no matter what the perception of others is.''."

What I wanted to say is the fact that physics is the slave of a higher authority, so to speak, namely observation. Observation that is defined, if you whish, to be reproducible regardless of the observer, i.e. in the same experimental conditions both you and I, in different labs should observe the same, say, ionization potential of the H atom.
Physical reality is defined, generally speaking, as the set of all hierarchies of observable phenomena, even if some observations have not been performed yet.
The models describing this physical reality are a different issue, but the most fundamental characteristic of a model is consistency with the physical reality as defined above (note that some models might be incomplete, or consistent at one level and inconsistent at others, etc.) If you eliminate the physical reality, we could end up as Asimov said in one of his books:we could both look at a basaltic stone, and you could claim it is basalt while I can claim with equal value of truth(in my own physical reality) that it is actually a ruby stone. This is the "mental case" trend I was talking about. Which in the best case leads to mysticism, but not to science.

Ibliss: "The world in which we live would simply be purely mathematical in nature. It doesn't mean that I cannot do physics anymore."

How could it be so? Mathematics is a purely abstract system, which needs input from the physical world. First you have to do "physics", and then math.

Ibliss: "What is true is that the question of why the scientific method works becomes relevant and now has to be explained (maybe that is what you meant)."

You have lost me here. Of course it works, because the consistency requirement mentioned above acts as feedback in the evolution/development of a model/understanding.

Ibliss: "I don't see this. There is no reason why today the universe works according to the same laws as yesterday. You have to postulate the existence of fundamental laws first."

No, I do not have to postulate anything, truth be told. I only need to do observations, find patterns and trends, and after verification, memorize them and apply them until I find observations that deviate from or invalidate these trends. At which point I rethink the trends, and the cycle continues as before.

Ibliss: "You cannot invoke the AP, because our existence is compatible with, say, changing the masses of electrons by tiny but measurable amounts."

No,I cannot, you are right. But for the time being I have too litle information/knowledge to actually make such a connection. And the anthropic principle is nothing more than a trick, if you like, that covers this lack of knowledge.

Ibliss: "Note that I want to explain the observation of physical reality that these things do not happen. Saying that it doesn't because we don't observe it doesn't explain it. Newton could have said that apples fall toward the ground because he opbserved it. True, but that doesn't explain his observation."

Well, I agree with you here, observation does not mean explanation. But the consistency requirement mentioned above will at certain points (when and if enough info/knowledge becomes available)lead you to the explanation, as it has happened before.

Ibliss: "Similarly, I want to know why the scientific method works."

I guess the above "feedback" explanation would be a good starting point for such a discussion.

Pasti: ''Why does the existence of the concept of physical reality bother you so much? Alternatively, why does the principles of general covariance/invariance bother you? You consider them incorrect?''

What bothers me is that ''real'' a physical world implies the existence of fundamental objects which cannot be further explained. At a certain point you are then forced to say that things are the way they are because that's what we observe.

Since this assumption is not necessary, I am sticking with the idea that the physical world is in fact purely mathematical in nature.


Pasti: ''Alternatively, why does the principles of general covariance/invariance bother you? You consider them incorrect?''

These principles don't bother me at all!


Pasti: ''Let me see. I just destroyed 25 of the 50 pages I wrote for my paper,so I created info, and I destroyed some, and the net balance is that I actually created info.''

This is just an illusion. If you take this seriously you could violate the second law of thermodynamics (just let Maxwell's demon dump information without increasing the entropy of the rest of the world).


Pasti: ''As for the Hawking radiation, do net get too excited, since in the context of information creation/annihilation the BH is not a very relavant example, in the sense that the system is much too simple, and does not reflect the overall physical reality (see above childish example). If I look to the attempts made today in the context of quantum gravity to characterize information contained in the horizon of the black hole, it reminds me of the Fall of the Constantinopole, when with the turks at their gates the church could find nothing better to do that debate hom many angels can exist on the tip of a needle!''


Well, you could just as well argue that momentum isn't exactly conserved. We have only rigorously tested it in very simple systems...


Pasti: ''Ibliss: "The world in which we live would simply be purely mathematical in nature. It doesn't mean that I cannot do physics anymore."

How could it be so? Mathematics is a purely abstract system, which needs input from the physical world. First you have to do "physics", and then math.''

Well, you are postulating a physical world, but yet no one knows exactly what that means. It could be that the ''physical world'' is just as abstract as any mathematical world.


Pasti: ''Ibliss: "What is true is that the question of why the scientific method works becomes relevant and now has to be explained (maybe that is what you meant)."

You have lost me here. Of course it works, because the consistency requirement mentioned above acts as feedback in the evolution/development of a model/understanding.''

But why is our world so extremely consistent that it can be captured in a simple model?


Pasti: ''No, I do not have to postulate anything, truth be told. I only need to do observations, find patterns and trends, and after verification, memorize them and apply them until I find observations that deviate from or invalidate these trends. At which point I rethink the trends, and the cycle continues as before.''


This can only work if you assume that simpler models are more likely to be correct than more complex models. Then you hope that the process converges to the correct model. Schmidhuber and Tegmark have explained this in their papers.


Pasti: ''But the consistency requirement mentioned above will at certain points (when and if enough info/knowledge becomes available)lead you to the explanation, as it has happened before.''

Yes, but you have to make certain assumptions. Ultimately your brain can only store a finite amount of information, which is an infinitessimal fraction of the total information present in the universe. Yet we claim that it is possible to ''compress'' all of the information present in the universe to a tiny amount (the number of bites needed to specify the (as of yet uknknown) laws of physics plus initial conditions).

This is an assumption that can only be further explained in models which treat apperent physical universe we live in as one member of an ensemble of all possible worlds.

Ibliss: "What bothers me is that ''real'' a physical world implies the existence of fundamental objects which cannot be further explained."

This is something I have heard in several instances, from several people, and in my oppinion is incorrect, at least for the time being. It does not necessarily imply the reductionism that you mention, although many claim the opposite. This is an already biased view. Any present reductionism reflects only the level of the present knowledge/explained phenomenology, and based on this present level of knowledge there is no way one can forcast that this trend will continue. It is perfectly possible that this reductionist scheme to be actually divergent, so to speak.

Ibliss: "At a certain point you are then forced to say that things are the way they are because that's what we observe."

Not necessarily, see above. But you can definitely say that things are AS we observe them, and not because we observe them. there is a subtle difference.

Ibliss: "Since this assumption is not necessary, I am sticking with the idea that the physical world is in fact purely mathematical in nature."

And the evidence for your assumption is...? Of course, you can make this assumption, but then how is your scheme better than the reductionist scheme above that you don't agree with? You have given up a concept only to postulate another.


Ibliss: "These principles don't bother me at all!"

Well, maybe they should, because in the framework of GR they are exactly the definition of physical reality, if you think about it.


Ibliss: "This is just an illusion. If you take this seriously you could violate the second law of thermodynamics (just let Maxwell's demon dump information without increasing the entropy of the rest of the world)."

Give me some credit Ibliss. The example is childish, but not that childish. It does not violate anything, since what I write on paper depends on the amount of paper and 0.5 leads in the universe so to speak, which both are finite, as is the writer, energetically speaking.

But if you don't like this example, consider the following. Pump down a chamber, and then fill it from a tank with Ar, and let the Ar thermalize. After thermalization, using classical mechanics, Monte-Carlo and whatever you like devolve the gas up to the point where it enters back into the tank. Do you think this can be done?

Ibliss: "Well, you could just as well argue that momentum isn't exactly conserved. We have only rigorously tested it in very simple systems..."

I am afraid you misunderstood me. Think of my statement as of the Maldacena conjecture:works in simple/particular cases but not in the general case.
The comparison you made with conservation oof momentum is not exactly to the point, no offence. Conservation of momentum, of corse within experimental errors, has been confirmed not only for simple systems, but for all systems where such conservation is relevant.This is the reason why it is believed to be a "fundamental law" until the contrary is observed. But this is not the case for the conservation of information law that you mentioned, which has been only theorethically developed for very simple geometries, and has not been tested experimentally beyond such simple cases, it tested at all.

Ibliss: "Well, you are postulating a physical world, but yet no one knows exactly what that means. It could be that the ''physical world'' is just as abstract as any mathematical world."

I am not postulating anything. I am observing, interpreting, observing again, etc. There is no postulation (in the mathematical sense) in physics beyond the mathematical formulation. The "postulates" in physics are merely the conclusions of observations, and they are believed to hold true only until they are contradicted. Think about it.

But then, as I said before, in your case you give up concept to replace it with a true postulate, that of a "mathematical reality", which is even less supported than the "physical reality" one.

And yes, you are right, in the end the "physical reality" can be as abstract as your mathematical reality, but this cannot be used as an excuse, so to speak, to introduce unsupported assumptions, or unobservable assumptions, as the case may be.


Ibliss: "But why is our world so extremely consistent that it can be captured in a simple model?"

Wha'? Which model is that, because I haven.t heard of it yet. What you have are a bunch of theories, some of them consistent (mostly the classical ones), some of them inconsistent (mostly the quantum ones), some of them can be coupled, not al of them can be unified, some of them we don't know yet what they are, etc. more to the poimt, you have the electroweak theory which is inconsistent in the sense of renormalization, not to mention the inconsistencies trailed along from quantum mechanics, you have the strong-nuclear theory, which can be coupled but not unified with the former, and has similar inconsistencies, you have only classical gravitation and a plethora of theories as to what quantum gravitation might be, let alone any atempt to unifying it with any of the former, you don't know how to de QFT consistently in curved spacetimes, and you have classical theories that are mostly consistent within experimetal bounds, but there is no clear ideea how classical theories can be actually obtained from the corresponding quantum ones, since, of course, we don't exactly know how to quantize a classical theory. And I coud ramble much more on this topic.
So where is the simple model that you mentioned?


Ibliss: "This can only work if you assume that simpler models are more likely to be correct than more complex models. Then you hope that the process converges to the correct model. Schmidhuber and Tegmark have explained this in their papers."

I am less familiar with Schmidhuber, I only have your refs, but I certainly do not agree with Tegmark. He makes statements typical to the theorist who's never done any experimental work except the dreaded labs in undergrad.
In physicas you DO NOT assume that there is a correct model or an incorrect model. You only do observations, interpret it, assume that your interpretation is correct and then test is again against newer observations. If these newer observations contradict your interpretation, you strive for a more correct one. If not, you assume with caution that your interpretation might be correct and be on the lookout for less evident contradictions. In other words, in physics you go where observation takes you (although modern theoretical physics has gotten out of control in this sense, due to lack or relevant observations).


Ibliss: "Yes, but you have to make certain assumptions. Ultimately your brain can only store a finite amount of information, which is an infinitessimal fraction of the total information present in the universe. Yet we claim that it is possible to ''compress'' all of the information present in the universe to a tiny amount (the number of bites needed to specify the (as of yet uknknown) laws of physics plus initial conditions)."

Let me answer you with a question, to be viewed int he conyext of informational reductionism. When was the last time you used the phlogistic theory to interpret observations?

Ibliss: "This is an assumption that can only be further explained in models which treat apperent physical universe we live in as one member of an ensemble of all possible worlds."

And the proof of your statement in regard the the "...can only be further explained..." is where?
Furthermore, what makes you think that with the present level of knowledge you can describe correctly "the big picture"? The present knowledge is notoriously too sparse for this purpose, not to mention that if you culd actually do that, no new information could enter your picture, you know what I want to say.

Physics does not work in this way, despite the "media" evidence to the contrary. Physics develops in baby-steps, regardless of how eager are the practitioners, and it NEVER tries to explain anything beyond the present level of knowledge (in the sense that the theories are tested in small/comfortable increments, so to speak, without attemting to explain everything at once). I am aware how this sentence sounds, but I hope you will get my point. Case in question: the Big Bang. Only for the layman is the BB a physical reality.For the "G-men", they don't really take it very seriously in this respect, it is just a singularity indicating the breakdown of the theory, and potentially be beginning of new physics.

Hi Pasti,

let me address a few of your comments.

Pasti: ''This is something I have heard in several instances, from several people, and in my oppinion is incorrect, at least for the time being. It does not necessarily imply the reductionism that you mention, although many claim the opposite. This is an already biased view. Any present reductionism reflects only the level of the present knowledge/explained phenomenology, and based on this present level of knowledge there is no way one can forcast that this trend will continue. It is perfectly possible that this reductionist scheme to be actually divergent, so to speak.''

Well, that's even more reason to abandon the idea of ''real'' physical universe.


Pasti: ''Ibliss: "Since this assumption is not necessary, I am sticking with the idea that the physical world is in fact purely mathematical in nature."

And the evidence for your assumption is...? Of course, you can make this assumption, but then how is your scheme better than the reductionist scheme above that you don't agree with? You have given up a concept only to postulate another.''


No evidence for it, but also no evidence against it, so why not try to do without? Now you do have to adopt certain postulates to make progress that aren't explicitely present in single universe theories (what is the measure on the set of all possible universes, e.g.). However, as I tried to explain , all physicists make implicit assumptions about this when interpreting experimental results (Occam's Razor).

Pasti: ''I am not postulating anything. I am observing, interpreting, observing again, etc. There is no postulation (in the mathematical sense) in physics beyond the mathematical formulation. The "postulates" in physics are merely the conclusions of observations, and they are believed to hold true only until they are contradicted. Think about it.''

It's precisely the ''mathematical formulation'' that you mentioned.

We have found so far is that nature is so extremely regular that a small set of postulates suffices to describe the outcome of experiments below, say, 100 GeV.

So, you have a handfull of (as far as we know) arbitrary constant, that defines the standard model and general relativity. Even though we already know that these theories are not consistent, we nevertheless claim that experimental outcomes are correctly described by these theories provided we don't go to too high energies.


Ok, I will address some of the other points you raised later.

Pasti: ''But if you don't like this example, consider the following. Pump down a chamber, and then fill it from a tank with Ar, and let the Ar thermalize. After thermalization, using classical mechanics, Monte-Carlo and whatever you like devolve the gas up to the point where it enters back into the tank. Do you think this can be done?''

No, because the Ar interacts with the walls of the chamber and thus the initial state of the Ar cannot be recovered from the final state of the Ar alone.


Pasti: ''I am afraid you misunderstood me. Think of my statement as of the Maldacena conjecture:works in simple/particular cases but not in the general case.
The comparison you made with conservation oof momentum is not exactly to the point, no offence. Conservation of momentum, of corse within experimental errors, has been confirmed not only for simple systems, but for all systems where such conservation is relevant.This is the reason why it is believed to be a "fundamental law" until the contrary is observed. But this is not the case for the conservation of information law that you mentioned, which has been only theorethically developed for very simple geometries, and has not been tested experimentally beyond such simple cases, it tested at all.''

But what about unitary time evolution:

i h-bar d|psi>/dt = H|psi>

Have any experiments detected violations of this rule for isolated systems?


Pasti: ''Ibliss: "This is an assumption that can only be further explained in models which treat apperent physical universe we live in as one member of an ensemble of all possible worlds."

And the proof of your statement in regard the the "...can only be further explained..." is where? ''

I meant this. When you abandon the notion of a (God given) single physical universe, you are left with an ensemble of all possible universes, each one ''as physical'' as another one. So, you will now have to explain why we live in this particular universe instead of another. There is no reason to assume that the answer to such questions can be found, but at least such questions do make sense in this setting. In single universe theories it is not clear that the question has any meaning at all.


Pasti: ''In physicas you DO NOT assume that there is a correct model or an incorrect model. You only do observations, interpret it, assume that your interpretation is correct and then test is again against newer observations. If these newer observations contradict your interpretation, you strive for a more correct one. If not, you assume with caution that your interpretation might be correct and be on the lookout for less evident contradictions. In other words, in physics you go where observation takes you (although modern theoretical physics has gotten out of control in this sense, due to lack or relevant observations).''

The very act of interpreting means that you are searching for a model. Now, in may cases that model manifests itself in a very compelling way, so you may say that no ''searching'' is involved. However, that brings us back to the question why nature is so regular.

Explaining someting means that your model contains less information than is contained in the original experimental data. Otherwise it would be trivial curve fitting. This approach has been successful and there is no way conventional physics can explain why.

Another example. Fermi's theory of the Weak interaction is now known to be the low energy limit of electroweak interaction. However, there are an infinite number of (ugly) non-renormalizable theories that have the correct low energy limit. According to your arguments they could all have been correct and there would be no preference for the theory we now know to be correct.

I agree that they could in principle all have been correct, but that the electroweak theory was more likely to be correct, because it contains fewer arbitrary parameters.

Within the framework of your ''philosophy'' the verification of the electroweak theory raises more questions: Why this particular one with 2 new parameters, and not one of the trillions of others which contain zillions of arbitrary parameters?

Ibliss: ?Well, that's even more reason to abandon the idea of ''real'' physical universe.?

You have lost me here. OK, I understand that you are a proponent of a mathematical reality replacing the good ol? physical reality, but the arguments I offered do not justify in the least your statement above. Let me try another avenue, clearer I hope. Do you think that any and every observation regarding the surrounding nature can be translated into a mathematical model? At least for the time being the answer is no. So for the time being, any comprehensive mathematical model will necessarily be an incomplete description of the nature.
Now, is this a trend that is likely to be universally valid (that some observations will never be expressible in mathematical language)? I have no ideea, and no one has any ideea. Are there more or less educated guesses? Not at this time. We only have speculations. What could actually help us answer these questions? The physical reality for sure. The mathematical reality never, unless you compare it to the observations, i.e. with the physical reality. Sure, there is the possibility a la Umberto Eco?s ?Foucault?s Pendulum? to actually devise all the possible models (there is still the question how you could even do this practically with only partial knowledge available), and then compare them with observations to see which one(s) match. But you still cannot rid yourself of the physical reality, even in this case. You need the standard for comparison!


Pasti: ?And the evidence for your assumption is...? Of course, you can make this assumption, but then how is your scheme better than the reductionist scheme above that you don't agree with? You have given up a concept only to postulate another.?


Ibliss: ?No evidence for it, but also no evidence against it, so why not try to do without? Now you do have to adopt certain postulates to make progress that aren't explicitely present in single universe theories (what is the measure on the set of all possible universes, e.g.). However, as I tried to explain , all physicists make implicit assumptions about this when interpreting experimental results (Occam's Razor).?

OK, let?s suppose indeed that it is worth to try your approach, and let?s forget about the evidence and arguments against it. And now let?s suppose that you develop your multiverse theory, and you find (and you will necessarily find so) that there are several ?universes? infinitesimally close to the observations, within your measure. I.e. you will find several universes, with different degrees of theoretical complexity that fit your observable universe. What will you do then? Which will you choose, with only partial knowledge of the ?whole?? So you still need Occam?s Razor, and not only that, you will also need all the assumptions one makes in a multiverse, for the obvious reasons. So if indeed you are true to Occam?s Razor principle, you have just developed a theory requiring a much larger number of assumptions than the one that is already ?on the market?, so by Occam?s razor, you should drop it and take the minimal one. Of course, unless you find an effect describable only in your multiverse theory, which unfortunately, by design, is not testable. So what have you gained? Insight? Not any more insight than you could get from the theory on the market. Intelectual satisfaction? Definitely. But unfortunately, the latter is not essential in understanding nature?


Pasti: ''I am not postulating anything. I am observing, interpreting, observing again, etc. There is no postulation (in the mathematical sense) in physics beyond the mathematical formulation. The "postulates" in physics are merely the conclusions of observations, and they are believed to hold true only until they are contradicted. Think about it.''

Ibliss: ?It's precisely the ''mathematical formulation'' that you mentioned.?

And how about those observations that cannot be put in mathematical language, even if this is only for the time being, so to speak?

Ibliss: ?We have found so far is that nature is so extremely regular that a small set of postulates suffices to describe the outcome of experiments below, say, 100 GeV. So, you have a handfull of (as far as we know) arbitrary constant, that defines the standard model and general relativity. Even though we already know that these theories are not consistent, we nevertheless claim that experimental outcomes are correctly described by these theories provided we don't go to too high energies.?

OK, so you have a handfull of constants. According to the viewpoint, this may or may not have any significance whatsoever (you know, the fundamental constants are just unit matching fudge factors and so on and so forth ? I don?t subscribe to the ideea and I am not sure if you do). But nevertheless, significance of the constants aside, you still have more than only two models, that cannot be unified. What makes you think that there will be such a GUT, even in this context? Sure, people hope, but even if their hope will become reality, the unification of physics with biology has not even begun, and so on and so forth. So what makes you think that such a comprehensive model could exist?


Ibliss: ?No, because the Ar interacts with the walls of the chamber and thus the initial state of the Ar cannot be recovered from the final state of the Ar alone.?

Well, there you go. No matter the reason, the situation I presented you is a perfectly valid physical situation, and in the process you have lost information.


Pasti: ''I am afraid you misunderstood me. Think of my statement as of the Maldacena conjecture:works in simple/particular cases but not in the general case.
The comparison you made with conservation of momentum is not exactly to the point, no offence. Conservation of momentum, of course within experimental errors, has been confirmed not only for simple systems, but for all systems where such conservation is relevant. This is the reason why it is believed to be a "fundamental law" until the contrary is observed. But this is not the case for the conservation of information law that you mentioned, which has been only theorethically developed for very simple geometries, and has not been tested experimentally beyond such simple cases, it tested at all.''

Ibliss: ?But what about unitary time evolution?? Have any experiments detected violations of this rule for isolated systems??

Not to my knowledge, but then why is this relevant to anything? The observable universe is NOT isolated (according to modern observations, the cosmological horizon has roughly 3000 MPc/H, and as for the entire universe, we know even less than about the observable one?.
So where does unitary evolution come into play?


Pasti: ?And the proof of your statement in regard the the "...can only be further explained..." is where? ?

Ibliss: ?I meant this. When you abandon the notion of a (God given) single physical universe, you are left with an ensemble of all possible universes, each one ''as physical'' as another one.?

Nothing ?God given? about such an assumption. It is based on observation/observational capabilities. As soon as we can observe something that contradicts this assumption, it will change accordingly. If you give up this assumption, as you suggest, you are left with whatever you can imagine, including your multiverse theory.

Ibliss: ?So, you will now have to explain why we live in this particular universe instead of another. There is no reason to assume that the answer to such questions can be found, but at least such questions do make sense in this setting. In single universe theories it is not clear that the question has any meaning at all.?

I agree that you can do all you say in your setting. But how is this relevant to anything? Let?s back up a bit, and review the idea. You give up a concept backed up by observation in favor of a concept with no observational support whatsoever, you create a conundrum stemming directly from the introduction of the unsupported concepts, and than you claim that the answer is somehow relevant to the phenomenology in a single universe? Sounds quite fishy to me.
The question of why do we exist in this universe makes sense in single universe theories, there is no doubt about this issue. But I once again doubt that we will be able to find any cogent answer to it at this moment in time, with the little we know. We don?t know yet what life is and how it has appeared, and by going to multiverse theories you won?t solve these problems either. They must first be solved in a single universe, and only after they are solved we can attempt to ask questions of the nature that you mention. Otherwise you will solve only artificially created conundrums, which by design cannot elucidate question to which you don?t know the answers (you should remember that the way you construct a model in physics is by knowing the answers beforehand, from observations, and not the other way around; when you extend the model infinitesimally beyond the known answers, you are looking in fact for ?experimental? questions and hoping that the model already includes in its built the right answer that will come from observation).

Ibliss: ?The very act of interpreting means that you are searching for a model. Now, in may cases that model manifests itself in a very compelling way, so you may say that no ''searching'' is involved. However, that brings us back to the question why nature is so regular.?

No Ibliss, a theory is not necessarily fully translatable in a mathematical model. Ideally, people hope that it would be, but then historically sometimes it was necessarily to invent the language necessary to translate the theory into (Newton and Leibnitz), sometimes it was not necessary to translate anything into mathematical language to develop a theory (Faraday), and sometimes, there are observations that we don?t even know if they are translatable into mathematical language (life).

Ibliss: ?Explaining something means that your model contains less information than is contained in the original experimental data. Otherwise it would be trivial curve fitting. This approach has been successful and there is no way conventional physics can explain why.?

Of course it can. It is called symbolism/symbolistic representation, and it?s been around since almost prehistory. All symbols contain much more information than the representation itself, from cave paintings to hieroglyphs to pictography to whatever else you like. Mathematically, if it pleases you, you have the theory of hierarchies and categorization, applied to symbolistic language/representations.
Ibliss: ?Another example. Fermi's theory of the Weak interaction is now known to be the low energy limit of electroweak interaction. However, there are an infinite number of (ugly) non-renormalizable theories that have the correct low energy limit. According to your arguments they could all have been correct and there would be no preference for the theory we now know to be correct.?

Ibliss, you are giving the wrong counterexample. At the time the electroweak theory was developed, renormalizability was already considered to be a sine qua non requirement for any quantum theory, due to the earlier success of QED. Renormalizability is a requirement (albeit purely mathematical in character) that has been observed to hold valid in constructing models consistent with experimental observations (you will have to agree with me that recovering from a mathematical model a value matching the observation up to the 14th decimal is a heck of a consistency, which is the case for QED). Is it empirical? Sure.Has it been observed to be working? Sure again. Could it fail, say for gravity? Of course.
If the renormalizability requirement would have been absent, then the situation would have been drastically different, and indeed one should have had to use Occcam?s razor criterion, unless something else could have qualified as a selection criterion.


Ibliss: ?I agree that they could in principle all have been correct, but that the electroweak theory was more likely to be correct, because it contains fewer arbitrary parameters.?

Well, not necessarily because of that. In your argument, the criterion was renormalizability, and not necessarily simplicity.

And yes, in developing a theory one expressly includes the ?additional? Occam?s Razor ?principle?. But then, you will ask why should such a principle be included in such a task. The answer is simple enough, in principle at least. Once again it has been observed that roughly speaking, more complicated theories ?contain? more complicated phenomenology, which should be observed if the theories are correct. If some of the predictions of such theories yield unobserved phenomenology, or incorrect phenomenology, then these theories are discarded. If you apply this ?selection? method to all the theories that are candidates for a given set of observations, maybe not surprisingly, you will end up with the simplest theory fitting the data. This is the essence and the reason for Occam?s Razor ?principle?. The practice however, turns out to be much more difficult, if you know what I mean.

Ibliss: ?Within the framework of your ''philosophy'' the verification of the electroweak theory raises more questions: Why this particular one with 2 new parameters, and not one of the trillions of others which contain zillions of arbitrary parameters? ?

Oh, come on Ibliss. You know exactly what I was trying to say in my ?philosophy. Using any other selection criterion or criteria leads you to the same questions. Even after choosing somehow the best model, the question of why does the best model for the Omega theory contain exactly x parameters and not y remains a more or less xalid question, and you know it.

I won't be able to reply to all your comments today. Let me address a few points.

Pasti :''Do you think that any and every observation regarding the surrounding nature can be translated into a mathematical model? ''

There is no proof that it can't be done. According to quantum mechanics (Copenhagen interpretation), observations cannot be precisely expained using a mathematical model. There is no model that will predict outcome of experiments. However, there are other interpretations of QM in which no fundamental randomness occurs.

Also, it could be that QM is an approximation of a deterministic model (see e.g. some papers written by 't Hooft).


Pasti: ''OK, let's suppose indeed that it is worth to try your approach, and let's forget about the evidence and arguments against it. And now let's suppose that you develop your multiverse theory, and you find (and you will necessarily find so) that there are several &#8220;universes&#8221; infinitesimally close to the observations, within your measure. I.e. you will find several universes, with different degrees of theoretical complexity that fit your observable universe. What will you do then? Which will you choose, with only partial knowledge of the &#8220;whole&#8221;? So you still need Occam's Razor, and not only that, you will also need all the assumptions one makes in a multiverse, for the obvious reasons. So if indeed you are true to Occam's Razor principle, you have just developed a theory requiring a much larger number of assumptions than the one that is already &#8220;on the market&#8221;, so by Occam's razor, you should drop it and take the minimal one. Of course, unless you find an effect describable only in your multiverse theory, which unfortunately, by design, is not testable. So what have you gained? Insight? Not any more insight than you could get from the theory on the market. Intelectual satisfaction? Definitely. But unfortunately, the latter is not essential in understanding nature&#8230;''

Well, Occam's Razor (or choosing the ''minimal'' model) is a rather vague concept that can be made mathematically rigorous in certain ensemble theories. It is the only thing that you gain in practice, nothing more. The rest is intellectual satisfaction, I agree with that.

Pasti: ''No Ibliss, a theory is not necessarily fully translatable in a mathematical model. Ideally, people hope that it would be, but then historically sometimes it was necessarily to invent the language necessary to translate the theory into (Newton and Leibnitz), sometimes it was not necessary to translate anything into mathematical language to develop a theory (Faraday), and sometimes, there are observations that we don't even know if they are translatable into mathematical language (life).''

Yes, but I don't see why life wouldn't be translatable into a mathematical model. Life is just a consequence of organic chemistry, so in principle life is an emerging phenomenon that should also arise inside computer models programmed to similate the right (relevant) rules.


About electroweak theory, maybe that was not a good example. However, from the perspective of statistical physics, one could argue that the success of renormalizable theories is not surprising. Prabably all the irrelevant (non renormalizable) terms just flow to zero when you renormalize the TOE.