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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 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).''
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 nonrenormalizable terms in the Lagrangian. Where does the preference for simple elegant theories which contain only a few coupling constants come from?




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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...
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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?




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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.
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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 mysticoscientological 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).




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timer




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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".




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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 spacetime 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.




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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 spacetime 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.




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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.




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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, MonteCarlo 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 strongnuclear 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 babysteps, 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 "Gmen", 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.




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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.




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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, MonteCarlo 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 hbar dpsi>/dt = Hpsi>
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) nonrenormalizable 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?




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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) nonrenormalizable 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.




Joined: Jan 2005
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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 “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…''
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.




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