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The way forward, a different view.

  1. May 26, 2010 #1
    Hello all!

    I am new to Physics Forums but since i started a couple of days ago i've been reading obsessively in the "beyond SM" category.

    Here are some of my observation on the methods used to push the boundaries further.
    To any admins that might read this, please don't move the post just because there isn't any maths in it, that sorta would prove my point.

    Now to the matters at hand:

    My observations are that in trying to move the boundaries forward physicists and mathematicians are searching for a basic symmetry group to describe gauge symmetry and ST-symmetry under one roof.
    This constant suggesting of new groups, first SU(5), then SU(10), E6, E8, E8xE8, et.c. et.c.
    seems to me to be in analogy with the case of the monkeys and typewriters that eventually will produce Shakespeare. (Now im not trying to insult anybody, its just a classical philosophical thought experiment).

    I am not a "mathofob" i know my way around Diff. Geom. and Lie Alg. and so on, but my view of math (in contrast to alot of mathematicians) is that math is just a language.

    Now you might come at me with Dirac, and his strictly mathematical way of deriving his eq.
    but what he did was just to express, in the language of math, SR + QM.

    And here is my point, we need a new physical/philosophical idea/principle.
    QM was due to positivism. SR and GR was due to relativism. We need a new -ism!!!!

    What we are doing now is QFT + GR + X = Y. Math-models of Y could be anything, this is one equation for two unknowns.
    If we try long enough we might find a model that fits, but considering that "the universe is not only queerer than we imagine, but queerer than we can imagine" this might take a very long time. We might even hit it without realising.

    So here is a little pushforward in the philosophical aspect of TOE. (pun intended)

    Questions:

    1. Is the universe logically derivable. That is, can we generate all numbers in our TOE without measurment?

    1.b. If not, how many variables do we want there to be? Is 1 more beautiful than 2?

    1.c. If so, what does Gödels theorem suggest about our reality? Is incompleteness more ugly than paradox?

    2. Is the classical interpretation of positivism valid? Considering Boltzmans eq. and the now proposed extra dims.

    2.b. What would a new positivism look like that would accommodate both QM and Stat. Mech?

    3. What is the relation between mathematics and the universe in which it arises? Is Math the same in all universa?

    3.b. If not, can we say anything about our universe based on the mathematics possible in it?

    3. and one 1. are interconnected but not the same question.

    4. What is matter? (in all models people suggest fermionic and bosonic fields, but nobody asks why there is a distinction between matter particles or what the word "particle" means)

    5. What is the proper object with which to describe a universe? Manifold, set, category, class or something more general? In other words what is the fundamental property of a universe? An object to which laws apply? (here we get a bit into mathematical linguistics)

    Well i have alot of other questions but i think you get the point. In parallel to varying our mathematical models we should also vary our philosophical models.

    Love to hear your reaction.
     
    Last edited: May 26, 2010
  2. jcsd
  3. May 26, 2010 #2
    I believe the universe is derivable from logic. I know of an attempt to derive physics from logic with full mathematical/logical details. But it's not peer reviewed yet.

    It seems the starting premise of all science is that there is a reason for everything and all things co-exist and do not contradict the existence of anything else that exists. This means that all facts in the universe are consistent with every other, which means every conceivable thing logically proves or implies the existence of every other conceivable thing no matter how small.

    We have two abstract systems for thinking about all this: logic and math. Logic studies how the truth or falsity of one statement relates to the truth or falsity of another statement. We can use logic to study facts in reality by letting facts that exist be represented by statements about them that are true. This was probably the original use of logic to begin with.

    And math is used to count various items in reality. So if we assign a different set of numbers to each fact, or lay coordinates to the space of facts, whatever they are, no matter how small, then I would think it would be possible in theory to derive the laws of physics from a mathematical coordinate system imposed on sets. The problem would be to discover how to mathematically describe implication.



    I don't believe that physics is an attempt to find every conceivable mathematical equation that is true. Actually a TOE would be an attempt to find only one equation that is true, which happens to describe everything.
     
  4. May 26, 2010 #3
    Interesting reply friend! Nice to see im not the only philosophysicist.

    I don't really make a distinction between math and logic, according to Gödel one should though, but as long as we keep adding whatever piece of math that is not provable in our logical system as an axiom, logic produces all math, this procedure is done sometimes (not as blatantly as i describe it, but one adds axioms that generates whatever proof one wants. As long as its consistent with the other axioms). Maybe that says something about what "a proof" actually is.


    I believe Wightman and also others have tried to derive QFT from a set of axioms with some success and some setbacks (its is not a complete characterization), but in a TOE one must allow for much more general axioms, i.e. not of the kind "signature of the metric is Lorentzian".
    But maybe say something about what it means that two points in ST are not the same point for example.

    " I believe the universe is derivable from logic."

    That would be very nice to see, it would appeal to my aesthetics, but does that mean that all constants (electron mass/ charge et.c.) are produced by the theory not yet peer reviewed?
    If you believe that, do you also believe that Logic and in extension also math are the same in all universes, that is to say that math and logic transcends physical reality? In that case if our universe is logically derivable, then it is the only possible universe, one cannot in that case imagine universa with fewer or more dimensions than ours for example.

    As regards to Gödel, if our universe is logically derivable within an (strong enough) axiomatic system, there will always exist mathematical statements about reality that are not provable. That means that in theory we can never know everything about our universe.

    In a derivable TOE the universe and everything in it should be derivable. That is to say, if math is does not transcend physical reality all math should be derivable. Now idont know if thats an argument for the transcendence of math or for the non deriveability of the TOE.


    "...coordinate system imposed on sets..."

    That sound to me like a category
     
    Last edited: May 26, 2010
  5. May 26, 2010 #4
    I'm not sure whether a derivation from logic would not result in symmetry principles that might break in arbitrary directions. But I think general principles, say, like QM or GR might emerge from such an effort.

    We don't know that. I don't believe that everything mathematical is necessarily physical. I do believe that everything physical is necessarily derivable from math. A TOE of one equation resulting in endless implications does not mean there unprovable physical things. A starting premise that all things necessarily imply everything else I think precludes the possibility that there is something out there that is not derivable/provable.
     
  6. May 26, 2010 #5
    That i do agree with, simply because it must be so, that is the definition of a TOE that it includes in certain limits bot QM and GR. But i dont think we are on the same page as to what it means to logically derive a universe.
    Here is my definition of a logically derived universe:
    Def: A logically derived universe is a mathematical construction in which all physically relevant constants can be derived from mathematically/logically motivated equations.

    That is to say, no need for any kind of measurement. If this in fact is possible then there are two cases:

    1.The Logic/Math used to derive such a TOE is unique to our universe, i.e. the structure of the universe induces a logic. As is the case with computer worlds, for example.

    2.Mathematics and Logic are the same in all universa, i.e. math transcends the universe. As would be the case if aliens from a universe with 48T+55S dimensions have the same theorems true for them as they are for us. In that case (funny enough) those aliens could not exist since we have the same math/logic, and we have derived our universe as a logical necessity. Thus there is only one universe, namely ours.

    Now we could say that the TOE is not logically derivable, say that one paremeter should be measured, the energy content of the universe at the big bang, or the fine structure constant or some other constant, then that constant should pinpoint all relevant information, as the number of space dimensions, number of time dimensions, number and size of coupling constants, relevant gaugesym. groups, so on and so forth.

    There might be another way, because none of these ideas sound very appealing.
     
  7. May 26, 2010 #6
    Is logically derivable the same as completely deterministic? Part of logic is probability theory. Since logic is so abstractly general in nature, it applies to everything and does not necessarily dictate every specific instance to which it applies.
     
  8. May 26, 2010 #7
    Uhhh, call me not philosophically sophisticated, but wasn't mathematics proven to not be a part of logic? Wasn't that part of the whole Frege, Russel thing? Wasn't logicism abandoned? What or how in your view would empirical facts be derivable from purely logical considerations? The universe may possess certain structural logical relations, but this doesn't imply that it is those relations. Again, I kind of see it is the whole Humean "fork in the road" the relations-of-ideas versus matters of fact, to me, it seems that mathematics and logic describes certain structural relations between things, but how would certain features of the universe be logically neccessary. Also, that leads to a selection problem; why would the mathematical structures that describe the world of experience do so, and why don't all of the other mathematical structures in this mathematical universe not describe empirical phenomena? If Mathematics is just a language in your view, then why do you advocate a sort of mathematical reality? Does that reduce reality to semantics?
    Also, I think you somewhat misunderstand Physics history, there were no "isms" that lead to scientific discovery, I am NOT saying that philosophical thought and considerations are not good in aiding physicists think about reality, simply that these people did not proceed according to an "ism". They may have been pushed toward an ism, appropriated the physics to a new philosophical framework in order to view it through new lens, but certainly no "ism". Relativism? If by Leibnitzian and Machian relative space views, which were still empirically based, them yes. Positivism? If by positivism you mean, interpret only the facts and no metaphysical suppositions, this was a neccessity demanded by QM, and reading Niels Bohr's philosophy doesn't lead one to him being a positivist, same for Heisenberg.
    Also, what of the "superflous" mathematics that describes reality? What of classical mechanical mathematics? What of geometric optics? and other theories? What counts as a logically deriveable part of the "objective" universe? Structures imposed on us from our limitations and perspective, that is not only our "human" perspective but also our inertial, spatio-temporal perspective. What of time? Does time not exist in your reality? What then is causation? A logical relation? A counterfactual? How is it that me throwing something causes it to fly through the air? How is that derivable from "logical" principles?
    What, to you, is Mathematics? Logic? Language? I don't mean to sound rude, I just simply am skeptical and have a lot of questions. I'm curious how you would deal with many of them, I feel like your running too far ahead of yourself with mathematical/metaphysical speculation. Philosophy is fantastic, but Kant spoke of the limits of speculative metaphysics.



    *Sorry mods for all of the philosophy talk, I do realize that this most likely is the wrong forum, despite the pleas of the OP. Maybe somebody more knowledgable in the actual Physics can chime in
     
    Last edited: May 26, 2010
  9. May 27, 2010 #8
    Hello JD!

    Im am not advocating anything, as you can see in my posts its either questions or i give several possibilities, i understand you position and agree with it! I said it myself, math is language. But i might be wrong, there might be truth in math, i certainly know alot of mathematicians who think so. Some think that there is a one-to-one correspondence between math and physical reality; that is to say, every mathematical object will describe something in reality. Now again im not advocating that, im just saying that is a possibility.

    As comes to physics history i beg to differ, but lets not say more about it. Who knows what paths Einstein, Bohr and Heisenberg followed to reach their understanding, I believe at least Einstein to have started with philosophical principles, but i may be wrong.

    That bit about geometric optics, and so on, yes there are theories that describe reality, and they function as models and sometimes as mere bookkeeping, the quark model started of as bookkeeping. But we are talking about a Theory of Everything. Now my questions are related to ho we would like to see this theory.
    How would you like the theory to be, what would sound beautiful to you?
    How many physical constants should be measured and put in to the theory?

    That bit about "what is time?" and so on i did not understand at all.

    And as to being knowledgeable in physics, i do consider myself a bit more than a layman since i've been doing it a while, but again, there must be philosophical aspects to an eventual TOE. (that is the only opinion i truly hold, what philosophical aspects, who knows that is what we are discussing)
     
  10. May 27, 2010 #9
    Just to clarify here a bit. Math equations do not contain physics, we measure stuff and input the right values into the equations and then math eq. contain physics. So constants such as c or h relate math to reality.
    Over the centuries when our understanding have grown, the number of these constants have been steadily declining, since deeper relations give the constants as products of a fewer set of more fundamental ones. I am not sure about the exact number you can google it but i believe we are down to 23 constants to be measured and input into the theory.

    In some sense understanding the universe is finding deeper relations that give the constants as consequences.

    Now here come the point, in our imagined TOE, how many constants should be input?
    (i know i did this above, but i try to be clearer this time)

    0: means that one can mathematically generate our universe, say for example speed of light has to do with geometry of spacetime at small scales, so on and so forth. The implications of this would be literally astronomical.

    1: means that the universe is not derivable, when we have our TOE we still have to measure one constant to input, and all other are then given. Which constant should this be?
    2: well you get the point.... the biggest differences are between strictly positive and zero constants, but i think the difference between 1 and 2 is also worth considering?
    What would that mean?
     
  11. May 27, 2010 #10
    I don't think we really have a choice. Either everything is derivable from logic, or something in the universe is illogical. But that might be taken as the definition of insane: something completely illogical definately exists. Most people don't cross that line; instead they choose to believe we just haven't discovered how it all fits together yet.

    It may or may not be true that mathematics can be derived from logic. I'm not really too sure about Godel's Incompleteness Theorem yet. But that does not prevent us from using math to count objects. And I don't think it prevents us from finding a TOE since we are only looking for one equation, not every possible equation.

    As for how many constants of nature will need to be measured in a TOE, I wonder what happens if a TOE predicts symmetry principles that must break in arbitrary ways? It may be that we have to make a measurement and get a different constant for each symmetry that is broken. Does this mean that reality is not derivable from logic? Or does that mean that probablity theory becomes a part of that logic? The logic proceeds both before and after the symmetry breaks. Is the break an actual disconnect in logic? Or does the logic predict only the possible universes that may exist with those symmetries?
     
  12. May 27, 2010 #11
    I see I see, ok, well then that is fair, and again I apologize for seeming rude. We don't need to speak more about the physics history issue if you wouldn't like to, I do agree about Einstein coming from philosophical consideration, but not entirely, I feel saying an "ism" drove the discoveries neglects the physics aspects.
    Regarding your questions about how we would like to see it, how many constants etc. I suppose I haven't really thought about that, it seems too aesthetically subjective at my point, I simply hope to observe nature and find some things out about it. I suppose if I had to choose I would prefer it if we could derive some of the more fundamental constants (I don't know of all 23) such as c, and h from physical considerations of some underlying physical theory, though I simply don't know if that is possible.
    What I was saying with the "time" bit is that mathematics is a creation that does not contain the active behavior of time. That is not to say that we cannot model behavior in time, simply that mathematics doesn't seem to possess time in itself. From that, if physical reality was deriveable from logic, how would you deal with the problem of time using timeless logic? Considering time, many find time to be intimatley connected to causality, and causal asymmetry. From this, I was asking that, logically, how would causality be represented? As a counterfactual logical relation? Or what?
    It seems to me, that it is losing the "forest through the trees" or whatever that saying is. Go outside, and go to a creek or a river and ponder how those interactions are logically neccessary or deriveable. How the random flurrys of vortices and all the turbulent flow emerges, and at what point does the flow of the whole have neccessity from the "logic" of H20?
    But I don't mean to be caught up on that snag again, because I'm sure you get the point. I do agree that new philosophical perspective could breed new ways of viewing reality, I suppose going back to that my issue may be semantical in nature, that is I just don't like the sound of "We need a new 'ism'" because it paints a picture of people searching for a philosophy to intuit their physical understanding to, but I feel an active synthesis of a new philosophy may breed creative thought and a new Physics.
    Finally, regarding the Godel question, I wanna preface this by saying that I do not know mathematical logic to the point of following the actual derivation of Godels prrof and as such my comment will strictly be limitied to what others say about it. But, the Incompleteness theorem about there existing true, but non-proveable propositions within any axiomatic system, doesn't speak to me about our reality itself per se. (I'm sure you can see that may be because I kind of divorce myself from Platonist Mathematics, and as such don't think that Godel's theorem says things in a "one-to-one" way about our reality). I think ultimatley, it speaks to our reality models, it seems evident that in a completely "final theory of everything" if there is one, it would be either self-referential and thus not completely explanatory, or must drop the 100% objective stance of being able to explain everything in terms of something else, because eventually we will run outside the realm of empiricism, by continuing to create entities. Though also, the axioms from which we derive our theory, may simply be subjective experience itself, but then we must abandon complete objectivity. That is not to say that I believe reality to be subjective, because I do not, but not objective in the naive sense.
    Finally, 4..I think is in the proccess of being answered, some of it is linguistical, that is, "what is a particle?" we don't even know if a particle is the fundamental description of matter definatley, that is a particle as conceived as osme type of roaming point-mass. I'm not quite sure (is anyone?) how quantum fields condense into "particulate"matter. Surely even the smallest "particles" aren't what we think of when we linguistically say "particles". And 5 simply will not be known, if we knew it we'd be pursuing it, it may not even exist yet, it most likeley is a combination of several things. Sorry for the long post that doesn't have much structure
     
  13. May 27, 2010 #12
    I just wrote that post before friend posted his, so I didn't get to review what he said. I think your making a "either/or" fallacy. Have you ever considered that quite possibly reality is not able to be broken up into mutually exclusive options? Experience, to me, verifies that life is not logic. What does introducing probability into logical necccessity do? "It is logically necessary that either this or this are logically possible"? How do you deal with evolutionary dynamics? Emergent systems? Societal dynamics? Economics? Psychology? Why the insistence on the universe having to be deriveable from logic? What is logic? It was created by humans, that is not to say that it has no objectivity, but is it the be-all-end-all which existence must be? There are illogical or non-rational aspects of being and there are things which exhibit logical structure, but are not deriveable from logic, that is they are not simply logic. More broad, what is the scope of a TOE? simply an equation that describes space-time dynamics and the emergence of matter structures? or does it describe absolutley everything? Just questions to consider
     
  14. May 27, 2010 #13
    As soon as you try to describe a physical situation with a statement which is either true or false, logic becomes relevant to physics. Do you think you are able to come up with any theory without making statements which might be true or false? I think that's impossible. The smallest possible entities are still described with propositions whose truth value must be considered.

    If physics is not completely reducible to logic itself, then your search for a TOE must necessarily end on some physical particle which cannot be explained further. You end in a question, not an answer; you will never have a TOE. Questions end when the answer is reduced to reason itself. For then there is no other questions to ask except about the principles of reason itself. And if we start questioning our ability to reason, then we will never be sure about anything.

    There have been attempts to describe reality with mathematics and attempts to derive math from logic. Perhaps in some limited way this is the way to derive a TOE. But if we don't use math or logic, we will never have a TOE. It seems the only question is how to derive physics from logic.

    My understanding is that the logic behind reality is that all facts are consistent, no fact in reality contradicts the existence of any other fact in reality. I think that is a fair assumption to make no matter how small the facts may be. And then there is always counting the facts using math. If we don't assume any other properties to the most fundamental entities, other than they either exist or not and can be assign coordinates, then I believe it's possible to derive the rest, or at least the possibilities that could exist. Send me a Private Message if you want to see the details.
     
  15. May 27, 2010 #14
    Don't get me wrong, I am not advocating a non-mathematical TOE at all, this seems impossible.I suppose I have not yet reached a position of utmost certainty about rationalist principles, I have not quite reached the point where I can accept logic as completely human-independant. I am not saying that the theory will have no truth values, truth values follow from mathematical form, but I do doubt that we can derive physics completely from logic. I think it is possible that you are right, we may not end in a whole answer, I feel it may be such that we either keep going or form a self-referential system. No matter what questions will exist, again, if Physics is derivebale from logic you will still have the question of why some logico-mathematical strucures are manifested through physical reality and some aren't. Also, if we reduce physics to logic/mathematics then Godel's principle will apply, what will be our axioms for such a system? No matter what we'll be left with un-answearble questions and loose ends. Reason itself has limits.
     
  16. May 27, 2010 #15
    Now we are getting started!!

    So no totally derivable physics, it seems to be a consensus!

    Lets say that we only need one input parameter then, what would that be? It seems to me that planks constant or speed of light are very fundamental, i have a hard time imagining what mathematical procedures would produce them, probably some converging sums, or a ratio of sorts, well anyway.

    What i would like to see as the generating parameter is the total energy content of the universe at the start. (This has been determined to some degree, although i would like the TOE to actually tell me what energy is.) That would entail that the number of space and time dimensions as well as the signature of the metric should be functions of this initial energy. This in turn entails that we cannot model the early universe as a manifold with definitive dimension. Now in the definition of a manifold there is nothing that prevents us to have varying dimensions in different points (open sets actually), so maybe a good starting point would be a superposition in every point of an infinite number of dimensions and signatures (maybe even imaginary signatures and dims, it would be nice if the starting manifold was algebraically closed). Then by choice of initial energy, one would collapse this "wave function of geometries". This has been proposed previously i believe, by de Witt.
     
  17. May 27, 2010 #16
    Sorry i didnt realize you had responded so many posts, i only read the last post, sorry bout that!!

    There is some interesting stuff there, i will comeback and respond, when i get some sleep.

    But you have both said things like "illogical" and "self referential", now sorry about being such a bore, but if there is an inconsistency, a paradox, then Gödels theorem does not hold, Gödel says, that an axiomatic system cannot be complete and coherent at the same time, thus allowing for a paradox would mean that we can have a mathematically derived and complete theory. But on the other side with a paradox in a logical system one can derive anything. But on the other side again, isn't the state at the start one big singularity? Maybe one can have a controlled paradox. Maybe a universe is a process that starts with a paradox and the dynamics is just the system trying to correct the paradox, that would give a neat explanation to the law of increasing entropy, and again i might be going too far in saying maybe that entails proton decay if we assume a totally symmetric system to be a state of infinitely delocalized energy (plane wave photons, the heat death as it is called)?
    I bring up proton decay because in almost all theories trying to go beyond SM protons decay into positrons neutrinos and photons. (this is however not observed so its a no go)
     
  18. May 28, 2010 #17
    No matter what, though, there is to be unanswered questions and paradox within a framework of metaphysical or rationalist principles, there is always room for more questions, whether this is a result of the erroneous structure of our language and thought, I do not know, simply that if we do have an axiomatic system, there will be questions, if we do not there will be questions, paradoxes.
    I am sorry if I seem not open enough to this discussion, but I feel as if there is a slight discord in the way in which we are proceeding here. We are trying to philosophically speculate about the end outcome of a theory of everything, which is good, but we are constraining our thought to the conceptual system of the current trends-of-thought in physics. This seems to be a good thing to do, and when discussing current physics, it is a very good thing to do, but when discussing the outcomes of an end theory that could be extremely far in the future, it seems ill-fated to discuss using the contemporary theoretical terms what the outcome will be. Contemporary theoretical terms are part of a language-structure that has meaning, but extending the domains of applicability brings it to meaninglesssness. Considering, philosophically, the result of a TOE must be spoken of in broad vague terms, because this is the only way we can consider new ways of viewing reality. This for me is the goal pf philosophy. We are trying to stimulate new angles by which to view reality, and possibly think about the direction of explanation. For, me, we must always return to what is explanation? What is theory? Not run too far ahead in what the final theory may look like. We may be led to things that we have yet to dream of. Consider other eras in Science trying to speculate within the conceptual framework of their current research what a FINAL theory would be like, they would speak in the terms and langauge available, but we know that this is ill-fated. Sometimes I seem to think that (if I may be allowed a metaphor) Science proceeds asymptotically towards "reality" or "truth" (whatever that means), but we never know where the asymptotes are, nor where we functionally lie in relation to them. From this, I can't speculate and feel as if I'm speculating clearly, about a TOE.
     
  19. May 28, 2010 #18
    The way forward is always the same and will never change imo.
     
  20. May 28, 2010 #19


    That would be a paradox only if you stick to naive realism and believe that some future physics theory will return us to solid objects in space and time and matter being composed of tiny solid balls. Realistially, it simply isn't going to happen and matter is definitely NOT what it seems on the classical level. Relax your grip on reality and enjoy the new 'understanding' of matter, it might be mind-bending but it's surely enlightening and does sound promising as far as it concerns prospects for reaching some minor philosophical truths.
     
  21. May 29, 2010 #20
    What do you mean by "the way forward will always be the same and will never change"? Do you mean that the way to true knowledge of reality proceeds linearly? Or do you mean that there is an "objective" structure of reality that is "the way forward" and as such it is independant of human thought and so it will remain the same? Regardless, either way we are apprehending reality by proceeding from a limited knowledge and attempting to know more "truth". Even if "the way" exists independantly of this, this does not imply that "the way" as it objectively exists will be a straight path for us. This has been proven by history. Walking in an unkown forest and searching for the only path to the river, will not necessarily yield a straight way forward, the path may exist independantly of us, but either way we are lost in the forest and must take turns to get there, we may feel as though the way we are going is the right way, but sure enough there will be more turns. I would agree with Cantor to not hold an absolute realist "objective" view, but my point is more that even if you hold this view, we still cannot speak of a TOE with idle speculation using the vocabulary of current theoretical frameworks.
     
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