
#19
Jun308, 11:49 PM

Sci Advisor
P: 1,663

People get so confused about background independance. In many ways its a completely misleading term that is defined differently by different authors and pretty much synonomous with layman fog.
For instance, there is no sense in which Reuters asymptotic safety program is more or less background independant than String theory. In fact, probably quite less. Particularly in cases which are well under control (AdS/CFT) or with lots of SuSY present (where you will get explicitly emergent quantum geometry in certain nonperturbative regimes). Also Lolls program is completely 100% background *dependant* in the sense that there is exactly one prescribed way to define her lattice parametrization, you have no choice in deforming around the 'man' made construct.. Also, its important to emphasize that it is most assuredly not a fundamental quality that a theories must possess. It is utterly trivial to formulate GR for instance in a way that explicitly breaks much of the diffeomorphism symmetry and makes explicit use of coordinates. It is still GR, its just been gauge fixed. 



#20
Jun408, 12:10 AM

Astronomy
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PF Gold
P: 22,803

As for your claim that Loll's CDT is 100 percent background dependent, you will really have to take that up with Loll. It sounds ridiculous, the only way I can make sense is to suppose that you are reasoning by drawing analogies which Loll would simply not. Conventionally, among nonstring QG folks, background dependence means you start with a manifold already provided with a metric. GR starts with a manifold without a metric. So does Loll. Therefore in the usual straightforward sense her approach is as B.I. as General Relativity itself. same spirit. Trying to draw analogies and bend words around to make out it is not can only lead to semantic quibbling, I fear. Just go along and say what you want, Haelfix. there is no reason for me to wish to argue the point with you. 



#21
Jun408, 01:01 AM

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P: 1,663

"same spirit."
Which is semantics and not physics or mathematics. You can start with a given metric in GR just fine, and lo and behold, its still GR. No different than String theory. Alternatively, you can work in the worldsheet and leave the full spacetime manifold geometry unspecified and if you switch pictures you will see a fully dynamical quantity (the target metric field) fluctuating all over the place, and even changing its topology. As for CDT... *ALL* Lattice theories are 'background dependant' with the following definition: You input a starting *choice* of how you draw your lattice. It can be random, or it can be fixed. The details of this process, should drop out in the continuum limit assuming you have a consistent theory. So we will call a lattice theory 'background independant ' where the continuum, infinite volume limit is taken and all details of the choice drop out. We will further call such a choice consistent, if it encapsulates the correct semi classical limit, or in technical terms it is a relevant deformation of a renormalization group fixed point. When you do something on a computer, there is no such analytic process.. Thus it is background *dependant* by definition. Now there is a further technical requirement in CDT, that is that all solutions derived by this method are topologically restricting. They all require a specific choice of foliation. Which is completely background *dependant* from the point of view of the path integral. You are essentially by hand, excising all topologies that dont have this particular property. In various other authors terminology, that is called 'quantum background dependance' So the point is, just throwing words blindly around is vacuous b/c there are about 20different completely disparate concepts being thrown around into one catch all 'term' in the layman literature and on this board. It needs to stop. 



#22
Jun408, 01:21 AM

Astronomy
Sci Advisor
PF Gold
P: 22,803

See http://physicsforums.com/showthread.php?t=238605
I've quoted Loll's abstract and highlighted where she says the approach is background independent. I think I understand what she means and it makes sense. It is correct professional usage among her colleagues. I think you mean something else by 'background independent'. Unless you were to write one of the authors and get straightened out so you both mean the same thing, discussion is impossible. I gather that there must be no one unique correct meaning. Since Loll says her approach is B.I. and Laurent Freidel says his is B.I. and Rovelli says his is B.I. and they would all agree among themselves. But you and many string theorists (apparently using the term differently) seem to disagree. You suggest it is a term used by laymen, but I don't hear it much from laymen at all. I hear it recently a lot from QG professionals. The concept is evidently important, but not one that I can discuss with you because you attach different meanings to it. 



#23
Jun408, 01:58 AM

P: 859





#24
Jun408, 02:19 AM

P: 1,667

With respect to your points on CDT: indeed, it is not an ordinary path integral since the geometries are GIVING you a foliation (it is not that you pick a coordinate system and evaluate for all geometries as the standard formulation would require). The real question is "what does it mean?". If it were simply a (partial) gauge fixing, then the relevant terms should be included in the action (but the problem is that nobody knows what gauge it is) and one should integrate out the Lagrangian multiplier and the time function (and obviously this would lead to an effective action different from EinsteinHilbert). Since no such corrections are made, one concludes that an adhoc gauge dependent counter term has been added which would induce a preferred cosmic timelike field. Now, one could guess that (somehow) this slicing with clear geometric significance does not matter and drops out in the continuum limit  but I woudn't bet on it (since one would reasonably expect the lattice regularization to be a regularization of the modified continuum theory). That would indeed make the theory background independant, but it is clearly a highly non trivial thing (just like finding a needle in the haystack is) :) On the positive side, the theory is at least unitary which cannot be said of other "background independant" approaches. 



#25
Jun408, 03:13 AM

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P: 1,663

"I agree essentially with what you say. As for a definition of background independance (with respect ordinary differentiable manifolds M) : "A theory on M is BI (or simply covariant) if and only if the Lagrangian does not contain non dynamicalfields nor Lagrange multipliers"."
Correct, but keep in mind different physicists will butcher this definition in many different ways. For instance, the full string theory is BI in the above sense, but not background independant in the LQG sense since there are metric fields that appear explicitly (and you really want something more like a connection variable), even though they are 100% varied in the action. Point being, there is absolutely no one standard way across all programs where the term is uniquely defined. Its simply not the same thing to say a lattice theory is BI vs say a HartleHawking path integral being BI vs a nonperturbative field theory being BI vs AdS/CFT etc etc. 



#26
Jun408, 03:53 AM

P: 2,799

I agree that the notion of TOE is a bit silly, if you see it as a thing, or static understanding that will one day be carved in stone.
I guess my view is more that the closest thing to a TOE is the process that is the journey of progress that may or may not result in a TOE, and I see no universal measure of progress and neither do I think the final desination or existence of destination of the journey is very meaningful to speculate about. And that might suggest to focus on ther process of progress, rather than speculation of what we may or may not come to find out. We don't know where we will end up, but OTOH I don't need to know that. All I need is the answer to me next question. And how can my decision progress on that matter be understood to emerge an evolve? This is why I found this remark interesting "I can imagine that string theory in that case may become its own new discipline; that is, a mathematical science that is devoted to the study of the structure of physical theory and the development of computational tools to be used in the real world. The theory would be studied by physicists and mathematicians who might no longer consider themselves either."  http://aps.arxiv.org/PS_cache/arxiv/...805.0543v1.pdf In this spirit it seems physical theory itself, is just a relative state, or result from a process. I also think the notion of background independence in fuzzy. If it simply means not starting with a metric in a manifold, then i can help thinking of the manifold itself as a "background". I'd expect this manifold to also be explain in terms of something less complex. With "the theory of physical theory" I really meant the opposite, that it might aim to describe the process of evolving theories, rather than just properties of a single TOE. And by consistency this reasoning should then be applied to itself, so that the theory of theories is itself evolving. Not that I see how string theory is that, but it was the question to ask if someone else can see that. I got the impression that was the ambitious vision Moataz H. Emam had of string theory. Which if true, would be even better than a old style TOE if it might describe the inductive and progressive step in "theory of theory", as it would describe the most nontrivial step, what to do what if your theory is wrong. Then you need a theory of the theory anyway, that guides you in revision. So as I see it, the question of what the "TOE" is not interesting. It's how we, given our incompetence and limited brainpower, should make the quickest progress. /Fredrik 



#27
Jun408, 04:16 AM

P: 1,667

Some clarifications (and more accurate wording) : I agree essentially with what you say. As for a definition of background independance (with respect ordinary differentiable manifolds M) : "A theory on M is BI (or simply covariant) if and only if the Lagrangian does not contain non dynamicalfields nor Lagrange multipliers".
With respect to your points on CDT: indeed, it might not be an ordinary path integral since the geometries are giving you a foliation and it is not clear where the latter comes from (that is, one should start from the full path integral, divide out the gauge degrees of freedom (in one way or another) and study the resulting effective action). The real question is "what might happen?". If it were simply a gauge fixing, then the effective action would probably differ from Einstein Hilbert (non trivial gauge dependent Jacobians). Since no such corrections are made, one could conclude that an adhoc gauge dependent counter term has been added which could induce a preferred cosmic timelike field (note moreover that physical gauge conditions often only exist locally and run into ton's of global problems  so one has serious reasons to suspect that something else is going on here). Now, one might guess that (somehow) such details of the path integral measure are irrelevant in the continuum limit (but this is extremely unlikely). That would indeed make the theory a quantized version of general relativity, but it is clearly a highly non trivial thing (just like finding a needle in the haystack is) :) I would think people have thought about this issue but I do not know a reference from the top of my head. So, one issue is whether CDT is the quantization of general relativity; another one would be wheter it corresponds to the quantization of some classical action at all (since as I said, it is not clear which gauge condition has been imposed). If the latter is not satisfied, then one could say it is not BI (but the first issue is much more pressing of course). On the positive side, the theory is at least unitary which cannot be said of other "background independant" approaches. Moreover, one should try out something, right? 



#28
Jun408, 07:56 AM

P: 1,667





#29
Jun1108, 09:45 PM

P: 5

Dear Marcus,
I meant to differentiate beween Quine's confirmation holism and Karl Popper's theories; Popper noticed that two types of statements are of particular value to scientists. The first are statements of observations, such as "this is a white swan". Logicians call these statements singular existential statements, since they assert the existence of some particular thing. They can be parsed in the form: There is an x that is a swan, and x is white. The second are statements that categorize all instances of something, such as "all swans are white". Logicians call these statements universal. They are usually parsed in the form: For all x, if x is a swan, then x is white. Scientific laws are commonly supposed to be of this type. One difficult question in the methodology of science is: How does one move from observations to laws? How can one validly infer a universal statement from any number of existential statements? Inductivist methodology supposed that one can somehow move from a series of singular existential statements to a universal statement. That is, that one can move from 'this is a white swan', 'that is a white swan', and so on, to a universal statement such as 'all swans are white'. This method is clearly deductively invalid, since it is always possible that there may be a nonwhite swan that has somehow avoided observation. Yet some philosophers of science claim that stringy science is based on such an inductive method. ========= If there is indeed a TOE, which, in physics, is ofcourse only a measure to combine General Relativity with Quantum Mechanics, the kind of physicalism that Karl Popper clings to, does indeed state that a physcial theory also has to be a metaphysical theory (of everything). In this view a physicalismtrue TOE could go a little something like this; Einstein and physicists and philosophers before and after him have spent a great deal of effort trying to explain how the Universe works. Scientists have spent the last 75 years or so trying to tie together all known phenomena to explain the nature and behavior of all matter and energy in existence. Since physics has made little progress in discovering the Grand Unification Theory an interesting question arises. Why have the best minds of the past and present failed to discover the truth about our Universe. Since the time of Isaac Newton who began the era of Classical Mechanics and modern day physics we have all been trying to unlock the secrets of how the Universe works. Many of the greatest intellects of all time have attempted to find a simple explanation for material existence and the central cause of force, action at a distance. The question of why so many great minds could not solve this problem eventually led the author of the theory to come up with a reasonble explanation for our failure to solve this great mystery. It seemed reasonable to assume that perhaps something might be wrong with our approach and that possibly a mistake was made somewhere in the past. The mistake would creat a paradigm shift that would take physics in the wrong direction. If this idea is correct the only explanation that makes sense is that somewhere along the way we began to attempt to solve an inequality. In other words we switched onto a track that was a dead end, a red herring so to speak. What if for the past hundred years or so we have been trying to prove something, that is not true. What if we have been trying to prove that a=b and in fact a<>b. If we did not know this fact we could spend centuries trying to prove an incongruity. ============= If there would be such a case as where the above is true, it might defy our manyworldsinterpretation itself. If such a case would exist in where there would be some sort of a complete quantum mechanics or some sort of super relativity, a manyworldsinterpretation would not be needed and invalidate the possibility of string theory being the theory of physical theory Your question in fact reveals an important paradox, concerning such a string theory manyworldsinterpretation, as to the fact of the matter that if many worlds exists, all worlds have different physics theories. So indeed string theory would then perhaps be the theory of physical theory. But such a case could be a selffulfilling prophecy and might even be described as the paradox In this it reveals exactly this dichotomy between Karl Popper and Quine (also see falisifiability) 



#30
Jun1208, 01:05 AM

P: 2,799

Is there a way at all to by means of poolproof deductions find universal statements from existential ones? If the answer is no, then to me, that suggests that more than ever changes the focus of the nature of law. And it my suggest an alternative quest. The quest isn't to "find the universal laws of nature", it is to find out the nature and "dynamics" of law. This is the perspective I have personally adopted. But MAYBE in each particular case, there is a "preferred" logic that can be locally attained like a sort of local steady state equilibrium. And maybe we can related the structure of this logic to the structure of spacetime and also matter. And maybe there is even a bound to the "set of logic". IF you consider logic as a set of rules from manipulating structures, then if the structures are limited in complexity then the logic that can live there may also be bounded. Maybe if we look at the simplest possible systems, we may not be left with alot of choices, this is what I'm trying. I am trying to ask these questions, like what is the logic in line with the above, of Einsteins Gravity. And what is the logic of the standard model of particle physics? /Fredrik 



#31
Jun1808, 09:07 PM

P: 5

I could have an answer to your quest.. There is such a thing as the CurryHoward correspondence which combines logicality with mathmatical proof. From deduction we can see that physics/mathmatics and logicality/metaphysics could in fact be related. As the CurryHoward correspondence is the direct relationship between computer programs and mathematical proofs. Also known as CurryHoward isomorphism, proofsasprograms correspondence and formulaeastypes correspondence, it refers to the generalization of a syntactic analogy between systems of formal logic and computational calculi that was first discovered by the American mathematician Haskell Curry and logician William Alvin Howard. Curved space often refers to a spatial geometry which is not “flat” where a flat space is described by Euclidean Geometry. Curved spaces can generally be described by Riemannian Geometry though some simple cases can be described in other ways. Curved spaces play an essential role in General Relativity where gravity is often visualized as curved space. The FriedmannLemaîtreRobertsonWalker metric is a curved metric which forms the current foundation for the description of the expansion of space and shape of the universe. This curvature can be seen in many ways. Some logic suggests that logical 'spira mirabilis' are metaphysically and physically explainable. A logarithmic spiral, equiangular spiral or growth spiral is a special kind of spiral curve which often appears in nature. The logarithmic spiral was first described by Descartes and later extensively investigated by Jakob Bernoulli, who called it Spira mirabilis, "the marvelous spiral". Spira mirabilis is another name for the logarithmic spiral. Although this curve had already been named by other mathematicians, the specific name ("miraculous" or "marvelous" spiral) was given to this curve by Jakob Bernoulli, because he was fascinated by one of its unique mathematical properties Logarithmic spirals are selfsimilar in that they are selfcongruent under all similarity transformations (scaling them gives the same result as rotating them). They are also congruent to their own involutes, evolutes, and the pedal curves based on their centers. The size of the spiral increases but its shape is unaltered with each successive curve. Possibly as a result of this unique property, the spira mirabilis has evolved in nature, appearing in certain growing forms such as nautilus shells and sunflower heads. Bernoulli eventually chose a figure of a logarithmic spiral and the motto Eadem mutata resurgo ("Changed and yet the same, I rise again") for his gravestone. 



#32
Jun1808, 09:27 PM

P: 5

There are also some older standing theories about combining Einstein's relativity with quantifiable gravity.
There is the Kaluza–Klein theory, or KK theory, for short, which is a model that seeks to unify the two fundamental forces of gravitation and electromagnetism. The theory was first discovered by the mathematician Theodor Kaluza who extended general relativity to a fivedimensional spacetime. The resulting equations can be separated out into further sets of equations, one of which is equivalent to Einstein field equations, another set equivalent to Maxwell's equations for the electromagnetic field and the final part an extra scalar field now termed the "radion". In the attempt to explain the MichelsonMorley experiment, Lorentz proposed that moving bodies contract in the direction of motion ( George FitzGerald had already arrived at this conclusion with length contraction.) Length contraction, according to Hendrik Lorentz, is the physical phenomenon of a decrease in length detected by an observer in objects that travel at any nonzero velocity relative to that observer. This contraction (more formally called Lorentz contraction or LorentzFitzgerald contraction) only becomes noticeable, however, at a substantial fraction of the speed of light; and the contraction is only in the direction parallel to the direction in which the observed body is travelling. Lorentz worked on describing electromagentic phenomena (the propagation of light) in reference frames that moved relative to each other. He discovered that the transition from one to another reference frame could be simplified by using a new time variable which he called local time. The local time depended on the universal time and the location under consideration. Lorentz publications made use of the term local time without giving a detailed interpretation of its physical relevance. In 1900, Henri Poincaré called Lorentz's local time a "wonderful invention" and illustrated it by showing that clocks in moving frames are synchronized by exchanging light signals that are assumed to travel at the same speed against and with the motion of the frame. By 1904, Lorentz added time dilation to his transformations and published what Poincaré named Lorentz transformations. It was apparently unknown to Lorentz that Joseph Larmor had used identical transformations to describe orbiting electrons. Larmor's and Lorentz's equations look somewhat unfamiliar, but they are algebraically equivalent to those presented by Poincaré and Einstein. Lorentz' '1904' paper includes the covariant formulation of electrodynamics, in which electrodynamic phenomena in different reference frames are described by identical equations with well defined transformation properties. The paper clearly recognizes the significance of this formulation, namely that the outcomes of electrodynamic experiments do not depend on the relative motion of the reference frame. The '1904' paper includes a detailed discussion of the increase of the inertial mass of rapidly moving objects. In 1905, Einstein would use many of the concepts, mathematical tools and results discussed to write his paper entitled "Electrodynamics" known today as the theory of special relativity. Because Lorentz laid the fundaments for the work by Einstein, this theory was called the LorentzEinstein theory originally. The increase of mass was the first prediction of special relativity to be tested, but from early experiments it appeared that his prediction was wrong; this led Lorentz to the famous remark that he was "at the end of his Latin." The confirmation of his prediction had to wait until 1909 when Lorentz published his "Theory of Electrons" based on a series of lectures in Mathematical Physics he gave at Columbia University. If one would apply one of the more recent postulates in relativity, a supposed super relativity, being 'Space' is not a void but is in fact a solid composed of variations of three fields; Gravitational, Magnetic and Electrostatic in an unconfigured format and it as such is continuous and unbounded; one could come to some different conclusion as to Lorentz's nonmoving frame. Einstein added that no kind of observation at all, even measuring the speed of light across your frame of reference to any accuracy you like, would help find out if your frame of reference was "really at rest". This implies, of course, that the concept of being "at rest" is meaningless. If Einstein is right, there is also no natural restframe in the universe 



#33
Sep1008, 05:13 AM

P: 2,799

Maybe I gave up too early, but her reasoning and writing style drove me nuts :) Marcus did you read this, all of it? If so, what did you think? /Fredrik 


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