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| Strings. [image: freeimages.com] |
I am a Princeton physics major who regularly reads your wonderful blog.
I recently came across a curious passage in Brian Greene’s introduction to a reprint edition of Einstein's Meaning of Relativity which claims that:
“Superstring theory successfully merges general relativity and quantum mechanics [...] Moreover, not only does superstring theory merge general relativity with quantum mechanics, but it also has the capacity to embrace — on an equal footing — the electromagnetic force, the weak force, and the strong force. Within superstring theory, each of these forces is simply associated with a different vibrational pattern of a string. And so, like a guitar chord composed of four different notes, the four forces of nature are united within the music of superstring theory. What’s more, the same goes for all of matter as well. The electron, the quarks, the neutrinos, and all other particles are also described in superstring theory as strings undergoing different vibrational patterns. Thus, all matter and all forces are brought together under the same rubric of vibrating strings — and that’s about as unified as a unified theory could be.”Is all this true? Part of the reason I am asking is that I am thinking about pursuing String Theory, but it has been somewhat difficult wrapping my head around its current status. Does string theory accomplish all of the above?
Thank you!
An Anonymous Princeton Physics Major”
Dear Anonymous,
Yes, it is true that superstring theory merges general relativity and quantum mechanics. Is it successful? Depends on what you mean by success.
Greene states very carefully that superstring theory “has the capacity to embrace” gravity as well as the other known fundamental forces (electromagnetic, weak, and strong). What he means is that most string theorists currently believe there exists a specific model for superstring theory which gives rise to these four forces. The vague phrase “has the capacity” is an expression of this shared belief; it glosses over the fact that no one has been able to find a model that actually does what Greene says.
Superstring theory also comes with many side-effects which all too often go unnoticed. To begin with, the “super” isn’t there to emphasize the theory is awesome, but to indicate it’s supersymmetric. Supersymmetry, to remind you, is a symmetry that postulates all particles of the standard model have a partner particle. These partner particles were not found. This doesn’t rule out supersymmetry because the particles might only be produced at energies higher than what we have tested. But it does mean we have no evidence that supersymmetry is realized in nature.
Worse, if you make the standard model supersymmetric, the resulting theory conflicts with experiment. The reason is that doing so enables flavor changing neutral currents which have not been seen. This became clear in the mid 1990s, sufficiently long ago so that it’s now one of the “well known problems” that nobody ever mentions. To save both supersymmetry and superstrings, theorists postulated an additional symmetry, called “R-parity” that simply forbids the worrisome processes.
Another side-effect of superstrings is that they require additional dimensions of space, nine in total. Since we haven’t seen more than the usual three, the other six have to be rolled up or “compactified” as the terminology has it. There are many ways to do this compactification and that’s what eventually gives rise to the “landscape” of string theory: The vast number of different theories that supposedly all exist somewhere in the multiverse.
The problems don’t stop there. Superstring theory does contain gravity, yes, but not the normal type of gravity. It is gravity plus a large number of additional fields, the so-called moduli fields. These fields are potentially observable, but we haven’t seen them. Hence, if you want to continue believing in superstrings you have to prevent these fields from making trouble. There are ways to do that, and that adds a further layer of complexity.
Then there’s the issue with the cosmological constant. Superstring theory works best in a space-time with a cosmological constant that is negative, the so-called “Anti de Sitter spaces.” Unfortunately, we don’t live in such a space. For all we presently know the cosmological constant in our universe is positive. When astrophysicists measured the cosmological constant and found it to be positive, string theorists cooked up another fix for their theory to get the right sign. Even among string-theorists this fix isn’t popular, and in any case it’s yet another ad-hoc construction that must be added to make the theory work.
Finally, there is the question how much the requirement of mathematical consistency can possibly tell you about the real world to begin with. Even if superstring theory is a way to unify general relativity and quantum mechanics, it’s not the only way, and without experimental test we won’t know which one is the right way. Currently the best developed competing approach is asymptotically safe gravity, which requires neither supersymmetry nor extra dimensions.
Leaving aside the question whether superstring theory is the right way to combine the known fundamental forces, the approach may have other uses. The theory of strings has many mathematical ties with the quantum field theories of the standard model, and some think that the gauge-gravity correspondence may have applications in condensed matter physics. However, the dosage of string theory in these applications is homeopathic at best.
This is a quick overview. If you want more details, a good starting point is Joseph Conlon’s book “Why String Theory?” On a more general level, I hope you excuse if I mention that the question what makes a theory promising is the running theme of my upcoming book “Lost in Math.” In the book I go through the pros and cons of string theory and supersymmetry and the multiverse, and also discuss the relevance of arguments from mathematical consistency.
Thanks for an interesting question!
With best wishes for your future research,
B.
Awesomestring theory says it best.
ReplyDeleteDear Sabine - thanks for what is the most concise and clear answer to this question that I have read anywhere (but fully share).
ReplyDeleteMy colleagues sailed our ship out to the high sea, sunk it and declared victory, and I saw no way forth -sad that it turned out this way- other than to leave the field and work on problems where I can walk into a lab and draw inspiration from my experimentalist friends.
You forgot to mention that the theory is background dependent and perturbarive. Oh, and there's five of them (M-theory would solve all this problems... Unfortunately it hasn't even been shown (rigorously) to exist, let alone formulated!
ReplyDelete... 1) SUSY demands proton decay. Proton decay is not observed.
ReplyDeleteDOI:10.1103/PhysRevD.95.012004, arXiv:1610.03597
... 2) A derived non-silly cosmological constant magnitude is incompatible with SUSY. DOI:10.3847/0004-637X/829/1/47, arXiv:1607.01128
... 3) SUSY's symmetry postulate can be empirically falsified within an hour in a brightspec.com microwave spectrometer. If analytical chemistry can trash physical theory, theory had better look.
... 4) It's worse than that. The Big Bang Theory, Season 11, Episode 24, "The Bow Tie Asymmetry," Product Code T12.15624, 10 May 2018; arXiv:1401.8242
There must be some kernel of truth to string theory. And the but,in my opinion they are breaking up a structure artificially. First of all we don't know if planck area is more fundamental than planck length. A solid sphere can be modeled as a hollow sphere and a spinning hollow sphere can be modeled as spinning ring. Planck time may be somewhat fundamental of a rotation but that doesn't mean that there aren't processes that can operate differently
ReplyDeleteWe have to travel on the outside of earth. Neutrinos can go right through in a straight line. Magnetic fields have all kinds of distorted shapes around the earth. So try modelling what one cannot see at the planck scale. It is correct,but it is wrong.
A "Superanswer", . . To begin with, the “super” isn’t there to emphasize the answer is awesome, but to indicate it requires some layers of metacognition to deal with.
ReplyDeletehttps://abstrusegoose.com/272
Sheldon saves everything with his Super Asymetric approach ;-lol
ReplyDeleteWow Dr. H. That is a comment for a lifetime... at least very great between-the-lines career advice!
ReplyDeleteAnalyzing even the first sentence of string theory, I detect multiple incondistencies.
ReplyDelete" 1D or 2D strings vibrating in 11 dimensions."
°1D or 2D items cannot be 'strings', just mathematical abstractions, nothingness.
°Strings vibrating does not cause them to behave in many extra dimensions, it's still just 3D (well, perhaps 3+1)
°Vibrating, a mechanical feature, is something which will never happen to 1D or 2D mathematical concepts, nothingness does not vibrate.
It bothers me enormously how a theory ('of everything'!) is allowed to start out with such a total disrespect for basic mathematical, physical and logical notions known to us all.
Whatever it is you stack on top of that to save, or elaborate on the theory, it will never mount up to anything reality holds in store for us to discover.
Best, Koenraad
Kudos...a very nice reply...ordering your book.
ReplyDeleteSome random thoughts from someone probably not smart enough to work in string theory (or smart enough not to work in string theory):
ReplyDeleteIf you go into string theory, you will be one of many. What will be your contribution?
Check out the alternatives first, such as Loop Quantum Gravity. If you choose string theory, you should know why you didn't choose something else.
Think outside the box and get in early on something completely different, such as shape dynamics. Maybe high risk, but potentially high payoff.
Remember that even John Baez gave up working on quantum gravity. Check him out (he's a cool dude) and see if you want to go where he doesn't.
Bee
ReplyDeleteas I understand it, string theory doesn't give rise to classical GR, but GR + scalar field, the scalar field is NOT the Higgs field, and has to take special values to avoid coming into conflict with observation.
it sounds like string theory is epicycles on epicycles, in order to avoid it from coming into conflict with observation
do you think As gravity is where theoretical effort should be invested in? or are its pros and cons?
I got the same email and gave a less careful response. For one thing, I think it's really bad for people to stick their optimistic hopes about string theory - or any modern theory of physics that hasn't been successful yet - into an introduction to a book by Einstein. It can easily confused beginners. It's almost like a trick for promoting the theory.
ReplyDeleteThe righteous defensive groupthink, after half century of not making a contact with experiment (while many of its objectives and original hopes ended with a disappointment), would be a good reason alone not to join the string community... I am sure there were some people even in 1990s who went on to study Marxism-Leninism.
ReplyDeleteString theory is something I know fairly well. In fact with the death of Polchinski I began reading my copy of his two volume set and am now early into the second volume. I am pretty open about what people should study. If an undergraduate comes to me and says they want to study medieval French I tell them to go for it. I am tired of this idea, mostly from economists, everyone should study something that will get the J*O*B.
ReplyDeleteSupersymmetry and M-theory has found its reality interestingly in solid state physics. The AdS_2 ~ CFT_1 correspondence has some bearing on edge states and Mott insulator and superconducting states of cold matter. Nature in some sense has a sort of recherche property where structures on one scale occur on other scales. So it seems not at all unreasonable to thing superstring theory will be found to be some structure behind the universe. It might not be the ultimate structure, but it may be some part of it.
The moduli fields, ghosts and b & c field etc, most likely occur in an AdS spacetime. Our observable universe on some holographic screen may satify a constraint that b = b-bar = c = c-bar = 0. Remember that quantum gravitation exists primarily in the bulk of the AdS, while quantum fields are on the boundary, D-branes and holographic screens, and boundaries or holographic screens have CFT or QFT. Quantum gravitation in the UV, where it takes a lot of energy to excite the field, is dual to the low energy and stronger gauge fields on screens, horizons etc. The duality or equivalence is if you think about it the Einstein field equation.
"no one has been able to find a model that actually does what Greene says"
ReplyDeleteThis is a matter of definition. What is the standard model? At one level of analysis, it's a gauge field theory with a particular local symmetry, and with fermions and a Higgs scalar in particular representations of those groups. All that, you *can* get from string theory, in a variety of ways; and this is what people call a string-theoretic realization of the standard model.
However, if we want, not just the standard model as I just defined it, but the standard model *with the measured values of its parameters*, then not only has this not been demonstrated within string theory, but in fact it's presently beyond demonstration, because the values of those parameters for any given "stringy standard model" cannot be reliably calculated. At the moment one aims simply to have a qualitative resemblance, e.g. one quark is heavy (the top quark) and the others are light.
So one could say that these stringy standard models *do* contain the electromagnetic force, the weak force, the electron, neutrinos, and so on, but that the detailed couplings and masses are presently incalculable and probably wrong - unless the right vacuum *has* already appeared in the literature, awaiting only the development of the mathematical techniques of calculation which will demonstrate that it's the one.
Koenraad,
ReplyDeleteStrings in string theory don't have substructure; they are fundamental like particles in the standard model are fundamental. There is nothing whatsoever mathematically wrong with that. Best,
B.
how would you answer the same or similar question, except its on Loop Quantum Gravity?
ReplyDeletePenn state has a very active grad students in Loop Quantum Gravity.
neo,
ReplyDeleteRegarding your first comment, it's not one scalar field but many, and I explained that in my blogpost, so not sure why you feel like you have to repeat it.
As to the second question, I wouldn't. There are only so many hours in my day.
Bee
ReplyDeletewith more scalar fields, doesn't that leave open to more potential conflicts with observation?
has there been any attempts to either observe or rule out these additional scalar fields?
any generic predictions these scalar fields make, that can be tested at the LHC or precision measurements in CMB or gravity?
neo,
ReplyDeleteYes, they lead to potential conflicts with observations. No, you can't rule them out because you can invent ways to hide them. No, there are no generic predictions. Yes, there are predictions from specific models, and yes these can be tested, and to the extent that they made predictions that have been tested they were ruled out.
neo,
ReplyDeleteI have found this reference very useful with regards to the question what all those additional fields would do. Look in particular at Figure 3, where it says in the caption "a compactification picked at random from this list is most likely to contain of the order of 30 axions".
i'll look at it thanks.
ReplyDelete30 axions sounds like a lot that can result in observation consequences either for LHC such as branching ratios or gravitational observations.
do each of those additional scalar fields also have a supersymmetric partner?
wouldn't this also be an additional source of FCNC?
neo,
ReplyDeleteYes, people have looked for axions a the LHC and other experiments. I don't think they have the right coupling to induce FCNCs. In any case, I'm not a walking axion encyclopedia and I suggest you ask the arXiv, not me.
Hello Sabine,
ReplyDeleteI understand that strings are postulated to have no substructure. But the way it is proposed now, they are 1D or 2D, which is a purely mathematical concept. You cannot assign any characteristics to it other than mathematical characteristics. So vibrating strings is a no go scenario right from the start.
One cannot eat a pancake with a thickness of zero.
Koenraad,
ReplyDeleteI have no idea what you are talking about. Strings have 1 spatial dimension. The second dimension is time. This is theoretical physics. Of course they are mathematical concepts. How do you think wave-functions are any less mathematical concepts? You are displaying some serious misunderstandings here.
It seems we have indeed arrived at a disagreement here, but I did not misunderstand I think. I'm pointing out that 1D or 2D will not suffice to model things, you need building blocks which are 3D, that should be the postulate, because 1D or 2D does not model anything that connects to reality as I explained.
ReplyDeleteIt has a lot to do with emergence. Theorists try to model some fundamental components without substructure (in the case of ST), but it leads to assigning mechanical characteristics to mathematical abstractions.
That problem goes away if you accept the notion of non-fundamental building blocks to start from. It resolves the problem of something 'infinitely small'. And then have the modesty to say we simply do not to know what the non-fundamental building block is made of.
The emergence in this approach thus exists in many consecutive layers.
Koenraad,
ReplyDeleteWhat you say is just nonsense. All that's necessary for a theory to be viable is that its predictions are compatible with observations. Whether Koenraad Van Spaendonck proclaims that it can't be done is utterly irrelevant. I will not approve further uninformed comments from you.
"the dosage of string theory in these applications is homeopathic at best."
ReplyDeleteZing! That is gonna leave a mark....
Bee: The blog link to your book’s Amazon sales page, doesn’t.
ReplyDelete@Michael John Sarnowski: A sphere or spherical annulus has one center inversion point plus unlimited mirror planes and rotation axes containing its center. Four cuts dissect spheres into two identical homochiral halves, la coupe du roi, DOI:10.1515/zkri-2015-1863.
Perhaps any achiral 2D or 3D symmetric form can be cut into homochiral non-enantiomers. Spheres have an unlimited number of hemispheric initial even or odd number of cuts. Condensed matter and vacuum symmetry lifting compromises "beautiful" theory. Thereafter. either parameterize (curve fit) or ab initio write ugly pertinent theory.
Uncle,
ReplyDeleteDoesn't what? Both links (one in the text, one in the sidebar) are working fine for me.
To all,
ReplyDeleteThere appears to be different references to scalar fields here. We have references to moduli scalar fields, to axions and to other maybe related scalars associated with compactification. I thought I would try to indicate the distinctions between these.
The moduli scalar fields are ghost fields, such as Popov ghosts, which Grassmann variables as auxiliary scalar fields meant to prevent problems in path integrals. Gauge fields have moduli spaces where each point represents a form of gauge redundancy. There are multiple configurations of a gauge field that gives rise to the physically relevant field. The electrodynamic example of (φ, A) as potentials that then give rise to the electric and magnetic fields E = -∂A/∂t - ∇φ and B = -∇×A. The rescaling of the vector potential A → A + ∇f, for f some scalar results in the same magnetic field. The moduli space is then a set of different gauge conditions and in a sense is an orbit space for diffeomorphisms between different gauges. We then want to "mod this out," and the ghost fields are gadgets that allow you to do that. How this happens involves complicated mathematics with the Virasoro algebra, which leads to the removal of these gauge redundancies as well as the ghost fields. This is a part of the no-ghost theorem.
The Britto Cachazo Feng Witten (BCFW ) recursion is a way of removing redundancies without the need of auxiliary scalar fields. This is an on shell theory, which in a way means it only sums on the most expected path or in a way that it is non-quantum.
There is the axion field which is a way that the CP violations of weak interactions are removed from the QCD field. This is the Peccei–Quinn theory which posits a CP violating term call the θ term. This in the Lagrangian is θ^2F_{ab}*F^{ab}. There are other factors in this which I ignore here. The F_{ab} is the electromagnetic field tensor and the * is the Hodge dual. This means this term is θ^2E·B. For a standard EM wave E·B = 0, but this is an inhomogenous term. The angle θ is very small and is considered to be a field so θ → φ and with a kinetic term ∂_aφ∂^aφ. Consequently there is this differential equation ☐ φ = E·Bφ. This means an EM field will very weakly couple to the scalar to generate these axions. Attempts have been made to find axions by detecting odd deviations of the QED field. The E·B is very small, as is the angle θ, which means the mass of the axion is very small. These are however a contender for dark matter.
The final version of these scalars is a supergravity effect with Calabi-Yau compactification. There is a moduli space for the CY three-form that in spacetime gives rise to scalar fields. This is a much more difficult subject to discuss in depth, for it requires discussions of Ricci flat CY manifolds, the Hodge diamond and field equations on the compactified CY space. This occurs with type IIA string theory compactified on the CY to give a lower energy N = 2 supergravity field. There are scalar fields that emerge as a byproduct of this. Please do not quote me on this, but since in M-theory the various types of string theories are equivalent or transformable into each other, I suspect these scalars are related to the ghost fields. The ghost fields I mention above most often pertain to the 26-dimensional bosonic string. As these ghosts in a sense "go away" I suspect the same happens to these scalar fields on the 4-dim spacetime. I am not aware of anyone having demonstrated this, so this is my own hypothesis and could easily be wrong.
Bee,
ReplyDeletefrom your post
"Within superstring theory, each of these forces is simply associated with a different vibrational pattern of a string. And so, like a guitar chord composed of four different notes, the four forces of nature are united within the music of superstring theory. What’s more, the same goes for all of matter as well. The electron, the quarks, the neutrinos, and all other particles are also described in superstring theory as strings undergoing different vibrational patterns. Thus, all matter and all forces are brought together under the same rubric of vibrating strings — and that’s about as unified as a unified theory could be"
I've asked string theorists this question, to elaborate.
how does the vibration of a string that makes up an electron differ from a muon or tau?
how does vibration differ between electron and neutrino?
how does the string vibration differ between an electron and quark, or a photon or gluon?
how does it differ between electron and neurtralino?
how does just vibration give quarks and gluons color charge and greater mass, than leptons ?
how specifically does vibration of one entity, the string give rise to the difference in electric charge, mass, color charge, boson vs fermion, Sm and its susy partners?
... While we are here,
ReplyDeletehttps://www.youtube.com/watch?v=L5zOnnFZVBs&t=11m22s
https://www.youtube.com/watch?v=L5zOnnFZVBs&t=12m32s
https://www.youtube.com/watch?v=L5zOnnFZVBs&t=14m44s
... "Nobody's ever thought of it." Scripts are written with academic consultation. Something is brewing.
Google Chrome. When I click the upper right link to Amazon (I don't see an image of the cover - but I have ad-blocking), I get a general menu absent any mention of "Lost in Math."
https://www.amazon.com/?tag=backreactio08-20&linkCode=w30
Terrible Internet Explorer is the same. I have anti-malware that chokes 121 "user-enhancement" taps. That may be interactive.
https://edri.org/microsofts-new-small-print-how-your-personal-data-abused/
... Backloaded to Win7.
The leading Twitter solicitation displays to spec, linking to
https://www.hachettebookgroup.com/titles/sabine-hossenfelder/lost-in-math/9780465094264/
"All that's necessary for a theory to be viable is that its predictions are compatible with observations."
ReplyDeleteI'm not sure I understand your position here. Are you saying that a mathematical model whose axioms and postulates have no basis in physical reality can nonetheless be considered scientifically viable?
Back to the original question.
ReplyDeleteNo, I wouldn't recommended putting your all your study eggs in the String theory basket. I'd advise focusing on a more concrete field and, if keen on String theory, pursue it as passion on the side.
I'm a geologist (palaeontology) that does 'nitty gritty' geology. It doesn't prevent me from dabbling in my own research. In fact it enhances my enthusiasm. I have no need to 'produce' anything and no stake in outcomes... Science for for the sake of science.
An aside. Not to be critical but you should have enough background in physics to make your own judgement without relying on what Brian Greene states in a book. Are you reading actual published papers? Do you find the methodolgy, conclusions, etc. well done? I enjoy Greenes's books, talks, etc. but it is usually directed at a layman like myself. In contrast there are a couple of 'popular' paleontologists who make declarations that leave those of us in the field rolling our eyes.
I first heard of String theory from Science Digest in 1972. 46 years late it hs morphed and is more as fascinating than ever.I
neo,
ReplyDeleteIt's not the vibration that makes the difference but the gauge groups.
Uncle,
ReplyDeleteYes, will be your ad-blocker then.
Lawrence,
ReplyDeleteSorry about the conflation of scalar fields. I know about "the" axion of course, but I'm somewhat confused as to what the 30+ axions in string theory refer to if not moduli, and while you are here could you clarify what, if anything, is the relation to dilaton fields?
bud rap,
ReplyDeleteI don't understand the question. I think both you and Koenrad have a confusion about how a theory in physics works. You have a set of axioms, you have an identification between math-things and observables, and if the theory makes correct predictions for observables you gain confidence in it. What does it mean for an axiom to have "a basis in physical reality"? I have no idea, but whatever you mean by it it's utterly irrelevant. If it works, it works.
neo asks what makes one particle type different from another, in string theory. Exact answers are possible but they can be somewhat elaborate, and they also vary according to the model. In heterotic models like those that Brian Greene worked on, in which all strings are closed, the important mechanisms (e.g. generations from harmonics of the Calabi-Yau, GUT breaking by fluxes) are quite different to those at work in a model with open strings (e.g. gauge groups from brane stacks, standard model fermions from intersections of brane stacks).
ReplyDelete" bud rap,
ReplyDeleteI don't understand the question. I think both you and Koenrad have a confusion about how a theory in physics works. You have a set of axioms, you have an identification between math-things and observables, and if the theory makes correct predictions for observables you gain confidence in it. What does it mean for an axiom to have "a basis in physical reality"? I have no idea, but whatever you mean by it it's utterly irrelevant. If it works, it works."
But why is it then, that some theories make correct predictions and others don't ?
If play lottery for a few decades, one might come across the correct equasion which provides new physics, but generally speaking a less tax money wasting approach is preferred.
And that would involve guiding criteria towards improved equasions. You write a book about a.o. this.
So the words matter, the reasoning matters, the logic matters,checking the simple funtionalities of things matters, answering to as many criteria as possible matters.
Best, Koenraad
Superstring Theory is like epicycles. If you assume enough of them you can prove the Universe spins around the Earth.
ReplyDeleteSabine asked ... could you clarify what, if anything, is the relation to dilaton fields?
ReplyDeleteThe axion and dilaton are found to emerge from string theory with gravity. We can also seen them in a large matrix from SO(24) theory that includes gravitation. This is an toy model for the rank equal to 24 of the 26 dimensions of the bosonic string. The additional 2 dimensions being tachyonic physics that is ignored or that exists in black hole singularities etc. The matrix has symmetric and antisymmetric parts corresponding to the Ricci curvature and gauge fields respectively. The trace of this matrix defines scalar fields corresponding to the axion and dilaton.
This can also be seen with string theory more explicitly. If we have the operators a^†_n a_n and b^†_n b_n for string modes there are form a closed string left and right moving modes that form a proper Hamiltonian with terms like
a^†_n b^†_{-n},
a_n b{-n},
a^†_n b{-n},
b^†_n a_{-n}
where Nöther’s theorem demands that the frequency or mode for left and right be equal. If they are not equal this gives a preferred direction for the string and this violates momentum conservation. We then have a Hamiltonian for the form
H = a^†_n b^†_{-n} + a_n b{-n}
for spin 2 particles. Each of these operators corresponds to the raising and lowering of a vector boson s = 1 field. We may think of the operators as carrying a color index and in this Hamiltonian there is a sum over that index, so the Hamiltonian is color neutral.
Hamiltonian terms a^†_n b{-n} and b^†_n a_{-n} are spin 0 scalar fields. This would correspond to
H_± = a^†_n b{-n} ± b^†_n a_{-n}
One is the dilaton and the other the axion. Right off I can't remember which is the dilaton and which is the axion. The axion in this case is a bit different than the QCD version. Here the Lagrangian is θ^2H_{ab}*H^{ab}, where the H_{ab} symbol pertains to a dual field to the color field of QCD. This field is weak at low energy and stronger at high energy, with the field is not anti-screening as with QCD. The graviton and scalar fields are entanglements or compositions of these QCD-dual fields. The dilaton field φ emerges as I said above. The relationship between these two approaches to the dilaton field, QCD and the dual to QCD, is not something I understand.
This latter approach is I think amenable to both string theory and competing LQG, DT gravity and so forth. I have though not seen any developments along these lines. This might in some ways serve to constrain string theory in some way by either providing a solution set or conversely maybe by providing a kernel or Lagrange multiplier for solutions that do not obtain.
A good physics theory is one out of which comes much more physics than what went into it. Special relativity, General Relativity, quantum mechanics. String theory (I am told) has had a lot of wonderful mathematics come out of it, but no physics. Hast la vista, baby!
ReplyDeleteMitchell yes that is what i was asking about. thanks
ReplyDeletebtw how would you answer to Bee's observation in the OP?
It appears Peter Woit has a lot more influence than one might suppose. At risk of wearing out my welcome here I thought I would give some commentary on the whole business of quantum gravity.
ReplyDeleteString theory is really not a theory. In some sense that is a correct assessment. It is really a framework of physical hypotheses. The vast amount of structure in it is not well constrained to understand physics of the observable universe very well. On the other hand, a study of the basic bosonic string is really a very advanced study of complex variables. Contrary to popular opinion the basic idea of string theory is fairly accessible to those with some focused thought, patience and persistence. Superstring theory is more abstract, for now Grassmann variables enter into the theory of observables and one has this strange intertwine of quantum fields and spacetime we call supersymmetry.
It has to be pointed out that any theory of quantum gravity has lapses with observable physics. Quantum behavior of gravitation occurs close to the so called Planck scale. This is an extreme scale of things. It is not hard to do a calculation where you take the de Broglie wavelength of a particle λ = h/p, h = 2πħ = Planck unit of action, and set this equal to the Schwarzschild radius of a black hole r = 2GM/c^2. The momentum in the de Broglie for a particle at rest is just p = Mc. We put this together to compute the wavelength of a black hole and this is the Planck distance â„“_p = sqrt{Għ/c^3}. This is 1.6×10^{-33}cm. It is not hard to see the energy of such an interaction is a Planck unit of energy about 10^{17}TeV. This is 16 orders of magnitude larger than the LHC! Gravitation has a coupling constant GM^2 that scales with mass squared, or equivalently energy squared, which is why there is the large 10^{24}kg mass of Earth required to give a rather modest force. A ball bouncing off a floor in a millisecond is accelerated more than what gravitation provides in its fall. This illustrates how electromagnetism, which is involved in the bonding of atoms etc, is much stronger. Any theory of quantum gravitation would require probing nature at this interaction energy.
The LHC is ~ 10TeV, and so the same technology would have to be scaled up to 10^{16} times the size of the LHC. This would mean the ring would have to be on the order of 1000 light years in radius. The energy required to run it would be proportionately larger. The LHC has 10^{10}j of energy in magnets and the beam holds 10^{9}j of energy. This means the LHC operates on a gigawatt of power. The sun generates about 4×10^{26}watts. So to run this imaginary Planck collider you would need to harness a star with something similar to these fanciful science fiction ideas of a Dyson sphere.
The data collection would not be easy either. Let us assume you had two protons impact at a transPlanckian energy to generate a few Planck mass equivalent of a quantum black hole. This will decay into a host of particles. In fact if we assume it decays purely into protons and anti-protons that would mean 10^{20} such particles would emerge. Then secondary processes would result in far more particles. This would mean a detector would have to detect a mole of particles (6.02×20^{23}) or more and the track finding algorithm would have to back out the quantum gravity from this. This is also a tall order.
So whether one is talking about superstring theory or LQG or other approaches the experimental issues are daunting. The only prospect I see is to look for traces of quantum hair, say generalized BMS symmetry (Strominger) or fuzzballs (Mathur) and so forth in gravitational wave signatures. In this way we let nature do the heavy lifting.
I knew the second I finished reading this blog post that I would see comments by people who haven’t actually studied these things; trying to have in depth discussions when they have major misconceptions about what’s really going on.
ReplyDeleteGo talk to your professors about this, that’s what they get paid to do. Or take a calculus course at your local community college. Sabine has to deal with this stuff way to often.
Bottom line if your going to ask a question don’t act like you know what you are talking about when you don’t (which defeats the purpose of asking that question...)
P.S. I think “Princeton physics major” might not be an actual Princeton physics major....
Lawrence Crowell said... "superstring theory or LQG or other approaches the experimental issues are daunting" 1) Baryogenesis, 2) Sakharov conditions, 3) Vacuum is ~10^(-9) mirror asymmetric selective to hadrons. Measured proton/antiproton magnetic moments are divergent here.
ReplyDeleteBuild a rigid extreme chiral divergent molecule bearing a nitrile, the whole being a prolate rotor sweeping the dipole moment. Enantiomers' microwave rotational spectra will be slightly displaced. One hour, 40,000:1 signal to noise. 1986, 30:1 S/N exemplar, DOI:10.1515/zna-1986-1107
Beautiful theory demands exact vacuum mirror symmetry toward hadrons, uncreating baryogenesis. Such theory is empirically sterile, knock wood. Trivially look.
Bee,
ReplyDeletewould you advice princeton undergrad interested in QG to go to AS gravity over strings and loops?
Nathan,
ReplyDeleteRegarding your PS: I've had the same suspicion, so let me be clear that I have no evidence whether the person is who they pretend to be. (Traced back the email, result is inconclusive: Kinda in the right area.)
Haha well at least it was a good question
Deleteneo,
ReplyDeleteYou may have noticed that I didn't give any advice in my response. I think it's up to everyone by themselves to make their own decisions on what is or isn't a promising research direction. The only advice that I usually give to students is to not specialize too early and have at least two legs on which to stand.
I think what Koenraad and bud rap are trying to say is that a theory has to be tied to the natural world if one claims it to be physical. Which is completely true, from a mathematical fitting to data you can only make predictions about what happens, but not answer why.
ReplyDeleteMath answers to the question what and physics to why. Since string theory cannot answer to the why adequately, I would classify it as almost purely mathematical. If someone someday makes an observation as to why something happens, and ties it strongly to the mathematical framework of string theory, only then can it be considered a physical theory. And I at least think that a theory has to be physical (or have the promise of someday becoming physical) for it to be taken seriously as a theory of the natural world.
But don't get me wrong, it's also completely fine to fiddle with mathematical fittings and afterwards try to work out the physics. That is the state of quantum physics, for example, which has been wildly successful in the what department although we are still working out the why.
Lawrence,
ReplyDeleteThanks, this is very helpful.
Koenraad,
ReplyDelete"But why is it then, that some theories make correct predictions and others don't ?"
Not a question that science has anything to say about. Maybe consult a priest or philosopher.
Sabine,
ReplyDeleteYour responses to my comments are disrespectfull.
Best, Koenraad
Bee or Mitchell
ReplyDeleteis there any specific model of string theory that 1- give deSitter not anti-DS, 2 gives GR and hides the additional scalar field, 3 reproduces the MSSM and not additional particles 4 supresses FCNC and 5 compactified the additional dimensions
"Maybe consult a priest or philosopher."
ReplyDeleteMaybe, if they have studied philosophy of mathematics. Your assumption that mathematics is dependent on physical phenomena betrays your true sentiments. On the assumption that the two are independent, there *can* be demonstrated correspondence (Tarski; Popper) between mathematical theory and physical result, theory being the primary tool of analysis. Your assumption, however, allows no role for theory not constructed following observation -- thus, what you call predictions, are just retrodictions, made prior to experiment.
t h ray,
ReplyDelete"Your assumption that mathematics is dependent on physical phenomena..."
I didn't assume any such thing.
bee:
ReplyDeleteyour forthcoming book chapter descriptions ( http://lostinmathbook.com/index.php/content/table-of-contents) are great. LOL. hard tobelieve that the publisher let you use them.
naive theorist
"I didn't assume any such thing."
ReplyDeleteThen perhaps you can explain where the theory of correct predictions came from. I.e., how does one qualify correct predictions over failed ones?
t h ray,
ReplyDeleteI am saying if it makes correct predictions, it doesn't matter where it came from.
Okay. If not from theory -- where then?
ReplyDeletet h ray,
ReplyDeleteBrains? Computers? Alien messages? For what science is concerned, it doesn't matter.
So we're going to assume these origins, mystical or not, have no theories of their own? That "science" consists solely of manifest properties?
ReplyDelete"I am saying if it makes correct predictions, it doesn't matter where it came from."
ReplyDeleteOh but it does matter! The ultimate goal of science is to understand the nature of physical reality, not just calculate some observed outcomes. If you can't evaluate the underlying qualitative assumptions of the model vis a vis empirical reality then you can have no assurance that the model accurately represents physical reality. It could just be clever math (Ptolemy) covering up for erroneous qualitative assumptions. Note that this doesn't mean that such a model is necessarily erroneous, just that it cannot be assumed correct.
In an earlier comment you said "I think both you and Koenrad have a confusion about how a theory in physics works." It's not that I don't understand how things work in the realm of modern physics, I do. It is precisely "the way things work" that I am criticizing.
Hello Sabine,
ReplyDeleteYou've seen this well known clip by R.F.
https://youtu.be/NM-zWTU7X-k
The nuance in all of those considerations matters.
You state : I am saying if it makes correct predictions, it doesn't matter where it came from.
It matters to a serious extent if you have any intention of expanding or imrpoving the theory at some point in the future when data pointed out the boundaries of its validity.
And the theory made correct predictions because it came from the right place (or the best possible place given a certain era).
I am a lay person, but my understanding is that a “theory” in this context is an explanation for observed phenomena which typically make express or implicit predictions about as-yet-unobserved phenomena.
ReplyDeleteIf these predictions turn out true, then the theory is, to that extent at least, “correct”.
Thus, Sabine commented (on May 13 that, “... if the theory makes correct predictions for observables you gain confidence in it. ... If it works, it works.”
So, “... how does one qualify correct predictions over failed ones?”
Observation?
sean s.
As a phenomenologist, you have a deep understanding of the source-sink relation. How does one distinguish one from the other?
ReplyDeleteA problem I see here is that many of the questions here lapse from physics into metaphysics. There are a number of things science is not well suited to answer. Generally these are what might be called why questions. Science is better suited to address what questions.
ReplyDeleteKoenraad asked, "But why is it then, that some theories make correct predictions and others don't?" I will say that I think the ultimate foundations of physics is plain vanilla quantum mechanics. All the fancy stuff with strings or quantum fluctuations of spacetime, loops etc may just be plain vanilla quantum mechanics in disguise. Koenraad's question would then be equivalent to asking why is quantum mechanics the foundation? For that matter; why quantum mechanics? The problem is that physics has no answer. The quanta may just reflect how the vacuum is a dual set of states that are eigenvalued of complementary operators. The philosopher might object, and the theologian even more so, that this is not really a nothing. This thing called nothingness is a bit like the Tao that has no final description. Why the quantum? Why the sort of vacuum of quantum fields? We don't have any way to know the answer to this question.
There is further the relationship between physics and mathematics that has appeared here. String theory being rather mathematical with lot of algebraic geometry and topology raises speculations of this sort. Tegmark has advanced certain ideas that I frankly think are horrendous category flaws. Plato in the age of Pericles' Athens suggested something concerning realms of physical and ideal forms. Plato suggested the word or Logos is what bridges them. If you want a theologically inclined short synopsis of Plato's philosophy read the opening of the Gospel of John. Roger Penrose in his Road to Reality suggests a sort of triality between physics, math and mind. My reply to a question on the relationship between physics and mathematics is that we really do not have the foggiest idea.
The problem is that mathematics is not really an empirical subject. Chaitin has suggested with computers there is a sort of empiricism in mathematics now. However, numerical tests are not quite the same as performing observations, tests and measurements of nature. Also with mathematics theorems are proven. Even though the definition of what constitutes a proof has run into some Gödel type of difficulties, there is still enough of a firmness of the concept of a proof. By way of contrast scientific theories are not prove. They can only be supported with evidence, and found to contradict data outside of some domain of experience. As a result any proposal that physics and mathematics are equivalent runs into these category problems. A weaker statement on some relationship is not easily had, for such a relationship suggests some category equivalency --- a partial functor. While mathematics has served as a language of nature, we have no idea why this is and we have no idea of any fundamental relationship between physics and mathematics.
"Then perhaps you can explain where the theory of correct predictions came from."
ReplyDeleteI think you should study Popper on falsification. He basically says that theories are generated randomly and then the ones that are non-falsifiable and those that are false are culled. It is probably not an accident that this idea looks a lot like how natural selection works in improving the fitness of lineages of living things.
Obviously, this method of random theory generation is very, very inefficient. To have any chance of success, you need to narrow down the search to those theories that are "likely" based on what we already know. All this talk about whether or not String Theory is worthwhile studying is also about this question: Is String Theory likely to result in successful predictions of observable phenomenons.
Our revered host has written a book about one aspect of this question about what theories are likely to be successful.
"I.e., how does one qualify correct predictions over failed ones?"
Interesting question which has been answered by Popper decades ago. The answer proofs to be simple.
A correct prediction can be identified as a predicted observation that can be verified by any reasonable observer. The proverbial example is the theory that "All swans are white". This theory can be found in folklore, or it can appear to you in a dream after a bad meal. It does not matter. This theory predicts that when I encounter a swan, I will observe that it is white. This theory will be debunked if I find a swan that is black. Every reasonable observer who can see (blind observers can use a suitable sensor) will agree whether or not a swan is white or black. So, this theory was debunked after black swans were found.
The basic idea is that you generate as many predictions as possible from a theory, and then do experiments and observations that should show these predictions if the theory was true. If one of these experiments/observations fails to confirm the prediction, the theory is considered false.
How do you generate these prediction? Again, you can do it randomly. But that is not very efficient. There are better ways.
Bud rap said “It could just be clever math (Ptolemy) covering up for erroneous qualitative assumptions”
ReplyDeleteSo, Ptolemy gave us a wrong model that ultimately limited our ability to understand the universe? Thankfully Copernicus came along with a true nature of physical reality?
Well no Copernicus gave us heliocentric circular orbits. Just another model that was wrong.
Kepler made them ellipses. Another model. Also wrong. No way of explaining those orbital anomalies due to gravitational interaction.
Newton? Could not explain the orbit of Mercury due to relativistic effects. Another timewaster limiting science by working with an incorrect model.
I think it is well over a hundred years since we flattered ourselves with believing we had the ultimate answer, the ultimate description of reality, and just needed to prove it. Now we just look for better models that help us delve deeper.
The question here I think is whether String theory is a better model and is it helping?
Lawrence,
ReplyDelete" ... we have no idea of any fundamental relationship between physics and mathematics."
Then what does one call mapping of numerical results to physical phenomena?
Rob van Son,
ReplyDelete"I think you should study Popper on falsification. He basically says that theories are generated randomly and then the ones that are non-falsifiable and those that are false are culled."
I think I know Popper reasonably well. Popper's view is indifferent to how theories are generated, true; however, there is no question that *theory is primary.* Popper differed from most philosophers of science in his day, by taking David Hume seriously -- no amount of observation can verify a theory. And especially, no *inductive* program of the kind Sabine promotes, can lead to a falsifiable theory.
t h ray;
ReplyDeleteAs a phenomenologist, you have a deep understanding of the source-sink relation. How does one distinguish one from the other?
If you can identify a source-sink relation as such; distinguishing one from the other should not typically be difficult.
sean s.
Lawrence;
ReplyDeleteIf one of these experiments/observations fails to confirm the prediction, the theory is considered false.
Some theories may be correct within limits, but incomplete otherwise (Newton v. Relativity v. whatever comes next ...). A failed prediction demonstrates a flaw in a theory, but not necessary a total debunking of the entire theory.
sean s.
Michael;
ReplyDeleteTheories by Ptolemy, Copernicus, Kepler, Newton, et al. may have been wrong (in the sense of not perfect) but they were certainly not timewasters; a wrong theory can be quite valuable. They are imperfect models that can lead to less-imperfect models on the path of that “deeper delve”.
sean s.
t h ray;
ReplyDelete”Then what does one call mapping of numerical results to physical phenomena?”
Mapping; identifying correspondence between numerical results and physical phenomena. That correspondence (which can be observed) does not necessarily reveal any fundamental relationship.
... no amount of observation can verify a theory. And especially, no *inductive* program of the kind Sabine promotes, can lead to a falsifiable theory.
If one treats verification or falsification as absolutes, perhaps. But observation can verify that theoretical predictions match reality within the limits of observation, or that, based on premises, some theory is probably false.
sean s.
t h ray,
ReplyDeleteI am grateful for your interesting comments on the subject but I would appreciate if you could please discontinue assigning opinions to me that I have never voiced and in fact do not hold. I am not advocating an "inductive program," indeed in my book I am complaining that physicists have forgotten how to deduce properly. Having said that, you shouldn't forget that any deduction starts with assumptions which you can never prove to be true. Best,
B.
@ Sean S: The statement If one of these experiments/observations fails to confirm the prediction, the theory is considered false. is due to Rob van Son I did mention theories failing outside some domain of measurement. They can otherwise be good theories, such as classical mechanics.
ReplyDelete@ T H Ray: Then what does one call mapping of numerical results to physical phenomena? That is a way that data supports theory. Mathematics has played a role with physics ever since Galileo laid down the kinematics of velocity and acceleration. However, sticking with Newton with F = ma = md^2x/dt^2 we have no idea why nature generally prefers second order differential equations for the dynamical description of the position of a particle. We just know that this works pretty well. Does anything tell us there is some deep interconnections with physics and mathematics that makes this so? I don't think so.
Theories fun to play with. Many people become passionate upholders of certain theories while dismissing others. String theory starts from the quantum field theory perspective and derives gravitational-like physics, or at least a graviton. Loop Quantum Gravity (LQG) and Causal Dynamic Triangulation (CDT) start more from Einstein and attempt to work the other way. The string and M-theory people have more analytic results, but string theory as the LQG/CDT people point out is background dependent. One needs to have a Minkowski or anti-de Sitter spacetime as a given with graviton as perturbations on that. The LQG/CDT theories are background-independent, but these do not yield results readily.
The two approaches might not be that foreign to each other. Feynman pointed out that quantum gravitation on the tree level is equivalent to the classical theory. With CDT we have these polytopes on spatial manifolds that are connected to spatial manifolds on other spatial manifolds by light rays. The two sets of polytopes are Poincare duals, and this is an implicit Fourier transform. So the background in string theory can easily be of this form.
Michael Sharples,
ReplyDelete"So, Ptolemy gave us a wrong model that ultimately limited our ability to understand the universe? Thankfully Copernicus came along with a true nature of physical reality?"
To the first question, yes. The Ptolemaic model did indeed limit our ability to understand the cosmos and despite your subsequent efforts to strenuously refute straw man arguments, you actually make the case for the importance of building mathematical models on sound qualitative analytics.
There is a clear line of progressive refinement from Copernicus to Kepler to Newton to Einstein that was only possible because Copernicus reset the qualitative model from geocentric to heliocentric. No such progress occurred during the millennium plus reign of Ptolemaic cosmology. You can't get from Ptolemy to Kepler/Newton/Einstein without the qualitative reset that Copernicus provided.
Which brings us to String Theory. As Koenraad pointed out, the fundamental assumptions of the model (one dimensional strings) have nothing to do with physics; they are pure mathematical concepts. They come to us unburdened by the empirical constraints of science.
Whereas Ptolemy's qualitative model can be said to have been wrong, it was, nonetheless, a qualitative model. String theory doesn't even have a physically meaningful qualitative model. It is in that sense that Peter Woit's borrowed epithet "not even wrong" is appropriate to string theory. (https://en.wikipedia.org/wiki/Not_even_wrong)
Lawrence Crowell: "There are a number of things science is not well suited to answer."
ReplyDeleteThe scientific method is just our attempt to apply the best epistemic standards we have to understanding our universe.
Mathematics is what you get when you insist on the highest standards of logical rigor in reasoning about abstractions.
So I think it reasonable to say that if science and mathematics are not "well suited to answer" a question, then the question is either not meaningful or in some fundamental sense unanswerable.
bud rap: "String theory doesn't even have a physically meaningful qualitative model."
ReplyDeleteI think most would agree that is the key failure of String Theory's progress. I was more concerned at the suggestion that String Theory fails as a useful model at Line 1 because it is a purely mathematical abstraction.
That should never be a disqualifier when modelling the Universe. While we are listing historical greats then Maxwell springs to mind.
Oh, and Sean s., my description of Newton as a timewaster was very firmly tongue-in-cheek.
Consider the Milgrom Denial Hypothesis: The main problem with string theory is that string theorists fail to realize that Milgrom is the Kepler of contemporary cosmology.
ReplyDeleteA Physicist's Physicist Ponders the Nature of Reality (Edward Witten interviewed by Natalie Wolchover), Quanta Magazine, 28 Nov. 2017
Has Witten failed to grasp the magnitude of Milgrom's achievement?
B,
ReplyDelete" ... you shouldn't forget that any deduction starts with assumptions which you can never prove to be true."
One can, however, show them false or superfluous. That's why a constructed theory is primary. I sincerely apologize for attributing inductivist opinions to you -- I haven't read your book (I'll get around to it). I based my opinion on what you wrote a couple of years ago about the "experimental search for quantum gravity." Hoping to find a theory, by experiment, is inductive.
Best,
Tom
Lawrence,
ReplyDelete"@ T H Ray: 'Then what does one call mapping of numerical results to physical phenomena?' That is a way that data supports theory."
Doesn't answer the question. The function of mapping starts with the map (theoretical construction). The map is filled in with data. I'd call that a fundamental relation between physics and mathematics.
t h ray,
ReplyDeleteWhat you get from experiment is data that allows you to tell which theories work and which don't. Experiment of course doesn't give you a theory by itself, and if that's what you think I said you misunderstood. (To be more precise, I was probably referring to models, not to theories, but not sure the distinction matters for the present purpose.)
B,
ReplyDeleteA theory is a model. Without it, how do you know what you're looking for? What "works"? Then, suppose one has a theory of models that work (e.g. string theory), what experimental data would falsify the underlying assumptions? One can't say that string theory is unfalsifiable, on the one hand -- and yet accounts for every known physical interaction, on the other.
So one expects to find an unknown physical interaction, using known experimental methods?
I think the problem is flatland thinking, a problem that Joy Christian identified long ago. So long as one is working in a framework assuming 3 dimensions, one gets 3-dimension results--reasonable to assume, except that Christian has shown an extended framework includes hyperspace. Which necessitates dropping the 3-dimension assumption, replacing it if you will, with an assumption of 3-sphere (4 dimension) dynamics. And he has outlined experimental ways to falsify 4-dimension dynamics in our locally real 3 dimensions--that's the model, independent of a theory.
Unless one is willing, like Einstein, to challenge assumptions--axioms--one is unlikely to make the leap out of flatland. Worse, one imagines the leap and calls it magical. After all, that model works just fine in 3 dimensions.
t h ray,
ReplyDeleteI don't see the point of this discussion, but when I say "theory" I do not mean "model." A theory is a prescription for how to identify mathematical structures with observables. If you want to make a prediction with it, however, you need a model. Example: The standard MODEL is a quantum field THEORY. If a model doesn't fit with data, it may be the model that's wrong or it may be the theory that's wrong. That Anti-de-Sitter space (a model) doesn't describe our universe, for example, doesn't mean that general relativity (a theory) is wrong. And so on. I know this isn't standard terminology, but please take it as my definition. I think it agrees reasonably well with how most physicists use the terms.
B,
ReplyDelete"Example: The standard MODEL is a quantum field THEORY. If a model doesn't fit with data, it may be the model that's wrong or it may be the theory that's wrong."
Okay. Except the standard model is not a (complete) quantum field theory. String theory is, and it fits all the data. It's too successful in fact -- predicts 500+ vacua, and provides no way to determine the lowest state. So why shouldn't we just trust the standard model? -- it doesn't have enough dimensions. And so on.
We gotta get out of flatland. A flatland model won't do anything but verify its own assumptions.
t h ray,
ReplyDeleteEvery model has a limited range of applicability and the standard model works just fine, I don't know what your problem is with it. As to your comments about string theory: you can't make predictions with a theory, you need a model...
B,
ReplyDeleteI don't have any more problem with the standard model than, as you say, its domain and range.
As I said previously, a theory of models (string theory) does predict models. A model is for testing, not predicting--one would not have gotten the model without predicting it. Theory is primary.
t h ray;
ReplyDeletewhat do you mean by a “theory of models”? A theory containing a model? A theory consisting of a model?
“Theory of models” sounds kinda meta ... like a philosophical theory ABOUT science instead of a scientific theory.
sean s.
t h ray,
ReplyDelete"The function of mapping starts with the map (theoretical construction)."
Well, that's exactly backwards. No one can make a map of a territory without first making observations and measurements of the territory. You cannot produce a reliable map of Africa by contemplating your navel! Why would you think otherwise?
Maybe that's the way you were taught to do science. But it's backwards, it's wrong, and it isn't even logically defensible. Contrary to your beliefs, science is essentially an inductive process since it is, by definition, the study of those things that can be observed and measured (broadly inclusive of instrumentation). If you don't start there you wind up with the equivalent of angels dancing on the head of a pin or string theory, the outcome being solely dependent on your metaphysical proclivities.
OTH, I more or less agree with this statement:
"Which necessitates dropping the 3-dimension assumption, replacing it if you will, with an assumption of 3-sphere (4 dimension) dynamics."
My only reservation would be to say that you need to supplement 3D analytics with 4D, not replace. The hypersphere you allude to is an observable.
Consider an expanding spherical wavefront of light omnidirectionally outbound from a galaxy. That is a hypersphere. You can even calculate a redshift for it at increasing radial distances using the Schwarzschild equation and a reasonable density estimate for the enclosed matter term. The source galaxy is a 3D object however and must be treated as such. Physical reality is both 3D and 4D; it cannot be reduced to one or the other.
@T H Ray: I think Sabine's answer is hard to improve on. There are three layers that are theory, phenomenology and experiment. Supersymmetry is a great example of this. Supersymmetry is a theory that is a pure mathematical framework. By itself it says nothing explicit about particles. You have to "hang" a model on it, which has been the standard model. There are then supersymmetric extensions of the standard model of electroweak interactions. These models are on the verge of being falsified. However, supersymmetry as with the case of string theory is finding growing support in solid state physics and there are now interesting developments of stochastic dynamics based on supersymmetry. Same theory, different phenomenologies or model systems.
ReplyDeleteExperimental data is not a map from theory, but only evidence that makes a particular model system credible. It is more in the way of a police investigation and finding data that supports a case against a suspect, or maybe that evidence is contradictory to a guilty scenario.
Sean,
ReplyDelete"what do you mean by a 'theory of models'?"
I mean the theory from which models are derived is sufficiently robust. String theory is a perfect example of a robust theory, having few ad hoc assumptions.
bud,
ReplyDelete"'The function of mapping starts with the map (theoretical construction).'
Well, that's exactly backwards. No one can make a map of a territory without first making observations and measurements of the territory. You cannot produce a reliable map of Africa by contemplating your navel! Why would you think otherwise?"
I don't think otherwise. Then again, we are not making a map of Africa. Give thought to the meaning of a mathematical function--it's far from navel gazing. One can venture into the jungle without a map; without a plan, however, one has to believe that every discovery is an accident. Is that what the scientists you know believe?
" ... you need to supplement 3D analytics with 4D, not replace. The hypersphere you allude to is an observable." True. We are addressing assumptions--one can't keep the 3D limit without replacing it with a 4D limit, even though the 2-sphere (3D) is extensible.
you cannot derive a model from a theory.
ReplyDeletet h ray;
ReplyDelete“One can venture into the jungle without a map; without a plan, however, one has to believe that every discovery is an accident.”
As I thought; your comments are philosophical, metaphysical. Epistemological, I think.
I believe most commentators on this thread have moved beyond that. But OK.
sean s.
"you cannot derive a model from a theory."
ReplyDeleteOne must derive a model from a theory. Or live with unconstructed models.
sean,
ReplyDeleteWhere have you moved? To inductive generalizations?
t h ray,
ReplyDeleteI told you above what I mean with theory and model. You are not using this nomenclature (which I believe is rather common in my discipline). Neither have you told us what you mean with those words. I am merely telling you that according to the nomenclature I have proposed above, your statements are nonsense.
t h ray;
ReplyDelete“One must derive a model from a theory.”
You appear to be using the word “theory” to refer to any and all ideas, notions, guess-work, etc.. That is too vague to be meaningful in the context of this conversation.
sean s.
t h,
ReplyDelete"I don't think otherwise. Then again, we are not making a map of Africa. Give thought to the meaning of a mathematical function--it's far from navel gazing. One can venture into the jungle without a map; without a plan, however, one has to believe that every discovery is an accident."
The metaphor is usually presented as, "The map is not the territory." You seem confused about what that means. It means that, by its very nature, a map contains far less information about the territory than the territory itself does. Every map or model is incomplete - by a lot. So there is no logical basis for your claims. You need to rethink them.
Discovery can't happen by following the known map routes. Everything there has already been discovered. Discovery lies off the map.
As to your comment about 3D/4D, you are describing a mathematical problem. I described physical reality as a composite of 3D (mass) and 4D (electromagnetic energy) states. That's what is out there. If you can't model that, its your problem, not physical reality's, which gets along fine without your models, be they good, bad or indifferent.
B.
ReplyDelete"I told you above what I mean with theory and model." Above:
" ... The standard MODEL is a quantum field THEORY. If a model doesn't fit with data, it may be the model that's wrong or it may be the theory that's wrong."
You may not think it matters, though I will be more specific:
A physical THEORY is a set of closed logical judgments based on fundamental assumptions, and incorporating one or several testable models.
The consequence of not deriving model from theory, obviates one's ability to challenge assumptions and make closed logical judgements. That's why it matters. If one dares to step outside the orthodoxy, one risks his career and public ridicule. I gave the example of Joy Christian's substitution of the 3-sphere boundary for the 3-dimension boundary.
You can given yourself a clue to the importance of theory by answering one simple question: On what closed logical judgement is the theory of quantum mechanics based?
And to keep on topic--string theory does not suffer this shortcoming.
t h ray,
ReplyDelete"The consequence of not deriving model from theory, obviates one's ability to challenge assumptions and make closed logical judgements. That's why it matters. If one dares to step outside the orthodoxy, one risks his career and public ridicule."
As I said above, a theory is a set of mathematical axioms together with a prescription for how to identify mathematical structures with observables. It does *not* contain a definition for what's the actual situation you look at, for that you need a model. Please keep in mind the example I gave you: The standard MODEL is a quantum field THEORY. If you test the standard MODEL you cannot rule out quantum field THEORY per se, you will only ever rule out the model.
As to quantum mechanics, not sure what you mean there. The std definition is some list of axioms that you can look up in a book. But if you want to do an actual experiment you need a MODEL for the system, not just the axioms of quantum mechanics. You need for example something like, say, it's a bipartite state with a so-and-so distribution or what have you. Simply put, the theory doesn't contain the information necessary to model a real-world system. You need extra information for that. Though in rare cares a theory gives rise to what's known as "model-independent predictions". String theory eg predicts 6 extra-dimension of space, regardless of what the model. Model-independent predictions are exceedingly rare though. Best,
B.
B,
ReplyDeleteWe're not saying anything different, in principle. "The standard MODEL is a quantum field THEORY. If you test the standard MODEL you cannot rule out quantum field THEORY per se, you will only ever rule out the model."
That's true. The model is the testable element of theory. Quantum field theory is not testable. HOWEVER, unless one can tie the model to a closed logical judgment in the theory, one engages in circular logic. That's why the question (On what closed logical judgement is the theory of quantum mechanics based?) is important. If quantum mechanics is not logically closed, it isn't testable in any objective sense. That is, one can draw no objective conclusion from a test that ostensibly maps theory to result. The result is not model independent, but theory independent. Yet we validate quantum mechanics as a theory, because the theory of quantum fields is not testable. (Such is true for the whole family of probabilistic theories.)
Now, we have the theory of quantum mechanics and the theory of quantum fields, neither of which are OBJECTIVELY testable. They are theories without basis -- totally self-referential. Einstein was once asked by a reporter how he arrived at general relativity. "By challenging an axiom," he replied -- meaning he replaced Euclid's fifth axiom with an axiom of non-Euclidean geometry. The model of general relativity is now testable, and has been successfully tested.
String theory does not predict 6 extra dimensions of space. It assumes them, and then details (models) the consequences of this added assumption. Because a test has not been devised for the model, the theory remains a mathematical theory, and it should not be ridiculed for that -- the terms are all objective, all closed.
I have felt Joy Christian's pain the last decade, for the same reasons. He did not provide a theory -- he provided a framework for testability of the theory of quantum mechanics, giving it closed logical form and thus completing it. Which also replaced the assumption of the limits of space with another.
All three approaches -- general relativity, string theory and Christian's -- are mathematically complete. Should one prefer mathematical completeness over probabilism for a physical theory? I don't know. Until we follow through with testing models that include new assumptions, none of us will know.
Sean,
ReplyDelete"You appear to be using the word 'theory' to refer to any and all ideas, notions, guess-work, etc.. That is too vague to be meaningful in the context of this conversation."
Yep. Actually, it's the only context for theory that's meaningful. Einstein said, "Imagination is more important than knowledge." So it is.
t h ray;
ReplyDeleteActually, it's the only context for theory that's meaningful.
Words by themselves do not have a context;
words by themselves are used in a context;
words by themselves have meanings.
In the context of this thread, theory means what Dr. B and others have been telling you. It is not the vague general meaning you are using; it’s a relatively specific meaning.
Context matters.
sean s.
bud,
ReplyDelete"The metaphor is usually presented as, 'The map is not the territory.' You seem confused about what that means."
Do I? I didn't even bring it up.
"It means that, by its very nature, a map contains far less information about the territory than the territory itself does."
What does one know about the nature of a map?
"Every map or model is incomplete - by a lot."
How does one determine that?
"So there is no logical basis for your claims."
You sure?
"You need to rethink them."
I do. Every day.
T. H. Ray,
ReplyDeleteYou wrote: Now, we have the theory of quantum mechanics and the theory of quantum fields, neither of which are OBJECTIVELY testable. They are theories without basis -- totally self-referential. Quantum mechanics has successfully passed thousands of different experimental tests, all performed numerous times. Quantum mechanics is probably the most battle tested modern theory. Quantum field theory is a way of parameterizing a wave function with types of operators, usually called something like a and a^†n. The one departure from quantum mechanics is that operators separated by spacelike intervals, think of those operators at a point that would require traveling faster than light to reach, has zero commutators. This in effect buries away some nonlocality of quantum mechanics. Since entanglement phases are only distinguishable at high energy at distances of at most 10^{-13}cm this is not a big loss. This helps in calculations from getting nonlocal physics erroneously rolled into causal amplitudes. However, with black holes this assumption may not hold.
You also wrote: String theory does not predict 6 extra dimensions of space. It assumes them, and then details (models) the consequences of this added assumption.
String theory does not assume these dimensions. They are calculated. They are dimensions where anomaly cancellations prevent degeneracies of commutators with Virasoro and Kac-Moody algebras of operators. It is a rather technical issue so I will not go into depth here. For the strict bosonic string the cancellation is for 26 dimensions, with 2 of those dimensions tachyonic. For closed strings with Ramond and Neveu-Schwarz conditions, one without a twist and the other with a twist, this gives a graded algebraic system. The simplest cancellation occurs at 10 dimensions and a more involved theory is in 11-dimensions. Vafa, as I recall, is touting a 12 dimensional version as well.
Lawrence,
ReplyDelete"Quantum mechanics is probably the most battle tested modern theory. "
In what battle space?
"They are dimensions where anomaly cancellations prevent degeneracies of commutators with Virasoro and Kac-Moody algebras of operators."
Demonstrating that the theory cannot live in fewer dimensions. Thus, assumed. A constructed assumption in a physical theory is indifferent to mathematical origin, or else we would not be able to validate mathematical proofs both forward and backward when applying them to physical manifestations. Strings can't live in 3 dimensions, without violating special relativity, so we add dimensions until we can cancel all anomalies mathematically -- but physically the number remains an assumption.
THR (originating comment): The function of mapping starts with the map (theoretical construction). The map is filled in with data. I'd call that a fundamental relation between physics and mathematics.
ReplyDeleteBR: "The metaphor is usually presented as, 'The map is not the territory.' You seem confused about what that means."
THR: Do I? I didn't even bring it up.
If you are going to employ the metaphor of mapping you are implying the existence of the territory which is being mapped. Setting aside for a moment the truism that the map is not the territory, it is the temporal sequence you invoke that is, scientifically speaking, illogical and a fundamental misrepresentation of the relation between physics and mathematics.
Science does not begin in theory (with a map), whether philosophical, metaphysical, or mathematical. Science begins with observation and measurement, and from there models and theories are constructed to account for those observations and measurements. But of course, observation and measurement are inherently limited in nature.
This does not present a problem for science per se, as it is just one of the facts of existence. It does, however, present an opportunity for theorists (of whatever stripe), to go rummaging in their human imaginations in search of fanciful theories lying far, far beyond the empirical constraints of science.
On the resulting ill-conceived maps there be Many Worlds and Parallel Universes and etc. Whatever their value as entertainment to those who concoct those maps, such excrescences from the human imagination have no scientific value. They are as unrelated to physical reality as the ancient concepts of heaven and hell.
So where does string theory fit in all this? It is simply a product of your erroneous conception of the fundamental relationship between physics and mathematics. Physical reality, and thus physics, underlies mathematics because math is a product of the human imagination which is itself a product of physical reality.
The inverted view, which you appear to hold, is that physical reality is somehow a product, via mathematics, of the human imagination. Thus from mathematical considerations alone a proper description of physical reality can be derived. This is a logically indefensible from a scientific perspective.
The centrality of human existence to physical reality is a recurring logical fallacy, a product of human hubris that, over millennia, has taken many forms, none of which have ever had any relevance to science. This is very much inclusive of the mathematicism error, the metaphysical belief that human derived mathematics somehow underlies physical reality.
Whatever the mathematical merits of string theory as a "closed logical judgement", that closure takes place beyond the realm of science. String theory is only a mathematically-based metaphysical speculation that tells us nothing meaningful about the nature of physical reality. Science, it is not.
bud,
ReplyDelete"Science does not begin in theory (with a map), whether philosophical, metaphysical, or mathematical. Science begins with observation and measurement, and from there models and theories are constructed to account for those observations and measurements."
Therein, the problem. An inductive approach induces only the fantasies that you hold in contempt.
Look, I realize that the followers of this forum are overwhelmingly anti-string theory. I merely wish to bring to attention that it is worth studying as a physical theory, because it is a physical theory -- one that obviates a number of ad hoc and superfluous assumptions. Complete.
"String theory is only a mathematically-based metaphysical speculation that tells us nothing meaningful about the nature of physical reality."
All physics is metaphysical speculation. Until it isn't. From a realist perspective, metaphysical realism is real if it is objectively determined. Our perception of the world evolves as we evolve in understanding.
t h,
ReplyDelete"An inductive approach induces only the fantasies that you hold in contempt."
On the contrary it is the deductive approach that produces angels dancing on the head of a pin and string theory. You simply postulate an unobservable and go merrily off spinning logically consistent loop de loops in a reality vacuum. This approach is, apparently, endlessly amusing to certain philosophers, metaphysicians, mathematicians, and theologians.
But physics and science generally do not work that way. They begin with observations and measurements which are evaluated logically to produce theories and models that are then checked against existing data and ongoing observations and measurements. It is the continuous feedback loop between observations/measurements and analysis that constitutes the doing of science.
If you are arguing that modern physics oftentimes does not work that way I would agree with you. But the problem always seems to arise when empirical evidence is cavalierly dismissed in favor of theoretical models. That is, deductive logic applies: a model is a priori true and all discrepancies with physical reality are accounted for within the logical structure of the model because it is by definition true - reality be damned. Do we agree on this?
Science, inclusive of physics, is not a body of metaphysical speculation, no matter what they taught you back there in philosophy school. Science is the open-ended investigation into the nature of physical reality employing the complimentary probes of empiricism and logic.
Science stands apart, in its achievements, from philosophy, metaphysics, logic, mathematics, and etc because of its empirical grounding. No empiricism, no science, but lots of angels and one-dimensional strings. You can launch a rocket to the moon with science, but you can only launch an argument with the rest.
bud,
ReplyDelete"It is the continuous feedback loop between observations/measurements and analysis that constitutes the doing of science."
There are two types of feedback. Only one of them leads to a closed judgment, which is the basis of my argument. The positive open feedback loop that you describe gives the illusion of movement, because it appears to cull models while more strongly verifying the model originally tested. What is actually happening is the testing of various interpretations of the theory, which in itself signals a problem -- it leaves no room for negative feedback, which we know occurs in natural systems. Negative feedback needs no interpretation: is not gravity, in its simplest definition, a human-independent system of universal negative feedback? Gravity is a one-way interaction, and so not tractable to the empirical feedback loop you favor.
" ... deductive logic applies: a model is a priori true and all discrepancies with physical reality are accounted for within the logical structure of the model because it is by definition true - reality be damned. Do we agree on this?"
No. A model is not true by definition. (Popper applied the term 'verisimilitude' to models which are progressively approaching truth, based on the Popper-Tarski correspondence theory.) Correspondence between reality and theory is therefore an equality IFF reality can expand to meet the theory. If half of naturally occurring events are eliminated a priori from experimental tests, however, empiricism is a liability.
"Science, inclusive of physics, is not a body of metaphysical speculation, no matter what they taught you back there in philosophy school."
Can we refrain from personal comments?
"No empiricism, no science, but lots of angels and one-dimensional strings."
I don't know about angels, but one-dimension strings are a well founded physical concept. Both string theory and LQG can benefit from Joy Christian's empirically-testable framework.
t h ray appears to be caught in his own self-confirming “positive feedback loop”.
ReplyDelete“Correspondence between reality and theory is therefore an equality IFF reality can expand to meet the theory.” [emphasis added]
Ah. Solipsism.
sean s.
Sean,
ReplyDelete"Ah. Solipsism."
You misunderstand solipsism.
t h ray;
ReplyDelete“You misunderstand solipsism.”
Perhaps true, but the idea of reality expanding to meet a theory seems close enough.
sean s.
sean,
ReplyDelete" ... the idea of reality expanding to meet a theory seems close enough (to solipsism)."
So you believe in a static universe. Read what I actually wrote; how is correspondence equal to solipsism?
The article was so nice and I have to appreciate it, but as a student with pure supertheoretical(!) interests, I have to say that 'there are many physicists, who faced experiments apposing their theories sharply at the time that they were proposed. I remember Gell-Mann once told that 3 experiments were apposing with his theory and at the end they turned out to be wrong.
ReplyDeleteWell, at the moment we have no kind of expriment to falsify ST, so maybe it's even in a better position in comparison with Gell-Mann's theory of quarks(just as an example). On the other hand there are some significent mathematical evidences that makes stirngs more serious to deal with.(Witten-Sieberg theorem and tqft in 3+1D and many more...)
In my opinion the theory does not seem to be that much ad hoc.
Another point is that FCNC do "exist" within the context of SM but according to GIM mechanism but their cross sections are too small that we can't find them.
t h ray
ReplyDelete"So you believe in a static universe."
I believe reality does not change (i.e. “expand”) in response to our theories. Reality is what it is; it is our theories that need to change to correspond to reality, not vice-versa
“Read what I actually wrote;...”
I did. Did you not notice the quote from what you actually wrote? Let me help by citing your comment again:
“Correspondence between reality and theory is therefore an equality IFF reality can expand to meet the theory.” [emphasis added]
-- t h ray; 9:00 AM, May 23, 2018
“... how is correspondence equal to solipsism?”
Your comment spoke of reality changing in response to theory; which is a solipsistic idea.
If you think correspondence is equal to “reality expanding to meet a theory” then the equality between correspondence and solipsism is implicit in what you actually wrote.
Perhaps you were getting at something else. If that’s so, you’ve been unclear about what it is. What you actually wrote seems solipsistic.
sean s.
Sean,
ReplyDeleteYou've completely misinterpreted what I said. I think we should leave it at that.
t h ray;
ReplyDeletePlace the blame on me if you like; but readers are not responsible for muddled writing. We can leave it at that.
sean s.