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Been examining a newer way of looking at Feymann integrals that greatly helps simplify some of the mathematics. The method employs the charge conjugation relations to simplify allowable interactions on Feymann integrals. https://arxiv.org/pdf/hep-ph/9601359 Figured this would get a bit of interest for discussion.

Yeah, it rings a bell: https://www.scienceforums.net/search/?q="MHV"&quick=1

Please, do tell us. I gave you an early alert that you need to up your game. This is a good chance for you to start making some sense. Getting on the nerves of people is certainly no way to push your arguments forward. I find your first statement surprisingly bold. QM and GR have proven to be extremely difficult to reconcile so far, if not impossible. The only ways I've heard of to make sense of quantum corrections to all levels and include gravity are superstrings, LQG, and MHV amplitudes. MHV makes next-to-impossible calculations actually doable. The problem is you lose track of explicit Lorentz invariance and locality. And, of course, you need to devise experimental techniques to ramp up the energies of the experiments to Planck scale. Please, tell us also about that one necessary characteristic for a sensible theory of quantum gravity. For dramatic effect, you can use the spoiler function, like this, Q: What is the one characteristic that a quantum theory needs? A: I'm looking forward to your illuminating answers.

I think you mean non-separability in space. I haven't the foggiest idea what separability in time means, as separable or not is an attribute of the state that depends on how it factorises --or not-- in the particle-identity tags* (state)12=(state)1(state)2 --separable-- or, as is the case for the singlet state (state)12=(state)1(state)2-(state)2(state)1 --non-separable. Once an inertial system is chosen, there's only one coordinate time. On the other hand, it's perfectly possible to make a classical-mechanical model of interaction non-local. Newtonian interactions at a distance are a perfect example. So no, it's not a discriminating attribute between classical and quantum. It's just an artifact of the approximation. If someone removed the Sun from its place, it would take us a little over 8 minutes to be able to tell. We have no experiment that says that, but we're pretty sure it's true. * Even though particle identity doesn't really mean "identity" as we understand it in the classical world. It's a dummy tag, really, a labelling artifact. (My emphasis.) I think you mean local, but that's probably a typo. FW theory. This is a theory of classical (not quantum) electrodynamics in which Feynman, for reasons that were purely heuristic --see below--, wanted to dispose of the field altogether, and assume a direct interaction between charged particles that gave rise to a completely local, relativistically causal electrodynamics. Google: "Heuristic hypothesis" In this method Feynman, after a suggestion from Wheeler, imposed the condition that the force per unit charge (the field in disguise) be half-retarded and half-advanced. But of course, the final constriction is that the total solution from all the electrons in the universe propagated in a retarded way and be totally causal and local. Feynman found that he had to impose the condition that spatial infinity be a perfect absorber of EM radiation. Pretty weird, but it worked mathematically. Observation: You can perhaps always introduce an interaction between pairs ab initio that is formally non-local, and then impose boundary conditions that restore locality --in this case, the perfect absorber at infinity. You can always have an infinite expansion in spatial derivatives of the interaction (and therefore, non-local) but you impose that the sum of all the infinitely many terms be local. You can play with that ad infinitum. It's just a change of variables. In fact, I know of another perfect example in which the separation of variables makes locality non-manifest. The so-called MHV approach to solve quantum field theories. The reason that we today do not believe that the WF model is telling us anything significant about non-locality is, of course, that we happen to know that the world is quantum, and not classical, on the one hand; and on the other hand, that the alleged non-locality has no observable consequences, because of reasons I've just explained. When you study quantum electrodynamics, you see very clearly that the advanced waves correspond to antiparticles, not to any bizarre waves propagating backwards in time. If you're surprised by this mathematical fact, it's very understandable: In quantum field theory, if you want to have field variables that commute at space-like intervals --and therefore have a theory that preserves causality, and forbids superluminal propagation-- you actually need positrons. These are not actually waves propagating backwards in time, they're only degrees of freedom of the field for which the amplitudes have to be "interpreted" backwards, so to speak. This is key to the Feynman prescription for the propagator. Feynman explains this point --not very clearly, I must say-- in this famous Dirac-Memorial conference --he starts at 10' 35'' with the words "now, here's a surprise": Here's the most revealing part of the transcript. Pay attention, please, to the words "apparently moving backwards in time." So that's all there is to it in the quantum version. You need antiparticles if you want to guarantee locality and causality. Feynman, of course, never doubted locality and relativistic causality. Well, I'm sorry. It does. They all are quadratic expressions in the wave function, and satisfy local conservation law of energy, momentum, and angular momentum (both orbital and spin.) This is all mainstream. See below for local conservation of probability density and continuity equation, plus Wiki reference added. What you're measuring there is a correlation that was there from the get-go. No wonder it "is superluminal" to you --and perhaps others who don't understand this particular point--, as it is not the speed of anything. I've told you before. The Book of Psalms is the same everywhere, not because different versions of it are communicating telepathically with each other, but because they were written long before the present time. Correlation is not causation, nor necessarily interaction. You've got a point there, but that's not totally true. We always have our reliable good old Ockam's razor. There are also TIQM (transactional interpretation of quantum mechanics), DH (decoherent histories approach), Nelson's SQM (stochastic quantum mechanics), etc. None of these models have been proven falsifiable, which is not the same as saying they are not falsifiable. What's SD? That is not correct. So local it is that a simple calculation from the Schrödinger equation allows you to derive the continuity equation for the square of the absolute value of the wave function. Probability satisfies the accepted paradigm of a local conservation law. Probability flux getting out of surface = - time rate of variation of probability inside the surface Totally dumbed down: No probability can get out of a volume without going through its surface. This is a theorem you can prove from the Schrödinger equation. Here it is: https://en.wikipedia.org/wiki/Schrödinger_equation#Probability_current I've tried to simplify the maths, but I can provide you a complete and detailed proof, if you're interested. If you sample the web for opinions on this, you will find lots of confusion. For example: And more high-level: https://physics.stackexchange.com/questions/18762/locality-in-quantum-mechanics Etc. Even if you don't understand the maths, quickly skimming through the previous forums will help you size up the level of confusion. ... ... And finally, Hugo Tetrode, 1921-22? Well, yeah. Quantum mechanics was completed around 1926. So I'm gonna pass on that.

I'm a bit hazy about this, because it's been a while. There's a lot that has to do with prescriptions you adopt just because you want your fields to propagate causally. After some investigation, you find out that your Fourier expansion of the fields must contain both, \[e^{-ip_{\mu}x^{\mu}}\] and, \[e^{ip_{\mu}x^{\mu}}\] with the ordering prescription given by, which amounts to prescribing the "positive energies" to propagate forwards in time, and the "negative ones" to propagate backwards. I don't think this is a big deal: After all, you're interpreting what you energy-dimensional parameter E is doing in your physics. So far you're kind of forcing your amplitudes to behave causally (microcausality). If you do all that, you get amplitudes that commute outside of their causal cones (anti-commute, if they're fermions): \[\left[\varphi\left(x\right),\varphi\left(x'\right)\right]=i\delta^{\left(3\right)}\left(\boldsymbol{x}-\boldsymbol{x}'\right)\] provided that, \[\left(x-x'\right)^{2}<0\] (depending on signature criterion). Then you proceed to solve Heisenberg's evolution eq. in the Dirac or interaction picture. \[\varphi_{\textrm{int}}=e^{-iH_{\textrm{int}}t}\varphi e^{iH_{\textrm{int}}t}\] Then you substitute this expression into the Heisenberg evolution equation in the Dirac picture and discover that the solution must include the time ordering given by Dyson's formula: \[\varphi_{\textrm{int}}\left(t\right)=\left[T\exp\int_{0}^{t}dt'H\left(t'\right)\right]\varphi_{\textrm{int}}\left(0\right)\] So far, so good. It's complicated, you have implemented what you know about the world, as well as used the room that the quantum formalism gives you to represent the states (change picture to a unitarily equiv. one). The really weird step, IMO, comes now. If you try to expand this as a Fourier series in harmonic oscillators, you have an infinite sequence of differently-ordered powers of creation and annihilation operators, so you (again, IMO) kind of pull a rabbit out of a hat by re-defining your formal series as, \[:\varphi_{\textrm{int}}\left(t\right):=:\left[T\exp\int_{0}^{t'}dt'H\left(t'\right)\right]\varphi_{\textrm{int}}\left(0\right):\] The colon-bracketing means that everything that has differently-ordered power of creators and annihilators, is re-ordered so that all the creators are to the left (and conv. for the annihilators). When you do that, you don't end up with the same operator. It's a different one! Then comes the use of Wick's theorem, by using the vacuum state. The re-ordering that you've imposed proves now very useful, because the annihilators to the right kill the vacuum, so that you remove a lot of junk. I think, or vaguely remember, that the steps are justified. This is not the way most people learn QFT. In the old days people invested a lot of time in understanding the gradual steps. Today, everything is considered justified and people tend to jump as swiftly as possible to Feynman diagrams, so they can do calculations. I just want to add (and sorry for a lengthy and perhaps obscure explanation) that in order to rigourously get to Feynman graphs, there are quite many (mainly combinatoric) steps farther ahead. Basically you must remove over-counting due to your re-ordering, because, obviously, when you identify expressions like, \[a^{\dagger}aa^{\dagger}\] and, \[aa^{\dagger}a^{\dagger}\] with, \[:a^{\dagger}aa^{\dagger}:=:aa^{\dagger}a^{\dagger}:=a^{\dagger}a^{\dagger}a\] you must keep track of how many times this last term appears by re-ordering operators. Sorry for such a lengthy attempt at an answer, I may not have been very helpful. Take it just as an appetiser, and feel free to ignore it. Sorry if you know many of these things. --------------------------------------------------------------------- I suppose my succinct answer to your question would be: Dyson's time ordering appears to me as quite natural, because it's a step for you to make your solution formally satisfy the evolution eq. But steps come later that, although immensely useful and allegedly "rigorous" by many people, do present fuzzy areas, at least to me. I'd love to understand them better. For me it's a work in progress, maybe a lifetime-long project, to get to understand the fundamentals satisfactorily enough. PD: Both @Duda Jarek and you have made comments about topology that I think are very interesting and point in the direction that I would like the theory to go. AAMOF, it was Gerard 'tHooft, Polyakov, among others, one of the first pioneers to try to develop a more geometric language for QFT. I can't say that's the ticket, but it sounds to me like a much more promising scope. Other things are going on in QFT. Have you guys heard of MHV amplitude calculations? It's a very quickly-developing subject.

The typical energy scales of quantum theory and gravity are vastly different. There is no reason to expect that gluons have much directly to do with gravity; of course as they carry energy-momentum they do couple to gravity, but the gravitational force between gluons etc is tiny. The situation is less clear near the scale of quantum gravity, which is probabily near the Planck scale. However, we just don't have great models at that kind of scale and so who knows. Now something you maybe interested in is using techniques from the strong force for gravity calculations. The so-called MHV amplitude that were originally developed for gluon scatterings were realised by Witten to have a geometric interpretation via twistor string theory. These methods have been applied to gravitational amplitudes. So in this sense yes, the strong force and gravity are related, but formally.

So we all have a better idea of where you are coming from, can you give examples of this. Some of the most important results seem to stem from mathematically trying to understand what quantum field theory 'is'. String theory has also led to techniques that can be applied to point-particle QFTs; for example Witten's understanding of MHV amplitudes using twistor string theory. That said, most of the really interesting results really are in linking strings/fields to geometric and topological structures.

This is no different to lots of things in physics. For example, electromagnetic theory does not really tell us what the electromagnetic field 'is'. It tells us how to mathematically model electromagnetic phenomena and allows us to make predictions of such phenomena. So in general relativity you really have to adapt a similar way of thinking. We know how to model gravitational phenomena using mathematical models that use space-time without really telling us what space-time 'is'. Okay, so you don't actually have a new model of gravity, really you have an attempt at an interpretation of general relativity. You will need a mathematical framework to construct a model or a theory. Now, there are some nice links between the strong force and quantum gravity; MHV amplitudes and twistor sting theory. So people have thought a lot about using ideas from QCD in quantum gravity. For sure perturbative quantum GR is not well-defined, but it is of course okay as an effective theory. Also, it maybe possible that quantum GR or something close to it exhibits asymptotic safety, which means that it is well-defined as a quantum theory just not perturbativley. Well, without a proper model we cannot really discuss this. This is more the scope of philosophy. The best I can really say is that 'because the field equations say so'. I cannot imagine a much better answer than that. Maybe you could try to argue something following the path from special to general relativity and some arguments about the gauge principal, but really this is in hindsight. Again you will need to do some mathematics to help at all. Indeed, for composite particle the major contribution to the mass comes from the binding energy. The Higgs field is responsible for the mass of elementary particles.

String theory is considered as a good candidate for a unified description of fundamental particles and gravity. However, the difficulty with the string landscape and the anthropic principle mean that string theories make few specific predictions. This and other issues mean that the "string dream" has yet to be realised and doubt has been cast on the possibility of string theory as a unification scheme. That said, string theory has taught us a lot about non-trivial generalisations of point-particle theories, quantum gravity and mathematical symmetries (such as T and S, the AdS-CFT correspondence and mirror symmetry). Even if string theory turns out not to be the correct way to unification the lessons learned are invaluable. As you may know string theory has its conception in the theory of hadrons. This was quickly proceeded by a point-particle theory called QCD. Now there seems to be a return to this origin in the form of gravity-gauge duality. It is known that roughly (gauge theory)[math]\times [/math](gauge theory) = (gravity theory). This was first realised via "stringy arguments" (this was first done to tree level by Kawai, Lewellen and Tye , but has seen been generalised to higher loops and shown to be true in field theory.) Related to this is the work of Witten (and now many others) on MHV amplitues and twistor string theory. In essence, people are doing calculations in gravity to get results in gauge theories. So far, this is inherently supersymmetric but people are working on more realistic models. Sting theory is by no means dead. Merged post follows: Consecutive posts merged I don't think this is quite right. The LHC will not probe the string scale. However, it is possible that supersymmetry and extra dimensions will be discovered. Both are consistent with string theory and I would take them to be "circumstantial evidence" and a "good sign" we are on the right lines, but not concrete evidence. As John Ellis once told me "String theory needs supersymmetry more than supersymmetry need string theory".

I would not say I am on the fence. I am aware of the many similarities (I mean mathematically) between general relativity and "more conventional" gauge theories such as electromagnetism. I am not an expert in this field. As I don't know what you already know or what level you are at it is difficult to give a very clear answer to your original post. I don't fully understand or appreciate the links between gravity and gauge theories, the relations are non-trivial. But due to these relations you can think of them as being the same. I will need to clarify this. Take for example the Kawai-Lewellen-Tye relations. They suggest the correspondence (at least in perturbation theory to tree level) [math]gravity = (gauge\hspace{5pt} theory )\times (gauge \hspace{5pt}theory)[/math] These relations are best understood using string theory and as far as I know, they are not fully understood starting from the Einstein-Hilbert action. Anyway, it is possible to use gauge theory to make calculations in (perturbative) quantum gravity. Also, maybe more interestingly is that one can get at gauge theory calculations via quantum gravity/string theory. Today this is a hot topic, (viz MHV amplitudes and twistor string theory). So far most of this is supersymmetric, people are working on getting at non-supersymetric theories like QCD. As for gravity being only attractive, unless you have some exotic matter present then gravity is always attractive. A Klay points out, unless we have some real evidence for repulsion why add it? Also, if a quantum theory of gravity is to reduce to general relativity then the graviton would have to be spin-2. So, technically your question is deeper than I suspect you realised Cheers Klay

I think that one of the most interesting things is that gravity and gauge theories are not so different. Both are (classically) geometrically very similar. Really both Yang-Mills and general relativity are described in terms of principle (and associated vector) bundles. For Yang-Mills we have an [math]SU(n)[/math] principle bundle and for general relativity the important bundle is the frame bundle. Even more interesting are the relations between them such as the AdS-CFT correspondence, the Kawai-Lewellen-Tye relations and MHV Amplitudes via twistor methods. ------------------------------------------------------------ Tootsie Rolls are chewy chocolate-flavoured candies that have been manufactured in the United States for more than 100 years. The cylindrical cocoa-flavored candies come individually wrapped, and are an American cultural icon.* *Wiki.

Losing support from who and why? What I might accept is that string theory may be losing support from the theoretical physics community as a possible unification scheme, but that does not mean that string theory is useless. Quite the contrary, string theory is getting back to it's roots as a description of strong physics and this makes it very interesting and useful. This new look at the possibility of describing strong physics by a string theory is the AdS/CFT correspondence which relates a gravity theory to a gauge theory. One is able to do gauge theory calculations using gravity! This is one of the great properties of string theory, it allows one to geometrically construct gauge theories. (You can construct gauge theories by stacking branes and conneting them with strings). One issue so far is that the gauge theories are supersymmetric and as of yet do not quite reflect physical gauge theories. This is all work in progress by many people and the out look it good. Other areas of interest include twistor string theory and MHV amplitudes, integrability of N=4 super Yang-Mills and the AdS/CFT corrspondence, D-Brane Dynamics and Gauge Theories and many other things... So string theory is not dead and is far from being useless in phsyics. Woit is wrong!

I don't know what you are asking here. What is true, is that gravity can be viewed as "two copies" of a standard gauge theory. This deep fact allows one to relate caluclations in gravity and gauge theory. You should look up things like MHV amplitudes and the Kawai, Lewellen, and Tye relations. These things relate tree-level amplitudes in gravity and gauge theory. It has also been shown how to go further that tree-level. Thsi stuff is not very familiar to me, so you will have to do your own research here.

I was told that most of the lattice field theory work on QCD is trying to explain experimental results form many years ago. On the theoretical side twistor string theory and MHV (maximally helicity violating ) tree amplitudes in (super) QCD, has become a big thing.