A Brief History of String Theory: From Dual Models to M-Theory (The Frontiers Collection)

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Dean Rickles. Innbundet Fri frakt! Om boka. History and Mythology. Theoretical Exaptation in String Theory. I think he has done an impressive job especially in view of the obstacles that needed to be overcome: string theory's convoluted history, the highly mathematical nature of the subject, and the many common misconceptions that exist. There will surely be much more historical study of this subject in the future, so it is very fortunate that this book will be a reliable source. Theory was in a rather sorry state. Most of the work was concerned with model building to try and get some kind of foothold on the diversity of new phenomena coming out of the latest generation of particle accelerators.

There was genuine uncertainty about the correct framework for describing elementary particles, and even doubts as to whether there were such things as elementary particles. In the immediate aftermath of WWII, there was extreme confidence in the available theoretical frameworks, and little concern with foundational issues.

One of the central problems was triggered by the strong interactions, involving hadrons,2 describing the properties of nuclei. True to their name the strongly interacting particles have large coupling constants determining how strongly they interact with one another, so the standard field theoretical tool of expanding quantities in powers of these constants fails to give sensible results.

This situation led to a move to bypass quantum field theory and instead deal directly with the fundamental constraints—and other general properties characteristic of the strong interaction—on the S-matrix that are expected of a good relativistic quantum theory i. String theory did not spontaneously emerge from a theoretical vacuum; it emerged precisely from the conditions supplied by this profound foundational disenchantment. Therefore, any such combination of relativity and quantum will involve many-body physics.

This is compounded as the energy is increased. If the coupling constant is greater than 1, then going to higher order in the perturbation series and adding more and more particles means that the corrections will not be negligible so that the first few terms will not give a good approximation to the whole series. Quantum field theory was out; Unitarity and Analyticity were in. Personally, I so disliked that idea that when I got my first academic job I spent most of my time with my close friend, Yakir Aharonov, on the foundations of quantum mechanics and relativity. As mentioned in the preceding chapter, Susskind would go on to make important contributions to the earliest phase of string theory research, including the discovery that if you break open the black box that is the Veneziano amplitude, you find within it vibrating strings.

In his popular book The Cosmic Landscape Susskind compares this black box ideology to the behaviourst psychology of B. Skinner [50, pp. It was, of course, resolved to the satisfaction of many physicists in quantum chromodynamics [QCD] by a complex series of discoveries, culminating in a solid understanding of scaling and renormalization, dimensional regularization, non-Abelian gauge.

In this first part we describe this state of affairs, and introduce the mathematical and physical concepts, formalism, and terminology necessary in order to make sense of early and large portions of later string theory. This part might therefore also serve as a useful primer for those wishing to learn some string theory by providing some of the original physical intuitions and motivations. There were many more mesons lurking below the surface.

Unifying the profusion of mesons and baryons posed one of the most serious challenges of mid-twentieth century physics. For a good recent historical discussion, see [2] see also: [29, 44]. However, QCD, while an excellent description of the high-energy behaviour of hadrons, still cannot explain certain low energy features that the earliest dual models leading to string theory had at least some limited success with.

From Dual Models to M-Theory

The gluons are themselves coloured which implies that they self-interact. This results in a characteristic property of quarks, namely that they are confined within hadrons, unable to be observed in their singular form.

Why String Theory is Right

Accounting for this tube-like behaviour was considered to be an empirical success of the early string models of hadrons, as we see below. The challenge was further intensified as technological advances made possible proton accelerators8 and bubble chambers capable of registering events involving hadrons by photographing bubbles formed by charged particles as they dart through a superheated liquid, thereby superseding earlier cosmic rays observations.

This infects the natural observables in particle physics too. One of the observable quantities is the scattering cross-section which basically offers a measure of the scattering angle made by colliding beams, or a beam and a static target. This tells you the likelihood of a collision given that two particles are moving towards one another. The magnitude of the cross-section is directly proportional to this likelihood.

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The cross-section itself is a function of the energy of the incoming beams, and if one examines the behaviour of the cross-section as a function of this energy, one can find peaks such that one can ask whether they correspond to particles or not. By comparison, the Cosmotron at Brookhaven reached energies of just 3 GeV, though at the time of its first operation it was six times more powerful than other accelerators. For a good, technical review of these experiments see [31]. The quantum numbers of the particles can then be computed from the curvature of paths, thus enabling under the assumption of energy-momentum conservation the identification of various particle types.

They would simply not travel far enough to leave a track before decaying. Of course, bubble chambers cannot allow one to see such particles, but one can infer their existence by observing decay products via various channels see Figs. However, Chew [8, pp. Decay products are a negative kaon, a neutral kaon, and a positive pion. Image source CERN, The search for patterns in this jumble of data led to the discovery of a new symmetry principle and a deeper quark structure underlying the dynamics of hadrons.

This work can be viewed in terms of a drive to systematise. As we will see below, it was consideration of hard scattering processes that led to quantum field theory once again providing the framework in which to couch fundamental interactions. What such processes revealed was a hard, point-like interior structure of hadrons, much as the classic gold foil experiments of Rutherford had revealed a point-like atomic nucleus. Image source CERN annual report of , [3, p. If so, then the others might be constructed as bound states of some small number of elementary particles.

Of course, the quark model postulated a deeper layer of elements of which the new particles were really bound states. One of the crucial approximation methods employed in the construction of dual models that of infinitely many narrow hadronic resonances was developed in the context of current algebra. One of the most hotly pursued approaches, S-matrix theory, involved focusing squarely on just those properties of the scattering process—or more precisely of the probability amplitude for such a scattering event—that had to be obeyed by a physically reasonable relativistic quantum field theory.

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The combination of these general principles with minimal empirical evidence drawn from observations of hadrons was believed to offer a way of eventually getting a predictive physics of strong interactions. Heisenberg actually named the object that achieves this condensation and imbued it with far more significance than Wheeler ever did. This might, as in the case of quantum electrodynamics [QED] be provided by a quantum field theory, which delivers up an S-matrix as an infinite expansion in the coupling constant as we saw, in the case of QED this e2 In it he argues that the S-matrix methodology, of employing general mathematical principles to constrain the physics at least, of the strong interaction , was perfectly viable and bore much fruit, despite the confirmation of QCD that knocked S-matrix theory off its pedestal.

I agree with this general sentiment, and string theory can be found amongst such fruit. In this case what is ignored as unphysical or meaningless since unobservable, since too short-lived are the unmeasurable processes occurring between initial and final states of a collision process. In effect one draws a black box around the innards of the process and focuses on the particles entering and leaving the box and the probabilities of their doing so. The S-matrix catalogues these possible relations between inputs and outputs along with their various probabilities.

Measurable quantities such as scattering crosssections can be written in terms of the matrix elements of the unitary S-matrix operator S. Once scattering matrix elements have been fixed, then all cross-sections and observables have thereby been determined. The rough chronology that follows is that renormalisation techniques are developed, leading to quantum electrodynamics with its phenomenal precision , leading to the demise of S-matrix theory.

It was the subsequent fall from grace of quantum field theory at the hands of mesons that led to the resurrection of S-matrix theory, as we will see see Fig. Chen Ning Yang and Robert Mills had argued otherwise, of course, in order to preserve gauge invariance now generalised to non-Abelian cases , but this view famously discredited by Pauli had to wait for an understanding of confinement and the concept of asymptotic freedom to emerge.

As in many episodes in the history of physics, what was essentially a mathematical result, here from complex analysis, led in to a breakthrough in physical theory. Analytic continuation allows one to extend the domain of definition of a complex function. A complex function is said to be analytic or holomorphic, in mathematical terms if it is differentiable at every point in some region. This allowed the properties of the S-matrix to be probed almost independently of field theoretical notions in a quasi-axiomatic fashion with very little by way of direct experimental input.

The spatial dispersion of light into different colours occurs because the different wavelengths possess different effective velocities when traveling through the prism. A good guide to dispersion relations is [41]. It was Murray Gell-Mann at the Rochester conference [23] who had initially suggested that dispersion relations might be useful in computing observables for the case of strong interaction physics.

In simple terms, the idea is to utilise S-matrix dispersion relations to tie up experimental facts about hadron scattering with information about the behaviour of the resonances independently of any underlying field theory. More technically, this would be achieved by expressing an analytic S-matrix in terms of its singularities, using Cauchy-Riemann equations. Chew developed this initially in collaboration with Goldgerber, Low, and Nambu: [4] into the general idea that strong forces correspond to singularities of an analytic S-matrix.

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A Brief History of String Theory | Not Even Wrong

This idea of crossing also harks back to Murray Gell-Mann, this time to a paper coauthored with Marvin Goldberger [22]. Of course, if analyticity is satisfied, then the operation of analytic continuation can amplify knowledge of the function in. Of course, this also implies that energy, momentum, and angular momentum are conserved. This formal condition is the mathematical counterpart of causality i. This condition has its origins in the dispersion relations of classical optics—see footnote Or, in other words, probability that is, the squared modulus of the amplitude must be conserved over time.

This also includes the condition of coherent superposition for reaction amplitudes. As indicated above, one of the central objects of the physics of elementary particle physics is the scattering or transition amplitude A. This is a function that churns out probabilities for the outcomes of collision experiments performed on pairs of particles21 —note, this is not the same as the matrix of such described above.

It takes properties of the particles as its argument. There might be many such possible routes, in which case one has a multichannel collision process, otherwise one has a single channel process. Such channels are indexed by the kinds of particles they involve and their relative properties. In scattering theory one is interested in inter-channel transitions; i.