String Theory Essay

String Theory Matter–Energy Interface ISU Project

Michael Mohamed SPH4U0-C G. LeBreton June 1st, 2009

String Theory - Abstract SPH4U0-C ISU Project By Michael Mohamed This essay serves as an introduction into string theory. This is meant to be as non-mathematical and simplistic as possible for the reader. Some topics discussed in the essay include: general relativity, quantum mechanics, strings, multiple dimensions, Calabi-Yau manifolds, duality, supersymmetry, branes, M-theory, black holes, and the spacetime continuum. Some of the concepts are only touched on briefly and described primarily in order to either explain their fundamental connection to string theory or demonstrate a string theory based approach to these topics.

1. Introduction: A New Kind of Physical Theory This section serves as an introduction and primer to the reader concerning the subject matter. It introduces the three main ideas described in the following paragraphs concerning general relativity and quantum mechanics, string theory and multiple dimensions, the various applications of string based theories and concluding with a prospective outlook on the future of physics research.

2. The Quantum Relativistic Mess A description is given to general relativity and quantum mechanics, both of which are used as standard theories in modern physics. An explanation is given as to why the two theories are mutually incompatible. The need for a new theory is emphasized, leading into the introduction of string theory.

3. Strings, Multiple Dimensions, and Supersymmetry This section introduces the concept of a string as the fundamental building block of all matter. This then leads into a description of multiple dimensions in the shape of a Calabi-Yau manifold. The concept of supersymmetry and duality in string theory is introduced. These concepts are then used to explain the resolution of the aforementioned problems in the current physical theories.

4. M-Theory: The Theory of Everything? This theory serves to delve deeper into cutting-edge physics research through the introduction of M-theory. M-theory is shown to have many wide reaching implications in physics theories in its ability to unify various problems in the current theory which may become sensible through the use of multidimensional branes. Some of these topics include: black holes, the big bang and flop transition wrapping.

5. Conclusion: The Future of Physics This section attempts to summarize all of the various concepts introduced and summarize them as simply as possible. Some speculation is given on possible physical developments in the future and problems in physics that may be resolved through their utilization.

String Theory Essay Assignment SPH4U0-C ISU Project By Michael Mohamed 1. Introduction: A New Kind of Physical Theory Throughout the history of science various paradigm shifts have taken place which have radically altered both the scientific tools with which mankind has to observe and predict the world it lives in. The theory of gravity was changed radically from the former Newtonian model in the early 1900s by the work of Albert Einstein in his theory of general relativity. At this time there were huge breakthroughs in the field of quantum mechanics by scientists such as Niels Bohr, Werner Heisenberg, Erwin Schrödinger and Richard Feynman among countless others [8]. What was once considered the standard model was found inadequate over time and scientists struggled to rethink their current understanding of the universe in the search for a theory that might unite all physical phenomena together. In modern times, this goal has still gone unmet. However, theoretical scientific research has lead to the development of a new theory that could overtake the current standard model; this essay will attempt to describe this new candidate referred to as String Theory. The basic concepts of String Theory will be described first of all through the current inadequacy of modern physical theories, following with the concept of strings, multiple dimensions and supersymmetry, and concluding with the description of M-theory and its critical applications in physics problems, some of which still remain unsolved today.

2. The Quantum Relativistic Mess The current standard model of physics has a fundamental flaw: it is actually two separate theories, the theory of General Relativity and the theory of Quantum Mechanics. Both theories provide accurate and sensible predictions when applied to their respective extremities; General Relativity works best when predicting the phenomena associated with gargantuan celestial bodies, whereas Quantum Mechanics works best when predicting the phenomena associated with extremely small bodies such as protons, electrons, quarks and photons [3][8]. While both theories are accurate when used correctly, any attempt to use both theories simultaneous in attempting to understand certain phenomena cause the theories to break down. This might result in physically impossible measurements such as zeros that should not occur as well as infinities that should not appear [5]. The theory of General Relativity utilizes the concept of a smooth and curved three dimensional surface on which all bodies of mass rest; gravity in then understood to come as a result of large masses bending space-time and causing smaller masses to fall toward or around them. One of the most important features of the relativity is the perfect smoothness the space-time continuum is described as having, which as is later shown, becomes the undoing of the theory itself. The theory of Quantum Mechanics states that for small particles such as electrons and photons, no deterministic predications can be made about any property of the particles action; the best approximation then is to utilize various

probabilities which can be predicted given information about various states of the particles [8]. This is due to the nature of such small particles which are turbulent and extremely varied in their action; as one attempts to zoom closer in to observe the actions of small particles, the more distorted and turbulent their movement begins to seem. Using the constants G, c, and a constant was found for the smallest observable length in which phenomena could be observed until the quantum fluctuations became completely unpredictable; the Planck Length [3]. A problem then arises in attempting to unify the two theories: because the space-time continuum is predicted to be infinitely smooth, it should be theoretically possible to continuous zoom into it while observing the continuum becoming smoother; however due to Quantum Mechanics, zooming in closer should eventually cause the distortion of quantum fluctuations to make itself more and more apparent over time [3]. These disturbances to the space-time continuum become most apparent at Planck length, and render it impossible to probe further without causing one theory to have to ignore the other. This doesn’t make sense in certain contexts such as a black hole and during the big bang where extremely heavy and small particles are involved, demanding the use of both theories. This fundamental problem may be solved within the framework of String Theory where both Quantum Mechanics and General Relativity may be united. 3. Strings, Supersymmetry and Multiple Dimensions String theory diverges entirely from former ideas in physics in that instead of working with point-like particles in four perceivable dimensions, it works with versatile strings comprised of energy in several unperceivable dimensions. Strings can comprise all of the particles, both force and mass based, in the known universe while still producing evidence of newer particles. The particles become similar to notes in a musical instrument, distinct due to their frequency and energy; strings vibrating at varying frequencies and amplitudes produce all of the building blocks of particles and matter that we understand today while introducing many of its own [3]. Strings can be closed or open and are typically as long as Planck length. String theory also introduces the concept of supersymmetry. Supersymmetry is the concept that every force particle has a matter superpartner that has ½ of the spin of the original particle; this can help to unify particles together and to show that quantum physics can be modelled without the augmentation from numerical adjustments [2]. Supersymmetry has also lead to the emergence of gravitons, massless particles of spin 2 which carry the gravitational force. This is useful as it can help to unify the four fundamental forces together; while the three quantum mechanical forces could be unified under electroweak theory, gravity had been excluded [3]. At increasingly shorter distances, the strength of the forces begin to converge into a single value; previous theoretical and experimental work showed that the forces nearly equal each other in strength at some distance, however the inclusion of supersymmetry into the model allows quantum fluctuations to be cancelled and the forces to eventually become equal. One detriment of supersymmetry is the doubling of all the particles that should be predicted due to the lack of any superpartner’s being discovered.

The concept of duality in string theory is essentially that a two different models applied to the same problem can create the same result and that two phenomena with different observations can both be true at the same time; this has been used to prove that Planck Length being the minimum observable distance [3]. Because strings are comprised of energy, the more energy they have the longer they can be, and via E = mc2 they will also be heavier. The energy of a string can be related to its winding number, the amount of times it can wrap around an object; energy is proportional to radius times the winding number. Similarly, energy is proportional to the vibrational number, a number describing the uniform motion of the string, multiplied by the inverse of the radius. The total energy of the string is the sum of these products. A pattern appears in string theory such that if the radius is inverted, the total energy remains the same. Because the two views of the radius are equally valid, two different distances can always be observed: the two distances are caused by either heavy-string modes or light-string modes (as mass relates to energy) [3]. This provides two views of the universe, one where it is much smaller than Planck length itself, and another where it is the size we observe; the distance observed always correlates to light-string modes. When Planck Length distances are to be probed (such as in observation of a black hole), the breakdown of quantum mechanics and general relativity instead becomes a shift whereby closer zooming (smaller distances) into a space becomes expanded (larger distances) due to the duality that arises from the energy equality of heavy and light-string modes. String theory incorporates a view of ten dimensions, the observable three spatial dimensions, the single time dimension, and six more spatial dimensions. These dimensions take the form of a Calabi-Yau manifold, a curled up six dimensional shape [3]. Similarly to how a piece of paper may not appear to have width when observed from far away, the six dimensional Calabi-Yau manifolds are essentially unnoticeable. A string has only one dimension, as the dimensions of the universe increase so do the dimensions which the string can vibrate through. One problem of quantum mechanics is the negative probabilities that arise in certain calculations. Using calculations incorporating multiple dimensions, these negative probabilities tend to vanish, vanishing completely with nine spatial dimensions. The dimensions of the universe tightly constrain the possible vibrations of strings; therefore the amount of dimensions can be related to the various properties of the particles that we can observe [9]. Why there are 9 spatial dimensions cannot be fully explained outside of mathematical expression. However, the various properties arising from string theory tend to be consistent with the observable universe and offer various tools that may unify general relativity and quantum mechanics. 4. M-Theory: The Theory of Everything? In the history of string theory research, there were at one point five slightly different theories, however all of these theories were eventually united under a new theory called M-theory. This theory extends the previous idea of one-dimensional strings into multidimensional membranes, or branes; an example of this might be a two-brane, which is essentially a string with an added dimension, forming a shape similar to an elastic band or a ribbon [1]. M-theory lead to the discovery that the multidimensional calculations previously performed are inaccurate; to fully eliminate all negative probabilities there must be ten spatial dimensions, forming eleven in total [3]. Similarly, the amount of brane types expands to ten, named one-branes (strings), two-branes, three-branes etc.

Branes are predicted to wrap around tears in space-time known as flop transitions which may occur, forming something similar to a very small black hole within a Calabi-Yau manifold in the process [10]. This tiny sub-Planck length black hole eventually disintegrates into a massless photon, providing a solid link between black holes and quantum mechanics [4]. Theoretically, a black hole can be constructed using only carefully manipulated branes; a theoretical black hole of this kind could have all its constituents measured as scientists would already know what comprises it. Using this black hole, the previously unexplainable relation between a black hole’s entropy (amount of disorder) and its area could be related to a theoretical black hole and explained entirely in terms of branes [3]. Because of M-theory’s many triumphs in terms of describing black holes while remaining consistent with other string theories, scientists believe that it may eventually become a “theory of everything” that can explain all the various components of the universe accurately, including the big bang itself. 5. Conclusion: The Future of Physics So far it’s been demonstrated that string theory is not only capable of describing the universe in the common ways people already, but is also in many ways capable of explaining some of the problems that have plagued physicists for decades. This has lead to excitement in the field of physics with researchers working on string theory itself, but also on the Large Hadron Collider which may provide string theory with some experimental backing [3]. String theory itself has been almost entirely theoretical using only approximated equations which cannot provide definite predictions, only relations. Some problems that still need to be addressed by string/M-theory: Can information re-emerge from a black hole’s evaporation? What occurred during the Big Bang earlier than we can predict? Why is the cosmic background radiation so uniform throughout the universe? Why do only three of the spatial dimensions appear so large? Are there other universes with entirely different physics behind them that can still be modelled with string theory? Overall, the future of physics has much discovery ahead of it; if string theory is further developed into the next standard model of physics, it will be only one more paradigm shift bringing mankind closer to a complete understanding of the universe.

String Theory Bibliography and References SPH4U0-C ISU Project By Michael Mohamed 1. Sati, H. (November, 2008). A higher twist in string theory. Journal of Geometry and Physics, j.geomphys.2008.11.009. Retrieved May 5th, 2009 from Sheridan College’s www.sciencedirect.com database. 2. Friedan, D., Martinec, E., Shenker, S. (1986). Conformal invariance, supersymmetry and string theory. Nuclear Physics B, Issue 271, 0550-3213(86)90356-1. Retrieved May 3rd, 2009 from Google Scholar’s indexed journal search. 3. Green, B. (1999, 2003). The elegant universe. (2nd ed). New York (NY): Vintage Books. 4. Horowitz, G. T., Welch, D. L. (February, 1993). Exact three dimensional black holes in string theory. Physical Review Letters, hep-th/9707188, NFS-ITP-93-21. Retrieved May 4th, 2009 from Cornell University Library’s www.arXiv.org database. 5. Sorkin, R. D. (February, 1993). Impossible measurements on quantum fields. In National Science Foundation, Directions in General Relativity (pp. 293-305). ISBN 0521452678. Cambridge: Cambridge University Press. 6. Natsuume, M. (June, 1993). Natural generalization of bosonic string amplitudes. ArXiv preprint, hep-th/9302131. Retrieved May 4th, 2009 from Cornell University Library’s www.arXiv.org database. 7. Calcagni, G., Nardelli, G. (September, 2008). Nonlocal instantons and solitons in string models. Physics Letters B, j.physletb.2008.09.016. Retrieved May 5th, 2009 from Sheridan College’s www.sciencedirect.com database. 8. Feynman, R. (1985, 2006). Quantum Electrodynamics (QED). (3rd edition). Princeton (NJ): Princeton University Press. 9. Witten, E. (March, 1995). String theory dynamics in various dimensions. Nuclear Physics SectionB, hepth-9503124, IASSNS-HEP-95-18. Retrieved May 4th, 2009 from www.citebase.org database. 10. Beccaria, M., Forini, V., Tirziu, A., Tseytlin, A. A. (December, 2008). Structure of large spin expansion of anomalous dimensions at strong coupling. Nuclear Physics B, j.nuclphysb.2008.12.013. Retrieved May 5th, 2009 from www.sciencedirect.org database.