Presentation 7_6 8.56.41 AM (2)
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This document discusses monopole lensing and how it relates to Lorentz symmetry breaking. Monopole lensing is the phenomenon where the speed of light varies at different points in space due to a monopole, which is similar to gravitational lensing. The author sets up a mathematical model in Mathematica to study monopole lensing by modeling the monopole field profile and using Euler-Lagrange equations. Interestingly, the model results in an unexplained bump that persists even when trying to improve accuracy. Future work could look more into detecting monopoles and further investigating the cause and properties of the light bending bump.
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Presentation 7_6 8.56.41 AM (2)
- 1. Lorentz Symmetry Breaking: Monopole Lensing Ben Guan 07/06/2016
- 2. • What is Monopole?What is special about it? (size, shape…) • What is Monopole Lensing? • How does ML affect the path of light? • How is Monopole Lensing similar to Gravitational Lensing? • How does Monopole Lensing related to Lorentz Symmetry Breaking? • What is the mathematical model that we used? • What are some of the interesting findings? • What aspects are interesting to look at in the future? Introduction:
- 3. What is Monopole? • Tensor Field: Generalization of a scaler field or a vector field which assigns a scalar or vector to each point in space. (Ex: Electric & Magnetic Field) • Size: Not well determined (Very tiny) Electric Monopole? Magnetic Monopole?
- 4. What is Monopole Lensing? Fermat’s Principle (AKAThe Principle of Least time): light travels fromA to B, it will choose the path which will minimize the time Coupling Parameter: 𝜉 − Knob (Attractive: 𝜉 > 0, Repulsive: 𝜉 <0) This Phenomenon which Speed of light vary at different points in space is an example of Lorentz Symmetry Breaking (Pictures Illustrates Gravitational Lensing)
- 5. How Did I Set Up the Mathematical Model? 4 steps to set up the Model in Mathematica: 1. Polar Coordinate----dS 2. Interpolation of g(r) function 3. Euler-Lagrange Equation 4. Set Up the Numerical Integration Symbol Clarification • f2= Speed of light in tangential direction • 𝛽 − Impact Parameter • r − Distance from the light to the monopole 0 2 4 6 8 10 r 0.2 0.4 0.6 0.8 1.0 g r Monopole Field Profile Graph
- 6. Just like me, there is a interestingly looking bump here. • What cause the bump? • Three Hypothesis: Accuracy and Precision Goal Limit of Integration (infinity) The extension of the interpolation function • Solutions: Increase Accuracy, U-sub, Extension of g(r) The bump seems to persist! • Where it occurs? • Bump Ratio = 𝛼𝑚𝑎𝑥 𝛼𝑖𝑛𝑓𝑖𝑛𝑖𝑡𝑦
- 7. Interesting Stuff to Look Into in the Future: How can we detect Monopole? (no experience so far) More interesting Monopoles (Vanilla, Pineapple, Chocolate Mint…) The trajectory of light bending And of course, the bump!
- 8. Thank you! Acknowledgement: Shout out to Kamuela Lau, Doc Brown and Professor Seifert for sharing their previous research accomplishments and providing guidance.
Editor's Notes
- we inputted different xei values and recorded where the maximum would occur and what the bump ratios (ratio of the maximum value and to asymptotic value) are