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5 files changed, 83 insertions(+), 64 deletions(-)diff --git a/index.gmi b/index.gmi@@ -20,6 +20,7 @@ I don't have any gemlogs yet, check back soon! ## Updates -=> notes/physics.gmi 2021-03-24 - Notes > Physics > Born's rule -=> notes/physics.gmi 2021-03-19 - Notes > Physics > Representation Theory +=> notes/physics/dirac-equation.gmi 2021-04-25 - Notes > Physics > Dirac Equation +=> notes/physics/index.gmi 2021-03-24 - Notes > Physics > Born's rule +=> notes/physics/index.gmi 2021-03-19 - Notes > Physics > Representation Theory => notes/index.gmi 2021-03-19 - Added dream journaldiff --git a/notes/index.gmi b/notes/index.gmi@@ -3,7 +3,7 @@ These are my notes. Here you will find things I have been thinking about recently. I plan on collecting all of my thoughts here. Perhaps they will end up as articles, who knows. -=> physics.gmi Physics +=> physics/index.gmi Physics => gemini-notes.gmi Gemini Note Taking ## Dream Journaldiff --git a/notes/physics.gmi b/notes/physics.gmi@@ -1,61 +0,0 @@ - -# Physics - -## Born's Rule - -=> https://www.quantamagazine.org/the-born-rule-has-been-derived-from-simple-physical-principles-20190213/ Quanta article on Born's rule - -> The problem is that Born’s rule was not really more than a smart guess — there was no fundamental reason that led Born to propose it. “It was an intuition without a precise justification,” said Adán Cabello, a quantum theorist at the University of Seville in Spain. “But it worked.” And yet for the past 90 years and more, no one has been able to explain why. - -> Born’s probability postulate is where the puzzle really is. [..] If we could understand where the Born rule comes from, we might finally understand what the vexed concept of measurement really means in quantum theory. - -## Representation Theory - -=> https://scholar.harvard.edu/files/noahmiller/files/representation-theory-quantum.pdf Representation Theory and Quantum Mechanics - -> Representation theory is important in physics for a billion reasons, but here is one: Hilbert spaces are complex vector spaces, so any group action on a Hilbert space will necessarily be a group representation. Therefore, if we want to understand how groups can act on quantum mechanical state spaces, we must understand representation theory. This shouldn’t be very surprising. Quantum mechanics is really just glorified linear algebra, and representation theory is all about using linear algebra to study groups. - -### Moment maps? - -First time I've heard of "moment maps": - -> The topic with the least explicit foreshadowing is the relationship between Hamiltonian mechanics, the moment map, and quantization, which is the last topic of these notes. The story of the moment map is perhaps my favorite one here, if only because it is poorly explained everywhere else. The moment map gives a much richer connection between symmetries and conserved quantities than Noether’s theorem, and should be better known by physics students. - -## Future of Matter - -=> https://futureofmatter.com/ Michael Nielsen's Future of Matter - -This site has a lot of interesting articles on the future of matter. What possible phases of matter that don't exist naturally could we create? How does anyonic quasiparticle matter behave? - -=> https://en.wikipedia.org/wiki/Anyon Anyons -=> https://en.wikipedia.org/wiki/Quasiparticle Quasiparticle - -### Topological Order - -Creating new phases of matter via long distant entanglement. Can potentially lead to robust quantum error-correcting computers if the anyon model is physically realizable. - -=> https://en.wikipedia.org/wiki/Topological_order Topological Order -=> https://en.wikipedia.org/wiki/Topological_quantum_computer Topological Quantum Computer - -## Quantum Information - -Really enjoyed Mermin's book on Quantum Computer Science. Still need to read Nielsens book as well. - -## Inertia - -Interesting quote by Feynman: - -> But the motion to keep the planet going in a straight line has no known reason. The reason why things coast for ever has never been found out. The law of inertia has no known origin. - -=> https://ca1lib.org/book/2284985/0d164e The Character of Physical Law @ z-library - -### Quantized Inertia - -A modified-newtonian-dynamics-like (MOND) theory (Modified Inertia from a Hubble-scale Casimir effect). Kind of far out but proposes an explanation of inertia via Unruh radiation. - -* Explains galaxy rotation without the need for dark matter -* Implies GR might be wrong in some subtle way -* Predicts very small but non-zero photon mass -* Has many testable predictions including electric rockets - -Unlikely to pan out but would be really cool if it doesdiff --git a/notes/physics/dirac-equation.gmi b/notes/physics/dirac-equation.gmi@@ -0,0 +1,16 @@ + +# Dirac Equation + +=> https://motls.blogspot.com/2010/12/beauty-of-dirac-equation-and-its.html Interesting notes from this post by Lubos Motl + +> However, the Dirac equation leads to many conclusions and extensions that will are going to discuss in some detail: + +* need to second-quantize the Dirac field; antiparticles; quantum field theory; +* non-Abelian charges of the fermionic particle; QCD +* mass term coming from the Higgs mechanism instead of an explicit number +* Weyl fermions; higher-dimensional generalizations; general understanding of spinors and other representations of Lie groups in maths +* supersymmetric extensions +* similar equations with a higher spin, e.g. the spin-3/2 equation for gravitinos +* superstring theory as the final extension of the Dirac equation + +> If you think rationally about the beauty of the Dirac equation, and you're not constrained by taboos - e.g. a ban on the question where the beauty comes from you will figure out that the beauty really boils down to the properties of spinor representations of the Lorentz group. Once you know that, you want to know all kinds of similar "beauties". In other words, you should comprehensively learn and analyze the theory of representations of Lie groups and Lie algebras.diff --git a/notes/physics/index.gmi b/notes/physics/index.gmi@@ -0,0 +1,63 @@ + +# Physics + +=> ./dirac-equation.gmi Dirac Equation + +## Born's Rule + +=> https://www.quantamagazine.org/the-born-rule-has-been-derived-from-simple-physical-principles-20190213/ Quanta article on Born's rule + +> The problem is that Born’s rule was not really more than a smart guess — there was no fundamental reason that led Born to propose it. “It was an intuition without a precise justification,” said Adán Cabello, a quantum theorist at the University of Seville in Spain. “But it worked.” And yet for the past 90 years and more, no one has been able to explain why. + +> Born’s probability postulate is where the puzzle really is. [..] If we could understand where the Born rule comes from, we might finally understand what the vexed concept of measurement really means in quantum theory. + +## Representation Theory + +=> https://scholar.harvard.edu/files/noahmiller/files/representation-theory-quantum.pdf Representation Theory and Quantum Mechanics + +> Representation theory is important in physics for a billion reasons, but here is one: Hilbert spaces are complex vector spaces, so any group action on a Hilbert space will necessarily be a group representation. Therefore, if we want to understand how groups can act on quantum mechanical state spaces, we must understand representation theory. This shouldn’t be very surprising. Quantum mechanics is really just glorified linear algebra, and representation theory is all about using linear algebra to study groups. + +### Moment maps? + +First time I've heard of "moment maps": + +> The topic with the least explicit foreshadowing is the relationship between Hamiltonian mechanics, the moment map, and quantization, which is the last topic of these notes. The story of the moment map is perhaps my favorite one here, if only because it is poorly explained everywhere else. The moment map gives a much richer connection between symmetries and conserved quantities than Noether’s theorem, and should be better known by physics students. + +## Future of Matter + +=> https://futureofmatter.com/ Michael Nielsen's Future of Matter + +This site has a lot of interesting articles on the future of matter. What possible phases of matter that don't exist naturally could we create? How does anyonic quasiparticle matter behave? + +=> https://en.wikipedia.org/wiki/Anyon Anyons +=> https://en.wikipedia.org/wiki/Quasiparticle Quasiparticle + +### Topological Order + +Creating new phases of matter via long distant entanglement. Can potentially lead to robust quantum error-correcting computers if the anyon model is physically realizable. + +=> https://en.wikipedia.org/wiki/Topological_order Topological Order +=> https://en.wikipedia.org/wiki/Topological_quantum_computer Topological Quantum Computer + +## Quantum Information + +Really enjoyed Mermin's book on Quantum Computer Science. Still need to read Nielsens book as well. + +## Inertia + +Interesting quote by Feynman: + +> But the motion to keep the planet going in a straight line has no known reason. The reason why things coast for ever has never been found out. The law of inertia has no known origin. + +=> https://ca1lib.org/book/2284985/0d164e The Character of Physical Law @ z-library + +### Quantized Inertia + +A modified-newtonian-dynamics-like (MOND) theory (Modified Inertia from a Hubble-scale Casimir effect). Kind of far out but proposes an explanation of inertia via Unruh radiation. + +* Explains galaxy rotation without the need for dark matter +* Implies GR might be wrong in some subtle way +* Predicts very small but non-zero photon mass +* Has many testable predictions including electric rockets + +Unlikely to pan out but would be really cool if it does