Theories [The Physics Travel Guide]

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--- theories [2018/05/07 06:59]
jakobadmin [Overview]
+++ theories [2020/04/09 20:35] (current)
68.142.63.195 [Overview] Removed sexist material
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 | | ,| -| AA |-|.|AA=[[theories:speculative_theories:quantum_gravity|Quantum Gravity]]
 | |!@4| | | ||| !@4 | |
-| BB | |||  CC |  | |BB=[[theories:quantum_field_theory|Quantum Field Theory]]|CC=[[theories:general_relativity|General Relativity]]
+| BB | |||  CC |  | |BB=[[theories:quantum_field_theory|Quantum Field Theory]]|CC=[[models:general_relativity|General Relativity]]
 | |!@4| | | ||| !@4 | |
-| DD| |||  EE |  | |DD=[[theories:quantum_mechanics|Quantum Mechanics]]|EE=[[theories:special_relativity|Special Relativity]]
+| DD| |||  EE |  | |DD=[[theories:quantum_mechanics|Quantum Mechanics]]|EE=[[models:special_relativity|Special Relativity]]
 |  || | | ||| !@4 | |
 | | || |||  FF |  | |FF=[[theories:classical_mechanics|Classical Mechanics]]
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 The crucial difference between classical and quantum mechanics is that the algebra for observables is non-commutative, as encoded in [[advanced_notions:uncertainty_principle|Heisenberg's uncertainty principle]]((In words the non-commutativity, it makes a tiny difference ($sim \hbar$) whether we first measure the momentum or the location of a particle)). Apart from this difference, we can again use everyday space, configuration space, phase space or Hilbert space((See the discussion at [[theories:quantum_mechanics|quantum mechanics]])). The question why we need to change our "naive" algebra to a non-commutative one is the what discussions about the [[https://physicstravelguide.com/theories/quantum_mechanics#tab__interpretations|interpretation of quantum mechanics are all about]]. The procedure where we start with a classical theory an construct the corresponding quantum theory is known as [[advanced_tools:quantization|quantization]].
-{{:paper.journal.6.png?nolink&400|}}
-Another instance where classical mechanics becomes invalid is when our objects move at speeds close to the speed of light $c$. In such systems, the correct theory is [[theories:special_relativity|special relativity]]. The difference between special relativity and classical mechanics is that we now use Minkowski space instead of our everyday Euclidean space. Again we can equivalently use the corresponding configuration space, phase space or a Hilbert space.  When the objects in our system move so slowly that we can treat effectively $c$ as infinity, we can use classical mechanics.
-Next, when we are dealing with tiny objects that move at speeds close to the speed of light, both, quantum mechanics and special relativity, fail. If we combine the lessons learned in quantum mechanics and special relativity properly we end up with [[theories:quantum_field_theory|quantum field theory]]. Here the fields obey a non-commutative algebra and it is conventional to describe quantum fields either in Hilbert space or configuration space((see the discussion at [[theories:quantum_field_theory|quantum field theory]])). The Hilbert or configuration space in //interacting// quantum field theory is more complicated since the particles described by quantum fields can have an internal structure and this internal structure becomes important when fields interact((Examples, for internal structure are [[advanced_tools:gauge_symmetry|gauge symmetry]] and [[basic_notions:spin|spin]]. For example, for spin $1/2$ particles the internal space is $\mathbb{C}^2$. For [[advanced_tools:group_theory:u1|$U(1)$]] gauge symmetry we get a copy of the unit circle $S^1$ (since $U(1)\simeq S^1$) above each spacetime point.)). Hence our physics not only happens in spacetime but also in internal spaces. The theory that deals with physics in internal space is known as [[theories:gauge_theory|gauge theory]]. The appropriate geometrical tool to describe physics in spacetime and internal spaces at the same time are [[advanced_tools:fiber_bundles|fiber bundles]].
+Another instance where classical mechanics becomes invalid is when our objects move at speeds close to the speed of light $c$. In such systems, the correct theory is [[models:special_relativity|special relativity]]. The difference between special relativity and classical mechanics is that we now use Minkowski space instead of our everyday Euclidean space. Again we can equivalently use the corresponding configuration space, phase space or a Hilbert space.  When the objects in our system move so slowly that we can treat effectively $c$ as infinity, we can use classical mechanics.
-A third instance where classical mechanics fails is in systems where gravity is strong((For example, in the neighborhood of large stars or [[advanced_notions:black_hole|black holes]])). In such systems, the correct theory is Einstein's [[theories:general_relativity|general relativity]]. Here the Minkowski space of special relativity becomes replaced with a more general Lorentzian manifold. Hence spacetime only looks locally like Minkowksi space and is otherwise curved.
+{{:paper.journal.6.png?nolink&400 |}}
+Next, when we are dealing with tiny objects that move at speeds close to the speed of light, both, quantum mechanics and special relativity, fail. If we combine the lessons learned in quantum mechanics and special relativity properly we end up with [[theories:quantum_field_theory|quantum field theory]]. Here the fields obey a non-commutative algebra and it is conventional to describe quantum fields either in Hilbert space or configuration space((see the discussion at [[theories:quantum_field_theory|quantum field theory]])). The Hilbert or configuration space in //interacting// quantum field theory is more complicated since the particles described by quantum fields can have an internal structure and this internal structure becomes important when fields interact((Examples, for internal structure are [[advanced_tools:gauge_symmetry|gauge symmetry]] and [[basic_notions:spin|spin]]. For example, for spin $1/2$ particles the internal space is $\mathbb{C}^2$. For [[advanced_tools:group_theory:u1|$U(1)$]] gauge symmetry we get a copy of the unit circle $S^1$ (since $U(1)\simeq S^1$) above each spacetime point.)). Hence our physics not only happens in spacetime but also in internal spaces. The theory that deals with physics in internal space is known as [[models:gauge_theory|gauge theory]]. The appropriate geometrical tool to describe physics in spacetime and internal spaces at the same time are [[advanced_tools:fiber_bundles|fiber bundles]].
+A third instance where classical mechanics fails is in systems where gravity is strong((For example, in the neighborhood of large stars or [[advanced_notions:black_hole|black holes]])). In such systems, the correct theory is Einstein's [[models:general_relativity|general relativity]]. Here the Minkowski space of special relativity becomes replaced with a more general Lorentzian manifold. Hence spacetime only looks locally like Minkowksi space and is otherwise curved.
 So far, there is no theory that works for systems with strong gravity and tiny objects that move close to the speed of light. The //hypothetical// theory that combines the lessons of general relativity and quantum field theory is known as [[theories:speculative_theories:quantum_gravity|quantum gravity]].
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 [{{ :787px-modernphysicsfields.png?nolink |Image by GYassineMrabet published under a CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)], via Wikimedia Commons}}]
 <--
--->Physical theories as women#
-<blockquote>0. Newtonian gravity is your high-school girlfriend. As your first encounter with physics, she's amazing. You will never forget Newtonian gravity, even if you're not in touch very much anymore.
-. Electrodynamics is your college girlfriend. Pretty complex, you probably won't date long enough to really understand her.
-. Special relativity is the girl you meet at the dorm party while you're dating electrodynamics. You make out. It's not really cheating because it's not like you call her back. But you have a sneaking suspicion she knows electrodynamics and told her everything.
-. Quantum mechanics is the girl you meet at the poetry reading. Everyone thinks she's really interesting and people you don't know are obsessed about her. You go out. It turns out that she's pretty complicated and has some issues. Later, after you've broken up, you wonder if her aura of mystery is actually just confusion.
-. General relativity is your high-school girlfriend all grown up. Man, she is amazing. You sort of regret not keeping in touch. She hates quantum mechanics for obscure reasons.
-. Quantum field theory is from overseas, but she doesn't really have an accent. You fall deeply in love, but she treats you horribly. You are pretty sure she's fooling around with half of your friends, but you don't care. You know it will end badly.
-<cite>http://www.physics.mcgill.ca/~arobic/funny/physicalwomen.html</cite></blockquote>
-<--
 <tabbox Field Theories vs. Particle Theories>

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