Editing 2904: Physics vs. Magic
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| − | + | This is a comic about the differences between magic and physics. [[Miss Lenhart]], a school teacher, says that {{w|physics}} is applying forces to objects continuously over time, while magic tells you the outcome, but not how it'll get there. She gives an example of a magical curse that causes the recipient to slay their brother by midnight (or possibly noon); it's not science because it doesn't say what will cause them to take this action. She then states that the {{w|laws of thermodynamics}} and other laws are also magic, with {{w|Lagrangian (physics)|Lagrangians}} being deep magic. | |
| − | This comic | ||
| − | The | + | The joke is that these basic physical laws have been discovered empirically, but we don't know ''why'' they're true. So by the logic in the second panel, they're essentially like magic, since they specify a result without explaining how we get there. It may be possible to derive some of them from the others, but eventually we hit bottom and we have to say "because it just is", and that's like magic. |
| − | The second panel | + | The second panel alludes to Newtonian mechanics, which is formalized mathematically as an initial value problem; that is to say, the initial conditions of a system are known, and the rules relating the current condition of a system to the evolution of that system over time are specified. As humans, we are used to thinking of the present being a known state and the immediate future depending only on the present, so the Newtonian formalism makes intuitive sense as a picture of the world. The last panel contrasts this humorously with a series of physics ideas which violate this basic assumption in increasingly unsettling ways. |
| − | + | Thermodynamics, in particular equilibrium thermodynamics, the most studied branch and that most familiar to physics students, frames its questions in terms of the most likely state for a system to evolve to eventually. In this sense, the predictions of thermodynamics do not depend on the present state of the system, and do not help predict its intermediate behaviour. They only predict what the state of the system will be after a long enough time has elapsed for the system to have stopped evolving; in other words, to have reached equilibrium. Looked at in this way, thermodynamics seems to violate the principle outlined in the first panel; however, most people will be intuitively comfortable with the idea that one can ask sensible questions about long term stability without considering the details of how the system gets there. | |
| − | {{w|Conservation law}}s | + | {{w|Conservation law}}s arise naturally from Newtonian physics, but it is not necessarily clear intuitively how. Low level explanations tend to take the form of an understandable but fairly un-illuminating derivation from calculus and elementary algebra, while at a more advanced level they are shown to relate to symmetries of a physical system in a way which is very general and powerful, but nonetheless extremely abstract and mysterious. Either way, the end result — a conservation law — is a statement about how a system will be for ever, regardless of its evolution. This also violates the principle stated in the first panel, and it violates it in a way which seems intuitively stranger than thermodynamics. Conservation laws also appear in particle physics, where such elementary properties as the charge, spin, and parity of a system don't change... with some exceptions, involving the {{w|Wu experiment|weak nuclear force}}. |
| − | Lagrangian mechanics | + | Lagrangian mechanics is a reformulation of classical physics. It is exactly equivalent to Newton's laws. However, while Newtonian Mechanics is formulated in terms of specific forces acting on an initial state, and allows one to predict the final state by evolving the system forwards in time, Lagrangian mechanics instead takes the initial and final states of a system as inputs, and gives a rule which states which trajectories between those states are physically allowed. This is apparently a direct contravention of the principle in the first panel. In fact, it much more closely resembles the definition of magic given; one of the most surprising and counter-intuitive facts in physics is that the intuitive Newtonian worldview is exactly mathematically equivalent to the magical-seeming Lagrangian and closely related Hamiltonian pictures.{{acn}} For this reason the comic refers to Lagrangians (the central tool of Lagrangian mechanics which serves as a description of the system dynamics) as 'Deep Magic', as it is really the ultimate expression of the 'magical' side of physics. |
| − | + | {{w|Teleology}} is a branch of causality often associated with religion or magical thinking, that argues from the end result, instead of the cause of things. | |
| + | In this sense, the comic may also be alluding to disputes about possible teleological aspects of the {{w|stationary-action principle}}, that can be used to derive Newtonian, Lagrangian and Hamiltonian equations of motion, and even general relativity, as well as classical electrodynamics and quantum field theory. | ||
| + | For simple classical systems it can usually be stated as follows:"Given that the particle begins at position x1 at time t1 and ends at position x2 at time t2, the physical trajectory that connects these two endpoints is an extremum of the action integral." The Wikipedia article goes on to state: "By specifying some but not all aspects of both the initial and final conditions (the positions but not the velocities) we are making some inferences about the initial conditions from the final conditions, and it is this 'backward' inference that can be seen as a teleological explanation." | ||
| + | However, since the principle can be used to derive both integral laws (that appear to be arguing from the result) and the usual differential laws (that appear to be arguing from the cause), one can argue that these seemingly contradictory forms of causality are in fact not contradicting each other, since they are mathematically equivalent. | ||
| − | The title text | + | The title text seems to be mixing the diagram shown on the whiteboard with the curse of the comic. The first prediction is (according to Miss Lenhart) a physics prediction about a nonmagical {{w|trebuchet}}, whereas the second prediction would be something from deep magic. |
==Transcript== | ==Transcript== | ||
