Daily Archives: July 3, 2022

Quick Calculation 3.10

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A First Course in String Theory

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Equation (3.96) has content: if you move a particle along a closed loop in a static gravitational field, the net work that you do against the gravitational field is zero.

Prove the above statement.

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Eq. (3.96):

\displaystyle{\vec g = - \nabla V_g}

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By the gradient theorem (aka the fundamental theorem of calculus for line integrals):

\displaystyle{\int _{\gamma }\nabla \varphi (\mathbf {r} )\cdot \mathrm {d} \mathbf {r} =\varphi \left(\mathbf {q} \right)-\varphi \left(\mathbf {p} \right)}

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— Me@2022-07-03 04:27:19 PM

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2022.07.03 Sunday (c) All rights reserved by ACHK

Schrodinger’s cat, 3.4

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A macroscopic system (such as a cat) may evolve over time into a superposition of classically distinct quantum states (such as “alive” and “dead”).

— Wikipedia on Quantum superposition

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The components of a superposition must be indistinguishable states.

A superposition is neither an AND state nor an OR state.

AND or OR are only possible for more than one state.

AND or OR are only possible for at least 2 (distinguishable) states.

The cat is not in a superposition state of “alive” and “dead”.

Instead, it is in a mixed state of “alive” and “dead”.

A mixed state is an OR state (of at least 2 distinguishable states).

— Me@2022-07-03 11:02:24 AM

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2022.07.03 Sunday (c) All rights reserved by ACHK