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Oct
23
comment If something is not moving in space, is it moving on the time axis at the speed of light?
Fair enough @Ben Crowell. I think I first heard this statement in Greene's The Elegant Universe. It's interesting that "light doesn't age" seems to be used more regularly than "objects at rest move through time at the speed of light," when in some sense they're on equal footing. Agree / disagree?
Oct
23
revised If something is not moving in space, is it moving on the time axis at the speed of light?
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Oct
22
awarded  Informed
Oct
22
answered If something is not moving in space, is it moving on the time axis at the speed of light?
Oct
16
revised What is the significance of clamping the center of the spring?
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Oct
16
answered What is the significance of clamping the center of the spring?
Oct
15
revised Normalization of a wavefunction that's superposition of two unknown energy eigenfunctions
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Oct
15
answered Normalization of a wavefunction that's superposition of two unknown energy eigenfunctions
Oct
13
revised The Delta-Function Potential
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Oct
13
answered The Delta-Function Potential
Oct
11
answered Potential due to a continuous charge distribution on ring
Oct
10
comment Frequency of Oscillations about Circular Orbit
The Taylor expansion of $U_{eff}\left(r\right)$ is $U_{eff}\left(r_*\right) + k_{eff} \left(r - r_*\right)^2 / 2 + O\left(r^3\right)$ (since $dU_{eff}/dr$ at $r_*$ is $0$), where $k_{eff} = d^2U_{eff}/dr^2$ evaluated at $r=r_*$ is an effective spring constant. If that's not clear, note that $F_{eff}\left(r\right) = -dU_{eff}/dr = - k_{eff} \left(r-r_*\right) + O\left(r^2\right)$. The angular frequency of small oscillations is then $\left(k_{eff}/m\right)^{1/2}$.
Oct
10
revised Frequency of Oscillations about Circular Orbit
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Oct
10
revised Frequency of Oscillations about Circular Orbit
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Oct
10
awarded  Critic
Oct
10
revised Frequency of Oscillations about Circular Orbit
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Oct
10
answered Frequency of Oscillations about Circular Orbit
Oct
10
revised Numerical error with simulation of electric charge in homogeneous magnetic field
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Oct
10
revised Numerical error with simulation of electric charge in homogeneous magnetic field
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Oct
9
revised Food calories vs gravitational potential energy
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