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2d
comment Counting Problems in Physics
Non-trivial counting is often done in group theory.
2d
comment Show that getting parallel transported does not change angle between them- Tensors
If you use google, there are lots of lecture notes on GR, but they require understanding of calculus, linear algebra, mechanics, differential geometry, differential equations etc.
2d
comment Show that getting parallel transported does not change angle between them- Tensors
I'm using $\nabla_a$ instead of ${}_{;a}$ and $s$ is the affine parameter of $X^a$.
Jul
17
comment How to understand “accelerating charge radiate” using intuition?
There is an intuitive way to understand this as Compton scattering: a flux of photons is scattered by an electron, hence the electron is accelerated and the radiation comprises the scattered photons.
Jul
15
comment Are there any hamiltonian systems without a periodic orbit?
A free particle does not have periodic orbit.
Jul
15
comment Why doesn't matter pass right through other matter if atoms are 99.999% empty space?
Also of relevance here is the cross-section for the scattering, which indicates that in most cases the effective size of the particle for the interaction is not related to the physical size, if one calculates it classically as the OP suggests.
Jul
12
comment A rigorous treatment of distributions in quantum mechanics
Messiah's book covers the formalism with rigour, but is a bit old and verbose.
Jul
12
comment Is the apparent lack of (Ricci) curvature in the Schwarzschild metric due to a choice of coordinates?
There are many ways to measure curvature (and more than one type of curvature). The Ricci scalar is one of them, but the Riemann tensor is the one we use to say whether a spacetime is curved or not, and it is nonzero for the Schwarzschild metric, therefore it is curved.
Jul
12
comment Temperature of Bose-Einstein-Condensate in space
The temperature in space in vacuum in absence of radiation etc is $2.7 \text{K}$ due to the CMB, while on Earth it is $300 \text{K}$ on average. This makes it easier to reach lower temperatures in space, but I cannot argue about specifics in this case.
Jun
30
comment Why isn't water running faster hotter?
Temperature depends only on the random motion of the molecules, not on their coordinated motion, because the latter preserves the entropy of the system. This is not related to the relative speed of the molecules to first approximation, because if a high-speed current hits you, it won't affect the temperature of the surrounding molecules and the energy you'll absorb will only be kinetic energy, not thermal.
Jun
30
comment Relation between the determinants of metric tensors
About the last equation: shouldn't it be $4! \tilde{\epsilon} = -3! \tilde{n}\wedge {}^3\tilde{\epsilon}$ by the definition of the wedge product?
Jun
28
comment Duality in arbitrary finite dimension using the Levi-Civita tensor
The relation between the double dual of a $p$-form and the $p$-form in dimension $n$ is given by $\star\star \alpha = (-1)^{s+ p(n-p)} \alpha$, where $s$ is the number of minus signs in the signature of the metric and $\star$ denotes the Hodge dual. This is easy to prove by doing the permutations over the indices. Note that the Hodge dual acts only on forms, namely totally anti-symmetric covariant tensors.
Jun
26
comment Why is radiation for an ultrarelativistic charge zero on axis?
This is related to relativistic beaming, namely that in the frame of the relativistic particle the environment is observed as if a ray at $\theta=\pi/2$ turns into one at $\theta' \approx 1/\gamma$. Also, the direction of radiation is near parallel to the velocity of the charge.
Jun
26
comment Why isn't invariant notation common?
@innisfree The physical theory is developed in terms of invariants and the experiments require measurements, hence the introduction of coordinate systems. I'm not certain what your questions are.
Jun
25
comment Metric expansion of space and Newton's second law
Cosmological expansion is of the intergalactical distance; at smaller scale, various forces that lead to formation of structures preserve distances.
Jun
25
comment Why $e$ in the formula for air density?
Also, it can be thought of as the Boltzmann distribution in presence of gravitational field, in which case the exponential is related to the definition of entropy.
Jun
25
comment Killing vectors in flat FLRW metric
I believe I've found it: the Hölder inequality connects the minimum of the energy functional with that of the length functional, according to this, but this argument applies only for a riemannian manifold, not a lorentzian one.
Jun
25
comment Killing vectors in flat FLRW metric
Do you happen to know under which conditions we are allowed to use the lagrangian without the square root to derive the geodesics? I faintly recall an inequality that is related, but I haven't seen anywhere a rigorous proof about this.
Jun
24
comment Killing vectors in flat FLRW metric
You're allowed to set $\dot{x} = 0$, so why don't you do so? Everything else looks correct to me.
Jun
24
comment Why isn't invariant notation common?
Wald is a nice reference with this notation. I believe that it depends on the nature of the problem: 1. theoretical, more abstract problems require manipulation of invariants and introducing coordinates often leads to confusion, 2. measurements, on the other hand, require introduction of a coordinate system, which is often done as a final step after statement of the theory.