1,039 reputation
127
bio website
location
age
visits member for 1 year, 8 months
seen 16 hours ago

2d
comment Why does Pluto's orbit cross Neptune's orbit?
The solar system is not stable, as it demonstrates chaotic behaviour on time-scale of order of ten million years, as indicated by numerical simulations. In particular, the probability of collision is ~1% before the Sun dies. See this for details.
2d
comment Is it possible that black holes are also neutron stars, but so dark that we cannot see them?
@RobJeffries Yes, sorry. I wrote that the Schwarzschild radius is of order 1 km, meaning that in general it is smaller than the radius of a neutron star, which is one order higher. I was giving rough estimates, because the equation of state is not known and exact values may change in the future. The range you give is realistic.
Jul
29
comment Is it possible that black holes are also neutron stars, but so dark that we cannot see them?
@RobJeffries According to p.12,15, of this, it is 7-11 km with the most conservative estimate being 9 km. This estimate hasn't changed much since Shapiro & Teukolsky was published.
Jul
25
comment Calculate loudness of sound: why am I getting contradictory answers?
Also, the temperature gradient in the vertical direction is known to affect the propagation of sound waves significantly.
Jul
22
comment Counting Problems in Physics
Non-trivial counting is often done in group theory.
Jul
21
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.
Jul
21
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.