tag:blogger.com,1999:blog-19025291575744287302017-03-30T15:39:08.891+02:00cosmology question of the weekCQW is an educational resource for theoretical physics and astrophysics, field theory, relativity and cosmology. we post a new question every wednesday for students to get and for teachers to stay in shape.CQWnoreply@blogger.comBlogger234125tag:blogger.com,1999:blog-1902529157574428730.post-1183566395183210742017-03-29T00:00:00.000+02:002017-03-29T00:00:08.933+02:00measurement of the Planck-constantcould one use naturally occuring Planck-spectra for determining the Planck-constant? what would be a viable experiment and would the Sun or the CMB provide a better measurement?<br /><br />spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-22543164128416721182017-03-22T00:00:00.000+01:002017-03-22T00:00:05.245+01:0040, 20, 10imagine that one measures the 40 components of the Christoffel-symbol by observing geodesic motion: in what way are the 20 components of curvature fixed? and how does that determine the 10 components of the metric?<br /><br />spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-23795340213130493582017-03-15T00:00:00.000+01:002017-03-15T00:00:24.750+01:00intuition from the geodesic equationwhat would be your argument why the Christoffel-symbol $\Gamma^\rho_{\mu\nu}$ needs to be symmetric in the lower two indices $\mu$ and $\nu$?<br /><br />spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-20250841578443794112017-03-08T00:00:00.000+01:002017-03-08T00:00:10.935+01:00Lorentz force and accelerationplease explain why the 6 entries of the Maxwell field tensor $F_{\mu\nu}$ determine 4 components of 4-acceleration, and how it is possible to infer all 6 entries from experimenting with a charge.<br /><br />spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-25730033552527406512017-03-01T00:00:00.000+01:002017-03-01T00:00:11.147+01:00Christoffel-symbols and geodesic motionwhy does one need 40 entries of the Christoffel symbol to determine the 4 components of 4-acceleration? can one, from observation of geodesic motion, infer all 40 components?<br /><br />spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-40688137613332307062017-02-22T00:00:00.000+01:002017-02-22T00:00:29.414+01:00charge asymmetry, part 2if the charge of electrons was not the exact opposite of the charge of protons, the rings of Saturn would act as a current loop, resulting in a magnetic field. could you estimate the magnitude of the magnetic field (in terms of its dipole moment)?spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-73332100840699137052017-02-15T00:00:00.000+01:002017-02-15T00:00:09.236+01:00gravitational field of the hot suncould you estimate by how much the gravitational field of the sun is larger because of the high internal energy compared to simply the rest mass? can one write down a correction factor as a function of temperature $T$?<br /><br />spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-72923817033810958572017-02-08T00:00:00.000+01:002017-02-08T00:00:02.621+01:00spin-down of the Crab-pulsarthe Crab-pulsar is a rapidly spinning magnetic neutron star, which induces very large electric fields in the surrounding Crab-nebula, where the resulting electric currents are dissipated by Ohm losses. could you estimate the time-scale of this process and judge if it's a viable model for explaining the spin-down?<br /><br />spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-65814400275539289682017-02-01T00:00:00.000+01:002017-02-01T00:00:18.081+01:00electromagnetic dualitycould you provide an argument (both for the equations of motion and the Lagrange-density) why in empty space electrodynamics is invariant under the replacement $\vec{E}\rightarrow\vec{B}$ and $\vec{B}\rightarrow -\vec{E}$?<br /><br />spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-5570595469324604252017-01-25T00:00:00.000+01:002017-01-25T00:00:01.069+01:00gravity and retardationthe field equation of general relativity is invariant under time-reversal (and parity inversion). in what way is retardation of the gravitational field generated by a matter distribution is preferred over advanced potentials?<br /><br />spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-13173733597821131742017-01-21T19:07:00.001+01:002017-01-21T19:07:09.294+01:00forces in relativityrelativistic forces are always velocity dependent but velocity dependent forces are not necessarily relativistic... is that true?<br /><br />this post is in celebration of $10^5$ views!<br /><br />CQWnoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-55209634933262075592017-01-18T00:00:00.000+01:002017-01-18T00:00:11.520+01:00very heavy and very lightcan you explain why the ratio between the Hubble mass (i.e. the mass inside the Hubble volume today for a critical universe) and the Planck mass is about $10^{60}$? why are stars roughly in the middle (on a logarithmic scale)? or even more puzzling: why's the ratio between Hubble and Planck-mass about equal to the ratio between stellar masses and the masses of nucleons?<br /><br />spirounoreply@blogger.com2tag:blogger.com,1999:blog-1902529157574428730.post-70319455695039085262017-01-11T00:00:00.000+01:002017-01-11T00:00:13.435+01:00forces on dust particlescan you compute the ratio between radiation pressure and gravity acting on a dust particle in the solar system? could one relate the two forces to the mass of the Sun and establish a minimal mass from which on there would be no dust and hence no planetary system?<br /><br />we wish all CQW-readers a successful year 2017 full of cosmological discoveries.spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-91573604502029271842017-01-04T00:00:00.000+01:002017-01-04T00:00:03.668+01:00funny way of writing Maxwell's equationscan you reformulate the Maxwell-equations in terms of the complex-valued field $\vec{X} = \vec{E}+\mathrm{i}\vec{B}$? would there be potentials $\Phi$ and $\vec{A}$ for $\vec{X}$, and can one even find a covariant formulation?<br /><br />CQWnoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-11983794070505792742016-12-21T00:00:00.000+01:002016-12-21T00:00:29.656+01:00comets and their tailswhy is the tail of a comet curved? and could you estimate how fast the curvature of the tail could change?<br /><br />with this very christmassy question we wish all followers of CQW a merry x-mas and a happy and successful year 2017. we hope to see you again in january.spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-84925212571146962142016-12-14T00:00:00.000+01:002016-12-14T00:00:20.639+01:00Poynting-flux and magnetic chargesin the derivation of the Poynting-theorem one needs to substitute a term $\vec{B}\mathrm{div}\vec{B}$, which is equal to zero due to the fact that the magnetic field is purely rotational, $\mathrm{div}\vec{B} = 0$. insisting to introduce magnetic charges by requiring $\mathrm{div}\vec{B} = 4\pi\rho_\mathrm{mag}$, would that lead to a violation of energy-momentum conservation? are there other arguments, e.g. from the covariance of electrodynamics, why this is not possible?<br /><br />spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-27567291032128169942016-12-07T00:00:00.000+01:002016-12-07T00:00:22.516+01:00electrodynamics with non-conserved chargesfollowing up on last week's question: could one construct a theory of electrodynamics with non-conserved charges, i.e. where $\partial^\mu\jmath_\mu\neq 0$? what consequences would that have?<br /><br />spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-17443329537782847632016-11-30T00:00:00.000+01:002016-11-30T00:00:12.477+01:00gravitational fields for non-conservative systemsEinstein's field equation links the Einstein-tensor $G_{\mu\nu}$ to the energy-momentum tensor $T_{\mu\nu}$, which is divergence-free, $\nabla^\mu T_{\mu\nu}=0$. energy-momentum conservation is usually established by considering fields whose Lagrange-density $\mathcal{L}$ does not have an explicit dependence on time or position, leading to the definition of $T_{\mu\nu}$ with the corresponding continuity. in what way would fields $\phi$ with $\mathcal{L}(\phi,\nabla^\mu\phi,x^\mu)$ source a gravitational field?<br /><br />spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-22993163792184926732016-11-23T00:00:00.000+01:002016-11-23T00:00:18.214+01:00dark staris it possible to construct a gravitationally bound ball of photons?<br /><br />spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-4737464423674587452016-11-16T00:00:00.000+01:002016-11-16T00:00:01.611+01:00dissipation time scalethere are many structures visible in Jupiter's atmosphere. can you estimate a dissipation time scale for the turbulent motion?<br /><br />spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-91098054325737226772016-11-09T00:00:00.000+01:002016-11-09T00:03:11.540+01:00motion or not?can you show that a cosmological fluid in a FLRW-universe it at rest in all freely falling frames, but shows recession motion?<br /><br />spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-39420150114823351552016-11-08T16:12:00.003+01:002016-11-08T16:12:34.973+01:00implications of a confirmed $\Lambda$this post is in celebration of $2^{16}$ views!<br /><br />imagine that future experiments have constrained the dark energy eos-parameters to be $w_0=-1$ and $w_a=0$ at high precision: would that imply that we have confirmed that the covariant divergence $\nabla^\mu g_{\mu\nu}$ of the metric $g_{\mu\nu}$ is zero, implying a metric connection, at least under the FLRW-symmetries?<br /><br />CQWnoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-47316787843088823792016-11-02T00:00:00.000+01:002016-11-02T00:00:23.292+01:00cosmology works?a freely-falling observer experiences the metric $g_{\mu\nu}$ of generated by any energy-momentum distribution $T_{\mu\nu}$ as being of Minkowskian shape $\eta_{\mu\nu}$. the observer would conclude that there is no curvature and consequently, no gravitational fields and that the energy-momentum is vanishing.<br /><br />but isn't that what we're doing in cosmology? as a freely-falling observer we aim to determine the energy-momentum of all cosmological fluids $T_{\mu\nu}$ expressed in terms of their density parameters $\Omega$ and their equations of state $w$. but how can one measure the energy-momentum-tensor of a gravitating matter distribution with a gravitational experiment?<br /><br />spirounoreply@blogger.com1tag:blogger.com,1999:blog-1902529157574428730.post-61920693642593198692016-10-26T00:00:00.000+02:002016-10-26T00:00:03.488+02:00spherical gravitational waveis it possible to have a spherically symmetric gravitational wave around an object?spirounoreply@blogger.com0tag:blogger.com,1999:blog-1902529157574428730.post-89709935040920248282016-10-19T00:00:00.000+02:002016-10-19T18:10:57.922+02:00electricity and gravitywhy is there a cosmological constant (even) in the classical Poisson-equation, $\Delta\Phi = 4\pi G\rho + \lambda$, but no such term in the wave-equation of electrodynamics, $\Box A^\mu = 4\pi\jmath^\mu$?<br /><br />spirounoreply@blogger.com0