can you show that the integral $\int\mathrm{d}^nx\:C(r)$ of the correlation function $C(r)$ as a function of distance $r$, $r^2=\sum_{i=1}^n x_i^2$, of a random field in $n$ dimensions vanishes?

# cosmology question of the week

CQW 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.

## Wednesday, February 3, 2016

## Wednesday, January 27, 2016

### Lorentz boosted resistor

last post in the series "relativistically moving electric circuits": a resistor heats up due to an electric current moving through. but could you boost into a frame in which the electrons are at rest, in which case there would be no heat generation? how would you reconcile the two observations with Lorentz-transforms?

## Wednesday, January 20, 2016

### Lorentz boosted capactitor

imagine to observe a charged capacitor from a moving frame of reference. can you explain inituitively how the electric field is Lorentz-transformed?

## Wednesday, January 13, 2016

### Lorentz boosted coil

can you explain how the magnetic field of a moving coil would be transformed into an electric field if the coil is in motion relative to an observer?

## Wednesday, January 6, 2016

### redshift drift

welcome back to CQW in 2016 with a question about redshifting:

can you construct a cosmological model in which the redshift of distant objects stays constant? would that mean that the last-scattering surface of the CMB has a constant distance?

can you construct a cosmological model in which the redshift of distant objects stays constant? would that mean that the last-scattering surface of the CMB has a constant distance?

## Wednesday, December 23, 2015

### Hubble-collapse

can you show that the density inside a sphere which contracts according to a Hubble-law $\upsilon(r)\propto -r$ remains homogeneous? what's the relation between density $\rho$ and time $t$?

we wish all our readers and followers merry x-mas and a happy and successful year 2016. we hope to see you again in january.

we wish all our readers and followers merry x-mas and a happy and successful year 2016. we hope to see you again in january.

## Wednesday, December 16, 2015

### Schwarzschild radius of electrons

if electrons are truly pointlike particles, would it be a problem for the field lines emanating from the charge to cross the Schwarzschild radius?

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