how in the world do FRB's "release enough energy to power the world for three centuries." If we don't know how and when they are happening, how can we measure their energy? Can someone explain?
We measure the energy of signals received at our radio telescopes - our units are Janskys, which correspond to 10^-26 watts per square metre per hertz of bandwidth, and we can calibrate our telescopes using noise diodes or known sources in the sky.
So for FRBs, we get the received brightness, and if we can measure the distance, we can use the basic inverse square scaling to estimate how much energy it had at the source. (Why inverse square? Because the area of a sphere is 4 pi R^2 - if you go twice as far away, the signal is spread out over 4 times the area, and so on.)
The key problem is a distance estimate for the FRBs - we have a pretty precise measurement for FRB 121102 because we identified its host galaxy and measured the redshift to that galaxy, so we know how far away it is. That's now been done for 2 other sources. For the rest, we can use the pulse dispersion, which measures the integrated column density of electrons along the line of sight, along with models for our galaxy and the intergalactic medium, to get some idea. It's not as good, but better than nothing.
This assumes a spherical signal propagation. But signals from antennas, and even from many natural emitters, aren't spherical. It's also possible that the signal is highly directional, like a jet. So, I'm pretty skeptical of these power estimates. For sure the transmitter has a lot of power, but how much exactly? I don't think we can really tell.
Sure, that's an excellent point. In case you read late replies: we recognize this, and parameterize the burst energy [1] by a beaming scale factor, \Delta\Omega/4\pi. (It still drops off as the inverse square, though, as long as you're not in the near field.)
The problem is, while you can reduce the energy requirement by making the beams narrow, that increases the total number of sources by the same factor. When we say that there are between 5000-10,000 FRBs all over the sky every single day, we are referring to FRBs beamed towards us. If you apply a 10% beam, your energy requirement drops by 10x, sure, but the source count goes up by 10x.
Right now, we don't have a large enough plausible progenitor population, even at 1x, for these FRBs. It's a really fun problem.
Our sun for example is emitting enough energy in all directions to power the world for 300 years (over the course of 300 years), and most of it misses us.
Our sun isn't particularly impressive in terms of energy and such compared to other astro-objects, so I feel like these kinda of events releasing so much energy are to be expected.
"Our sun for example is emitting enough energy in all directions to power the world for 300 years (over the course of 300 years), and most of it misses us"
I think you're saying any amount of energy can be produced by any amount of power, if the amount of time is unspecified. Which is true, but not substantive.
