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Is it possible to something as problematic as that and with what tech it is possible?

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Update (15 Febrary 2016): Advanced LIGO has recently announced detection of gravitational waves from a binary black hole merger event.

The papers can be found here: https://papers.ligo.org


Gravitational-wave observatories, already exist and aim to detect gravitational waves before 2017, with the first science data-taking with the new advanced LIGO and advanced Virgo instruments becoming online next summer and next year respectively.

More interferometers will come online in the coming years, such as KAGRA and INDIGO.

LIGO has two interferometers, one in Hanford, WA and one in Livingston, LA. Virgo is located near Pisa, Italy. KAGRA is being built in Japan and INDIGO will be built in India.

More to read:

http://en.wikipedia.org/wiki/Gravitational-wave_observatory

https://en.wikipedia.org/wiki/LIGO

https://en.wikipedia.org/wiki/Virgo_interferometer

https://en.wikipedia.org/wiki/KAGRA

https://en.wikipedia.org/wiki/INDIGO

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In short, yes.

However, it is highly nontrivial and has not been directly detected. We have indirect evidence of gravitational radiation. In binary pulsar systems the rotation frequency will increase over time because some of the mass of the system gets radiated away. This effect has been verified to agree with general relativistic predictions quite well. (Quite well in the sense that we are measuring something thousands or millions of light years away.) Direct detection is $in$ $principle$ possible with a simple mechanical detector. See Straumann (2013) for an excellent review of gravitational radiation. (Beware, some of the math puts Wald to shame.)

Here is an outline of his oscillator argument: Gravitational wave detectors are instruments that are highly sensitive to the weak tidal forces (curvature) induced by gravitational waves. Consider two masses $m$ connected by a massless spring of equilibrium length $2l_0$. Let $\omega_0$ be the frequency of the oscillator and assume that the damping time $\tau_0$ is much larger than the period $1/\omega_0$. If the separation between the two masses is $2(l_0+\xi(t))$, then the relative separation $\xi(t)$ satisfies the differential equation $$\frac{d^2\xi}{dt^2}+\tau_0^{-1}\frac{d\xi}{dt}+\omega^2_0\xi=\text{tidal acceleration}$$ The "tidal acceleration" can be obtained from the equation for geodesic deviation. This can be solved for $\xi(t)$. What we see is an incredibly small effect, and we must have a ridiculous $Q$ factor to see anything significant.

This is why we use laser interferometers nowadays. Look up the Wiki article for that. There are some good links above that are about interferometers.

Back in the day, we used antennae that scattered quadrupole radiation. Or at least, in theory they did. They obviously didn't work. See Weinberg (1972) for a review.

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