Indeed, the interesting point is that differently from electromagnetic radiation that we can see only after recombination (as @mattia_emma said, about 370000 years after the Big-Bang), gravitational waves are not limited by this and theoretically we could detect something before that period. Current detectors don’t have the sensitivity to do so (at least, for the phenomena we know / we suppose to know), we hope that this will be possible with the next generation of detectors such as Cosmic Explorer, Einstein Telescope and LISA, even if this is hard to say now
“theoretically we could detect something before that period.”
I would like to know more about this. How could this be possible?
Also, I don’t really understand the purpose of studying Q Transform. In what way does the Fourier Transform fall short of its purpose?
Up to now we have many hypothesis (more or less reasonable, “exotic”, the paper mentioned by @mattia_emma https://arxiv.org/pdf/1801.04268.pdf is for sure a good summary): it’s very important to mention that we expect these phenomena, far in time and space, to arrive to us with a very small strain (much smaller with respect to that detected up to now). Generalizing, we expect many phenomena during the first ages of the Universe to emit GW, ranging from inflation related effects to topological defects. Up to now, what we can do is to put upper limits based on the current observations (i.e. say “these phenomena should have a strain below this value”)
There is a very strong assumption in performing the Fourier Transform (FT), namely that your signal is stationary in time: if so, the FT will give a “compact” representation of your signal (e.g. the FT sin(2pi f t) is a delta function).
With gravitational waves (GWs) this assumption fails because your signal evolves in both time and frequency (i.e. the frequency increases with time for compact binaries), so if you take the FT of this you’ll have something “spread” among many frequencies that doesn’t take into account for the time dependence of your signal.
Q transform (very briefly, this topic has much more details) allows to represent your signal both in time and frequency, very similar to what does a musical score (if you think about music, of course you’ll not have a fixed frequency or a stationary signal but many different frequencies changing in time: a Q-transform of a song means that you listen to this song properly, a Fourier Transform of this song means that you listen to all the sounds of this song at the same time)
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In yesterday lecture, when explained about constrain,
what does it means about delta L =10^-18 m ??
In the lecture, portray like thin of reflecting mirror. Is it right?
If that true, if we made more thin mirror had more sensitivity? Or it had technical problem?
Thanks
Hi, yesterday we explained that to detect a gravitational wave, we need to appreciate a difference of distance of about (\delta L = 10^-18 m). Our detectors are like huge Michelson interferometers, this distance can be measured with the interference of light. To reach such sensitivity, we need several ingredients such as
- Almost perfectly reflecting mirrors
- High laser power
- Components of the interferometers isolated from the ground
- etc etc
Sensitivity is not only given by mirrors
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Delta L = 10^-18 m is basically the absolute (equivalent) displacement that GWs causes on mirrors. Since GWs cause a relative equivalente displacement of delta L / L = 10^-21: having a 10^3 m arm brings to 10^-18 m. Then, using optics like a Fabry-Perot cavity, photons are basically trapped inside the arm, going back and forth multiple times. This gives a longer effective arm to return a bigger delta L. Only a little amount of light passes through the mirror to come back to the detector, while most of light turn back in the arm. This latter reason is one of the many reasons for which we want thick mirrors.
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thick mirror? Not a thin mirror??
Thin mirror can leak?
Sorry , i’m little confusing on it.
Yes these mirrors have an high reflectivity but at some point your photon has to go out from the Fabry-Perot cavity; the reflectivity is such that the photon perform an average number of (if I’m not wrong) about 70 round trips within the cavity before going out
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Is Q-transform and waterfall diagram the same?
What parts of time and frequency component should we take in the Q transform?
Hi @abdyoyo, I’m not really sure about how the time-frequency representation is obtained in a waterfall diagram, but Q-transform technically is a time-frequency representation obtained through a continuous wavelet transform done with Gaussian wavelets, which ensure you to have the best time-frequency resolution (see e.g. Uncertainty principle - Wikipedia). So, Q-transform should give you a representation involving a certain frequency component “nearby” a certain time (how much “nearby” is given by the Q parameter, see [gr-qc/0412119] Multiresolution techniques for the detection of gravitational-wave bursts)
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Do we need to submit all the assignments of all three tutorials by 17 May itself? Or can we submit it till 18th May morning?..
Hi @Anushka , there is no deadline to submit the assignements for the tutorials
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