# Questions about the instruments and the measuring

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Topic 189958

Hello everyone,

I am repeating some questions here I already asked mistakenly in the Café. I'll try to formulate them a little better now and include the answers Maschenschalk had already given. I should send ahead that, even though as informatics student I am quite good in mathematics, but have some kind of mental blockade towards physics... I seem to be unable to deal with even Newtons stuff, let alone Einstein. :)

1. Why is it problematic that we're inside a gravity well? The fact that the equipment stands on firm ground is positive as far as I can see it and all influence that I could think of has only a frequency of 2/day. Isn't the gravity of earth, sun and moon and other astral bodies within the solar system relatively stable?

2. If I understood the document right the vibrations expect do have an amplitude of less than a thousendth than an atomic nucleus... this is a little hard to understand, since the mirrors used are made of a complex molecular structure... wouldn't that be like measurung the distance from earth to moon to the precision of an inch by directing it onto the Himalaya? I hear that the coating of the mirrors is a complex problem that keeps quite some scientists busy... but however you do it... it is still just molecules, isn't it?

3. How can you "direct" the instrument to one part of sky? I mean you can impossibly block out gravity from other directions...

4. This may be part of the answer to "3"... how can you even measure any pulse? Both the laser and the far mirror should be equally effected and vibrating to gravitronic waves, shouldn't they? Unless the wave would come in directly along the axis, but even then, you'd only have then an interference pattern would have to be registered within a millionth of a second (or 4km, understood as timespan).

5. Wouldn't it be better to set this experiment up in space? Like one mirror at the end of a 4 km foldable bar from the ISS? This way we wouldn't have to wonder wether the 150 Hz pulse it picked up didn't come from the wheels of a car passing by the testing site...

6. A last question to which I actually do not assume to be able to understand the answer. Those pulsars we're all looking for rotate. And they do rotate around there center of mass. Why would they emmit gravitronic waves then, since their center of mass does not move at all?

Well, as I said, I don't know much about physics so forgive me if the questions are naive and thanks for easy-to-understand answers. :)

Happy processing and computing everyone!
Björn

MarkF
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### Questions about the instruments and the measuring

I don’t understand the context the context of the first two questions. Maybe the these two links will help with the rest.
LIGO
S3 preliminary results

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### Well, the questions arose

Well, the questions arose after reading the S3 preliminary results document.

To the first:

http://einstein.phys.uwm.edu/PartialS3Results/node5.html wrote:
However a great deal of complication is introduced because our gravitational-wave detectors (LIGO [5] and GEO [6]) are Earth-based. The Earth's motion as it spins about its axis and orbits the Sun changes the gravitational wave as measured by the detector.

As you said, the influence of astral bodies with the solar system is already precomputed out... so why would the mere fact that we are in a gravity well be so problematic? Probably a silly question since the answer is most likely "it isn't".

To the second:

http://einstein.phys.uwm.edu/PartialS3Results/node8.html wrote:
Thus a strain $h=10^{-21}$ in the LIGO 4km arms corresponds to a change in the arm length of $4 \times 10^{-18}$ meters. This is about one thousand times smaller than the size of an atomic nucleus!

I just find it hard to imagine that any mirror, lense or prism works with such a precision...

klasm
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Regarding your first question I think the emphasis should be on the fact that the earth moves, both around the sun and that it spins around its own axis, rather than its own gravity.

Regarding the second question. The machine detects change in distance rather than the distance itself. As long as the mirrors are not changing rapidly with time this can be done with much higher precision.

There has been a number of popular science papers about this, you might have acces to some of the things in this list

Tom Awtry
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### Björn – Both Mark and klasm

Björn – Both Mark and klasm can more than adequately address your very well though out questions, in comparison to myself, but to perhaps add my own two cents worth into the thread I found the following, which may be of some enlightenment also.

Within this link is a somewhat non technical description of The Laser Interferometery Space Antenna (LISA) developed by NASA in conjunction with the Jet Propulsion Laboratory (JPL). As I understand the project’s scope the LISA observatory will be complemented by both resonant-mass and laser-interferometry ground detectors meaning an international network of gravity wave observatories (LIGO).

Hopefully, the aforementioned link, although a bit off the subject, will provide both by its content and very good graphics some answers to your appreciated inquisitiveness.

Thanks for letting me butt into the thread!

Regards,
Tom

Ben Owen
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### Björn, 1. Being in a

Björn,

1. Being in a gravity well isn't a problem in itself. The fact that it keeps the detectors moving creates the time-dependent Doppler shifts that Einstein@Home has to work very hard to deal with. And the fact that lots of other things (cars, etc) are also stuck in the gravity well rattling the detectors is a problem.

2. This one got some scientists confused, too, before LIGO was built. We say we are measuring displacements of order 10^-18m, a thousandth the size of a proton (10^-15m) or a billionth the typical spacing between atoms (10^-9 or 10^-10m). How is that possible? Basically because the bright spot on the mirrors is 10^-1m wide, so it averages over a great many atoms.

Actually the big noise source here is the thermally excited vibrational modes of the test mass - it's ringing like a bell because the atoms all jiggle at finite temperature. And the amplitude of those vibrations is much, much larger than the spacing between atoms. (Can't remember the number offhand.) Again it's averaging that does it (and the frequency response).

Here's something handy to remember: When you're adding N independent random things, the total grows as N but the random error grows only as the square root of N. So the fractional error goes down as the square root of N. That's how we solve this one, and for that matter the laser shot noise too. It's called "Poisson statistics" if you want to learn more.

3. Try here.

4. I'm not quite sure what you're asking, but it sounds like this question.

5. The big proposed space-based experiment is called LISA, and there is a thread called Why not just wait for LISA?. Actually LIGO and the others are doing their best at 150Hz. The trouble is going much below 50Hz, where the seismic noise rapidly gets worse. And we know there are more pulsars down there, including Vela which is tantalizingly close....

6. This thread might have the answer you're looking for, and it's still pretty recent.

As you might tell, I just spent some time clicking through my previous posts. You can do this by clicking on my name next to this post and clicking on "previous posts". In my case that's actually a decent first approximation to a Science FAQ.

Hope this helps,
Ben