Does the GW only chang space but not time?
5 May 2009 16:01:05 UTC
Topic 194334
(moderation:
Are the gravity waves that wee are searching for supposed to change space at the detector but not the time?
If both time and space change equally you should not be able to detect anything at all or do I missing something here.
Actually I am sure I missing a lot, just wondering. :)
Does the GW only chang space but not time?
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Excellent question, I think here you'll find is an excellent answer :-).
CU
Bikeman
Thank you Bikeman! Just to
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Thank you Bikeman!
Just to check that I got this right.
Does that mean that you get one wavelength in a light beam sent trough the leg pointing towards the gravity source and an other wavelength in the leg that is orthogonal to the first leg and that the detection is that you observe a interference pattern when you combine the two light beams?
RE: Thank you
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I'm not a physicist, but from what I understand: Almost....
Well, the effect is strongest when both arms are in the plane orthogonal to the direction to the source (the source is directly above , or under, the L-shaped detector). In this position, the length of the arms will change periodically with the frequency of the wave, and yes, this will be detected by interference of the two laser beams.
A nice visual representation of the spatial effects caused by a GW is found here : http://en.wikipedia.org/wiki/Gravitational_wave
The animation from the Wikipedia page shows what a GW (with a certain polarization, see the Wiki text for details) coming from the direction of your eyes will do to a ring of masses. Figure an L shaped detector inscribed in this ring and you get the idea.
CU
Bikeman
Thanks again Bikeman! You
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Thanks again Bikeman!
You guys are a goldmine of information.
That wobbly loop is just
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That wobbly loop is just mesmerising isn't it? :-)
It all comes down to light. It's the basis of our understanding of lots of science.
You can think of each photon that travels back and forth along the interferometer arms as having it's own personal phase counter. By counter I don't mean a clock or wristwatch, although you may be tempted to visualise it as such. The phase is a pure number, it goes from zero to 2 * PI and immediately restarts at zero, to 2 * PI, back to zero ...... in an endless cycle. We can characterise this phase activity with respect to our measurement axes. Time and space. So if the photon goes forward a certain distance while the phase makes a single round trip, from zero right around back to zero again say, then we call that distance the wavelength. If the photon takes a certain amount of time to do a single phase cycle then we call that the period. The reciprocal of that is said to be the frequency ie. how many cycles per second. There is also a less well used term - the wavenumber - which is the reciprocal of the wavelength ie. how many cycles per meter.
So the next question is who, or what frame, is/are the measurements being taken with respect to? Which length rulers and time clocks are in use? As Bikeman's link explains it doesn't matter much. This is a core concept in relativity. If you multiply the frequency by the wavelength then you get the speed of the photon. This is always the same number, a constant, no matter who is doing it [ Einstein's breakthrough of Special Relativity ]. The nett effect is that both space and time are measured as the photon moves along because of it's personal phase counter.
Now fire two initially identically phased photons ( a beautiful key property of lasers ) in two perpendicular directions - the interferometer arms - and check their relative phase upon return. If they still match then the photodetector gives a 'double' response. If one comes back half way around the phase cycle compared to the other then the photodetector gives a 'null' response. Plus a gradation of response for phase differences between those extremes. This is a quantum mechanical property of photons ( and other particles ) that they can interfere with one another's detection chances. Hence the name interferometer to the apparatus which displays this for us, either enhancing or diminishing a response from our electronics. [ I say chance and use quotes '' above, as the complete story includes a long detour into QM that we don't need here. ]
Maybe 'phase comparator' is a more helpful name. The signals we analyse are recordings of those phase comparisons as determined by the photodetectors. We endeavour to tease out those phase changes caused by distant astronomical events ( yeah! ), or deliberate 'hardware injections' for testing purposes ( nudge the mirror ), from the more mundane local ones ( boring! ) - like tides, trees falling, earthquakes, aeroplanes ......
Cheers, Mike.
( edit ) One possible source of confusion ...... these phases, wavelengths, frequencies discussed above are of the light beams we use to measure the GW's. The phases, wavelengths, frequencies of the gravity waves themselves are another topic again.
( edit ) and to be exact the speed of light is a constant 'in free space' or 'in inertial reference frames', which to a good enough approximation we are dealing with.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Hmmmm ... some more thoughts
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Hmmmm ... some more thoughts if you'll tolerate them. :-)
The arms of the US interferometers are about 4km long. A round trip is thus ~ 8km. At light speed this is :
time = distance/speed = 8000/(3 x 10^8) = (8/3) x 10^(-5) seconds
say, close enough to 25 microseconds give or take.
Now suppose a gravity wave is passing by at a typical frequency - let's choose the detector's 'sweet spot' for detection of 200 Hz. So one cycle of GW 'movement', where each end of the arm is appreciably moving with regard to the other, is going to take :
time ( period of GW wave ) = 1/200 = 0.005 = 5 milliseconds = 5000 microseconds
So for each whole arm wiggle from a GW going by we get :
photon round trips = 5000/25 = 200
You could think of the following analogy. Two strong guys each holding up their end of a long log, upon which one places some laser/mirror system. While they are certainly beefy fellows they can't move the log very fast, so if you get them to wiggle the ends up and down alternately ( one going down when the other is going up ) the photons in our gadget are just screaming back and forth along the top of the log meantime. Probably a Gazillion photon transits for each complete log wiggle. Or if you go really silly with a ( hypothetical! ) ultra-super-duper-slow-motion camera, and then replay a single round trip of a photon from one beefy guy to the other and back, then these chaps and the log are going to look stationary. Or you'd have to look real hard to find any movement.
So when we measure a gravity wave, which admittedly propagates at the speed of light, the progress of change along the dimensions of the interferometer arms is so slight during a single photon circuit of them. Put another way, the wavelength of the GW @ 200Hz is huge :
distance = speed x time = 3 x 10^8 x 0.005 = 1.5 x 10^6 meters = 1500 km
and the 4km interferometer arm is only going to sample a teensie fraction of that per photon circuit. A little bug with a ruler on the back of our log.
If you consider each single transit a 'snapshot' of the spacetime 'length', then by stringing such together you get a roughly continuous movie of these phase comparisons that I mentioned earlier. This becomes our data stream for analysis here at E@H.
Cheers, Mike.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Thank you Mike! The
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Thank you Mike!
The polarization seams to be the key thing here.
Will the polarization will be at its maximum if the rotation plane is perpendicular to the detector plane and if the two panes are parallel there will be no polarization and no wave will be detected?
Tomas
RE: Thank you Mike! The
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AH, you're catching on!! You'll be sorry you asked now .... :-)
Yup, that wobbly circle is what is known as a quadrupolar pattern. So an expansion along one axis entails a contraction along the perpendicular one, in a cyclical fashion as you see illustrated. Now the interferometer arms, for whichever facility ( Hanford, Livingston, GEO, Virgo, TAMA .... ) is being considered, are also aligned ( pretty much exactly ) perpendicular too. So the signal we get using the arms ( think of the whole IFO as an antenna if you like ) will depend on the relative orientation of the incoming GW with respect to the IFO at any given moment/period of time.
Some geometry, alas :
- the direction of propagation of the GW is along the line of some 3D vector. It's coming from wherever the celestial events that generated it are situated in the sky.
- the IFO's, being attached to the Earth, are always moving due to Earth's rotation ( once per day ) and Earth's travel around the Sun ( once per year ).
- so this important relative orientation is a moment to moment proposition.
- because of the momentary direction of travel of the IFO in space there is, of course, really a velocity too. So there is a Doppler type effect of an IFO's 'perception' of the wave compared with it's source. For simple purposes you can assume the source is effectively 'at infinity' so there is no parallax type effect occurring during short time periods at least. That factors in to the expected frequency of the gravitational wave, compared to whatever generated it, as measured on this moving platform. Higher pitch when approaching, and lower pitch when receding, no change if neither. Just like the standard example of a train with blaring whistle scooting past.
- the wobbling of the GW is perpendicular to the 3D vector mentioned above. So let's pretend I am standing facing the 'X' arm at Hanford, with my head-to-toes axis vertical. My left arm ( in this case ) is to the side of the IFO 'Y' arm, and my right arm nearer the visitor's parking bay just outside.
- so let's assume a GW is traveling straight towards me, 'dead on' so to speak. The oscillation is wholly within a plane transverse to the incoming GW 3D vector. Got that in mind? Good, 'cos it gets worse. :-) :-)
- now the wave itself has one more degree of freedom to describe. The rotation of the oscillation pattern about that direction of propagation. This is termed the polarisation of the wave.
- if, say ( looking at Bikeman's animation now ) the upper-to-lower axis of the wobbly wave is aligned with my head-to-toes axis then I am going to get shorter and fatter followed by taller and thinner. Cyclically. Thus so with IFO arms.
- this is an arrangement of maximal response from our antenna. The 'X' arm suffer no deflection, and the 'Y' the full deflections possible during the passage of the wave. So we get the best phase differences for our photons flying around our ( well LIGO's actually ) big expensive gadget. Are you with me? If so you are doing quite well. :-)
- now slightly change the setup. Same as above but rotate the direction of the incoming GW's direction by 45 degrees about my head-to-toes axis. So that 3D propagation vector is now aligned along a line at 45 degrees to both interferometer arms. Think as carefully as you can about this. Both arms are now stretching and contracting but they are matching each other in length changes with each passing instant. So those quick photons, that are transiting far faster than the wave can change shape, are going to suffer no relative phase difference. NO SIGNAL!!
- this is a 'null' response from the IFO. There are other geometries, a multitude of intermediate configurations, giving quite a range of measurable 'reception'. I won't exhaust you, or myself, describing them but it follows the logic given here. Mathematics takes care of this, and some clever people have that sorted.
- also it's a good thing that the waves are of quite small amplitude, ~ 10^(-21), else I'd resemble a messy blob of stuff on the otherwise clean floor at Hanford! ** :-)
Here's a really good visual representation that summarises the full geometric gore :
lifted straight from Peter Saulson's book Fundamentals Of Interferometric Gravitational Wave Detectors. Buy it, he's a great guy .... :-)
- each of the three funny looking 'peanuts' shown here is, effectively, the detector response to GW signal configurations we are discussing over the full range of possible directions of approach of a GW. Formally this is known as an antenna response function or somesuch.
- the edges of the floor of the bounding boxes describe the directions of the IFO arms. The corner station is right in the centre, where the pinching is extreme for the middle diagram say.
- where you see the pattern bulging out at a particular direction is where the signal reception is good, if pinched/puckered in the reception goes to zero. The leftmost is for one polarisation arrangement, the middle one for the one rotated by 45 degrees, and the rightmost for both/unpolarised/average.
- due to the magic of 'linear superposition' any GW can be seen as some weighted sum of the two polarisation base types.
Have a lie down. Let the waves wash over you ... :-) :-)
Cheers, Mike.
( edit ) ** and the floor would be cracked up rubble too. This is why it is a good thing not to live nearby binary systems!
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
Hi Mike! Just came back from
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Hi Mike!
Just came back from long day on my work
and I will take my time to study this carefully.
Thank you.
Tomas
I should add that, looking at
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I should add that, looking at the left and middle peanuts now, there is a rough 'anti-symmetry' between the polarisation base types. So what's good along one incoming direction for a given polarisation can be negated by rotating the wave polarity by 45 degrees around it's propagation vector ( ie. incoming direction unaltered ). And vice versa.
I'm pretty sure I can post some other diagrams to firm up the geometry we are discussing. Stay tuned ....
A picture is worth a thousand words ! :-) **
Cheers, Mike.
( edit ) ** - or two thousand of mine!
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal