Detector Watch S6 V2

No. One needs to distinguish photons that are used for various control purposes from those that give us the gravitational wave sensing.

We are comparing those two paths in the arms for interference. We try to ensure light is in the same phase before the splitter that sends them to one or other arm. For those that return to exit via the anti-symmetric port, from there on they are all on the same path. Regardless of what interference has or hasn't occurred between the arms the photons then suffer the same phase changes onwards together after leaving the dark port. So the phase difference ( for a given frequency ) is fixed beyond the recombination of light from the arms. Moving/realigning the post-OMC PD's positions won't change any relative phase shift that has already occurred.

So Barry The Photon might have been born, laser synchronised in phase, together with Charles The Light Particle : but their experiences may only differ if Barry took the X arm while Charles took the Y. Or vice-versa. What particularly matters for our GW signal photodetectors is that both Charles' and Barry's relative phases are compared. There's quantum mechanical probability amplitudes and whatnot here determining whether an electron get's shoved to move along in our subsequent circuits, so we want Charles and Barry to combine votes on that. Plus it's good to have PD's that like to soak up as many photons of interest as possible, hence we get as many Barry/Charles pairs as we can.

A 'wavefront' answers the question : if I start at some given place, what possible future positions ( some time, some place ) exists for me at some particular chosen phase value? It will be some 2D surface(s). If I chose a different phase value I'll get in general a different surface. So I can speak of the '90 degree' wavefront, or the '2.5578 radians' wavefront. Admittedly phase is often quoted in 'angle' language, which can be confusing as polarisation ( another topic entirely ) is quoted as angle too. Best to think of phase as a pure number that ranges from zero to some maximum value which you can't exceed - you start back at zero instead! You can't wind around under zero either, as you then get put up to that maximum. This is termed modulo arithmetic. Note that although I can subtract/add a full cycle of phase and get the 'same' phase, for some specific photon, that then means some earlier/later time and closer/further distance from source. So wavefront language is a way of discussing the propagation in time and space of particles, like photons, that have underlying cyclic phase character.

So if I am Edward the Electron inside the PD crystal ( .... minding my own business .... circulating around The Nucleus .... shooting the breeze and downing wine spritzers with the other electrons in the 'hood .... ) and then Barry and Charles arrive in possibly different phases at my position at a particular time. I'll compare them and decide accordingly to absorb energy and hiss off. Or not and continue to hang around. Note that Barry's wavefronts will in general be different from Charles', but it is possible that they may meet Edward in phase ie. their wavefronts of that phase happen to co-incide at Edward's place. Another way to express matters is that generally when they arrive the photons will be on wavefronts of different phase. If Eddy was asleep when they turned up, and they were compared elsewhere deeper in the crystal that's OK. Or if someone else got to them before Ed too. Or if Barry and Charles entered laterally displaced from Edward .... etc. What matters is that some electron in the active volume does the job.

Well the situation is different for those sideband photons we use to control the interferometer geometry in realtime, than it is for the likes of Bazza and Chuck who are 'science' photons. I think I may have been a bit misleading in an earlier post. In any case the wave front sensors used for IFO length sensing do have to be concerned with whether or not a wavefront ( read 'surface of constant phase' ) hits square on. That is so that one can have a single position/meaning for the 'end' of an arm or cavity. That's why there are many pickoff points around the interferometer : take a sample of the traffic, select photons of interest ( frequency, phase, polarity ... ) from that, count how many you have, repeat continuously.

It is a matter of ( considerable!!! ) convenience that we use the same laser, vacuum space, optics etc to host/house the control elements. Michelson & Morley did it all by hand.

Thank you! If the rabbit and/or the poo glows -> run away!

Cheers, Mike.

Both Hanford and Livingston have had their share of woes this last week or so. I am reminded of the old rhyme about 'for want of a nail a horseshoe was lost, for want of a horseshoe a horse was lost, ...'.

Livingston can lock, but at around 8W only, getting bumped out with seismic noise - generally from earthquakes around the world and the pounding of the Atlantic waves against the continent. There is/was a tricky problem of timing between circuits reading out the data and handing them on to buffers. 'wait' cycles were being inserted sometimes, thus introducing variable delays and now it appears one circuit is giving a rising edge when another is expecting a falling edge from it. So for the moment :

I recall one of the earlier space shuttle launches delayed for similiar reasons - a redundant set of onboard computers that didn't quite catch what each other was saying. One textbook I have on digital circuit design says 'there are three important concerns - timing, timing and timing'. :-)

As for Hanford :

So it's great to see it running again ( I did sense some angst ). These IFO's are complex beasts indeed.

Now let's look at the lengths in this picture :

LA, LB, L1, L2, L3, L4 can all be changed individually by moving one or more mirrors. We'd call these independent length degrees of freedom. But while retaining the idea of independence, we could instead use combinations of these lengths :

Lccav = common cavity length = ( LA + LA ) / 2

Ldcav = differential cavity length = ( LA - LB ) / 2

Lcmic = common michelson length = ( L2 + L3 ) / 2

Ldmic = differential michelson length = ( L2 - L3 ) / 2

Lprc = power recycling cavity length = L1 + ( L2 + L3 ) / 2 = L1 + Lcmic

Lsrc = signal recycling cavity length = L4 + ( L2 + L3 ) / 2 = L4 + Lcmic

Don't worry too much about the factors of 2. The common lengths are a sum, the differential lengths are a difference.

We still have 6 degrees of freedom in length. In our minds we can think of any one of these varying, possibly while all the others are constant. But that's not to say the required mirror movements are simple to alter one of these composite lengths while keeping the others constant.

For instance if I wanted to change Lccav, while leaving Ldcav alone - I would alter LA and LB by the same amount and in the same sense. The sum of these two lengths would change but not their difference. So I could enact that by moving ETMA and ETMB both toward/away from the corner station where the beam splitter is. This will not change any of L1, L2, L3, or L4 either.

Ldcav is particularly important as the phase differences between the arms accumulate over many transits ( Fabry-Perot ). As far as GW reception goes this is where the money is.

Lccav is available for say keeping FP cavities in resonance while some tidal changes alter the relations between the end stations and the corner. Or some change in the laser frequency even.

Lcmic is not terribly interesting as the IFO doesn't really change character if this alters alone. You could do this by shifting ITMA, ETMA, ITMB and ETMB all together in the same sense and amount toward/way from the corner station. As we're keeping Ldmic constant then we don't introduce a shift in phase difference between the two arms.

What do you think of Ldmic?

Remember PRM is there to flick/keep the photons back into the gadget. It's position is adjusted to match phase relationships of light coming from the left, with those from it's right. In fact you could keep plain L1 as a degree : you'd leave the BS where it was ( or as determined by other ideas ) and alter where PRM sits. Ditto for L4 and the SRM. Remember SRM doesn't exist for Enhanced LIGO.

Indeed this entire discussion doesn't reveal the exact current operation ( which I don't know the setup and/or control code for ), but speaks of the general design flavour.

Remember the sidebands? These are frequencies of light from the laser, modulated by Pockel's cells, that are 'nearby' the base/carrier. One could adjust Lprc so that both the carrier and a sideband would be resonant. This is a similiar problem to finding least common multiples in integer mathematics. Take the numbers 3, 4 and 5 : you can find multiples of any of these separately, but is there a number which is a multiple of all three? Certainly! 60 for instance, and thus any multiple of 60 too. ( Bricklayers do this regularly by finding lengths that have convenient relationships in order to match the alignment of the bricks when separate courses meet. You don't have to, but it reduces the stuffing about with fractional bricks and aids the cohesion of the join ). All I want is the photons of different frequencies all coming back to the reflective surface of the PRM in the right phase.

You could imagine being some little bit of code whose job it is to read some photodiode level - say telling me how much light is leaking back out via the PRM - then deducing a direction and amount to alter the PRM's position - thus sending out control signals to the actuators ( say magnets & coils attached to the PRM ) - in order to restore the received PD level to some nominated 'ideal' setting. A cycle of read/calculate/adjust ..... ad infinitum. A feedback loop!

You could be yet another bit of code that holds the common cavity length at some preset - which another piece of code could decide the desired value of! I'd be fiddling with more mirror positions in this case, but the key point is that it's do-able without altering the other degrees. In fact as the IFO progresses from 'cold' to power up then to lock etc it is really the successive engagement ( I don't know the exact sequence ) and 'settling down' of feedback loops toward their respective 'preset goals', in order to finally achieve science data mode.

Enough for now! I'll read up on the more difficult alignment issue - the setting of the angles of the mirrors. The precision required is to do far better than simply hitting the barn door! :-) :-)

Cheers, Mike.

Now that I think about it I might try to clear out a road block for you. In anticipation. I know it caused me a lot of angst. It's not a terrible problem, but it can be an unsettling issue when trying to get one's head around the whole GW thingy.

There are two equivalent viewpoints of gravitational waves. Some treatments aren't overt in which view is being used. The physically measurable results are identical either way. For this discussion let's ignore all those pesky sources of error and disturbance, and focus on GW's passing through only.

#1 Here I am sitting around using a 'usual' reference system. Say I'm at an IFO corner station. I've surveyed matters as precise as I can. When undisturbed my mirrors, dangling vertically from their suspending wires, aren't moving as I perceive them. A GW comes along and sets them in motion, with my laser system telling me that. My reference distances haven't altered, but the position of the mirrors with respect to that have.

#2 I choose to define my mirrors as 'freely falling', and also I am saying that my coordinate system is defined by such freely falling bodies. That means they suffer no non-gravitational forces. But actually they do, via those suspending wires. However the mirrors aren't restrained along the axis of motion that I will examine, in the horizontal plane. I consider that the mirrors are a fixed distance apart. A GW comes along and changes the meaning of a given separation though. So the mirrors haven't moved with respect to my markers, it's the space between the markers that has expanded/contracted! A bit obtuse perhaps. This is called the TT gauge view, for 'transverse traceless', a phrase based on some arcane language. 'Transverse' means the expansion/contraction is at right angles to the direction of motion of the wave - compare with longitudinal compression/rarefaction of air density along the line of propagation of a sound wave, say. I'm not very clear upon what 'traceless' implies, but I think it's something to do with how 'worldlines' are represented on diagrams.

The viewpoints are the same basically due to the Equivalence Principle! I can be in a non-free-falling frame - sitting in my chair getting supported by electromagnetic forces - and view the mirrors accelerating with respect to my unaltered reference frame. Or I can tag along with the mirrors and observe how their separation remains the same ( because I defined them to be that way ), but note that space is warped.

The absolutely key point is that light is indifferent to this. The phase evolution from mirror to mirror in either case is the same.

Cheers, Mike.

( edit ) Nah! A tensor is like a matrix that transforms between co-ordinate systems in 'good' ways - it preserves the 'character' of the problem, and we don't have to worry about being fooled by some inadvertent/special choice of reference frame. So the Earth has the certain geometric properties that we all love and know irrespective of how one sets up co-ordinates to describe it. The trace of a tensor is a way of combining it with itself, similiar to a vector dot product. You get a scalar - a single number. A vector dot product gives us the square of the length of the vector, which is an invariant across all choices of co-ordinate systems. That's what we want for physical system descriptions when we relate different viewpoints. A traceless tensor is one that has trace = zero. For our problem that relates to masses not accelerating with respect to the co-ordinate frame when a GW goes by .... so they don't move!!