Re: [Phys-L] billion dollar gamble

[John Denker <jsd@av8n.com>]

On 5/23/19 5:09 PM, David Craig wrote:
>  when did Kip ask you, and what exactly was he interested in having you work on?

This is back in roughly 1975.  I don't remember all the
details, but here is an approximate reconstruction:

NOTE: In general, when a project is near completion, you
can make a *list* of what needs doing.  In contrast, in
the early days, there is no point in making a list, 'cuz
everywhere you look there is an unlimited supply of things
to work on.  I'm not sure anybody asked me to work on
anything in particular.  Everybody was in "kid in a candy
store" mode.  Grab something and start chewing.

Most of what needed doing was way over my head, but one
thing where I could kinda maybe get some traction was the
vibration isolation system.  The allowable vibration in
the mirrors was 20 orders of magnitude smaller than the
vibration in the local bedrock.

Back then they had cobbled together something really
primitive, involving lots of layers:
   platform
   damped spring
   platform
   damped spring
   platform
   damped spring
   platform
   damped spring
and so on, for about 20 layers.  But it was completely
unsatisfactory for multiple reasons.  For one thing, the
damping came from some rubbery compound that would never
be allowed in a high-vacuum system.  And yes, the damping
had to be inside the vacuum space.  It would be neither
feasible nor necessary to provide vibration isolation
for the mile-long pipes.  Instead, isolate just the
measuring apparatus inside the vacuum.

I had enough of an electrical engineering background to
see it as a *filter* design problem.  The filter had to
have a gain of 1 at DC (which is another way of saying
the suspension had to support the weight of the apparatus,
on average).  And then the gain had to roll off so that
it was -400 dB at 1 kHz.  That's a serious filter.

Having 20 layers all the same is no good.  It results in
a grossly overdamped filter.  What you want is something
more like a Butterworth filter, with a bunch of poles
arranged on a semicircle in the complex s-plane.
  https://www.maximintegrated.com/en/app-notes/index.mvp/id/733
  https://dsp.stackexchange.com/questions/35073/filter-design-by-distributing-poles-and-zeros-on-parametric-curves

Isolating high-frequency vibrations is straightforward:
You can do it with a big mass and a floppy spring.  The
floppy spring is nontrivial;  to provide a big force
with a small spring constant requires a huge length.
And there is not much room inside the vacuum chamber.

I figured you could handle the low-frequency vibrations
using electronics + actuators (electromagnets and/or
piezos).

If you put the /corner frequency/ of your filter at a low
enough frequency, you don't need too many poles;  20 octaves
at 20 dB per octave will get you to 400 dB.  The gravity
waves are 1 kHz so a corner at 1 millihertz corresponds to
20 octaves (i.e. a factor of 10^6) in frequency.

There would be terrible problems (including reliability
problems) building an analog op-amp filter with a pole at
1 millihertz;  ordinary resistors and capacitors aren't
good enough for that.  If you touch it or even breathe on
it you'll ruin it.  HOWEVER, you can build a digital filter
and feed it into a 20-bit DAC.  Nowadays that is the first
thing anybody would think of, but back in 1975 that was
pretty exotic.  Back then most physicists didn't know a
whole lot about digital filter synthesis.

I didn't know enough to immediately carry out such a task,
but I could teach myself the required skills.  There was
no chance that the result would be good enough, but it
would be better than what they had at the time, and would
probably provide a foundation for figuring out what the
next step should be.

This part of the project didn't involve general relativity,
just a lot of fancy engineering.

I decided not to tackle that.  Instead I did other stuff
-- easier and higher paying -- for a couple of years, then
went off to grad school.

I imagined building up from the bottom, like on an optics
table.  What they actually use builds down from the top,
in the form of a compound pendulum.  OTOH the basic idea of
using electronics to handle the low-frequency components and
mechanical springs to handle the high-frequency components
turns out to be the right answer:
  https://www.ligo.caltech.edu/page/vibration-isolation

Nowadays optical tables and even cargo trucks use active
suspensions -- but they didn't back then.

Disclaimer:  I have not thought about this for 44 years.
Not all the details are guaranteed correct.