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In this episode, we dive deep into gravitational wave astronomy, with Christopher Berry and John Veitch, two senior lecturers at the University of Glasgow and experts from the LIGO-VIRGO collaboration. They explain the significance of detecting gravitational waves, which are essential for understanding black holes and neutron stars collisions. This research not only sheds light on these distant events but also helps us grasp the fundamental workings of the universe.
Our discussion focuses on the integral role of Bayesian statistics, detailing how they use nested sampling for extracting crucial information from the subtle signals of gravitational waves. This approach is vital for parameter estimation and understanding the distribution of cosmic sources through population inferences.
Concluding the episode, Christopher and John highlight the latest advancements in black hole astrophysics and tests of general relativity, and touch upon the exciting prospects and challenges of the upcoming space-based LISA mission.
Our theme music is « Good Bayesian », by Baba Brinkman (feat MC Lars and Mega Ran). Check out his awesome work at https://bababrinkman.com/ !
Thank you to my Patrons for making this episode possible!
Yusuke Saito, Avi Bryant, Ero Carrera, Giuliano Cruz, Tim Gasser, James Wade, Tradd Salvo, William Benton, James Ahloy, Robin Taylor,, Chad Scherrer, Zwelithini Tunyiswa, Bertrand Wilden, James Thompson, Stephen Oates, Gian Luca Di Tanna, Jack Wells, Matthew Maldonado, Ian Costley, Ally Salim, Larry Gill, Ian Moran, Paul Oreto, Colin Caprani, Colin Carroll, Nathaniel Burbank, Michael Osthege, Rémi Louf, Clive Edelsten, Henri Wallen, Hugo Botha, Vinh Nguyen, Marcin Elantkowski, Adam C. Smith, Will Kurt, Andrew Moskowitz, Hector Munoz, Marco Gorelli, Simon Kessell, Bradley Rode, Patrick Kelley, Rick Anderson, Casper de Bruin, Philippe Labonde, Michael Hankin, Cameron Smith, Tomáš Frýda, Ryan Wesslen, Andreas Netti, Riley King, Yoshiyuki Hamajima, Sven De Maeyer, Michael DeCrescenzo, Fergal M, Mason Yahr, Naoya Kanai, Steven Rowland, Aubrey Clayton, Jeannine Sue, Omri Har Shemesh, Scott Anthony Robson, Robert Yolken, Or Duek, Pavel Dusek, Paul Cox, Andreas Kröpelin, Raphaël R, Nicolas Rode, Gabriel Stechschulte, Arkady, Kurt TeKolste, Gergely Juhasz, Marcus Nölke, Maggi Mackintosh, Grant Pezzolesi, Avram Aelony, Joshua Meehl, Javier Sabio, Kristian Higgins, Alex Jones, Gregorio Aguilar, Matt Rosinski, Bart Trudeau, Luis Fonseca, Dante Gates, Matt Niccolls, Maksim Kuznecov, Michael Thomas, Luke Gorrie, Cory Kiser and Julio.
Visit https://www.patreon.com/learnbayesstats to unlock exclusive Bayesian swag 😉
Takeaways:
⁃ Gravitational wave analysis involves using Bayesian statistics for parameter estimation and population inference.
⁃ Nested sampling is a powerful algorithm used in gravitational wave analysis to explore parameter space and calculate the evidence for model selection.
⁃ Machine learning techniques, such as normalizing flows, can be integrated with nested sampling to improve efficiency and explore complex distributions.
⁃ The LIGO-VIRGO collaboration operates gravitational wave detectors that measure distortions in space and time caused by black hole and neutron star collisions.
⁃ Sources of noise in gravitational wave detection include laser noise, thermal noise, seismic motion, and gravitational coupling.
⁃ The LISA mission is a space-based gravitational wave detector that aims to observe lower frequency gravitational waves and unlock new astrophysical phenomena.
⁃ Space-based detectors like LISA can avoid the ground-based noise and observe a different part of the gravitational wave spectrum, providing new insights into the universe.
⁃ The data analysis challenges for space-based detectors are complex, as they require fitting multiple sources simultaneously and dealing with overlapping signals.
⁃ Gravitational wave observations have the potential to test general relativity, study the astrophysics of black holes and neutron stars, and provide insights into cosmology.
Links from the show:
- Christopher’s’ website: https://cplberry.com/
- John’s website: https://www.veitch.me.uk/
- Christopher on GitHub: https://github.com/cplb/
- John on GitHub: https://github.com/johnveitch
- Christopher on Linkedin: http://www.linkedin.com/in/cplberry
- John on Linkedin: https://www.linkedin.com/in/john-veitch-56772225/
- Christopher on Twitter: https://twitter.com/cplberry
- John on Twitter: https://twitter.com/johnveitch
- Christopher on Mastodon: https://mastodon.scot/@cplberry@mastodon.online
- John on Mastodon: https://mastodon.scot/@JohnVeitch
- LIGO website: https://www.ligo.org/
- LIGO Gitlab: https://git.ligo.org/users/sign_in
- Gravitational Wave Open Science Center: https://gwosc.org/
- LIGO Caltech Lab: https://www.ligo.caltech.edu/page/ligo-data
- Exoplanet, python package for probabilistic modeling of time series data in astronomy: https://docs.exoplanet.codes/en/latest/
- Dynamic Nested Sampling with dynesty: https://dynesty.readthedocs.io/en/latest/dynamic.html
- Nessai, Nested sampling with artificial intelligence: https://nessai.readthedocs.io/
- LBS #98 Fusing Statistical Physics, Machine Learning & Adaptive MCMC, with Marylou Gabrié: https://learnbayesstats.com/episode/98-fusing-statistical-physics-machine-learning-adaptive-mcmc-marylou-gabrie/
- bayeux, JAX models with state-of-the-art inference methods: https://jax-ml.github.io/bayeux/
- LBS #51 Bernoulli’s Fallacy & the Crisis of Modern Science, with Aubrey Clayton: https://learnbayesstats.com/episode/51-bernoullis-fallacy-crisis-modern-science-aubrey-clayton/
- Aubrey Clayton’s Probability Theory Lectures based on E.T Jaynes book: https://www.youtube.com/playlist?list=PL9v9IXDsJkktefQzX39wC2YG07vw7DsQ_
Transcript
This is an automatic transcript and may therefore contain errors. Please get in touch if you’re willing to correct them.
Transcript
In this episode, we dive deep into
gravitational wave astronomy with
2
Christopher Berry and John Vich, two
senior lecturers at the University of
3
Glasgow and experts from the LIGO -VIRGO
collaboration.
4
They explain the significance of detecting
gravitational waves, which are essential
5
for understanding black holes and neutron
stars collisions.
6
This research not only sheds light on
these distant events, but also helps us
7
grasp
8
fundamental workings of the universe.
9
Our discussion focuses on the integral
role of Bayesian statistics, detailing how
10
they use nested sampling for extracting
crucial information from the subtle
11
signals of gravitational waves.
12
This approach is vital for parameter
estimation and understanding the
13
distribution of cosmic sources through
population inferences.
14
Concluding the episode, Christopher and
John highlight the latest advancements,
15
in black hole astrophysics and tests of
general relativity, and touch upon the
16
exciting prospects and challenges of the
upcoming space -based LISA mission.
17
So strap on for episode 101 of Learning
Bayesian Statistics, recorded February 14,
18
2024.
19
Hello my dear Bayesians!
20
Today, I want to thank Julio
21
joining the Good Basion tier of the show's
Patreon.
22
Julio, your support is invaluable and
literally makes this show possible.
23
I really hope that you will enjoy the
exclusive sticker coming your way very
24
soon.
25
Make sure to post a picture in the slide
channel.
26
And now, on to the show.
27
Christopher Barry, John Vich, welcome to
Learning Basion Statistics.
28
Thank you very much for having us.
29
Yes, thank you a lot for taking the time,
even more time than listeners suspect, but
30
we're not gonna expand on that.
31
But yeah, I'm super happy to have you on
the show and we're gonna talk about a lot
32
of things, physics, of course
astrophysics, black holes and so on.
33
But first,
34
How would you both define the work you're
doing nowadays and how did you end up
35
working on this?
36
I can go first.
37
I guess I'm slightly older than
Christopher.
38
I started doing gravitational waves when I
was a physics student at Glasgow.
39
I got involved with the LIGO, actually the
GEO experiment first of all, which is the
40
Gravitational Weight Detector in Germany.
41
Its bigger brother is the LIGO and the
LIGO detectors that we're going to talk
42
about more today.
43
And ever since then, I mean, thought the
project was fantastic.
44
I'll you all about it.
45
I just wanted to get involved in the
discoveries of gravitational waves and
46
what they can tell us about black holes
and so on.
47
I got involved back in my PhD.
48
My PhD was largely about gravitational
waves we could maybe detect in the future
49
with an upcoming space -based mission
called LISA, due for launch in the 2030s.
50
I remember
51
my advisor telling me, I hope you're OK.
52
There's not going to be any real data.
53
And I was like, yes, that's great.
54
I just want to play around with the theory
stuff.
55
And then I guess fate conspired against
me.
56
After my PhD, I moved to the University of
Birmingham.
57
That's where I first started working with
John.
58
We were at University of Birmingham
together.
59
And I got involved in LIGO, VEGO data
analysis.
60
And we happened to make our first
detection just a couple of years after I
61
joined in 2015.
62
And we've been very busy since then
analyzing all the signals, figuring out
63
the astrophysics of them.
64
So each individual source and then putting
them together to understand the population
65
underneath.
66
So now we're both at the University of
Glasgow working on analyzing these
67
gravitational wave signals and
understanding what they can teach us about
68
the universe.
69
Yeah.
70
So as Liesner can already tell, I guess,
71
Fascinating topics, lots of things to talk
about and dive into.
72
But maybe to give us a preview of things
we're going to talk about a bit more.
73
You guys are also using some patient stats
writing in these analysis, am I right?
74
Yeah, so I think we look at, I guess, two
levels of Bayesian stats.
75
So the first is what we refer to as
parameter estimation.
76
So given a single signal trying to figure
out what are the properties of the source.
77
So the signals we most often see are, say,
two black holes spiraling in together.
78
So we look at the patterns of
gravitational waves that it emits.
79
And from this, we can match templates and
then infer.
80
These are the masses of the two black
holes.
81
This is the orientation of binary, the
distance to the binary, and parameters
82
like that.
83
So we use Bayesian stats and the sampling
algorithms like nested sampling to mop out
84
a posterior probability distribution.
85
And then I guess the second level of this,
we do what we call a population inference,
86
so a hierarchical inference of given an
ensemble of different detections,
87
correcting for our selection effects that
we can detect some signals easier than
88
others.
89
What is the underlying astrophysical
distribution?
90
So what is the distribution of masses of
black holes out there in the universe?
91
Yeah.
92
So fascinating things.
93
And John, you want to maybe add something
to that?
94
Just as a teaser, we're going to dive a
bit later in the episode into what you
95
guys actually do.
96
So as Christopher just said, nested
sampling, population inferences, but
97
anything you want to add?
98
teaser for Easter.
99
I would add something about the background
of how it works within the LIGO scientific
100
collaboration.
101
So when I started doing my PhD, my
advisor, Graham Wohn, taught me about
102
Bayesian statistics, Bayesian inference,
and I never learned it as an undergraduate
103
at all.
104
I just leave my mind, like, here we have
this mathematical theory of learning.
105
Why are we using this everywhere?
106
And in those days, it really wasn't being
used very much in LIGO.
107
because a lot of the people that started
the collaboration were coming from a
108
physical perspective and they were very
frequentists.
109
They were counting and cutting all of
their events to try and measure the
110
discovery that takes place on it or
whatever.
111
So it was kind of novel in that patient's
way back then.
112
But since then, as Christopher said, it's
been applied all over the place to all
113
kinds of different problems.
114
So it's been quite exciting to watch that
back over the years.
115
I remember we had a...
116
We had our first detection and we were
lighting up our results.
117
And I think at that time still a lot of
the collaboration was very frequent.
118
So we were writing in our papers, we have
a posterior probability distribution for
119
the masses and there are people going,
hey, what's that?
120
What's a posterior?
121
We've never come across this before.
122
Can you explain it to us?
123
And now it is very much accepted.
124
And yeah, everyone has a new detector.
125
Where are the masses?
126
I want to see this probability
distribution.
127
What do you think drove that evolution and
that change?
128
I think Bayesian statistics is very
popular in other parts of astronomy.
129
So in a sense, it was kind of inevitable
that it would make its way over to
130
gravitational wave astronomy as it's only
a matter of time.
131
But I think the problems that we were
trying to solve, particularly for the
132
parameter estimation,
133
type analysis did lend itself to a
Bayesian analysis because you have a
134
unique event.
135
You you're not, we only see a very small
number of gravitational waves.
136
We see them all the time, but it's still
measurable.
137
The dozens, not the millions.
138
So we have to make the most of every
single one.
139
The second one, the ratio is rather low.
140
So graphs from the other side.
141
is also very important if you want to do
science.
142
Yeah, that makes sense.
143
And so it was mainly driven by just
patient stats entering a need in what you
144
wanted to do basically, which is something
I often see in fields where psychology,
145
from what I've seen in the last few years,
for instance, psychometrics, things like
146
that, have seen a big rise in patient
statistics because they have been able to
147
answer the questions that researchers had
and that they could not answer with the
148
tools they had before.
149
So basically, a very practical, oriented
view of things.
150
And then afterwards, let's say the more
epistemological philosophical side of
151
things enters to also justify that.
152
But...
153
But most of the time it's a very practical
driven mindset, which is great, right?
154
Because in the end, why you care about
that is just, is that the right tool to
155
answer the questions I have right now?
156
And yeah, for what it's worth.
157
Yeah, go ahead, John.
158
The pragmatism is what's put in the table
at the end of the day, but during my PhD,
159
I was trying to look...
160
or not the kind of black hole binaries
that we'll talk about later, but from
161
monochromatic waves.
162
So you imagine doing a Fourier transform
of some data and you have a single spike,
163
and it has a bit of modulation on it.
164
But really there's no information about
that spike in any area of the prime space
165
outside of the spike.
166
So I learned about Bayesian statistics and
tried to do MTMC on this problem, which
167
was kind of like the most pathological
problem that you'd be trying to do MTMC
168
on.
169
that basically reduces itself to doing an
exhaustive search for the ground or space.
170
So I was kind of convinced by the
epistemology originally rather than the
171
thesis and the only nature that we used
for the sake.
172
Yeah, yeah.
173
Yeah, yeah.
174
That makes sense.
175
And as you were saying also that patient
studies is popular in other parts of
176
physics.
177
That's definitely true in a sense that,
for instance, in the core developers of
178
MC, of Stan, you have a lot of physicists,
often coming from statistical physics and
179
historically even the algorithms that we
even use, MCMC algorithms, have been
180
developed mainly by physicists or for
physics purposes.
181
So there is really this integration here
almost historically.
182
And that made me think that if listeners
are interested, there is an interesting
183
package that's called Exoplanet.
184
And that's basically a toolkit for
probabilistic modeling of time series data
185
in astronomy, but with a focus on
observations of exoplanets.
186
So that's different from what you guys do,
but that's using PIMC as a backend.
187
So that's why I know it.
188
And that's...
189
mainly developed by Dan, Firm and Macky,
if I remember correctly.
190
I'll put that in the show notes for people
who are interested because that is
191
definitely something to check out if you
are doing that kind of models.
192
And that made me think that I didn't even
thank our matchmaker because today is
193
February 14th, but actually this episode
was made possible thanks to a matchmaker,
194
Cupid, if you want, of patient statistics,
Johnny Highland.
195
Thanks a lot for putting me in contact
with Christopher and John.
196
Johnny is a faithful listener and I am
very grateful for that and for putting me
197
in contact with today's guests.
198
And so you mentioned already, Christopher,
that you two work on the LIGO -VIRGO
199
collaboration.
200
Maybe...
201
Yeah, tell us a bit more about that
collaboration, what that is about, and
202
what the goal is, so that listeners have a
clear background.
203
And then we'll dive into the details.
204
So yes, LIGO -VIRGO -CAGRA is a
collaboration of collaborations.
205
So each of LIGO -VIRGO and CAGRA operate
their own gravitational wave detectors.
206
So these are remarkable experimental
achievements.
207
We're talking devices that can measure
208
Distortions in space and time is what
we're looking for.
209
So in effect, what we do is we time how
long it takes a laser to bounce up and
210
down between some mirrors in one direction
compared to another.
211
We're looking for a part of less than one
part in 10 to the 21.
212
So it's equivalent to measuring the
distance between the Earth and the sun to
213
the diameter of a hydrogen atom, or the
distance from here to Alpha Centauri to
214
the width of a human hair.
215
So over many decades,
216
experimentalists have developed the
techniques to build these detectors to
217
design them.
218
And we're now in a very fortunate
situation that we have multiple of these
219
detectors operating across the world.
220
So we have two LIGO detectors in the US,
one in Livingston, Louisiana, one in
221
Washington, in Hanford.
222
And we've got Virgo in Italy, just outside
Pisa, Kagra underground in Japan, and
223
coming decade another LIGO to be built in
India.
224
And each of these observatories is looking
for gravitational wave signals.
225
The ideal source for gravitational waves
would be a binary of two black holes or
226
two neutron stars, very dense objects
coming together, merging very quickly,
227
very strong gravity, very dynamical
objects.
228
And we can detect these gravitational
waves and with those do astronomy.
229
So instead of using a telescope to make
observations with light, we're using these
230
gravitational wave detectors to look for
gravitational waves in undercover.
231
the astrophysics of these sources.
232
Yeah.
233
Yeah.
234
Thanks.
235
So that's a very clear explanation.
236
It's a bit like being able to hear the
universe itself only looking at it, right?
237
So that's another way of getting
information about the universe that maybe
238
allows us to also answer questions that we
had, but we were not able to answer only
239
with a telescope data.
240
Is that the case or is that mainly
241
information that's parallel and similar.
242
Yes.
243
Go ahead.
244
Yeah, I think that's one of the most
exciting things about this is completely
245
set in the electron spectrum using the
structural squeezing space itself by these
246
buckles and neutrons.
247
The waves that we've been offering are of
an oil from the sea.
248
So, as you said, the detectors are picking
up
249
essentially the equivalent of sound waves,
bulk motion of the material rather than
250
the jiggling of atoms.
251
We're talking about the jiggling of whole
stars, movement of them in their orbits.
252
And because you're looking at the bulk
motion rather than the surface of the
253
object, you can see right into the heart
of what's going on in some of these very
254
violent events.
255
In principle, we should be able to see
also inside supernovae if there are
256
enough...
257
motion of material during the core
collapse.
258
That would also give off gravitational
waves that we could see, although their
259
thoughts would be much weaker than those
that we're looking at in the moment.
260
I see.
261
One thing that's particularly nice we can
do as well is really test how gravity
262
behaves in very extreme environments.
263
John, I don't know if you want to mention
something about looking at the ring down
264
of black holes.
265
Sure.
266
I mean, as Christopher says, there's a
very detailed prediction for how two stars
267
should approach each other in their own
spiral over time.
268
And the equations are horrendously
complicated.
269
talking about the full view of general
relativity.
270
But once they've collided and they form a
larger black hole, suddenly everything
271
becomes rather simple and acts just like a
wine glass that's been excited with a fork
272
and then it actually decays down and
settles into its final state.
273
Therefore a black hole that happens
extremely fast because they want to
274
settle down as quickly as they possibly
can, if you like.
275
So the notes that we give off are
milliseconds long rather than seconds
276
long.
277
But the frequencies in the damping times
of those notes are measurable with their
278
picture waves.
279
And by looking at them and comparing them
to each other, we can check to see that
280
the predictions of the theory are indeed
what we would see in the world.
281
So far, they seem to be the case.
282
Yeah.
283
Something I'm wondering is that these
collisions that you're talking about, they
284
are happening millions of light -wears
away.
285
How are we even able to study them and
also maybe tell us what we already have
286
learned from them?
287
They're really quite rare events, the
types of collisions that we're seeing.
288
I mean, this is why there are millions,
hundreds of millions or even billions of
289
light years away is because they're so
rare in the universe that we need to look
290
out a very long way before we see one
often enough to make the detections often.
291
So they do happen in local galaxies as
well as the reason to think it wouldn't,
292
but it's just they're so rare.
293
I've seen one near black source.
294
Yeah.
295
Yes, they are remarkably energetic.
296
The amount of energy that is output as
gravitational waves when you've got, say,
297
two black holes coming together is
phenomenal.
298
For just that moment as they smash in
together, more energy, so the luminosity,
299
the amount of energy per unit time emitted
right at that peak is higher in
300
gravitational waves than if you were to
add up.
301
or the visible light from all the stars
that you could see in the universe.
302
So it's a phenomenal amount of energy just
over a very short way.
303
So yeah, we just need to be listening to
the universe to see these, to discover
304
these sources and find out what they're
trying to tell us.
305
The energy flux from these black hole
collisions, despite the fact that they're
306
hundreds of millions of light years away,
is actually comparable to the flux from
307
the full moon.
308
So the brightest object in the night sky,
309
is surpassed by gravitational wave
signals, except we can't see the
310
gravitational waves because they don't
interact very strongly with matter.
311
And it's only by building these incredibly
sensitive detectors to pick up their
312
effect on distances that we can still look
at.
313
Yeah, that's just fascinating to me that
we're even able to see...
314
like hear these waves in a way.
315
So, yeah, just to finally point home,
there's so much energy that you're
316
carrying away, but the effect is so tiny,
as Chris said, 10 to the minus 21, no
317
less.
318
Yeah.
319
If you think about how those two things
could be true at once, it's telling you
320
that it takes an enormous amount of energy
to produce a tiny distortion in space.
321
So it's very, very difficult to walk
space.
322
And that's...
323
the consequences of general malpractice.
324
Yeah.
325
And then, so I think now it's a good time
for you to tell us.
326
So maybe Christopher, you can tell us
that.
327
How do you use patient stats to extract as
much information as possible from these
328
tiny wave signals?
329
How is base useful in this field?
330
And how do you also actually do it?
331
Are you able to use any...
332
widespread open source packages or do you
have to write everything yourself?
333
How does that work concretely?
334
Yes, so for the type of sources we've been
seeing these binaries, we have predictions
335
for what the signal should look like.
336
So we have a template that is a function
of the parameters and we have a decent
337
understanding of the properties of our
noise.
338
So the data is a combination of the signal
plus some noise which you assume to be
339
stationary over the short time scales that
we're analyzing and characterized such
340
that the noise at individual frequencies
is uncorrelated.
341
So if you like, you get your data,
transform it to the frequency domain,
342
subtract out your template, you should be
just left with noise, which is Gaussian at
343
each frequency bin.
344
And so you have a lot of Gaussian
probabilities that you combine to get.
345
So that gives us our likelihood.
346
You map that out, you change your
parameters for your template.
347
evaluate that at another point in
parameter space, map that out with your
348
suitable prior, and you end up with your
posterior probability for a single event.
349
The number of parameters that we're
typically dealing with is something like
350
15 for typical binary.
351
Maybe that goes up to 17 when we add in a
couple of extra ones, a few more if we're
352
maybe looking at tests of general
relativity.
353
So it's enough that exploring the
parameter space can't be just done by
354
gridding it up and exploring it.
355
We generally use some kind of stochastic
sampling algorithm.
356
But it's not one of these problems, at
least yet, where we've got millions of
357
parameters and it's a really high
parameter space.
358
In terms of the algorithms that we use to
explore parameter space, we've got a long
359
history of using MCMC and nested sampling
for these.
360
And John's really the expert on this.
361
So, John, do want to say some more about?
362
We'll get to that, yeah.
363
Oh, you are done?
364
OK, perfect.
365
So yeah, John, maybe if you can tell us.
366
Yeah, maybe let's start with nested
sampling that you use a lot for your
367
inferences.
368
So can you talk about that, why that's
useful, and also why you end up using that
369
a lot in your work?
370
Which problem does that solve?
371
So nested sampling is an alternative to
MCMC.
372
I don't know if you're...
373
listeners will all have encountered it
before.
374
If you're a regular user of MCMC though,
it's definitely worth a look.
375
It was invented in 2006 -2007 by John
Scaling.
376
He was a physicist.
377
The idea is that you're actually trying to
evaluate the evidence, the normalization
378
constant of the posterior to allow you to
do model selection in a basic way.
379
But as a by -product, it can generate
samples from the Bistidia as well.
380
So this popped up around about the time
that I started a full stock position in
381
Birmingham and thought, well, why don't we
give it a go and apply it to the problem
382
of compact binaries.
383
So at that point, there was no off -the
-shelf package available to do this.
384
And so we had to create our own.
385
That was all coded up in C for so time.
386
It wasn't such a big thing.
387
There was thousands of lines of code and
all that.
388
But yeah, so the reason is that you might
prepare it for MCMC.
389
People were trying to solve the same
problem with parallel tempered MCMC.
390
The compact binary parameter space has a
fair amount of degeneracies, multiple
391
data, and in amongst those modes.
392
They make it difficult to sample the
waveforms are facilitated in a nonlinear
393
problem.
394
It can be quite complicated.
395
Getting a decent exploration of the prior
was proving to be difficult for the MCMC.
396
Hence the need for parallel tempering.
397
And this is something that works a little
bit differently because it starts off by
398
sampling the whole prior in the first
place.
399
So you know, say thousands of points,
they're called live points.
400
scatter them across the entire prior and
then compute the likelihood for every one
401
of those.
402
If you then eliminate the point that has
the lowest likelihood and replace it with
403
one that has the higher likelihood of the
lowest one, then people still have a
404
thousand points, so they will all have a
likelihood higher than the worst one.
405
And you can see that, roughly speaking,
the volume of that remaining set of points
406
will be about
407
999 thousandths of the original one just
by random large numbers.
408
And so if you repeat that process, always
replacing the point of the next iteration,
409
you'll have 999 thousandths of 999
thousandths of the original.
410
And so eventually you'll shrink in a
geometric fashion the volume that your
411
points are contained within.
412
And...
413
In doing so, you're walking uphill, you're
moving towards the peak of the posterior.
414
So, what I have seen to see it is
guaranteed to terminate once you have held
415
the climb up, which was a nice feature.
416
And it gives you the evidence for doing
multi -selection.
417
Once you've done the entire chain, you can
resample those points from the chain and
418
weight them according to the posterior to
produce either independent samples or
419
weighted.
420
posterior samples are to meet.
421
Yeah, so it's a really effective
algorithm.
422
I like it because it's reliable.
423
And as I say, your run is guaranteed to
finish.
424
It might take a long time, but it will get
there.
425
There are of course, places where it falls
down.
426
If you don't have an upline, you can end
up missing a mode.
427
The challenge is really how do you explore
that constrained prior distribution.
428
And so over the years, there have been
different approaches to doing that.
429
The one that I started, I was coding in
Oracle Struct, was using MCMC inside the
430
nested sampling.
431
So just do a little MCMC chain to draw the
next sample, which works fine, especially
432
because we already knew how to do MCMC's
for this problem quite well.
433
But other people have invented the
ellipsoidal multiness algorithm, was one
434
of the first very popular.
435
off -the -shelf solutions and that was
used also for gravitational waves.
436
These days there are more modern, I
packages that do everything you need,
437
either with MCMC or with side sampling or
more complicated things like normalizing
438
flows.
439
I should mention the Bowman or most of the
gravitational wave using dynasty, which is
440
next to sampling.
441
myself and the students, there's no force
with it.
442
That's the image that connects it
something with artificial intelligence
443
that attempts to use some machine learning
to accelerate this whole process.
444
Well, that sounds like fun.
445
Yeah, I'm definitely going to link to
Genesty.
446
So the package you're using right now to
do the NST sampling in the show notes and
447
If you have anything you can share on this
new package you're working on, for sure,
448
please add that to the channel.
449
These listeners will be very interested.
450
And maybe you want to add a bit more about
this project.
451
So how would you use machine learning in
this way to help you do the nested
452
sampling?
453
Yeah, I can say something about that.
454
It's a cool idea.
455
I mean, the...
456
Enabling technology for this is a tool
called the normalizing flow.
457
And I don't know if you've talked about it
in podcast before, but they have a way of
458
approximating complicated distributions
using single ones with a remapping of the
459
coordinate system.
460
So in that context, we were trying to make
a good fit to the jump proposal for the
461
sample, if you like, because that has to
evolve.
462
with the scale of the problem as the
nested sample proceeds.
463
The mode shrinks and it can shrink by a
factor of 10 to the 20 over the course of
464
the run.
465
So you're going to need something adaptive
to continue to have good efficiency.
466
So we took this normalizing flow technique
and applied it to this problem of fitting
467
the existing samples.
468
And then the advantage being that it
allows you to draw independent samples, a
469
bit like the ellipsoidal.
470
technique, but it doesn't require a fixed
shape.
471
So it's able to make more complicated
shapes for distribution.
472
Yeah, I'll pop the link in and people are
very welcome to give a go.
473
Yeah, for sure.
474
Yeah.
475
So folks give it a go, try it.
476
If you see issues, report them on the
GitHub, even better.
477
If you can do a PR, I'm sure John will
appreciate it.
478
And actually, so that could not be better
because I will refer people to episode 98
479
of the podcast where I talked with Maridu
Gabriel, who is one of the persons
480
developing these kinds of methods.
481
And we talked exactly about that.
482
Adaptive MCMC augmented with normalizing
flows.
483
And we...
484
talked in the episode about how it offers
a powerful approach, especially for
485
sampling multimodal distributions, how it
also scales the algorithm to higher
486
dimensions, how you can handle discrete
parameters, and how all these ongoing
487
challenges in the field.
488
So if you're interested in the nitty
gritty details of what John just
489
mentioned, I recommend listening to
episode 98 because, well, Marilou is
490
really a f***.
491
One of the persons developing all that
stuff.
492
Sounds super interesting Alex.
493
I'm amazed at the power of some of these
new techniques.
494
There's a revolution going on at the
moment in this area.
495
It's a good time to be involved.
496
Yeah, I know for sure.
497
I will link to that.
498
Also, Colin Carroll, who is one of the
PIMC developers, he also has a new
499
package, well, working on a new package
called Biox.
500
And I know that they implemented these
normalizing flow algorithm.
501
And so now you can use that in PyMC
directly through BIOX and to use that kind
502
of algorithm and handle your multi
-dimensional, multi -model distributions
503
more easily.
504
So I also link to that because it's
definitely super interesting if you have
505
lots of weird distributions.
506
Like that.
507
And Christopher, to come back to you, you
also mentioned that you guys do population
508
inferences.
509
And that's hierarchical models where you
use a bunch of observations to infer the
510
underlying distribution of the sources of
the signal, if I understood correctly.
511
So what does that look like?
512
What do you guys do here?
513
Yeah, so we do the calculation in a couple
of stages that we always run the parameter
514
estimation to get the events parameters
for just one signal of time first.
515
And so the result of that is a set of
posterior samples calculated with a
516
fiducial prior.
517
And what we want to do is then divide out
that prior, put in a population model, see
518
how well that fits.
519
So calculate the, I guess, the evidence.
520
under the assumption of a particular set
of hyperparameters.
521
And then we have an inference one level up
where we vary the population parameters,
522
the hyperparameters for the population
model, explore that to see what fits work.
523
So that really is starting to get the
astrophysics.
524
So looking at the distribution of masses,
are there more low mass black holes and
525
high mass black holes?
526
How does that scale?
527
Is there a little?
528
bumps in the distribution and things like
that.
529
So, yeah, it's next level up.
530
The likelihood isn't quite as expensive as
evaluating the waveforms, but we have some
531
data handling issues of reading in order
of the posterior samples.
532
And key to this is, as I alluded to, is
correcting for the selection effects so
533
that we need to account for the fact that
with our gravitational wave detectors, we
534
can preferentially see some sources over
other sources.
535
So if you were just to look at our
536
distribution of sources that we detect,
you'll see, hey, there are lots of 30
537
solar mass black holes, there aren't too
many 10 solar mass black holes, and if you
538
didn't know about our selection effects,
you can actually assume, okay, the
539
universe is full of 30 solar mass black
holes, and 10 solar mass ones are much
540
rarer.
541
Whereas because our detectors are more
sensitive to the high mass signals, those
542
are intrinsically louder, so we can see
them further away, we can see more of
543
them.
544
Once you correct for the selection
effects, you actually see it's the other
545
way around, there are many more
546
At least there should be many more 10
solar mass black holes than 30 solar mass
547
black holes.
548
And the fact we don't see so many 50 solar
mass black holes, 90 solar mass black
549
holes, tells you that the distribution
does drop off quite rapidly.
550
So this is a field that's growing quite
nicely as we get more and more detections.
551
Your uncertainties on the population
basically go as the square root of the
552
number of detections.
553
what we're seeing a lot of work on is what
does one assume for the population model.
554
So when we started off with, I guess,
following what is common in astronomy, we
555
put a power law through for the masses,
just infer the power law index basically
556
in the normalization for the overall rate
and see how that worked.
557
Then we like that's a bit simplistic.
558
Let's add in a couple more parameters.
559
Let's have
560
say a little peak, a Gaussian add on top
of that to get peak.
561
Let's say have two parallels with the
break, see how those fit.
562
Let's put in another peak.
563
And now people are looking at semi
-parametric models.
564
So OK, what if we add a spline on top of
that?
565
See how we can vary that.
566
Or what if we do something really
flexible, so allow a bunch of kernels to
567
come together and further the population
to get out of there?
568
So a lot of.
569
A lot of the work at the moment is trying
to see what is a good fit for the data and
570
then checking is this overly complex?
571
Are we overfitting?
572
Is there a little bump there?
573
Is that just because of a pass on
fluctuation that we've only seen so many
574
events?
575
So a small number of statistics means
there's a few more here and a few fewer
576
there.
577
Or is there actually some feature of the
underlying population, which may be a hint
578
to how stars are formed?
579
I think it's quite an interesting time at
the moment from this testing out models,
580
trying to determine do they fit the
observations quite well.
581
And I'm very excited for getting the
results of our upcoming observing runs
582
when we're having a much larger number of
detections and we'll really be able to
583
constrain the models to higher accuracy
and precision.
584
Yeah, so that's super interesting.
585
And so here to understand what you're
doing, it's like your...
586
hearing different sounds and you're trying
to infer not really what the sound is
587
about, but what is emitting that sound?
588
What is the source of that sound?
589
And the issue is that these sounds can be
emitted by a lot of entities and a lot of
590
these sources you don't really care about
because I know they are on earth, they are
591
like, but what you're interested in are
the sources.
592
outside, which are in space and which tell
you something about the universe, which
593
here would be mainly neutron stars and
black holes colliding.
594
How weird was that characterization?
595
Yes, I guess maybe a nice analogy might
be, imagine you have a room full of people
596
and you're trying to judge the composition
of the room.
597
And some of the people there, you have a
bunch of librarians who are very quiet.
598
And you have some heavy metal stars who
are very, very loud.
599
And so you've made your recording of the
audio in the room, and then you need to
600
try and reconstruct that.
601
OK, I can only hear one librarian.
602
But given that the librarians are very
quiet, there's probably a whole host of
603
other librarians who I just missed because
they're being too quiet.
604
and I can hear lots of electric guitars
going on, so I know there's some rock
605
stars here, but I know they're very loud
and easy.
606
I probably will have detected 100 % of
those, so correct for those bias from the
607
detection.
608
We're very fortunate actually in
gravitational wave detection that we can
609
calculate our selection effects.
610
It's quite easy for us to determine what
sources we can detect and what we can't.
611
This is a standing problem in astronomy
that you're
612
We only have one universe, so we need to
make sure we understand what we're seeing.
613
And you can know what you detect, but it's
very hard to know what you're not
614
detecting.
615
So a lot of astronomy is trying to correct
for these.
616
And if you have a telescope, that can be
very difficult because you've got to
617
calculate, OK, not just what did I see,
but what could I have seen?
618
So that would depend on where I was
pointing the telescope.
619
It would depend on the weather on a
particular day and how cloudy it was.
620
Whereas with our gravitational wave, it's
much simpler.
621
What we do is we can inject the
terminology we use.
622
We simulate signals, put those into our
data, run our detection pipelines on that,
623
and see what fraction of the signals that
we injected would we recovered and from
624
that work out.
625
As a function of source parameters, what
was the probability that something was
626
detected?
627
And then use that in renormalizing our
likelihood to establish.
628
Okay, how many of these sources should
have there have been given that we saw
629
this money?
630
Okay, it helps a lot that gravitational
waves are not blocked by anything in the
631
universe that we know about except for
other black holes But even then other
632
black holes tend to be very small So when
we are able to calculate exactly what the
633
source is doing it means that we've got a
very good idea of what we will see.
634
It doesn't really matter what's in the
entropy space.
635
The two veins of astronomy are dust and
magnetic fields, and gravitational waves
636
are just don't really care about any of
those two things.
637
Yeah, okay.
638
I see.
639
And that's actually a good thing.
640
Indeed, that's quite a luxury to be able
to compute your own selection bias.
641
That's pretty amazing.
642
Me, who've done a lot of political
science, you usually cannot do that, so
643
I'm very jealous.
644
And can you tell us actually where does
that noise come from?
645
Because it seems like you're saying there
is a lot of noise in your observations.
646
Thankfully, you are able to tame that
somewhat easily.
647
Can you tell us a bit more about that?
648
And John, it seems like you want to add
something about that.
649
Most of the noise, all the noise is not of
extraterrestrial origin.
650
It's coming from the detectors and coming
from the environment around the detectors.
651
So in order to understand that you have to
know a little bit about how to light over
652
a porp.
653
So imagine a giant in all shape, four
kilometres long, in bits of light, with
654
the letters at the ends of the arms
shining a laser into the coin, if like.
655
It gets split into two and sent down both
arms, bounces off them into the end and
656
then comes down.
657
and if they aren't the same length then
the light will constructively interfere or
658
destructively, I may have that wrongly
written.
659
The point is if they aren't at different
lengths or if they're changing lengths
660
then the pattern of the light that comes
out will change over time.
661
So we are really worried about anything
that can change that output of the laser
662
in the detector.
663
And so that could be due to the laser
itself.
664
All lasers have some noise in them.
665
So the lasers that they use in these
detectors are some of the most stable
666
lasers that you can use.
667
have been invented from scratch basically
for this one.
668
It could be the thermal motion of the
atoms in the matrix of the complex.
669
It would be better in that, simply having
a wide enough laser beam approaching the
670
whole surface of the metal, cancelling out
the mean motion to the low enough level to
671
get it ready.
672
But the laser also
673
You know, there's energy and that energy
fishes on the mirrors of radiation, which
674
causes the mirrors to move a little bit.
675
And now, think about the algorithms, the
laser energy is carried by photons, which
676
are ultimately quantum objects, so they
get off the radar distinctly.
677
Kind of raindrops on the roof, if you
imagine, or if you're in a tent, you get
678
raindrops of rain.
679
That's kind of what it's like.
680
The lasers are enormously hard.
681
still they are made of individual photons.
682
And so there's a shot noise associated
with them, just due to the statistical
683
fluctuation in the number of photons that
are writing per second.
684
Then we've got the environment as well,
which is especially dominant at low
685
frequencies.
686
So we can't sense anything below about 10
Hertz with these detectors that are above
687
the ground.
688
because of seismic motion.
689
Now we do have a lot of techniques to try
and screen the mirrors out in the motion
690
of the Earth.
691
They're hung on suspended optics, which
act as a natural filter to prevent ground
692
motion from propagating through to the
mirror.
693
But even so, we need to have active
oscillation systems as well.
694
And on top of all of that, even if you
manage to screen out all the mechanical
695
coupling,
696
There's unfortunately the gravitational
coupling that we can't spin out because we
697
actually want to measure gravity in the
first place.
698
So if you imagine a seismic wave as a
pressure wave in the rock, I mean, when
699
pressure is high, the rock is actually
compressed slightly.
700
And because it's compressed, it's denser
than average.
701
And because it's denser than average, it
exerts a gravitational pull on the mirrors
702
that tends to pull them along.
703
with the seismic waves.
704
So this tiny effect, I mean, you've
probably never even thought about it, but
705
it's there as a small gravitational
coupling of seismic waves to the detector.
706
And you can't really get around these
things tall on the earth.
707
And so that's why one of the challenges
that we're working on at the moment is
708
looking at sending a detector into space,
which is hopefully going to open up a
709
whole new range of...
710
objects for us to look at.
711
Yeah, thanks a lot, That's definitely
clear, and I didn't have, indeed, any idea
712
of all these sources of noise, which is
pretty incredible that we're able to
713
filter that out, knowing that already the
signals you're looking at are already so
714
weak.
715
So it feels pretty incredible to still be
able to do it, even though the signals are
716
weak.
717
and the result of noise.
718
It's really amazing the technology that is
required to do these experiments has been
719
developed decades and decades for people
to develop it and almost all aspects of
720
the detectors have to be invented for that
purpose.
721
There's very little off -the -shelf
technology and of course the spinoffs from
722
that then taken up in other areas but it's
the pure science that was driving the
723
development of the law.
724
Yeah, exactly.
725
It's like, it's not even as if the all the
engineering of these was already available
726
and you could just go on Amazon and buy
it, right?
727
You have like everything has to be
developed custom for these and you don't
728
even know if that's going to work before
you actually try it out.
729
So that's like all these endeavors are
absolutely incredible.
730
And so that makes me think and I think on
these Christopher, you will have stuff to
731
add.
732
Because, so if I understood correctly, all
these detectors that we have right now are
733
on Earth.
734
These gravitational waves detectors.
735
Hopefully, we'll be able to do a video
documentary on Learned Bay stats in one of
736
these detectors.
737
It's just some of the backstage I'm
telling to the listeners.
738
We'll see if that's possible.
739
But, so these detectors are on Earth.
740
If you go to space and were able to put
one of these detectors around the earth or
741
I don't know, in space floating somewhere,
I'm guessing that solves these problems,
742
even though there are other sources of
issues if you do that in space.
743
But if I understood correctly, the LISA
mission is space -based.
744
And so is that a way of doing that?
745
Can you tell us a bit more about that?
746
Christopher and...
747
Yeah, mainly tell us what the discoveries
will be with that.
748
Also the data analysis problems that will
engender, especially when it comes to the
749
size of the data, I'm guessing.
750
Yeah.
751
So Lisa's Space Space Gravitational Wave
mission, it's led by the European Space
752
Agency with NASA as a junior partner
there.
753
And the idea is we...
754
launch a constellation of satellites, so
three satellites that will orbit around
755
the Sun lagging behind the Earth in a
triangular formation and we bounce the
756
lasers between them to make the same sort
of measurements that we do for
757
gravitational waves but over a much larger
scale, so really massive arms.
758
So this is great because we can avoid the
ground -based noise that John mentioned
759
and this
760
is really good.
761
So for Lisa, we're not trying to see
exactly the same sources as with our
762
ground -based detectors, but we're trying
to look for lower frequencies.
763
So one of the things we've learned in
astronomy over the last century or so is
764
that each time you're observing the
universe in a new way, you discover new
765
things.
766
So we want to look at a different part of
the spectrum of gravitational waves.
767
So Lisa's most sensitive is the millihertz
range, so much lower frequencies.
768
And a much lower frequency gravitational
wave,
769
corresponds to a bigger source.
770
So these could be the same type of binary,
but just much further apart in that orbit,
771
so much earlier before they come in and
merge much further apart.
772
Or we could be looking at much more
massive objects, so massive black holes.
773
We believe at the center of every galaxy
is a massive black hole.
774
Our own galaxy has one about four million
solar masses, four million times the mass
775
of our sun.
776
And we think galaxies merge, and so the
massive black hole should merge.
777
And so we'd be able to see these out to a
much greater distance.
778
So Lisa's objective is to see what we can
observe in the gravitational wave sky at
779
these much lower frequencies.
780
And there's a whole host of different
sources.
781
So these massive black hole mergers we
should be able to see out across the
782
entire history of the universe.
783
We should be able to see regular stellar
mass black holes.
784
So black holes formed from.
785
stars at the end of their lives spiraling
into these supermassive black holes.
786
It's a topic I've studied quite a lot.
787
Those signals are extremely complicated.
788
The orbits they undergo are very
intricate, which is great if we observe
789
one because we can measure the parameters
to tiny, tiny precision, to one part in a
790
million, something like that.
791
But it's a huge pain from a data analysis
point of view because you've got to find
792
the part of parameter space where this is.
793
And we're also going to see
794
huge numbers of binaries in our own galaxy
of white dwarfs, maybe neutron -style
795
white dwarfs, so the wide binaries here.
796
And so the real data analysis problem for
LISA will be how to fit all of this
797
information all at once, because with our
ground -based detectors, at least at the
798
moment, we basically just see here's a
signal and then here's another signal.
799
So you can analyze each signal in
isolation.
800
With Lisa, you cannot you see everything
all at time.
801
Some of these lights, they don't
supermassive black hole mergers might be
802
quite short to compare to place a
localized in time, but they will still be
803
overlapping these long lives.
804
So the the in spiraling objects or the
very wide bindings will basically be there
805
for the entire mission or a large fraction
of the mission.
806
So to analyze the data, you need to fit
everything or this is what we call a
807
global fit problem.
808
And you
809
So you potentially have hundreds of
thousands of sources, each with a dozen
810
parameters or so, maybe less than simpler
sources.
811
But you've got to do all of these all at
the same time.
812
And it potentially does matter how you do
this, because things like the massive
813
black hole binaries are extremely loud, so
signal -to -noise ratios of thousands.
814
So if you get that wrong by just a little
percentage,
815
residual power in your data stream would
be enough to bias your measurements of the
816
quieter signals underneath.
817
So this is a huge, I think possibly the
most complicated data analysis problem in
818
astronomy and we're just starting to
figure out how we're going to tackle this.
819
So yeah, space -based detectors I think
extremely exciting, a whole host of new
820
sources that we can see, a new host of
astrophysics that we can unlock through
821
these observations, but also
822
some extremely complicated data analysis
challenges that need to be tackled and
823
solved before the mission launches in the
2030s.
824
And what's the timeline on this mission?
825
Are we close to launch?
826
Where are things right now?
827
So just in the last couple of months, the
mission was approved by ESA.
828
So that's them looking at the designs and
going, OK, we think we can build this.
829
And now the serious work on putting it
together comes.
830
So it's due to launch in the 2030s,
exactly when that be, I'm sure.
831
People are very confident on when it will
be, but we know space -based missions are
832
hard.
833
So it might, maybe, maybe it's a little
early to say exactly what date it will
834
launch.
835
But it will go up and then there'll be a
little period of commissioning and then it
836
will start observing.
837
So in the late 2030s, we should hopefully
get the observations from that.
838
So the current timeline, 2035 for launch,
which I guess is...
839
Good news to any of your listeners who are
inspired by the problems that we're
840
talking about and think this is really
cool and think that maybe they'd like to
841
tackle these problems.
842
There's certainly enough time to go out,
get a degree, start a PhD in the field
843
before we get the real data.
844
Yeah, for sure.
845
Exactly.
846
And also, historically, these kind of huge
missions tend to take a bit of delay.
847
So, you know, like...
848
You can start your PhD on this.
849
I mean, that's better to launch later than
to launch on time, but have a mission that
850
fails, right?
851
Yes.
852
We're talking a billion euro cost of these
things.
853
So you definitely don't want to explode on
the launch pad.
854
Exactly.
855
Way better to take a few more months and
do some double checks than just launch
856
because we said we would launch on that
arbitrary date.
857
Yeah, the space agencies do take these
things.
858
It's been fascinating seeing the order,
the things that needed to be rubber
859
stamped to get the approval for the
mission.
860
So very good work people getting that
done.
861
So there are also other proposed space
-based missions, some potential ones in
862
China.
863
There's a potential follow -up mission, I
guess, slightly in the future, maybe in
864
Japan that's been proposed for a few
years.
865
status of these, I guess, it's difficult
getting the funding for these things.
866
So I think it's an exciting time in the
field.
867
Hopefully we'll expand the range of
gravitational waves we can detect and
868
that'll be great.
869
Yeah, yeah, for sure.
870
And I mean, that must be...
871
So I don't know how directly involved you
are on these, Lounch, but I'm guessing
872
that if you're still working on these
when...
873
the mission launches, I'm pretty sure the
day of the launch, you will be pretty
874
nervous and excited.
875
Have you already lived that actually, or
would that be new to you?
876
So I mean, the closest analogy would have
been there was a technology mission to
877
test some of the key components of Lisa
called Lisa Pathfinder that went up a few
878
years ago, an extremely successful
mission.
879
And so watching that from the sidelines,
my PhD was on LISA.
880
If this mission didn't work, then there'd
be no LISA mission.
881
So all my PhD work would be in vain.
882
But thankfully, it worked very well and
worked better than what was hoped for, in
883
fact.
884
So that was great.
885
And I guess that's a real testament to the
experiment, as saying I was feeling
886
worried because it was my PhD work.
887
But there really people in the field who
have spent their entire careers working on
888
this technology, you know, multiple
decades.
889
So it's all.
890
Yeah, real testament to their
determination, I guess, their vision going
891
into a field right at the beginning before
anything worked to look at these things.
892
It's also honestly quite remarkable that
we somehow managed to convince the funding
893
agencies to fund these things for so long
before there would be scientific returns.
894
So, yeah, we're extremely grateful that
they had the forethought and the patience
895
to invest in something so long before it
would give returns.
896
Yeah, definitely.
897
Yeah, that must be absolutely fascinating.
898
John, anything you want to add on that?
899
I think Christopher is doing a great
overview of WISA, which indeed will be an
900
enormous challenge on the ground.
901
There are also plans to take things
forward into the 2030s and beyond.
902
Currently, there are two major...
903
detectors in the kind of scoping design
stage.
904
One is led by the Europeans called the
Einstein Telescope and the other one is
905
led by the US called Cosmic Explorer.
906
They're taking different approaches.
907
They're both going by detectors.
908
The challenge there is to lower the noise
floor.
909
So giving them a sort of order of
magnitude improvement in the range that
910
you can see things to, which translates to
911
thousand -fold increase in the volume that
you can see things to, more or less.
912
At these kinds of distances, you do
actually have to worry about the size of
913
the universe, getting in the way of these
calculations.
914
But yeah, these new experiments will
require a new infrastructure.
915
So they're also going to require a new
batch of experiments from national,
916
indeed, European land.
917
best friend.
918
A lot of the data analysis challenges for
those are kind of similar to the ones that
919
we're tackling with the current generation
of ground -based detectors.
920
But the major difference is that the
signals would be much longer because the
921
low frequency end is really the target for
improvement.
922
I think that's the way that the binaries
chop.
923
I mean, okay, I told you that they sort of
make this characteristic, whoop, type
924
noise.
925
Maybe you can find a sample.
926
and pluck out my pale imitation.
927
The lower in frequency you start, the
longer the signal will be.
928
That multiplies the amount of data that
you have to analyze, which with a Bayesian
929
problem can be a bit challenging.
930
If you're doing many millions of light
-weighting evaluations, you don't want
931
each light -weighting evaluation to be
expensive.
932
And also the signal -to -noise ratio will
be huge.
933
Least effects are 10 higher.
934
So you will run into problems with our
uncertainties on the nature of the
935
sources.
936
So the models that we have are very good
theoretical models at the moment and
937
they're good enough for the current
generation of detectors, but they will
938
break down once observations become good
enough.
939
They will probably show the crops in
theories, which I should say is probably
940
not a fundamental part in the theory.
941
I think most people probably would put
their money on general relativity being
942
correct.
943
The problem is that there is a translation
layer between general relativity and the
944
types of temperament we can use it that
requires approximations and shortcuts and
945
models to be created.
946
So there's challenges with modeling and
balance that are quite difficult to
947
overcome and people are searching that as
well at the moment.
948
Yeah, fantastic.
949
Thanks a lot, guys.
950
That's really fantastic to have all these
overviews of the missions.
951
And actually, I'm wondering, so with all
that work that you've been doing, all
952
these studies that you've been talking
about since we started recording, we've
953
been able to study actually what
954
we want to do, right?
955
So study the astrophysics of black holes
and also some tests of general relativity,
956
as you were saying, Christopher.
957
Can you tell us about that and mainly what
are the current frontiers on those fronts?
958
What are we trying to learn with the
current missions?
959
That's a big question.
960
So general relativity, I guess, we really
want to find somewhere where it doesn't
961
work.
962
So for the point of view of understanding
gravity, there's this tension within
963
physics that how do you reconcile general
relativity with quantum theory?
964
And that is rather tricky and the whole
host of different theoretical frameworks
965
to try and reconcile this.
966
But we don't know for certain what the
answer is.
967
And finding some hint where general
relativity breaks down would give a
968
pointer in the right direction.
969
Of course, finding a place where general
relativity breaks down is very difficult.
970
The place where I think it makes sense to
look most is the most extreme environment.
971
So where is gravity strongest?
972
Where is the spacetime most dynamical?
973
Where do things change the quickest?
974
So black hole mergers, I think, are
really, and the gravitational wave
975
signals, they admit, are the
976
best place to look for that.
977
So that's why we're looking there.
978
And what we'd really love to find is some
deviation from general relativity that we
979
could actually be certain is a deviation
from general relativity and not just a
980
noise artifact.
981
So I think we're pursuing a whole host of
different things to look for deviations
982
there.
983
On the astrophysics point of view, there's
just so much we don't know about the
984
progenitors of these sources.
985
So how do
986
we end up with black holes and neutron
stars.
987
So stars are pretty important in
astronomy.
988
Exactly how they work is kind of
complicated.
989
So there's a lot of uncertainties in that.
990
And I think it's really quite remarkable
how rapidly the field has progressed.
991
So back in 2015, before we made our first
detection, it wasn't at all certain that
992
we would find pairs of black holes
orbiting each other and merging.
993
We knew there would be neutron stars.
994
But we didn't know they're black holes
because we'd never seen them.
995
They're really hard to see other than
gravitational waves.
996
That's kind of why we built the
gravitational wave detectors.
997
But we hadn't seen any of them.
998
So our first detection confirmed, yes,
they exist.
999
And they exist in sufficient numbers that
we can actually detect them.
Speaker:
And then the follow up was when we
measured the masses, they were about 30
Speaker:
times the mass of our sun.
Speaker:
We'd never seen black holes in that mass
range before.
Speaker:
We now know, yep, there's quite a few of
them.
Speaker:
But whether you can form black holes that
big,
Speaker:
tells you something about the way that
stars live, how much mass they lose
Speaker:
through their lifetime.
Speaker:
So that's a key uncertainty that we don't
really understand about how stars evolve.
Speaker:
So now, as we're building up statistics,
really teasing out the details of the mass
Speaker:
distribution, what is the biggest black
hole that you can build?
Speaker:
Currently, we know there are these black
holes that form from stars collapsing.
Speaker:
And we know there are these massive stars,
massive black holes, millions of solar
Speaker:
masses.
Speaker:
lightest ones, hundreds of thousands, tens
of thousands.
Speaker:
But we don't know, is there a continuous
distribution of black holes in between?
Speaker:
So are there hundreds of thousands of mass
black holes?
Speaker:
So that's one of the key things to figure
out.
Speaker:
Is there a key thing?
Speaker:
Where do these big, really big, massive
black holes come from?
Speaker:
And how do stars evolve?
Speaker:
The details of all the different ways that
you could end up with massive black holes
Speaker:
that people theorized?
Speaker:
Which ones are correct?
Speaker:
In what ratio out there?
Speaker:
And then I guess one...
Speaker:
One additional key thing, we talked about
black holes in nature gravity.
Speaker:
We've talked about how you form black
holes in neutron stars.
Speaker:
But there's also what neutron stars are
really made of.
Speaker:
So neutron stars, from the name you might
suggest, OK, they're made of very neutron
Speaker:
-rich matter.
Speaker:
But actually, what happens inside the core
of a neutron star, we get a whole host of
Speaker:
different phase changes, really quite
exotic matter going on that we can't hope
Speaker:
to replicate in the lab here on Earth.
Speaker:
So we really don't know.
Speaker:
this behaves.
Speaker:
If we did, that would be really
informative for understanding the dynamics
Speaker:
of the particles that make those.
Speaker:
So by making measurements of the neutron
stars we observe, how much they stretch
Speaker:
and squeeze, we can hopefully get some
constraints on what neutron stars are made
Speaker:
of, which would be an exciting frontier
there.
Speaker:
John?
Speaker:
One thing that I think we can zoom out
from looking at the individual black holes
Speaker:
and neutron stars and
Speaker:
Still with the theme of trying to
understand gravity is on the other scale
Speaker:
is cosmology, the very, very largest
scales, how is the universe evolving over
Speaker:
time?
Speaker:
Hopefully with the current generation and
the next generation, we'll be able to do
Speaker:
cosmology in a completely different way
than what we have done up until now.
Speaker:
By looking at the gravitational wave
signal, so those...
Speaker:
properties of those signals, the fact that
we know exactly what they look like, their
Speaker:
amplitude and how it would case with
distance means that they can be used as an
Speaker:
independent co -coxmology.
Speaker:
Now we've already done this with the
prying intrastar signal and with black
Speaker:
holes that we've seen up to now,
relatively low numbers of sources such
Speaker:
that the constraints that we're able to
cook are not yet competitive with the best
Speaker:
constraints that we can get from other
techniques.
Speaker:
But going forward, as the numbers improve,
as the SNRs and the applies ratio
Speaker:
improves, this is going to get better and
better over time.
Speaker:
And so even if we don't see anything on
the scale of the individual black holes,
Speaker:
if this agrees with general relativity, it
could still help us en masse to pin down
Speaker:
what's going on with cosmology, where
there are many things that we don't
Speaker:
understand, including discrepancies in the
existing constraints we have.
Speaker:
No one.
Speaker:
And I'm curious, among all of these
burning issues, burning questions, if you
Speaker:
could choose one that you're sure you're
going to get the answer to before you die,
Speaker:
what would it be?
Speaker:
I don't know how long I'm going to live,
but the thing that really motivates me is
Speaker:
trying to understand whether the black
holes that we're seeing really are the
Speaker:
things that you can write down with pencil
and paper when you're teaching people
Speaker:
general relativity, or are they more
complicated than that in reality?
Speaker:
I think if there was one problem I have to
choose in this field, that would be the
Speaker:
one that I found the most interesting.
Speaker:
I think I'd really like to know the answer
to that one as well.
Speaker:
I think that might be one of the most
challenging to actually get the solution
Speaker:
to.
Speaker:
The best way to answer it might be to
travel into a black hole.
Speaker:
But then the question of whether you
observe anything before you die becomes
Speaker:
rather technical.
Speaker:
Yeah.
Speaker:
Certainly something not advised for your
listeners to give that a go.
Speaker:
Yeah, I am not sure it would end up like
Matthew McConaughey in The
Speaker:
What's the movie?
Speaker:
You know that?
Speaker:
Interstellar.
Speaker:
So Kip Thorne is one of the founders of
LIGO.
Speaker:
One of the recipients of the Nobel Prize
for Gravitational Analytics.
Speaker:
He's behind Interstellar.
Speaker:
So he advised on a lot of it.
Speaker:
Yeah, the bit at the end is not backed up
by science.
Speaker:
For sure.
Speaker:
At least for now.
Speaker:
They originally were going to have the
wormhole thing that opens up in
Speaker:
Interstellar.
Speaker:
They're going to have that detected with
gravitational waves at LIGO.
Speaker:
Unfortunately, Christopher Nolan cut that
bit.
Speaker:
Oh, that's a shame.
Speaker:
It wasn't in the film.
Speaker:
Maybe that would be for Interstellar 2.
Speaker:
We don't know.
Speaker:
So guys, thanks a lot.
Speaker:
I've already taken a lot of your time.
Speaker:
And I still have a good talk for you.
Speaker:
hours because this is really really
fascinating but it's time to call it a
Speaker:
show before that though as usual i'm gonna
ask you the the two questions i ask every
Speaker:
guest at the end of the show first one if
you had unlimited time and resources which
Speaker:
problem would you try to solve um who
wants to start
Speaker:
I think if you're really serious about the
unlimited time resources, then the most
Speaker:
pressing problem I think would be nothing
to do with adaptation waves, but it's more
Speaker:
to do with the climate breakdown.
Speaker:
So if you want an honest answer, that's my
answer, is solve climate change.
Speaker:
That's a very popular answer.
Speaker:
Get nuclear fusion working.
Speaker:
That would be very nice.
Speaker:
In our field with infinite resources, I
tackle the quantum theory of gravity and
Speaker:
get the evidence for that.
Speaker:
Would be nice.
Speaker:
Yeah, definitely.
Speaker:
That is a great answer.
Speaker:
And I think also some people answered
that.
Speaker:
So you're in good company, Christophe.
Speaker:
And second question, if you could have
dinner with any great scientific mind
Speaker:
dead, alive or fictional, who would it be?
Speaker:
Maybe Chris, the only answer for, uh,
dead, I think for this podcast, and James
Speaker:
would be my choice.
Speaker:
You may know him if you're a Bayesian.
Speaker:
Yeah.
Speaker:
Um, I think he would be very good dinner
company.
Speaker:
Um, his textbook was one of the formative
influences on me as a young Bayesian.
Speaker:
Yeah.
Speaker:
Yeah.
Speaker:
Yeah, for sure.
Speaker:
And, uh, there is a, there is a really
great, uh, YouTube.
Speaker:
series playlist by Aubrey Clayton, who was
here on episode 51.
Speaker:
So Aubrey Clayton wrote a book called
Bernoulli's Fallacy, The Crisis of Modern
Speaker:
Science.
Speaker:
Really interesting book.
Speaker:
I'll link to the episode and also to his
YouTube series where he goes through E .T.
Speaker:
Jane's book, Probability Theory, I think
it's called.
Speaker:
which is a really great book, also really
well written and already goes through its
Speaker:
chapters and explain the different ideas
and so on.
Speaker:
So that's also a very fun YouTube playlist
if you want I'm definitely going to go and
Speaker:
look that up.
Speaker:
Awesome, yeah.
Speaker:
I'll send that your way.
Speaker:
And Christopher?
Speaker:
One of my favorite books, yeah.
Speaker:
I don't know, I think I might be somewhat
boring and just go for Einstein for the...
Speaker:
of both gravity, I think he'd like to know
what we're up to.
Speaker:
And also just to see what, you know, his
thoughts were being about being such a
Speaker:
public intellectual and what it was like
being that would be being cool.
Speaker:
I could invite a guest might be
interesting to get Newton along as well,
Speaker:
and see what they think about gravity.
Speaker:
But I think that would be quite awkward in
a conversation, I get the feeling, not the
Speaker:
socially the most interactive.
Speaker:
Yeah, yeah.
Speaker:
Do you think Einstein would accept at that
point the, like all the advances in, like
Speaker:
all the ramifications of actually general
relativity and so on and the crazy
Speaker:
predictions that that was making and in
the end, most of them, like for now, at
Speaker:
least were true, but at the end of his
career, he was not really accepting that.
Speaker:
Do you think he would accept that now?
Speaker:
I think he would accept the general
relativity and he would be delighted to
Speaker:
find that we've seen some of the effects
that he never thought he observed.
Speaker:
And again, he himself knew the general
relativity couldn't be the final answer to
Speaker:
the correction of gravity.
Speaker:
So he'd probably also be interested to
know how we've seen any signs of it
Speaker:
breaking down.
Speaker:
And I think the stuff that motivated him
towards the end of his career is
Speaker:
probably...
Speaker:
still what's motivating a lot of people.
Speaker:
Well, if you are invited to such a dinner,
please let me know and I will gladly come.
Speaker:
Awesome guys.
Speaker:
I think it's time to call it a show.
Speaker:
You've been wonderful.
Speaker:
Thanks a lot for taking so much time.
Speaker:
As usual, I will put resources and a link
to your websites in the show notes for
Speaker:
those who want to dig deeper.
Speaker:
The show notes are huge for this episode,
I can already warn listeners.
Speaker:
So lots of things to look at.
Speaker:
And well, thank you again, Chris and John
for taking the time and being on this
Speaker:
show.
Speaker:
Thank you very much.
Speaker:
I may put in one thing that your listeners
might like.
Speaker:
They're interested in trying gravitational
wave data analysis.
Speaker:
Data are public.
Speaker:
They can look up the Gravitational Wave
Open Science Center, download the data
Speaker:
there.
Speaker:
Also, they'll find links to tutorials.
Speaker:
There are workshops held fairly regularly
that they can maybe sign up to to get some
Speaker:
data analysis experience.
Speaker:
And there's a whole list of open source
packages for gravitational wave data
Speaker:
analysis linked from those so they can go
and have a look at themselves.
Speaker:
Yeah, this is indeed a very good ad.
Speaker:
Thank you very much, Christopher.
Speaker:
I actually already put these links in the
show notes and forgot to mention them.
Speaker:
So thank you very much.
Speaker:
Because we're all very dedicated to open
source and open source here.
Speaker:
So if any of the listeners are interested
in that, like how these things are done,
Speaker:
You have all the packages we've mentioned
in the show notes, but also the open
Speaker:
source and open science efforts from your
collaborations, Christopher and John.
Speaker:
So definitely take a look at the show
notes.
Speaker:
Everything is in there.
Speaker:
Thank you guys.
Speaker:
And well, you can come back on the podcast
any...
Speaker:
Any time, hopefully around 2034 to talk
about Lysa and the space -based mission.
Speaker:
I'll put it in my calendar.