Talking About Dark Matter - Sixty Symbols

0:00 Professor say, let's go.

0:02 What would you like to regale me with today?

0:04 What are we talking about?

0:05 It's uh it's it's as a result of a conversation I've had recently

0:09 with a very famous experimental physicist in Glasgow called Jim Hough, in fact,

0:15 Professor Sir James Hough, who has been in charge of a group there which

0:19 is responsible basically for the mirrors that go on LIGO,

0:22 the interferometer that's measuring gravitational waves.

0:26 And without those mirrors and the the precision of those mirrors,

0:30 we wouldn't have detected anything.

0:31 So, we were chatting and he was telling me about um Lord Kelvin and and that he

0:38 was going to try and get a plaque for Lord Kelvin where he lived in Glasgow.

0:42 He was a professor in Glasgow.

0:45 And he said Kelvin was amazing and he did all sorts of thing

0:47 including back in 1904 coming up with the idea of dark matter.

0:52 And we don't associate dark matter A with Lord Kelvin, I don't.

0:55 We'd normally associate it with a guy called

0:57 Fritz Zwicky who came up with it in 1933.

1:01 And here's Jim telling me that Lord Kelvin

1:04 who's famous for his work on thermodynamics, right?

1:06 Kelvin.

1:07 Zero Kelvin is named after Kelvin, the temperature.

1:10 So, I was amazed and I thought I'd better find out a little bit about this.

1:14 And indeed, it's not dark matter as we think of it today,

1:18 which is a totally new particle that's nothing to do

1:21 with the particles that you and I are made of.

1:23 But he did come up with the realization that there

1:26 could be something within our galaxy that we couldn't see.

1:28 He argued we needed it and he called it effectively dark matter.

1:32 And the the the the technique he used to come up

1:36 with it is a technique that was then adopted by people like Zwicky.

1:40 So, you could in some sense indeed say that that Lord

1:44 Kelvin in 1901 to 1904 would came up with the idea

1:49 of that that there's these extra matter in the universe

1:52 that we can't see and that so it's dark matter.

1:56 He was born in 1824.

1:58 He died in 1907.

2:00 So, at the end of the 19th century, right?

2:03 We still didn't know the universe had had galaxies other than our own.

2:07 We could see the Andromeda galaxy.

2:08 There were these fuzzy blobs,

2:09 but many people thought they were actually within the Milky Way.

2:13 And at the turn of the century,

2:15 they were beginning to see evidence of the stars.

2:17 They could track the stars across the sky

2:20 and they could see them moving with velocities.

2:22 And they were these velocities were about 20, 50,

2:27 of up to 100 km a second that they'd see them going.

2:30 They'd see them going across.

2:31 Doppler shifts was in its infancy and they

2:33 were beginning to see evidence of the stars

2:35 moving away from us in on radial directions with the same sort of velocities.

2:39 And so, he asked this question.

2:41 He said, well, okay.

2:43 Are these a sensible type of speeds?

2:46 I mean, this is what's remarkable to think about

2:48 the many of these scientists that they they you know,

2:50 he's famous for his work on on thermodynamics.

2:54 He's famous for his work on engineering.

2:56 And here he was turning his mind to stars moving across the sky.

3:00 So, he he he did a calculation.

3:03 The calculation was motivated by his love

3:05 of thermodynamics because in thermodynamics,

3:08 he'd consider particles and particles moving.

3:10 And so, he said, well, let's imagine our galaxy.

3:13 It's made up of stars.

3:14 I'll treat the stars as molecules.

3:16 And I'll say that they're evenly distributed.

3:19 So, the density of the galaxy is uniform.

3:22 And then I'll say that they start with sort of zero velocity.

3:25 I'll just say they start like a might glass and then I'll ask,

3:29 what happens to them?

3:30 Well, they're being attracted by gravity.

3:32 So, they begin to move.

3:33 And and what he did he did he worked out was what

3:35 would be the typical velocity that you would expect these stars to have.

3:40 And so, he was finding that in order to account for the the fact

3:46 that you see velocities of between 20 to 100 km a second,

3:51 he needed of order a billion stars to be

3:56 within what the the the the region they could see.

3:59 And the region they could see was about a kiloparsec, about 3,000 light years.

4:03 So, you consider a sphere of about 3,000 light years.

4:07 You you put all the stars uniformly in that sphere and you just let them evolve

4:12 under under gravitational pull and they sort

4:15 of move through each other and back and forth.

4:18 And and he was he said,

4:20 if you're going to get velocities that are of what we see,

4:23 then he would have needed about a billion stars.

4:27 Well, at the time, they only saw about 10, 20 million stars.

4:33 He needed a billion stars.

4:35 And so, he said, if these the if these objects are moving

4:39 with this velocity and the only stars in there are the ones we see,

4:44 then they're moving too quickly.

4:46 The gravity due to say the 50 million that you

4:49 could see won't be enough to stop the stars shooting out.

4:52 And so, the Milky Way will just break up.

4:54 But it hasn't broken up.

4:55 There it is.

4:55 And so, he said, therefore, one way of accounting for this is there must be

5:00 matter out there in the Milky Way that we can't see.

5:04 So, it's dark matter.

5:06 And so, this was the first time somebody had linked

5:10 the idea of there being something

5:11 dark that could still interact gravitationally.

5:14 Apply the brakes.

5:14 To apply the brakes.

5:15 It didn't need to be lit up to be affecting something gravitationally.

5:19 Now, he didn't think of it as dark matter as we currently think of dark matter,

5:23 which is a brand new type of particle that we haven't found yet.

5:27 He thought of it maybe there were stars that had sort of burnt out and so,

5:32 they'd just gone too dim.

5:33 There might be rogue he called them rogue planets that are there,

5:36 just massive planets that we just can't see.

5:39 Other things that are just could be made up of the stuff that we're

5:42 used to, but that we just can't see cuz they're not lighting up.

5:46 But he did another really important thing in doing this calculation.

5:49 The principle he used was basically consist was energy,

5:52 energy conservation in that he said, if a galaxy is to be stable,

5:57 then the kinetic energy of the stars of the stars moving,

6:00 that kinetic energy must be less than the binding energy due to gravity.

6:05 And so, what you equate is the kinetic

6:08 energy of the stars with the gravitational potential energy.

6:11 That's giving you the binding energy.

6:12 That relationship which he used is actually known as the virial theorem.

6:17 And that's what people like Zwicky were using that you need to have

6:21 this sort of equality between the kinetic energy and the potential energy.

6:25 And that was crucial to his calculation and that's what gave him his bounds.

6:30 And so, even though the the actual details um are not right in the you know,

6:36 as as as time went on, telescopes got better, we realized that for example,

6:42 he was understandably looking at stars that were

6:44 nearer to to us than further away.

6:46 So, their results were biased by that.

6:49 He could only see out to about a kiloparsec.

6:51 Well, it goes much further for the size of a galaxy.

6:54 But the principle of this equipartition of the energy between

6:57 the kinetic energy and the potential energy is still there.

7:00 And that was what was used by Zwicky.

7:02 So, he wrote this up in 1901.

7:04 It's a Nature article in which he talked about these that seem to be

7:08 going too quickly compared to what kinetic

7:11 theory would tell you they should be doing.

7:13 The amount that things were out by, the mass

7:16 of the darkness that he required for things to work,

7:19 presumably was different from what it is now that Yeah, that's right.

7:22 So, for example, he was he did do one interesting thing.

7:26 So, he said he needed about a billion, right?

7:28 To to to to account for the the velocities and In fact, what is it?

7:33 How much do we It's about 100 billion, 200 billion, right?

7:36 So, he's out by a factor of 10.

7:37 And in fact, he had done he he did something else though.

7:40 He he sort of tried to get an an upper bound.

7:42 He said, imagine it's 10 billion, I think is what he did.

7:45 And he said, if it's 10 billion,

7:47 then then the velocities will will just be too big

7:50 and they and it won't it won't won't have worked.

7:52 And so, he's he he managed to sort of say, well,

7:55 okay, it's going to be of order a billion or so.

7:57 And in doing so, he put a bound on on the size of the galaxy,

8:00 but but it turns out, you know, that's just not quite right.

8:03 It's order of 100 billion.

8:04 The reason it's order of 100 billion is that we've got all this dark matter.

8:08 What has changed for us to know that it's not just a bunch of burnt

8:12 out stars and rocks causing it and it

8:14 is in fact some exotic undiscovered particle.

8:17 What has changed that has eliminated that as a possibility?

8:21 Yeah, well, that's a really good question.

8:23 Cosmology has changed, I suppose.

8:25 Cosmology has emerged,

8:27 which means that we now need to understand not just a single galaxy,

8:31 but the expansion of you know, the role of all the galaxies.

8:35 So, that means we now need to understand

8:36 the matter that's not just within one galaxy, but within lots of galaxies.

8:41 And in particular, we then need to understand

8:43 the motion of one galaxy relative to another.

8:45 Galaxies are sort of not just randomly distributed.

8:49 They they sort of cluster together.

8:50 And so, now rather than being kiloparsecs,

8:52 thousands of parsecs apart, they're megaparsecs, like millions of parsecs apart.

8:57 And yet they're moving relative to one another.

9:00 And the it's known that the luminous amounts of matter

9:03 matter there wouldn't be enough to account for that.

9:07 Not only that, what you can because the universe is evolving

9:10 and it went through a radiation era into a matter dominated era,

9:14 there's a an epoch called nucleosynthesis.

9:17 Nucleosynthesis is when the first nuclei form.

9:20 The the proton connects a proton forms, for example.

9:24 That's the nucleus of a of a hydrogen atom.

9:27 From that epoch, you can constrain how much luminous material,

9:32 baryonic material there must be in the universe.

9:35 And that's the thing that tells you there clearly isn't enough of that.

9:39 Remember, he he was wanting to use that.

9:41 He was calling them dead stars and boulders and things.

9:44 Boulders and things.

9:44 Things you and I know of.

9:46 So, it's known that that isn't enough to give

9:48 me the motion of the clusters of galaxies.

9:50 And that's what Zwicky was measuring.

9:52 He was using this idea of the virial theorem again to say,

9:55 why are the galaxies sort of moving

9:57 relative to one another with these large velocities?

9:59 Why are they not shooting by?" Because the velocities are

10:02 too big compared to the gravitational pull of the luminous matter.

10:06 And he then said, "Well,

10:07 there must be something else." He called it dark matter.

10:09 But it's known from nuclear synthesis it can't be the baryonic matter,

10:13 so it must be something new.

10:14 And that that is what's changed really.

10:16 So, just to make sure I understand,

10:18 the reason we know it's not boulders and dead stars and things

10:21 like that is not that we would have seen them by now,

10:24 it's that we know we couldn't have formed enough of them.

10:27 Like we know enough about the formation

10:28 of matter that we know we couldn't make them.

10:29 we know we know enough about how much matter there can

10:32 be in the universe as a whole to know that the density

10:35 of matter that you require is not enough for for for the clusters

10:38 of galaxies is not enough to give me to give me that.

10:42 There was one thing that maybe I just add about Kelvin.

10:45 You know, he was a pioneer of the kinetic theory of gases,

10:48 you know, how gases move with respect to one another.

10:50 From that, he was a pioneer in understanding the idea of entropy,

10:53 the second law of entropy.

10:55 He's the one that said,

10:57 "We can actually use temperature as a way of talking about energies."

11:01 And it's uh he's the one that said we can have an absolute temperature.

11:05 And that's where the Kelvin is,

11:06 zero Kelvin is your absolute zero for temperature.

11:10 So, he did all of this.

11:11 But then it turned out he also did

11:13 a whole load of stuff um from the engineering side.

11:16 So, for example, he was a big player

11:19 in the laying of electrical lines through to the US.

11:23 And in particular, he developed a way of controlling

11:27 the distortion of signals going along the cables.

11:29 And he worked out ways of of making sure the signals propagated.

11:33 But he was extremely smart and canny.

11:36 And he So, he patented stuff like this.

11:39 And so, he became super super wealthy out of all of this.

11:43 So, he he became, you know,

11:45 he he bought mansions in in up in Glasgow and the way he had his family.

11:49 So, he was just a multi-talented guy, but also a very on the ball.

11:55 [laughter]

11:56 of the total energy density in the universe is made of stuff that we don't know.

12:03 Well, it it's dark, obviously.

12:04 It's appropriate.

12:05 It's chocolate.

12:06 You know, they they they go around.

12:08 And he was looking at the speed of rotation

12:11 as you move away from the center of the galaxy.

12:13 So, he'd pick some object that was emitting light

12:15 and he'd look at how rapidly it was going around.