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← 18. Hubble's Law and the Big Bang (cont.)

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  1. Professor Charles
    Bailyn: We've been talking
  2. about the expansion of the
    Universe and in answer--I want
  3. to follow up on something I said
    kind of in answer to a question
  4. last time, which is that it
    turns out that the expansion of
  5. the Universe alone doesn't
    require you to have a Big Bang.
  6. There are other explanations,
    or in particular,
  7. one other class of explanation,
    which is compatible with the
  8. observation of the expanding
    Universe, but doesn't exactly
  9. lead to a Big Bang,
    in the sense that we think of
  10. it today.
    And so, I want to talk about
  11. these alternatives.
    This is Frontiers and
  12. Controversies as of 1950.
  13. In 1920, you'll recall,
    they were worried about whether
  14. the spiral nebulae were island
    galaxies of their own,
  15. or not.
    That was settled by Hubble's
  16. observation.
    In the 1950s,
  17. it had become clear that it
    really is true that the Universe
  18. is expanding.
    But there were two categories
  19. of explanation that were being
    put forward to explain that,
  20. and deciding which is which was
    the current big topic of the
  21. day.
    So, the Universe expands.
  22. And what do we make of this
  23. Well, one option is the Big
    Bang, what we now call the Big
  24. Bang, which, as I've mentioned,
    implies that in the past,
  25. everything was closer together.
    It was denser,
  26. and that creates other changes.
    If things get denser,
  27. they also get hotter,
    you may remember from
  28. chemistry.
    So, this implies in the past
  29. things were different from how
    they are now.
  30. They were denser,
    hotter, and that in the future,
  31. it'll go the other way.
    Things will become sparser and
  32. cooler.
    And there may be other changes
  33. associated with this.
    There may be different kinds of
  34. galaxies in the past from now
    and different kinds of galaxies
  35. now, as compared to the future,
    and so forth.
  36. But the Universe is a place
    whose bulk properties can change
  37. in time.
    So, things change in time.
  38. And the implication is that you
    can extrapolate this back to an
  39. initial singularity--that there
    was a moment,
  40. at some point in the past,
    where all currently existing
  41. space was piled up in a single
  42. The way I talked about this
    last time was that the scale
  43. factor was equal to zero,
    and so, there is this
  44. implication of an initial
  45. Now, the initial singularity is
    not the kind of thing that can
  46. be verified scientifically,
    because all the physical laws
  47. break down the same way they do
    in the singularity inside a
  48. black hole,
    or in an event horizon,
  49. or something like that.
    But nevertheless,
  50. that's the implication.
    That's the extrapolation of
  51. this set of ideas.
    But, at least,
  52. at the time,
    that was not the only set of
  53. ideas that could explain this
  54. There was an alternative,
    which was described as the
  55. "steady state."
    I should say that both of these
  56. names were given to these ideas
    by people who supported the
  57. "steady state."
    Big Bang was--that phrase was
  58. used as an insult by the "steady
    state" people to make fun of the
  59. ideas of the Big Bang,
    which we now actually know to
  60. be correct.
    And that's why that particular
  61. phrase is, in a way,
    so misleading--that they were
  62. deliberately trying to obscure
    and insult some of the ideas in
  63. the Big Bang.
    From time to time,
  64. astronomical organizations and
    popular magazines run contests
  65. to rename the great theory and
    come up with some better name
  66. that won't give you in your mind
    the impression of an explosion
  67. coming out from some central
  68. And people send in suggestions
    and it never gets anywhere.
  69. We're stuck with the Big Bang.
    But it is good to remember that
  70. it was named by its opponents,
    who supported the "steady
  71. state."
    So, how would this work?
  72. The central idea here is that
    the Universe expands,
  73. but then, new matter and energy
    is created to fill in the voids,
  74. as the Universe expands.
    So, sure, all galaxies are
  75. moving away from us.
    But new galaxies are being
  76. created where the old galaxies
    used to be.
  77. And the consequence of that is
    that the past and the future
  78. both have similar bulk
  79. The density,
    the overall density,
  80. is the same.
    And other characteristics are
  81. the same, because as things move
    further away,
  82. you've simply replaced them
    with other things like them.
  83. And so, now,
    you have to kind of invent some
  84. way of creating matter and
  85. But that's not nearly as bad as
    creating a whole Universe,
  86. which is what you have to do in
    the case of the Big Bang.
  87. So, in this case,
    the past and the future are the
  88. same.
    It also implies that the
  89. Universe is eternal in contrast
    to the Big Bang,
  90. where there is this initial
  91. which one then instantly asks,
    well, how did that happen and
  92. what happened before it?
    So, we get around that.
  93. This is an eternal process.
    And it's also infinite.
  94. And so, we don't have to start
    asking these awkward questions
  95. about what's outside the
  96. And so, people found this,
    in some ways,
  97. much more satisfying.
  98. And so, there were these two
    quite different explanations of
  99. the observed fact that the
    Universe was expanding.
  100. Now, the historians of science,
    who have studied this
  101. controversy, some of whom make
    the claim that which side you
  102. ended up on in the 1950s,
    before there was a lot of
  103. evidence either way,
    this was kind of a
  104. philosophical rather than a
    scientific question at the
  105. time--that which side you ended
  106. here, depended largely on your
    religious beliefs or lack
  107. thereof.
    And they document this--a lot
  108. of the work on the Big Bang and
    a lot of the supporters of the
  109. Big Bang were,
    as I mentioned last time,
  110. Catholics.
    In one important case,
  111. this guy Lemaitre,
    who worked out all the
  112. equations, was in fact a
    Catholic priest,
  113. also a physicist in his spare
  114. And this is a nice kind of
    idea, because from that point of
  115. view--because it gives you this
    initial moment of creation,
  116. which is--if you're a religious
    person, it's relatively easy to
  117. come up with a reason why that
    might have happened.
  118. On the other hand,
    a lot of the scientists,
  119. particularly in Britain,
    where the "steady state" was
  120. largely developed,
    were of a kind of atheistic or
  121. agnostic turn of mind,
    and they didn't like this
  122. initial singularity.
    And they liked the idea of an
  123. eternal infinite Universe,
    as actually Einstein did,
  124. too, because you didn't have to
    have a creation event,
  125. and you didn't have to invoke
    the kinds of ideas that come
  126. along with that.
    And there's some dispute over
  127. how much this really mattered to
  128. But what was clear is in the
    1950s, this was not a question
  129. for which there was scientific
    evidence either way.
  130. And so, what the scientific
    evidence said was that the
  131. Universe expanded.
    And then, you could follow
  132. either of these arrows.
  133. however, these two hypotheses
    make quite different
  134. predictions, which in the end,
    turned out to be testable.
  135. And, in particular,
    what it predicted,
  136. if the Big Bang makes this very
    strong prediction that the past
  137. is fundamentally
    different-looking from the
  138. present.
    Now, over the course of a human
  139. lifetime, this isn't going to
    make a lot of difference.
  140. The galaxies don't get that
    much further away from us in
  141. twenty or thirty years.
    But one can actually look into
  142. the past by looking at things
    that are far away.
  143. This is because the speed of
    light is finite.
  144. When we look at the Sun,
    we don't see the Sun as it is
  145. right now.
    We see the Sun as it was eight
  146. minutes ago, when the light
    started to travel toward us,
  147. because the Sun is eight light
    minutes away.
  148. If we look at Alpha Centauri,
    the nearest star other than the
  149. Sun, if Alpha Centauri blew up
    or disappeared or something
  150. right now,
    we wouldn't know about it for
  151. four years because it's four
    light years away.
  152. Similarly, if we look at a
    galaxy that's 10 megaparsecs
  153. away, a parsec is three light
    years, so a megaparsec is three
  154. million light years.
    Some galaxy that's 10
  155. megaparsecs away,
    that's 30 million light years
  156. away.
    So, we're seeing it not as it
  157. is, but as it was 30 million
    years ago.
  158. Now, it turns out that in the
    course of cosmic time,
  159. a few million years here or
    there doesn't make any
  160. difference to anybody.
    But once you get into billions,
  161. now you're talking cosmic time.
    And so, if you look at things
  162. that are billions of light years
    away, that turns out to be a
  163. substantial fraction of the age
    of the Universe predicted by the
  164. Big Bang.
    We'll get back a little later
  165. in this lecture to how you
    determine what the age of the
  166. Universe is supposed to be.
    But if you go back a
  167. substantial fraction of the age
    of the Universe,
  168. if you look back over distances
    that great,
  169. then you predict that you ought
    to see things that look
  170. different from the galaxies you
    see today,
  171. because the Universe at that
    time was denser and hotter,
  172. and the galaxies were younger
    on average,
  173. and you ought to be able to see
    some kind of differences.
  174. So, the past is different from
    the present, and this is
  175. observable through this concept
    of the "lookback time."
  176. Just the fact that the further
    away something is,
  177. the longer it's taken the light
    to travel to you.
  178. And so, you're actually seeing
    things not as they are right
  179. now, but as they are in the
  180. And so, you can imagine a great
    research project where you sort
  181. of look at nearby galaxies to
    see how things are in the
  182. current day.
    Then, you look at really,
  183. really distant ones,
    some substantial fraction of
  184. the age of the Universe ago,
    and you ask yourself the
  185. question, "Are those galaxies
    the same as the galaxies that
  186. exist today,
    or are they,
  187. in some sense,
  188. So that's a testable prediction.
    There's also a testable
  189. prediction on this side,
    which is that you ought to
  190. actually be able to find these
    places where the new matter and
  191. energy is being created,
    because that's a constant
  192. ongoing process.
    It has to be,
  193. because it's got to fill in the
    empty spaces left behind by the
  194. expanding galaxies.
    So, the prediction over here is
  195. that there exist places of
    matter and energy creation.
  196. So, this is potentially
  197. And in the 1960s,
    evidence was actually found
  198. that kind of decided this
    question, which is why we now no
  199. longer believe in the "steady
  200. And two things happened;
    actually, there were a number
  201. of things that happened.
    But one of them was the
  202. discovery of what were called
  203. These are now known to be
    accreting supermassive black
  204. holes, but they didn't know
    that, then.
  205. So, this is in the 1960s.
  206. That's what we think they are
    now, but they didn't know it
  207. then.
    All they knew is that they had
  208. discovered a great source of
    huge amounts of energy.
  209. And you'd think that this would
    be a very good thing--some kind
  210. of unknown energy source would
    be just the thing for the
  211. "steady state" people,
    because that's what they needed.
  212. They needed some kind of source
    of mass energy creation,
  213. and indeed, that was claimed
    for a little while.
  214. The main characteristic of
    these things is that they have
  215. very high redshifts,
    which implies very large
  216. distances, because velocity is
    proportional to distance.
  217. That's the Hubble Law.
    Everybody agreed that the
  218. Hubble Law was right.
    So, these things were known to
  219. be large distances away.
    And so, if you're a "steady
  220. state" person,
    you say, well,
  221. that's great.
    If they're so far away,
  222. they must be incredibly bright,
    otherwise we wouldn't be able
  223. to see them, and there's our
    energy source that we require.
  224. If you're a Big Bang person,
    what you say is,
  225. now we've finally found a bunch
    of things that are really far
  226. away and we can ask the
  227. "Are things that are that far
    away the same as in the local
  228. Universe, or are they
  229. And what it turned out--one of
    the very first things that was
  230. discovered is that there were
    many more quasars in the past
  231. than there are now.
    And so, whatever they are,
  232. supermassive black holes or
    whatever hypothesis you have for
  233. these things,
    it turns out,
  234. they're dying out.
    There were more of them in the
  235. past then there are now.
    They were brighter.
  236. And so, here is an example of a
    significant change in the
  237. composition of the Universe,
    which is the thing that's
  238. predicted by the Big Bang.
    And so, although initially,
  239. it looked like quasars might be
    helpful to the "steady state,"
  240. as soon as they started to get
    enough of them so you could do
  241. these kinds of statistical
  242. it became the first really
    strong evidence that the
  243. Universe was changing in time.
    This was not the only thing
  244. that was discovered in the
  245. Another thing is the so-called
    cosmic microwave background,
  246. and we'll talk much more about
    that later on.
  247. Right now, I just want to say
    that what this is,
  248. is it's radiation that was
    created--that was generated when
  249. the Universe was much denser
    than it is now,
  250. much hotter than it is now.
    In fact, it comes from
  251. radiation emitted by ionized
  252. So, this is when the whole
    Universe was at 10,000 degrees
  253. or so Kelvin--obviously much
    hotter than the Universe is
  254. right now, and much smoother.
    All this hydrogen,
  255. rather than being locked up in
    individual stars or in--and
  256. stars concentrated in individual
  257. all this hydrogen was very
    smoothly distributed around
  258. space.
    And so, this came from a
  259. time--this radiation,
    which you can easily detect
  260. with radio telescopes and the
  261. comes from a time when then
    Universe was much denser,
  262. hotter, and smoother than it is
  263. in accordance with the
    prediction of the Big Bang.
  264. So, this provided very strong
    support for the Big Bang.
  265. And the discoverers of this
    have got--there have been Nobel
  266. prizes given out on a regular
    basis for discoveries related to
  267. the cosmic microwave background.
    And as I say, we'll come back.
  268. I'll talk about that at some
    length later on.
  269. Another thing that was
    discovered is that the Universe
  270. is pretty clearly,
    mostly, 3/4 hydrogen and 1/4
  271. helium.
    Just about every cosmic object
  272. you see, not the Earth,
    but the Solar System as a
  273. whole, has those proportions.
    And all stars have these
  274. proportions and all galaxies
    consist of stars that have these
  275. proportions.
    And it turns out,
  276. this could be explained by the
    Big Bang.
  277. When it was denser,
    hotter, and smoother in the
  278. early Universe,
    it was hot enough for hydrogen
  279. fusion--hydrogen fusion into
  280. But it didn't last very long
    because the Universe was
  281. expanding and cooling,
    and you need to have very high
  282. temperatures in order to have
    hydrogen fusion.
  283. That's why it can only happen
    in the center of the Sun,
  284. or in an atomic bomb explosion,
    or something like that.
  285. And so, the Universe,
    for about three minutes,
  286. was hot enough for hydrogen to
  287. And if you ask yourself,
    what fraction of the hydrogen
  288. fused during the time the
    Universe was hot enough for that
  289. to occur,
    the answer turns out to be,
  290. about a quarter of it--in exact
    agreement with the currently
  291. observed fractions of hydrogen
    and helium in the Universe.
  292. So, this is in first three
  293. There's a famous popular book
    from the 1980s called The
  294. First Three Minutes,
    which discusses this,
  295. by Steven Weinberg.
    In the first three minutes,
  296. one quarter of hydrogen fuses
    into helium, and afterwards,
  297. no more, because it's too cool
    for these reactions to occur.
  298. So, that was another piece of
    evidence that the Big Bang was
  299. the right explanation and the
    "steady state" was not.
  300. Yes, question?
    Student: Is it actually
  301. three minutes or is that just
  302. Professor Charles
    Bailyn: Sorry.
  303. Student: It is actually
    three minutes?
  304. Professor Charles
    Bailyn: So,
  305. if you start from time zero,
    when everything is put
  306. together,
    after three minutes the
  307. Universe has cooled sufficiently
    so that you can't have hydrogen
  308. fusion, generally.
    Then, no more nuclear reactions
  309. occur until much,
    much later, when stars formed.
  310. And, we know how fast the
    Universe is expanding because we
  311. can measure the Hubble Constant
  312. And so, you know how long it
    takes for the Universe to expand
  313. to the point where the
    temperature drops enough so that
  314. there's no general hydrogen
    fusion anymore.
  315. And then, you do this little
    calculation to how much fuses
  316. during that time.
    Other questions?
  317. Okay.
    More recently,
  318. with the Hubble Space Telescope
    and other big ground-based
  319. telescopes,
    we've discovered that you can
  320. now see galaxies that are very
    far away, that are as they were
  321. a substantial fraction of the
    age of the Universe ago.
  322. And, by now,
    it's clear that galaxies evolve
  323. and that the statistical
    demographics of galaxies--how
  324. many there are,
    how massive they are,
  325. how big they are,
    all those kinds of things--that
  326. those statistics change
    dramatically over the course of
  327. the Universe--over the course of
    the amount of lookback time that
  328. we can currently observe.
    So, galaxies evolve very
  329. significantly.
    So, everything points toward
  330. the Big Bang and away from the
    "steady state," much to the
  331. surprise of a lot of the
    scientists who felt,
  332. possibly correctly,
    given what was known in the
  333. 1950s, that the "steady state"
    was a much more elegant
  334. solution.
    And so, let's see.
  335. The fable here is the demise of
    the "steady state."
  336. And the moral,
    well, there are various morals
  337. to this, but let me be
    provocative and say that,
  338. sometimes science is
  339. not anti-religious.
  340. Because it could have come out
    the other way,
  341. right?
    It could have turned out that
  342. this "steady state" was right.
    And then, you wouldn't have had
  343. this moment of creation and you
    wouldn't--and Pope John Paul II
  344. wouldn't have been so
    enthusiastic about astrophysics.
  345. In just the same way,
    it might have turned out that
  346. human beings are fundamentally
    different from all other species
  347. of animals.
    And if that had been true,
  348. the geneticists would have
    discovered that instead of what
  349. they did discover.
    And so, there's a feeling,
  350. particularly in current
    political debates,
  351. that scientists are somehow
    intrinsically anti-religious,
  352. and I think that isn't true.
    It isn't one way or another.
  353. It's just a way of finding
    stuff out.
  354. And sometimes,
    as in this particular case,
  355. you might find out that the
    atheists, or whatever the
  356. atheists had proposed,
    is wrong.
  357. And that's actually what
    happened in this particular
  358. case.
    So, the demise of the "steady
  359. state" is one of the big things
    that happened in the latter half
  360. of the twentieth century.
    And so, now,
  361. the scientific evidence is
    very, very strongly in favor of
  362. the Big Bang.
    I should define what I mean,
  363. I think, by the Big Bang
    Theory, because,
  364. as I said, this is a phrase
    coined by its enemies.
  365. And it's one of these phrases
    like "black hole," which
  366. actually doesn't have a
    technical definition,
  367. and you get into trouble by
    people using it in different
  368. ways.
    And so, if what you mean by
  369. this is that,
    in the past,
  370. the Universe was denser and
  371. and smoother--because it's
    constantly forming new stars and
  372. galaxies.
    Everything is getting more
  373. lumpy with time--and that you
    can extrapolate this to an
  374. initial singularity,
    then, I think there's extremely
  375. strong scientific evidence in
    favor of this.
  376. But you have to keep your eye
    on this word "extrapolate,"
  377. because sometimes the Big Bang
    is used to describe this moment
  378. of initial creation,
    or whatever you want to call it.
  379. This initial moment of infinite
    density, and somehow everything
  380. starting to expand.
    You can't observe that.
  381. That's one of these things that
    you can't see now,
  382. or with our current theories at
    any point in the future.
  383. And so, that's an extrapolation.
    That's not an observation.
  384. And that's a fundamentally
    different thing.
  385. So, if you use Big Bang to
    indicate that particular moment,
  386. then you can say that the
    scientific evidence for that
  387. actual moment isn't strong,
    and indeed, couldn't even exist
  388. within our current theories,
    because all of physics breaks
  389. down, there.
    And so, what I mean when I say
  390. that there's a lot of scientific
    support for the Big Bang is,
  391. there is support for this idea
    that the Universe is changing in
  392. time.
    It was denser,
  393. hotter, and smoother in the
    past, and that if you
  394. extrapolate this back,
    there was an initial
  395. singularity some number of years
  396. And you can actually figure out
    how many years ago that was,
  397. which is what I'm about to do
  398. And so, this is now the kind of
    currently accepted theory.
  399. I should say,
    there are a few remnant
  400. holdouts from the "steady state"
    type, who annoy the rest of us
  401. by not giving in.
    And there's actually been some
  402. interesting controversy over the
    years about,
  403. you know, how much telescope
    time do you give to people whose
  404. proposal is to look for the
    places where mass is created in
  405. the "steady state" theory,
    if nobody else believes that
  406. theory anymore.
    And, by now,
  407. the answer is none,
    but it took quite a while to
  408. get to that point.
  409. Student: Do people ever
    lie about what they're going to
  410. observe?
    Professor Charles
  411. Bailyn: Do people lie about
    what they're going to observe?
  412. Excellent--the graduate
    students are amused.
  413. No.
    What happens is this.
  414. You have to present--so,
    you have to write these
  415. proposals, because the
    telescopes are over-subscribed.
  416. And you have to come up with a
    plausible thing that you're
  417. going to do.
    Now, it then varies how this is
  418. actually done in operation.
    In the space telescope,
  419. for example,
    what you have to do is,
  420. then, you fill out what's
    called a Phase II form,
  421. which tells exactly where the
    space telescope is supposed to
  422. point and for how long.
    And you submit that,
  423. and they upload it and they do
  424. If you deviated drastically
    from the target list you gave
  425. them when they approved your
    proposal, that'll get flagged
  426. and they won't do it.
    On the other hand,
  427. on ground-based telescopes,
    you kind of go to the
  428. telescope, and still,
    in many cases,
  429. you operate it yourself.
    And there's not a lot of
  430. control over where you point the
  431. The control then happens later.
    One of the key components of a
  432. proposal for telescope time is
    what you did with the data you
  433. got from the last amount of
    telescope time they gave you.
  434. And, you know,
    you have to list all the
  435. publications,
    or if you haven't actually
  436. gotten to publishing anything,
    which is usually the case with
  437. me recently, you have to show
    little graphs or,
  438. you know, describe the data and
    what you're going to do with it
  439. and so forth.
    And one of the things--I sit on
  440. these committees that make these
    kinds of decisions.
  441. And one of the things you look
    for is if they haven't done
  442. interesting work and,
    kind of, done what they claimed
  443. they would do the last time
    round, their proposal goes down
  444. to the bottom.
    You're always looking for ways
  445. to trash other people's
    proposals, because you've got
  446. seven times more--in the case of
    the space telescope,
  447. you've got seven times more
    proposals than you can grant,
  448. of which only a small handful
    are not worth doing.
  449. And so, any opportunity you
    have to say, you know,
  450. these guys are bozos--you
    definitely take that
  451. opportunity,
    because otherwise you have way
  452. too many good proposals left
  453. So, there's a kind of internal
    control that isn't explicit on
  454. this sort of thing.
    And after a while,
  455. you know, if people keep
    getting up in public and saying,
  456. you know, quasars are sources
    of mass energy creation and
  457. therefore support the "steady
    state"--even if they're a great
  458. big quasar expert,
    you start to get a little bit
  459. queasy about giving them large
    amounts of telescope time that
  460. might be more profitably used by
    someone else.
  461. This, then, gets interpreted by
    the remnant "steady state"
  462. supporters, or whoever the
    minority idea might be,
  463. of a hugely oppressive
    scientific bureaucracy,
  464. you know, not allowing the
  465. wonderful thinker to do their
    own thing.
  466. And that, sometimes,
    is true, but not often.
  467. Most of the time,
    it's the sane people not
  468. allowing the insane people to
    use the telescopes,
  469. and that's actually a much more
    common thing.
  470. And so, while it can be good
    propaganda to say,
  471. yeah, these oppressive,
  472. bureaucratic people--mafia who
    run the scientific world are not
  473. allowing my great idea to get
    any opportunities to prove
  474. itself.
    Most of the time,
  475. it turns out,
    the establishment is right.
  476. And so, there is this
    interesting question about
  477. allocation of resources.
    It's not just telescope time,
  478. more importantly,
    even, money.
  479. There's a big debate right now,
    for example,
  480. in the theoretical physics
    community about string theory.
  481. String theory is the hot theory
    of everything.
  482. And everybody is supposed to be
    a string theorist,
  483. in theoretical physics,
    at the moment,
  484. except for a few people who
    point out that it hasn't
  485. actually been all that
    successful in explaining
  486. anything.
    In fact, it hasn't explained
  487. anything, ever.
    And therefore,
  488. might one not want to consider
    alternative theories?
  489. And then, the string theorists
    say, but, you know,
  490. this is a really good idea.
    We've got to continue to look
  491. at it.
    One day we'll get it right and
  492. we'll figure out everything.
    And so, there has now,
  493. recently, been some popular
    books that claim that string
  494. theorists are oppressing
    everybody else by not letting
  495. other kinds of good ideas be
  496. and by not letting smart young
    people who are working on other
  497. things--by not hiring them into
  498. and so forth.
    It's an interesting argument,
  499. and ongoing,
    in the string theory community.
  500. It's, sort of--as I
    said--they've been writing
  501. popular books on both sides of
  502. so, it's kind of busted out
    into--you're going to read about
  503. this, now, in the New York
    Review of Books,
  504. and places like that.
    And so, what you do about
  505. minority ideas--ideas that are
    not supported by the current
  506. paradigm of a given scientific
    subject is a very tricky one,
  507. and a very interesting one,
    and one that needs to be
  508. reevaluated from time to time.
    And, in fact,
  509. cosmology may be approaching
    such a moment,
  510. where a genuinely new idea is
    going to have to be required.
  511. We're probably not quite there
    yet, but we'll talk about
  512. alternative cosmological
    theories toward the end of the
  513. course.
    Sorry, I didn't mean to go off
  514. on this, but it's on my mind,
    because, as I said,
  515. I serve on these committees,
    so you have to think about
  516. these things.
    Actually, the space telescope
  517. people did a very interesting
  518. At one point they decided--I
    don't think they ever actually
  519. followed through on this--that
  520. or some small amount of the
    time--different scientific
  521. resources sometimes have
  522. like, 5% of the time goes for
    risky science.
  523. Science that's really weird,
    and probably won't work--but if
  524. it works, it's incredibly
    important because committees
  525. tend to not to want to do that.
    They tend to want to do the
  526. things that they know are going
    to produce some good result.
  527. And so, sometimes,
    the people who organize these
  528. things force the committees to
    have a little category of
  529. special, weird projects.
    And then, of course,
  530. what happens?
    Five years later,
  531. they analyze,
    you know, where did all the
  532. good science come from?
    And if it didn't come from the
  533. weird projects,
    which is almost certainly the
  534. case--although not 100%
    certainly the case,
  535. but generally the case--then
    they say, look we've wasted 5%
  536. of our money,
    telescope time,
  537. whatever it is.
    We're going to close down this
  538. program.
    And then, you kind of have to
  539. start over again.
    So, how weird is weird?
  540. Difficult to say.
    All right.
  541. The expansion of the Universe.
    We now believe,
  542. for the reasons I outlined,
    that this indicates a kind of
  543. Big Bang idea,
    which means we can extrapolate
  544. back to the moment that it all
    started, and we can calculate
  545. how long it took.
    Let me do a simpler
  546. calculation, but exactly
  547. Supposing you're in a car.
    You're in a car and you're
  548. driving at a speed of 50 miles
    per hour.
  549. And you are 100 miles away from
    your starting point.
  550. How long have you been driving?
  551. So, this, they taught you how
    to solve in seventh grade.
  552. If you are 100 miles away,
    you take time is equal to
  553. distance over velocity
  554. So 100 miles.
    You're going 50 miles an hour.
  555. That means you must have been
    going for two hours.
  556. Not such a hard problem.
    There's a hidden assumption
  557. though--sorry?
    Student: Speed is
  558. constant?
    Professor Charles
  559. Bailyn: Speed is constant,
    yeah--provided that the speed
  560. is constant.
  561. Okay.
    But let's make that assumption.
  562. Let's assume that the Universe
    is expanding at the same rate
  563. all the time.
    How long has it been going?
  564. Well, take some galaxy,
    any galaxy.
  565. It turns out,
    it doesn't matter which galaxy.
  566. And say--so,
    galaxy A is at distance
  567. D.
    It's moving at velocity
  568. V, away from us.
    You know, that's the whole idea.
  569. So, how long has it been since
    it was right on top of us?
  570. Well, so, it's been going for a
    time equal to D/V.
  571. By exact analogy with the
    distance, velocity,
  572. time, questions that they ask
    you about--you know,
  573. cars driving to Cleveland,
    and stuff.
  574. So, it's been going for time,
    T= D/V.
  575. But now, in the case of
    galaxies, there's this
  576. interesting relationship--that
    V = H/D.
  577. So, D/V = 1/H.
  578. And that can be measured.
    That's Hubble's Constant.
  579. And so, the age of the Universe
    is equal to 1 over the Hubble
  580. Constant, provided that the
    expansion has been at a constant
  581. rate.
  582. Let me remind you,
    H has been measured.
  583. It's 70 kilometers per second
    per megaparsec.
  584. That's kind of an interesting
  585. You've got kilometers per
  586. Both of those are measures of
  587. This is basically velocity over
    distance, but velocity contains
  588. a distance within it.
    So, if you were to cancel those
  589. two distance terms in some way,
    you'd have that the units of
  590. the Hubble Constant are 1 over
  591. So, the units of 1 over the
    Hubble Constant are seconds.
  592. It's a measure of time.
    It's reciprocal time.
  593. 1/H is a measure of time.
    What is that time?
  594. It's the age of the Universe.
    What do I mean by the age of
  595. the Universe?
    That's how long it has been
  596. since all galaxies and all
    objects in the Universe,
  597. all points in the Universe,
    were piled on top of one
  598. another.
  599. Student: [Inaudible]
    Professor Charles
  600. Bailyn: Let's see,
    did I write it wrong?
  601. V equals – yeah.
    I wrote it wrong.
  602. V = HD.
    Thank you.
  603. And so, now,
    what am I going to do?
  604. I'm going to divide both sides
    by H.
  605. I'm going to divide both sides
    by V, and then it comes
  606. out right.
    Sorry, thank you very much.
  607. Stop me when I do that.
    Right, because this is the
  608. Hubble Law.
  609. Okay.
    So, how old is the Universe?
  610. Well it's 1/70 kilometers per
    second per megaparsec.
  611. That actually is not a very
    useful unit of time.
  612. So, let's see if we can do
  613. H is equal to 70
    kilometers per second per
  614. megaparsec.
    Now, we want to cancel the
  615. kilometers per megaparsec.
    So, what we want to multiply
  616. this by is the number of
    megaparsecs in 1 kilometer.
  617. That's a very small number,
  618. It's some tiny fraction,
    because a megaparsec is huge.
  619. It's, you know,
    three million light-years,
  620. or something like that,
    and a kilometer,
  621. not so huge.
    So, let's calculate this term.
  622. That's going to be--1 kilometer
    is 10^(3) meters.
  623. One megaparsec--a mega is
    10^(6), so parsec is 3 x 10^(16)
  624. meters.
    And so, this is equal to 1/3
  625. times--10^(-22)--10^(-19) equals
    3 x 10^(-20),
  626. right?
    But it's 70 of those.
  627. So, H is equal to 7 x
    10^(1) x 3 x10^(-20),
  628. which is equal to 20 x
    10^(-19), or 2 x 10^(-18).
  629. In units of 1 over seconds.
    So, 1/H,
  630. we know now,
    in seconds, is equal to 1 / (2
  631. x 10^(-18) seconds).
    That's (1/2) x 10^(18) or 5 x
  632. 10^(17) seconds.
    One year is equal to 3 x 10^(7)
  633. seconds.
    So, the age of the Universe in
  634. years is (5 x 10^(17)) / (3 x
  635. which is something like 1.7 x
    10^(10), or 17 billion years.
  636. So, that's the answer.
    The Universe is 17 billion
  637. years old.
    It's not quite the answer
  638. because of that assumption,
  639. The assumption was that the
    Universe is expanding at the
  640. same rate all the time,
    and that's not necessarily
  641. true.
    And the next thing we're going
  642. to do is ask the question,
    "What happens if the expansion
  643. rate of the Universe changes
    with time?"
  644. It probably does.
    It almost certainly does,
  645. because the Universe is filled
    with mass.
  646. What does mass do?
    Mass exerts--well,
  647. Newton would have it that mass
    exerts gravitational force.
  648. It slows down the expansion of
    the Universe.
  649. So, what do you expect?
    You expect the Universe to be
  650. slowing down gradually.
    And this gives rise to a couple
  651. of possibilities,
    and I think I mentioned this
  652. briefly in passing.
    Now, we're going to do a
  653. more--in more detail.
    This is the scale factor of the
  654. Universe, which started at 0.
    Here's time.
  655. Here's now.
    Here's whatever the scale
  656. factor of the Universe is now,
    and what has happened.
  657. Here's what it looks like if
    there's no change.
  658. So, this is constant expansion.
    And so, it is this amount of
  659. time that turns out to be 17
    billion years.
  660. But in fact,
    it seems likely that the
  661. Universe is, in fact,
    slowing down.
  662. So, what does that look like?
    Well, that means that in the
  663. future it's going to do this.
    That means that in the past,
  664. it was doing this,
    because it's presumably been
  665. slowing down since the very
  666. And that means that the
    Universe started later than you
  667. think, because it started
    expanding more quickly than it
  668. is now,
    and then it's been slowing down.
  669. So, in fact,
    you might say that what we've
  670. really shown is that the
    Universe has to be less than 17
  671. billion years old.
  672. By the way, this calculation is
    why it was such bad news when
  673. Hubble got the answer wrong.
    You will recall from the
  674. problem set, Hubble thought that
    the Hubble Constant was 500
  675. kilometers per second per
  676. 500 is a bigger number.
    It means--it's what?
  677. Seven times bigger than we
    currently believe.
  678. That means that Hubble's
    estimate of the age of the
  679. Universe was a factor of 7
    smaller than 17 billion years,
  680. which is about 2.5 billion
  681. So, the implication of Hubble's
    result in the Big Bang context,
  682. at least, was that the Universe
    was 2.5 billion years old.
  683. That was very bad news,
    because the geologists had
  684. already figured that the Earth
    was 4 billion years old.
  685. And it's not good news to have
    a planet that's a factor of two
  686. older than the Universe.
    And so, this was part of the
  687. initial suspicion of the Big
    Bang explanation.
  688. Part of the reason people tried
    to develop "steady state" ideas
  689. was that Hubble's calculation of
    the constant gave you an age of
  690. the Universe that was in
    contradiction to existing
  691. geological ages measured on
  692. By now, we're up to 17 billion
    years and that seems to--that's
  693. fine.
    The Earth is only 4.5 billion
  694. years old, so there's no
    conflict there anymore.
  695. There are some star clusters
    that are known to be 12 or 13
  696. billion years old,
    and they caused some trouble
  697. for some values of the Hubble
    Constant until quite recently.
  698. Okay.
    But then, this begs a question;
  699. namely, "What's going to happen
    in the future?"
  700. Could it be that the expansion
    of the Universe stops,
  701. turns around,
    and comes back,
  702. leading to a "big crunch,"
    another one of these technical
  703. terms?
    And how much mass would the
  704. Universe have to contain for
    that to be true?
  705. So, let me do that calculation
  706. This is something we know how
    to do.
  707. This is an escape velocity
  708. You know, you throw a pen up in
    the air.
  709. If you throw it slowly,
    it stops, turns around,
  710. and comes back.
    If you throw it fast,
  711. it goes away.
    Or, to put it a different way,
  712. if you throw a pen up in the
    air at some velocity,
  713. whether it comes back or not
    depends on the gravitational
  714. force of the planet you're
    standing on,
  715. which, in turn,
    depends on the mass and the
  716. density of that planet.
    So, if you set your Universe
  717. into motion, it's expanding
  718. Depending on the density of the
    Universe, it can stop,
  719. turn around,
    and fall back,
  720. or it can keep going.
    So here's the calculation.
  721. Here's us, or any other
  722. It works no matter what you do.
    Then there's some galaxy,
  723. some distance,
    D, away from us.
  724. It's moving outwards at a rate
    of some velocity,
  725. V, where V is
    related to D by this
  726. equation--second per megaparsec,
    that's right.
  727. And then, what's trying to pull
    it back?
  728. Well, the mass inside of this
    region is trying to hold it
  729. back.
    It's only the mass inside of
  730. that region because the mass
    outside of the--we talked about
  731. this in the context of planets.
    This all cancels out.
  732. And so, what is the escape
  733. So, the escape velocity,
    you may recall,
  734. is the square root of what?
    2 GM/D.
  735. That's the escape velocity of
    this object.
  736. Let me make sure I haven't
    screwed this up.
  737. No, that's right.
    And so, the question is,
  738. "Is V greater than
  739. All right.
    So, let's evaluate this.
  740. What's M?
    M is equal to the
  741. density times the volume.
    Density--we'll call that--give
  742. it its usual symbol of ρ.
    And the volume is 4/3 π
  743. D^(3).
    That's the volume of this
  744. sphere of material.
    And you'll see why I translated
  745. into density in a minute.
    The velocity is equal to
  746. H times D.
    So, the question is:
  747. is H times D
    greater than the square root of
  748. 2 G/D times the mass,
    ρ 4/3 πD^(3)?
  749. All right, let's square both
  750. I've got to get rid of this
    square root sign.
  751. So H^(2)D^(2).
    Is H^(2)D^(2)
  752. greater than 2 G ρ 4/3
  753. And we've got D^(3) /
    D, so that's
  754. D^(2).
  755. And here's the key thing:
    the Ds cancel.
  756. The distance cancels.
    It doesn't matter which galaxy
  757. you pick.
    It doesn't matter how far away
  758. that galaxy is.
    You get the exact same result
  759. for every portion of the
    Universe you examine.
  760. So, the question becomes,
    "Is the density less than
  761. 3H^(2) / 8 π G?"
    I've just rearranged the terms.
  762. This is the ρ.
    It's still on the less-than
  763. side.
    I've taken the-- 2 x 4 = 8,
  764. that's this 8.
    There's a π,
  765. that goes down here.
    This 3 comes over on top,
  766. and the H^(2) stays
    where it is.
  767. So, this quantity is defined as
    the critical density.
  768. If the density of the Universe
    is less than the critical
  769. density, the Universe expands
  770. If the density of the Universe
    is greater than the critical
  771. density, then the Universe
  772. So, we can calculate this.
    This is all constants on this
  773. right-hand side.
    We've measured H,
  774. so we know what that is.
    3 x 2 x 10^(-18),
  775. that's H.
    We worked that out,
  776. squared, over 8 π 7 x
  777. And now, it's just arithmetic.
    And I'll tell you the answer.
  778. You can work it out for
  779. I got 6 x 10^(-27),
    and this is in units of
  780. kilograms per meter cubed.
    That's a really small density.
  781. It doesn't take much to hold
    the Universe back.
  782. On the other hand,
    the Universe is really big.
  783. Obviously, the density of this
    room, of the air in this room
  784. is, you know,
    30 orders of magnitude bigger.
  785. That's why the Earth isn't
    expanding, because we're so
  786. dense that our little region of
    the Universe has turned around
  787. and re-collapsed long since.
    But if you take the Universe,
  788. as a whole, planets are rare.
    Stars are rare.
  789. Galaxies, even, are rare.
    And it turns out,
  790. as we'll discuss next time,
    that the Universe is actually
  791. fairly close in bulk.
    If you take a large enough
  792. region that includes all the
    empty space, it turns out that
  793. the average density of the
    Universe is actually
  794. surprisingly close to this
    critical value at which the
  795. Universe will be balanced
    between expanding forever and
  796. re-collapsing.
    And so, we'll talk about how
  797. you actually measure the average
    density of the Universe,
  798. and thus, determine the fate of
    the Universe,
  799. next time.