William M. Briggs

Statistician to the Stars!

Philosophic Issues in Cosmology V: What Measurements Tell Us—Guest Post by Bob Kurland

Distance Ladder from Skynet University (UNC)

Distance Ladder from Skynet University (UNC)

Bob Kurland is a retired, cranky, old physicist, and convert to Catholicism. He shows that there is no contradiction between what science tells us about the world and our Catholic faith.

Read Part IV.

When you can measure what you are speaking about, and express it in numbers, you know something about it, when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the stage of science.—Lord Kelvin.

The following types of data are primary: positions and luminosities of stars and galaxies (including x-ray, UV, visible, IR, microwave and radio-frequency radiation ); wavelengths of spectral lines from these objects; Doppler shifts of such wavelengths (shifts in the wavelength that depend on the velocity of the object emitting the radiation); frequencies, intensities and polarizations of the microwave cosmic background radiation (CBR).

It’s important to realize that there is a “ladder” of inferences of secondary data from these primary data. For example, the distances of nearby stars (10-100 light years or so distant from us) can be estimated relatively accurately by parallax measurements. From the intensity of light observed, one can then estimate accurately the intrinsic brightness of these stars. One can then use other properties, at known distances, to set up what are called “standard candles”: properties that relate to the intrinsic brightness, so that the intrinsic brightness can be inferred, to give from the observed intensity an inferred distance.

Mass Density and Curvature of Space

Various standard candles are used at various distances, including cepheid variables to supernovae and galactic lensing of quasars. One of the first standard candles was the intrinsic brightness of the Cepheid variables. Hubble used these to estimate the distance of stellar objects and to construct his plot of red shift versus distance, which was the basis for the expanding universe theory. Since that time more accurate measures have given very good linear relation between red-shift (velocity moving away from us) and distance from us.

One can also count the number of objects within the field of view and from this count make an estimate of the total number of objects to be seen, and thus infer the total (baryonic-ordinary) mass. From this astronomical data one can infer the following: the actual ratio of matter to a critical value; this ratio is designated “Omega 0” (with uppercase Greek letter). If Omega 0 is > 1, space-time is positively curved (like a sphere) and the universe expansion will eventually turn into a collapse, for a “big crunch”; if Omega 0 is = 1 space-time is flat and the universe will expand in a uniform way; for Omega 0 <1, the universe is curved as in a saddle surface, and will expand indefinitely.

Dark Energy

Observations of red shifts from distant supernovae and from temperature anisotropies in the cosmic background radiation suggest that there is a “dark energy”, a pressure (as in the “lambda” constant in Einstein’s original formulation) that makes the expansion of the universe accelerate. (What this is saying is the expansion rate is slower for older, more distant objects, faster for more recent, closer objects, so there is an acceleration of the rate.)

Evidence for an Expanding Universe

The following observations, in addition to the red shift, confirm the picture of a universe expanding from a hot big bang: the cosmic background radiation, the relative abundance of hydrogen to helium in the universe (about 3/1) and the lack of heavy elements in far distant galaxies. The cosmic background radiation is like the embers of a burnt-out fire, the embers of the hot “Big Bang” spread evenly throughout the universe. The small irregularities in the cosmic background radiation indicate the fluctuations that grew into stars and then galaxies. The relative abundance of hydrogen to helium is consistent with models of element formation that took place at an early, high temperature stage of the universe. For far distant galaxies (10 billion years light distance, say), they are also at an early stage of development (remember, going in distance is also going back in time) and therefore heavy elements have not yet formed by the collapse of red giant stars.

Ellis lists (among others) the following common misconceptions about the expanding universe:

  • Misconception 1: The universe is expanding into something. It is not, as it is all there is. It is just getting bigger, while always remaining all that is.
  • Misconception 2: The universe expands from a specific point, which is the centre of the expansion. All spatial points are equivalent in these universes, and the universe expands equally about all of them. Every observer sees exactly the same thing in an exact RW geometry. There is no centre to a FL universe.
  • Misconception 3: Matter cannot recede from us faster than light. It can, at an instant; two distantly separated fundamental observers in a surface {t = const} can have a relative velocity greater than c if their spatial separation is large enough. No violation of special relativity is implied, as this is not a local velocity difference, and no information is transferred between distant galaxies moving apart at these speeds. For example, there is presently a sphere around us of matter receding from us at the speed of light; matter beyond this sphere is moving away from us at a speed greater than the speed of light. The matter that emitted the CBR was moving away from us at a speed of about 61c when it did so.

The next in this series will deal with the Anthropic Principle.

9 Comments

  1. There’s a famous scene from Woody Allen’s 1977 movie “Annie Hall”

    Doctor in Brooklyn: Why are you depressed, Alvy?
    Alvy’s Mom: Tell Dr. Flicker.
    [Young Alvy sits, his head down – his mother answers for him]
    Alvy’s Mom: It’s something he read.
    Doctor in Brooklyn: Something he read, huh?
    Alvy at 9: [his head still down] The universe is expanding.
    Doctor in Brooklyn: The universe is expanding?
    Alvy at 9: Well, the universe is everything, and if it’s expanding, someday it will break apart and that would be the end of everything!
    Alvy’s Mom: What is that your business?
    [she turns back to the doctor]
    Alvy’s Mom: He stopped doing his homework!
    Alvy at 9: What’s the point?
    Alvy’s Mom: What has the universe got to do with it? You’re here in Brooklyn! Brooklyn is not expanding!
    Doctor in Brooklyn: It won’t be expanding for billions of years yet, Alvy. And we’ve gotta try to enjoy ourselves while we’re here

    This has always bugged me. Is Brooklyn expanding, or isn’t it?

  2. “This has always bugged me. Is Brooklyn expanding, or isn’t it?”

    If you accept the theory that space-time itself is expanding like a balloon, as opposed to just having everything moving outward from a central point in a statically infinite space time, then yes, it is. It’s just that the expansion is unmeasurably tiny at less than interstellar distances.

  3. geez guys, thanks for your comments…yep, everything’s expanding. There was a great science-fiction story (from the 40’s) by I think Anson McDonald, a guy goes back in time, but he’s much bigger…whence giants.

  4. Thanks for the replies. The reason I ask, years ago I read the following:

    His mother is correct. Matter sticks together through atomic forces that are strong enough to overcome cosmic expansion. Thus objects like bacteria or human bodies or planets do not take part in the expansion. Similarly, the gravitational effects that make the planets orbit the Sun, the Sun orbit the centre of the Galaxy, and the Galaxy interact with the other Local Group Galaxies, are strong enough to overcome the cosmic expansion. Thus planetary systems, galaxies and groups of galaxies do not take part in the expansion. But when we consider the distances involved between clusters of galaxies, the expansion of space takes over. Webb, Stephen, Measuring the Universe: The Cosmological Distance Ladder, Springer Verlag, Berlin 1999, p. 266.

    This appears to concur with what Michael Weiss wrote at the Original Usenet Physics FAQ when asked “If the universe is expanding, does that mean atoms are getting bigger? Is the Solar System expanding?” His answer was: Mrs Felix is right. Neither Brooklyn, nor its atoms, nor the solar system, nor even the galaxy, is expanding. The Universe expands (according to standard cosmological models) only when averaged over a very large scale. … In newtonian terms, one says that the Solar System is “gravitationally bound” (ditto the galaxy, the local group). So the Solar System is not expanding. The case for Brooklyn is even clearer: it is bound by atomic forces, and its atoms do not typically follow geodesics. So Brooklyn is not expanding. http://math.ucr.edu/home/baez/physics/Relativity/GR/expanding_universe.html

    Hence my confusion.

  5. Johan, the explanations of your last post (5:18 pm) is correct. Woody Allen and maybe MattS is a comedian.

    Bob, I can’t find the Anson McDonald (Heinlein) story.

  6. Johan, if you remember Alvy’s soliloquy at the end of the move, it doesn’t matter if Brooklyn is expanding or not. We need the eggs.

  7. Scotian, I may have the author wrong… I’ll try looking in my back copies of Astounding Science Fiction (if I can blow the dust off).
    And let me see if I can understand Johan’s reply. Forces are dependent on distance. So, in order that forces stay constant, distances between constituent particles have to remain constant (if you picture force laws rather than intermediate particles shuttling energy). OK…that is then a reasonable answer. (Until you go back to t approximately 0).

  8. Gary says “Johan, if you remember Alvy’s soliloquy at the end of the move, it doesn’t matter if Brooklyn is expanding or not. We need the eggs.”

    Yes, I do 🙂 For those not in the know:

    Alvy Singer: [narrating] After that it got pretty late, and we both had to go, but it was great seeing Annie again. I… I realized what a terrific person she was, and… and how much fun it was just knowing her; and I… I, I thought of that old joke, y’know, the, this… this guy goes to a psychiatrist and says, “Doc, uh, my brother’s crazy; he thinks he’s a chicken.” And, uh, the doctor says, “Well, why don’t you turn him in?” The guy says, “I would, but I need the eggs.” Well, I guess that’s pretty much now how I feel about relationships; y’know, they’re totally irrational, and crazy, and absurd, and… but, uh, I guess we keep goin’ through it because, uh, most of us… need the eggs.

    I’m not saying Annie Hall is a deep philosophical movie, but it’s certainly one of Allen’s better movies.
    Anyway, I was just curious to hear what a retired, cranky, old physicist had to say about the fate of Brooklyn 🙂

  9. Sander van der Wal

    August 12, 2014 at 3:41 am

    There is the Big Rip hypotheses: http://en.wikipedia.org/wiki/Big_Rip.

    The hypothesis relies crucially on the type of dark energy in the universe. The key value is the equation of state parameter w, the ratio between the dark energy pressure and its energy density. At w < −1, the universe will eventually be pulled apart. Such energy is called phantom energy, an extreme form of quintessence.

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