The Way of Science

UNIT 4

Cosmology and Relativity

The red shift
This, our last and longest yardstick, will also deliver to us the first evidence for the "Big Bang" model of an expanding Universe. To understand this powerful new measuring tool, some additional background is absolutely necessary. Some of this material may seem unrelated at first; hang on, it's all important, and it will all come together in a satisfying intellectual synthesis.

Do stars and/or galaxies show detectable motion? Consider first nearby stars of our Galaxy. These do show lateral ("proper") motion. That's not surprising, since the Galaxy is rotating. What about other galaxies? (From here on, we will concern ourselves only with galaxies, the basic "units" of the Universe's large masses.) Galaxies appear to be stationary over very long times, and are apparently fixed and immobile in spacetime. But suppose they were not moving laterally, but moving radially. That kind of motion would be undetectable directly, because of the enormous distances involved (think about it). To determine whether or not radial motion is occurring, we must turn to the Doppler effect. This topic is covered very briefly in your text, pp.147-148. Be sure that you understand the basic principle, which we will review in class: if a wave source and a receiver are moving radially (away from or towards each other), then the apparent wavelength will not be the same as the one emitted at the source. In the case of sound waves, the difference is in pitch (higher vs. lower notes). Do not confuse this change in wavelength with a change in loudness! It's easy to demonstrate Doppler effect for sound, since the speed of sound is relatively slow, and even a car moving at moderate speeds produces an easily-heard change of pitch as it passes the listener. It's harder with light, because of its speed, but with the proper tools, red or blue shift (the Doppler effect for light) can be detected.

Be sure to understand that if one knows the intrinsic wavelength (the "real" wavelength emitted by the source), then one can determine both the direction of motion (towards or away from the receiver) and the speed of motion since the amount of shift is proportional to speed. That's very important!!! If apparently unmoving galaxies are actually moving radially, we could detect this motion only if we knew what wavelengths were actually being emitted. That's possible via a lovely bit of technique called spectroscopy.

You already are familiar with the EM spectrum. Consider that tiny portion called visible light, from long (red) to short (violet) wavelengths. Combining all these frequencies in the right proportions gives us white light (like sunlight), but it's easy to break up this white light (or any mixture of frequencies) and produce a spectrum. You may have seen a demonstration of this phenomenon in high school: sunlight is passed through a prism, and the resulting rainbow of colors displayed on a screen. (Drops of water in the air do the same thing to produce rainbows in the sky.)

A glowing solid, liquid or gas under high pressure emits a full range of colors, called a "continuous spectrum." A glowing gas under low pressure (like starlight coming from the within the depths of the star) emits only some wavelengths, producing a pattern of bright lines. Different kinds of atoms/ions/molecules/etc. emit characteristic "bar codes" in these emission spectra. Each chemical element, for example, has a characteristic "fingerprint" by which it can be identified. A third type of spectrum, of major importance for our radial motion search, is called an absorption spectrum. The elements in a very thin gas at temperatures lower than the emitting material will absorb at exactly those frequencies that they emit when hotter and denser. This absorption will produce the element's "fingerprint or "bar code" as a pattern of dark, rather than bright, lines on a calibrated photographic plate.

A star's interior produces a continuous spectrum. The outer atmosphere of the star is cooler and under less pressure, and converts this continuous spectrum into an absorption spectrum. Directing the light from our star (Sol) through a device (such as a prism, or a slit, or a diffraction grating) allows one to investigate the chemistry of the sun. See the "enrich your life" footnote, below. Doing the same with the light from the billions of stars in a distant galaxy compare its wavelengths with a laboratory reference scale. If the absorption spectrum of a galaxy matches our reference exactly, then no radial motion is taking place. If wavelengths are blue-shifted (shortened) or red-shifted (lengthened), then radial motion is happening, and we can now calculate how fast the galaxy is moving (since amount of shift is proportional to speed).

When galaxies are examined for shift, a remarkable state of affairs appears. A few galaxies, all relatively close to our Galaxy (according to the Cepheid yardstick) show blue shift. However, all other galaxies show red shift. And: the greater the distance to a galaxy, the greater the shift, and therefore the greater the speed of recession. This statement is Hubble's Law, and it allows one to construct an enormously long new yardstick. If distance and speed of recession are mathematically related, then measurement of red shift can be converted to distance. The exact relationship depends on a constant called the Hubble Constant, whose value gets more precise with passing years. Now one can determine distance to celestial objects that are very far, and/or do not show Cepheids. (Keep that Hubble Constant in mind for later, when we will look at the possibility that it is not a constant, but varies with distance. Hold that thought in your memory banks, and we will resurrect it when considering the possible revolution in cosmology that is in progress right now.)

"Enrich your life" footnote: in the mid-19th century, these dark lines ("Fraunhofer lines") that matched sodium's signature were found in the sun. This first bit of solar chemistry also revealed faint unidentifiable lines near hydrogen's "signature." In 1868, a solar eclipse allowed analysis of light from the solar corona: this light is unfiltered by the solar atmosphere, and it revealed a distinct "bar code" that could not be matched to anything yet discovered. The new element was named helium (from the Greek helios, the sun). About 23 years later, helium was discovered on Earth. Note how powerfully this event supports our basic idea that the laws of chemistry and physics apply outside the labs on Earth.

Our new yardstick is based on measuring the amount of red shift. Since red shift is directly proportional to speed, and speed is directly proportional to distance, one can now calculate an approximate distance to any glowing celestial object. Our new scale is now measured in billions of light years.

Something even more important has come out of the red shift observations. Although it might appear that, somehow, we (the observers in our Galaxy) are standing still at the center of everything, in fact we too are moving. The analogy usually used to illustrate this state of affairs is the "raisins in baking dough" image. Read about this image in your text; in class, we will begin with a simpler version: ants on an expanding balloon. Briefly: a partially expanded balloon has, on its surface, many attached ants (they cannot go for a walk), and these very intelligent ants observe that their world appears to be flat. (It's a very large balloon, and the curvature is not visible.) They also know that they are each confined to their spot on the balloon (like humans thinking that the Earth is flat, from simple initial observations). If the balloon is now made larger, what would any ant (and every ant) see? It doesn't matter which ant you pick. An ant would observe all its nearest neighbors moving away more slowly than the next nearest ones. With greater distance from the observer ant, speed is greater, but each ant sees exactly the same thing: an illusion of being immobile at the center of everything. Since these are very smart ants, each one concludes that it only appears to be standing still, and other ants (galaxies) would share that illusion. They would also conclude that what is moving is not the ants (galaxies), but the balloon (spacetime) to which they are attached. They also conclude that there is no "center of the Universe." The raisin-in-dough example simply adds a third dimension: where the ants believe that they live in a two-dimensional spacetime (which is somehow expanding), the intelligent raisins would believe that their Universe is three-dimensional, and expanding in all three.

At this point, students frequently ask "expanding into what?" Ask this question in class. One suitable answer is "turnips." How's that for confusion?

If spacetime itself is expanding, it must have been smaller in the past. How small, and how far back in time? We are now ready to examine the "Big Bang" model, and the evidence from other observations which corroborate or falsify the model.

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