Newton's theory of gravity (part 1)

I fear that I got a bit ahead of myself at the end of the last post on the spectral lines of hydrogen. To fully close the circle between dark matter and everything I've been talking about in the last few entries, we do need to cover Newton's theory of gravity. Therefore, I will try to do so now, so that we can put this particularly sequence to rest.

First, on talking with a friend earlier today, I was asked, "I always hear the term "Newtonian gravity: is there any other kind?" This is exactly the kind of question I need to be asked, because otherwise I forget that I've been studying this stuff for 10 years. The answer is yes, there is another kind of gravity; more precisely, the answer is that there is a more complete form of gravity, namely Einstein's Theory of General Relativity (and possible string theory is a yet more complete form, although I'll leave that argument to Brian Greene's The Elegant Universe). Newton observed the effects of gravity and described those effects using math. However, he didn't describe how gravity works. To borrow an analogy directly from Greene's book, when my mom (and no, Greene didn't refer explicitly to my mom in his book [he did address himself directly to "you," but I don't think my mom has read it]) uses her computer, she doesn't know how it actually works (i.e. little electrical signals flashing through a chip). She only knows how to use it to write an article or to read this blog (sometimes she is unsure even how to do those tasks, at which times, coincidentally enough, she often checks in with her favorite son). Newton gave us a personal computer (gravity) and told us how to use it to write articles and check email (the equations), but he didn't tell us how it actually works (how is gravity transmitted, or how does the apple "know" it has to fall to the ground?).

In addition, Newton's formulation was only an approximation that was incorrect on certain scales (which are largely inaccessible to us and unobservable in our day to day lives). For example, I'll poach another commonly used illustration; from far away, a Seurat painting looks like a smooth picture. Newton's theory of gravity is accurate when viewed "from far away," which more or less is the point from which we all experience gravity. Up close, however, and all the dots become clear. While Newton got the big picture right, he did not describe the dots. General relativity can handle both the smooth "far away" view, but also the rough "up close" view.

That's why we can talk about "Newtonian gravity." For all intents and purposes, we could just talk about gravity and we'd all be referring to Newton, but since this is a physics blog, I figure I should try to be more precise in my language. In the next post, I'll actually use Newton's equations to look at the rotation of galaxies.



The image of Seurat's Sunday Afternoon on the Island of La Grande Jatte was scanned by Mark Harden

Spectral analysis

As mentioned in the last post, the Bohr atom is not correct, quantum mechanically speaking. It does, however, do an excellent job in modeling the simplest atom, that of hydrogen. Hydrogen is the lightest element, consisting of one proton with one electron in orbit. With the Bohr atom model, we know that the orbiting electron can exist in various discrete orbits, corresponding to different energies. In addition, we know that when the electron jumps between these levels, it emits or absorbs a photon. Finally, we know that the energy of a photon is proportional to its frequency, which is related to its wavelength or color. Putting all this together, we can predict that a hydrogen atom will emit or absorb very specific colors of light.

We are now talking about "spectral analysis." The OED (do you like the use of the OED, mom?) defines spectrum in a couple of ways, but I'll print two of them here. First, a general definition for physicists: "An actual or notional arrangement of the component parts of any phenomenon according to frequency, energy, mass, or the like." Physicists often talk about an energy spectrum, a frequency spectrum, etc., and what we mean is exactly the definition given by the OED - breaking up some group or data set into its components.

A second definition is this: "The coloured band into which a beam of light is decomposed by means of a prism or diffraction grating. Also, a dark band containing bright lines produced similarly; such a (coloured or dark) band, or the pattern of lines in it, as characteristic of the light source; hence, the pattern of absorption or emission of light or other electromagnetic radiation over any range of wavelengths exhibited by a body or substance." Now this is exactly what I'm talking about. The general idea is familiar - anyone who has seen a rainbow has seen light broken up into its various colors. When applied to the hydrogen atom, the spectrum is the characteristic colors of light that can be emitted or absorbed. Using the Bohr model, we can predict which wavelengths can interact with hydrogen (this may be the subject of another quantitative post).

At right is an image of a tube filled with hydrogen that is being excited by high voltage (taken from here). The light passes through grating to separate the spectral lines, with the result being the smaller lines shown to the right. All hydrogen, anywhere in the universe, will emit these colors when excited.

And now we finally get back to dark matter. In the first post, I talked about how we can tell how fast the galaxies are spinning using redshift or the Doppler effect. That's because any hydrogen in those distant galaxies will have the same spectrum as hydrogen on Earth, which means the hydrogen in the distant galaxy is emitting the same wavelengths of light that we can measure here on Earth. As discussed in the Doppler effect posts, since light is a wave, its wavelength will be shifted via the Doppler effect depending on the speed of the source. Because we can measure the relationship between the different lines, we can use the observed shifts to deduce the rotational speed of the source galaxy (one side spins away from us, one side spins towards us). And voila, now we know that the galaxies are spinning too fast and that there must be matter we aren't seeing (well, we would see that if we understood Newtonian gravity, which will be the topic a future post, I'm sure).

The above plot taken from the website of an MIT experiment, FIRE, shows the redshift for three real objects. Why is it called "redshift?" Most objects in the universe are moving away from us, and when the source of light is moving away, the light shifts towards the red end of the spectrum (or towards lower energy).