## Thursday, July 6, 2006

### Funny thing about the universe... (Part 2 of 3)

Part 1

Previously I addressed other steady state universes, however the next considered cosmological model is Dobson's.

The kind of universe Dobson suggests is what I call a spatially finite, infinitely recycling universe. I shall describe roughly and refine later. In this type of universe as matter approaches the "edge" it gets recycled back into the "interior" of the universe. The mechanism used to recycle the matter is described by basic tenets of quantum mechanics (QM). The uncertainty principle states that two conjugate observables (ignore the jargon for now, just try for the concept) can only be measured to within a certain ratio of each other. In this case we are speaking of momentum and position. Or mathematically

(change in momentum) * (change in position) ≥ (Planck's Constant) / 2.

Or a little more crudely (but more readably)

(uncertainty in momentum) * (uncertainty in position) ≥ (a very small number) / 2.

Therefore, if we measure the position of a particle with some arbitrary precision, that is, we reduce the uncertainty in the position, the uncertainty in the momentum must be great enough to make the quantity of the two numbers greater than or equal to Planck's constant (a very small number) divided by two. Furthermore, if we measure a particle's position with infinite precision, then its momentum would have to balloon to infinite proportions to keep the inequality.

The idea is complicated, but there is an apt analogy in music. Earlier I mentioned "conjugate observables", well it so happens that time and frequency are conjugate observables. Think of a single note. If we want to measure it's frequency, or pitch, we have to hear the note for at least as much time as it takes for one wavelength so we can accurately have a measurement of what note is being played, well then the longer the note is played the more accurately you can measure it's frequency, but the less you can confine its duration. The conjugate is more readily conceivably true. Think of a note confined to a very short time duration. Like a millisecond. What would it sound like? Well, it would probably sound like a tap, or a click, more percussive than like a note. And that's the point, the shorter time you confine a note to be played in, the less accurately you can know its frequency.

Dobsonian cosmology hinges on the uncertainty principle and on something called “red shift”. When Edwin Hubble (yes, THAT Hubble) discovered that everything in the universe was moving away from everything else, he based this discovery on something called a Doppler shift. One property of traveling waves is that when the source of the waves is traveling toward you the frequency of the waves is shifted up (waves hit you with a higher frequency) and when the move away they are shifted down (or they hit you less frequently). This phenomenon is commonly demonstrated by emergency response vehicles that pass you quickly with siren blaring. The pitch (frequency) of the siren shifts from high to low as it passes you, it’s Doppler shifted because the source of the wave is moving.

Similarly, light (an electromagnetic wave) can be shifted if the source is in motion. Recall that red light is low frequency, and blue light is higher frequency. Hence, we refer a retreating light source as emitting “red-shifted” light and an approaching source as “blue shifted”.

Hubble observed red-shifted light coming from almost every cosmological body he viewed, so he concluded that things were falling away from each other. We know that these other bodies are indeed falling away, and not just emitting “dimmer” light (lower frequency) because of a type of supernova called a type 1a supernova. Without going into the details, it basically acts like a “standard candle”, that is, it always emits the same amount of light whether it occur here in the Milky Way, or somewhere more distant. So by observing these objects we can judge its distance and red-shift (that is, its velocity away from us).

The strange part is that the further into space we look the more red-shifted things get. Or stated another way, the red-shift isn’t constant, it grows (linearly). Because of this growing redshift, then when matter gets very, very far away from us (observers on the Earth) then its light gets very, very redshifted. Which means that its velocity gets very high, but red light means low energy. So, Dobson believes, high velocity low energy implies low mass. This low mass has “very interesting consequences”. Low mass further implies low momentum, and therefore a low uncertainty in momentum. Whew… there’s a long line of deductions.

So, Dobson believes that this low uncertainty in momentum at the “edge” of the universe must be compensated for by a high uncertainty in position as dictated by the uncertainty principle under QM. Therefore, this huge uncertainty in position can recycle matter from the “edge” back to the “interior” of the universe indefinitely.

This cosmology has interesting implications.