Limitations

I hear the distant cries. I see the disappointed faces. I know what I have done.

Yesterday, I neglected to create a post about my class. I wish the construction of the universe allowed limitless undertakings each day. Alas, it is not so. Some days a mortal must choose between his wishes and his responsibilities. I chose the latter, postponing response until today. 

In our world, limitations exist in a thousand forms in a thousand places. Even to those who understand the depths of physics, ultimate boundlessness is not granted. Physicists constantly struggle to maximize signal amplification and extend equipment capability while minimizing error. Each of these has its limit. 

Even our sight has a line of demarcation beyond which our instrumentation senses nothing. At a point known as the Hubble radius, there is a wall of microwaves traveling away from our planet at the speed of light (c). The Speed of Light! Newtonian Mechanics says this is the limit speed at which light can be observed. And still we can receive signals from this background radiation as it flies away. 

There is a greater surprise. Hubble's law says an object moving at the speed c now, moved faster yesterday. The math shows, that when the wave was emitted, this front was moving at twice the speed of light. Twice the Speed of Light! Still, the particle can reach us on earth; A limitation disproved!

Perhaps, it is up to us to question all limits we perceive to be true.

Domination

Cosmology, like a woman, inspires you to take on the most adventurous of tasks at one moment, then it kicks your confidence out from under you the next. Sunday I declared my victory over the devious dealings of this callous science, and to day I lie in the rubble of my own self-proclaimed greatness. The theories of a radiation dominated universe crushed those of us with little grasp on methods of mathematical manipulation. It's difficult enough trying to solve equations pertaining to the visually observable world, but when one studies cosmology, 90% of the work has to do with that which is invisible to everyone except those who can see the matrix (I'll take the red pill please).

For those of you who don't quite understand what I am leading you to believe, let me explain. The universe can either be:

a) Dominated by matter

b) Dominated by radiation

c) Dominated by unknown particles

d) Dominated by me

In case a) we are most concerned about measuring the effect of gravity on our universe since that is the force which is trying to bring all masses closer together. In a radiation dominated universe, it's not nuclear radiation that concerns us the most (though my roommate Dave will tell you that we are concerned. See What Dave Wants, Dave Getz). To physicists radiation refers to any wave emitted from a source including any of the waves in the electromagnetic spectrum i.e. visible light, x-rays, or microwaves. If we inhabit this universe, then the pressure effects of these waves effect our everyday life the most. It is possible case c) is true, but at this time there is nothing known about the effects of the unknown. If d) is true I demand tithings!

As I was saying before, the class mathematically derived the effects of a radiation dominated universe. To the untrained student (me) there is not much of a difference between matter and radiation equations: Radiation domination implies density varies with 1/a^4 and matter domination it changes according to 1/a^3. To a cosmologist this is the difference between reality and reality television. Imagine the early universe. When you jump, gravity isn't doing most of the work to keep you down. Instead, you are at the mercy of the pressure from a densely packed front of electromagnetic waves which push you around in random directions.

Welcome to the real world.

Going the Distance

I did it! Yes, ladies and gentlemen, I did it! Perera gave us an equation in class and I solved it, right there while in my seat. Sure, I felt the pressure. I even felt like giving up, but no, Thomas is not a quitter. He tries until he can try no more. And guess what... that's right, he went the distance.

I know what you are thinking: "Ok Thomas, you can prove that astronomical distance varies with the two thirds power of time, so what?" Well my curious friend, this solution means nothing. It means nothing unless we know how far we are from stars and other systems. So, the class spent the day putting distance into perspective. In the following list, there are approximations for distance.

Earth's Diameter = 13,000 km

Distance Traveled by My Mom's Minivan 

(Happy Mom's Day!) = 150,000 km

Sun's Diameter = 1.4 million km

Distance from Earth to Sun = 1 Atomic Unit (AU) = 150 million km

1 Light Year = 9.5 trillion km

1 Parsec (pc) = 206,265 AU = 3.3 light years

Distance traveled by the light 

from the first time I flipped a switch = 160 trillion km

Distance to next galaxy = 700 kpc

Diameter of local group of galaxies = 1 Mpc = 1 million parsecs

Diameter of Virgo cluster = 17 Mpc

Diameter of Virgo supercluster = 50 Mpc

That means even light, moving at the universal speed limit, would take 165 million years to cross the supercluster which we call home. Beyond Virgo, there are ten thousand upon ten thousand (perhaps millions upon millions (or even billions upon billions (or... you get the story))) more superclusters spanning the universe.

Now you say, "Thomas, how do we know these distances?" It turns out that scientists have tape measures specifically designed for the task... No, really... One cosmologist gets into his spaceship and travels at the speed of light in one direction, and the cooler cosmologist gets into his bright red flying saucer littered with lightning decals and flies at the speed of light in the other direction (Boy you're gullible!). 

In reality, where I chose to live 2/3 of the time, it is not necessary to go the distance. Scientists develop methods where no traveling is necessary, except by the photons we receive. By observing the luminosity of cepheids, type 1a supernovae, or entire galaxies, we can determine the distance of these far off structures. It also helps to know a little trig if you are interested in determining diameters of large bodies.

So, the next time you are trying to "Go the Distance", remember there's likely a small particle which will travel through snow, heat, and galactic thunderstorms (Star Trek anyone?) for you, but no matter what, you'll be stuck doing the math.

Errors

It's day two and I must already admit to a blunder, a minor error, a slip of the tongue. As it turns out, the universe probably isn't finite. According to observations and the acceleration equation, the universe seems to be flat and infinite. Yet, concurrently, space is infinitely expanding. Wrap your mind around that one for a moment.

However, even this theory could result from an error in calculation. If the theorists' attempts at developing equations to explain the universe are similar to my attempts at deriving their equations, error isn't just probable, it's guaranteed. At three different times Perera asked us to solve equations on our own and three times I failed to find the correct answer. I know this isn't rocket science, but it is cosmology, so please, don't laugh at me because I don't measure up to Einstein or Hubble. After all, even measurement is subject to error.

All of the material that is to be presented to us during "Measuring Ancient Light" is divided into two major and equally important categories: cosmology and measurement theory. If a scientist can't measure data accurately, how will he ever be able to say "I told you so?" This part of the class started with a thorough investigation of measurement error. It turns out that even seemingly basic designs result in statistical error (blame randomness) or systematical error (blame engineers). Through persistence, dedication, and a little blood, scientists have developed ways to diminish these variances through the creation of novel devices like electrical components which change resistance depending on the pressure they feel or nearly static cosmic radiation receivers which can sense pico-sized (smaller than nano-sized) particles and waves. 

From this we can derive this simple lesson: Even if your life is plagued with error at the moment, hard work will reduce the probability of these blunders and allow you to witness mind-blowing phenomena.

Day 1

22 english letters and 2 greek letters. That's how many different variables and labels we saw on day one. Why? I am taking a class called "Measuring Ancient Light" at Illinois Wesleyan University during the month of May. That's right, it's one subject, 5 hours a day, 17 days of class including finals. "Then why the title," you ask. Well, the good doctor Perera has professed that he will relieve us of his presence for 1.5 days. That leaves the 10 bewildered students with 15 and a half days to persuade Perera to drop the final so we don't have to stress out over learning 24 variables.

 

These variables compose about two dozen equations and principles, from the simple (F=ma) to the highly technical (Friedmann's Equation... due to certain symbols I don't even have the capability to type it out). Throw in a few time derivatives, a deep understanding of newtonian mechanics, electromagnetism, and about one page on the theory relativity and what you get is a fluid equation that by its complexity must explain a substance that is completely alien to anything I'm used to. What happens when we use the fluid equation to help find the derivative of Friedmann's equation? The answer: We get homework.

Velocity flow, inertial frames, Birkoff's theorem, cosmological time, Hubble's "constant", this random variable k which keeps popping up: I don't know if there is time enough to understand the principles expressed on day one, let alone a entire semester of cosmology.

Despite this, I have hope. I, a miniscule observer living on a puny blue planet in a homogeneous, isotropic, finite universe who sees distant large bodies of mass continually moving further and further away even as my gravity feebly attempts to pull even massless light towards me, have hope.

 

See, I learned something already.