Stephon Alexander

Complexity of Simplicity

Over the last 30 years in the field of cosmology, physicists have reached the consensus that our physical
Universe, which spans the size of 3000 Mega Parsecs (1 Parsec is on the order of 10 Trillion miles), began its life some 14 billion years ago from a primordial quantum soup. A few milliseconds before that epoch (known as the radiation dominated era) microwave data tells us that the universe underwent an extremely rapid expansion of space- from the size of an atom to the size we see today! The initial conditions during this so-called inflationary epoch were remarkably simpler than the universe, let alone world in which we inhabit.

I have spent the last 5 years of my research career working on the details of the inflationary epoch. I am still befuddled by the following question: How did all this complexity arise? In other words, was complexity
part of the blueprint of the universe. Surely, from the point of view of the inflationary paradigm the answer is no. Therefore, something is missing from my point of view in the study of the 'early universe'. I think that part of the problem is related to the conceptual problems in quantum mechanics in the context of inflation. For one thing, we know that the quantum fluctuations generated during inflation (which are responsible for the generation of galaxies), while having a simple description mathematically (they are scale invariant) suffer the same foundational problems of the collapse of the wavefunction. What is this problem?

Quantum mechanics tells us that all the information about a physical system is encoded in a wave pattern of potentiality. When this system is observed (and it could be observed in many different ways)
all of the potentiality is manifested into one singular observable. The physical system once coexisting in
a probability wave of all possibilities 'collapses' into (by the act of observation) into one thing. The only problem for inflation here is where or what is the observer?

Well enough of this, perhaps my friends in CogSci can help resolve this paradox-Whence the complexity.

The Problem of Time

I forget who said it, but the quote goes something like this:
"Even Einstein, the master of time, ran out of it"
I know thats cruel of me. But I have a good point. The fact is that Einstein was never a master of time.
We all know by now that Einstein discovered a deep and permament insight into the nature of space and time. He called this framework General Relativity. No longer was space and time some empty stage that things move about; it is dynamical and can fluctuate, bend, form singularities, evaporate etc. Just like Maxwell equations govern how electric and magnetic fields behave in the presence of charged entities, the Einstein field equations tell us (in a very complicated set of equations) how space and time will behave in the presence of matter and energy. Well enough of the is pedagogy. My point is that the Einstein equations can be rewritten in a form where time does not exist. How could this be? General Relativity is based on a fundamental principle which simply states that the laws of physics do not change if you make a shift in the reference frame of the system under study. Objects will fall on Mars as well as on Earth (albeit at different rates). Mathematically speaking this means that the theory has a specific symmetry, called
diffeomorphism invariance. This means that I can relabel a function with different coordinate systems but the function will always look the same (stated naively). It turns out that the Einstein equation has a diffeomorphism symmetry related to shifting time forwards or backwards and the laws of physics according to General relativity does not care. Therefore, time is gone!

What does this mean? Why does there seem to be physical time? More on that later.