About Me

!nversed Poignancy!

...I am an eclectic amalgamation of many seemingly paradoxical things. This can be exemplified in both my seemingly endless persistance on many topics and arguments, as well as my careful cautiousness on other topics and arguments. This is largely due to how astute I am of the topic: more knowledge, more persistant; less knowledge, obviously more cautious. I also have times of obsessive compulsions regarding certain things (mostly just my thoughts, however)...

Life and Death

!nversed Poignancy!

Life

An assembly

Possibly impossible

Perfectly interchangeable..

Death

That lives most upright

Beyond the unspoken

Neither a squiggle nor a quibble..

She and Me

!nversed Poignancy!

She

A daffodil

Tyrannizer of me

Breaking the colors of dusk!..

Me

The rising sun

Infringed with violations

The impurity in the salt..

Love and Poetry!

!nversed Poignancy!

Love

A puerile desire

Buried in the heart

Never leaves..

Poetry

Sentimentally melodramatic

Cursively recursive

My thoughts idiotic!

What if..Time was a real axis!?

Scribbled by Bharath C On September 18, 2009
A lot of people who think about time tend to emerge from their contemplations and declare that time is just an illusion, or (in modern guise) some sort of semi-classical approximation. And that might very well be true. But it also might not be true; from our experiences with duality in string theory, we have explicit examples of models of quantum gravity which are equivalent to conventional quantum-mechanical systems obeying the time-dependent Schrödinger equation with the time parameter right there where Schrödinger put it.

And from that humble beginning — maybe ordinary quantum mechanics is right, and there exists a formulation of the theory of everything that takes the form of a time-independent Hamiltonian acting on a time-dependent quantum state defined in some Hilbert space — you can actually reach some sweeping conclusions. The fulcrum, of course, is the observed arrow of time in our local universe. When thinking about the low-entropy conditions near the Big Bang, we tend to get caught up in the fact that the Bang is a singularity, forming a boundary to spacetime in classical general relativity. But classical general relativity is not right, and it’s perfectly plausible (although far from inevitable) that there was something before the Bang. If the universe really did come into existence out of nothing 14 billion years ago, we can at least imagine that there was something special about that event, and there is some deep reason for the entropy to have been so low. But if the ordinary rules of quantum mechanics are obeyed, there is no such thing as the “beginning of time”; the Big Bang would just be a transitional stage, for which our current theories don’t provide an adequate spacetime interpretation. In that case, the observed arrow of time in our local universe has to arise dynamically according to the laws of physics governing the evolution of a wave function for all eternity.

Interestingly, that has important implications. If the quantum state evolves in a finite-dimensional Hilbert space, it evolves ergodically through a torus of phases, and will exhibit all of the usual problems of Boltzmann brains. So, at the very least, the Hilbert space (under these assumptions) must be infinite-dimensional. In fact you can go a bit farther than that, and argue that the spectrum of energy eigenvalues must be arbitrarily closely spaced — there must be at least one accumulation point.

Sexy, I know. The remarkable thing is that you can say anything at all about the Hilbert space of the universe just by making a few simple assumptions and observing that eggs always turn into omelets, never the other way around. Turning it into a respectable cosmological model with an explicit spacetime interpretation is, admittedly, more work, and all we have at the moment are some very speculative ideas. But in the course of the essay I got to name-check Parmenides, Heraclitus, Lucretius, Augustine, and Nietzsche, so overall it was well worth the effort.

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