Background Music for the Gamma Song

For those who want to make other songs on the line of the Llama song/Gamma Song, the background music layed out during the recording of the Gamma Song has been uploaded here. Record your lyrics in a reasonably normal voice in sync with this piece, and then speed it up to around 150%, depending upon the inherent squeakiness of your voice … If you do make a nice little song, please do drop a comment here with a link to your work - I’d enjoy a good laugh anyday!

God’s game

What if the laws of physics keep changing with time? And by changing with time, I don't mean just a continuous evolution of fundamental constants (like what Dirac proposed). Here I consider a hypothetical situation where the universe is a game being played between its creator and the contained "intelligent" creations. In short I am going to take the anthropic principle to a ridiculous level. The laws of physics are the way they are because some one believed them to be that way and managed to convince others that they were so. Physicists be warned, only philosophers should consider the following seriously. (To me it is a joke).

In the beginning, only the earth existed, surrounded by a sphere called the sky, on which stars and the sun used to revolve daily, moving on projections of epicycles onto that sphere. When people started charting the stars and started discovering some patterns, the creator became more careful, lest it make mistakes in moving the planets on the sky. So it receded the sky to the edge of the solar system, set the earth and the planets in motion around the sun, and continued to rotate the shell of the fixed stars, till much later when the first parallax distance measurement experiment was about to be started. So on and so forth, more and more structure was added to the universe, as the capability of human astronomical observation grew.

Meanwhile people like Galileo and Newton observed patterns in the dynamics of the world, which the creator had probably been running till that point purely out of whim, and probably influenced by convenience. They came up with concepts of force, inertia etc, which seemed to the creator to be a reasonable way to run the world at the macroscopic scale, and so it adopted these propositions as actual laws of nature (It continued to run microscopic dynamics on whim, you see where this is going ). Better still, Newton thought he could explain planetary motion in terms of gravity … So it initialized gravity, and now the solar system could be left to evolve on its own in a self consistent way.

Same is the story of chemistry and quantum mechanics. Scientists started to find more and more patterns in the microscopic world, till they ended up with a mathematical model that well described the creators whim. When this model was perfected and tested, the creator let it loose on the universe. So it was with relativity, when Einstein proposed that the ether as proposed by earlier scientists was not required, and that a nice Minkowski metric on the spacetime could explain all its weird properties, the ether was gotten rid of, and the universe was made Lorentz covariant. Einstein kept giving god a tough time. General coordinate invariance also had to be introduced, and general relativity incorporated into the universe, because so many humans thought it was a beautiful theory, and the creator was forced to agree. The creator made the mistake of leaving behind redshifts in distant galaxies, and now consistent signatures of the big bang had to be created. Some errors in calculations on its part, led to the scientific community to finally conclude that there must be dark matter and dark energy. And then there was dark matter and dark energy!
In the twenthieth century poor god had to create a QED vacuum, an electroweak vacuum with a broken symmetry, a horribly complex, yet beautiful as ever, QCD vacuum. And fortunately these things did not outright contradict the laws having been imposed on the large scales. But we kept nitpicking, found mathematical inconsistencies, and launched into string theory. Poor god! It was bad enough having to keep track of so…o many 0D fundamental particles, but now it had to start doing dynamics of 1D fundamental objects?

These days the creator must be going mad. Every morning it must be rapidly reading through all the journals of physics, hoping someone comes up with a TOE (theory of everything), so that this game can be ended once and for all declaring us the winners, setting up these laws in the universe, so that it can finally retire and let the universe evolve on its own.

But what if we have reached a stalemate? What if its mathematically impossible (mathematics is assumed sacred here) to model god's disparate whims in one consistent framework? What if god has given up? Does there need to be a good theory of quantum gravity?

The gamma song

On April 25th 2006, while studying for a cosmology examination, my friend Shanthanu and I heard the llama song. Subsequently, while considering the relative importance of D Gamma and Gamma-Gamma terms in the einstein tensor for density perturbations in the universe, phonetically pleasing combinations of gammas with other words kept on arising, and we decided to make a Gamma song. And well, here it is:

http://pages.physics.cornell.edu/~rsundararaman/GammaSong

And these are in the lyrics, in case you don’t have speakers :

here's a gamma, there's a gamma
and another little gamma,
real gamma, virtua' gamma,
gamma gamma, look!

gamma gamma, Riemann gamma
tangent, Wick rotate-a gamma
gamma gamma, squareroot gamma
gamma gamma, look!

I was once a Tensor,
I lived in a space,
but I never saw the way
the indices were raised
I was just an A-mu,
but that fixed a gauge,
And now listen little child,
to this verbiage

did you ever see a gamma,
miss a gamma, hit a gamma,
gamma's gamma, curve of gamma
gamma gamma, look!

Affine gamma, Dirac gamma,
Chiral gamma, Basu, gamma,
gamma with psi bar, a drama,
gamma gamma, look!

is it all in bold now?
is this all so weird?
is it made of tangent bundle?
h-cross, sigma, beard
Now our song is losing spin,
we've run out of … look!
time for me to retire now,
and become a crook!

Rotation and Time travel

General Relativity is one of the most beautiful theories in physics. Simply by changing the global concept of inertial frames to a local version, and connecting the curvature of the space-time manifold to the matter and energy distribution, we get a relativistic theory of gravity. The speed of light is inherited from special relativity, and Newton's Gravitational constant is inherited by matching the low velocity, low field results with Newton's theory. No new parameters are introduced into this theory making it highly vulnerable to attack by experimental counter-evidence. In spite of this, it has survived reasonably stringent experimental tests over the last 100 years. It is by far the most appealing theory of classical gravity.

Enter Kurt Godel. This fantastic mathematician caused many a great mathematicians to go mad with his famous incompletenss theorem. He has done a fair amount to perturb physicists as well. In 1949, he published a solution of general relativity, which represented a homogenous rotating universe. This universe was a very strange solution indeed. Firstly it was Anti-Machian. Contrary to the Machian philosophy that the inertial frames would be the set of frames in which the "fixed stars" do not rotate, in this solution the inertial frames see the matter of the universe rotating, and in the frame in which the matter is at rest, corealis forces act on any moving object. Godel showed moreover, that in this solution, time doesn't care enough about moving forward forever. He showed that you could have rockets propelled appropriately, that would go in a loop and come back to the same point in spacetime. Such a loop is referred to as a closed time loop (CTC). It is time-like because everywhere, the particle is travelling at a speed less than that of light, and yet it returns to the same point in spacetime. By the same token you could have propelled rockets that return to the same point in space before they left!

You may ask why bother, the solution doesn't sound like our universe anyway … As far as we know, the matter is stationary in our inertial frames. Why is it surprising that such a strange solution has such strange properties. However, that is not the end of the story. A few years later closed time like loops (CTCs) were discovered in other solutions of general relativity, the Kerr solution, the Von Stockum solution, the Raychoudhari-Som solution and many more. One thing common to all these solutions - Rotation. (Besides rotating solutions, the wormhole class of solutions can also have CTCs). And some of these solutions are not far from reality. In particular when a massive star collapses to a blackhole, it would be described by a Kerr solution, because no matter how slowly it is rotates before collapse, it would gain significant angular velocity as it collapses (conservation of angular momentum).

In the 70s, Stephen Hawkings proposed a chronology preservation conjecture to rule out solutions that permitted "time travel". However, this proposition did not have any physical grounds, as explicit physical paradoxes could not be constructed with these solutions to rule them out. Some people started proposing designs for time machines based on these solutions, primarily the Von Stockum solution for the rotating cylinder and the Kerr solution for the rotating blackhole. However, people still don't understand the implications of CTCs in these solutions well enough to conclude without doubt that time travel would indeed be possible in such a case.

A few groups of general relativists are still studying these solutions to understand what exactly a CTC means, and whether their presence would imply a contradiction of physical laws. In particular, they are trying to study what would happen if a thermodynamic system were moved along a CTC. Would its entropy keep increasing as it loops around, or would the entropy increase upto a point, and then necessarily decrease, so that the CTC is closed with respect to entropy too, i.e the entropy returns to the same value every time it goes around the loop. This would suggest that the CTC should be interpreted as time itself being cyclic, rather than a phenomenon of time travel in a universe with time propagating forever forward.

Does general relativity permit time travel? No one yet knows for sure. One thing is clear - the meaning of time in general relativity is not clear.

What a day to start …

What a day to start blogging … The truth is that today marks a great day for me on both my primary interests. It is today that I finally began to understand the standard model of particle physics, and managed to play Beethoven’s Fur Elise completely for the first time. But would anyone believe me if I claimed that today?

Well for the former, I can offer no evidence, but for the latter, luckily I recorded every attempt and I can offer my first successful attempt as proof.